structural design project of super tall building chicago spire

7/17/2019 Structural Design Project of Super Tall Building Chicago Spire

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CHICAGO SPIRE

Chicago, Illinois

2011 – 2012

ASPIRE

Master of Engineering

Structural Design Project



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ASPIRE PROJECT TEAM

Joseph BeaudetteCornell University

Canton, New York

J. David MuenchUniversity of Massachusetts – Amherst

Medway, Massachusetts

Connor Bruns

Project Leader

Cornell University

Potomac, Maryland

Catherine T. Mulhern

Project Leader

Smith College

Winchester, Massachusetts

Joseph A. Caccio Jr

Cornell University

Monroe Township, New Jersey

Stephanie Richmond

Cornell University

Ellicott City, Maryland

Nicholas Chack

Columbia University

New York, New York

Kristy L. Scales

Syracuse University

Berkshire, New York

Katherine McEntee Coumes

Cornell University

Boston Heights, Ohio

Tom Shouler

Project Leader

Cornell University

Smithtown, New York

Jonathan Dobrin

Cornell University

Montreal, Quebec

Neelang Tiwari

MS Ramaiah Institute of Technology

Indore, M.P., India

Diana Foster

Cornell University

Wilmette, Illinois

Alex Vandenbergh

Cornell University

State College, Pennsylvania

Jeffrey Liu

Pennsylvania State University

Staten Island, New York

Chung Yu Wang

Cornell University

Taipei, Taiwan

Dan Lu

Cornell University

Potomac, Maryland

Muzi Zhu

Tianjin University

Tianjin, China

Sh d h Sh d Ph D



ACKNOWLEDGEMENTS

The 2011-2012 Master of Engineering project team, ASPIRE, would like to thank our professional

advisors from Thornton Tomasetti, Chicago: John Peronto (Associate), and Mary Williams (Senior

Engineer). Mr. Peronto and Ms. Williams volunteered significant time to provide guidance and

structure to our project. Their technical knowledge of structural engineering specific to tall

buildings played an instrumental role in our project.

ASPIRE would also like to thank our faculty advisor, Dr. Shideh Shadravan, for her daily support.

Dr. Shadravan provided both project team and individual guidance vital to our development asMasters students.

The design team would also like to thank the support staff of MIDAS Information Technology Co.

for the assistance and troubleshooting with the MIDAS GEN 3D structural modeling software.

Finally, we would like to acknowledge the Cornell University Department of Civil and

Environmental Engineering faculty and staff. In particular, we would like to thank Professor

Christopher Earls, Professor Ken Hover, Professor T.D. O’Rourke, Cameron Wilkens, Paul Charles,and Karen Browning.



EXECUTIVE SUMMARY

ASPIRE designed the gravity, lateral, and foundation systems, utilized finite element software forstructural optimization, designed steel and concrete connections, and studied the effects of creep

and shrinkage during a year-long analysis of the Chicago Spire.

Preliminary analysis included research of different lateral load resisting systems in order to select

the system that would best suit the needs of the structure. The lateral system chosen was a central

concrete core with outriggers and belt trusses connecting the core with the exterior steel columns.

The gravity design of the structure explored the use of non-composite and composite beams andcolumns in the Spire. ASPIRE selected steel beams with a composite metal decking system. A

column load takedown based on tributary areas was used for the preliminary column design.

The Chicago Spire was modeled using MIDAS Gen, a structural finite element software, to accurately

understand the lateral behavior of the building. A sensitivity analysis was performed to resize the

concrete core, the outriggers, and the belt truss members from the initial hand calculation sizes.

Core wall thicknesses were optimized across the height of the building. Vertical columns and

transfer columns were redesigned as a series of steel built-up shapes through energy optimization

methods.

The foundation system featured the design of a seven level below-grade parking garage and a

retaining wall along the site perimeter. Rock-socketed caissons were designed to support the

tower, extending from the base of the building to the bedrock 119 feet below grade.

There are hundreds of connections in the Chicago Spire ranging from standard steel connections tocomplex designs for the outriggers and the lobby level mega-columns. Several steel-to-steel and

composite connections were designed throughout the tower.

A study of concrete creep and shrinkage estimated differential settlement between the concrete

core and the exterior steel columns using the GL2000 model. Creep and shrinkage are dependent

on variables such as loading schedule, curing period, and material properties, making it difficult to

predict the actual amount of creep and shrinkage. However, failure to acknowledge these effects

leads to cracks in the concrete and uneven floors.

Through the course of the project, ASPIRE faced many challenges that required the design team to

seek guidance from outside sources, including weekly meetings with our faculty advisor and bi-

weekly conference calls with our professional advisors from Thornton Tomasetti. The structural

design of the Chicago Spire was a collaborative effort of eighteen students and the advisors The



TABLE OF CONTENTS

ASPIRE PROJECT TEAM .......................................................................................................................................................... i

ACKNOWLEDGEMENTS ........................................................................................................................................................ ii

EXECUTIVE SUMMARY ........................................................................................................................................................ iii

TABLE OF CONTENTS............................................................................................................................................................. v

LIST OF FIGURES ............................................................................................................................................................... viii8

LIST OF TABLES ...................................................................................................................................................................... xi

1.0 Introduction ............................................................................................................................................................... 1

1.1 Chicago Spire: Background and Location ................................................................................................. 2

1.2 Project Scope ........................................................................................................................................................ 3

1.3 Design Process ..................................................................................................................................................... 4

2.0 Design Criteria .......................................................................................................................................................... 5

2.1 Tall Building Design........................................................................................................................................... 5

2.2 Lateral System Determination ...................................................................................................................... 6

2.3 Typical Floors and Column Layouts ........................................................................................................... 8

2.4 Gravity Design Loads ........................................................................................................................................ 9

2.5 Lateral Design Loads ....................................................................................................................................... 10

2.6 Load Combinations .......................................................................................................................................... 13

2.7 Serviceability Requirements ........................................................................................................................ 14

3.0 Gravity Design ......................................................................................................................................................... 16



3.5 Façade Beam Design ........................................................................................................................................ 27

3.6 Column Design ................................................................................................................................................... 28

4.0 Lateral Load Resisting System Design .......................................................................................................... 33

4.1 Structural System Overview ........................................................................................................................ 34

4.2 Preliminary Core Wall Design ..................................................................................................................... 36

4.3 Auxiliary Lateral Systems ............................................................................................................................. 41

4.4 Finite Element Model ...................................................................................................................................... 45

4.5 Core Wall Reinforcement Design ............................................................................................................... 52

4.6 Energy Optimization ....................................................................................................................................... 53

4.7 Eigenvalue Analysis ......................................................................................................................................... 56

5.0 Steel and Concrete Detailing ............................................................................................................................. 59

5.1 Typical Connections ........................................................................................................................................ 60

5.2 Complex Connections ..................................................................................................................................... 65

6.0 Foundation Design and Detailing .................................................................................................................... 72

6.1 Soil Properties ................................................................................................................................................... 73

6.2 Retaining Wall Design..................................................................................................................................... 74

6.3 Parking Garage Slab Design.......................................................................................................................... 75

6.4 Bell Caisson Design .......................................................................................................................................... 76

6.5 Rock-Socketed Caisson ................................................................................................................................... 77

7.0 Long-Term Deflection Effects ........................................................................................................................... 82

7 1 C l S 83



9.0 Appendix ................................................................................................................................................................... 94

9.1 Gravity Design Loads ...................................................................................................................................... 95

9.2 RWDI Recommended Wind Load .............................................................................................................. 96

9.3 Seismic Load Summary ............................................................................................................................... 101

9.4 Core Slab Design Summary ....................................................................................................................... 105

9.5 Link Beam Summary .................................................................................................................................... 106

9.6 Beam Spans and Tributary Areas ........................................................................................................... 109

9.7 Slab and Decking Summary ....................................................................................................................... 110

9.8 Composite Beam Summary ....................................................................................................................... 111

9.9 Initial Gravity Design Column Comparison ........................................................................................ 112

9.10 MIDAS Gen Gravity Loads .......................................................................................................................... 113

9.11 Column Validation Summary .................................................................................................................... 117

9.12 MIDAS Sensitivity Analyses ....................................................................................................................... 118

9.13 Core Wall Reinforcement ........................................................................................................................... 121

9.14 Creep and Shrinkage .................................................................................................................................... 122

10.0 Drawings ..................................................................................................................................... C-2.001 - S-4.004

11.0 Calculations ................................................................................................................................................. C1-C297



LIST OF FIGURES

Figure 1.1: Chicago Spire ...................................................................................................................................................... 1

Figure 1.2: Chicago Spire Site Location .......................................................................................................................... 2

Figure 1.3: Bank Location .................................................................................................................................................... 4

Figure 2.1: Outrigger and Belt Truss System Sketch (Taranath 1988, 279) ................................................... 6

Figure 2.2: RWDI Wind Tunnel versus ASCE7 Directional Procedure Forces ............................................. 11

Figure 3.1: Structural Beam Labeling System ............................................................................................................ 18

Figure 3.2: Tributary Area Breakdown for External Bays .................................................................................... 19

Figure 3.3: Tributary Area for Joist 1 ............................................................................................................................ 19

Figure 3.4: Gravity Load Paths for Design Process .................................................................................................. 20

Figure 3.5: Core Slab Detail ............................................................................................................................................... 21

Figure 3.6: Core Slab Design Locations, Directions, and Numbering ............................................................... 21

Figure 3.7: Tributary Areas for Link Beam Design. ................................................................................................. 22

Figure 3.8:Typical Composite Beam and Decking System .................................................................................... 24

Figure 3.9: Tributary Areas for the HSS Beam .......................................................................................................... 27

Figure 3.10: Steel Column Load Paths .......................................................................................................................... 29

Figure 3.11: Bank 3 Steel Column Layout.................................................................................................................... 29

Figure 3.12: Bank 1 Steel Column Layout.................................................................................................................... 30

Figure 3.13: Typical Core Column Section, Banks 1-3 ............................................................................................ 31

Figure 3.14: Composite Column Section ...................................................................................................................... 32



Figure 4.4: Outriggers Spanning Two Mechanical Floors ..................................................................................... 41

Figure 4.5: Compression Block and Steel Strain from Weak Axis Bending ................................................... 47

Figure 4.6: Initial Discontinuity Check under Gravity Loads .............................................................................. 48

Figure 4.7: a) BU1 and b) BU2 .......................................................................................................................................... 49

Figure 4.8: Discontinuity Test Comparison between Original and Final Design ........................................ 50

Figure 4.9: Deformed Shape for 50 year MRI Wind Loads (NTS) ...................................................................... 51

Figure 4.10: Optimization Material Use versus % Reduction of Drift ............................................................. 55

Figure 4.11: From Left to Right: a) Mode Shape 1; b) Mode Shape 2; c) Mode Shape 3 .......................... 58

Figure 5.1: a) Elevation and b) Plan of Typical Welded Column Splice .......................................................... 60

Figure 5.2: Elevation of Floor Joist to Girder Connection ..................................................................................... 61

Figure 5.3: Elevation of HSS Beam to Cantilever Connection.............................................................................. 61

Figure 5.4: Elevation of Built-up Column to Radial Girder and Cantilever Connection ........................... 62

Figure 5.5: Elevation of Circumferential Girder to Column Plate Connection ............................................. 63

Figure 5.6: a) Elevation and b) Section of Radial Girder to Core Wall Connection .................................... 64

Figure 5.7: 3D Rendering of Base of Mega-Column to Caisson Connection .................................................. 66

Figure 5.8: Bottom of Outrigger Connection .............................................................................................................. 67

Figure 5.9: Elevation of Outrigger and Radial Girder Connection to Concrete Core ................................. 68

Figure 5.10: a) Embedded Steel Frame and b) Cross Bracing and Point Loads .......................................... 69

Figure 5.11: 3D Rendering of Mega-Column Connection ...................................................................................... 70

Figure 5.12: Singular Transfer Column Connection Front and Side Elevation ............................................ 71

Fi 5 13 S li T f C l C i F d Sid El i 71



Figure 6.4: Elevation of Rock-Socketed Caissons ..................................................................................................... 77

Figure 6.5: Detail of Caisson .............................................................................................................................................. 78

Figure 6.6: Limit states from Left to Right: a) Stress, b) Settlement and c) Uplift ...................................... 78

Figure 6.7: Elevation of Ring Beam ................................................................................................................................ 79

Figure 6.8: Plan View of Ring Beam Resistance to Soil Pressure ....................................................................... 79

Figure 6.9: a) Compression and b) Tension Stresses in Rock-Socketed Caisson ........................................ 80

Figure 7.1: Concrete Strength Gain with Time .......................................................................................................... 84

Figure 7.2: Concrete Elastic Modulus Gain with Time ........................................................................................... 84

Figure 7.3: Initial Strength Gain of Concrete for Various Cement Types........................................................ 87

Figure 7.4: Typical Strain Values for a Single Floor ................................................................................................ 88

Figure 7.5: Core Deformations per Floor ..................................................................................................................... 89

Figure 7.6: Total Core Displacement over Time ....................................................................................................... 91

Figure 9.1: Built Up Column Sensitivity Results to Dead Load ........................................................................ 119

Figure 9.2: Core Wall Thickness Sensitivity Results to Dead Load ................................................................ 120

Figure 9.3: Belt Truss and Outrigger Sensitivity ................................................................................................... 120



LIST OF TABLES

Table 1.1: Floor Bank Summary ........................................................................................................................................ 4

Table 2.1: Summary of Exterior Columns per Bank .................................................................................................. 8

Table 2.2: Unfactored Design Loads per ASCE 7-05 (psf) ....................................................................................... 9

Table 2.3: Seismic Lateral Forces .................................................................................................................................... 12

Table 3.1: Typical Values for Vibrational Analysis Calculations ........................................................................ 26

Table 3.2: Summary of Estimated Vibrations ............................................................................................................ 26

Table 3.3: HSS Beam Design Summary ......................................................................................................................... 27

Table 3.4: Factored Loads from Gravity at Ground Level ..................................................................................... 31

Table 4.1: Critical Core Wall Unfactored Design Loads ......................................................................................... 36

Table 4.2: Controlling Stresses for Core Wall Design ............................................................................................. 38

Table 4.3: Initial Core Wall Reinforcement Requirements .................................................................................. 40

Table 4.4: Initial Core Thickness by Bank ................................................................................................................... 40

Table 4.5: Summary of Column Properties for each Column Section .............................................................. 43

Table 4.6: Stress Reduction in each Bank from Outriggers .................................................................................. 43

Table 4.7: Summary of Core Wall Thicknesses with Outriggers and Columns ............................................ 43

Table 4.8: System Stiffness Summary ........................................................................................................................... 44

Table 4.9: Initial MIDAS Model Element Properties ............................................................................................... 45

Table 4.10: Final MIDAS Model Element Properties ............................................................................................... 48

Table 4.11: Initial and Final MIDAS Results ............................................................................................................... 50



Table 6.1: Critical Von Mises Stresses from ABAQUS Model ............................................................................... 81

Table 7.1: Cement Type Deformation Sensitivity Analysis .................................................................................. 86

Table 7.2: Core Total Deformations ............................................................................................................................... 88

Table 7.3: 20-Year Deformation Comparisons .......................................................................................................... 90

Table 9.1: RWDI Wind Load Combinations ................................................................................................................ 96

Table 9.2: RWDI Provided Wind Forces and Torsional Moments ..................................................................... 97

Table 9.3: Link Beam Dimensions ............................................................................................................................... 106

Table 9.4: Residential and Lobby Link Beam Summary ..................................................................................... 107

Table 9.5: Mechanical Floor Link Beam Summary ............................................................................................... 108

Table 9.6: Decking and Slab Thickness Summary for Composite Beam System ...................................... 110

Table 9.7: Unfactored Dead Load for Composite Beam System ...................................................................... 110

Table 9.8: Composite Beam Summary ....................................................................................................................... 111

Table 9.9: Initial Composite and Steel Column Comparison............................................................................. 112

Table 9.10: MIDAS Gen Unfactored Gravity Loads (kips / node) ................................................................... 113

Table 9.11: Composite and Steel Shapes for Lateral Design Column Validation...................................... 117

Table 9.12: Built-up Steel and Concrete Properties ............................................................................................. 118

Table 9.13: Sensitivity Analyses Element Properties .......................................................................................... 119

Table 9.14: Core Wall Reinforcement Details ......................................................................................................... 121

Table 9.15: Concrete Core Properties ........................................................................................................................ 126

Table 9.16: Steel Deflection Summary ....................................................................................................................... 126

T bl 9 17 H idi D f Chi 127



1.0 INTRODUCTION

1.0 Introduction

The 2011-2012 Master of Engineering Structural Design Project was the structural design of theChicago Spire (Figure 1.1), located on the west side of Lake Shore Drive in Chicago, Illinois. The

project was provided by John Peronto, P.E. and Mary Williams, P.E. of Thornton Tomasetti’s Chicago

office. Cornell University Lecturer Dr. Shideh Shadravan was the project advisor. The project team

consisted of sixteen Master of Engineering students and two undergraduates. The team members

provided a unique assortment of design experience, academic specialty, and cultural background.

This resulted in a realistic, professional experience similarly found at a design firm.



1.0 INTRODUCTION

1.1 Chicago Spire: Background and Location

The Chicago Spire is 2,000 ft tall on a strip of land between the Ogden Slip and the mouth of theChicago River (Figure 1.2). The tower contains approximately 3 million square feet of upscale

condominiums and amenities. The basement has 7 below-grade parking levels on top of rock

socketed caissons. The structural engineer of record was Thornton Tomasetti. The project was put

on hold in 2008 with only its foundation completed. Upon completion, the Chicago Spire would be

the tallest building in the Western Hemisphere.

Spanish architect Santiago Calatrava was the architect and engineer for the project. The design

highlights a spiraling exterior supported by an exterior column grid and a concrete core. Calatrava

compared the design to an imaginary smoke stack from a campfire lit by the indigenous Native

American tribes of Chicago.

i h



1.0 INTRODUCTION

1.2 Project Scope

The Master of Engineering team was charged with providing a complete structural design of thegravity and lateral system as well as foundation design, connections and details, and an analysis of

the effects from creep and shrinkage. The project required the eighteen team members to

collaborate as sub-teams to complete assigned deliverables, utilizing full engineering knowledge

and experience. The design of the cylindrical superstructure entailed expanding design limits into

unfamiliar areas through self-learning and provided resources.

The design project was split into ten deliverables through the academic school year. Deliverables

include submittal of white-paper reports, annotated engineering calculations, structural drawings,

and finite element models. Local and professional advisors provided design support through bi-

weekly teleconferences and daily correspondence.

Structural design was supplemented by academic field trips pertinent to tall building design.

ASPIRE traveled to New York City in November of 2011. This trip included a presentation by

Silverstein Properties and a site tour of Four World Trade Center, a 72-story skyscraper designed

by Leslie E. Robertson and Associates. In December 2011, team members visited the Rowan,Williams, Davies, Inc. (RWDI) wind tunnel testing facility in Guelph, Ontario, Canada. RWDI is a

leader in the field of wind tunnel testing, and has performed dynamic analysis for some of the

world’s tallest structures, including the Chicago Spire.



1.0 INTRODUCTION

1.3 Design Process

The structural design process began in August of 2011. ThorntonTomasetti provided ASPIRE with architectural geometry and a structural

elevation. A geotechnical report from STS Consultants, LTD and wind

tunnel testing results from RWDI were also provided. Co-project managers

were elected to oversee and organize the design approach for each

deliverable. They held weekly meetings, compiled deliverable

submissions, critiqued design tools, and served as the primary liaison to

the project advisors.

Initial design consisted of determining a lateral system and overall design

criteria including serviceability limits and load conditions. The structure is

split into four banks (Figure 1.3). The bottom of each bank consists of a

lobby level and the top of each bank consists of two mechanical levels.

Bank 1 is an exception where the ground floor lobby spans four floors for a

large open space atrium. Bank 4 was further split into two sub-banks for

design optimization as the structure’s tapering increases significantly at

floor 139. Table 1.1 summarizes the floor breakup per bank.

Table 1.1: Floor Bank Summary

Bank Floors

1 1-39

2 40-73

3 74-110

4.1 111-129

4.2 130-147

Revit Structure was used to construct a preliminary three dimensional

model. Element shapes and sizes were updated throughout the design

process. Initially, Revit was utilized to produce structural drawings;however, AutoCAD 2012 was ultimately used for the final drawings due to

inadequate computer graphic and RAM resources for Revit.

All structural elements were initially designed for gravity forces, and ultimately optimized using

MIDAS G h di i l l f l Th j hi hli h d i i

Figure 1.3: Bank Location

B a n k

1

B a n k

2

B a n k

3

B a n k

4



2.0 DESIGN CRITERIA

2.0 Design Criteria

Preliminary analyses required ASPIRE to study relevant tall building design. In adjunction witharchitectural constraints, this research was utilized to select specific structural systems for gravity

and lateral systems.

2.1 Tall Building Design

For years engineers have furthered the practice of structural engineering, designing increasingly

taller skyscrapers to meet the demanding vision of architects and owners. As buildings grow, more

efficient, specialized structural systems are needed to handle the loads. One of the first buildings to

clearly demonstrate the potential of the skyscraper was the Empire State Building, reaching 1250

feet in 1931 through the use of a standard riveted steel frame with simple portal bracing (Binder

2006, 42). Engineering has progressed onward from this simple system, reducing the amount of

material used while simultaneously increasing the height. One way of achieving this is through the

use of a high-density concrete core with outriggers and belt trusses at mechanical floors. This

strategy has allowed buildings like the Shanghai World Finance Center and the Burj Khalifa to soar

to heights over one and two thousand feet, respectively.

The Chicago Spire’s specifications are demanding, defining a building that is truly unique.

Outriggers and belt trusses for lateral restraint are limited to the mechanical floors, isolated

throughout the structures elevation. The residential floors contain spacious floor plans with evenly

spaced columns in a ring around the core. Cantilever beams extend from the radial frame to the

façade, allowing for unobstructed views in all directions.

For a building as slender as the Chicago Spire, the lateral system is often the limiting factor in

selecting a design. As buildings increase in height, the structural frames continue to decrease in

average weight per square foot. This is possible due to interaction between interior/exterior

components; high strength low-alloy steel; composite construction; wind tunnel tests; and concrete

improvements in reinforcement and strength.

A vital piece of the Chicago Spire’s design is a system to resist lateral loads. Lateral loads are more

variable than gravity loads and increase significantly with building height. Lateral systems are

designed with the tower’s strength, stability, and rigidity in mind. For tall buildings, serviceability

usually controls the design. Inter-story deflection, also called floor-to-floor drift, and dynamic

effects, such as vortex shedding and vibrations, are concerns for slender buildings.



2.0 DESIGN CRITERIA

2.2 Lateral System Determination

The Chicago Spire’s architecture plays a significant role in selecting a feasible lateral system.Clearance requirements in residential and lobby floors limit regions where the exterior column grid

and concrete core can integrate to resist lateral forces. The two primary components of the chosen

lateral system are the high-strength concrete core and the exterior column system.

2.2.1 Outriggers and Belt Trusses

Mechanical floors will include outriggers and belt trusses to effectively stiffen the structure and

incorporate the exterior column grid with the core. The outriggers will span from each exterior

column to the core wall two floors above. Belt trusses will circle the structure at the same floors.

Belt trusses enable the column grid to systematically resist induced shear forces and moments. The

lack of architectural constraints in mechanical floors allows for large steel members to span in

regions normally occupied in residential floors. The outriggers and belt trusses are effective in

reducing both inter-story and global drift. Additionally, these transfer a 20-40% of the exterior

axial forces into the concrete core.

Outriggers and belt trusses are extremely difficult and timely to construct. However given the

architectural constraints of the project, they are a necessity to meet serviceability requirements.

Construction scheduling must consider the delay and dead time when outriggers floors are erected.

Figure 2.1 shows an outrigger and belt truss system sketch for a typical lateral restraint system.



2.0 DESIGN CRITERIA

2.2.2 Core and Shear Walls

The core of the Chicago Spire will consist of thick concrete shear walls integrated through link

beams and a reinforced concrete, two-way slab.

Concrete is a versatile building material with its own strengths and weaknesses. Concrete is

economic, fire-resistant, and long-lasting. Concrete walls can be almost any shape or size as long as

they harden uniformly to limit cracking. A disadvantage of concrete is the increased section

required to support a specified load. However, this larger section can increase structure stiffness,

decrease global deflection, and minimize floor vibrations.

Another weakness of concrete is the construction time involved with slip formwork erection,

pumping, pouring, and curing. The increased construction time results in increased labor costs,

which should be balanced by material savings.

One important consideration for a concrete core is the effect of creep and shrinkage. With steel or

composite columns, the vertical elements will ultimately experience differential settlement. This

must be pre-calculated and accounted for during construction.



2.0 DESIGN CRITERIA

2.3 Typical Floors and Column Layouts

Four typical floors can be used to fully represent the loading in the Chicago Spire. These typicalfloors include the lobby and amenities, residential floors, mechanical floors, and the parking floors.

The number of columns per bank decreases to optimize column sizing and spacing (Table 2.1).

Load diagrams have been prepared for each of the typical floors selected and can be viewed in

S0.001.

Table 2.1: Summary of Exterior Columns per Bank

Bank Columns

1 21

2 21

3 14

4.1 14

4.2 14



2.0 DESIGN CRITERIA

2.4 Gravity Design Loads

Gravity loads include element self-weight as well as superimposed dead loads and live loads asdefined by ASCE 7-05. Loading diagrams look specifically at loads acting on the floor slabs;

detailing which load is applied in a certain area. This information is used to design beams, columns,

and slabs for gravity loads. Loads from column self-weight, lateral forces, and façade line loads are

not included in loading diagrams.

Dead loads include self-weight of reinforced concrete slabs and composite decking when applicable.

Values were updated throughout the design process once all slab thicknesses, concrete densities,

and decking specifications were made. Table 2.2 summarizes the unfactored gravity forces used for

design. Appendix 9.1 displays the calculations for the specific loads in Table 2.2.

Table 2.2: Unfactored Design Loads per ASCE 7-05 (psf)

Dead

Load

Superimposed

Dead Load

Live Load

Lobby 32 57 100

Residential 33 34 55

Mechanical 39 10 240

Parking 150 42 40

Mechanical Core 55 10 240

Residential and Lobby Core 55 57 100



2.0 DESIGN CRITERIA

2.5 Lateral Design Loads

Lateral loads are extremely important in the design of tall buildings, and they are the controllingfactor the Chicago Spire design. Tall and slender structures such as the Spire are extremely

susceptible to wind and seismic forces. ASCE 7-10 was used to estimate wind and seismic forces.

Wind tunnel testing results were also provided and used in comparison to the code defined wind

loads.

2.5.1 ASCE 7-10 Wind Loads

Chapter 26 was utilized to calculate various factors, which include basic wind speed, wind

directionality factor, exposure category, topographic factor, gust effect factor, and enclosure

classification. Chapter 26 calculations can be found in Calculation 2.2.1. The following assumptions

were made throughout the calculation.

Basic wind speed, V = 120 mph ASCE 7-10, 26.5-1B

Wind directionality factor, Kd = 0.85 ASCE 7-10, 26.2-1

Exposure Category D (Flat, unobstructed wind over water) ASCE 7-10, 26.7

Building, Enclosed ASCE 7-10, 26.2

Occupancy Category IV (Iconic structure) ASCE 7-10, 1.5-1

These factors are then used in the Directional Procedure in Chapter 27 to calculate windward andleeward pressures. The main wind force-resisting system from 27.4 is used to calculate the wind

pressures for windward and leeward walls. The code calculated wind pressures were multiplied by

respective lateral tributary areas to produce a net wind force at each floor.

Loads from ASCE 7-10 are very conservative and ambiguous for the Chicago Spire. The calculations

were performed to provide baseline values to compare against wind tunnel data. For code

calculations, the building is assumed to be prismatic and regular-shape, so that windward, leeward,

and side walls can be identified. Effects like vortex shedding are not addressed.

The ASCE 7-10 wind loads are calculated with basic wind speeds corresponding to a mean

recurrence interval of 1700 years. These results should be considered for design only. ASCE 7-10,

Figure CC-3 provides 50-year MRI basic wind speeds which can be used for serviceability criteria.



2.0 DESIGN CRITERIA

2.5.2 RWDI Wind Tunnel Forces

Thornton Tomasetti provided ASPIRE with a wind tunnel analysis of the Chicago Spire. The report,

prepared by RWDI, contained forces (Fx and Fy) and torsional moments (Mz) for each floor. The

report lists recommended wind load combinations which will be discussed in a later section. The

maximum resultant of the combinations for Fx and Fy were plotted against the ASCE 7-10

directional procedure forces. Figure 2.2 shows these results and a confirmation that wind tunnel

forces should be used for strength design and serviceability criteria. Appendix 9.2 shows all RWDI

Wind Tunnel Data and recommended wind load combinations.

The RWDI forces are for a 100-year MRI. For checking serviceability criteria, a reduction factor of0.83 is used to estimate 50-year MRI forces.

Figure 2.2: RWDI Wind Tunnel versus ASCE7 Directional Procedure Forces

2 0 DESIGN CRITERIA



2.0 DESIGN CRITERIA

2.5.3 ASCE 7-10 Seismic Load Calculations

ASCE 7-10, Chapters 11 and 12 were used to estimate seismic loads for the Chicago Spire. The

complete seismic calculations are in Calculation 2.3.

The overall weight of the building was needed to perform seismic loading analysis. The building is

broken down into 8 Mechanical floors, 8 Lobby floors, and 131 Residential floors for a total of 147

floors. The effective seismic weight, W, was calculated using an initial estimate for core wall,

column, and cladding self-weight. Following the design of columns and core walls, the effective

weight and resulting seismic forces were updated. The effective seismic weight was found to be

650,000 kips. The base shear was calculated assuming a seismic response coefficient, Cs, of 0.10.The following formulas were used to determine the seismic lateral loads at each floor.

ASCE 7-10, 12.8-11

∑

( ) ASCE 7-10, 12.8-12

∑ ASCE 7-10, 12.8-13

where

Fx ,Fi = lateral seismic forces induced at any level i or x

Cvx = vertical distribution factor

V = total design lateral base shear

wi , wx = portion of the total effective seismic weight of the structure located to level

i or x

hi , hx are the height from the base to level i or x

k= exponent related to the structure period

Vx = design story shear at any story

Table 2.3 summarizes the results at the base and top floor of the structure. See Appendix 9.3 for all

lateral forces, story shears, and moments.

2 0 DESIGN CRITERIA



2.0 DESIGN CRITERIA

2.6 Load Combinations

The following load combinations from ASCE 7-05, 2.3.2 were used throughout the design process.Load combinations were used in both engineering hand calculations and in the MIDAS Gen 3D

model. The RWDI wind tunnel recommended combinations from Appendix 9.2 were used as a sub-

level of load combinations when wind applied.

1.4D

1.2D + 1.6L

1.2D + 1.6W + 1.0L 1.2D + 1.0E + 1.0L

.9D + 1.6W

.9D + 1.0E

The following load combinations from ASCE 7-05, CC.1.2 were used in for drift serviceability

criteria. The RWDI wind tunnel recommended combinations from Table 9.1 were used as a sub-

level of load combinations with a reduction factor of 1.20.

1.0D + .5L + .7W

2 0 DESIGN CRITERIA



2.0 DESIGN CRITERIA

2.7 Serviceability Requirements

Serviceability limit states are the conditions in which the routine functions of a structure areimpaired because of local deformation of building components or because of occupant discomfort.

These limit states are affected by static loads from the occupants and their possessions, snow or

rain on roofs, temperature, dynamic loads from human activity, wind, or the operation of the

building service equipment. Serviceability criteria for the Chicago Spire should be selected from the

limits specified in design codes to ensure both functional as well as economical design when

constructing a building with desirable retail space.

Serviceability criteria for the Chicago Spire are controlled by:

Excessive deflection or rotation

Excessive vibrations

Total and local (floor-to-floor) building drift

Tower accelerations

The criteria used depend on the function of the building. General guidance on serviceability limitsis provided in sections CC1.1, CC1.2, and CC1.3 of ASCE 7-10.

2.7.1 Deflection

Vertical deflections arise primarily from:

Gravity loads (dead loads and live loads)

Effects of temperature, creep and differential settlement

Construction tolerances and errors

For the Chicago Spire, the deflection limit for horizontal members is as follows:

Δ ≤ L/360 ASCE 7-10, CC1.1

These limits will prevent any visible deflection or impairment of window and door operation. Snow

loads are negligible in the Chicago Spire, thus only dead and live loads are considered when

meeting deflection criteria. The suggested load combination is:

D + L ASCE 7-10, CC-1a



3.0 GRAVITY DESIGN



3.1 Geometry and Loading

The Chicago Spire geometry is based on provided architectural drawings as well as teamassumptions based on design calculations and the elevation drawings. Assumptions for the Chicago

Spire geometry and loading are listed below.

Beam spans and associated tributary areas are calculated from the Revit model.

Two cantilever beam spans (short and long) are considered for each typical floor plan. The spans

are estimated from the provided structural elevation drawing.

Exterior face consists of curved, load bearing HSS beams.

Mechanical and lobby floor plans have three joists per internal bay. Residential floor plans have

two joists per internal bay.

Radial girders and cantilever beams are fixed-fixed to reduce net moment at the respective

connection.

All other beam connections are considered to be simply supported.

3.1.1 Tributary Areas

Joists, circumferential girders, angled girders, and HSS beams bear loads from the design loads

shown in Table 2.2 (pg 9). A floor beam denomination system is shown in Figure 3.1. Calculation

3.1 displays the calculation steps for gravity design tributary area. More specific assumptions for

the tributary area calculations are listed below.

Rectangular shapes are used to estimate all tributary areas.

Column-to-façade distance is assumed to be constant throughout the rise of the tower.

Typical floor plans are considered to have internal bays and external bays.

o Internal bays consist of floor joists and radial girders.

o External bays consist of cantilevers, HSS beams, and angled girders.

HSS 1 extends from the short cantilever to the end of the long cantilever and back down to

another short cantilever. HSS 2 spans between two short cantilevers. See Figure 3.2.

In external bays bounded by HSS 1, the HSS beam bears ¼ of the area, the angled girder bears ½

of the area, and the circumferential girders bears ¼ of the area. See Figure 3.2.

In external bays bounded by HSS 2, the HSS beam bears ½ of the area, and the column girder

bears ½ the area. See Figure 3.2.

3.0 GRAVITY DESIGN



Figure 3.1: Structural Beam Labeling System

HSS 1

HSS 2

3.0 GRAVITY DESIGN



Figure 3.2: Tributary Area Breakdown for External Bays

Figure 3.3 shows the tributary area for a typical joist. The base length is the average adjacent joist

lengths, and the height is the beam spacing.

Figure 3.3: Tributary Area for Joist 1

3.0 GRAVITY DESIGN



3.1.2 Loading and Load Paths

The following equations are used for the deflection serviceability requirements and the gravity

beam design.

Serviceability: D + L

Strength Design: 1.2D + 1.6L

There are several load paths considered for the gravity design process. Figure 3.4 summarizes the

paths for the gravity loads summarized in Table 2.2 (pg 9). The façade load was assumed to be 10

psf and the floor-to-floor height of 13 ft, 2 in. This results in a line load of 132 plf.

Façade (plf)

HSS Beams

DL, LL, SDL (psf)

Angled Girders Joists

Radial GirdersCantilevers

Columns

Link Beams

Core Walls

Column Girders

Foundation

3.0 GRAVITY DESIGN



3.2 Core Slab Design

The core slabs were designed as reinforced concrete floors. The core requires a large number of

voids for elevator shafts and mechanical openings. ASPIRE used reinforced concrete instead of

composite decks to account for these different span lengths and configurations. Slab thicknesses

and reinforcement was determined to provide appropriate moment capacity.

Loads for core slab design are shown in Table 2.2 (pg 9). For each bank, four typical slabs were

designed. These slabs are labeled in Figure 3.6. The numbering is identical for the same locations

on different banks. Slab design 4 is assumed to be typical for slab sections not included in the

numbering or not identical to other numbered slabs. Appendix 9.4 summarizes the core slabreinforcement. Calculation 3.2.1 shows the design steps following ACI 318-08 for one-direction

slabs.

Figure 3.5: Core Slab Detail

3.0 GRAVITY DESIGN



3.3 Link Beam Design

Link beam sizes were determined by the loading condition from Table 2.2, pg 9. Five different link

beams were selected from plan to be designed. These designs can then be extrapolated to size the

remaining link beams within the core. The tributary areas were estimated fairly conservatively

(Figure 3.7).

Figure 3.7: Tributary Areas for Link Beam Design.

There were several assumptions used to carry out the design of the link beams within the core

structure:

Length of curved beams equal to length of arc centerline. Steel to concrete connections from radial girders fixed to curved beams act as point loads on the

centerline of the beam.

All beams are simply supported.

Sand-lightweight concrete is used throughout.

3.0 GRAVITY DESIGN



3.4 Composite Beam Design

Composite beam design was used for all above grade beam systems surrounding the concrete core.

The initial gravity design compared a non-composite beam system to a composite system. The

composite system required smaller W-shapes and less concrete for the slabs.

3.4.1 Slab and Decking

Specific deck sizes were selected from the Vulcraft Steel Roof & Floor Deck, 2008 manual with

respect to constructability as well as minimizing the material weight. Specific assumptions for the

slab and decking calculations are listed below.

Floor-to-ceiling heights must remain constant in all residential and lobby levels.

When calculating weight of the steel, steel beam systems were modeled as a group of W12x29

shapes.

Weight of steel is assumed to be 500 pcf.

Decking system is simply supported over steel framing as a continuous beam.

Decking runs perpendicular to all floor joists and circumferential girders. Decking comes in 30 in

or 36 in widths and can be either shop or field cut to meet the architectural requirements of the

slab edge.

Appendix 9.7 summarizes the decking and slab thickness used for composite beam design.

Calculation 3.3.1 summarizes the composite deck sizing calculations.

3.4.2

Composite Beam Sizing

The design procedure found in Bungale S. Taranath’s Steel, Concrete, & Composite Design of Tall

Buildings was used in conjunction with Chapter I of the AISC Steel Construction Manual. Sample

composite beam calculations can be found in Calculation 3.3.2. Assumptions for composite design

are listed below.

Unshored construction will be used and all pre-composite loading conditions must be considered.

Area of corrugated steel decking and concrete between top of flange and top of decking will be

considered negligible.

All shear studs will be ¾ in. diameter and 3 in. long before welded to steel beam.

Lateral-torsional buckling is not a concern for the completed structure.

Angled girder design is assumed to be perpendicular to the decking direction

3.0 GRAVITY DESIGN



The radial girders on mechanical floors were designed for weak axis bending. These girders are

rotated 90 degrees to increase the constructability and strength of the outrigger connections.

Appendix 9.5 summarizes the preliminary composite beam design

Figure 3.8:Typical Composite Beam and Decking System

3.4.3

Serviceability

3.4.3.1 Deflection

All beams were checked under pre-composite and post-composite load conditions against

deflection requirements set in Section 2.7.1. For uniformly distributed beams modeled as simply

supported, deflection was calculated using the following equation:

4

max

5

384

wl

EI

where

I = Is for pre-compositeI = Ieff for post-composite

The following checks were made against the pre- and post-composite deflection.

3.0 GRAVITY DESIGN



Cantilever beams and radial girders received point loads from adjacent beam members. Beam

deflection was calculated using the principles of superposition from separate scenarios of single

point loads.

3.4.3.2 Vibration Analysis

Vibration from human movement and walking excitation must be considered as a serviceability

design requirement for the Chicago Spire’s gravity design. Serviceability loads and beam

deflections are used to calculate the floor’s natural frequency per AISC Design Guide 11, equation

3.3:

0.18n

total

g f

AISC Design 11, 3.3

The following assumptions are made throughout the vibration analysis test.

Vertical column frequencies are not taken into account

Beam and decking are non-continuous over the bays. This assumes that each bay is independent fromthe others.

Transformed moment of inertia must be used for deflection equations.

The natural frequency, f n, is used to calculate the ratio between the peak acceleration and gravity

(ap/g), which is compared to the acceleration limit (ao/g) based on the type of occupancy. For the

Chicago Spire, the occupancy condition is residential, and per AISC Design Guide 11, Table 4.1 the

acceleration limit is 0.5%. The peak acceleration is calculated from equation 4.1:

0.35 n f p o

a P e

g W

AISC Design 11, 4.1

where

Po = excitation

β = modal damping ratio

W = effective weight supported by the component.

Peak acceleration from Equation 4 1 is compared to the acceleration limits set in Section 2 7 2 The

3.0 GRAVITY DESIGN



Table 3.1: Typical Values for Vibrational Analysis Calculations

Residential Mechanical Lobby Units

Number of joists framing into

girders

2 3 3

Thickness of corrugation 1.5 2 1.5 in

Weight of decking 1.78 3.29 1.78 psf

Theoretical volume of concrete 0.253 0.292 0.253 ft3/ft

2

Total Load 60 65 60 psfFrom AISC Design Guide 11, Table 4.1

β 0.2 0.2 0.2

Po 65 65 65 lbs

When a member or bay is subjected to excitation at its natural frequency, f n, the beam will reach its

maximum vibrational displacements. The natural frequencies of members depend on their stiffness

and mass. Members analyzed individually showed a natural frequency in the range of 3 Hz to 22 Hz;

however, when analyzed as a combined system yielded natural frequencies between 3 Hz and 10

Hz. The peak acceleration for the Chicago Spire was found to be between 0.040% and 0.246%. See

Table 3.2 for the full range of values.

Table 3.2: Summary of Estimated Vibrations

Type Bank ap/g ao/g

Residential 1 0.332% 0.50%

Mechanical 1 0.099% 0.50%

Lobby 1 0.199% 0.50%



Lobby 2 0.086% 0.50%



Lobby 3 0.073% 0.50%

Residential -1 4 0.146% 0.50%

R id i l 2 4 0 130% 0 50%

3.0 GRAVITY DESIGN



3.5 Façade Beam Design

The beams running along the slab edge support the façade and design loads from Table 2.2. These

beams were designed as hollow structural section (HSS) to account for large, curved spans. Section

geometry of HSS beams allows for increased constructability and resistance to torsion. Blodgett’s

Design of Welded Structures was used to calculate end torsion of the curved beams. The following

assumptions were made throughout the HSS beam design process.

Tributary area was calculated from the Revit model (Figure 3.9)

Other than torsion at the beam ends and angular twist, all other calculations for bending moment

and shear capacity assume that the beam is straight.

Figure 3.9: Tributary Areas for the HSS Beam

A preliminary section was chosen for all perimeter façade beams. Table 3.3 summarizes this

design.

Table 3.3: HSS Beam Design Summary

3.0 GRAVITY DESIGN



3.6 Column Design

Vertical columns and slanted transfer columns were selected given the gravity design load

combination in Section 3.1.2. Axial loads for column design were calculated using a column load

takedown. The structure was split fourteen subsections for the column schedule. Initial composite

and steel shapes were chosen for these locations. These sizes serve as a baseline for structural

software modeling and energy optimization. The column sizes are expected to change multiple

times once lateral forces are analyzed for strength and serviceability.

All vertical concrete has a 28-day compressive strength of 14,000 psi. High density concrete,

ρc=160 pcf, is also used in all composite columns and the concrete core wall. Design tools for axialforces, vertical columns sizing and transfer columns sizing can be found in Calculation 3.4.

3.6.1 Column Load Takedown

A column load takedown tool calculated axial forces given factored design loads and respective

tributary areas. Axial forces were calculated for the exterior columns and the core bearing walls.

Beam columns transfer eccentric loads at mechanical floors due to the chosen column grid

summarized in Table 2.1. Two gravity load paths, shown in Figure 3.10, allow for the design of four

types of columns. Column 1 extends the entire height of building while Column 2 of Banks 3 and 4

is transferred to two columns, 3a and 3b, for Banks 1 and 2. Figure 3.11 and Figure 3.12 display the

typical column grid for Bank 1 and Bank 3, respectively. For constructability purposes the column

details should be similar in each subsection.

3.0 GRAVITY DESIGN



Figure 3.10: Steel Column Load Paths

Column 1

Column 2

3.0 GRAVITY DESIGN



Figure 3.12: Bank 1 Steel Column Layout

Axial loads for the core were also found using the column load takedown. The core was notoriginally designed for solely gravity forces. The core loads from the column load takedown were

utilized in the three dimensional finite element model as nodal forces.

The core is divided into four shear walls, an East-West pair, and a North-South pair. The shear

walls act as coupling units through the reinforced concrete link beams and slab. The column load

takedown calculated axial forces for individual shear walls. Elevator shaft openings throughout the

tower limit the core wall shapes. Generic core wall geometry was simplified to the cross section

shown in Figure 3.13. In Bank 4 the reduced shaft opening space and the tapering of exterior

columns leads to an exception to the typical core geometry.

Column 1

Column 3a/3b

3.0 GRAVITY DESIGN



Figure 3.13: Typical Core Column Section, Banks 1-3

Calculations were performed at each level for each type of column. Tributary area was multiplied

by the distributed load to get the resultant axial column load. In cases where there is more than

one type of loading, the corresponding area is used. Cumulative axial loads at the ground level can

be used for foundation and mega-column design (Table 3.4).

Table 3.4: Factored Loads from Gravity at Ground Level

DL SDL LL

(kips) (kips) (kips)

Column 1 5,600 7,600 7,600

Column 3a 4,200 5,800 5,800

Column 3b 4,200 5,800 5,800

E-W Core 9,700 13,100 24,200

N-S Core 12,100 14,200 43,400

Does not include column and core self-weight

3.6.2 Initial Vertical Column Design: Composite and Steel Shapes

Axial forces from the column load takedown were used to optimize the column material and size for

3.0 GRAVITY DESIGN



The initial column sections of the Chicago Spire were optimized for strength, economy, and

architectural constraints. Composite columns were designed following AISC Chapters I, G1 and G2.

Steel columns were designed using AISC Chapters H1. Column behavior from lateral load

combinations was not considered for this deliverable. Figure 3.14 shows a typical composite

column section with a W-shape and reinforcement encased in concrete.

Figure 3.14: Composite Column Section

Appendix 9.9 summarizes the initial column sizes for each subsection of the Spire.

3.6.3

Transfer Column Design

At mechanical floors, angled beam-columns transfer gravity loads from one bank to another. As the

height of the structure increases, the building tapers and radial column grids reduce in diameter.

Figure 3.15 shows the different transfer column configurations for each bank. The columns were

designed in accordance with AISC Chapter H1 because they are subject to both axial and flexural

forces.

Using the loads from the column load takedown, nominal moments and compressive strengths

were calculated. The columns were designed to satisfy flexural and axial limit states. Upon

preliminary analysis, it was discovered that typical W-shapes were not sufficient for the combined

loading criteria. Built up columns or W-shapes with cover plates are needed to fully satisfy the

design loads.

4.0 LATERAL LOAD RESISTING SYSTEM DESIGN



4.0 Lateral Load Resisting System Design

ASPIRE conducted a three phase lateral system design for the Chicago Spire. First, a preliminary

lateral analysis modeled the building as a cantilever tube representing the reinforced concrete core.

Each bank was assigned an initial wall thickness and inner radius to optimize the critical tensile and

compressive stresses at the base of the bank. The preliminary core thicknesses were very large and

unfeasible for construction and design, so additional investigation was necessary.

This deliverable incorporates the columns into the lateral design and assesses the need for

additional lateral systems. Outriggers and belt trusses have been added to create an integrated

system. The core and the columns act together to resist lateral forces and torsional moments fromwind and seismic load combinations. A three-dimensional model was created with MIDAS Gen to

run load cases in static and dynamic analyses. Core walls, outriggers, and belt trusses were sized

using sensitivity analyses to meet serviceability requirements defined in Section 2.7.

Critical moments and axial forces, taken from the finite element model, showed the preliminary

sizing from the gravity design to be inadequate. Ultimately, column steel area was increased to

improve the structure’s stiffness. This was critical to lateral deflection and gravity load shedding at

outrigger levels.




4.1 Structural System Overview

The overall structural systems are critical to the lateral design of the Chicago Spire. The Chicago

Spire includes a reinforced concrete core surrounded by radial exterior columns. In three isolated

mechanical sections, two-story trusses span between the radial columns and the core, acting as

outriggers that tie the movements and rotations of the columns to the core. Outriggers are also

effective in shedding gravity loads from the columns to the concrete core. Belt trusses also

surround these levels to tie the columns together into a cohesive unit.

While the gravity system was designed for code defined loads and calculated tributary areas, lateral

forces are both unpredictable and significant. Statistical analyses are typically performed todetermine the critical wind and seismic lateral forces for both design and serviceability conditions.

Wind tunnel loads and torsional moments were provided by RWDI and provide an accurate

estimate of 100-year MRI forces on the Chicago Spire. ASCE 7 design procedures for wind loads

produce extremely conservative results for tall, slender buildings.

The core of the building is primarily designed to be a stiff lateral load-resisting system. Although

size and openings are constrained by architectural specifications, the core still needs to resist

critical wind and seismic forces. These forces develop an overturning moment in the core that

induces tensile stresses on the windward side of the core and compression stresses on the leeward

side. The moment induced in the core near the top of the building is fairly negligible, necessitating

a core of only a few feet thick. However, near the base, this moment can be significant enough to

control the overall core design. Concrete has a strong resistance to compressive stresses, yet is

weak in tension. The core is heavily reinforced with flexural reinforcement to resist the tension

stresses. Additionally, the outrigger and belt truss system helps reduce the overturning moment,

thereby reducing the tensile stresses. Figure 4.1 shows the locations of the belt truss and outrigger

system at mechanical floors.




Figure 4.1: 3D model of Outrigger and Belt Truss Locations

Belt Truss

Outrigger


4 2 P li i C W ll D i



4.2 Preliminary Core Wall Design

Hand calculations were completed to estimate initial core wall thicknesses and reinforcement limits

based on the compressive strength of concrete and the modulus of rupture. Wind tunnel testing

provided by RWDI proved to be more accurate than ASCE design loads. All exterior framing,

foundations, slabs, and columns are ignored in these calculations. The Chicago Spire’s core is

assumed to act as a cantilever resisting lateral forces from seismic activity or wind and axial forces

from self-weight, dead loads, and live loads. Calculations 4.2 and 4.3 summarize the engineering

calculations used to develop baseline core wall thicknesses when considering both a system with

and without outriggers.

4.2.1

Core Wall Design Loads

A combination of wind tunnel data, ASCE 7-05 and ASCE 7-10 were used to find forces, stresses, and

moments at each floor.

ASCE 7-10 used for seismic load calculation

ASCE 7-05 2.3.2 basic load combinations used for wind strength design

ASCE 7-05 CC.1 basic load combinations used for wind serviceability verification

RWDI 100 year MRI Wind Tunnel Testing Information Used for wind serviceability load

calculation (Appendix 9.2).

The loads at the bottom floor of each bank were used to calculate controlling tensile and

compressive stresses. The loads used in the calculations are in Table 4.1 below. The floor at the

base of each bank was assessed for a conservative approach.

Table 4.1: Critical Core Wall Unfactored Design Loads

Core Gravity Loads Lateral Moments

Total Dead

Load

(SDL + DL)

Total

Live Load

Core Self Weight

Above Floor

ASCE 7-10

Seismic RWDI Wind Tunnel

Bank Floor kips kips kips k-ft k-ft

1 1 81,958 84,464 594,387 8.82E6 9.41E62 40 56,024 59,908 282,275 5.49E6 5.16E6

3 74 33,366 37,076 141,506 2.86E6 2.42E6

4a 111 15,356 21,238 38,397 8.02E5 5.70E5

4b 130 6,810 13 496 15 825 2 25E5 1 20E5


The loads in Table 4 1 have been determined from various design tools:



The loads in Table 4.1 have been determined from various design tools:

Dead load, superimposed dead load, and live load are from a column load takedown created

for the gravity design deliverable. The column load takedown calculated loads for each corewall section. These values were scaled to represent the total unfactored loading on the

assumed tube for each floor.

Seismic moments were calculated as the sum of all moment arms from lateral seismic

forces, Fx.

Wind moments were calculated as the sum of all moment from critical lateral wind forces.Recommended wind load combinations were considered. A critical resultant force from the

effects of Fx and Fy at each floor was used for the preliminary design moments. Wind

moment calculations ignore torsional moments provided by RWDI testing.

4.2.2

Core Wall Design

The concrete cantilevered tube was designed to resist the previously calculated gravity and lateral

loads. The inner radius and core wall thickness were adjusted at each bank to account for the

varying loads throughout the building. The strength design load combinations from Section 2.6.

The compressive stress block due to the gravity load was combined with the lateral stress diagram

to calculate net compressive and tensile stresses at the extreme outer fiber of the core. Shear forces

and moments were calculated from the distributed seismic and wind forces. Figure 4.2 displays a

sample combination of gravity and lateral induced stresses.




The following equations were used:

( , )

gravity lateral comp tens

P M c

A I

where

c = distance from center to extreme outer fiber

I = second moment of area

A = section area of concrete tube

Pgravity = critical gravity load

Mlateral = critical moment from lateral forces

The controlling compressive and tensile stresses from the load combinations were compared to

allowable stresses found in ACI 318. Table 4.2 summarizes the design comparison between the

controlling stresses from the six load combinations to the allowable stress values. The

reinforcement is designed assuming the steel yields first, allowing Φ = 0.90.

Table 4.2: Controlling Stresses for Core Wall Design

1 2 3 4a 4bNet Compression = 6.468 4.647 3.552 2.066 1.050 ksi

Net Tension = -3.610 -2.989 -2.698 -1.463 -0.465 ksi

Allowable Compression = 0.55*φ * f'c = 6.93 ksi ACI 318 (14.5.2)

Allowable Tension = 7.5 * (f'c).5

= -0.887 ksi Φ = 0.90

The equations for net compression and tension are dependent on the cross sectional area of the

core and the moment of inertia. The core thickness and inner radii were adjusted to meet the

allowable compression constraint, as shown in the next section. The grey highlighted cells in Table

4.2 exceed the modulus of rupture; however, preliminary analysis ignores concrete reinforcement




Figure 4.3: Distributed Lateral Load for Core Wall

Bernoulli’s equation was used to calculate the maximum tip deflection from the uniform loads

calculated from the RWDI forces.

The maximum global tip deflection was calculated to be 10 ft (Calculation 4.1). This fails the global

serviceability requirement; however, this does not account for the contribution of outriggers orexterior columns.

4.2.4 Reinforcement Requirements

y w

24 E Ix

4

c1

6x

3

c2

2x

2 c3 x c4




4.3 Auxiliary Lateral Systems



4.3 Auxiliary Lateral Systems

Tall building design is typically controlled by seismic or wind forces. Reinforced concrete core

walls and columns cannot resist the overturning moment and base shear without an additional

lateral system. Additional lateral systems were employed to create a cohesive, stiff structure to

optimize design and meet serviceability requirements. Lateral systems require large beam

members or truss systems with architectural constraints often controlling their location and design.

4.3.1 Need for Auxiliary System in the Chicago Spire

The core thicknesses determined in the Section 4.2 calculations are excessive and unfeasible forconstruction. In order to reduce core wall thicknesses, outriggers will be constructed as large

transfer girders on the mechanical floors of Banks 1-3. These will span two levels from the exterior

columns to the concrete core wall.

Figure 4.4: Outriggers Spanning Two Mechanical Floors

Preliminary calculations show that outriggers will increase the moment of inertia and stiffness ofthe structure. This decreases the net stresses at each bank. The concrete core wall thicknesses are

reduced to optimize the compressive strength requirements. These final thicknesses are used as

base points for the MIDAS Gen structural model. To determine the stiffness of the perimeter

column system it was necessary to first determine the effective moment of inertia of the circle of


The effective moment of inertia was determined by drawing a centerline through the middle of the



building and calculating the distance of each individual column from that centerline. The moment

of inertia for an object not centered on the centroid is:

I CL = I object + Ad 2

where

Iobject = moment of inertia of column

A = section area of column

d = distance from centroid to center of object

The moment of inertia of the columns, Iobject , is insignificant compared to Ad2 and can be neglected.

I CL ≈ Ad 2

The following assumptions were made for the core wall calculations utilizing outriggers and

exterior columns.

Steel and composite column section properties are from initial gravity design.

Increase in concrete volume and area from columns considered negligible for stresses from

gravity loads.

Itotal = Icore + 0.7*Icolumns where 0.7 is an assumed factor provided that outriggers and belt trusses

are not infinitely stiff.

Calculations use smallest column size per section for a conservative approach.

Table 4.5 highlights the effective Modulus of Elasticity, moment of inertia and stiffness of each

column section throughout the structure.


Table 4.5: Summary of Column Properties for each Column Section



Bank Level # Columns Column Radius (ft) Eeff (ksi) Ieff (ft4) EI (kip-in2)

4 145 14 53.5 29000 4050 2.44E+124 134 14 53.5 29000 4050 2.44E+12

4 123 14 53.5 29000 7905 4.75E+12

4 113 14 53.5 29000 12721 7.65E+12

3 100 14 61 29000 22613 1.36E+13

3 87 14 61 29000 29306 1.76E+13

3 75 14 61 29000 35457 2.13E+13

2 64 21 68.5 8873 197001 3.62E+132 52 21 68.5 10953 197001 4.47E+13

2 41 21 68.5 12481 197001 5.10E+13

1 29 21 75.5 10458 373939 8.11E+13

1 17 21 75.5 11700 373939 9.07E+13

1 5 21 75.5 9390 538473 1.05E+14

1 Lobby 7 75.5 9390 538473 1.05E+14

The moment of inertias from Table 4.5 were combined with the core wall moment of inertia to

determine new compressive and tensile forces following a similar procedure described in Section

4.2.2. Table 4.6 summarizes the reduction in tensile and compressive forces at each bank. Despite

minimal effects to the top of the Spire, outriggers make a significant contribution in Banks 1 and 2.

Table 4.6: Stress Reduction in each Bank from Outriggers

% Reduction in Each Bank: 1 2 3 4a 4b

In Applied Compression 17% 10% 3% 2% 1%

In Applied Tension 30% 16% 6% 5% 3%

The same loads and procedure described in Section 4.2.5 were used to calculate new core wall

thicknesses that incorporate the outriggers. Table 4.7 summarizes the preliminary calculations for

core wall thicknesses incorporating auxiliary lateral systems.

Table 4.7: Summary of Core Wall Thicknesses with Outriggers and Columns

B k 1 2 3 4 1 4 2


The need for belt trusses and outriggers was assessed qualitatively and these members were not

f ll d d h AS G f d l h b ll b 1 30



specifically designed. For the MIDAS Gen software model, the members will be W14x730 to

increase structural stiffness.

4.3.2 Relative Stiffness of Structural Systems

A basic analysis of the stiffness of the core and column systems was conducted to ensure uniform

performance under applied loads. In order to perform as a cohesive system, the stiffness of the

reinforced concrete core needs to be similar to that of the outrigger and column system. The stiffer

system will take a proportionately larger amount of the stresses than the other system. Therefore,

if the column and outrigger system is stiffer than the core, the full capacity of the core would not be

used and columns could potentially be overstressed to the point of failure.

The relative stiffness of the core and column system will be compared by using the product of the

elastic modulus and the moment of inertia.

Each bank has different section properties, so the core was analyzed in five different segments

corresponding to Banks 1, 2, 3, 4.1, and 4.2. The values for each bank are tabulated in Table 4.8

below.

Table 4.8: System Stiffness Summary

Bank

Core Stiffness,

EI (kip-in2)

Column Stiffness,

EI (kip-in2)

Sum

(kip-in2)

Sum-to-Core

% Increase

0.7-Reduced

Sum (kip-in2)

0.7-Reduced

Sum-to-Core

% Increase

4.2 3.48E+13 2.44E+12 3.72E+13 7.00% 3.65E+13 4.90%

4.1 3.48E+13 7.65E+12 4.24E+13 21.99% 4.01E+13 15.40%3 1.14E+14 2.13E+13 1.35E+14 18.73% 1.29E+14 13.11%

2 1.95E+14 5.10E+13 2.46E+14 26.15% 2.31E+14 18.30%

1 2.65E+14 1.05E+14 3.70E+14 39.58% 3.38E+14 27.71%

The two systems, although separate, will be connected via outriggers spanning from the core to the

columns on the mechanical levels. To determine the effect of the combined systems, each system

can be idealized as a spring with a stiffness equivalent to that of the actual system. The two

“springs” will be connected in parallel by the outriggers, and by simple elastic behavior theory, the

system will have an effective stiffness of the sum of the two springs’ individual stiffness. However,

this value assumes a perfectly rigid connection by the outriggers between the core and the columns.


4.4 Finite Element Model



A detailed structural analysis of the Chicago Spire was conducted using MIDAS Gen. All material

properties and baseline element shapes were taken from initial lateral and gravity design. Verticalmembers, outriggers and belt trusses, and core wall thicknesses were resized throughout the

iterative modeling process based on element forces and moments, and serviceability requirements.

4.4.1 Initial Modeling Process

A three-dimensional model of the Chicago Spire was created in MIDAS Gen to model the behavior of

the building in response to dynamic and static forces. The following modeling procedures andassumptions were made for the initial model.

The model spans from the lobby at ground elevation to the top of level 144.

The tuned mass damper and hypothetical mechanical floors at the Spire’s peak are not

considered. All below-grade elements are not modeled.

The mega-columns and core wall at the ground elevation are fixed to the ground.

Table 4.9 summarizes the initial elements properties modeled in MIDAS.

Table 4.9: Initial MIDAS Model Element Properties

Structural Member Element Type Material Property

Core Wall Plate, thick with drilling DOF RC, C14000

Column B1 B2 B3 General Beam SRC, C14000, A992

Column B4 General Beam S, A992

Transferring Column General Beam S, A992

Radial Beam General Beam SRC, C4000, A992

Column Beam General Beam SRC, C4000, A992

Link Beam General Beam RC, C4000

Outrigger and Belt Truss Truss SRC, C4000, A992

(S)RC: (Steel) Reinforced Concrete

CXXXX: Concrete and f’c (psi)

MIDAS G li i i f d i l f’ 10 000 i h h d l f


Core walls are modeled as thick plate element with drilling DOF, since out-of-plane shear is

not considered negligible



not considered negligible.

Core walls contain openings as shown in structural and architectural drawings.

Composite beams were simplified to W-Shape Steel Reinforced Concrete (SRC) in crosssection properties. The widths chosen in these SRC beams are based on the effective widths

of the composite beam from the gravity design.

All structural elements have been applied fixed-fixed end-releases. Cantilevers and angled

floor girders outside of the exterior column grid were not considered.

4.4.2 Loading and Load Combinations

All design loads were applied as nodal point forces. The column load takedown from Section 3.6.1

and provided wind tunnel information were used to calculate gravity and lateral forces. The

following procedures summarize the applied loads for design and serviceability criteria.

The wind forces from the wind tunnel testing are used directly for strength design. The

wind forces and torsional moments from Appendix 9.2 were applied to each level along the

z-axis.

The wind tunnel recommended combinations from Appendix 9.2 were used as a sub level ofload combinations.

A reduction factor of 0.83 (1/1.2) was applied to the RWDI wind loads to reduce the 100

year MRI loads to a 50 year MRI loads for serviceability design.

Unfactored dead loads and live loads from the column load takedown were applied to nodes

at column ends. Superimposed dead load and dead load combined for total dead load.

Appendix 9.10 summarizes the nodal gravity forces used in MIDAS Gen.

The total unfactored dead load and live load for the core was split equally into nodal forces

to the nodes connecting the radial girders to the core walls or link beams. Appendix 9.10summarizes the nodal gravity forces used in MIDAS Gen

MIDAS Gen calculates material self-weight in the analysis, thus no self-weight is considered

in applied dead loads.

The load combinations from Section 2.6 are used for both strength and serviceability.

4.4.3

Iteration and Element Redesign

Column Validation

Original MIDAS Gen sizes for vertical columns, transfer columns, and mega-columns were from the




Figure 4.5: Compression Block and Steel Strain from Weak Axis Bending

The forces and moments for all load combinations were plotted on the interaction diagram. Steel

shapes, concrete dimensions, and reinforcement specifications were adjusted to optimize the

column design. This process was repeated several times with new column sizes recycled into

MIDAS Gen model and new forces and moments plotted on the interaction diagrams. Appendix

9.11 shows the composite and steel column sizes after several iterations of column validation.

Exterior Steel Stiffness

The new column sizes showed severe discontinuity under gravity forces due to the core and

outriggers being significantly stiffer than the columns. The columns were showing tension forces as

seen in Figure 4.6.

Several sensitivity analyses were used to troubleshoot the model and reduce the load sheddingshown in Figure 4.6 and the excessive deflection. The analyses are summarized in Appendix 9.11.




Figure 4.6: Initial Discontinuity Check under Gravity Loads

Final Design

The final design of the MIDAS Gen model saw several improvements from the original model. The

improvements resulted in acceptable drift under serviceability loads and reasonable load shedding

under gravity loads. The following changes helped reach these goals. Table 4.10 shows the final

model element properties.

Increased steel area in exterior column grid.

Reduced thickness of core walls.

Reduced size of belt truss members.

Table 4.10: Final MIDAS Model Element Properties

Core WallThickness by

Bank (ft) Belt

Truss Outrigger

Vertical Column Size by Bank

1 2 3 4 1 2 3 4

7 4 3 2 W14 53 W14 730 BU1 BU1 BU2 BU2




Figure 4.7: a) BU1 and b) BU2

The final MIDAS Gen model included the built-ups in Figure 4.7 encased in concrete. However, the

concrete was ultimately deemed unnecessary negligible in composite action given the high steel

area. The final design will consist of solely, steel exterior columns.

4.4.4 Results Comparison

The final design was a significant improvement from the original MIDAS Gen design based on

gravity design and preliminary lateral studies. Although Figure 4.8 shows an increase in ultimatecompressive forces, the load shedding at the mechanical floors follows the industry standard of

≈20%. Tension members no longer exist and the overall shape of the compression graph follows

the expected graph of a single column line extending up a building. Table 4.11 shows a sample

comparison of MIDAS results.




Figure 4.8: Discontinuity Test Comparison between Original and Final Design

Table 4.11: Initial and Final MIDAS Results

Initial Final Allowable (400

h)

Base Shear kips 27,500 49,000 N/A

Global Deflection ft 6.71 4.48 5.0

Maximum Inter-story Drift in 0.88 0.56 0.40


The troubleshooting and iteration of the MIDAS model proved to be the most tedious and time

consuming aspect of the Chicago Spire structural design. Ultimately the model produced acceptable



global deflection and forces for connection, foundation, and core wall design.


4.5 Core Wall Reinforcement Design



Core walls were designed using the final MIDAS Gen model thicknesses as reinforced concrete

shear walls. The shear and flexural reinforcement was designed using loads, shears and momentspulled from the MIDAS Gen model. Reinforcement was designed separately for the North-South

and East-West core walls on Bank 1, Bank 2 and Bank 3, and for the sole coupled core wall of Bank

4. The horizontal shear capacity was calculated using MIDAS Gen section areas and loads, and

spacing and reinforcement were selected based on the required steel ratio. These values were

subsequently applied to the core’s actual shape. Minimal vertical shear exists, thus the vertical

reinforcing was designed based on required steel ratio.

For the first three banks, the North-South (NS) and East-West (EW) cores worked together to resist

flexural moment, and the moment capacity of the coupled cores was calculated using the vertical

reinforcement. For Bank 4, the cores worked together to resist moment along their weak axis, but

resisted moment individually across their strong axis. For this latter moment, the moment-axial

force pairs were plotted on a column interaction diagram produced using vertical reinforcing steel.

For all banks, the vertical reinforcing was sufficient to resist moment.

The following assumptions were used to design of the core reinforcement.

MIDAS Gen core section areas were sufficiently similar in size and shear capacity to actual core

size and shear capacity.

Core walls were designed for critical loads at the base of each bank.

Reinforcement details could be designed based on a sub-area of a concrete gross area, and then

applied to a different area of concrete, as long as steel ratios are kept constant.

The link beams allow the core walls in a given bank to act as a single beam. Ties will be sufficient for any given reinforcement configuration.

Core wall section areas are conservative to simplify design procedure. If there is sufficient area

outside of these approximations so as to exceed the spacing of the reinforcement, reinforcement

will be extended into that area.

Appendix 9.13 summarizes the reinforcement spacing and sizes for each bank. Calculation 4.5

shows the reinforcement design calculations.


4.6 Energy Optimization



The vertical system for the final MIDAS Gen model consisted of a column schedule of two steel built-

ups, BU1 and BU2. An energy optimization of the tower’s lateral load resistance system wasperformed to resize vertical elements. This analysis was not performed using the displacement

optimal design feature of MIDAS Gen, but rather through an energy method design tool. MIDAS

results were needed for component forces, and grouping by element type and location. The energy

method used is outlined in “Energy-Based Design of Lateral Systems” (Baker, 1992), and was based

on establishing equal energy density on all members. Once complete, each member contributes to

the lateral resistance with equal efficiency, ultimately optimizing the design.

The scope of the energy method analysis included members in which large axial forces were

induced during lateral loading: namely all columns and outrigger trusses. Each bank of columns

was broken down into three sub-sections, for the purpose of reducing column sizes with building

height, as axial forces decrease. Belt trusses and induced moments were secondary concerns and

thus were not included in this analysis.

An optimization design tool details the procedure (Calculation 4.6). The tool requires both “real”

and “virtual” axial forces generated from lateral loads only. “Real” forces used in the analysiscorresponded to the 0.7 wind load combination at 50 year MRI, as prescribed by ASCE 7-10.

“Virtual” or “notional” axial forces were obtained by applying a unit dummy load to the tip of the

building, revealing the virtual work of each member. The following equation was used to calculate

the required areas.

1500.5 0.5

1

1( ) ( ) [ ]i req i i j j j

jreq

A n F L n F

E

where

Areq = minimum required area

Δreq = target drift

E = modulus of elasticity, 29,000 for steel

n = virtual axial force

F = real axial force


Because of the tower’s symmetry and the fact that wind loads can occur in any direction, the critical

required area for each sub-section was applied to all members in that sub-section.



Initial MIDAS Gen modeling targeted a global drift requirement of h/400. The first objective for theenergy optimization was a target drift of 4 ft (h/500). Steel built-up columns were used at the

lower levels and W-sections were used at the higher levels where applicable. The new members

are summarized and compared to baseline values in Table 4.12.

Table 4.12: Optimization Results for Δ = h/500

Baseline

Area

Optimized

Area

Area

Provided

Proposed

SectionType Floors in2 in2 in2

Bank 1

Mega-columns 1-4 848 903 920 BU1

Vertical 5-16 848 800 800 BU2

Vertical 17-28 848 748 768 BU3

Vertical 29-37 848 678 688 BU4

Transfer 38-39 848 587 608 BU5

Outrigger 38-39 215 175 178 W14x605

Bank 2

Vertical 40-52 848 571 576 BU6

Vertical 56-63 848 509 512 BU7

Vertical 64-71 848 500 512 BU7

Transfer 72-73 848 602 608 BU8

Outrigger 72-73 215 151 162 W14x550

Bank 3

Vertical 74-87 688 468 480 BU9

Vertical 88-99 688 335 347 BU10

Vertical 100-108 688 244 250 BU11

Transfer 109-110 688 159 162 W14x550

Outrigger 109-110 215 48 52 W14x176

Bank 4

Slanted 111-122 688 153 162 W14x550

Slanted 123-133 688 135 134 W14x455

Slanted 134-144 688 96 101 W14x342


Table 4.13: Material Savings for Δ = h/500

Volume reduction in steel (ft3) 66800



Weight reduction in steel (tons) 16700

% reduction 36

This same optimization method was similarly used to create an understanding of what additional

materials would be required to increase the Chicago Spire’s performance. The steel, shown in tons,

needed for decreases in global drift (by 5%, 10%, 15%) are included in Figure 4.10.

Figure 4.10: Optimization Material Use versus % Reduction of Drift


4.7 Eigenvalue Analysis

A b it ti i l l i f d i th fi l d l i MIDAS G Th



A subspace iteration eigenvalue analysis was performed using the final model in MIDAS Gen. The

first 15 mode shapes were found. Table 4.14 summarizes the natural frequency and period of thefirst fifteen mode shapes. The expected period for mode one of a tall building is n/10, where n = the

number of floors. The eigenvalue analysis results show periods similar to the expected of 15 sec.

Table 4.14: Natural Frequency and Period of first 15 mode shapes

Mode No. Frequency Frequency Period

(rad/sec) (cycle/sec) (sec)

1 0.4098 0.0652 15.33

2 0.4313 0.0686 14.57

3 0.6378 0.1015 9.85

4 1.3013 0.2071 4.83

5 1.4131 0.2249 4.45

6 1.7807 0.2834 3.53

7 2.4401 0.3884 2.57

8 2.9056 0.4624 2.16

9 3.1205 0.4966 2.01

10 3.4213 0.5445 1.84

11 3.9564 0.6297 1.59

12 4.2083 0.6698 1.49

13 5.9338 0.9444 1.06

14 6.4212 1.0220 0.98

15 7.0179 1.1169 0.90


Table 4.15: Modal Mass Participation

Mode No. Translation in X Translation in Y Rotation about Z



MASS(%) SUM(%) MASS(%) SUM(%) MASS(%) SUM(%)

1 0 0 63.05 63.05 0 0

2 62.35 62.35 0 63.05 0 0

3 0 62.35 0 63.06 60.87 60.88

4 0 62.35 17.52 80.58 0 60.88

5 18.37 80.72 0 80.58 0 60.88

6 0 80.72 0 80.58 18.45 79.33

7 0 80.72 5.67 86.24 0 79.33

8 6.58 87.30 0 86.24 0 79.33

9 0 87.30 0 86.24 4.27 83.59

10 0 87.30 3.50 89.74 0 83.59

11 0 87.30 0 89.74 6.01 89.60

12 2.49 89.79 0 89.74 0 89.60

13 0 89.79 1.98 91.72 0 89.60

14 0 89.79 0 91.72 1.70 91.31

15 2.24 92.02 0 91.72 0 91.31


The first two modes of the building are translation modes in orthogonal directions. The third mode

is a torsional mode which primarily acts on the Bank 4. Figure 4.11 shows all three modes from the

MIDAS Gen model. The periods for the first three mode shapes are: 15.33 seconds, 14.57 seconds,



MIDAS Gen model. The periods for the first three mode shapes are: 15.33 seconds, 14.57 seconds,

and 9.85 seconds respectively. The corresponding modal participations are: 63.05%, 62.35%, and60.87%. This indicates that the first three modes are low frequency and the majority of the mass

will be affected at those frequencies. The next three modes show the second mode shape for the

different directions of translation. The sum of the modal participation of the first 15 modes in x-

translation, y-translation, and torsion are all over 90%.

5.0 STEEL AND CONCRETE DETAILING

5.0 Steel and Concrete Detailing

Thousands of connections exist over the height of the building ranging from simple framing



Thousands of connections exist over the height of the building ranging from simple framing

connections to complicated mega-column terminations. ASPIRE identified typical connections thatare prevalent throughout the tower and several classifications of complex connections. A full

structural design would look at all the iterations of each connection to fully understand how each

area load and each bank changes the connection. One occurrence of each connection has been

identified for a full structural design. The same process and design tools can be applied to other,

similar instances.

Element geometry had a significant impact of the type of connections that could be used. All

columns have been finalized as steel members, minimizing the prevalence of composite

connections. The most common composite connection is between radial floor girders and the

concrete core. The use of W-shapes versus built-up sections also affected decisions between bolted

and welded connections.

Ultimately all of the columns were built-up from 4 in thick steel plates which limited column

connections to welds. Connections were standardized for the built-up columns to ensure that

despite column section changes, similar connections can be used. Various failures were checkedper AISC requirements depending on the type of connection.


5.1 Typical Connections

Five typical steel to steel connections and one typical composite connection will be used in the



yp yp p

Chicago Spire. Radial girders and cantilevers will be connected to the outer ring columns withmoment resisting connections; circumferential girders will be connected to the outer ring column

with single plate connections; the joists will be connected to girders using single angle shear

connections; the HSS beams running along the outside of the building will be connected to the

cantilevers with angles bolted to the cantilever and welded to the HSS section; and column splices

will connect each column with welded plates.

The following typical connection design calculations follow AISC Steel Design Guide and can be

found in Calculation 5.1.

5.1.1 Welded Column Splice

All typical exterior columns are built-up steel shapes and will be spliced using steel plates. The

column splices were designed by welding plates to connect each face of the connecting columns

(Figure 5.1). This was the most economical design because of the similar column sizes throughout

the structure. This type of splice minimizes the footprint of the columns, allowing them to meetarchitectural constraints. Column splices were designed against all load combinations to resist

tension, moment, torsion and shear forces.


5.1.2 Floor Joist to Girder

The floor joists are connected to the radial girders with single angle, shear connections. At each



connection, two joists connect to opposite sides of the radial girder web. The girder web is not

thick enough to weld at each side, therefore bolts were used (Figure 5.2). This greatly decreases

the amount of field welds required during construction. The initial trial bolt number was calculated

to withstand shear and bearing. Then all failure modes were checked, including bearing and tear

out, shear yielding and rupture, and block shear of the angles and both webs.

Figure 5.2: Elevation of Floor Joist to Girder Connection

5.1.3

Cantilever to HSS Section

The connection between the cantilever beams and HSS Sections is similar to the single angle shear

connection except the angle leg adjacent to the HSS section is welded instead of bolted (Figure 5.3).

Also, an additional weld connects the top flange to the HSS beam to add rigidity to the connection.

Weld

Weld


5.1.4 Cantilever and Radial Girder to Column

Moment connections to the columns are required for both the radial girders and cantilevers. For

h b fl l ill b ld d l ll d h l fl b d b l



the beam flanges, two angles will be welded along all edges to the column flange above and below

the incoming beam and then bolted to the flange of the beam.

For the beam, web, two rectangular plates will be welded perpendicularly to the column,

sandwiching the web of the incoming beam. Bolts will be connected through predrilled holes in

both the plates and the web. Figure 5.4 shows the elevation detail of the moment connections.

Initial plate dimensions and bolt configurations were chosen based on member geometry and

adjusted throughout the design process. Bolt sizes were determined from the required momentcapacity of the connection. All applicable failure modes were checked including plate yielding in

flexure, shear, and bearing; bolt yielding in tension and shear; and web yielding, crippling, and

buckling.

Figure 5.4: Elevation of Built-up Column to Radial Girder and Cantilever Connection


5.1.5 Circumferential Girder to Column

The circumferential girders were designed as pinned-pinned and thus could be designed with a

bolted connection One plate is welded perpendicular to the built up exterior column using a fillet



bolted connection. One plate is welded perpendicular to the built-up exterior column using a fillet

weld. The circumferential girder is then placed with its web adjacent to the plate with its flanges

above and below the plate. The plate and column girder are then bolted together. The size and

number of bolts used were determined based on the shear and bearing capacity of the bolts.

The weld of the plate to the column web was also checked. Column web yielding, crippling and

buckling were checked along with block shear, bearing and tear out, shear yielding and shear

rupture of the girder web and plate. Figure 5.5 shows the typical circumferential girder to column

connection.

Figure 5.5: Elevation of Circumferential Girder to Column Plate Connection

Weld


5.1.6 Radial Girder to Core

Radial girders are connected to the core by a single, shear single plate connection and headed

anchor bolts Headed anchor bolts are welded to a steel anchor plate and cast into the exterior of



anchor bolts. Headed anchor bolts are welded to a steel anchor plate and cast into the exterior of

the concrete core. A single steel plate is welded perpendicular to the base plate using a fillet weld.

The radial girder is then bolted with its web adjacent to the plate, with its flanges above and below

the plate. Figure 5.6 details the composite connection between the radial girder and the core wall.

The single plate bolt details were determined based on the shear and bearing capacity of the bolts.

Plate geometries are based on bolt spacing and beam dimensions. Maximum plate thickness is

determined such that the plate moment strength does not exceed the moment strength of the bolt

group in shear. The capacity of the connection is calculated as the minimum capacity for the limitstates of shear yielding, shear rupture, block shear rupture, shear buckling, and flexural yielding of

the plate and girder weld as well as bearing strength at bolt holes, bolt group shear strength, and

weld capacity.

Figure 5.6: a) Elevation and b) Section of Radial Girder to Core Wall Connection

The headed anchor bolts details were determined based on the tensile and shear capacity of the

steel anchor bolts and the concrete. The capacity of the connection is determined by an interaction

of the design tension strength and design shear strength of the connection. Design tension strength

is calculated as the minimum capacity for the limit states of steel strength of anchors in tension,

concrete breakout strength of anchors in tension, and pullout strength for anchors in tension.

Design shear strength is calculated as the minimum capacity for the limit states of steel strength of

anchors in shear, concrete breakout strength of anchors in shear, and concrete pryout strength of

anchors in shear.

Weld


5.2 Complex Connections

Several configurations of complex connections are found throughout the Chicago Spire, particularly



at mechanical floors and at the tower’s base. These connections combined simple welds and boltswith gusset plates, encased steel, and prefabricated nodes to resist forces and moments produced

by the MIDAS Gen model.

5.2.1 Mega-Column Base to Foundation

This connection is located at the bottom of the mega-columns and is responsible for transferring

the loads from the superstructure to the foundation. The foundation consists of two 10ft diameter

caissons embedded six inches from the bottom of a caisson cap, much like a pile cap.

The connection to the foundation presented a challenge due to the geometry of the mega-columns.

The mega-columns are three slanted columns connecting to a single point, creating a large shear

force at the base as well as a large concentrated compressive forced. A typical base plate design

was initially considered to transfer the load however, because of the high loads, the base plate

became infeasible and another option had to be considered. Aspire had thought of using an

embedded steel shape to be able to connect the three mega-columns coming down as well as theembedded shape into the shaft of the caissons to properly transfer loads to the caissons. A built-up

steel beam was used to connect the three columns, while a shaft column was used to transfer the

tension to the caisson (Figure 5.7).

The three node column will resist the compressive force coming from the super structure through

bearing and will use shear studs to resist the shear. The three column beam was checked for

failures such as bearing, local web crippling, and local web yielding. Together this connection is

able to adequately transfer the load to the caissons while being the most economical solution.

While the steel shapes embedded into the caisson cap will resists the axial and shear loads, the

caisson cap will resist the bending moments by reinforcing steel bars. The caisson cap was

designed considering bending moments about the X and Y direction using principals of reinforced

concrete slab design. Calculation 5.2 summarizes the mega-column to foundation design.




Figure 5.7: 3D Rendering of Base of Mega-Column to Caisson Connection

Mega-column

Embedded Steel

Pile Cap

Built-up

Steel Beam

Caisson


5.2.2 Base of Outrigger

Across the height of the structure, the exterior columns angle inwards as the diameter of the building

decreases. The intersection of angled and vertical columns will be prefabricated, and the incoming and



g p g

outgoing columns will be spliced to the prefabricated section above and below the connection node.

Moment connections will be needed between the prefabricated column section and the bottom of the

outrigger, the radial girder, and the cantilever. The flanges of the outrigger and column are too thick to

punch through; thus welds will be used for the connection. Two plates will be used in the connection to

improve the constructability of the connection. The first plate will be welded to the face of the column,

and the second plate will be welded to the incoming outrigger and radial girder.

Both flanges and the web of the outrigger will be welded to the end plate. Next, two angles and two

rectangular plates will be welded to the plate and subsequently bolted to the radial girder (Figure 5.8).

For the incoming outrigger, in addition to checking the strength of the welds, several failure modes were

checked including plate yielding in shear and bearing; rupture of beam flange to plate welds; and

beam web shear yielding (Calculation 5.3.1).

Outrigger

Girder

Vertical

Columns


5.2.3 Outrigger to Core Connection

At each mechanical floor of the tower, outriggers primarily stiffen the connection between the steel

frame and concrete core. These outriggers mainly help reduce the overall structural system’s



lateral deflection. Therefore, to ensure that the outriggers perform in such a way, the outrigger

connection with the concrete core was given major attention.

The outrigger connection consists of two gusset plates that sandwich the flanges of the outrigger

member and radial girder above the mechanical floor (Figure 5.9). Most girders in the building;

however, were oriented with vertical webs and horizontal flanges. The gusset plate connection

required rotating the floor girders by 90 degrees so that the gusset plates can be bolted to the

flanges of both outrigger and girder. Gusset plate bolts were sized and design according to AISCSection J and accounted for failure modes such as block shear and plate yield (Calculation 5.3.2).

Figure 5.9: Elevation of Outrigger and Radial Girder Connection to Concrete Core

The exact connection between the gusset plate and concrete core went through a few design

iterations. Initially, the gusset plates were fillet welded to steel plates bolted to the concrete core,

similar to the typical radial girder connection (Section 5.1.6). However, the high outrigger loads

required around 500 bolts for such a connection Eventually an alternative design was developed

Rotated

Radial Girder

Outrigger

Embedded

Steel Frame

Concrete

Core


The following assumptions were made for the model.



All members were assumed to be fully braced, simulating the frame’s embedment in concrete.

All beams and columns are connected by moment connections. Connections details would be

designed as per Section 5.1.1.

The top and bottom nodes of the frame are assumed to be fixed in all directions and rotations.

Diagonal braces are added to the frame as compression only truss members (Figure 5.10). These

fictitious members simulate how the concrete struts when the steel frame reacts to load. The brace

sizes are relatively similar to the steel frame members, with steel frame having a greater stiffness toensure that a majority of the load is absorbed by steel instead of concrete.

For the final model, all loads from outriggers are applied axially to the nodes at which outrigger

members connect with the frame. Axial loads are based on from critical load combinations from the

final tower MIDAS model (Figure 5.10).

Figure 5.10: a) Model of Embedded Steel Frame and b) Model with Cross Bracing and Point LoadsThrough iterative design of steel sections, W33x152 members were selected for columns and

W14x665 members for beams. The outriggers and radial girders at the mechanical floor between

Bank 3 and 4 were both W14x730. The W33x152 section when oriented along its weak axis, would


5.2.4 Top of Mega-Column

The top of the mega-column connection consists of two different connection configurations. Figure

5.11 shows the two scenarios: an interior column angled in one orientation and two exterior



columns angled in two orientations. All of the mega-columns are steel built-up columns.

In addition to the mega-columns, the connection also consists of a vertical built-up terminating at

the top of each mega-column. Although both columns identical steel sections, lower column will be

referred to as the mega-column, and the upper column as the vertical column.

The mega-column and vertical column connection is a prefabricated node. The node is constructed

with shop welded plates extending from the node faces to improve the constructability of the fieldcolumn splice. The column splice will ultimately consist of four plates welded onto the columns to

transfer tension, torsion, and shear. Half of the welds will be done in the shop, and half will be done

in the field. The prefabricated design improves constructability and connection strength. The node

also allows for standard splices that do not have to transfer massive forces and moments over an

angled connection. The radial and circumferential girders will be designed as per Sections 5.1.1

and 5.1.5.

Figure 5.11: 3D Rendering of Mega-Column Connection


5.2.5 Transfer Column

Transfer columns exist at the mechanical levels where the exterior column radius decreases.

Between Banks 2 and 3 some transfer columns are also designed for the reduction in total exterior

l h f l f d ff f h l



Figure 5.12: Singular Transfer

Column Connection Front and Side

columns. The transfer column connection consists of two different configurations, with typical top

and bottom welded column splices.

The mechanical space between Bank 2 and Bank 3 contains

both of the typical transfer column connections found in the

Chicago Spire. The column grid reduces from 21 columns in

Bank 2 to 14 columns in Bank 3. Seven of the columns in

Bank 2 are designed for the first configuration in Figure5.12. Fourteen of the columns in Bank 2 are designed for the

second configuration in Figure 5.13.

In the first configuration, two field welded column splices

occur at the top of the Bank 2 column and at the bottom of

the Bank 3 column. The connecting member is a

prefabricated connection node that is built to resist

compression, tension, shear, moment, and torsion.

In the second configuration, forces from the Bank 3 column

are transferred to two Bank 2 columns below. Figure 5.13

shows the required angled transfer column. With this

configuration there are three typical field welded column

splices that occur at the top of the Bank 2 column and at the

bottom of the Bank 3 column. The node between Bank 3 andthe angled transfer column split will be prefabricated, along

with the transfer column between the bottom of the node

and the welded column splice at the top of the Bank 2

column.

The welded column connections are comprised of four plates surrounding the members. For each

splice, two plates will be shop welded to the connection node, and two plates will be shop welded to

the columns. Welded column calculations are shown in Calculation 5.1.1.

Figure 5.13: Split Transfer Column

Connection Front and Side Elevation

6.0 FOUNDATION DESIGN AND DETAILING

6.0 Foundation Design and Detailing

The Chicago Spire foundation includes a deep foundation system to support the 150 floor tower

d th fl ki R k k t d i d i il d t f d ti



and the seven floor parking garage. Rock-socketed caissons, driven piles under a mat foundation,concentric top of rock slurry wall rings, and a mat foundation on hardpan were all options to

support the tower. As stated in the provided Geotechnical Report, the latter two options were

considered costly, risky and time consuming. Therefore rock-socketed caisson will be used to

support the tower. The project received city permits to have an allowable net bearing pressure for

the rock of 300 tons per square foot.

The seven floor parking garage will have a retaining wall structure around the perimeter, which

will be internally braced by the floor slabs. The garage will be supported with belled caissons

bearing on hardpan.


6.1 Soil Properties

Information on soil conditions came from eleven test borings and 34 borings to obtain bedrock

cores (Geotechnical Report). The soil profile is 100 to 115 feet of primarily clay overburden on



dolomite bedrock. The site grades range in elevation from +10 to +7 Chicago City Datum (CCD).

The water table is five feet above the CCD. A one foot hardpan layer exists at -71 CCD. A detailed

soil profile is shown in Figure 6.1.

Soil properties were used to calculate apparent earth pressures and pore water pressures for the

foundation design.

Figure 6.1: Provided Soil Profile for Foundation Design


6.2 Retaining Wall Design

The perimeter of the foundation is supported by a 30 in thick,

reinforced concrete retaining wall. The wall was designed to

i h d f il i h h d

OVERTURNING



withstand failure against the earth pressures and pore water

pressure. The thick wall has a high self-weight which helps to

resist the lateral forces from the soil profile. The self-weight

also reduces the chances of bearing failure by distributing the

vertical force to a larger area of soil.

The Geotechnical Report includes a soil profile which consists

of sand and clays. The soil stiffness increases with depth. The

critical soil density is assumed to be 70 pcf to obtain the

worst-case effective pressure producing maximum horizontal

loads on the retaining wall. The buoyant force on soil due to

the ground water table reduces the effective vertical pressure.

A MASTAN analysis of the retaining wall was performed,

modeling the wall as a one way slab assuming the bottom sixfloor slabs from the parking garage brace the retaining wall.

As a conservative approach, the top two slabs are not

considered as bracing for the retaining wall; which leaves a

cantilever span at the top end of the retaining wall. The

retaining wall was checked for overturning, lateral sliding and

bearing failure (Figure 6.2).

The retaining wall is built through a top-down construction

process. The foundation soil is excavated with ring beams

constructed simultaneously at adequate unbraced lengths as

designed by the geotechnical engineer. Ring beams are then

removed from the bottom up as slabs and retaining walls are poured.

The soil layers become stiffer further below the ground surface. At a depth of 85 ft, there is a very

hard clay of undrained shear strength of 15 ksf. The retaining wall sits on this layer and the highbearing capacity prevents bearing failure. Construction joints are provided at every 20 ft to reduce

the longitudinal settlement and tilt.

C l l i 6 1 h h d i f h i i ll

BEARING

FAILURE

L A T E R A L S L I D

I N G

BRACING

HARD

CLAY

Figure 6.2: Failure Modes for

Retaining Wall Design


6.3 Parking Garage Slab Design

The reinforced concrete slab for the parking garage was designed as a two-way slab using the

equivalent frame method, as per ACI 318-08. An expansion joint is built between the two slab

ti t d ki Th f ll i ti d hil d i i th ki



sections to reduce cracking. The following assumptions were made while designing the parking

garage slab.

All slab design assumes rectangular slab sections designed to the maximum span calculated from

column locations in provided floor plans.

Outside of the building footprint, columns are spaced in an orthogonal grid.

Inside the building footprint, columns offset from an assumed orthogonal gridline by 6 ft or less

are considered on that gridline.

Core and foundation caissons bear the slab load.

Slabs are designed as cantilevers to the retaining walls.

Deformed Welded Wire Reinforcement (WWR) is used for flexural reinforcing design, Fy = 80

ksi.

Light weight concrete is used with a density, ρc = 110 pcf and a 28-day compressive strength,

f’c = 4000 psi.

Diameter of circular columns is 32 in. The slab was designed without interior beams or edge beams.

The parking slab design utilized MASTAN to model the moment frame connections between the

caissons and parking slabs for all seven floors. Design loads Section 2.4 were used to find the

maximum positive and negative moments along the slab. Per ACI 318-08, 13.2.1 and 13.6.4.1, the

critical moments are proportionally distributed to the column and middle strips of the slab width.

Drop panels were designed at the top of each column to reduce negative moment reinforcement.

The ultimate slab design was 12 in thick. The design does not call for interior or edge beams

because of the high strength WWR used for flexural reinforcement. WWR can be costly; however,

for large projects the steel savings outweigh the material cost

The design process and calculations are summarized in Calculation 6.2.1.


6.4 Bell Caisson Design

Belled Caissons are used to support the parking garage slab. Caissons were designed following

Chapter I: Design of Composite Members in the AISC Steel Construction Manual. Circular reinforced

concrete columns were used in the parking garage extending below the bottom slab into belled



concrete columns were used in the parking garage, extending below the bottom slab into belled

caissons, which rest on the hardpan at an elevation of 92 ft below the top slab of the parking garage.

The bell shape was needed to lower the applied pressure on the soil. The bell design minimized the

bearing pressure to be within the allowable pressure of 45 ksf. The columns unbraced lengths were

based on support from the parking garage slabs. The columns were designed as reinforced

concrete columns with steel reinforcing or W-shapes depending on the column load.

Calculation 6.2.3 follows the AISC procedure for bell caisson design. Figure 6.3 shows an elevationof the foundation and belled caissons.

Figure 6.3: Elevation of Bell Caissons


6.5 Rock-Socketed Caisson

6.5.1

Column Design

Caissons of 10 ft diameter using 14 ksi concrete were designed to carry the load from the core and



Caissons of 10 ft diameter using 14 ksi concrete were designed to carry the load from the core and

mega-columns to the bed rock. Each mega-column is supported by two caissons, whereas the core

is supported by 20 caissons. The caissons are socketed into the bed rock; limiting the settlement of

the caissons. Figure 6.4 shows an elevation view of the core and mega-column caissons.

Figure 6.4: Elevation of Rock-Socketed Caissons

Each caisson is a steel cylinder filled with concrete (Figure 6.5). The steel cylinder prevents any

soil-concrete interaction and provides a higher strength to the caisson due to composite action.

There is no uplift friction on the caisson by soil, as the steel provides a smooth surface withnegligible vertical friction. Stresses induced in the caisson due to the loads from super structure

are well within the allowable limits.

Mega-Column

Caisson

Mega-Column

Caisson

Core

Caissons

Bedrock




Figure 6.5: Detail of Caisson

Settlement is the controlling criteria in the design of caissons, as a higher differential settlement

may lead to severe structural damages. A stiffer base material provides greater resistance to the

settlement in the caisson. The loads carried by the caissons are obtained from the MIDAS-GEN

model and the Geotechnical Report. Three limit states, shown in Figure 6.6 were checked for the

caisson design (Calculation 6.3).


6.5.2 Ring Beam

A reinforced concrete ring beam was designed to connect the core walls to the rock-socketed

caissons. This will ensure a uniform distribution of the axial load to the 20 caissons. The ring beam

will also dissipate the shear force. The shear force is resisted by the passive earth pressure of the



ring pushing against the soil, by the friction between the soil and the slab, and by the bottom of the

ring beam. Figure 6.7 shows an elevation of the ring beam and its relation to the slab, core wall, and

rock-socketed caisson. Figure 6.8 shows the ring beam’s resistance to the horizontal soil pressure.

Figure 6.7: Elevation of Ring Beam

Soil Pressure


6.5.3 Finite Element Model

An ABAQUS model was developed to perform a finite element analysis and monitor the stresses in

the rock-socketed caisson. Each mega-column is supported by two circular caissons. These mega-

columns are inclined, which exerts a compressive pressure and a horizontal shear on the caissons



below it. The loads carried by the caissons were obtained from the MIDAS Gen model. Since the

caissons are encased in a steel cylinder, the vertical soil friction is negligible, and is not considered.

The following material properties are used in the ABAQUS model.

Young`s modulus of bedrock, Er = 3500 ksi

Poisson`s ratio of the bedrock, ν = 0.28

Friction coefficient for bed rock and caisson interaction = 0.3 Directionality of the friction is isotopic.

For the caisson and bedrock socket, interaction property is modeled as contact, and the contact

property is modeled as tangential. The bedrock and caisson are constrained as ties, where the

caisson is the master surface and the bedrock is the slave surface. After performing iterations to

obtain an optimum mesh configuration, the caisson and bedrock were meshed as triangular

elements.

The following stresses are obtained from the finite element analysis.

Caisson

Bedrock


It can be seen in Figure 6.9 that the maximum stresses occur at the top surface of the caisson. The

stresses decrease as we move down towards the middle portion of the caisson and at the

interaction of caisson and bedrock, higher stresses are encountered.

Table 6.1: Critical Von Mises Stresses from ABAQUS Model



Von Mises Stress Top Face Bottom Face

Maximum Compression stress (ksi) 6.3 3.7

Maximum Tension stress (ksi) 4.9 1.9

7.0 LONG-TERM DEFLECTION EFFECTS

7.0 Long-Term Deflection Effects

The aim of the creep and shrinkage calculations for the core and the columns is to determine the

deflection in each and the differential between the two. It can be predicted that the steel columns

will have minimal shrinkage as compared to the core, so this should be accounted for during



construction. Things to consider in this calculation will include the construction schedule, curing

conditions, loads, geometry, and strength of the concrete and steel.

When a load is applied on the structure, there is an initial elastic strain, which occurs when the load

is placed on the column. In addition to this, there is a creep strain, which starts when a load is

applied, and a shrinkage strain, which begins as the concrete begins to dry. Both of these increase

over time and approach the ultimate strain value. The ultimate creep coefficient and shrinkage

strain are both determined by the curing conditions, the concrete mixture, and the construction

schedule. All of the calculated values for deflection will need to be considered in the final

construction to meet serviceability requirements, particularly the difference between the

deformation in the core and the columns.


7.1 Conceptual Summary

The aim of this chapter is to determine the creep and shrinkage of concrete in the core, as well as

elastic deformations in both the core and columns. It is very important to evaluate the differential

deformation between the core and columns to alleviate unexpected stresses and deformations. It



can be predicted that the steel columns will have minimal deformation as compared to the core, so

this will need to be accounted for during construction. Variables to consider in the deformation

calculations will include the construction schedule, curing conditions, loads, geometry, and strength

of the concrete and steel.

When a load is applied on a steel column or the concrete core, there is an initial elastic strain, which

occurs when the load is added. In addition to the immediate elastic strain, in the concrete core

there is a long-term creep strain, which starts when a load is applied, and a long-term shrinkage

strain, which begins as the concrete begins to dry. Both of these long-term strains increase over

time and approach the ultimate strain value. The ultimate creep coefficient and shrinkage strain

are both affected by the curing conditions, the concrete mixture, and the construction schedule. All

of the calculated values will need to be considered in the final construction to meet serviceability

requirements, particularly the differential deformation between the core and the columns.


7.2 Creep and Shrinkage Analysis

Several simplifying assumptions about the core composition and geometry were made in the

analysis. The 28-day strength of the concrete is 14,000 psi as specified earlier in the project. Per

ACI 209R, t he GL2000 method assumes the concrete’s elastic modulus is a function of the strength,

d ifi i d d f i l l h l h i i i i



and specifies a time-dependent function to calculate the actual strength at any given point in time,

as indicated in Figure 7.1 and Figure 7.2.

Figure 7.1: Concrete Strength Gain with Time


The core was assumed to be a cylindrical tube of concrete, with constant radius and thickness

throughout each bank. The amount of steel reinforcement within the core was calculated

previously, so the values from that calculation were used in this analysis. Appendix 9.14, Table 9.15

outlines core properties and dimensions used in the analysis. In addition, per the recommendation

of a professional engineer, the core will be analyzed using the same model and methods as a typical

column



column.

The construction schedule of the spire was extremely important to the creep and shrinkage

calculations. Aspire assumed a 4-day cycle for floor construction, meaning a new floor would be

added every 4 days. Although this seemed like a very fast-paced schedule, it is important to note

that the Burj Khalifa was constructed successfully using a 3-day cycle (Abdelrazaq, 2008). In

addition, three simplifying assumptions for analysis were made:

Curing time: 4 days

Loading age: 4 days

Construction loads occupy the top 4 floors at any given point during construction.

It is important to note that these assumptions may not be entirely realistic, but will give

conservative values for strain. The construction loads are assumed to be mainly composed of heavy

machinery and lifting equipment, which will move up the spire as new floors are constructed. Once

the construction period has ended these loads will no longer exist.

The exact sequence of construction was not considered. After consulting professional engineers,

ASPIRE concluded that the main focus of this analysis should be the long-term deformations of the

Spire, which will not be significantly affected by the order of construction.

Due to the increased loading near the base of the tower compared to the top, the Spire was split up

into 13 vertical segments. The middle floor of each of these segments was considered to be

representative of the average deformation of the floors in the segment, and was analyzed. The floor

deformation for that middle floor was then multiplied by the number of floors in the segment,

giving a total deformation for the segment. The sum of the segment deformations results in the

total building deformation.

During the analysis, it was observed that the long-term creep and shrinkage rates had tapered off

around 20 years, so the analysis was completed for a 20 year span from the start of construction.This is consistent with ultimate creep values being calculated after 20 years of loading.


7.2.1 Columns

All the vertical columns in the spire were designed as built-up steel members, so they will not be

affected by any noticeable creep or shrinkage. As such, they were only analyzed for the elastic

deformation due to loading. The elastic deformation was calculated by:



The elastic strain analysis resulted in an overall deflection of 6.77 inches expected in the steel

columns over the 150-story building. See Appendix 9.14, Table 9.16 for the tabulated results for

each floor segment and Appendix 9.14.1 for a representative calculation of the strains. Calculation

7.1 summarizes the steel column deformation.

7.2.2 Core

The core analysis required that creep and shrinkage were considered, though they were negligible

or nonexistent in the steel columns. The effects of creep and shrinkage were calculated using the

GL2000 model. See Appendix 9.14.3 for a step-by-step qualitative approach to using the GL2000

model, and Appendix 9.14.1 for an example calculation. Calculation 7.2 summarizes the concrete

core deformation.

In the GL2000 model, several variables need to be chosen by the designer. The only variable

related to the concrete mix design is the cement type. The GL2000 can be used with Type I, II, or III

cements, which the designer must choose between. A sensitivity analysis revealed that Type III

cement will result in the lowest creep and shrinkage values, most likely due to its rapid initial

strength gain.

Table 7.1: Cement Type Deformation Sensitivity Analysis

Cement Type

Ultimate

Deformation

Type I 24.79

Type II 24.91Type III 23.95




Figure 7.3: Initial Strength Gain of Concrete for Various Cement Types

The GL2000 model also requires input data on the humidity that is expected for the concrete’s

environment. Using data from the National Climactic Data Center, the average humidity for Chicago

was determined to be 71.4%. The average over a full year is used because the core is expected to be

somewhat exposed to the environment for at least the first two years of construction, which is also

the period of the greatest creep and shrinkage strains. See Appendix 9.14, Table 9.17 for a

summary of the humidity data.

The steel reinforcement in concrete has a restraining effect on the creep strains. Since steel doesnot experience the long-term deflections as significantly as concrete, more steel in a given amount

of concrete will result in less overall deformation in that section of the core. The banks have steel

percentages ranging from 0.2% in Bank 4 to 5.4% in Bank 2, as seen in Appendix 9.14, Table 9.18.

In the analysis, both the amount of deformation in an unreinforced concrete “column” and our

reinforced “column” were calculated. The ratio of the reinforced to unreinforced strains was used

to modify the elastic, creep, and shrinkage results. It was observed that the reinforced concrete

would strain only about 10-15% of the unreinforced concrete.

The results of the analysis indicated that the creep strain would dominate the deformation,

followed by elastic strain and only a minimal effect from shrinkage strain due to the large volume-




Figure 7.4: Typical Strain Values for a Single Floor

The analysis of the creep and shrinkage for concrete resulted in an overall expected deformation of24.8 inches in the core. As can be seen in Table 7.2, approximately 75% of the ultimate deflection

occurs in the first two years, but there is still substantial movement out to 20 years, resulting in the

ultimate deformation of 24.8 in.

Table 7.2: Core Total Deformations

Time

(yr)

Deformation

(in)

Percentage of

Deformation

0 0 0%

2 18.8 76%

3 20.0 81%

10 23.0 93%

20 24.8 100%

Figure 7.5 breaks down the core deformations by floor. It is clearly seen that a majority of the




Figure 7.5: Core Deformations per Floor


7.3 Conclusion and Recommendations

The creep and shrinkage strain analysis resulted in very different deformations between the core

and the surrounding steel columns. As displayed in Table 7.3, the 24.8-inch deformation in the core

is greater than the 6.77-inch deformation in the steel by 18.0 inches. This differential deformation

can be very dangerous in tall buildings. Not only could aesthetically displeasing cracks form, but



serious structural issues could result as well. If this deformation is not designed for, as the core

deforms more than the columns, the floors will become slanted and connections will become

overstressed.

Table 7.3: 20-Year Deformation Comparisons

Core Deformation: 24.8 in

Steel Deformation: 6.77 in

Core-Column Difference: 18.0 in

Compensation / floor required: 0.12 in

To compensate for the differential settlement, the core should be built approximately 18 in higher

than the original design calls for. Since the creep and shrinkage model is inherently inaccurate up

to 20 -30%, additional height should be added in addition to the 18 in. For comparison, the Burj

Khalifa designers estimated a 12 in deformation in their core, but increased the design height of the

core by 22 in (Baker et al., 2007). Aspire recommends approximately a 30 in increase in the core

height based on this preliminary analysis to account for uncertainties.

As can be seen in Figure 7.6, the majority of the strains in the core will take place during the

construction period. This fact means that by the time the building needs to be serviceable, most ofits deformation will have occurred and need not be designed for. Also, the additional height that

was added for each floor-to-floor height will not be as noticeable throughout the life of the

structure. Rather, the floors will appear level and as designed for the tenants.




Figure 7.6: Total Core Displacement over Time

ASPIRE recommends further creep and shrinkage analysis in order to better understand the

behavior of the building. Creep and shrinkage laboratory tests are highly recommended as soon as

the concrete mix is decided upon. The data obtained from those tests can further improve the

accuracy of the GL2000 model. For instance, the ultimate shrinkage value in the GL2000 model is

approximated from a formula proportional to the square root of the mean compressive strength of

the concrete. Alternatively, this value can be determined from the laboratory test and inputted

directly into the analysis. In addition, the creep coefficient can be determined from the tests and

used instead of a very complicated formula approximation. Especially considering the unique

nature of a 14,000 psi concrete, it is highly advisable to further examine the creep and shrinkage

behaviors.

8.0 REFERENCES

8.0 References

Abdelrazaq, A., Kim, K. J. & Kim, J. H. (2008). “Brief on the Construction Planning of the Burj Dubai

Project, Dubai, UAE. Proceedings of the CTBUH 8th World Congress, 3rd-5th March 2008.

Dubai, UAE.” Published by the Council on Tall Buildings and Urban Habitat, Chicago. pp.

386-394.

American Concrete Institute. “Guide for Modeling and Calculating Shrinkage and Creep in Hardened

Concrete (ACI 209.2R-08).” ACI Manual of Concrete Practice, Part 1, 2010.

American Concrete Institute. ACI 318-08 Building Code and Commentary . 2008.

American Institute of Steel Construction. “Floor Vibrations Due to Human Activity.” American

Institute of Steel Construction, Steel Design Guide Series 11. 2003.

American Institute of Steel Construction. Steel Construction Manuel Thirteenth Edition, 2008.

American Institute of Steel Construction. Engineering for Steel Construction: A Source Book on

Connections, 1984.

American Society of Civil Engineers. Minimum Design Loads for Buildings and Other Structures.

2006. Reston, Virginia: American Society of Civil Engineers, 2006.

American Society of Civil Engineers. Minimum Design Loads for Buildings and Other Structures.

2010. Reston, Virginia: American Society of Civil Engineers, 2010.

Baker, William F. “Energy-Based Design of Lateral Systems.” Structural Engineering International .

Vol 2. No 2. 1 May 1992. p 99-102.

Baker et al. “Creep and Shrinkage and the Design of Supertall Buildings – A Case Study: The Burj

Dubai Tower.” American Concrete Institute. Special Publication, volume 246, pp. 133-148.

1 Sept 2007.

Binder, Georges. One Hundred and One of the World's Tallest Buildings. Australia: The Images

Publishing Group Pty Ltd, 2006. Google Books.

Blodgett, Omer W. Design of Welded Structures. Cleveland, OH: Lincoln, 1972. 8.2-2. Print.

"Chicago Spire " SkyScraperPage Skyscraper Source Media 2011 Web 14 Sep 2011

8.0 REFERENCES

Smith, S.E. “What Is a Mechanical Floor?” 29 July 2011. wiseGEEK.com. 15 Sep. 2011

<http://www.wisegeek.com/what-is-a-mechanical-floor.htm>.

Taranath, Bungale S. Steel, Concrete, & Composite Design of Tall Buildings. New York City: McGraw-

Hill Book Company, 1998.

Taranath, Bungale S. Structural Analysis & Design of Tall Buildings . New York City: McGraw-Hill



, g y g f g y

Book Company, 1988. Print.

Wight, J. and James MacGregor. Reinforced Concrete Mechanics & Design, Fifth Edition. Upper Saddle

River, NJ: Pearson Prentice Hall. 2009

Vulcraft. VULCRAFT Steel Roof & Floor Deck, 2008.

9.0 APPENDIX

9.0 Appendix

Appendix consists of supplementary information and summary tables. Following the appendix are

sample calculation and the complete structural drawing set.

Note that a “--“ indicates that the size, length, dimension, percentage, etc. is not applicable for the

given cell



given cell.

9.0 APPENDIX


Typical Floor

Dead

Load

Superimposed

Dead Load

Live

Load

(psf) (psf) (psf)

Lobby



Decking and Slab1 32

Assembly Areas (lobbies) 100

Acoustical fiber board 1

MEP Duct Allowance 10

Ceramic or quarry tile (1 1/2 in) on 1 in. mortar bed2 46

Total 32 57 100

Residential


Private rooms and corridors serving them 40

Partition Walls 15

Acoustical fiber board 1

Ceramic or quarry tile (3/4 in) on 1 in. mortar bed 23MEP Duct Allowance 10

Total 33 34 55

Mechanical


Catwalks 40

Machine Space 200

MEP Duct Allowance 10Total 39 10 240

Parking

Slab (150 pcf @ 12 in.)3 150

Garages (passenger vehicles only) 40

MEP Duct Allowance 10

Cement finish (1-in.) on stone-concrete fill 32

Total 150 42 40

Core

Slab (110 pcf @ 6 in.) 3

55

9.0 APPENDIX

9.2 RWDI Recommended Wind Load

Table 9.1: RWDI Wind Load Combinations



9.0 APPENDIX

Table 9.2: RWDI Provided Wind Forces and Torsional Moments

Floor

Fx

(kips)

Fy

(kips)

Torsional Moment, Mz

(kip-ft)

Critical Overturning

Moment (kip-ft x 106)

Critical Force

(kips)

1 27 20 44 9.41 27.42 53 40 96 9.28 54.6

3 53 40 102 9.16 54.4



4 53 40 109 9.04 54.4

5 53 40 144 8.92 54.5

6 53 40 195 8.80 54.4

7 53 40 212 8.68 54.3

8 53 41 233 8.56 54.49 53 41 239 8.45 54.3

10 53 41 240 8.33 54.2

11 53 41 252 8.21 54.1

12 53 41 264 8.10 54.2

13 53 41 275 7.98 54.4

14 53 41 287 7.87 54.4

15 53 42 298 7.76 54.516 53 42 306 7.64 54.7

17 53 42 314 7.53 54.7

18 53 42 324 7.42 54.9

19 53 43 335 7.31 54.9

20 54 43 345 7.20 55.1

21 54 43 354 7.09 55.2

22 54 44 364 6.98 55.423 54 44 372 6.88 55.6

24 54 44 381 6.77 55.8

25 54 45 392 6.66 56.0

26 54 45 399 6.56 56.1

27 55 45 411 6.45 56.3

28 55 46 418 6.35 56.5

29 55 46 427 6.25 56.730 55 46 433 6.14 56.9

31 55 47 443 6.04 57.2

32 56 47 451 5 94 57 4

9.0 APPENDIX

Floor

Fx

(kips)

Fy

(kips)


(kip-ft)



Critical Force

(kips)

39 57 49 470 5.26 58.7

40 57 49 470 5.16 58.7

41 56 49 437 5.07 57.7

42 56 49 442 4.98 58.0

43 56 49 447 4 88 58 1



43 56 49 447 4.88 58.1

44 57 50 453 4.79 58.4

45 57 50 457 4.70 58.5

46 57 51 465 4.61 58.9

47 57 51 467 4.52 59.2

48 58 51 473 4.43 59.5

49 58 52 477 4.35 59.9

50 58 52 480 4.26 60.1

51 58 53 484 4.17 60.4

52 59 53 487 4.09 60.7

53 59 54 490 4.00 61.0

54 59 54 492 3.92 61.2

55 59 55 498 3.84 61.6

56 60 55 502 3.75 62.0

57 60 56 503 3.67 62.3

58 60 56 506 3.59 62.6

59 61 56 509 3.51 63.0

60 61 57 514 3.43 63.3

61 61 57 513 3.36 63.5

62 62 58 515 3.28 63.9

63 62 58 518 3.20 64.1

64 63 59 539 3.13 65.2

65 63 60 544 3.05 65.5

66 63 60 546 2.98 65.9

67 63 60 529 2.91 65.5

68 64 61 534 2.83 66.1

69 64 61 535 2.76 66.4

70 64 62 538 2.69 66.7

71 64 62 538 2.62 66.8

9.0 APPENDIX

Floor

Fx

(kips)

Fy

(kips)


(kip-ft)



Critical Force

(kips)

78 62 60 403 2.16 64.0

79 62 60 406 2.10 64.6

80 62 60 400 1.99 64.6

81 62 60 399 1.98 64.7

82 63 61 399 1 92 65 1



82 63 61 399 1.92 65.1

83 63 61 399 1.86 65.4

84 63 62 402 1.80 65.9

85 63 62 398 1.74 66.0

86 64 62 401 1.69 66.5

87 64 63 403 1.63 66.9

88 64 63 400 1.58 67.1

89 65 64 401 1.52 67.6

90 65 64 396 1.47 67.6

91 65 64 398 1.42 68.2

92 66 65 401 1.36 68.6

93 66 65 399 1.31 68.9

94 66 65 394 1.27 69.0

95 66 66 389 1.22 69.3

96 67 66 388 1.17 69.6

97 67 66 368 1.12 69.9

98 68 67 387 1.08 70.4

99 68 67 385 1.03 70.6

100 68 68 384 0.99 71.2

101 69 68 386 0.95 71.8

102 69 68 382 0.90 72.0

103 70 69 384 0.86 72.8

104 70 69 383 0.82 73.2

105 71 69 382 0.78 73.7

106 71 69 383 0.74 74.1

107 72 69 382 0.71 74.6

108 72 69 380 0.67 74.9

109 70 69 381 0.64 73.0

110 70 69 381 0.60 73.0

9.0 APPENDIX

Floor

Fx

(kips)

Fy

(kips)


(kip-ft)



Critical Force

(kips)

117 70 68 315 0.39 72.9

118 71 68 312 0.36 73.4

119 71 69 310 0.34 73.9

120 71 69 307 0.31 74.0

121 72 69 304 0.29 74.6



121 72 69 304 0.29 74.6

122 78 76 314 0.27 80.9

123 70 68 260 0.24 73.0

124 66 63 266 0.22 68.4

125 67 64 264 0.20 69.2

126 67 64 258 0.19 69.2

127 66 64 251 0.17 68.8

128 67 64 248 0.15 69.2

129 67 64 242 0.13 69.7

130 68 64 237 0.12 70.6

131 69 65 233 0.10 71.2

132 69 65 225 0.09 71.2

133 68 64 217 0.08 70.9

134 68 64 211 0.07 70.8

135 68 64 202 0.06 70.2

136 67 63 193 0.05 69.6

137 67 62 185 0.04 69.2

138 66 62 176 0.03 68.3

139 65 60 165 0.02 67.1

140 62 58 148 0.02 64.5

141 59 55 129 0.01 61.7

142 76 71 115 0.01 78.8

143 71 67 104 0.00 73.8

144 55 51 92 0.00 56.6

145 59 55 92 0.00 60.8

146 59 55 92 0.00 60.8

9.0 APPENDIX

9.3 Seismic Load Summary

Floor LevelFloor

Type1

Lateral Force, Fx Story Shear , Vx Moment (Mx)

(kips) (kips) (kip-ft x 106

)1 L 0.01 6,563 8.82

2 L 0.05 6,563 8.74



3 L 0.11 6,563 8.65

4 L 0.19 6,563 8.56

5 L 0.3 6,563 8.48

6 R 0.43 6,562 8.39

7 R 0.58 6,562 8.308 R 0.76 6,561 8.22

9 R 0.96 6,560 8.13

10 R 1.18 6,560 8.04

11 R 1.43 6,558 7.96

12 R 1.7 6,557 7.87

13 R 2 6,555 7.79

14 R 2.32 6,553 7.7015 R 2.66 6,551 7.61

16 R 3.03 6,548 7.53

17 R 3.42 6,545 7.44

18 R 3.83 6,542 7.35

19 R 4.27 6,538 7.27

20 R 4.73 6,534 7.18

21 R 5.22 6,529 7.10

22 R 5.73 6,524 7.01

23 R 6.26 6,518 6.92

24 R 6.81 6,512 6.84

25 R 7.39 6,505 6.75

26 R 8 6,498 6.67

27 R 8.62 6,490 6.58

28 R 9.28 6,481 6.50

29 R 9.95 6,472 6.41

30 R 10.65 6,462 6.33

31 R 11.37 6,451 6.24

9.0 APPENDIX

Floor LevelFloor

Type1


(kips) (kips) (kip-ft x 106)

39 M 26.51 6,330 5.57

40 L 15.46 6,303 5.4941 R 15.69 6,288 5.40

42 R 16.46 6,272 5.32

43 R 17 26 6 256 5 24



43 R 17.26 6,256 5.24

44 R 18.07 6,238 5.16

45 R 18.9 6,220 5.07

46 R 19.75 6,201 4.99

47 R 20.62 6,182 4.9148 R 21.5 6,161 4.83

49 R 22.41 6,140 4.75

50 R 23.33 6,117 4.67

51 R 24.27 6,094 4.59

52 R 25.24 6,070 4.51

53 R 26.22 6,044 4.43

54 R 27.21 6,018 4.35

55 R 28.23 5,991 4.27

56 R 29.27 5,963 4.19

57 R 30.32 5,933 4.11

58 R 31.4 5,903 4.04

59 R 32.49 5,872 3.96

60 R 33.6 5,839 3.88

61 R 34.73 5,806 3.80

62 R 35.88 5,771 3.73

63 R 37.04 5,735 3.65

64 R 38.23 5,698 3.58

65 R 39.43 5,660 3.50

66 R 40.65 5,620 3.43

67 R 41.89 5,580 3.36

68 R 43.15 5,538 3.28

69 R 44.43 5,495 3.21

70 R 45.73 5,450 3.14

71 R 47.05 5,404 3.07



9.0 APPENDIX

Floor LevelFloor

Type1


(kips) (kips) (kip-ft x 106)

119 R 60.59 2,444 0.52

120 R 61.61 2,383 0.49121 R 62.64 2,322 0.46

122 R 63.68 2,259 0.43

123 R 64 73 2 195 0 40



123 R 64.73 2,195 0.40

124 R 65.79 2,131 0.37

125 R 66.85 2,065 0.35

126 R 67.93 1,998 0.32

127 R 69.01 1,930 0.30128 R 70.1 1,861 0.27

129 R 71.2 1,791 0.25

130 R 72.31 1,720 0.23

131 R 73.42 1,647 0.20

132 R 74.55 1,574 0.18

133 R 75.68 1,499 0.16

134 R 76.83 1,424 0.14

135 R 77.98 1,347 0.13

136 R 79.14 1,269 0.11

137 R 80.3 1,190 0.09

138 R 81.48 1,109 0.08

139 R 82.67 1,028 0.07

140 R 83.86 945 0.05

141 R 85.06 861 0.04

142 R 86.27 776 0.03

143 R 87.49 690 0.02

144 R 88.72 603 0.02

145 R 89.96 514 0.01

146 M 210.54 424 0.00

147 M 213.43 213 0.001 L: Lobby; R: Residential; M: Mechanical

9.0 APPENDIX

9.4 Core Slab Design Summary

All core slabs are 6 in. thick, 110 pcf lightweight concrete.

Bank 1 Span

Rebar inBoth

Directions

Rebar

Dist. Bank 2 Span

Rebar inBoth

Directions Rebar Dist.

(ft) # (in, o.c.) (ft) # (in, o.c.)



( ) ( , ) ( ) ( , )

Residential / Lobby: Residential / Lobby:

1 10.16 4 14 1 10.16 4 14

2 8.25 4 18 2 8.25 4 18

3 14.70 4 6 3 14.7 4 6

4 8.40 4 18 4 8.4 4 18

Mechanical: Mechanical:

1 10.2 5 12 1 10.16 5 12

2 8.3 5 18 2 8.25 5 18

3 14.7 5 6 3 14.7 5 6

4 8.4 5 18 4 8.4 5 18

Bank 3 Bank 4.1 / 4.2

Residential / Lobby: Residential / Lobby:

1 10.16 4 14 1 10.16 4 14

2 6.06 4 18 2 6.06 4 18

3 6.06 4 18 3 6.06 4 18

4 7.8 4 18 4 10.18 4 14

Mechanical:

1 10.16 4 8

2 6.06 4 18

3 6.06 4 18

4 7.8 4 16

9.0 APPENDIX

9.5 Link Beam Summary

Table 9.3: Link Beam Dimensions

Length Tributary Area Curvature, α Radius, r

Bank 1 (ft) (ft2) (deg) (ft)

1 31.0 120 -- --

2 9.34 84.0 -- --



3 32.2 484 42.0 40.0

4 18.3 110 -- --

5 40.6 97.9 -- --

Bank 21 31.0 120 -- --

2 9.34 84.0 -- --

3 32.2 484 42.0 40.0

4 18.3 110 -- --

5 40.6 97.9 -- --

Bank 3

1 11.2 75.6 -- --

2 9.34 70.9 -- --

3 13.2 122 43.0 15.4

4 14.0 65.2 -- --

5 40.6 97.9 -- --

Bank 4.1

1 9.65 65.2 -- --

2 9.65 120 -- --

3 12.9 92.3 -- --

4 9.68 40.3 -- --

5 40.6 97.9 -- --

Bank 4.21

2 9.65 97.9 -- --

4 9.68 27.9 -- --

5 40.6 97.9 -- -- 1 Bank 4.2 does not contain Link Beam Type 1 and 3

9.0 APPENDIX

Table 9.4: Residential and Lobby Link Beam Summary

b hbar # nbar

stirrup

#

sstirrup

Bank 1 (in) (in) (in)

1 16 16 9 6 3 7.22 6 10 9 2 3 4.2

3 48 16 9 20 4 7.1

4 10 16 9 3 4 7.1



4 10 16 9 3 4 7.1

5 20 16 9 6 4 7.1

Bank 2

1 16 16 9 6 3 7.2

2 6 10 9 2 3 4.23 48 16 9 20 4 7.1

4 10 16 9 3 4 7.1

5 20 16 9 6 4 7.1

Bank 3

1 6 12 9 2 3 5.2

2 6 10 9 2 3 4.2

3 28 16 9 11 3 7.24 10 10 9 2 3 4.2

5 20 16 9 6 4 7.1

Bank 4.1

1 8 8 9 2 3 3.2

2 8 10 9 2 3 4.2

3 30 16 9 10 4 7.1

4 8 6 9 2 3 2.2

5 20 16 9 6 3 7.2

Bank 4.21

2 8 10 9 2 3 4.2

4 8 6 9 2 3 2.2

5 20 16 9 6 3 7.21 Bank 4.2 does not contain Link Beam Type 1 and 3

9.0 APPENDIX

Table 9.5: Mechanical Floor Link Beam Summary

b hbar # nbar stirrup #

sstirrup

Bank 1 (in) (in) (in)

1 22 16 9 6 3 7.22 8 10 9 2 3 4.2

3 72 16 9 20 4 7.1

4 12 16 9 3 4 7.1



5 24 16 9 6 4 7.1

Bank 2

1 22 16 9 6 3 7.2

2 8 10 9 2 3 4.2

3 72 16 9 20 4 7.1

4 12 16 9 3 4 7.1

5 24 16 9 6 4 7.1

Bank 3

1 10 10 9 2 3 4.2

2 8 10 9 2 3 4.2

3 48 16 9 11 3 7.2

4 10 10 9 2 3 4.2

5 24 16 9 6 4 7.1

Bank 4.1

1 10 8 9 2 3 3.2

2 10 10 9 2 3 4.2

3 12 10 9 10 3 4.2

4 8 8 9 2 3 3.2

5 24 16 9 6 3 7.2

Bank 4.21

2 8 10 9 2 3 4.2

4 6 8 9 2 3 3.2

5 24 16 9 6 3 7.21 Bank 4.2 does not contain Link Beam Type 1 and 3

9.0 APPENDIX

9.6 Beam Spans and Tributary Areas

Bank 1

Lobby and Mechanical Joist 1 Joist 2 Joist 3

Circumferential

Girder

Angled

Girder

Radial

Girder

Long

Cantilever

Short

Cantilever

Length ft 15.3 17.7 20.1 22.5 27.9 37.0 21.2 9.1

Tributary Area ft2 122.9 150.3 174.9 223.4 285.9 -- -- --



Residential

Length ft 15.7 19.1 -- 22.5 27.9 37.0 21.2 9.1

Tributary Area ft2 173.3 236.5 -- 258.6 285.9 -- -- --

Bank 2


Circumferential

Girder

Angled

Girder

Radial

Girder

Long

Cantilever

Short

Cantilever

Length ft 14.3 16.3 18.3 20.4 25.3 31.2 19.2 8.7


Residential

Length ft 14.9 17.7 -- 20.4 25.3 31.2 19.2 8.7


Bank 3


Circumferential

Girder

Angled

Girder

Radial

Girder

Long

Cantilever

Short

Cantilever

Length ft 18.9 21.7 24.4 27.2 33.7 27.6 19.3 5.0


Residential

Length ft 18.9 23.1 -- 27.2 33.7 27.6 19.3 5.0


Bank 4

Lobby Joist 1 Joist 2 Joist 3 CircumferentialGirder AngledGirder RadialGirder LongCantilever ShortCantilever

Length ft 18.9 21.7 24.4 27.2 33.7 27.6 19.3 5.0

Tributary Area ft2

113 1 137 4 154 7 237 5 344 9

9.0 APPENDIX

9.7 Slab and Decking Summary

Table 9.6: Decking and Slab Thickness Summary for Composite Beam System

Lobby Residential Mechanical

Properties 1-3 4 1 2 3 4

Type 1.5VL22 1.5VL22 1.5VL19 2VLI16 2VLI19 2VLI20 2VLI16



t 2.5 2.5 2.5 2.5 2.5 2.5 2.5

Rib Height 1.5 1.5 1.5 2 2 2 2

Rib Spacing 6 6 6 12 12 12 12

All decking uses 6x6 - W1.4xW1.4 shrinkage mesh

Table 9.7: Unfactored Dead Load for Composite Beam System

Floor Type DL

Lobby 32 psf

Residential 33 psf

Mechanical 39 psfIncludes weight of concrete and decking

9.0 APPENDIX

9.8 Composite Beam Summary

Table 9.8: Composite Beam Summary

Bank 1 Joist 1 Joist 2 Joist 3 Angled

Girder

Circumferential

Girder

Radial

Girder

Long

Cantilever

Short

CantileverLobby W12x14

(30)

W12x26

(70)

W12x35

(80)

W14x82

(110)

W16x31

(45)

W21x73

(75)

W24x306

(32)

W14x193

(19)

Residential W12x14

(16)

W12x22

(19)--

W14x53

(110)

W14x34

(90)

W14x61

(80)

W21x182

(32)

W21x101

(14)



(16) (19) (110) (90) (80) (32) (14)

Mechanical W14x22

(15)

W14x30

(17)

W16x36

(20)

W18x76

(81)

W16x50

(44)W14x730

1

W27x539

(32)

W24x176

(14)

Bank 2

Lobby W12x19

(56)

W12x14

(32)

W12x19

(36)

W14x61

(50)

W12x45

(80)

W21x50

(63)

W24x250

(29)

W18x175

(14)

Residential W12x16

(29)

W12x16

(35)--

W14x43

(50)

W14x26

(80)

W16x36

(27)

W21x166

(29)

W21x101

(14)

Mechanical W12x19

(14)

W12x22

(32)

W12x26

(36)

W16x67

(75)

W12x45

(40)W14x730

1

W27x539

(29)

W24x250

(14)

Bank 3

Lobby W12X16

(37)

W12X35

(86)

W12X40

(96)

W14X120

(134)

W12X65

(108)

W18x55

(83)

W24x192

(29)

W18x106

(8)

Residential W12X22

(74)

W12X35

(92)--

W14x82

(134)

W14x43

(108)

W16x40

(24)

W21x201

(29)

W18x46

(8)

Mechanical W14x22

(36)

W14x30

(42)

W14x38

(48)

W21x111

(66)

W21x55

(81)W14x730

1

W36x442

(29)

W21x166

(8)

Bank 4.1Lobby W12X16

(37)

W12X35

(86)

W12X40

(96)

W14X120

(134)

W12X65

(108)

W18x55

(67)

W24x370

(29)

W18x106

(8)

Residential W12 x 22

(39)

W12 x 30

(92)--

W14 x 74

(132)

W14 x38

(106)

W16x36

(24)

W24x176

(25)

W18x50

(8)

Bank 4.2

Residential W12x22

(39)

W12x30

(92) --

W18x60

(66)

W14 x38

(106)

W16x36

(24)

W24x176

(25)

W18x50

(8)

1 W14x730 are rotated girders at the mechanical floors

9.0 APPENDIX

9.9 Initial Gravity Design Column Comparison

Table 9.9: Initial Composite and Steel Column Comparison

Column 1 / 21 Column 3a/3b1

Steel2 Composite2 Steel2 Composite2

Bank Level Shape Shape Concrete2(in) Shape Shape

Concrete

(in)

4 145 W14x99 W4X13 10X12 -- -- --



5 99 3 0

4 134 W14x99 W8X35 14X22 -- -- --

4 123 W14x193 W14X90 22X26 -- -- --

4 113 W14x311 W14X193 24X28 -- -- --

3 100 W14x426 W14X342 24X28 -- -- --

3 87 W14x550 W14X500 24X28 -- -- --

3 75 W14x665 W14X550 30X32 -- -- --

2 64

Sq. Pl.

24x4.25 W14X730 30X32 W14x455 W14x132 30X30

2 52

Sq. Pl.

24x5.25 W14X730 38X40 W14x605 W14x500 30X30

2 41 Sq. Pl. 26x6 W14X730 48X48 W14x730 W14x730 30X30

1 29 Sq. Pl. 28x6 W14X730 56X58

Sq. Pl.

24x5 W14x730 40X40

1 17 Sq. Pl. 32x6 W14X730 64X64

Sq. Pl.

26x6 W14x730 50X50

1 5 Sq. Pl. 36x6 W27X539 68X70

Sq. Pl.

28x6 W14x665 60X60

1 Lobby -- W14X730 72X74 -- W14x665 60X62

1 Column 2 only applies to Bank 3 & 4. Column 3a/3b only applies to Bank 1 & 2.

2 Columns were sized for both steel and composite configurations and then the optimal design was chosen.

The grey text shows the shapes and dimensions not chosen.

9.0 APPENDIX

9.10 MIDAS Gen Gravity Loads

Table 9.10: MIDAS Gen Unfactored Gravity Loads (kips / node)

Floor Type1 Column 1 Column 2 Column 3a/bCore

(Total Load for

all core walls divided

by # radial girders)

SDL + DL LL

SDL +

DL LL

SDL

+ DL LL

SDL +

DL LL



1 L 0.0 0.0 0.0 0.0

2 L 5.4 0.0 5.4 0.0

3 L 5.4 0.0 5.4 0.0

4 L 5.4 0.0 5.4 0.05 L 96.2 35.3 96.2 35.3 36.4 32.1

6 R 96.2 35.3 96.2 35.3 36.4 32.1

7 R 96.2 35.3 96.2 35.3 36.4 32.1

8 R 96.2 35.3 96.2 35.3 36.4 32.1

9 R 96.2 35.3 96.2 35.3 36.4 32.1

10 R 96.2 35.3 96.2 35.3 36.4 32.1

11R

96.2 35.3 96.2 35.3 36.4 32.112 R 96.2 35.3 96.2 35.3 36.4 32.1

13 R 96.2 35.3 96.2 35.3 36.4 32.1

14 R 96.2 35.3 96.2 35.3 36.4 32.1

15 R 96.2 35.3 96.2 35.3 36.4 32.1

16 R 96.2 35.3 96.2 35.3 36.4 32.1

17 R 96.2 35.3 96.2 35.3 36.4 32.1

18 R 96.2 35.3 96.2 35.3 36.4 32.1

19 R 96.2 35.3 96.2 35.3 36.4 32.1

20 R 96.2 35.3 96.2 35.3 36.4 32.1

21 R 96.2 35.3 96.2 35.3 36.4 32.1

22 R 96.2 35.3 96.2 35.3 36.4 32.1

23 R 96.2 35.3 96.2 35.3 36.4 32.1

24 R 96.2 35.3 96.2 35.3 36.4 32.1

25 R 96.2 35.3 96.2 35.3 36.4 32.1

26 R 96.2 35.3 96.2 35.3 36.4 32.1

27 R 96.2 35.3 96.2 35.3 36.4 32.1

28 R 96.2 35.3 96.2 35.3 36.4 32.1

9.0 APPENDIX

Floor Type1 Column 1 Column 2 Column 3a/b

Core (Total Load for



SDL + DL LL

SDL +

DL LL

SDL

+ DL LL

SDL +

DL LL

36 R 96.2 35.3 96.2 35.3 36.4 32.1

37 R 96.2 35.3 96.2 35.3 36.4 32.1

38 M 56.3 249.0 56.3 249.0 25.1 92.3

39 M 5.4 0.0 5.4 0.0 9.7 16.6



40 L 75.8 80.0 75.8 80.0 33.1 47.8

41 R 74.6 27.2 74.6 27.2 32.7 30.1

42 R 74.6 27.2 74.6 27.2 32.7 30.1

43 R 74.6 27.2 74.6 27.2 32.7 30.1

44 R 74.6 27.2 74.6 27.2 32.7 30.1

45 R 74.6 27.2 74.6 27.2 32.7 30.1

46 R 74.6 27.2 74.6 27.2 32.7 30.1

47 R 74.6 27.2 74.6 27.2 32.7 30.1

48 R 74.6 27.2 74.6 27.2 32.7 30.1

49 R 74.6 27.2 74.6 27.2 32.7 30.1

50 R 74.6 27.2 74.6 27.2 32.7 30.1

51 R 74.6 27.2 74.6 27.2 32.7 30.1

52 R 74.6 27.2 74.6 27.2 32.7 30.1

53 R 74.6 27.2 74.6 27.2 32.7 30.1

54 R 74.6 27.2 74.6 27.2 32.7 30.1

55 R 74.6 27.2 74.6 27.2 32.7 30.1

56 R 74.6 27.2 74.6 27.2 32.7 30.1

57 R 74.6 27.2 74.6 27.2 32.7 30.158 R 74.6 27.2 74.6 27.2 32.7 30.1

59 R 74.6 27.2 74.6 27.2 32.7 30.1

60 R 74.6 27.2 74.6 27.2 32.7 30.1

61 R 74.6 27.2 74.6 27.2 32.7 30.1

62 R 74.6 27.2 74.6 27.2 32.7 30.1

63 R 74.6 27.2 74.6 27.2 32.7 30.1

64 R 74.6 27.2 74.6 27.2 32.7 30.165 R 74.6 27.2 74.6 27.2 32.7 30.1

66 R 74.6 27.2 74.6 27.2 32.7 30.1

67 R 74 6 27 2 74 6 27 2 32 7 30 1

9.0 APPENDIX





SDL + DL LL

SDL +

DL LL

SDL

+ DL LL

SDL +

DL LL

74 L 57.9 61.5 2.2 0.0 57.9 61.5 24.3 33.2

75 R 57.0 20.9 57.0 20.9 24.0 18.8

76 R 57.0 20.9 57.0 20.9 24.0 18.8

77 R 57.0 20.9 57.0 20.9 24.0 18.8



78 R 57.0 20.9 57.0 20.9 24.0 18.8

79 R 57.0 20.9 57.0 20.9 24.0 18.8

80 R 57.0 20.9 57.0 20.9 24.0 18.8

81 R 57.0 20.9 57.0 20.9 24.0 18.8

82 R 57.0 20.9 57.0 20.9 24.0 18.8

83 R 57.0 20.9 57.0 20.9 24.0 18.8

84 R 57.0 20.9 57.0 20.9 24.0 18.8

85 R 57.0 20.9 57.0 20.9 24.0 18.8

86 R 57.0 20.9 57.0 20.9 24.0 18.8

87 R 57.0 20.9 57.0 20.9 24.0 18.8

88 R 57.0 20.9 57.0 20.9 24.0 18.889 R 57.0 20.9 57.0 20.9 24.0 18.8

90 R 57.0 20.9 57.0 20.9 24.0 18.8

91 R 57.0 20.9 57.0 20.9 24.0 18.8

92 R 57.0 20.9 57.0 20.9 24.0 18.8

93 R 57.0 20.9 57.0 20.9 24.0 18.8

94 R 57.0 20.9 57.0 20.9 24.0 18.8

95 R 57.0 20.9 57.0 20.9 24.0 18.896 R 57.0 20.9 57.0 20.9 24.0 18.8

97 R 57.0 20.9 57.0 20.9 24.0 18.8

98 R 57.0 20.9 57.0 20.9 24.0 18.8

99 R 57.0 20.9 57.0 20.9 24.0 18.8

100 R 57.0 20.9 57.0 20.9 24.0 18.8

101 R 57.0 20.9 57.0 20.9 24.0 18.8

102 R 57.0 20.9 57.0 20.9 24.0 18.8103 R 57.0 20.9 57.0 20.9 24.0 18.8

104 R 57.0 20.9 57.0 20.9 24.0 18.8

105 R 57 0 20 9 57 0 20 9 24 0 18 8

9.0 APPENDIX





SDL + DL LL

SDL +

DL LL

SDL

+ DL LL

SDL +

DL LL

112 R 63.7 22.8 63.7 22.8 23.7 23.3

113 R 63.7 22.8 63.7 22.8 23.7 23.3

114 R 63.7 22.8 63.7 22.8 23.7 23.3

115 R 63.7 22.8 63.7 22.8 23.7 23.3



116 R 63.7 22.8 63.7 22.8 23.7 23.3

117 R 63.7 22.8 63.7 22.8 23.7 23.3

118 R 63.7 22.8 63.7 22.8 23.7 23.3

119 R 63.7 22.8 63.7 22.8 23.7 23.3

120 R 63.7 22.8 63.7 22.8 23.7 23.3

121 R 63.7 22.8 63.7 22.8 23.7 23.3

122 R 63.7 22.8 63.7 22.8 23.7 23.3

123 R 63.7 22.8 63.7 22.8 23.7 23.3

124 R 54.6 19.4 54.6 19.4 25.3 34.4

125 R 54.6 19.4 54.6 19.4 25.3 34.4

126 R 54.6 19.4 54.6 19.4 25.3 34.4127 R 54.6 19.4 54.6 19.4 25.3 34.4

128 R 54.6 19.4 54.6 19.4 25.3 34.4

129 R 54.6 19.4 54.6 19.4 25.3 34.4

130 R 54.6 19.4 54.6 19.4 25.3 34.4

131 R 54.6 19.4 54.6 19.4 25.3 34.4

132 R 54.6 19.4 54.6 19.4 25.3 34.4

133 R 54.6 19.4 54.6 19.4 25.3 34.4134 R 54.6 19.4 54.6 19.4 25.3 34.4

135 R 54.6 19.4 54.6 19.4 25.3 34.4

136 R 54.6 19.4 54.6 19.4 25.3 34.4

137 R 54.6 19.4 54.6 19.4 25.3 34.4

138 R 54.6 19.4 54.6 19.4 25.3 34.4

139 R 54.6 19.4 54.6 19.4 25.3 34.4

140 R 54.6 19.4 54.6 19.4 25.3 34.4141 R 54.6 19.4 54.6 19.4 25.3 34.4

142 R 54.6 19.4 54.6 19.4 25.3 34.4

143 R 54 6 19 4 54 6 19 4 25 3 34 4

9.0 APPENDIX

9.11 Column Validation Summary

Table 9.11: Composite and Steel Shapes for Lateral Design Column Validation

Column 1 / 21 Column 3a/3b

Bank Level Steel ShapeConcrete

(in.)Steel % Shape

Concrete

(in.) Steel %

4 134 W14x233 -- -- -- -- --

4 123 W14x370 -- -- -- -- --



4 113 W14x550 -- -- -- -- --

3 100 W18x35 22x20 2.3% -- -- --

3 87 W18x50 22x22 3.0% -- -- --

3 75 W21x111 26x24 5.2% -- -- --

2 64 W24x146 30x26 5.5% W24x162 30x26 6.1%

2 52 W24x131 30x26 4.9% W24x146 30x26 5.5%

2 41 W24x162 30x28 5.7% W24x162 30x28 5.7%

1 29 W36x361 42x38 6.6% W36x330 42x34 6.8%

1 17 W36x330 42x34 6.8% W36x330 42x34 6.8%

1 5 W36x330 42x34 6.8% W36x330 42x34 6.8%

1 Lobby W40x324 46x38 5.5% W40x324 46x38 5.5%1 Column 2 only applies to Bank 3 & 4. Column 3a/3b only applies to Bank 1 & 2

9.0 APPENDIX

9.12 MIDAS Sensitivity Analyses

Steel built-ups shown in Table 9.12 were used in the MIDAS model for several sensitivity analyses to test

the axial discontinuity and lateral deflection of the model.

Table 9.12: Built-up Steel and Concrete Properties

Column Nomenclature As (in2) Ag (in

2) Gross dimension (in)

BU1 768 1600 40x40

BU2 640 1296 36x36



BU2 640 1296 36x36

BU3 476 1024 32x32

BU4 364 784 28x28

Three different sensitivity analyses were performed and are summarized in Table 9.13. The built-

ups in Banks 1-3 were changed and the larger built-up test resulted in less deflection. The

discontinuity results for the test are shown in Figure 9.1. Core wall thickness in Bank 3 was also

tested (Figure 9.2).

The sensitivity analysis for the effects of belt trusses and outriggers kept the core wall sizes to a

uniform one foot. While the results are relative to this unrealistic design, they show patterns in belt

truss and outrigger functionality given sizing and general existence.

Ultimately, the sensitivity analysis showed that the large belt truss and outrigger members were

causing large load shedding from the exterior columns to the core. Additionally, the large, built-up

steel shapes encased in concrete reduced drift and eliminated the tension forces from the original

column design.

9.0 APPENDIX

Table 9.13: Sensitivity Analyses Element Properties

Core Wall

Thickness by

Bank (ft)

Belt

Truss Outrigger

Vertical Column Size by Bank

Δmax 1 2 3 4 1 2 3

4

111-122 123-133 134-145

Built Up

10 8 4 3.3 W14x730 W14x730 BU1 /BU2 BU3 BU4 W14x550 W14x370 W14x233 5.34

10 8 4 3 3 W14x730 W14x730 BU1 BU2 BU2 W14x550 W14x370 W14x233 5 09



10 8 4 3.3 W14x730 W14x730 BU1 BU2 BU2 W14x550 W14x370 W14x233 5.09

Core Size

10 8 6 2 W14x730 W14x730 BU1 BU2 BU2 W14x550 W14x370 W14x233 5.06



Belt Truss and Outrigger


1 1 1 1 W14x730 None BU1 BU2 BU2 W14x550 W14x370 W14x233 8.34

1 1 1 1 None None BU1 BU2 BU2 W14x550 W14x370 W14x233 9.0

9.0 APPENDIX



Figure 9.2: Core Wall Thickness Sensitivity Results to Dead Load

Figure 9.3: Belt Truss and Outrigger Sensitivity

9.0 APPENDIX

9.13 Core Wall Reinforcement

Table 9.14: Core Wall Reinforcement Details

Horizontal Shear Vertical Shear Flexural

Thickness Bar Size Spacing Bar Size Spacing Bar Size Spacing

(ft) (in) (in) (in)

Bank 1

NS 7 18 6 10 12 10 12

EW 7 18 6 10 12 10 12



EW 7 18 6 10 12 10 12

Bank 2

NS 4 18 8 18 9 18 9

EW 4 18 9 18 10 18 10

Bank 3

NS 3 14 10 8 16 8 16

EW 3 14 9 7 12 7 12

Bank 4

4.1 2 18 7 6 14 6 14

4.2 2 8 17 6 14 6 14

9.0 APPENDIX

9.14 Creep and Shrinkage

9.14.1

Hand Calculations



9.0 APPENDIX



9.0 APPENDIX

9.14.2 Supplementary Materials

Table 9.15: Concrete Core Properties

Bank 1 2 3 4

Radius Ro 40 38 36 26 ft

Thickness t 8 6 4 3.33 ft

Total Volume / Floor Vc 23886 17417 11280 6721 ft3

Total Weight/Floor Wc 3822 2787 1805 1075 kips

Total Area/Floor A 1810 1319 855 509 ft2



Total Area/Floor At 1810 1319 855 509 ft

# of Columns 21 21 14 14

Steel Area As 2873 10187 715 123 in2

Area per core "column" 86 63 61 36 ft

2

Self-Weight per core "column" 182 133 129 77 kips

Table 9.16: Steel Deflection Summary

Floors Deflectionper Floor

Deformation perFloor Segment

Sum of Floor SegmentDeformations

(in) (in) (in)

Lobby 0.979 0.979 0.98

5-16 0.077 0.921 1.90

17-28 0.067 0.805 2.71

29-39 0.057 0.631 3.34

40-51 0.049 0.590 3.93

52-63 0.041 0.492 4.42

64-73 0.034 0.335 4.75

74-86 0.054 0.702 5.46

87-99 0.042 0.546 6.00

100-110 0.031 0.340 6.34

111-122 0.021 0.251 6.59

123-133 0.012 0.131 6.72

134-145 0.004 0.045 6.77

9.0 APPENDIX

Table 9.17: Humidity Data for Chicago

National Climatic Data for Humidity in Chicago, IL

(All Values in %) Morning Afternoon

January 78 70

February 78 67

March 79 63

April 77 58

May 77 57



June 79 58

July 82 60

August 86 61

September 85 61

October 81 59

November 80 66

December 80 71

Average 80.17 62.58

Average Humidity Between Morning and Afternoon

71.4%

Table 9.18: Concrete Reinforcement Data

Bank 1 2 3 4Core Radius Ro 40 38 36 26 ft

Core Thickness tc 8 6 4 3.33 ft

Core Circumference 251 239 226 163 ft

Rebar Spacing (in) 12 9 12 14 in

Rebar Spacing (ft) s 1 0.75 1 1.1667 ft

Bar Size 10 18 8 6

Number of Bars per Row nb 251 318 226 140

Stee Area per Bar Asb 1.27 4 0.79 0.44 in2

9.0 APPENDIX

Table 9.19: 20 Year Concrete Deflection

Deformation

per Floor

Deformation per

Floor Segment

Sum of Floor Segment

Deformations

(in) (in) (in)

0.371 0.371 0.37

0.088 1.054 1.43

0.078 0.937 2.36

0.068 0.752 3.11

0.005 0.057 3.17



0.004 0.049 3.22

0.004 0.035 3.26

0.220 2.857 6.11

0.175 2.274 8.39

0.133 1.468 9.86

0.715 8.585 18.44

0.419 4.611 23.05

0.145 1.737 24.79

9.14.3 Analysis Procedure for Creep and Shrinkage

Quantifying the amount of displacement in both the columns and core is essential for constructing a

serviceable building. If there is a large difference between the displacement of the columns and the

core that is not accounted for, floors will begin to slant over time and cause uncomfortable

situations for occupants.

The quantification of displacements depends on a multitude of factors, requiring an in-depth

analysis.

Step 1: Determine the expected loads on the concrete in question. The necessary loads are the DL,

SDL, the sustained portion of LL on the building. These loads will need to be broken up by floor

because the amount of creep is highly dependent on the amount of load and the sequence in which

it is applied.

Step 2: Create a construction schedule to determine when the concrete will be loaded with which

amount of load. For our skyscraper, as each of the 150 floors is added vertically, an additional load

9.0 APPENDIX

Step 4: Conduct laboratory tests to determine ultimate creep and shrinkage strains for the concrete

mixture specified in Step 3. The data from these tests will be used as initial values for creep and

shrinkage strains that will then be modified by calculated correction factors.

Step 5: Evaluate the geometries of structural elements. Correction factors based on the geometries

of the elements will be applied to the creep and shrinkage values calculated in order to obtain an

accurate estimate. Important geometric considerations are the height of the element as well as its

surface-to-volume ratio.

Step 6: Calculate the expected creep and shrinkage coefficients for loading, construction timing,

mixture composition properties and geometries per GL2000 Method from ACI 209 2R 27 These



mixture composition properties, and geometries per GL2000 Method from ACI 209.2R-27. These

coefficients are then used to factor the ultimate creep and shrinkage strain values obtained from

laboratory tests to calculate the final expected displacements.

Step 7: Compare the newly calculated strain values for the column and core concrete to determine

the anticipated differential displacement. The differences will be used to modify the column and

core heights to account for the eventual differential displacement in the concrete.

Assumptions from GL2000 Method:

The method is defined for concretes with mean compressive strengths less than 11,890 psi. Thecore compressive strength is 14,000 psi, but it is assumed that since mix details are not provided

this method still provides the best estimate for creep and shrinkage strains.

Type III cement was used to provide the highest initial strength gain, which led to the smallest

ultimate deformation of the core. Per this type of cement, values for the s and k parameters were

0.13 and 1.15, respectively.

In order to determine the correction term for humidity average data was taken from the National

Climatic Data Center for Chicago, IL. The average relative humidity over the year was found to be

0.71.

The time when curing stops and the time when subsequent loading is added were both taken to be

four days. Because of this, the correction term for drying occurring before loading does not affect

the creep coefficient.



11.0 Calculation Book



2011 – 2012

ASPIREMaster of Engineering

Structural Design Project

Table of Contents

1.0 General Notes ................................................................................................................ 1

1.1 List of Variables .......................................................................................................... 2

1.2 Color Key Explanation ................................................................................................ 7

2.0 Preliminary Load Analysis ..............................................................................................

2.1 Gra!ity "esi#n Loads .................................................................................................. $

2.2 %ind Load Cal&'lations ............................................................................................ 10

2.2.1 A(CE 7 %ind Load Cal&'lations......................................................................... 11

2.2.2 %ind )'nnel "ata ............................................................................................. 1$

2 * (eismi& Cal&'lations 2*



2.* (eismi& Cal&'lations ................................................................................................. 2*

2.*.1 (eismi& %ei#+t Cal&'lation ............................................................................... 2,

2.*.2 (eismi& Load Cal&'lations ...................................................................... ........... 2$

*.0 Gra!ity "esi#n .............................................................................................................. *2

*.1 )rib'tary Areas ......................................................................................................... ***.2 Core Area

*.2.1 Con&rete (lab "esi#n ........................................................................................ *$

*.2.2 Lin- eam "esi#n .............................................................................................. ,/

*.* loor Area ................................................................................................................. /1

*.*.1 Composite "e&-in# ........................................................................................... /2

*.*.2 Composite eam "esi#n ................................................................................... ,

*.*.* Vibration Analysis ............................................................................................. $*

*., Col'mns .................................................................................................................... $$

*.,.1 Col'mn Load )a-edon ................................................................................. 100

*.,.2 Composite Col'mn "esi#n .............................................................................. 11,

*.,.* (teel Col'mn "esi#n ....................................................................................... 11

,./ Core ebar "esi#n .................................................................................................. 1*1

,./.1 "esi#n of Core ebar for Verti&al and 8ori9ontal (+ear ................................ 1*2

,./.2 "esi#n of Core ebar for lex'ral Capa&ity .................................................... 1*,

,./.* an- , (tron# Axis endin# ............................................................................ 1*

,. Ener#y 3et+od 6ptimi9ation ................................................................................. 1/

,..1 6ptimi9ation Cal&'lations ............................................................................... 1/

,..2 esi9in# of 'ilt:'p 3embers ......................................................................... 11

/.0 Conne&tion "esi#n ..................................................................................................... 12

/.1 )ypi&al Conne&tions

/.1.1 %elded Col'mn (pli&e .................................................................................... 1*



/.1.2 loor ;oist to adial Girder Conne&tion .......................................................... 1

/.1.* Girder to Col'mn Conne&tions ....................................................................... 171

/.1., 8(( to Cantile!er Conne&tion ......................................................................... 177

/.1./ adial Girder to Con&rete Core ....................................................................... 10

/.2 ase of 3e#a:Col'mn Conne&tion ......................................................................... 1$

/.2.1 3e#a:Col'mn to Caisson Conne&tion ............................................................ 1$0

/.2.2 Caisson Cap 3oment einfor&ement ............................................................. 1$,

/.* 6'tri##er Conne&tions ........................................................................................... 1$

/.*.1 ottom of 6'tri##er to Col'mn Conne&tion .................................................. 1$7

/.*.2 )op of 6'tri##er to Core ................................................................................. 1$$

.0 o'ndation "esi#n ..................................................................................................... 21$

.1 etainin# %all ........................................................................................................ 220

.1.1 (oil Profile ....................................................................................................... 221

.1.2 Effe&ti!e Press're ........................................................................................... 222

.1.* etainin# %all "esi#n ..................................................................................... 22,

.*.1 Aba='s Analysis of Caissons ........................................................................... 2/1

.*.2 3e#a:Col'mn Caisson "esi#n......................................................................... 2/*

.*.* in# eam "esi#n ........................................................................................... 2//

.*., Core Caisson "esi#n ........................................................................................ 2/7

.*./ Caisson ebar .................................................................................................. 2/$

7.0 Creep and (+rin-a#e .................................................................................................. 20

7.1 (teel Col'mn "eformation ..................................................................................... 21

7.1.1 (teel Col'mn Properties and Loads ................................................................ 22

7.1.2 (teel Col'mn "eformation Cal&'lations ......................................................... 2*

7.2 Con&rete Core "eformation ................................................................................... 2/



7.2.1 Con&rete Core Properties and Loads .............................................................. 2

7.2.2 Con&rete Core "eformation Cal&'lations ....................................................... 27

.0 eferen&es ................................................................................................................. 2$

.1 Ener#y:ased "esi#n of Lateral (ystems by %illiam . a-er ............................... 270

.2 Geote&+ni&al eport for t+e C+i&a#o (pire ............................................................ 27,

1.0 General Notes

1.1 List of Variables 2

1.2 Color Key Explanation 7

The calculation book is a compilation of all the calculations performed for the design of The

Chicago Spire. The calculations shown are the final design calculations performed for eachdeliverable. Hand calculations and spreadsheets are included in the calculation book. The



spreadsheets included are demonstrative of the many calculations performed (Ex

Spreadsheet containing the design of a single column is attached. However! the

spreadsheet was used to design columns on multiple floors."

a = Whitney Stress Block Theory depth of compression zone

a = distance from support face to 1st bolts, in

A = torque coefficient

ao/ = acceleration limit for !ibrational analysis

ap/ = peak acceleration for !ibrational analysis

Ase," = effecti!e cross sectional area of sinle bolt, in#

A!/s = steel area/spacin ratio in#/in

A$ = area of %%%%%%%%%%%% &concrete, rebar, net area, etc', in#

b = beam/column (idth, in

b = eccentricity of cur!ature, in

B = anular t(ist coefficient

beff = effecti!e (idth of slab section, in

bf = flane (idth of a steel section, in

B ) = effecti!e panel (idth, inbo = punchin shear perimeter, in

1.1 List of Variables



* = concrete compressi!e force, lbs

c = concrete co!er, in

c = turbulence intensity factor

*+ = instantaneous center of rotation at the centroid of the bolt roup

*1 = effecti!e riidity

*all = allo(able compression, ksi

*app = applied compression, ksi*b = beam bendin coefficient

*c = centerline circumfrence, ft

*col = distance from concrete compression face to neutral a$is

cb = !ertical centroid of bolt roup, in

c = location of factored tensile force, in

* ) = effecti!e (idth factor

*( = (arpin constant, in-

d = structural depth, in &ote. for steel sections, this is the member depth'd = depth belo( rade &ft'

= (eld size, in

deff = effecti!e concrete depth, in

dist$ = distance, in

) = transformed )oist moment of inertia, in0/ft

= dead load

dm = moment arm, in

s = transformed slab moment of inertia, in0

/ftu = pretension multiplier

d = diameter of &bolt column rebar shear stud etc' in

f+c,a! = a!erae compressi!e strenth of concrete, ksi

f+c4comp = compressi!e stress in concrete, ksi

f comp = allo(able compressi!e stress, ksi

5cr = fle$ural bucklin stress, ksi

5 = factored dead load

5e = elastic critical bucklin stress, ksi

5277 = electrode strenth, ksi5lim = elastic bucklin limit

5 = factored li!e load

58s = factored seismic moment

58W = factored (ind moment

f n = natural frequency of the floor, 9z

f r = allo(able tension stress, ksi

f s = stress in concrete reinforcin steel

5s = force in concrete reinforcin steel, kip5S = factor of safety

f l l l k

f t = lateral tensile stress, ksi

5u = specified ultimate strenth of steel, ksi

5( = nominal strenth of (eld, ksi

5y = specified minimum yield strenth of steel section, ksi

5yr = specified minimum yield stress of reinforcin bars, ksi

= acceleration due to ra!ity, in/sec#

: = shear modulus, ksih = beam/slab depth, in

h = floor to floor heiht, ft

heff = effecti!e embedment depth of anchor, in

hf = factor for fillers

3c = moment of inertia of core, in0

3c = moment of inertia of the concrete section, in0

3comp = moment of inertia of the composite section, in0

3eff = moment of inertia for post4composite deflection, in0

3o = moment of inertia of column, in0

3s = moment of inertia of steel shape, in0

3sr = moment of inertia of reinforcin bars, in0

3t = transformed moment of inertia, in0

3$ = moment of inertia of stron a$is, in0

3y = moment of inertia of (eak a$is, in0

; = polar moment of inertia, in0

< = distance from flane to (eb (eld, in

< = effecti!e lenth factor

lc = clear distance bt(n ede of hole and ede of ad)acent hole, in

l c ede = clear distance, in dir> of force, bet(een ede of hole and ede of material, in

l c int = clear distance, in dir> of force, bet(een ede of hole and ede ad)acent hole, in

lcbtm = clear distance bt(n ede of hole and ede of material for bottom bolts, in

ld = embedment lenth, in

eh = horizontal ede distance, in

e! = !ertical ede distance, in

e$ = effecti!e lenth on stron a$is, ftey = effecti!e lenth on (eak a$is, ft

ird = (idth at irder, in

= li!e load

o = total open lenth in core, ft

o = openin lenth in core, ft

out = (idth at outrier, in

p = lenth of plate, in

( = lenth of (eld, inl ( = Whitmore Section (idth, in



8 = applied moment

8n = allo(able moment

8post = post4composite moment, kip4ft

8pre = pre4composite moment, kip4ft

8s = seismic moment, kip4ft

8u = ma$imum applied moment

8( = (ind moment, kip4ft

= bearin lenth, in

n = number of %%%%%% &number of bolts, shear studs, etc'

n = ratio bet(een steel and concrete modulus of elasticity

n = dynamic modular ratio

= tension force &from A*3?1@4@', kips

n = nominal tension strenth, kips

$ = nominal tension strenth of a roup of anchors/hooked bolt, lbs

= perimeter of column, in = total load, kips

cp = outer perimeter of cross section, in

e = 2uler bucklin load, kips

= applied a$ial load

h = perimeter of torsion reinforcin, in

n = allo(able column a$ial load

o = e$citation for !ibrational analysis, lbs

o = nominal a$ial compressi!e strenth (ithout consideration of lenth effects, kipsp = ankine+s passi!e earth pressure, kips

f lid ll

u = load at connection, kips

r$ = radius of %%%%% &column, bolt, etc', in

r$ = radius of yration &stron', in

ry = radius of yration &(eak', in

s = spacin, in

Sc = section modulus for compression, in?

Smin = minimum required section modulus, in?

Ss = section modulus of steel shape, in?

Stens = section modulus for tension, in?

S$ = section modulus &stron', in?

Sy = section modulus &(eak', in?

T = clear space, in

T = distance bet(een (eld centers, in

Tapp = applied tension, ksi

Tb = min> fastener tension, kips

tf = thickness of flane of steel section, in

Tn = nominal tensile capacity, kips



Tth = threshold torsional moment, kip4ft

Tu = ma$imum tension force, kips

Tu = ma$imum applied torsional moment, kip4ft

t( = thickness of (eb of steel section, in

t$ = thickness of %%%%%%% &concrete, plate, (all, etc', in

D = shear la factor

Dbs = block shear rupture reduction coefficient

Dbs = reduction coefficient

" = shear force, kips

" = basic (ind speed, mph

"6h = ad)usted horizontal shear, kips

"6h = partial composite action horizontal shear, kips

"c = allo(able shear in concrete, kips

"c = concrete !olume, ft?

"cp = ominal pryout strenth &roup', kips

"n = total shear capacity, kips

"sa = ominal strenth in shear, kips

"th = theoretical concrete !olume, ft?/ft

#

"u = ma$imum applied shear, kips

( = distributed load, plf

W = (eiht supported, lbf

(a = anle (idth, in

Wc = core (all self4(eiht, kip

(c = (eiht of concrete per unit !olume, pcf

G = anle of cur!ature, radians

G = anle of backfill abo!e (all, radians

H = modal dampin ratio for !ibrational analysis

H1 = concrete stress block coefficient

I = deflection, in

Jcu = concrete ultimate compressi!e strain

Js = strain in concrete reinforcin steel

Jys = steel yield strain

K = anle of t(ist, radians

L = modification factor reflectin the reduced mechanical properties of liht(eiht concrete

M = mean slip coefficient

Nactual = density of the steel in slab

Nbal =

O = ?>101PQ#-P0

Nc = density of concrete, pcf

Nclay = density of clay, psf

N = steel ratio

Ns = spiral reinforcement ratio

density of steel at (hich a balanced failure bet(een concrete crushin and steel yieldin in tension



Nsr = reinforcement ration for continuous lonitudinal reinforcin, A sr/A

Ns( = beam self (eiht density, lb/ft

Ract = actual stress per caisson, ksi

Rall = allo(able stress, ksi

Rc = net compression stress, ksi

Rc = allo(able stress in concrete, ksi

Rr = allo(able stress in rock, ksi

Rt = net tensile stress, ksi

= strenth reduction factor

$ = factored allo(able strenth &moment, a$ial, shear, bearin, etc>'

$ = modification factor for anchor bolts

U = anle of friction for soil, radians

1.2 Color Key Explanation

Color Key: User Input

Constant/Previous Calc.

Calc/Lookup

Yes Passes Check

No Fails Check

The yello$ cell inicates a user input. The user shoul input values "or the spreasheet to

calculate the results.

The gray cell inicates a constant or a previous calculation. %hen it is a previous

calculation& it is irectly re"erencing the cell $here the calculation $as per"or#e. 'othconstants an previous calculations are consiere inactive cells.



The green cell inicates that a check is !eing per"or#e an the conitions are satis"ie.

The re cell inicates that a check is !eing per"or#e an the conitions are not satis"ie.

The $hite cell inicates a calculation or a value that is o!taine via lookup. (n e)a#ple o" a

lookup $oul !e the various section properties o" a %*shape "or a speci"ic shape.

2.0 Preliminary Load Analysis

2.1

Gravity Design Loads 9

2.2 Wind Load Calculations 10

2.2.1

ASCE Wind Load Calculations 11

2.2.2 Wind !unnel Data 19

2."

Seismic Calculations

2.".1

Seismic Weig#t Calculation 2$

2.".2

Seismic Load Calculations 29




Loads taken from ASCE 7

Dead LoadSuperimposed

Dead Load

Live Load

(psf) (psf) (psf)

Decking and Slab 32

Assembl Areas (lobbies) !""

Acoustical fiber board !

#E$ Duct Allo%ance !"

Ceramic or &uarr tile (! !'2 in) on ! in mortar bed *

Total 32 +7 !""Decking and Slab 33

$rivate rooms and corridors serving t,em "

L o b b y

Typical Floor



$rivate rooms and corridors serving t,em "

$artition -alls !+

Acoustical fiber board !

Ceramic or &uarr tile (3' in) on ! in mortar bed 23


Total 33 3 ++Decking and Slab 3.

Cat%alks "

#ac,ine Space 2""


Total 3. !" 2"

Slab (!+" pcf / !2 in) !+"

0arages (passenger ve,icles onl) "#E$ Duct Allo%ance !"

Cement finis, (!1in) on stone1concrete fill 32

Total !+" 2 "

Slab (!!" pcf / * in) ++

Total ++ C o r e

R e s i d e n t i a l

M e c h a n i c a l

P a r k i n g

2.2 Wind Load Calculations

2.2.1 ASCE 7 Wind Load Calculations 11

2.2.2 Wind Tunnel Data 19



2.2.1 ASCE 7 Wind Load Calculations Created by: JLB,CJB,JAC,DBL 3/10/2012

Definition of Variables from ASCE 7 Chapter 26

Basic Wind Speed V 120 mph 2!"#$

Wind Directi%na&ity 'act%r (d 0")# 2!"!$

*+p%sre Cate-%ry D 2!".$3Sec%nd st Speed *+p%nent 11"# 2!"1$

ean 4%r&y Wind Speed 5%6er La6 *+p%nent 0"11 2!"1$

=e9erence t%%& that ca&c&ates 6ind &%ads 9%r stren-th acc%rdin- t% ASC* .10 and then c%mpares these a&es

t% 6ind tnne& data 9r%m =WD8 tests" See ass%ciated macthcad 9i&e and =WD8 9i&e 9%r inpt a&es"

ean 4%r&y Wind Speed 'act%r b 0")0 2!"1$

7rb&ence 8ntensity 'act%r c 0"1# 2!"1$

8nte-ra& Len-th Sca&e 'act%r & !#0 9t 2!"1$

8nte-ra& Len-th Sca&e 5%6er La6 *+p%nent 0"13 2!"1$

;%mina& 4ei-ht %9 Atm%sphere B%ndary Layer <- .00 9t 2!"1$

7%p%-raphic 'act%r (<t 1"00 2!")"2$

=i-idity '&e+ib&e

5ea> 'act%r 9%r Bac>-r%nd =esp%nse -? 3"@0 2!""#$

5ea> 'act%r 9%r =es%nant =esp%nse -V 3"@0 2!""#$

5ea> 'act%r 9%r Wind =esp%nse -= 3"@ 2!"11$

;mber %9 St%ries ; 1#0

5eri%d 7 1#"0 secBi&din- ;atra& 'reency n1 0"0. 4<

Bi&din- Width B 1#0 9t

Bi&din- Len-th L 1#0 9t

ean =%%9 4ei-ht h 2,000 9t

*ia&ent 4ei-ht 1,200 9t 2!""@$

Dampin- =ati% 0"02

ean 4%r&y Wind Speed V< 210 mph 2!"1!$8nte-ra& Len-th Sca&e %9 7rb&ence L< 1,01 9t 2!"$

Definition of Variables from ASCE 7 Chapter 26 cont!

= Ca&c&ati%n 8ntermediate Va&es =n 0"21 2!"13$

Eh 2"2 2!""#$

=h 0"2) 2!"1#a$

EB 0"22 2!""#$

=B 0"). 2!"1#a$

EL 0".3 2!""#$

=L 0"!# 2!"1#a$

=es%nant =esp%nse 'act%r = 1"@. 2!"12$

8ntensity %9 7rb&ence 8< 0"0) 2!".$

Bac>-r%nd =esp%nse 'act%r ? 0".1 2!")$

st *99ect 'act%r 9 1"12 2!""#$



*nc&%sre c&assi9icati%n *nc&%sed

0"1)

0"1)Cpi 2!"111$

5r%dct %9 8nterna& 5ressre C%e99icient and st*99ect

'act%r

Calculated Values from ASCE 7 Chapter 26

Basic Wind Speed V 120 mph (26.5)

Wind Directionality Factor Kd 0.5 (26.6)

!"pos#re $ate%ory D (26.&)

'opo%raphic Factor Kt 1.00 (26..2)

#st !**ect Factor * 1.12 (26.+.5)

!nclos#re $lassi*ication !nclosed0.1 Fi% (26.11,1)

,0.1

-,Second #st Speed !"ponent 11.5 Fi% (26.+,1)

/ominal ei%ht o* tmosphere Bo#ndary ayer % &00 Fi% (26.+,1)

Calculated Values from ASCE 7 Chapter 27

Wall Pressure Coefficients

3rod#ct o* ;nternal 3ress#re $oe**icient and #st,

!**ect Factor$pi

3lan en%th to Width 4atio B 1.00 Fi% (2&.,1)

Wind7ard Wall 3ress#re $oe**icient $p 0.0 Fi% (2&.,1)

ee7ard Wall 3ress#re $oe**icient $p ,0.50 Fi% (2&.,1)

Side Wall 3ress#re $oe**icient $p ,0.&0 Fi% (2&.,1)

ee7ard Velocity 3ress#re 1 8h 6-.0 ps* (2&..1)

Building Dimensions

oriontal Dimension , Ban9 1 B" 1+ *t

oriontal Dimension , Ban9 2 B" 1& *t

oriontal Dimension , Ban9 - B" 15- *t

oriontal Dimension , Ban9 B" 1-- *toriontal Dimension , Ban9 .2 B" 120 *t

Story ei%ht h 1-.2 *t

Eccentricity Calculation Values

Shear $enter and $enter o* :ass !ccentridity e4 0.0 *t (2&..6)

;ntensity o* '#r<#lence ; 0.0 (26.+,&)

3ea9 Factor *or Bac9%ro#nd 4esponse %= -.0 (26.+.5)

3 9 F * Wi d 4 - +

Eccentricity Calculation per Ban

!ccentricity *or 4i%id Str#ct#res e= 2.- *t (2&.,)

21.1 *t (2&..6)

,21.1 *t

!ccentricity *or 4i%id Str#ct#res e= 26.1 *t (2&.,)

1+.5 *t (2&..6)

,1+.5 *t

!ccentricity *or 4i%id Str#ct#res e= 2-.0 *t (2&.,)

1&.1 *t (2&..6)

,1&.1 *t

!ccentricity *or 4i%id Str#ct#res e= 20.0 (2&.,)

1.+ (2&..6)

1 +

Ban !

Ban "

Ban 2

e"> ey

e"> eyFle"i<le B#ildin% !ccentricity

Fle"i<le B#ildin% !ccentricity

Ban $

e"> ey

e"> ey

,1.+

!ccentricity *or 4i%id Str#ct#res e= 1.0 (2&.,)

1-. (2&..6)

,1-.

/otes

2 ;n all calc#lations> the ne%ati?e ?al#e o* $pi is #sed to %et lar%er ?al#es o* 7ind press#re. See Section 2&.,2

Ban !#2

1 Both 8h and 8i are ta9en conser?ati?ely to <e the ma"im#m 8 ?al#e *rom 7ind7ard press#re calc#lations. 'his

ma"im#m occ#rs at the 150th le?el

y

e"> eyFle"i<le B#ildin% !ccentricity

ASCE Ch 27 Wind Load Cases

Floor

(relative

to

ground)

Height

(relative

to

ground)

Width of

Buidling

Velocity

PressureExposure

Coefficien

t

Velocity

Pressure

Windward

Pressure

eeward

Pressure

!ide Wall

Pressure

Windward

Force

eeward

Force

!ideWall

Force

" # w $# %# p p p f f f PW& PW' P& P' FW& FW' F& F' F& F'

ine

oad

&'

ft ft psf psf psf psf l* l* l* psf psf psf psf l* l* l* l* l* l* +ipsft

, , -./ - 01 02 314 30. .50/6 32/51. 346056 02 02 314 314 .50/6 .50/6 32/51. 32/51. -45,12 -45,12 --

- -0 -.. - 01 02 314 30. .5104 32/2-2 3/4604 02 02 314 314 .5104 .5104 32/2-2 32/2-2 -4264/ -4264/ --

1 15 -.. - 05 0. 314 30. /4/-/ 32/4,0 3/4604 0. 0. 314 314 /4/-/ /4/-/ 32/4,0 32/4,0 -2401- -2401- -1

0 4, -.. - 0. 4- 314 30. -,-550 32/1/, 3/4604 4- 4- 314 314 -,-550 -,-550 32/1/, 32/1/, -5,/20 -5,/20 - 1

4 20 -.6 - 4, 40 314 30. -,5566 32/-66 3/4604 40 40 314 314 -,5566 -,5566 32/-66 32/-66 -52.24 -52.24 - 0

2 55 -.6 - 41 42 314 30. --,5.2 32/,52 3/4604 42 42 314 314 --,5.2 --,5.2 32/,52 32/,52 -5/62, -5/62, - 0

5 6/ -.5 - 40 45 314 30. --4,04 32./21 3/4604 45 45 314 314 --4,04 --4,04 32./21 32./21 -61/.5 -61/.5 - 0

6 /1 -.5 - 44 4. 314 30. --5/-, 32..4, 3/4604 4. 4. 314 314 --5/-, --5/-, 32..4, 32..4, -6264/ -6264/ - 0. -,2 -.5 - 42 4/ 314 30. --/415 32.616 3/4604 4/ 4/ 314 314 --/415 --/415 32.616 32.616 -6.-20 -6.-20 - 4

/ --/ -.2 - 45 2, 314 30. -1-552 32.5-2 3/4604 2, 2, 314 314 -1-552 -1-552 32.5-2 32.5-2 -.,16/ -.,16/ - 4

-, -01 -.2 1 46 2- 314 30. -10566 32.2,1 3/4604 2- 2- 314 314 -10566 -10566 32.2,1 32.2,1 -.1-6/ -.1-6/ -4

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

-05 -6/- -,, 1 50 5. 314 30. ./066 30-5-6 35,165 5. 5. 314 314 ./066 ./066 30-5-6 30-5-6 -1,//4 -1,//4 /

-06 -.,4 /6 1 50 5. 314 30. .50/. 30,250 35,165 5. 5. 314 314 .50/. .50/. 30,250 30,250 --5/5- --5/5- /

-0. -.-6 /0 1 50 5. 314 30. .041, 31/2,/ 35,165 5. 5. 314 314 .041, .041, 31/2,/ 31/2,/ --1/1/ --1/1/ /

-0/ -.0, /, 1 50 5. 314 30. .,44- 31.422 35,165 5. 5. 314 314 .,44- .,44- 31.422 31.422 -,../5 -,../5 .

-4, -.40 .6 1 50 5. 314 30. 66451 3164,1 35,165 5. 5. 314 314 66451 66451 3164,1 3164,1 -,4.50 -,4.50 .

-4- -.26 .0 1 50 5. 314 30. 644.0 31504. 35,165 5. 5. 314 314 644.0 644.0 31504. 31504. -,,.0- -,,.0- .

-41 -.6, ., 1 50 5. 314 30. 6-2,4 3121/4 35,165 5. 5. 314 314 6-2,4 6-2,4 3121/4 3121/4 /56/. /56/. 6

-40 -..0 66 1 50 5. 314 30. 5.212 31414, 35,165 5. 5. 314 314 5.212 5.212 31414, 31414, /1652 /1652 6

-44 -./5 60 1 50 5. 314 30. 52245 310-.6 35,165 5. 5. 314 314 52245 52245 310-.6 310-.6 ..600 ..600 6

-42 -/,/ 6, 1 50 5. 314 30. 51250 311-0- 35,165 5. 5. 314 314 51250 51250 311-0- 311-0- .45/4 .45/4 5

8esign Wind oad

Case - 8esign Wind oad Case -



2.2.1 ASCE 7 Wind Load CalculationsC-15


Floor

(relative

to

ground)

" 962PW& 962PW' 9 62P& 9 62P' :; 962FW& 962FW' 962F& 962F' :; 962F& 962F' 962PW& 962PW' 962P& 962P' 962FW& 962FW' 962F& 962F' 962F& 962F'

psf psf psf psf +3ftft l* l* l* l* +3ft l* l* psf psf psf psf l* l* l* l* l* l*

, 15 15 3-. 3-. 01 546/. 546/. 34461- 34461- 6/.2/ -,/2-/ -,/2-/ 15 15 3-. 3-. 546/. 546/. 34461- 34461- -,/2-/ -,/2-/

- 15 15 3-. 3-. 01 54562 54562 344505 344505 6/6,/ -,/0-1 -,/0-1 15 15 3-. 3-. 54562 54562 344505 344505 -,/0-1 -,/0-1

1 1/ 1/ 3-. 3-. 40 6--./ 6--./ 344221 344221 -,2/24 --264- --264- 1/ 1/ 3-. 3-. 6--./ 6--./ 344221 344221 --264- --264-

0 0- 0- 3-. 3-. 2- 65146 65146 34445. 34445. -154-, -1,6-2 -1,6-2 0- 0- 3-. 3-. 65146 65146 34445. 34445. -1,6-2 -1,6-2

4 01 01 3-. 3-. 2. .,,,. .,,,. 3440.0 3440.0 -4-6,4 -140/- -140/- 01 01 3-. 3-. .,,,. .,,,. 3440.0 3440.0 -140/- -140/-

2 04 04 3-. 3-. 50 .0,-4 .0,-4 3441// 3441// -20//6 -160-1 -160-1 04 04 3-. 3-. .0,-4 .0,-4 3441// 3441// -160-1 -160-1

5 02 02 3-. 3-. 56 .2215 .2215 3441-4 3441-4 -54014 -1/64, -1/64, 02 02 3-. 3-. .2215 .2215 3441-4 3441-4 -1/64, -1/64,

6 05 05 3-. 3-. 6- .65.1 .65.1 344-0, 344-0, -6010. -0-.-1 -0-.-1 05 05 3-. 3-. .65.1 .65.1 344-0, 344-0, -0-.-1 -0-.-1. 06 06 3-. 3-. 64 ./25/ ./25/ 344,42 344,42 -.-,.- -005-2 -005-2 06 06 3-. 3-. ./25/ ./25/ 344,42 344,42 -005-2 -005-2

/ 06 06 3-. 3-. 66 /-14. /-14. 340/5- 340/5- -..,/2 -021,/ -021,/ 06 06 3-. 3-. /-14. /-14. 340/5- 340/5- -021,/ -021,/

-, 0. 0. 3-. 3-. ., /162. /162. 340.65 340.65 -/4404 -05504 -05504 0. 0. 3-. 3-. /162. /162. 340.65 340.65 -05504 -05504

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

-05 2- 2- 3-. 3-. /1 56,00 56,00 3106-1 3106-1 -1-2-5 /,642 /,642 2- 2- 3-. 3-. 56,00 56,00 3106-1 3106-1 /,642 /,642

-06 2- 2- 3-. 3-. /1 546// 546// 311/11 311/11 --6455 .661- .661- 2- 2- 3-. 3-. 546// 546// 311/11 311/11 .661- .661-

-0. 2- 2- 3-. 3-. .0 51252 51252 311-01 311-01 -,100, .45/6 .45/6 2- 2- 3-. 3-. 51252 51252 311-01 311-01 .45/6 .45/6

-0/ 2- 2- 3-. 3-. .0 5,00- 5,00- 31-041 31-041 /.565 .-561 .-561 2- 2- 3-. 3-. 5,00- 5,00- 31-041 31-041 .-561 .-561

-4, 2- 2- 3-. 3-. .0 2.,/5 2.,/5 31,22- 31,22- /2,11 6.54. 6.54. 2- 2- 3-. 3-. 2.,/5 2.,/5 31,22- 31,22- 6.54. 6.54.

-4- 2- 2- 3-. 3-. .0 22.51 22.51 3-/65- 3-/65- /-05. 62510 62510 2- 2- 3-. 3-. 22.51 22.51 3-/65- 3-/65- 62510 62510

-41 2- 2- 3-. 3-. .0 2051. 2051. 3-./6- 3-./6- .66-4 612// 612// 2- 2- 3-. 3-. 2051. 2051. 3-./6- 3-./6- 612// 612//

-40 2- 2- 3-. 3-. .0 2-0/4 2-0/4 3-.-., 3-.-., .4,2/ 5/264 5/264 2- 2- 3-. 3-. 2-0/4 2-0/4 3-.-., 3-.-., 5/264 5/264

-44 2- 2- 3-. 3-. .0 4/-5, 4/-5, 3-60/, 3-60/, .,4,2 5522, 5522, 2- 2- 3-. 3-. 4/-5, 4/-5, 3-60/, 3-60/, 5522, 5522,

-42 2- 2- 3-. 3-. -0- 45/11 45/11 3-52/. 3-52/. -1,5-. 5021- 5021- 2- 2- 3-. 3-. 45/11 45/11 3-52/. 3-52/. 5021- 5021-

8esign Wind oad Case 1 8esign Wind oad Case 1 8esign Wind oad Case 0 8esign Wind oad Case 0



2.2.1 ASCE 7 Wind Load Calculations C-16


Floor

(relative

to

ground)

" 9250PW& 9250PW' 9250P& 9250P' :; 9250FW& 9250FW' 9250F& 9250F' :; F& F'

psf psf psf psf +3ftft l* l* l* l* l* l* l*

, 1, 1, 3-4 3-4 4. 4.54- 4.54- 30026, 30026, --/./5 .11-1 .11-1

- 1, 1, 3-4 3-4 4. 4.22, 4.22, 3002,6 3002,6 --/55/ .1,26 .1,26

1 11 11 3-4 3-4 54 2040/ 2040/ 300444 300444 -2/,60 .5..0 .5..0

0 10 10 3-4 3-4 66 26105 26105 3000., 3000., -./6.0 /,5-6 /,5-6

4 14 14 3-4 3-4 .5 5,,2/ 5,,2/ 3000-6 3000-6 1-1644 /0065 /0065

2 12 12 3-4 3-4 /4 510-5 510-5 300124 300124 10-1,, /225/ /225/

5 15 15 3-4 3-4 -,- 541,- 541,- 300-/, 300-/, 1456,2 /60/- /60/-

6 16 16 3-4 3-4 -,5 52.1, 52.1, 300-16 300-16 15,,.. /./46 /./46. 1. 1. 3-4 3-4 --- 56106 56106 300,50 300,50 16-.50 -,,0,, -,,0,,

/ 1. 1. 3-4 3-4 --5 5.4/6 5.4/6 300,,, 300,,, 1.10/0 -,-4/6 -,-4/6

-, 1/ 1/ 3-4 3-4 -1, 5/50, 5/50, 301/06 301/06 1/-/-- -,1256 -,1256

7 7 7 7 7 7 7 7 7 7 7 7 7

-05 0. 0. 3-4 3-4 -0/ 2,0-/ 2,0-/ 3-6.,, 3-6.,, -.1405 5.-1, 5.-1,

-06 0. 0. 3-4 3-4 -0/ 4.541 4.541 3-61,6 3-61,6 -65025 52.4/ 52.4/

-0. 0. 0. 3-4 3-4 -0/ 45/52 45/52 3-55-4 3-55-4 -6,162 5026/ 5026/

-0/ 0. 0. 3-4 3-4 -12 421.. 421.. 3-5,1, 3-5,1, -4.-45 5-0,. 5-0,.

-4, 0. 0. 3-4 3-4 -12 405-- 405-- 3-2416 3-2416 -4155, 2/,0. 2/,0.

-4- 0. 0. 3-4 3-4 -12 4-/04 4-/04 3-4.04 3-4.04 -06-60 2565. 2565.

-41 0. 0. 3-4 3-4 -12 4,126 4,126 3-414- 3-414- -0-5.6 244/6 244/6

-40 0. 0. 3-4 3-4 -12 0.2., 0.2., 3-0546 3-0546 -151,- 21116 21116

-44 0. 0. 3-4 3-4 -12 05/,0 05/,0 3-0,24 3-0,24 -1,6-2 4//26 4//26

-42 0. 0. 3-4 3-4 -12 02110 02110 3-145, 3-145, --211- 465.0 465.0

8esign Wind oad Case 4 8esign Wind oad Case 4



2.2.1 ASCE 7 Wind Load CalculationsC-17

Case 1 Loads (lb) Case 2 Loads (lb) Case 3 Loads (lb)

02 1 44 / 0 21 4 4/ 31 40 1 45 31 40 14 5 154005 154005 3-.1402 3-.1402 0126., 154005 154005 3-.1402 3-.1402

6,4/, 6,4/, 34.54/ 34.54/ 21.56 21.56 3054.6 3054.6 52-25 21.56 21.56 3054.6 3054.6

66605 66605 34.54/ 34.54/ 2.0,1 2.0,1 3054.6 3054.6 .5664 2.0,1 2.0,1 3054.6 3054.6

.04-. .04-. 34.54/ 34.54/ 51250 51250 3054.6 3054.6 -,0610 51250 51250 3054.6 3054.6

.65/. .65/. 34.54/ 34.54/ 52664 52664 3054.6 3054.6 --54/0 52664 52664 3054.6 3054.6

/--56 /--56 34.54/ 34.54/ 5.062 5.062 3054.6 3054.6 -15.4- 5.062 5.062 3054.6 3054.6

/4-,4 /4-,4 34.54/ 34.54/ 6,26. 6,26. 3054.6 3054.6 -025,2 6,26. 6,26. 3054.6 3054.6

/5551 /5551 34.54/ 34.54/ 614/6 614/6 3054.6 3054.6 -40102 614/6 614/6 3054.6 3054.6

/./01 /./01 34.54/ 34.54/ 64-// 64-// 3054.6 3054.6 -2,,,5 64-// 64-// 3054.6 3054.6

-, , /. , - ,, / ., 34 . 54 / 3 4. 5 4/ 62602 62602 3054.6 3054.6 -25--5 62602 62602 3054.6 3054.6

-,1.4. -,1.4. 34.54/ 34.54/ 66-05 66-05 3054.6 3054.6 -5-5.. 66-05 66-05 3054.6 3054.6

-, 4 25 5 - ,4 2 55 34 . 54 / 3 4. 5 4/ 6.414 6.414 3054.6 3054.6 -55.-4 6.414 6.414 3054.6 3054.6

-,5-5- -,5-5- 34.54/ 34.54/ 6/51, 6/51, 3054.6 3054.6 -6-261 6/51, 6/51, 3054.6 3054.6

,

1,,

4,,

5,,

.,,

-,,,

-1,,

-4,,

-5,,

-.,,

1,,,

, 02 6,

V e l o c i t y P r e s s u r e q

! " s # $

%ie&ht !#t$

Velocity Pressure 's( %ei&ht

,

1,,

4,,

5,,

.,,

-,,,

-1,,

-4,,

-5,,

-.,,

1,,,

, 22 --,

W i n d P r e s s u r e " ! " s # $

%ei&ht !#t$

Wind Pressure 's( %ei&ht

-, 6 54 / - ,6 5 4/ 34 . 54 / 3 4. 5 4/ .,606 .,606 3054.6 3054.6 -65,-1 .,606 .,606 3054.6 3054.6

-,/,42 -,/,42 34.54/ 34.54/ .-6.4 .-6.4 3054.6 3054.6 -.,-65 .-6.4 .-6.4 3054.6 3054.6

22-.- 22-.- 314012 314012 4-0.5 4-0.5 3-.140 3-.140 /1,21 4-0.5 4-0.5 3-.140 3-.140

-60/ -60/ 3/4/ 3/4/ -0,4 -0,4 36-- 36-- 102. -0,4 -0,4 36-- 36--

$ips $ips $ips $ips $ips $ips $ips $ips $ips $ips $ips $ips $ips

-60/,.4 -60/,.4 3/4.55, 3/4.55,-0,40-0 -0,40-0 36--4/2 36--4/2-0,40-0 36--4/2 36--4/2 102.,41 -0,40-0

2.2.1 ASCE 7 Wind Load Calculations C-18

2.2.2 Wind Tunnel Data Created by: 3/10/2012

Values obtined from RWDI wind tunnel test data file. Values represent 100 year return period.

Key

Raw Data from RWDI Wind unnel est

Cal!ulated Criti!al "oment and Criti!al #or!e from RWDI $oad Combinations

%d&usted 'alues to remo'e spi(es in Wind unnel Data

) * +,0-0 (sf

Load Combinations

1 3 , + 11 13 1 1 ,

+0 +0 100 100 30 30 0 30 30

30 30 30 30 + 100 + 100 0

1 3 , + 11 13 1 1, 1+ 20 21 23 2

1 ase 1-4+-2 0 2-,00 1+-400 -000 +.1 0.00 0.00 2,. 2.4 2.4 2 ,. 2 ,. 20. 21. 21. 21. 12., 1.+ 1.0 21.2 23.+ 23.3

2 $V2 1-4+-2 13 3-300 3+-,00 +-000 +.24 0.01 0.01 . +. +. . . 1.0 2.4 3.3 2.4 2. 33.4 32.1 2.3 ,., .

3 $V3 1-4+-2 2 3-100 3+-00 102-000 +.1 0.02 0.02 . +.2 +.2 . . 0.+ 2., 3.2 2., 2. 33., 32.0 2.1 ,. .

$V 1-4+-2 0 3-100 3+-,00 10+-000 +.0 0.03 0.0 . +.3 +.3 . . 0.+ 2.4 3.3 2.4 2. 33.4 32.0 2.1 ,. .

$V 1-4+-2 3 3-200 0-100 1-000 4.+2 0.0 0.04 . +. +. . . 1.3 3.2 3. 3.2 2. 3.0 32.3 2.3 ,.+ .

$V 1-4+-2 3-100 0-000 1+-000 4.40 0.0 0.13 . +.3 +.3 . . 1.2 3.1 3. 3.1 2. 3.0 32.2 2.2 ,.4 .

, $V, 1-4+-2 ,+ 2-+00 0-200 212-000 4.4 0.0 0.14 .3 +.1 +.1 .3 .3 1. 3.2 3., 3.2 2. 3.1 32.3 2.1 ,.4 .

4 $V4 1-4+-2 +2 3-000 0-00 233-000 4. 0.0 0.2 . +.2 +.2 . . 1., 3. .0 3. 2.4 3. 32. 2.3 4.0 .,

+ $V+ 1-4+-2 10 2-+00 0-00 23+-000 4. 0.0, 0.32 .3 +.1 +.1 .3 .3 1. 3. 3.+ 3. 2., 3.3 32. 2.2 ,.+ .

10 $V10 1-4+-2 11+ 2-400 0-00 20-000 4.33 0.04 0.0 .2 +.0 +.0 .2 .2 1. 3. 3.+ 3. 2., 3.3 32. 2.1 ,.4 .

11 $V11 1-4+-2 132 2-,00 0-,00 22-000 4.21 0.0+ 0.+ .1 +.0 +.0 .1 .1 1.4 3., .0 3., 2.4 3. 32. 2.1 ,.+ .

12 $V12 1-4+-2 1 2-400 0-400 2-000 4.10 0.10 0.+ .2 +.1 +.1 .2 .2 1.+ 3.4 .1 3.4 2.4 3. 32., 2.2 4.0 .,

13 $V13 1-4+-2 14 3-000 1-200 2,-000 ,.+4 0.10 0.+ . +.3 +.3 . . 2.2 .2 . .2 2.0 3.4 32.+ 2. 4.3 ,.0

1 $V1 1-4+-2 1,1 3-000 1-300 24,-000 ,.4, 0.11 0.40 . +.3 +.3 . . 2.3 .3 . .3 2.1 3.4 33.0 2. 4.3 ,.0

1 $V1 1-4+-2 14 3-000 1-,00 2+4-000 ,., 0.12 0.+2 . +.3 +.3 . . 2., . .+ . 2.2 3.1 33.2 2. 4. ,.2

1 $V1 1-4+-2 1+4 3-200 1-+00 30-000 ,. 0.13 1.0 ., +. +. ., ., 2.+ .4 .1 .4 2.3 3.2 33. 2., 4., ,.

1, $V1, 1-4+-2 211 3-200 2-200 31-000 ,.3 0.13 1.14 ., +. +. ., ., 3.2 .1 . .1 2. 3. 33. 2.4 4.+ ,.

5$-C5-5%C-D$

#loor $e'el

6 #or!es #7

Wind Tunnel Forces

8 #or!es #y

1+

30

,

9

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2= ;(ips=

for ea!> load !ase"oment of

Inertia ;ft=

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$e'el $V1 ;ft= #or!e #7 ;lb= #or!e #y ;lb=

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,0

30

2

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,0

20 21

,0

0 ,

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23

14 $V14 1-4+-2 22 3-00 2-300 32-000 ,.2 0.1 1.32 .+ +., +., .+ .+ 3.3 .2 . .2 2. 3. 33., 2.+ +.0 ,.,

1+ $V1+ 1-4+-2 23, 3-00 2-,00 33-000 ,.31 0.1 1., .+ +., +., .+ .+ 3. . .4 . 2., 3.4 33.+ 3.0 +.2 ,.+

20 $V20 1-4+-2 20 3-00 3-100 3-000 ,.20 0.1 1.2 .1 +.+ +.+ .1 .1 .0 .0 .2 .0 2.+ 3.1 3.2 3.3 +. 4.1

21 $V21 1-4+-2 23 3-00 3-00 3-000 ,.0+ 0.1 1.,4 .2 0.0 0.0 .2 .2 .3 .3 . .3 2,.0 3.3 3. 3.3 +., 4.3

22 $V22 1-4+-2 2,, 3-400 3-00 3-000 .+4 0.1 1.+ . 0.2 0.2 . . . . ., . 2,.1 3. 3. 3. +.+ 4.

23 $V23 1-4+-2 2+0 -000 3-+00 3,2-000 .44 0.1, 2.11 . 0. 0. . . ., .4 ,.0 .4 2,.3 3., 3., 3., 0.1 4.,

2 $V2 1-4+-2 303 -200 -300 341-000 .,, 0.1, 2.24 .4 0. 0. .4 .4 .1 ,.2 ,.3 ,.2 2,. 3,.0 3.0 3.+ 0. +.0

2.2.2 Wind Tunnel DataC-19

1 3 , + 11 13 1 1, 1+ 20 21 23 22 $V2 1-4+-2 31 -00 -,00 3+2-000 . 0.14 2. .0 0.4 0.4 .0 .0 . ,. ,., ,. 2,., 3,.3 3.3 .2 0., +.3

2 $V2 1-4+-2 32+ -00 -000 3++-000 . 0.14 2. .1 0.4 0.4 .1 .1 .4 ,.+ 4.0 ,.+ 2,.4 3,. 3. .2 0.+ +.

2, $V2, 1-4+-2 32 -00 -00 11-000 . 0.1+ 2.43 .3 1.0 1.0 .3 .3 .1 4.3 4.3 4.3 24.0 3,.4 3.4 . 1.2 +.,

24 $V24 1-4+-2 3 -400 -,00 14-000 .3 0.1+ 3.02 . 1.2 1.2 . . . 4. 4. 4. 24.1 34.0 3.0 . 1. +.+

2+ $V2+ 1-4+-2 3+ -000 -100 2,-000 .2 0.20 3.22 ., 1. 1. ., ., .4 +.0 +.0 +.0 24.3 34.3 3.2 .+ 1., 0.2

30 $V30 1-4+-2 342 -200 -00 33-000 .1 0.20 3.2 .+ 1. 1. .+ .+ ,.1 +.3 +.3 +.3 24. 34. 3. .1 2.0 0.

31 $V31 1-4+-2 3+ -00 -400 3-000 .0 0.20 3.2 ,.2 1.4 1.4 ,.2 ,.2 ,. +., +., +., 24., 34.4 3., .3 2.3 0.4

32 $V32 1-4+-2 04 -00 ,-100 1-000 .+ 0.21 3.43 ,. 2.0 2.0 ,. ,. ,.4 0.0 0.0 0.0 24.+ 3+.1 3.+ . 2. 1.0

33 $V33 1-4+-2 21 -400 ,-,00 4-000 .4 0.21 .0 ,. 2.2 2.2 ,. ,. 4.3 0. 0. 0. 2+.1 3+. 3,. .4 3.0 1.

3 $V3 1-4+-2 3 -000 4-000 ,-000 ., 0.21 .2 ,.4 2. 2. ,.4 ,.4 4. 0.+ 0.4 0.+ 2+.3 3+., 3,. .0 3.2 1.

3 $V3 1-4+-2 4 -300 4-300 ,-000 . 0.22 ., 4.1 2., 2., 4.1 4.1 4.+ 1.2 1.1 1.2 2+. 0.0 3,.4 .2 3. 1.+

3 $V3 1-4+-2 1 -00 4-,00 4-000 . 0.22 .4 4. 3.0 3.0 4. 4. +.3 1. 1. 1. 2+., 0.3 34.1 . 3.+ 2.3

3, $V3, 1-4+-2 , -400 +-000 +1-000 . 0.22 .+1 4., 3.2 3.2 4., 4., +. 1.+ 1.4 1.+ 2+.4 0. 34.3 ., .1 2.

34 $V34 1-4+-2 4, -400 +-000 ,+-000 .3 0.22 .13 4., 3.2 3.2 4., 4., +. 1.+ 1.4 1.+ 2+.4 0. 34.3 ., .1 2.

3+ $V3+ 1-4+-2 00 -400 +-000 ,0-000 .2 0.22 .3 4., 3.2 3.2 4., 4., +. 1.+ 1.4 1.+ 2+.4 0. 34.3 ., .1 2.0 $V0 1-4+-2 1 -400 +-000 ,0-000 .1 0.23 .4 4., 3.2 3.2 4., 4., +. 1.+ 1.4 1.+ 2+.4 0. 34.3 ., .1 2.

1 $V1 1-3+3-,11 2, -400 4-00 3,-000 .0, 0.31 .4+ ,., 2.3 2.3 ,., ,., +.1 1. 1.3 1. 2+. 0.1 3,.+ .0 3. 1.4

2 $V2 1-3+3-,11 0 -100 +-100 2-000 .+4 0.31 .20 4.0 2. 2. 4.0 4.0 +. 1.+ 1.4 1.+ 2+.4 0. 34.3 .3 3.4 2.2

3 $V3 1-3+3-,11 3 -200 +-300 ,-000 .44 0.31 .2 4.1 2., 2., 4.1 4.1 +.4 2.1 2.0 2.1 2+.+ 0. 34. . .0 2.3

$V 1-3+3-,11 -00 +-,00 3-000 .,+ 0.32 .4 4. 3.0 3.0 4. 4. 0.2 2. 2.3 2. 30.1 0.+ 34., ., .3 2.,

$V 1-3+3-,11 ,+ -00 +-+00 ,-000 .,0 0.32 ,.1 4. 3.1 3.1 4. 4. 0. 2., 2. 2., 30.2 1.1 34.4 .4 . 2.4

$V 1-3+3-,11 +3 -+00 0-00 -000 .1 0.32 ,., 4.+ 3. 3. 4.+ 4.+ 0.+ 3.3 3.1 3.3 30. 1. 3+.3 ,.2 .0 3.3

, $V, 1-3+3-,11 0 ,-200 0-400 ,-000 .2 0.32 ,.,+ +.2 3., 3., +.2 +.2 1.2 3. 3. 3. 30., 1.4 3+. ,. .3 3.

4 $V4 1-3+3-,11 1+ ,-00 1-300 ,3-000 .3 0.32 4.11 +. .0 .0 +. +. 1., .1 3.+ .1 30.+ 2.2 3+.4 ,., ., 3.+

+ $V+ 1-3+3-,11 32 ,-400 1-400 ,,-000 .3 0.32 4.3 +.+ .3 .3 +.+ +.+ 2.2 . . . 31.2 2. 0.2 4.0 .1 .3

0 $V0 1-3+3-,11 4-000 2-200 40-000 .2 0.32 4., 0.1 . . 0.1 0.1 2. .0 ., .0 31. 2.4 0. 4.3 . .

1 $V1 1-3+3-,11 4 4-300 2-00 4-000 .1, 0.32 +.0, 0. .4 .4 0. 0. 2.+ . .1 . 31. 3.2 0.4 4. .4 .0

2 $V2 1-3+3-,11 ,2 4-00 3-100 4,-000 .0+ 0.32 +.3+ 0., .1 .1 0., 0., 3. .+ . .+ 31.4 3. 1.1 4.+ ,.2 .

3 $V3 1-3+3-,11 4 4-400 3-00 +0-000 .00 0.32 +.,1 1.0 .3 .3 1.0 1.0 3.+ . .1 . 32.1 3.+ 1. +.1 ,. .,

$V 1-3+3-,11 +4 +-000 -000 +2-000 3.+2 0.32 10.03 1.2 . . 1.2 1.2 .3 .4 . .4 32.3 .2 1., +.3 ,.4 .0 $V 1-3+3-,11 ,11 +-00 -00 +4-000 3.4 0.32 10.3 1. .+ .+ 1. 1. .4 ,.3 ,.0 ,.3 32. . 2.1 +., 4.3 .

$V 1-3+3-,11 ,2 +-400 -+00 02-000 3., 0.32 10., 2.0 .3 .3 2.0 2.0 .2 ,.4 ,. ,.4 32.4 .+ 2. 0.1 4., .4

, $V, 1-3+3-,11 ,3, 0-000 -00 03-000 3., 0.32 10.++ 2.3 . . 2.3 2.3 ., 4.3 ,.+ 4.3 33.1 . 2.4 0.3 +.1 ,.2

4 $V4 1-3+3-,11 ,1 0-300 -+00 0-000 3.+ 0.32 11.30 2. .4 .4 2. 2. .1 4.4 4.3 4.4 33.3 ., 3.1 0. +. ,.

+ $V+ 1-3+3-,11 , 0-,00 -300 0+-000 3.1 0.31 11.2 3.0 ,.2 ,.2 3.0 3.0 . +.2 4., +.2 33. .0 3. 1.0 +.+ 4.0

0 $V0 1 3+3 ,11 ,,, 1 000 +00 1 000 3 3 0 31 11 +3 3 3 , , 3 3 3 3 , 1 + 4 + 3 + 4 33 4 3 4 1 3 0 4

Criti!al #or!e

;(ips=


2= ;(ips=

for ea!> load !ase#or!e #y ;lb= orsion "A

;lbft=

Criti!al

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ft )<=

InterBtory

Drift ;in=

otal Drift

;in=#loor $e'el

"oment of

Inertia ;ft=

?ei@>t %bo'e

$e'el $V1 ;ft= #or!e #7 ;lb=

0 $V0 1-3+3-,11 ,,, 1-000 -+00 1-000 3.3 0.31 11.+3 3.3 ,. ,. 3.3 3.3 ,.1 +.4 +.3 +.4 33.4 . 3.4 1.3 0. 4.

1 $V1 1-3+3-,11 ,+0 1-100 ,-200 13-000 3.3 0.31 12.2 3. ,. ,. 3. 3. ,.3 0.1 +. 0.1 3.0 ., .0 1. 0. 4.

2 $V2 1-3+3-,11 403 1-00 ,-400 1-000 3.24 0.31 12. 3.+ 4.0 4.0 3.+ 3.+ ,.+ 0., 0.2 0., 3.3 ,.1 . 1.+ 1.1 +.1

3 $V3 1-3+3-,11 41 1-,00 4-100 14-000 3.20 0.31 12.4 .1 4.2 4.2 .1 .1 4.2 1.0 0. 1.0 3. ,.3 ., 2.1 1. +.3

$V 1-3+3-,11 430 2-,00 +-00 3+-000 3.13 0.30 13.1 .2 +.2 +.2 .2 .2 +. 2.3 1.4 2.3 3.2 4. . 3.0 2. 0.

$V 1-3+3-,11 43 3-000 +-400 -000 3.0 0.30 13. . +. +. . . +.+ 2., 2.1 2., 3. 4., .+ 3.3 2.+ 0.4

$V 1-3+3-,11 4 3-00 0-00 -000 2.+4 0.30 13., .+ +.+ +.+ .+ .+ 0. 3.3 2., 3.3 3., +.1 . 3., 3. 1.3

2.2.2 Wind Tunnel Data C-20

1 3 , + 11 13 1 1, 1+ 20 21 23 2, $V, 1-3+3-,11 4+ 3-000 0-100 2+-000 2.+1 0.30 1.0 . +. +. . . 0.1 3.0 2. 3.0 3. 4.+ .1 3. 3.1 0.+

4 $V4 1-3+3-,11 442 3-00 0-,00 3-000 2.43 0.2+ 1.3 .1 0.0 0.0 .1 .1 0., 3. 3.0 3. 3.4 +. . 3.4 3. 1.

+ $V+ 1-3+3-,11 4+ 3-400 1-200 3-000 2., 0.2+ 1. . 0.3 0.3 . . 1.2 .1 3. .1 3.1 +., .+ .1 .0 1.+

,0 $V,0 1-3+3-,11 +0+ -100 1-00 34-000 2.+ 0.2+ 1.+3 ., 0. 0. ., ., 1. . 3.+ . 3.3 0.0 ,.2 . . 2.2

,1 $V,1 1-3+3-,11 +22 -200 1-+00 34-000 2.2 0.24 1.22 .4 0., 0., .4 .4 1.+ .4 .2 .4 3. 0.3 ,. . . 2.

,2 $V,2 1-3+3-,11 +3 -200 2-000 20-000 2. 0.24 1.0 .4 0., 0., .4 .4 2.0 .+ .3 .+ 3. 0.3 ,. . ., 2.

,3 $V,3 1-3+3-,11 +4 -200 2-000 20-000 2.+ 0.24 1.,, .4 0., 0., .4 .4 2.0 .+ .3 .+ 3. 0.3 ,. . ., 2.

, $V, 1-3+3-,11 +1 -200 2-000 20-000 2.2 0.2, 1.0 .4 0., 0., .4 .4 2.0 .+ .3 .+ 3. 0.3 ,. . ., 2.

, $V, 41-004 +, 0-+00 4-00 3++-000 2.3 0. 1.1 3. ,. ,. 3. 3. 4. 1. 0.4 1. 3. ,. .+ 1., 1.2 +.2

, $V, 41-004 +44 1-100 4-+00 02-000 2.2+ 0. 1.+ 3. ,.4 ,.4 3. 3. 4.+ 1., 1.1 1., 3., ,.4 .1 1.+ 1. +.

,, $V,, 41-004 1-001 1-200 +-200 00-000 2.23 0. 1,.1 3., ,.+ ,.+ 3., 3., +.2 2.0 1.3 2.0 3.4 4.0 .3 2.1 1., +.

,4 $V,4 41-004 1-01 1-00 +-00 03-000 2.1 0. 1,.4 .0 4.2 4.2 .0 .0 +. 2. 1., 2. 3.0 4. . 2. 2.1 +.+

,+ $V,+ 41-004 1-02, 2-000 0-200 0-000 2.10 0.3 14.2+ . 4. 4. . . 0.1 3.0 2.3 3.0 3. 4.4 .1 2.4 2. 0.

40 $V40 41-004 1-00 2-000 0-200 00-000 1.++ 0., 1+.03 . 4. 4. . . 0.1 3.0 2.3 3.0 3. 4.4 .1 2.4 2. 0.

41 $V41 41-004 1-03 2-100 0-00 3++-000 1.+4 0.10 1+.13 ., 4.4 4.4 ., ., 0.3 3.2 2. 3.2 3. +.0 .2 2.+ 2.4 0.42 $V42 41-004 1-0, 2-00 0-+00 3++-000 1.+2 0.1 1+. .1 +.1 +.1 .1 .1 0.4 3., 3.0 3., 3.4 +. . 3.3 3.2 1.1

43 $V43 41-004 1-040 2-400 1-200 3++-000 1.4 0.0 1+.+ . +. +. . . 1.1 .0 3.3 .0 3.+ +. .4 3. 3. 1.

4 $V4 41-004 1-0+3 3-200 1-,00 02-000 1.40 0.0 20.3 .+ +.4 +.4 .+ .+ 1. . 3.4 . 3.2 0.0 ,.2 3.+ .0 1.4

4 $V4 41-004 1-10 3-300 1-400 3+4-000 1., 0.3+ 20., .0 +.+ +.+ .0 .0 1., ., 3.+ ., 3.3 0.1 ,.2 .0 .1 1.+

4 $V4 41-004 1-11+ 3-400 2-00 01-000 1.+ 0.34 21.12 . 0. 0. . . 2.3 .3 . .3 3. 0. ,., . ., 2.

4, $V4, 41-004 1-132 -200 2-+00 03-000 1.3 0.3, 21.+ .+ 0.4 0.4 .+ .+ 2.4 .4 .0 .4 3.+ 1.0 4.1 .+ .2 2.+

44 $V44 41-004 1-1 -00 3-200 00-000 1.4 0.3 21.4 ,.1 1.0 1.0 ,.1 ,.1 3.1 .1 .3 .1 3,.0 1.2 4.3 .1 . 3.2

4+ $V4+ 41-004 1-1+ -400 3-00 01-000 1.2 0.3 22.21 ,. 1. 1. ,. ,. 3. . ., . 3,.3 1. 4. . .4 3.

+0 $V+0 41-004 1-1,2 -400 3-00 3+-000 1., 0.3 22. ,. 1. 1. ,. ,. 3. . ., . 3,.3 1. 4. . .4 3.

+1 $V+1 41-004 1-14 -00 -200 3+4-000 1.2 0.3 22.+0 4.2 1.+ 1.+ 4.2 4.2 .1 ,.1 . ,.1 3,. 2.0 +.0 .+ . .2

+2 $V+2 41-004 1-1+4 -400 -,00 01-000 1.3 0.33 23.23 4. 2.3 2.3 4. 4. . ,. .+ ,. 3,.+ 2. +. .3 .+ .

+3 $V+3 41-004 1-211 -100 -100 3++-000 1.31 0.32 23. 4.+ 2. 2. 4.+ 4.+ .+ 4.1 ,.3 4.1 34.1 2., +., . ,.3 .+

+ $V+ 41-004 1-22 -200 -300 3+-000 1.2, 0.31 23.4, +.0 2., 2., +.0 +.0 .1 4.3 ,. 4.3 34.2 2.4 +.4 ., ,. .1

+ $V+ 41-004 1-234 -00 -00 34+-000 1.22 0.31 2.1, +.3 2.+ 2.+ +.3 +.3 . 4. ,., 4. 34. 3.1 0.1 .+ ,., .3

+ $V+ 41-004 1-21 -,00 -000 344-000 1.1, 0.30 2., +. 3.2 3.2 +. +. .4 +.0 4.1 +.0 34. 3. 0.3 ,.2 4.0 .,+, $V+, 41-004 1-2 ,-000 -00 34-000 1.12 0.2+ 2., +.+ 3. 3. +.+ +.+ .2 +. 4. +. 34.4 3., 0. ,. 4. .0

+4 $V+4 41-004 1-2,, ,-00 -+00 34,-000 1.04 0.24 2.03 ,0. .0 .0 ,0. ,0. ., +.+ +.1 +.+ 3+.1 .1 1.0 ,.+ 4.+ .

++ $V++ 41-004 1-2+0 ,-,00 ,-300 34-000 1.03 0.2, 2.30 ,0. .2 .2 ,0. ,0. ,.1 ,0.3 +. ,0.3 3+.3 . 1.3 4.1 +.2 .4

100 $V100 41-004 1-30 4-200 ,-00 34-000 0.++ 0.2 2., ,1.2 . . ,1.2 ,1.2 ,. ,0. +.4 ,0. 3+. ., 1. 4. +. ,.2

101 $V101 41-004 1-31, 4-400 4-000 34-000 0.+ 0.2 2.42 ,1.4 .2 .2 ,1.4 ,1.4 ,.4 ,1.1 ,0.2 ,1.1 3+.4 .0 1.+ +.0 ,0.1 ,.,

102 $V102 41-004 1-330 +-000 4-100 342-000 0.+0 0.2 2.0 ,2.0 . . ,2.0 ,2.0 ,.+ ,1.2 ,0.3 ,1.2 3+.4 .1 2.0 +.1 ,0.3 ,.+

#loor $e'el"oment of

Inertia ;ft=

?ei@>t %bo'e


orsion "A

;lbft=

Criti!al

"oment ;(ip

ft )<=

InterBtory

Drift ;in=

otal Drift

;in=

Criti!al #or!e

;(ips=


2= ;(ips=

for ea!> load !ase

102 $V102 41-004 1-330 +-000 4-100 342-000 0.+0 0.2 2.0 ,2.0 . . ,2.0 ,2.0 ,.+ ,1.2 ,0.3 ,1.2 3+.4 .1 2.0 +.1 ,0.3 ,.+

103 $V103 41-004 1-33 +-400 4-00 34-000 0.4 0.2 2.30 ,2.4 .1 .1 ,2.4 ,2.4 4. ,1. ,0.4 ,1. 0.1 . 2.3 +., ,0.+ 4.

10 $V10 41-004 1-3 ,0-200 4-00 343-000 0.42 0.23 2.3 ,3.2 . . ,3.2 ,3.2 4. ,1.4 ,1.0 ,1.4 0.2 . 2. +.+ ,1.1 4.,

10 $V10 41-004 1-3+ ,0-,00 4-400 342-000 0.,4 0.22 2., ,3., .+ .+ ,3., ,3., 4., ,2.0 ,1.2 ,2.0 0. .4 2. 0.3 ,1. +.1

10 $V10 41-004 1-343 ,1-200 +-000 343-000 0., 0.21 2.+ ,.1 ,.3 ,.3 ,.1 ,.1 4.+ ,2.2 ,1. ,2.2 0. .0 2.4 0. ,1.4 +.

10, $V10, 41-004 1-3+ ,1-00 +-300 342-000 0.,1 0.20 2,.1 ,. ,., ,., ,. ,. +.3 ,2. ,1.4 ,2. 0.4 .2 3.1 0.+ ,2.2 +.4

104 $V104 41-004 1-0+ ,1-+00 +-00 340-000 0., 0.1+ 2,.3 ,.+ 4.0 4.0 ,.+ ,.+ +. ,2., ,1.+ ,2., 0.+ .3 3.2 1.1 ,2. ,0.0

2.2.2 Wind Tunnel DataC-21

1 3 , + 11 13 1 1, 1+ 20 21 23 210+ $V10+ 41-004 1-22 ,0-000 +-000 341-000 0. 0.14 2,.3 ,3.0 .3 .3 ,3.0 ,3.0 4.4 ,2.1 ,1.3 ,2.1 0. .4 2., +.+ ,1.3 4.4

110 $V110 41-004 1-3 ,0-000 +-000 341-000 0.0 0.14 2,.,1 ,3.0 .3 .3 ,3.0 ,3.0 4.4 ,2.1 ,1.3 ,2.1 0. .4 2., +.+ ,1.3 4.4

111 $V111 41-004 1-4 ,0-000 +-000 341-000 0., 0.1, 2,.44 ,3.0 .3 .3 ,3.0 ,3.0 4.4 ,2.1 ,1.3 ,2.1 0. .4 2., +.+ ,1.3 4.4

112 $V112 41-004 1-2 +-300 -+00 33,-000 0. 0.1 24.0 ,2.1 . . ,2.1 ,2.1 .+ ,0.1 +.3 ,0.1 3+. .3 1.2 4.+ +.4 ,.

113 $V113 24-43 1-, +-00 ,-200 333-000 0.1 0.0 24. ,2. ., ., ,2. ,2. ,.2 ,0. +. ,0. 3+. . 1. +.1 ,0.0 ,.,

11 $V11 24-43 1-44 +-400 ,-00 330-000 0., 0., 2+.02 ,2., .0 .0 ,2., ,2., ,. ,0.4 ,0.0 ,0.4 3+.4 .+ 1., +. ,0. 4.0

11 $V11 24-43 1-01 +-100 ,-000 322-000 0. 0. 2+., ,2.0 . . ,2.0 ,2.0 .+ ,0.1 +. ,0.1 3+. . 1.3 4.4 +., ,.

11 $V11 24-43 1-1 +-200 ,-000 31,-000 0.2 0.3 2+.4+ ,2.1 . . ,2.1 ,2.1 .+ ,0.1 +. ,0.1 3+. . 1.3 4.+ +.4 ,.

11, $V11, 24-43 1-2, ,0-000 ,-400 31-000 0.3+ 0.0 30.2+ ,2.+ .2 .2 ,2.+ ,2.+ ,., ,1.0 ,0.2 ,1.0 3+.+ .0 1.+ +. ,0. 4.2

114 $V114 24-43 1-1 ,0-00 4-300 312-000 0.3 0.34 30., ,3. ., ., ,3. ,3. 4.2 ,1. ,0., ,1. 0.2 . 2.3 0.0 ,1.1 4.,

11+ $V11+ 24-43 1- ,1-000 4-,00 310-000 0.3 0.3 31.02 ,3.+ ,.1 ,.1 ,3.+ ,3.+ 4., ,1.+ ,1.2 ,1.+ 0. .4 2. 0. ,1. +.2

120 $V120 24-43 1-, ,1-100 4-400 30,-000 0.31 0.33 31.3 ,.0 ,.2 ,.2 ,.0 ,.0 4.4 ,2.0 ,1.3 ,2.0 0. .4 2., 0. ,1., +.3

121 $V121 24-43 1-40 ,1-00 +-300 30-000 0.2+ 0.31 31. ,. ,., ,., ,. ,. +.3 ,2. ,1.4 ,2. 0.4 .2 3.1 0.+ ,2.2 +.4

122 $V122 24-43 1-+3 ,,-,00 ,-00 31-000 0.2, 0.2+ 31.+ 40.+ ,3. ,3. 40.+ 40.+ ,. ,+.0 ,4.2 ,+.0 . 1.2 ,.4 .2 ,4. ,.4

123 $V123 24-43 1-0 ,0-100 ,-,00 20-000 0.2 0.2, 32.22 ,3.0 .3 .3 ,3.0 ,3.0 ,., ,0.+ ,0.2 ,0.+ 3+.+ .0 1.4 +. ,0. 4.212 $V12 24-43 1-20 -,00 3-100 2-000 0.22 0.2 32., 4. 2.1 2.1 4. 4. 3.1 .1 . .1 3,.2 1.3 4. .4 .0 3.4

12 $V12 24-43 1-33 -00 3-+00 2-000 0.20 0.23 32.+ +.2 2.4 2.4 +.2 +.2 3.+ .+ .3 .+ 3,., 1.+ +.0 . .4 .

12 $V12 24-43 1- -00 3-+00 24-000 0.1+ 0.21 32.+0 +.2 2.4 2.4 +.2 +.2 3.+ .+ .3 .+ 3,., 1.+ +.0 . .4 .

12, $V12, 24-43 1-+ -100 3-00 21-000 0.1, 0.1+ 33.0+ 4.4 2. 2. 4.4 4.4 3. . .+ . 3,. 1. 4., .1 . .2

124 $V124 24-43 1-,2 -00 3-+00 24-000 0.1 0.1, 33.2 +.2 2.4 2.4 +.2 +.2 3.+ .+ .3 .+ 3,., 1.+ +.0 . .4 .

12+ $V12+ 24-43 1-4 ,-000 -000 22-000 0.13 0.1 33.2 +., 3.3 3.3 +., +., .0 ,.1 . ,.1 3,.4 2.0 +.1 .4 ,.1 .+

130 $V130 24-43 1-++ ,-+00 -00 23,-000 0.12 0.1 33. ,0. .1 .1 ,0. ,0. . ,. .+ ,. 34.1 2. +. ,. ,.4 .

131 $V131 24-43 1-,12 4-00 -400 233-000 0.10 0.12 33.4 ,1.2 . . ,1.2 ,1.2 .+ 4.0 ,. 4.0 34. 2.4 +.4 ,.+ 4.3 .0

132 $V132 24-43 1-,2 4-00 -00 22-000 0.0+ 0.11 33.,+ ,1.2 . . ,1.2 ,1.2 ., ,.4 ,.2 ,.4 34.3 2. +., ,.4 4.2 .+

133 $V133 24-43 1-,34 4-200 -300 21,-000 0.04 0.10 33.4+ ,0.+ .3 .3 ,0.+ ,0.+ . ,. .+ ,. 34.1 2. +. ,. ,.+ .

13 $V13 24-43 1-,1 4-100 -100 211-000 0.0, 0.04 33.+, ,0.4 .2 .2 ,0.4 ,0.4 .2 ,.3 ., ,.3 34.0 2.2 +.3 ,. ,., .

13 $V13 24-43 1-, ,-00 3-00 202-000 0.0 0.0, 3.0 ,0.2 3.4 3.4 ,0.2 ,0.2 3. ., .1 ., 3,., 1.4 4.+ ,.0 ,.1 .+

13 $V13 24-43 1-,,4 ,-000 2-+00 1+3-000 0.0 0.0 3.11 +. 3.2 3.2 +. +. 3.0 .0 . .0 3,.3 1.3 4. . . .3

13, $V13, 24-43 1-,+1 -00 2-00 14-000 0.0 0.0 3.1 +.2 2.4 2.4 +.2 +.2 2. . .0 . 3,.0 0.+ 4.0 .1 .1 3.+

134 $V134 24-43 1-40 -400 1-00 1,-000 0.03 0.0 3.20 4.3 2.0 2.0 4.3 4.3 1.4 ., .2 ., 3. 0.2 ,. . .2 3.113+ $V13+ 24-43 1-41, -00 0-00 1-000 0.02 0.03 3.23 ,.1 0.+ 0.+ ,.1 ,.1 0. 3. 2.+ 3. 3.+ +.3 . . .0 1.+

10 $V10 24-43 1-430 2-100 4-000 14-000 0.02 0.02 3.2 . 4. 4. . . 4.2 0.+ 0. 0.+ 3. ,.3 ., 2.3 1. +.

11 $V11 24-43 1-43 +-00 -00 12+-000 0.01 0.02 3.2, 1., .0 .0 1., 1., . 4.2 ,., 4.2 32.+ .2 2., 0.0 4.4 .+

12 $V12 24-43 1-4, ,-400 ,1-00 11-000 0.01 0.01 3.24 ,4.4 ,1. ,1. ,4.4 ,4.4 ,1. ,.+ ,.3 ,.+ 2.3 4.2 .+ .0 ,. ,2.+

13 $V13 24-43 1-4,0 ,1-000 -00 10-000 0.00 0.01 3.2+ ,3.4 ,.0 ,.0 ,3.4 ,3.4 .4 +.+ +. +.+ 3+. .3 1.3 +.4 ,0. 4.1

1 $V1 24-43 1-443 -00 0-,00 +2-000 0.00 0.00 3.2+ . 1. 1. . . 0.+ 3.3 2.+ 3.3 30.2 1. 3+.1 .4 3.+ 2.1


2= ;(ips=

for ea!> load !aseorsion "A

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1 $V1 24-43 1-4+ 4-00 -,00 +2-000 0.00 0.00 3.30 0.4 .1 .1 0.4 0.4 .4 ,. ,.0 ,. 32. . 2.1 +.2 4.0 .1

1 $V1 24-43 1-+0+ 4-00 -,00 +2-000 0.00 0.00 3.30 0.4 .1 .1 0.4 0.4 .4 ,. ,.0 ,. 32. . 2.1 +.2 4.0 .1

otal 4-++-000 4-2,-200 2-4-000

2.2.2 Wind Tunnel Data C-22

2.3 Seismic Calculations

2.3.1 Seismic Weight Calculation 24

2.3.2 Seismic Load Calculation 29

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C-29

Seismic Load Calculations Created by: CJB 4/27/2012

Floor Level Floor Type Weight Height wxhxk

Cvx Lateral Force Story Shear Moment

x wx, kips hx, t t!kips Fx, kips "x, kips k!t

147 Mechanical 5.21E+03 1935.50 1.95E+10 0.03252 213.43 213 0

146 Mechanical 5.21E+03 1922.33 1.92E+10 0.0320 210.54 424 2!10

145 "e#idential 2.26E+03 1909.17 .22E+09 0.01371 9.96 514 !393

144 "e#idential 2.26E+03 196.00 .11E+09 0.01352 .72 603 15!159

143 "e#idential 2.26E+03 12.3 .00E+09 0.01333 7.49 690 23!094

142 "e#idential 2.26E+03 169.67 7.9E+09 0.01315 6.27 776 32!11

141 "e#idential 2.26E+03 156.50 7.7E+09 0.01296 5.06 61 42!404

140 "e#idential 2.26E+03 143.33 7.67E+09 0.0127 3.6 945 53!747139 "e#idential 2.26E+03 130.17 7.56E+09 0.01260 2.67 1!02 66!194

13 "e#idential 2.26E+03 117.00 7.45E+09 0.01242 1.4 1!109 79!729

137 "e#idential 2.26E+03 103.3 7.34E+09 0.01224 0.30 1!190 94!33

136 " id ti l 2 26E+03 1790 67 7 23E+09 0 01206 79 14 1 269 110 003

& ' 6563! ( ' 5.6! ) ' 2

Calc*lati%n ba#ed %n ,CE 7-10 Chater# 11 and 12 %r #ei#ic l%ad#.



136 "e#idential 2.26E+03 1790.67 7.23E+09 0.01206 79.14 1!269 110!003

135 "e#idential 2.26E+03 1777.50 7.13E+09 0.011 77.9 1!347 126!711

134 "e#idential 2.26E+03 1764.33 7.02E+09 0.01171 76.3 1!424 144!445

133 "e#idential 2.26E+03 1751.17 6.92E+09 0.01153 75.6 1!499 163!191132 "e#idential 2.26E+03 173.00 6.1E+09 0.01136 74.55 1!574 12!934

131 "e#idential 2.26E+03 1724.3 6.71E+09 0.01119 73.42 1!647 203!65

130 "e#idential 2.26E+03 1711.67 6.61E+09 0.01102 72.31 1!720 225!34

129 "e#idential 2.26E+03 169.50 6.51E+09 0.0105 71.20 1!791 247!991

12 "e#idential 2.26E+03 165.33 6.41E+09 0.0106 70.10 1!61 271!571

127 "e#idential 2.26E+03 1672.17 6.31E+09 0.01052 69.01 1!930 296!075

126 "e#idential 2.26E+03 1659.00 6.21E+09 0.01035 67.93 1!99 321!46

125 "e#idential 2.26E+03 1645.3 6.11E+09 0.01019 66.5 2!065 347!793

124 "e#idential 2.26E+03 1632.67 6.01E+09 0.01002 65.79 2!131 374!979

123 "e#idential 2.26E+03 1619.50 5.92E+09 0.0096 64.73 2!195 403!032

122 "e#idential 2.26E+03 1606.33 5.2E+09 0.00970 63.6 2!259 431!937

121 "e#idential 2.26E+03 1593.17 5.73E+09 0.00954 62.64 2!322 461!60

120 "e#idential 2.26E+03 150.00 5.63E+09 0.00939 61.61 2!33 492!24

119 "e#idential 2.26E+03 1566.3 5.54E+09 0.00923 60.59 2!444 523!62

11 "e#idential 2.26E+03 1553.67 5.45E+09 0.0090 59.5 2!503 555!05117 "e#idential 2.26E+03 1540.50 5.35E+09 0.0092 5.57 2!562 5!767

Floor Level Floor Type Weight Height wxhxk

Cvx Lateral Force Story Shear Moment

x wx, kips hx, t t!kips Fx, kips "x, kips k!t

& ' 6563! ( ' 5.6! ) ' 2

10 "e#idential 3.60E+03 1422.00 7.2E+09 0.01214 79.66 3!275 922!604

107 "e#idential 3.60E+03 140.3 7.15E+09 0.01191 7.19 3!353 965!71

106 "e#idential 3.60E+03 1395.67 7.01E+09 0.01169 76.74 3!429 1!009!62

105 "e#idential 3.60E+03 132.50 6.E+09 0.01147 75.29 3!505 1!055!016

104 "e#idential 3.60E+03 1369.33 6.75E+09 0.01126 73.7 3!579 1!101!161

103 "e#idential 3.60E+03 1356.17 6.62E+09 0.01104 72.45 3!651 1!14!279

102 "e#idential 3.60E+03 1343.00 6.49E+09 0.0103 71.05 3!722 1!196!351

101 "e#idential 3.60E+03 1329.3 6.37E+09 0.01062 69.67 3!792 1!245!359

100 "e#idential 3.60E+03 1316.67 6.24E+09 0.01041 6.29 3!60 1!295!24

99 "e#idential 3.60E+03 1303.50 6.12E+09 0.01020 66.94 3!927 1!346!10

9 "e#idential 3.60E+03 1290.33 6.00E+09 0.00999 65.59 3!993 1!397!13

97 "e#idential 3.60E+03 1277.17 5.7E+09 0.00979 64.26 4!057 1!450!3296 "e#idential 3.60E+03 1264.00 5.75E+09 0.00959 62.94 4!120 1!503!797

95 "e#idential 3.60E+03 1250.3 5.63E+09 0.00939 61.64 4!11 1!55!041

94 "e#idential 3.60E+03 1237.67 5.52E+09 0.00919 60.34 4!242 1!613!096

93 "e#idential 3.60E+03 1224.50 5.40E+09 0.00900 59.07 4!301 1!66!946



93 "e#idential 3.60E 03 1224.50 5.40E 09 0.00900 59.07 4!301 1!66!946

92 "e#idential 3.60E+03 1211.33 5.2E+09 0.001 57.0 4!359 1!725!574

91 "e#idential 3.60E+03 119.17 5.17E+09 0.0062 56.55 4!415 1!72!962

90 "e#idential 3.60E+03 115.00 5.06E+09 0.0043 55.32 4!471 1!41!096

9 "e#idential 3.60E+03 1171.3 4.94E+09 0.0024 54.10 4!525 1!99!957

"e#idential 3.60E+03 115.67 4.3E+09 0.0006 52.9 4!577 1!959!531

7 "e#idential 3.60E+03 1145.50 4.73E+09 0.007 51.69 4!629 2!019!01

6 "e#idential 3.60E+03 1132.33 4.62E+09 0.00770 50.51 4!60 2!00!752

5 "e#idential 3.60E+03 1119.17 4.51E+09 0.00752 49.34 4!729 2!142!36

4 "e#idential 3.60E+03 1106.00 4.40E+09 0.00734 4.19 4!777 2!204!634

3 "e#idential 3.60E+03 1092.3 4.30E+09 0.00717 47.05 4!24 2!267!534

2 "e#idential 3.60E+03 1079.67 4.20E+09 0.00700 45.92 4!70 2!331!0531 "e#idential 3.60E+03 1066.50 4.10E+09 0.0063 44.1 4!915 2!395!177

0 "e#idential 3.60E+03 1053.33 4.00E+09 0.00666 43.71 4!959 2!459!91

79 "e#idential 3.60E+03 1040.17 3.90E+09 0.00649 42.62 5!001 2!525!11

7 "e#idential 3.60E+03 1027.00 3.0E+09 0.00633 41.55 5!043 2!591!032

77 "e#idential 3.60E+03 1013.3 3.70E+09 0.00617 40.49 5!03 2!657!430

76 "e#idential 3.60E+03 1000.67 3.61E+09 0.00601 39.45 5!123 2!724!361

75 "e#idential 3.60E+03 97.50 3.51E+09 0.0055 3.42 5!161 2!791!11

74 $%bby 3.77E+03 974.33 3.5E+09 0.00597 39.19 5!200 2!59!767

3.0

Gravity Design

3.1 Tributary Areas 33

3.2

Core Area

3.2.1

Concrete Slab Design 39

3.2.2

Link Bea Design !"

3.3 #loor Area "1

3.3.1

Co$osite Decking

3.3.1.1

Composite Decking Design 52

3.3.1.2 Composite Decking Hand-Calc. and Mastan Analysis 56

3.3.2 Co$osite Bea Design



3.3.2

Co$osite Bea Design

3.3.2.1 Joist Design Tool 64

3.3.2.2

adial !i"de"s 6#

3.3.2.3 otated adial !i"de" $eam Design ##

3.3.2.4 Ci"c%m&e"ential !i"de" Design '(

3.3.2.5 Cantile)e"s '3

3.3.2.6

H** +dge $eam Design ''

3.3.3

%ibration Analysis 93

3.! Coluns 99

3.!.1 Colun Loa& Take&o'n 100

3.!.2

Co$osite Colun Design 11!

Tributary Areas Calculations Chung Yu Wang

11/6/2011

Title: Tributary Area and Sizing of Flexural Elements under Uniformly Distributed Load for Bank 1,

Residential (5th

floor).



Figure 1: Typical Tributary Areas

Assumptions:

1) Except for elements in Bank 4, all elements in same bank have the same tributary area and

geometry if they are located at the same location of each floor.

2) The tributary areas of the joists are technically trapezoidal in shape, but we assume the tributary

area to be rectangular in shape with the width of the rectangle to be the base length of the

trapezoid.

3) HSS are load bearing members.

4) Angled Girder takes ½ of the tributary area and load from the following area, and HSS 1 takes ¼

of the tributary and load from the same area.


11/6/2011

Figure 2: HSS-AG Tributary Area

5) To estimate the area of the HSS-AG tributary area, we use Revit and rotate the slab so point B

meets point A. The corner of the slab is at the end of the cantilevering girder. Use straight

sketch lines to draw a boundary that encloses the area and take length measurements to find

the approximate, larger than actual, area.

6) The distances from columns to façade and from girder to façade are held constant throughout

the building.



J1L 188in pCJ1 103i

J2L 229in

pJ1J2 136in

b pCJ1 pJ1J2

2119.5i

wJ1L J2L

2208.5i

Area b w 173.026ft2

GL 270in J2L 229in

pJ2G 137i pJ1J2 136in

b pJ1J2 pJ2G

2136.5i


11/6/2011

Girder, G of Floor G (Floor Plan Given)

GL 245in

SF 282in

pJ2G 109i

pCG 813i

pGSF pCG

GLSF pCG

122.78in

Area SF GL

2

pJ2G pGSF

2

212.062ft

2




11/6/2011

Girder, G of Floor 5 (Bank 1)

Assume pGSF, distance from girder to exterior isheld constant throughout the building

GL 270in

pGSF 122in

pCG 896i

pJ2G 137i

SF GL

pCG

pCG pGSF( ) 306.763i

Area SF GL

2

pJ2G pGSF

2 259.343ft

2




11/6/2011

Angled Girder, AG of Floor 60 (Bank 2)

Assume AG takes 1/2 of this total area

A 295in

B 144i

C 291i

D 142in

E 212i

AGL 303i

A1 B C 4.19 104

in2

A2 D C2

A B( ) 3.269 104 in2

AreaAGA1 A2

259 012ft2



Angled Girder, AG of Floor 5 (Bank 1)

AreaAG2

259.012ft

GL 270in

GL60 245i

Factor

GL

GL601.102

AreaAG60 373 46in2

AreaAG Factor Area AG60 285.811ft2

AGL60 303i


11/6/2011

HSS1 of Floor 5

HSS 1 is the perimeter element that is taking part

of the tributary area. We assume that HSS1 has ¼

of the area or ½ that of the angled girder on the

same floor.

HSS2 of Floor 5

HSS1AreaAreaAG

2142.906ft

2



pGSF 122in

SF 307in

Area pGSF

2

SF 130.049ft2

C r e a t e d b y : A D V

1 1 / 3 0 / 2 0 1 1

S D

M

a x M ! m e n t

" n d R e a t $ ! n

R e b a r

R e b a r D $ % t &

p % ( )

' p % ( )

' * $ p + ( t )

' * $ p % / ( t , w $ d t h )

#

' $ n -

! & & )

0 0

3 & .

2

1 &

0

1

0 0

2 & 3

3

1 & 2

0

1 8

0 0

& 8

2

2 & 2

0

.

0 0

2 &

2

1 & 2

0

1 8

0

1 0

& .

2 & 3

1 2

0

1 0

3 & .

3

1 & 8

8

1 8

0

1 0

1 2 & 2

0

3 &

.

0

1 0

3 &

8

1 &

1

1 8

e r e d e % $ 5 n e d 4 % $ n 5 t h

e t ! ! l a n d t h e $ n ( ! r m a t $ ! n ( r ! m

t h ! % e r e % 4 l t % $ %

a n d e n d % r e a t $ ! n % a

r e a l 4 l a t e d 4 % $ n 5 ( a t ! r e d l ! a

d % &

B a n k 1

2 . 1

C o n c r e t e S l a b D e

s i g n



3 . 2 . 1

C o n c r e t e S l a b

D e s i g n

D e s i g n e d S l a b I n f o r m a t i o n

M m a x = w l 2 / 8

R x n = w l / 2

S l a b #

S p a n

S l a b D e p t h

D

' ( t )

' $ n )

' p % ( )

' p

R e % $ d e n t $ a l / ! b b y

1

1 0 & 1

.

.

& 0

1

2

8 & 2

.

& 0

1

3

1 &

0

.

& 0

1

8 &

0

.

& 0

1

M e h a n $ a l

1

1 0 & 2

.

& 0

2

2

8 & 3

.

& 0

2

3

1 &

.

& 0

2

8 &

.

& 0

2

h $ % % h e e t d $ % p l a y % t h e r e % 4 l t % ( r ! m 4

% $ n 5 t h e % l a b t ! ! l &

A l l % l a b % w e

t a b 4 l a t e d b e l ! w &

h e l !

a d % % h ! w n a r e 4 n ( a t ! r e d &

h e

m ! m e n t %

6 ! r m 4 l a % 7 % e

d

3 . 2

C-39

S D

M

a x M ! m e n t

" n d R e a t $ ! n

R e b a r

R e b a r D $ % t &

p % ( )

' p % ( )

' * $ p + ( t )

' * $ p % / ( t w $ d t h )

#

' $ n -

! & & )

1 0 0

3 & .

2

1 &

0

1

1 0 0

2 & 3

3

1 & 2

0

1 8

1 0 0

& 8

2

2 & 2

0

.

1 0 0

2 &

2

1 & 2

3

1 8

2 0

1 0

& .

2 & 3

1 2

2 0

1 0

3 & .

3

1 & 8

8

1 8

2 0

1 0

1 2 & 2

0

3 &

.

2 0

1 0

3 &

8

1 &

1

1 8

S D

M

a x M ! m e n t

" n d R e a t $ ! n

R e b a r

R e b a r D $ % t &

p % ( )

' p % ( )

' * $ p + ( t )

' * $ p % / ( t w $ d t h )

#

' $ n -

! & & )

1 0 0

3 & .

2

1 &

0

1

1 0 0

1 & 2

0

0 & 8

.

1 8

1 0 0

1 & 2

0

0 & 8

.

1 8

1 0 0

2 & 0

1 & 1

3

1 8

2 0

1 0

& .

2 & 3

8

2 0

1 0

1 & 8

1 & 3

1 8

2 0

1 0

1 & 8

1 & 3

1 8

2 0

1 0

3 & 2

2

1 &

1 .

B a n k 2

B a n k 3

2 . 1


s i g n



S l a b #

S p a n

S l a b D e p t h

D

' ( t )

' $ n )

' p % ( )

' p

R e % $ d e n t $ a l / ! b b y

1

1 0 & 1

.

.

& 0

1

2

8 & 2

.

& 0

1

3

1 &

0

.

& 0

1

8 &

0

.

& 0

1

M e h a n $ a l

1

1 0 & 2

.

& 0

2

2

8 & 3

.

& 0

2

3

1 &

.

& 0

2

8 &

.

& 0

2

S l a b #

S p a n

S l a b D e p t h

D

' ( t )

' $ n )

' p % ( )

' p

R e % $ d e n t $ a l / ! b b y

1

1 0 & 1

.

.

& 0

1

2

. & 0

.

.

& 0

1

3

. & 0

.

.

& 0

1

& 8

0

.

& 0

1

M e h a n $ a l

1

1 0 & 1

.

.

& 0

2

2

. & 0

.

.

& 0

2

3

. & 0

.

.

& 0

2

& 8

0

.

& 0

2 3 . 2

C-40

S D

M

a x M ! m e n t

" n d R e a t $ ! n

R e b a r

R e b a r D $ % t &

p % ( )

' p % ( )

' * $ p + ( t )

' * $ p % / ( t w $ d t h )

#

' $ n -

! & & )

1 0 0

3 & .

2

1 &

0

1

1 0 0

1 & 2

0

0 & 8

.

1 8

1 0 0

1 & 2

0

0 & 8

.

1 8

1 0 0

3 & .

1 &

0

1

S D

M

a x M ! m e n t

" n d R e a t $ ! n

R e b a r

R e b a r D $ % t &

p % ( )

' p % ( )

' * $ p + ( t )

' * $ p % / ( t w $ d t h )

#

' $ n -

! & & )

1 0 0

3 & .

2

1 &

0

1

1 0 0

+ +

+ +

+ +

+ +

1 0 0

+ +

+ +

+ +

+ +

1 0 0

3 & .

1 &

0

1

B a n k 4 . 1

B a n k 4 . 2

2 . 1


s i g n



S l a b #

S p a n

S l a b D e p t h

D

' ( t )

' $ n )

' p % ( )

'

R e % $ d e n t $ a l / ! b b y

1

1 0 & 1

.

.

& 0

1

2

. & 0

.

.

& 0

1

3

. & 0

.

.

& 0

1

1 0 & 1

8

.

& 0

1

S l a b #

S p a n

S l a b D e p t h

D

' ( t )

' $ n )

' p % ( )

'

R e % $ d e n t $ a l / ! b b y

1

1 0 & 1

.

.

& 0

1

2

+ +

.

& 0

1

3

+ +

.

& 0

1

1 0 & 1

8

.

& 0

1 3 . 2

C-41

C r e a t e d b

y : A D V

1 1 / 3 0 / 2 0 1 1

C o l o r K e y :

U s e r I n p u t

C o n s t a n t / ! r e " o u s C a l c #

C a l c / L o o k u p

& e

! a s s e s C ' e c k

( o

) a l s C ' e c k

p t

+ - a ,

k p t

n d 4 , n k p s

4 e b a r %

4 e b a r o # c #

n

p t

3 # .

3

1 # .

.

1 .

8 8

p l

$ n 9 l e e n d

1 .

2 2

l b s

1 8 0

p l

1 # .

k p s

L

8 ; # .

p l

r e t e s l a b

9 " e n t ' e n e

c e s s a r y n o r - a t o n #

F a c t o r e d L o a d i n g ( 1 . 2 D L + 1 . L L !

R e s " l t a n

t # n d r e a c t i o n ( f a c t o r e d !

I - p o r t a n t

I n o r - a t o n

2 . 1


s i g n

R e i n f o r c e d C o n c r e

t e S l a b D e s i g n

B a n k

1

L o c a t o n

1

$ l a b %

1

* K

+ a , + o - e n t n $ l a b

3 # .

3

k p

+

a , A l l o 5 a b l e + o - e n t

3 # 6

k p

L o a d s

D L

7 7 # 0

p l

D L

L L

1 0 0

p l

L L

$ D L

7 6

p l

$ D

O v e r a l l S l a b C h e c k

< ' s s ' e e t s a t o o l t o d e

s 9 n a s - p l y s u p p o r t e d r e n o r c e d c o n c

U n f a c t o r e d L o a d i n g

3 .

C-42

2 2 2 s s np

t

p t

E 5

c 1 # 7

E 3 3 E >

c 1 / 2

F A C I 3 1 ; 0 ; ; # 7

; # 8

A s s u - e d $ a n d

L 9 ' t 5 e 9 ' t C o n c r e t e

' c d

/ 2

y E A

s

 c E b F G ' t n e y s t r e s s b l o c k

<

u d a

/ 2

A C I 3 1 ;

= # 3 # 2 # 1

p e r o o t 5 d t ' o s l a b

A C I 3 1 ; 0 ; 6 # 8

1 2 E A b

/ s

0 # 0

0 1 ; E b ' F A C I 3 1 ; 0 ; 6 # 1

2 # 2 # 1

A s

H A

s - n

. 2 . 1


s i g n

$ a s i c S l a b % r o & e r t i e s

$ p a n l e n 9 t '

L

= # 8

8

t

$ l a b d e p t '

'

8

n

C o n c r e t e t y p e

1

C o n c r e t e s t r e n 9 t '

> c

. 0 0 0

p s

C o n c r e t e + o d u l u s o l a s t c t y

c

2 0 . 8

8 ; =

p s

4 e b a r s ? e

%

.

( o - n a l b a r d a - e t e r

d b a r

0 # 7

n

A r e a o b a r

A b a r

0 # 2

0

n 2

4 e b a r s p a c n 9 o # c #

s

1 .

n

4 e b a r $ p a c n 9 C ' e c k

* K

$ t e e l l a s t c + o d u l o u s

s

2 = 0 0

0 0

0 0

p s

$ t e e l $ t r e n 9 t '

y

8 0 0

0 0

p s

A r e a o s t e e l p e r o o t 5

d t '

A s

0 # 1

6

n 2

+ n - u - r e @ u r e d s t e e

l a r e a

A s - n

0 # 1 3 0

n 2

A r e a o s t e e l a c c e p t a b l e

&

$

C a l c " l a t i o n s f o r a R e &

r e s e n t a t i v e 1 ' f t i d t h o f t h

e S l a b )

C o n c r e t e c o " e r

c

0 # 6

7

n

$ t r u c t u r a l d e p t '

d

7 # 0

0

n

U l t - a t e t e n s l e o r c e

< u

1 0 0

= ;

l b s

U l t - a t e c o - p r e s s o n o r c e

C

1 0 0

= ;

l b s

C o - p r e s s o n ? o n e

a

0 # 2

7

n

1 / 2 o C o - p r e s s o n ? o n

e

a / 2

0 # 1

2

n

I n t e r n a l - o - e n t a r -

d a

/ 2

. # ;

;

n

A l l o 5 a b l e n t e r n a l - o -

e n t

+ n

. = 2

. 0

l b

A l l o 5 a b l e n t e r n a l - o -

e n t

+ n

. # 1

0

k p

L o a d a c t o r

0 # =

) a c t o r e d A l l o 5 a b l e + o - e n t

+

n

3 # 8

=

k p 3

C-43

e p t

A C I 1 0 # 2 # 6 # 3

A s s u - e s t e e l t e n s o n c o n t r o l s

A s s u - e s t e e l t e n s o n c o n t r o l s

0 # ;

7 E

1 E > c / y

E J

c u / J

s t e e

l N J

c u

A

s t e e

l / b E d

I & e s 0 # =

3 . 2 . 1


s i g n



C h e c k f o r * i e l d i n g o f S t e e l a n d S " f f i c i e n t l D " c t i l e F a i l " r e

C o n c r e t e C o - p r e s s " e A r e a ) a c t o r

1

0 # ;

7

C r u s ' n 9 s t r a n l - t o r

c o n c r e t e

J c u

0 # 0 0 3

$ t r a n l - t o r s t e e l

J y s

0 # 0 0

2 0 6

! e r c e n t s t e e l o r b a l a n c

e d a l u r e

b a l

2 # ; 7

A c t u a l p e r c e n t s t e e l

a c t u a l

0 # 2 ;

a c t u a l

M 0 # 8

2 7 E b a l

&

$

+ a , + o - e n t n s l a b

+ u

3 # .

3

k p

+ u

M +

n

&

$

3

C-44

3.2.2 Link Beam Design Created by: CJB, ADV 5/10/2012

Table 9.6: Link Beam DimensionsLength Tributary Area Curvature, α Radius, r

(ft) (ft2) (deg) (ft)

1 31 120 -- --

2 9.34 84 -- --

3 32.2 484 42 40

4 18.3 110 -- --

5 40.6 9.9 -- --

1 31 120 -- --

2 9.34 84 -- --

3 32.2 484 42 40

4 18 3 110

Bank 1

Bank 2

!"#$ $"eet $%&&ar#'e$ t"e re *#+ bea&$. !"e d#&e+$#+$ fr bea&$ #+ ea" ba+ are -re$e+ted #+

!ab*e 9.6. !ab*e 9. $%&&ar#'e$ t"e re#+fr#+g $tee* deta#*$ fr ea" re$#de+t#a* a+d *bby bea&. te

t"at t"e re$#de+t#a* a+d *bby bea&$ "ae t"e $a&e de$#g+ #t"#+ ea" ba+. !ab*e 9.8 $%&&ar#'e$ t"e

&e"a+#a* f*r *#+ bea&$.

Beam #



4 18.3 110 -- --

5 40.6 9.9 -- --

1 11.2 5.6 -- --

2 9.34 0.9 -- --

3 13.2 122 43 15.4

4 14 65.2 -- --

5 40.6 9.9 -- --

1 9.65 65.2 -- --

2 9.65 120 -- --

3 12.9 92.3 -- --

4 9.68 40.3 -- --

5 40.6 9.9 -- --

1 -- -- -- --

2 9.65 9.9 -- --

3 -- -- -- --

4 9 68 2 9

Bank 3

Bank 4.1

Bank 4.2

Table 9.7: Residential and Lobby Link Beam Summary

b h sstirru

(#+) (#+) (#+)

1 16 16 9 6 3 .2

2 6 10 9 2 3 4.2

3 48 16 9 20 4 .14 10 16 9 3 4 .1

5 20 16 9 6 4 .1

1 16 16 9 6 3 .2

2 6 10 9 2 3 4.2

3 48 16 9 20 4 .1

4 10 16 9 3 4 .1

5 20 16 9 6 4 .1

1 6 12 9 2 3 5.2

2 6 10 9 2 3 4.2

3 28 16 9 11 3 .2

4 10 10 9 2 3 4.2

Bank 3

Bank 2

Beam ! bar ! nbar stirru !

Bank 1



5 20 16 9 6 4 .1

1 8 8 9 2 3 3.2

2 8 10 9 2 3 4.2

3 30 16 9 10 4 .1

4 8 6 9 2 3 2.2

5 20 16 9 6 3 .2

1

2 8 10 9 2 3 4.23

4 8 6 9 2 3 2.2

5 20 16 9 6 3 .2

Bank 4.2

Bank 4.1

Table 9.8: Mechanical Link Beam Summary

b h sstirru

(#+) (#+) (#+)

1 22 16 9 6 3 .2

2 8 10 9 2 3 4.2

3 2 16 9 20 4 .1

4 12 16 9 3 4 .1

5 24 16 9 6 4 .1

1 22 16 9 6 3 .2

2 8 10 9 2 3 4.2

3 2 16 9 20 4 .1

4 12 16 9 3 4 .1

5 24 16 9 6 4 .1

1 10 10 9 2 3 4.2

2 8 10 9 2 3 4.2

3 48 16 9 11 3 .2

4 10 10 9 2 3 4.2

Beam ! bar ! nbar stirru !

Bank 3

Bank 2

Bank 1



5 24 16 9 6 4 .1

1 10 8 9 2 3 3.2

2 10 10 9 2 3 4.2

3 12 10 9 10 3 4.2

4 8 8 9 2 3 3.2

5 24 16 9 6 3 .2

1

2 8 10 9 2 3 4.23

4 6 8 9 2 3 3.2

5 24 16 9 6 3 .2

Bank 4.2

Bank 4.1

C r e a t e d b y :

T S

1 1 / 3 0 / 2 0 1 1

u d e s t h e e f f e c t s o f t o r s i o n

f o r c u r v e d b e a m s .

C o l o r " e y :

# s e r $ n %

u t

C o n s t a n

t / ' r e v i o u s C a l c .

C a l c / & o o ! u %

) e s

' a s s e s C

h e c !

* o

+ a i l s C h e c

- u

! i %

f t

n d 4 n ! i % s

a r (

a r S % a c i n g i n

3 . 2

8 . 9

7

. 8 2

. 0

% l f

8 , 9 8 0

l b

0

% l f

8 . 9 8

! i % s

. 8

% l f

8

% l f

$ m % o r t a n t $ n f o r m a t i o n

L o a d i n g ( 1 . 2 D 1 . ! L "

# n d r e a c t i o n

( f a c t o r e d "

3 . 2 . 2

L i n k B e a m D

e s i g n

R e i n f o r c e d C o n c r e t e B e a m D

e s i g n

T h i s s h e e t i s u s e d t o d e s i g n r e i n f o r c e d c o n c r e t e b e a m s , a

n d i n c l u

a n ! :

1

& o c a t i o n :

1

e a m (

3

O v e r a l l C h

e c k :

"

- a - o m e n t i n S l a b :

3 . 2

! i % f t

- a 5 l l o 6 a b l e - o m

e n t :

7 3 . 3

! i % f t

&

7 7 % l f

&

; ; .

& &

1 0 0 % l f

& &

1 ;

S &

7 9 % l f

S &

; .

6

2 < 8

U n f a c t o r e d L

o a d i n g

F a c t o r e d L

C-48

#ro$erties and DimensionsBeam Length L 3$.$ ft

Beam 0idth b 3 in

Beam *e%th h 1$ in

oncrete T2%e 1

oncrete "trength fc , %si

Light(eight oncrete 4actor 5c .) '6 31& .)

oncrete 7lastic odulus 7c $,+,+/ %si 8 5c9(c

1.)

9339fc1$

; '6 31& .), .+<ebar "i=e ) #

>ominal *ar *iameter dbar .+$) in

'rea of Bar 'bar .31 in$

>umber of Bars

"tirru% si=e 3 #

>ominal "tirru% *iameter dstirru% .3-) in

over c .-) in<ebar "%acing O.. s .$ in

<ebar "%acing heck OK '6 31& -.+

"teel 7lastic odulus 7s $/,, %si

"teel "trength f 2 +, %si

"teel 'rea 's 1.$3 in$

inimum <e?uired "teel 's&min .+ in$

8 .19bh '6 31& -.1$.$.1

inimum re?uired steel@ A7" 6f 's 's&min

Calc%lations for a re$resentative 1&ft 'idth of the sla(:

"tructural *e%th d 1.)+ in

Cltimate Tensile 4orce Tu -3,+31 lbs 8 f 29's

Cltimate om%ression 4orce -3,+31 lbs 8 Tu

om%ression Done a 1. in 8 E.)9fc9bF; 0hitne2 stress block

Galf of om%ression Done a$ ./ in

6nternal oment 'rm /.++ in 8 d&a$

'llo(able 6nternal oment n -11,$ lb&in 8 TuEd&'$F

n )/.3 ki%&ft

Load factor H ./

4actored 'llo(able oment Hn )3.3 ki%&ft %er foot&(idth of slab

Check for )ielding of steel and s%fficientl) d%ctile fail%re

I1 )

%er '6 31, /.3.$.1

*+,-R '6 31& "ection 11.$

"tructural *e%th d 1.)+ in

"hear at face of su%%ort .- ki%s

a!imum *esign "hear u,ma! . ki%s 8 & (9d

"hear <eduction 4actor Hv .-)

'llo(able "hear c . ki%s 8 $PEfcF9b9d; '6 31 11&3

<educed 'llo(able "hear Hvc 3.+ ki%s

.OR*/O0 '6 31& "ection 11.)

radius of curvature r . ft

angle of curvature Q .-3 rad

factored distributed load ( $/ %lf

4actored Torsion at ends Tu )/.1 ki%&ft 8 r$(9EQ9sinEQF & Q$ M sinEQ$F; see belo(

<eduction 4actor Hb ./4le!ural <esistance <fle! 1)$ %si 8 u EHbb(d

$F

'ngle of T(ist R .-$ rad 8 r$( E7c<fle!F; see belo(

'rea of Serimeter oncrete 'c% 3/+ in$

8 b9h M Eh & +F9+; '6 31 11.)

Outer Serimeter of ross&section %c% /+ in 8 $9Eb M $h & +F; '6 31 11.)

Threshold Torsion Tth +.)/ ki%&ft 8 H5PEfcF9E'$

c%%c%F; '6 31 11.).1EaF

th % c c% c%

ust heck Torsion@ A7"

'rea 7nclosed b2 Torsion <einf. 'oh $) in$

8 Eh & $c & dstirru%F9Eb & $c & dstirru%F; '6 31 11.)

Serimeter of Torsion <einf. %ch - in 8 $9Eh & $c M b & $cF; '6 31 11.)

'%%lied Torsional "tress Ta%%lied . ksi PEEubdF$ M ETu%h1.-'

$ohF

$F; '6 31 11.).3EaF

Torsional "trength Tstrength .)+/ ksi 8 HEcbd M PEfcFF; '6 31 E11&1F

6s the section large enough@ A7"

<eference:

Blodgett, Omer 0. Design of Welded Structures

6f Tstrength Ta%%lied

6f Tu Tth

3.3

#loor Area "1

3.3.1

Co$osite Decking

3.3.1.1 Composite Decking Design 52

3.3.1.2 Composite Decking Hand-Calc. and Mastan Analysis 56

3.3.2

Co$osite Bea Design

3.3.2.1 Joist Design Tool 64

3.3.2.2 adial !i"de"s 6#

3.3.2.3 otated adial !i"de" $eam Design ##

3.3.2.4

Ci"c%m&e"ential !i"de" Design '(

3.3.2.5 Cantile)e"s '3

3.3.2.6 H** +dge $eam Design ''

3 3 3 %ibration Analysis 93



3.3.3

%ibration Analysis 93

3.3.1.1 Composite Decking Design

Summary of Composite Decking Selections

Slab Depth

(in)Load Case

LL (psf)

SDL (psf)

Load (psf)

Rise Low Mid-

Low

Mid-

High High Low

Mid-

Low

Mid-

High High Low

Mid-

Low

Mid-

High High

!erage

"ramingLength (ft)

19.25 17 22.5 22.4 18.75 16.6 22 22.25 18.75 16.6 22 22.25

Radial

Length (ft) 31.36 26.75 24.03 31.80 31.36 26.75 24.03 31.80 31.36 26.75 24.03 31.80

Spans 3 3 3 3 4 4 4 4 4 4 4 4

#eight of

"raming (lbs)1155 1020 1350 1344 1500 1328 1760 1780 1500 1328 1760 1780

This table !ese"ts a s#$$a!% o& de'(i"g thi'("esses a"d de'( t%e based o" the t%e o& &loo! a"d ba"( t%e.

42

97

)$e"ities

100

57

157

*eside"tial +,te!io!

55

4.0 4.5

Me'ha"i'al

240

10

250

g ( )1155 1020 1350 1344 1500 1328 1760 1780 1500 1328 1760 1780

Span Dist (ft) 10.5 9 8.5 11 8 7 6.5 8 8 7 6.5 8

D$C% &'$ 1.5VL22 1.5VL22 1.5VL22 1.5VL19 1.5VL22 1.5VL22 1.5VL22 1.5VL22 2VLI16 2VLI19 2VLI20 2VLI16

DeckSlab

#eight (S")29.6 29.6 29.6 29.6 29.6 29.6 29.6 29.6 35.6 34.6 34.3 35.6

Low Rise Amenities

DATA

concrete density 110 lb/ft3

f'c of concrete 4 ksi

Ec of concrete 2408 ksi

slab thickness 4.5 in

Number of sans 4

!an len"th 8.0 ft

#/$ interior sans 21.3

%alue &( )E!

#/$ e*terior sans 21.3

%alue &( )E!

!elf +t of concrete slab 41.25 lf

si ,# 5- lf

unfactored ,# 8.25 lf

factored ,#nf12 11-. lf

si ## 100 lf

factored ## nf1 10 lf

dummy ,# 100 lf

dummy ## 100 lf

1) MOMENT CALCULATIONS

A AB B BC C

100 sf ,# on ll !ans 0 0.-08 61.03 0.3543 60.-08

100 sf ## on !an 1 only 0 0.83-1 60.805- 60.03143 60.13-1

100 sf ## on !an 2 only 0 0.042 60.14 0.5-1 60.543

100 sf ## on !an 3 only 0 0.243 60.214 60.00285- 60.543

100 sf ## on !an 4 only 0 0.023-1 60.405- 0.18 60.13-1

Adjust Dummy vaues !o" a#tua oads A AB B BC C

ctual ,# on ll !ans 0 0.-0 61.04 0.35 60.-0

7eak skied ## combination for aboe sketch 0 13 124 24 23

!um of ## moments from critical sans 0 1.13 61.0 0.-- 61.1

,# 9oment * 1.2 0 0.84 61.25 0.42 60.84

## 9oment * 1. 0 1.81 63.04 1.23 61.0

Tota Desi$n Moment %&'( *'+, %'- 1'+ %*'(

9a"nitude of !imle !an :actored 9oment 1.2, ; 1.##2/8

same for all locations0 2.2 62.2 2.2 62.2

<otal ,esi"n 9oment / !imle !an 9 0 1.1 1.3 0.-4 1.23

:actor =m +here <otal ,esi"n 9oment > =m+u?2 0 0.15 0.24 0.0 0.15

<his is a samle calculation to check the deckin" and concrete thickness for the lo+ rise amenities. =alculations

for all other floor tyes +as erformed in the same manner.

,ummy 9oments @isAft/ftB

9oments @isAft/ftB

C-53

*) REIN.ORCEMENT BAR CALCULATIONS

A AB B BC C A B C

Rein!o"#in$ Ba"s si/e C3 C4 C C4 C4 1.5%#22 1.5%#22 1.5%#22

rea of one bar s/barin2 0.11 0.2 0.44 0.2 0.2 0.354 0.354 0.354

Dar ,iameterin 0.3-5 0.5 0.-5 0.5 0.5 0.014-5 0.014-5 0.014-5

Ba" Cove"0in) 0.-5 0.-5 0.-5 0.-5 0.-5 0 0 0

!tructural ,eth d in 3.5 3.50 3.38 3.50 3.50 4.4 4.4 4.4

Sa#in$ 2etween 2a"s 0in) 13 13 13 13 13

9a*imum !acin" of bars in 13.5 13.5 13.5 13.5 13.5

Sa#in$ Re3ui"ement O45 )E! )E! )E! )E! )E! )E!

!teel rea in 16ft stri in2 0.10 0.18 0.41 0.18 0.18 0.35 0.35 0.35

9inimum steel areain2/ft 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

9a*imum steel areain2/ft 1.22 1.20 1.15 1.20 1.20 1.54 1.54 1.54

A"ea 2etween t6e imits5 )E! )E! )E! )E! )E! )E! )E! )E!

f y of steelksi 0 0 0 0 0 0 0 0

Es of steelksi 2000 2000 2000 2000 2000 2000 2000 2000

A AB B BC C A B C

<ension force assumin" !teel has yieldedkis .1 11.1 24.4 11.1 11.1 21.2 21.2 21.2

=omression force><ension force .1 11.1 24.4 11.1 11.1 21.2 21.2 21.2

=entroid of com.force a/2Fhitney 9odelin 0.0- 0.14 0.30 0.14 0.14 0.2 0.2 0.2

9oment rm bet+een < G= force in 3.53 3.43 3.23 3.43 3.43 4.3 4.3 4.3

Nominal 9oment =aacity 9n kis6ft 1.8 3.2 . 3.2 3.2 -.- -.- -.-

!tren"th Heduction factor I 0. 0. 0. 0. 0. 0. 0. 0. ssume section Jualifies for I>0.

Usa2e Moment Caa#ity 078Mn)09is%!t) %1'+ *': %,': *': %*': %+': %+': %+':

9oment based on ski loads and factored loads 9 u kis6ft 60.-4 2.5 64.3 1.4 62.- 60.-4 64.3 62.-

?s I9nK9u( )E! )E! )E! )E! )E! )E! )E! )E!

A AB B BC C

!train of the steel at yieldin" Ly 0.0020- 0.0020- 0.0020- 0.0020- 0.0020-

!train of the concreteLcu 0.003 0.003 0.003 0.003 0.003

M1 0.85 0.85 0.85 0.85 0.85

bal 0.0285 0.0285 0.0285 0.0285 0.0285

actual 0.00238 0.00440 0.01003 0.00440 0.00440

?s bal K actual( )E! )E! )E! )E! )E!

?s actualO0.25bal( )E! )E! )E! )E! )E!

Mes6 Tye

Rein!o"#ement Ba"s Ba"s to Mes6

Es of steelksi

.o"#e ; Moment Ca#uations

%eryfin" assumtions for calculations made

!teel rea in 16ft stri in2

9inimum steel areain2/ft

9a*imum steel areain2/ft

A"ea 2etween t6e imits5

f y of steelksi

9esh rea er foot in2

.5<hickness

Cove"0in)

!tructural ,eth d in

C-54

-) S<RIN4A=E STEEL BARS

Heinforcin" Dars siPe C4

rea of one bar s/barin2 0.2

Dar ,iameterin 0.5

!acin" bet+een bars in 18

9a*imum !acin" of bars in 18

!acin" HeJuirement &( )E!

!teel rea in 16ft stri in2 0.13

9inimum rea for !hrinka"e Dars in2/ft 0.10

rea "reater than min.reJuirement( )E!




C-55



C r e a t e d b y :

1 1 / 1 / 2 0 1 1

f r o m B a n k I n f o r m a t i o n

B e a m p a n

1 ! . "

#

# r o m T o $ e r % e

o m e t r y

B e a m T r ' b u t a r y ( r e a

1 2 "

# t 2

B e a m p a c ' n +

, . 1

#

o r e ' ( o a ' i n g o n ' i t i o n s

m p o s i t e

# r o m l a b 3 e

c k I n # o

l a b a n d 3 e c k ' n +

" 2

p s

B e a m e l # 7 e ' + * t

1

p l #

C o n s t r u c t ' o n L L

2 0

p s

o m p o s i t e

# r o m L o a d u m

m a r y

3 L

! 9

p s

L L

1 0 0

p s #

e ' ( o a ' i n g o n ' i t i o n s

m p o s i t e

l a b a n d 3 e c k ' n +

" , .

p s #

B e a m e l # 7 e ' + * t

1 6 . ,

p l #

C o n s t r u c t ' o n L L

" 2

p s #

o m p o s i t e

3 L

6 , .

p s #

L L

1 6 0

p s

n ' * e a ! t i o n s

m p o s i t e

, a ! t o r e '

3 L

2 . ;

k ' p s

L L

1 . ; 9

k ' p s

T o t a l

. !

k ' p s

o m p o s i t e

3 L

. 2 0

k ' p s

L L

; . , "

k ' p s

T o t a l

1 . 0

k ' p s

p r e d e t e r m ' n e d d e c k ' n + t y p e r u n

n ' n + p e r p e n d ' c u l a r t o t * e

s . & o ' s t n d r e a c t ' o n s a r e u s e d # o

r r a d ' a l + ' r d e r d e s ' + n .

C & B / ( 3

s i g n T o o l

n k :

1

U s e r I n p u t

I n p u t s

p e :

L o b b y

C o n s t a n t / P r e v . C a l c .

m :

& o ' s t 1

C a l c / L o o k u p

B a n k 1

) e s

P a s s e s C * e c

p e

1 2 - 1

o

a ' l s C * e c k

e %

)

& n f a !

t o

a ' l s ' n : o n e

) r e !

o m

u '

4 " 0 5

n g

6

* i $

1

o n

! 0 8

) o s t

! o

7 1

2 - 1

( s

. 1 6

' n

, a ! t o r e

d

1 1 . ;

' n

) r e !

o m

t #

0 . 2 2 !

' n

t $

0 . 2 0

' n

b #

" . ; 9

' n

-

1 . ;

' n "

) o s t

! o

I -

, , . 6

' n

1

p l

J o i s t n

4 a 5

6

' n

) r e !

o m

4 b 5

; 9

' n

b e # #

6

' n

= b 5

y b

1 2 . 1 6

' n

) o s t

! o

y t

" . 9

' n

o m p

" 1 ;

' n

t r

2 6 . 2

' n "

= I c / y b

c

, !

' n

= I c / y t

n d

* e a r s t u d c o n # ' + u r a t ' o n # o r @ o ' s t s

' n a l l b a n k s a n d # l o o r t y p e s $ ' t * a p

o u n

d ' n T a r a n a t * A s S t e e l , C o n c r e t e , &

C o m p o s i t e D e s i g n o f T a l l B u i l d i n g s

3 . 3 . 2 . 1

J o i s t D e

s

C r e a t e d b y :

1 1 / 1 / 2 0 1 1

C & B / ( 3

) r o p e r t i e s

t r e n + t *

y

! 0

k s '

t e t r e n + t *

u

6 !

k s '

< o d u l u s

s

2 ; > 0 0 0

k s '

e t e ) r o p e r t i e s

t e T y p e

L ' + * t $ e ' + * t

t e t r e n + t *

# A c

> 0 0 0

p s '

y o # c o n c r e t e

F c

1 1 !

p c #

< o d u l u s

c

2 > ! 9

k s '

= " " F c

# A c 0 . !

a r D a t ' o

n

1 1

= s / c

n ' D e ! k i n g ) r o p e r t i e s

t 3 e c k ' n + T y p e

1 . ! L 2 2

' c k n e s s

2 . !

' n

+ * t

t d

1 . !

' n

C

" 6

' n

P

6

' n

T

" . !

' n

B

1 . 9 !

' n

o m p o s ' t e 3 e p t *

1 ! . ;

' n

= t d G t s G d

s i g n T o o l

S t e e l

)

! ,

p l #

) ' e l d

t

1 > , 1

p l #

U l t ' m a t

2 > 1 6 9

p l #

l a s t ' c

<

< u

6 "

k ' p ? # t

= $ l / ,

o n ! r e

m ' n

2 2 . ;

' n

= < m a - / 4 0 . 6 6 y

5

C o n c r e t

C o n c r e t

3 e n s ' t y

s

1 . ;

' n "

l a s t ' c

<

t r

2 6 . 2

' n

< o d u

l a

p r e

1 9 . 0

k ' p ? # t

< o d e l e d a s p ' n ? p ' n

p o s t

! " . !

k ' p ? # t

< o d e l e d a s p ' n ? p ' n

S l a $ a

n

u l c r a

# t

l a b t * '

# b > 1

" , . 2

k s '

= 2

" 2 . "

k s '

= 4 <

p r e G <

p o s t

5 / t r

y

" " . 0

k s '

y J

)

T o t a l C o

o m p

!

k ' p ? # t

o m p

0 . 6 ,

k s '

= < c o m p

/ 4 n

t 5

o m p

1 . ,

k s '

p J

)

3 . 3 . 2 . 1

J o i s t D e s

C r e a t e d b y :

1 1 / 1 / 2 0 1 1

C & B / ( 3

S t u ' ) r o p e r t i e s

t e r

0 . 9 !

' n

*

" . 0 0

' n

+

6

' n

b s

n r ' b s

" 0

/ r ' b

1

a p a c ' t y

s t u d

1 9 . 2

= M n p e r r ' b N ( I C T a b l e " ? 2 1

u d s

" 0

' t e a c t ' o n

h e ! k s f r o m # I S I 3 . 2 ! . 1

a l D ' b * e ' + * t " Q

)

I " . 2 c . 1 . a

t u d 3 ' a m a t e r " / Q

)

I " . 2 c . 1 . b

t u d L e n + t * R 1 1 / 2 Q

)

I " . 2 c . 1 . b

e t e C o v e r R 1 / 2 Q

)

I " . 2 c . 1 . b

* ' c k n e s s R 2 Q

)

I " . 2 c . 1 . c

t u d p a c ' n + 1 , Q

)

I " . 2 c . 1 . d

e ( o a ' s 5 & n f a ! t o r e ' 6

m p o s ' t e

" "

p l #

o m p o s ' t e

1 2 6

!

p l #

e s i g n T o o l

S h e a r

4 ' 5

" , ;

k ' p

= 0 . , ! # A c

( c

3 ' a m e

t

4 ' ' 5

2 0 ,

k ' p

= ( s y

L e n + t *

*

2 0 ,

k ' p s

= ' ' 5

p a c ' n

+

o # D ' b

tio n

s t u d s

/

s

2 2 . ; 1

' n "

t u d c

a

e n s

2 6 . 2 2

' n

o # t u

m ' n

2 2 . ; 1

' n "

A *

1 0 . 1

k ' p s

= *

4

m ' n

? s

/ a v a ' l ? s 5 2 =

/ ( ' # 1 0 0 8 c o m p o s '

! 0 8

)

S t u '

o m ' n

1 0 . 1

k ' p

= A *

* e a r

r ' b s

" 0

* e a r

m

,

# t

C o n c r e

n

2 ! ,

k ' p s

= S M n = 4 s t u d s / r ' b 5 s t u d

n r ' b s m / l N ( I C l a b T

*

n J

)

* e a r

S e r v i !

I e # #

1 6 . "

' n

= I - G 4 I

c ? I -

5 4 A * / *

5 2

P r e C o

I -

, , . 6

' n

P o s t C

o

p r e

0 . 2 0 !

' n

= ! 7 L /

4 " , I 5

b e r

0 . 0 0

' n

p o s t

0 . " 6 "

' n

= ! 7 L /

4 " , I 5

6 0

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3.3.2.2b 2-Point Deflection Calculations Created by: ADV/CJB 11/1/2011

Input from Cantilever Worksheet Maximum Deflection

Es 29000 ksi Precomposite 0.2!!" in

Ie !9" in!

Postcomposite 0.#$3#0$$ in

Is !!" in!

#e$ %ei&'t 0(00)0 kip/in

*en&t' ))1 in

#pacin& 110 in

%nfactore& 'oa&s from Cantilever Worksheet

Precomposite Post Composite a b

Joist 1 !(2+ +(,9 kips 221 110 in a and b rom AI#C -an.a$

Joist 2 (!+ "(9 kips 110 221 in

Precomposite Deflection from( Post Composite Deflection from(

Joist 1 Joist 2 #e$ %ei&'t ota$ Joist 1 Joist 2 ota$

in in in in in in in in in

0(0 0 0 0 0 0(0 0 0 0

)() !()+0"E30 0(0001111", 1(1))E30 0(0001++1!9 )() +(2!909E30 0(0001,!1 0(00021990!

+(+ 0(0001,2), 0(000!),209 !(!01E30 0(000+!0" +(+ 0(0002!,01) 0(000+1"9" 0(000"+992

9(9 0(000)")21 0(0009++,9 9("09!2E30 0(001!!"0+! 9(9 0(000!91! 0(001)+"+9 0(00191,")1

1)() 0(000+,)02, 0(001+"") 0(0001,0"1) 0(002)2), 1)() 0(0009+!!!, 0(002)90! 0(00))!9"+

1+(+ 0(0010)",) 0(0029121+ 0(0002+1)+) 0(00)"91)1! 1+(+ 0(001!""0+ 0(00)++"2 0(001,02)

19(9 0(001!,,2!, 0(00)++)0" 0(000)+"!"2 0(00092)+ 19(9 0(00211+"9) 0(001"++2 0(00,)0)09

2)(2 0(0019"!,) 0(00!"9!1 0(000!909) 0(00,),00) 2)(2 0(002"!1"1 0(00+92"") 0(009,,!009

2+( 0(002+0)2 0(00+2,1+" 0(000+2,!99 0(009!909 2+( 0(00)++"9!! 0(00"",91! 0(012!"0"9

29(" 0(00)19",1 0(00,,"!9 0(000,,,00" 0(011,+0+," 29(" 0(00!"),, 0(011021+ 0(01+0)1

))(1 0(00)"9,! 0(009!22+0) 0(0009)")02 0(01!2"!9 ))(1 0(00"192 0(01))!00+ 0(01"922)

)+(! 0(00!+),) 0(0111,))2) 0(0011102 0(01+9),))1 )+(! 0(00+++""2 0(01"1"+! 0(022!",!+9

)9(" 0(00!+!22! 0(01)02"0+ 0(001291,,1 0(019,"1"01 )9(" 0(00,")022" 0(01"!!1) 0(02+2,129

!)(1 0(00+)2",, 0(01!9+",!, 0(001!"1,,, 0(022,,+!01 !)(1 0(0090+!9,, 0(02119202 0(0)02+99"

!+ ! 0 00,2)+2 0 01+990")" 0 001+,92)1 0 0290+9 !+ ! 0 010)+"+! 0 02!0!" 0 0)!!2)!!)

Ca$c.$ates de$ection .nder precomposite $oads and .nder s.perimposed dead and $i4e $oads .sin& princip$es o s.perposition( 5i4es de$ection at 100 $ocations

a$on& t'e beam 6'en it is s.b7ected to t6o point $oads(



!+(! 0(00,2)+2 0(01+990")" 0(001+,92)1 0(0290+9 !+(! 0(010)+"+! 0(02!0!" 0(0)!!2)!!)

!9(, 0(00"190),9 0(0190"0,,1 0(001"")12 0(0291!2, !9(, 0(011,)+"0, 0(02,01)+2 0(0)",0!)

)(0 0(0091",0 0(02122,2! 0(002092! 0(0)20+,! )(0 0(01)1+0) 0(0)002!9 0(0!)21,2!

+() 0(010222!9 0(02)!1"9)" 0(002)0+2," 0(0)9!,,+! +() 0(01!+!"90 0(0))1)9 0(0!,"0!292

9(+ 0(01129),"" 0(02+!!+ 0(0022)+, 0(0)9!+2001 9(+ 0(01+1")99 0(0)+)0+)1 0(02!90299

+2(9 0(012)9,+,9 0(02,"92,9 0(002,!)+"" 0(0!)0)!1+ +2(9 0(01,,+"+) 0(0)9!"92 0(0,2112

++() 0(01))11)1 0(0)012)) 0(0029+!9, 0(0!++!"9" ++() 0(019)901 0(0!2+""19 0(0+20,"29

+9(+ 0(01!+910" 0(0)2!11", 0(00)1""2) 0(002911+) +9(+ 0(021022, 0(0!"",1! 0(0++9)9!1+

,2(9 0(01",!), 0(0)!++010) 0(00)!110"2 0(0)9! ,2(9 0(022,!,9+ 0(0!90,00" 0(0,1"1"0!

,+(2 0(01,0,,9,9 0(0)+"",22 0(00)+))2! 0(0,9+9!+ ,+(2 0(02!!,2,)1 0(02221 0(0,++9),))

,9( 0(01"29",9+ 0(0)90,,!19 0(00)")9+ 0(0+12)01,+ ,9( 0(02+2221+ 0(0)2)9 0(0"1!+0+1

"2(" 0(019)),)2 0(0!122)""" 0(00!0,2!91 0(0+!")0111 "2(" 0(02,991"2) 0(0")+2,, 0(0"+)!9

"+(1 0(020,,9, 0(0!))1)"22 0(00!2""12, 0(0+")"1+!9 "+(1 0(029,,,29) 0(0+1)219 0(09109"""

"9(! 0(0220))+09 0(0!))912 0(00!001"9 0(0,1"+9,11 "9(! 0(0)1,!1!! 0(0+!1"!), 0(09,"1)

92(" 0(02)292),2 0(0!,2,"") 0(00!,0"02) 0(0,2,92!" 92(" 0(0))),,9 0(0++9)09 0(100)1)0!

9+(1 0(02!29 0(0!91)1)), 0(00!91100) 0(0,"92! 9+(1 0(0)1"!2"+ 0(0+9,, 0(10!,!20)1

99(! 0(02"1210! 0(00""20+ 0(0010")2 0(0"1"02+9) 99(! 0(0)+9"",2! 0(0,20)+)) 0(109020)

102(, 0(02,0++"9+ 0(0219,0 0(00)000! 0(0"!""++! 102(, 0(0)","+"! 0(0,!)!") 0(11)1!1+,2

10+(0 0(02")1!1", 0(0!0)29, 0(00!"!9"! 0(0",")21! 10+(0 0(0!0,!20, 0(0,+!9,2 0(11,0,1!2

109() 0(0290""" 0(0!109 0(00++2" 0(090+2!29, 109() 0(0!2)!+)99 0(0,"!!,+ 0(120,9)9+1

112(+ 0(0)0,,)911 0(0++!190 0(00"))11 0(09)2!"9+" 112(+ 0(0!!09"99 0(0"0190"! 0(12!2"9")1

11(9 0(0)19"01+, 0(0,,2222 0(0099!) 0(09,00"19 11(9 0(0!"2,! 0(0"1,2! 0(12,2102

119() 0(0))1+++" 0(0"++!),) 0(00+1!92 0(09,9"019+ 119() 0(0!,2,++ 0(0")0!1 0(1)0"1"1"

122(+ 0(0)!))002 0(09!+))1 0(00+29!22) 0(1000",+2 122(+ 0(0!919!"9" 0(0"!1"2+ 0(1)))"01!

1,2() 0(0!+92")1, 0(0,)1)!" 0(00,21+")! 0(111!"+99 1,2() 0(0+,2!"2!1 0(0"11!1,2 0(1!")"99+2

1,(+ 0(0!,)0!+1 0(0+!0,),, 0(00,1",9!9 0(110"999!1 1,(+ 0(0+,,",!, 0(0,9"""1 0(1!,+!+2")1,"(9 0(0!,+0!+2 0(0!2"2,! 0(00,1!,+0" 0(1101"1)!! 1,"(9 0(0+"21""9 0(0,"!,2+! 0(1!++912)

1"2(2 0(0!,"2,,+9 0(0!)"019" 0(00,0990" 0(109)0)", 1"2(2 0(0+"),1 0(0,+9""") 0(1!29"2

1"( 0(0!,9+"!!9 0(0)2+,10+ 0(00,0)29,) 0(10"2+"2" 1"( 0(0+",)",!9 0(0,!129, 0(1!!11,1

1""(" 0(0!"02!!12 0(020929 0(00+9"9, 0(10,0,+)2 1""(" 0(0+""1"9!! 0(0,),0++ 0(1!2+9+0!

192(1 0(0!,992, 0(00"+1,0! 0(00+",!0!1 0(10,2")1! 192(1 0(0+",,))1! 0(0,200,1 0(1!0,"0"29

19(! 0(0!,"+9")! 0(0!9,,)09 0(00+,,"!)) 0(10!22, 19(! 0(0+"9,!)) 0(0,01"91) 0(1)","++!

19"(" 0(0!,+)11 0(0!"2!),2" 0(00++,2)+9 0(102+9211 19"(" 0(0+"2"+",+ 0(0+")0111 0(1)+",9""

202(1 0(0!,))9)2 0(0!+"+!91" 0(00++11) 0(100,+0)+ 202(1 0(0+,"),21 0(0++)!90+ 0(1)!1"+2,+

20(! 0(0!+92), 0(0!!!!")" 0(00+!299" 0(09""001,1 20(! 0(0+,2!!02 0(0+!))"" 0(1)1"2+0+

20"(, 0(0!+!0"1,, 0(0!)9",!!! 0(00+29!22) 0(09++"9"!) 20"(, 0(0++02""1 0(0+22,2, 0(12",,"1!

212(0 0(0!,"!+!2 0(0!2!9++9! 0(00+1!92 0(09!!)091 212(0 0(0++09)+ 0(0+01+!,! 0(12,,!09"

21() 0(0!01+"1 0(0!09,+! 0(0099!) 0(09202)+, 21() 0(0+!902) 0(0"0129 0(122,1+1)21"(+ 0(0!!20+20+ 0(0)9!)09 0(00"))11 0(0"9!,0)1) 21"(+ 0(0+))!,!" 0(0"2!!2 0(1191,1","

221(9 0(0!)2!202 0(0),"+)""2 0(00++2" 0(0"+,,19)! 221(9 0(0+19,0)! 0(0)+0") 0(11,+1,!

22() 0(0!21,00+ 0(0)+2,92") 0(00!"!9"! 0(0")9)!))2 22() 0(0+0!29+, 0(01)+2!! 0(111,9210+

22"(+ 0(0!09"90)) 0(0)!+"111 0(00)000! 0(0"09,01"" 22"(+ 0(0",),21 0(0!9099") 0(10,"),0"

2)1(9 0(0)9,10929 0(0))0,))), 0(0010")2 0(0,,"92,9" 2)1(9 0(0+90,) 0(0!+"2)+1 0(10),29)!!

2)(2 0(0)")!!,9 0(0)1!990! 0(00!91100) 0(0,!,1!", 2)(2 0(0!9!,,1 0(0!!)9! 0(099!",1!+

2)"( 0(0)+"9""0, 0(029"!!,,+ 0(00!,0"02) 0(0,1!1+0+ 2)"( 0(02",9+1 0(0!222," 0(0912",)+

2!1(" 0(0))"2!)" 0(02"2)1909 0(00!001"9 0(0+"11!)+ 2!1(" 0(00,0)00 0(0)99+9)+ 0(090+,2)+2

2!(1 0(0))"0!29+ 0(02++22+1 0(00!2""12, 0(0+!,1,+" 2!(1 0(0!"!!129 0(0),+9!,! 0(0"+1)+2,)

2!"(! 0(0)21,)20+ 0(0202","9 0(00!0,2!91 0(0+12,!!"+ 2!"(! 0(0!+10!1,9 0(0)!)!! 0(0"1)",1+

21(" 0(0)0!9,99! 0(02)!!+!2 0(00)")9+ 0(0,,9"!0 21(" 0(0!),0)+ 0(0))19!)! 0(0,+"9,9!1

2(1 0(02",",!"2 0(021""220 0(00)+))2! 0(0!)029)2 2(1 0(0!122!)9 0(0)09,9,+ 0(0,22)219+

2"(! 0(02,00!9, 0(020)!000" 0(00)!110"2 0(00"01"+ 2"(! 0(0)",+))! 0(02",9+)9 0(0+,9,29

2+1(, 0(0229"+2 0(01""2)"1, 0(00)1""2) 0(0!,)0,91! 2+1(, 0(0)+2!"9 0(02++!9"! 0(0+2"9",9

2+(0 0(02))2!02 0(01,)),9 0(0029+!9, 0(0!)")!"9 2+(0 0(0)),2191! 0(02!!,1 0(0"2+,+2+

2+"() 0(021,+"9!) 0(01""2"! 0(002,!)+"" 0(0!0)9,91 2+"() 0(0)119!"," 0(022!"9+1 0(0)+"!!"+

2,1(+ 0(02001!)0" 0(01!!,0", 0(0022)+, 0(0),00""22 2,1(+ 0(02"+"0!"" 0(020!",1) 0(0!91+,+2

2,!(9 0(01"2,,)2) 0(01)09"2++ 0(002)0+2," 0(0))+"1"+, 2,!(9 0(02+191)"9 0(01"!)"9 0(0!!,)2,!

2,"() 0(01+++"11 0(011,,1!, 0(002092! 0(0)0!)0,)+ 2,"() 0(02),!022, 0(01+++!, 0(0!0!0+99

2"1(+ 0(01!"919" 0(010!9!!2! 0(001"")12 0(02,2+91!2 2"1(+ 0(021))9+!9 0(01!",!9 0(0)+19,1!2

2"!(9 0(01)2+009 0(0092,10"" 0(001+,92)1 0(02!210"2" 2"!(9 0(01900229" 0(01)12 0(0)212,"1

2""(2 0(011+"2)+, 0(00"10!1, 0(001!"1,,, 0(0212+9+1 2""(2 0(01+,!0"2) 0(011!,2 0(02"21+0,+

291( 0(0101+99" 0(00,001),1 0(001291,,1 0(01"!91)9 291( 0(01!+,"+, 0(0099122 0(02!!"00++

29!(" 0(00",2022+ 0(009+290+ 0(0011102 0(01,9))", 29!(" 0(012!9+0,, 0(00"!!199 0(0209)"0+,



29!(" 0(00",2022+ 0(009+290+ 0(0011102 0(01,9))", 29!(" 0(012!9+0,, 0(00"!!199 0(0209)"0+,

29"(1 0(00,))",+ 0(00!99)9" 0(0009)")02 0(01)2"+1, 29"(1 0(010)"09" 0(00,0,02) 0(01,+0"))

)01(! 0(00+0,,,2 0(00!09" 0(000,,,00" 0(01091)) )01(! 0(00",0+,, 0(00"02) 0(01!0910)

)0!(" 0(00!"9!,! 0(00)2"0,) 0(000+2,!99 0(00""02"12 )0!(" 0(00,01!1" 0(00!+!!!" 0(011+"+)!

)0"(1 0(00)"19+0) 0(002!!009 0(000!909) 0(00+"!!2 )0"(1 0(00!,)!"" 0(00)+01+" 0(0090,1,1

)11(! 0(002"91", 0(001"92"12 0(000)+"!"2 0(00120!"1 )11(! 0(00!09,21) 0(002+,9, 0(00+,,+9+!

)1!(, 0(002022)1+ 0(001))09!) 0(0002+1)+) 0(00)+1!+22 )1!(, 0(002"9,9,, 0(001""!2" 0(00!,"22+1

)1"(0 0(001)1,"1 0(000"+2), 0(0001,0"1) 0(002)09"! )1"(0 0(001"""!2, 0(001220"" 0(00)109)1

)21() 0(000,!0" 0(000!91012 9("09!2E30 0(001)!)+1! )21() 0(0010"1209 0(000+91 0(001,,+)9

)2!(+ 0(000)!122 0(000220"++ !(!01E30 0(000+0+", )2!(+ 0(000!""9+" 0(000)12+9 0(000"01+9

)2,(9 "(+,,,E30 (",+E30 1(1))E30 0(0001!00 )2,(9 0(00012!) ,(910,E30 0(00020)!+

))1() 0 0 0 0 ))1() 0 0 0

3.3.2.2c 3-Point Deflection Calculations Created by: ADV/CJB 11/1/2011


Es 29000 ksi Precomposite 0.06 in

Ie 10!" in#

Postcomposite 0.3 in

Is "90 in#

$e% &ei'(t 0)00#! kip/in

*en't( ++1 in

$pacin' "+ in

!nfactore" #oa"s from Cantilever Worksheet

Precomposite Post Composite a b

Joist 1 +)09 ")"" kips 2#" "+ in a and b rom AI$C ,an-a%

Joist 2 +)9. 10)+ k ips 1!. 1!. in

Joist + #).1 12)10 kips "+ 2#" in

Precomposite Deflection from$ Post Composite Deflection from$

Joist 1 Joist 2 Joist + $e% &ei'(t ota% Joist 1 Joist 2 Joist + ota%

in in in in in in in in in in in

0)0 0)00E300 0)00E300 0)00E300 0)00E300 0)00E300 0)0 0)00E300 0)00E300 0)00E300 0)00E300

+)+ 1)00E40. +)#2E40. #)+!E40. ")!"E40! 9)!.E40. +)+ 2)#1E40. )+E40. 9)#E40. 1)99E40#

!)! +)9E40. 1)+.E40# 1)1E40# +)#0E40. +)9E40# !)! 9).2E40. +)0.E40# +)"2E40# )"2E40#

9)9 ")"+E40. 2)99E40# +)!E40# ).0E40. ")+9E40# 9)9 2)12E40# !)E40# ")#1E40# 1)+E40+

1+)2 1)..E40# .)2#E40# !)..E40# 1)+1E40# 1)#!E40+ 1+)2 +)2E40# 1)19E40+ 1)#!E40+ +)02E40+

1!). 2)#0E40# ")0"E40# 1)00E40+ 2)00E40# 2)2.E40+ 1!). .)#E40# 1)"+E40+ 2)2#E40+ #)!#E40+

19)" +)#1E40# 1)1.E40+ 1)#1E40+ 2)"2E40# +)1"E40+ 19)" ")1"E40# 2)!0E40+ +)1.E40+ !).!E40+

2+)2 #).9E40# 1).#E40+ 1)"E40+ +).E40# #)2.E40+ 2+)2 1)10E40+ +)#"E40+ #)19E40+ ")E40+

2!). .)92E40# 1)9"E40+ 2)+9E40+ #)"0E40# .)##E40+ 2!). 1)#2E40+ #)#"E40+ .)+#E40+ 1)12E402

29)" )#0E40# 2)#E40+ 2)9.E40+ .)9#E40# !)!E40+ 29)" 1)E40+ .).9E40+ !)!0E40+ 1)#0E402

++)1 9)0+E40# +)00E40+ +).!E40+ )1"E40# ")1"E40+ ++)1 2)1!E40+ !)9E40+ )9.E40+ 1)!9E402

+!)# 1)0"E40+ +).E40+ #)20E40+ ")#9E40# 9)0E40+ +!)# 2)."E40+ ")09E40+ 9)+"E40+ 2)01E402

+9) 1)2E40+ #)19E40+ #)"E40+ 9)""E40# 1)1+E402 +9) +)0#E40+ 9)#"E40+ 1)09E402 2)+#E402

#+)0 1)#E40+ #)"#E40+ .).!E40+ 1)1+E40+ 1)+0E402 #+)0 +).2E40+ 1)10E402 1)2#E402 2)!9E402

#!)+ 1)!"E40+ .).2E40+ !)2"E40+ 1)2"E40+ 1)#"E402 #!)+ #)0+E40+ 1)2.E402 1)#0E402 +)0!E402

#9)! 1)90E40+ !)2+E40+ )00E40+ 1)##E40+ 1)!!E402 #9)! #).!E40+ 1)#1E402 1).E402 +)#+E402

.2)9 2)1#E40+ !)9E40+ )#E40+ 1)!0E40+ 1)".E402 .2)9 .)12E40+ 1)."E402 1)+E402 +)"2E402

.!)2 2)+"E40+ )#E40+ ")#"E40+ 1)!E40+ 2)0#E402 .!)2 .)0E40+ 1).E402 1)90E402 #)22E402

.9 . 2 !+E 0+ " .2E 0+ 9 22E 0+ 1 9+E 0+ 2 2+E 02 .9 . ! +1E 0+ 1 9+E 02 2 0!E 02 # !2E 02

Ca%c-%ates de%ection -nder precomposite %oads and -nder s-perimposed dead and %i5e %oads -sin' princip%es o s-perposition) 6i5es de%ection at 100 points a%on' t(e beam

7(en s-b8ected to t(ree point %oads)



.9). 2)!+E40+ ").2E40+ 9)22E40+ 1)9+E40+ 2)2+E402 .9). !)+1E40+ 1)9+E402 2)0!E402 #)!2E402

!2)" 2)"9E40+ 9)++E40+ 9)9.E40+ 2)10E40+ 2)#+E402 !2)" !)9+E40+ 2)11E402 2)2+E402 .)0+E402

!!)2 +)1!E40+ 1)02E402 1)0E402 2)2E40+ 2)!+E402 !!)2 ).E40+ 2)+0E402 2)+9E402 .)##E402

!9). +)#+E40+ 1)10E402 1)1#E402 2)##E40+ 2)"2E402 !9). ")2+E40+ 2)#9E402 2).#E402 .)".E402

2)" +)1E40+ 1)1"E402 1)21E402 2)!1E40+ +)02E402 2)" ")90E40+ 2)!"E402 2)!9E402 !)2E402

!)1 #)00E40+ 1)2E402 1)2E402 2)"E40+ +)22E402 !)1 9)."E40+ 2)"E402 2)"#E402 !)!E402

9)# #)29E40+ 1)+!E402 1)++E402 2)9.E40+ +)#1E402 9)# 1)0+E402 +)0E402 2)9"E402 )0"E402

"2) #)."E40+ 1)##E402 1)+9E402 +)11E40+ +)!0E402 "2) 1)10E402 +)2E402 +)11E402 )#E402

"!)0 #)""E40+ 1).+E402 1)##E402 +)2"E40+ +)9E402 "!)0 1)1E402 +)#!E402 +)2+E402 )"!E402

"9)+ .)1"E40+ 1)!2E402 1)#9E402 +)##E40+ +)9E402 "9)+ 1)2#E402 +)!!E402 +)+#E402 ")2+E402

92)! .)#"E40+ 1)0E402 1).#E402 +)!0E40+ #)1.E402 92)! 1)+1E402 +)".E402 +)##E402 ")!0E402

9.)9 .)9E40+ 1)9E402 1)."E402 +)!E40+ #)+2E402 9.)9 1)+9E402 #)0#E402 +).+E402 ")9!E402

99)2 !)09E40+ 1)"E402 1)!1E402 +)91E40+ #)#"E402 99)2 1)#!E402 #)2+E402 +)!1E402 9)+0E402102). !)#0E40+ 1)9.E402 1)!.E402 #)0.E40+ #)!#E402 102). 1).+E402 #)#2E402 +)!"E402 9)!+E402

10.)9 !)0E40+ 2)0+E402 1)!"E402 #)19E40+ #)"0E402 10.)9 1)!1E402 #)!0E402 +).E402 9)9.E402

109)2 )00E40+ 2)11E402 1)0E402 #)++E40+ #)9.E402 109)2 1)!"E402 #)"E402 +)"0E402 1)0+E401

112). )+0E40+ 2)19E402 1)2E402 #)#!E40+ .)09E402 112). 1).E402 #)9.E402 +)".E402 1)0!E401

11.)" )!0E40+ 2)2!E402 1)#E402 #)."E40+ .)22E402 11.)" 1)"2E402 .)12E402 +)"9E402 1)0"E401

119)1 )90E40+ 2)++E402 1).E402 #)0E40+ .)+.E402 119)1 1)"9E402 .)2"E402 +)92E402 1)11E401

122)# ")19E40+ 2)#0E402 1)E402 #)"1E40+ .)#E402 122)# 1)9!E402 .)##E402 +)9.E402 1)1+E401

12.) ")#E40+ 2)#E402 1)E402 #)92E40+ .)."E402 12.) 2)0+E402 .)."E402 +)9!E402 1)1!E401

129)0 ").E40+ 2).+E402 1)"E402 .)01E40+ .)!"E402 129)0 2)10E402 .)2E402 +)9E402 1)1"E401

1+2)+ 9)0+E40+ 2)."E402 1)"E402 .)10E40+ .)"E402 1+2)+ 2)1!E402 .)".E402 +)9"E402 1)20E401

1+.)! 9)29E40+ 2)!#E402 1)"E402 .)1"E40+ .)"!E402 1+.)! 2)2+E402 .)9E402 +)9E402 1)22E401

1+")9 9)..E40+ 2)!9E402 1)E402 .)2!E40+ .)9#E402 1+")9 2)29E402 !)0"E402 +)9!E402 1)2+E401

1#2)2 9)"0E40+ 2)+E402 1)E402 .)+2E40+ !)01E402 1#2)2 2)+.E402 !)1"E402 +)9.E402 1)2.E4011#. . 1 00E 02 2 E 02 1 !E 02 . +"E 0+ ! 0E 02 1#. . 2 #1E 02 ! 2E 02 + 9+E 02 1 2!E 01

Precomposite Deflection from$ Post Composite Deflection from$

Joist 1 Joist 2 Joist + $e% &ei'(t ota% Joist 1 Joist 2 Joist + ota%in in in in in in in in in in in

19.)2 1)22E402 2)!#E402 1)+!E402 .)1"E40+ .)+E402 19.)2 2)92E402 .)9E402 +)0+E402 1)19E401

19"). 1)22E402 2)."E402 1)+2E402 .)10E40+ .)!+E402 19"). 2)92E402 .)".E402 2)9.E402 1)1E401

201)" 1)22E402 2).+E402 1)2"E402 .)01E40+ .).2E402 201)" 2)92E402 .)2E402 2)"!E402 1)1.E401

20.)1 1)21E402 2)#E402 1)2#E402 #)92E40+ .)#1E402 20.)1 2)91E402 .)."E402 2)!E402 1)1+E401

20")# 1)21E402 2)#0E402 1)20E402 #)"1E40+ .)29E402 20")# 2)90E402 .)##E402 2)!E402 1)10E401

211) 1)20E402 2)++E402 1)1.E402 #)0E40+ .)1!E402 211) 2)""E402 .)2"E402 2)."E402 1)0E401

21.)0 1)19E402 2)2!E402 1)11E402 #)."E40+ .)02E402 21.)0 2)"!E402 .)12E402 2)#"E402 1)0.E401

21")+ 1)1"E402 2)19E402 1)0E402 #)#!E40+ #)""E402 21")+ 2)"+E402 #)9.E402 2)+"E402 1)02E401

221)! 1)1!E402 2)11E402 1)02E402 #)++E40+ #)+E402 221)! 2)9E402 #)"E402 2)29E402 9)"!E402

22#)9 1)1.E402 2)0+E402 9)"E40+ #)19E40+ #)."E402 22#)9 2).E402 #)!0E402 2)19E402 9).#E402

22")2 1)1+E402 1)9.E402 9)+#E40+ #)0.E40+ #)#2E402 22")2 2)0E402 #)#2E402 2)09E402 9)21E402

2+1). 1)11E402 1)"E402 ")"9E40+ +)91E40+ #)2!E402 2+1). 2)!.E402 #)2+E402 1)99E402 ")"E402

2+#)9 1)0"E402 1)9E402 ")#.E40+ +)!E40+ #)09E402 2+#)9 2).9E402 #)0#E402 1)"9E402 ").2E402

2+")2 1)0.E402 1)0E402 ")01E40+ +)!0E40+ +)91E402 2+")2 2).2E402 +)".E402 1)9E402 ")1!E402

2#1). 1)02E402 1)!2E402 ).!E40+ +)##E40+ +)#E402 2#1). 2)#.E402 +)!!E402 1)!9E402 )"0E402

2##)" 9)"9E40+ 1).+E402 )1+E40+ +)2"E40+ +).!E402 2##)" 2)+E402 +)#!E402 1).9E402 )#2E402

2#")1 9).2E40+ 1)##E402 !)!9E40+ +)11E40+ +)+E402 2#")1 2)2"E402 +)2E402 1).0E402 )0#E402

2.1)# 9)12E40+ 1)+!E402 !)2!E40+ 2)9.E40+ +)19E402 2.1)# 2)19E402 +)0E402 1)#0E402 !)!!E402

2.#) ")0E40+ 1)2E402 .)"#E40+ 2)"E40+ +)00E402 2.#) 2)09E402 2)"E402 1)+0E402 !)2!E402

2.")0 ")2!E40+ 1)1"E402 .)#2E40+ 2)!1E40+ 2)"1E402 2.")0 1)9"E402 2)!"E402 1)21E402 .)"E402

2!1)+ )9E40+ 1)10E402 .)01E40+ 2)##E40+ 2)!2E402 2!1)+ 1)"E402 2)#9E402 1)12E402 .)#"E402

2!#)! )+1E40+ 1)02E402 #)!1E40+ 2)2E40+ 2)#+E402 2!#)! 1).E402 2)+0E402 1)0+E402 .)0"E402

2!)9 !)"2E40+ 9)++E40+ #)22E40+ 2)10E40+ 2)2.E402 2!)9 1)!+E402 2)11E402 9)##E40+ #)!9E402

21)2 !)+2E40+ ").2E40+ +)"#E40+ 1)9+E40+ 2)0!E402 21)2 1).1E402 1)9+E402 ").9E40+ #)+0E402

2#). .)"1E40+ )#E40+ +)#E40+ 1)!E40+ 1)""E402 2#). 1)+9E402 1).E402 )E40+ +)92E402

2)9 .)+0E40+ !)9E40+ +)12E40+ 1)!0E40+ 1)0E402 2)9 1)2E402 1)."E402 !)9E40+ +)..E402

2"1)2 #)"0E40+ !)2+E40+ 2)"E40+ 1)##E40+ 1).2E402 2"1)2 1)1.E402 1)#1E402 !)21E40+ +)1"E402

2"#). #)+0E40+ .).2E40+ 2)#.E40+ 1)2"E40+ 1)+!E402 2"#). 1)0+E402 1)2.E402 .)#"E40+ 2)"+E402

2")" +)"1E40+ #)"#E40+ 2)1#E40+ 1)1+E40+ 1)19E402 2")" 9)1+E40+ 1)10E402 #)9E40+ 2)#9E402

291)1 +)++E40+ #)19E40+ 1)".E40+ 9)""E40# 1)0#E402 291)1 )99E40+ 9)#"E40+ #)1#E40+ 2)1!E402

29#)# 2)""E40+ +).E40+ 1).E40+ ")#9E40# ")"E40+ 29#)# !)"9E40+ ")09E40+ +).2E40+ 1)".E402

29) 2)##E40+ +)00E40+ 1)+2E40+ )1"E40# )#E40+ 29) .)"#E40+ !)9E40+ 2)9.E40+ 1).!E402

+01)0 2)02E40+ 2)#E40+ 1)0"E40+ .)9#E40# !)1E40+ +01)0 #)".E40+ .).9E40+ 2)#2E40+ 1)29E402

+0#)+ 1)!#E40+ 1)9"E40+ ")!#E40# #)"0E40# #)9!E40+ +0#)+ +)92E40+ #)#"E40+ 1)9+E40+ 1)0+E402

+0)! 1)2"E40+ 1).#E40+ !)0E40# +).E40# +)"E40+ +0)! +)0"E40+ +)#"E40+ 1).0E40+ ")0!E40+

+10)9 9)!.E40# 1)1.E40+ #)9"E40# 2)"2E40# 2)"9E40+ +10)9 2)+1E40+ 2)!0E40+ 1)11E40+ !)02E40+

+1#)2 !)".E40# ")0"E40# +).0E40# 2)00E40# 2)0#E40+ +1#)2 1)!#E40+ 1)"+E40+ )"2E40# #)2.E40+

+1)! #)#"E40# .)2#E40# 2)2E40# 1)+1E40# 1)++E40+ +1)! 1)0E40+ 1)19E40+ .)0E40# 2)E40+

+20)9 2)."E40# 2)99E40# 1)29E40# ).0E40. )!1E40# +20)9 !)1"E40# !)E40# 2)""E40# 1)."E40++2# 2 1 1E 0# 1 +.E 0# . "0E 0. + #0E 0. + ##E 0# +2# 2 2 "0E 0# + 0.E 0# 1 +0E 0# 1.E 0#

+2#)2 1)1E40# 1)+.E40# .)"0E40. +)#0E40. +)##E40# +2#)2 2)"0E40# +)0.E40# 1)+0E40# )1.E40#

+2). 2)99E40. +)#2E40. 1)#E40. ")!"E40! ")#E40. +2). )1.E40. )+E40. +)2"E40. 1)"2E40#

++0)" 0)00E300 0)00E300 0)00E300 0)00E300 0)00E300 ++0)" 0)00E300 0)00E300 0)00E300 0)00E300

3.3.2.3 Rotated Radial Girder Beam DesignCreated by: DBL 4/30/2012

Calculation shown for Bank 3-4 echanical !loor - "o# $irders

Geometry and Applied Loads

Len%th of &horter 'oist L1 234 in !ro( Drawin%

Len%th of Lon%er 'oist L2 2)* in !ro( Drawin%

Len%th of $irder L 300 in !ro( Drawin%

+nbraced Len%th of $irder l 100 in , L/3

"ributary rea of &horter 'oist "1 21.*3 in2

!ro( Drawin%

"ributary rea of Lon%er 'oist "2 2).)2 in2

!ro( Drawin%

##lied Dead Load DL 1)0 #sf

##lied Dead Load DL 00011 ksi

##lied Lie Load LL 100 #sf

Desi%n of the radial %irders at (echanical floor.

which (ust bend about their weak a<is $irders

oriented about their weak a<is enable the

%usset #late connections for outri%%ers

##lied Lie Load LL 0000* ksi

Dead Load !actor DL 12

Lie Load !actor LL 1*

DLL"otal 00023 ksi , DL5DL 6 LL5LL

"otal !actored Load 71 20 ki#s , 8"15DLL"otal6DL5Dsw15L19/2

"otal !actored Load 72 34 ki#s , 8"25DLL"otal6DL5Dsw25L29/2

Reactions, Internal Forces, Moments

eaction at &u##ort 1 1 30 ki#s , 871 58l -a96725b9/l

eaction at &u##ort 2 2 330 ki#s , 871 5a67258l -b99/l

&hear !orce in &ection ;

3* ki#s , 871 58l -a96725b9/l

Steel Strength

>o(inal &teel &tren%th !y 0 ksi

&teel eduction !actor ? 0

!actored &teel &tren%th ?!y 4 ksi

Selected Section and hec!s

Chosen &ection for 'oist 1 @section @12 < 22

Bea( &elf @ei%ht Density Asw1 0022 ki#/ft&ection odulus &< 24 in

3

Chosen &ection for 'oist 2 @section @12 < 22

Bea( &elf @ei%ht Density Asw2 0022 ki#/ft

&ection odulus &y 24 in3

Chosen &ection for $irder @section @14 < )30

Bea( &elf @ei%ht Density Asw 0)30 ki#/ft

&ection odulus &y 2) in3

a< Deflection (a< 022 in &"> nalysis. attached

llowable Deflection allowable 0) in , L/240

(a< allowable Ees

EesChecks fro( (o(ent. shear. and deflection

Section "roperties

rea of @eb dw ) in2

, bf 5tf F G&C200 $) 8for weak a<is9

Bea( de#th d 224 in

@eb width tw 30) in

@eb Hei%ht h0 1) in

!lan%e @idth bf 1) in

!lan%e "hickness tf 41 in

o(ent of Gnertia 8&tron%9 G< 14.300 in4

o(ent of Gnertia 8@eak9 Gy 4.)20 in4

&ection odulus 8&tron%9 &< 1.20 in3

&ection odulus 8@eak9 &y 2) in3

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C-85

3.3.2.5b Cantilever Deflection Tool Created by: ADV/CJB 11/1/2011


Es 29,000 ksi Precomposite 0.2 in

e!! ","#2 in$

Postcomposite 0.0 in

s %,2%0 in$

&e'! (ei)*t 0+01%0 kip/in

en)t* 2#2 in

-idpoint 11% in

!nfactore" #oa"s from Cantilever Worksheet

Precomposite Post Composite

-idpoint oad 20+%2 #0+%1 kips

Endpoint oad 10+%% 1.+#. kips

$recomposite Deflection from% $ost Composite Deflection from%

-idpt oad Endpt oad &e'! (ei)*t ota' -idpt oad Endpt oad ota'in in in in in in in in in

0+0 0+00E00 0+00E00 0+00E00 0+00E00 0+0 0+00E00 0+00E00 0+00E00

2+# #+.2E30. #+%.E30. %+##E30% 4+"0E30. 2+# #+40E30. #+42E30. 4+$2E30.

$+% 1+$0E30$ 1+$%E30$ 2+.2E30. #+10E30$ $+% 1+$4E30$ 1+$"E30$ 2+9%E30$

4+0 #+12E30$ #+2%E30$ .+%2E30. %+9.E30$ 4+0 #+29E30$ #+##E30$ %+%2E30$

9+# .+.1E30$ .+4"E30$ 9+9#E30. 1+2#E30# 9+# .+"0E30$ .+90E30$ 1+14E30#

11+% "+.%E30$ 9+01E30$ 1+.$E30$ 1+91E30# 11+% 9+00E30$ 9+1"E30$ 1+"2E30#

1#+9 1+22E30# 1+29E30# 2+20E30$ 2+4$E30# 1#+9 1+29E30# 1+#2E30# 2+%1E30#

1%+2 1+%.E30# 1+4.E30# 2+9"E30$ #+41E30# 1%+2 1+4$E30# 1+49E30# #+.#E30#

1"+% 2+1.E30# 2+2"E30# #+"4E30$ $+"1E30# 1"+% 2+2%E30# 2+##E30# $+."E30#

20+9 2+40E30# 2+""E30# $+"%E30$ %+0%E30# 20+9 2+"$E30# 2+9$E30# .+44E30#2#+2 #+#0E30# #+.$E30# .+9%E30$ 4+$$E30# 2#+2 #+$"E30# #+%1E30# 4+09E30#

2. . # 94E30# $ 24E30# 4 1%E30$ " 9%E30# 2. . $ 1"E30# $ #%E30# " .#E30#

Ca'c5'ates de!'ection 5nder precomposite 'oads and 5nder s5perimposed dead and 'i6e 'oads 5sin) princip'es o! s5perposition



2.+. #+94E30# $+24E30# 4+1%E30$ "+9%E30# 2.+. $+1"E30# $+#%E30# "+.#E30#

24+" $+%9E30# .+0%E30# "+$%E30$ 1+0%E302 24+" $+9$E30# .+1%E30# 1+01E302

#0+1 .+$4E30# .+92E30# 9+"4E30$ 1+2$E302 #0+1 .+4.E30# %+0$E30# 1+1"E302

#2+. %+29E30# %+".E30# 1+1$E30# 1+$#E302 #2+. %+%2E30# %+9"E30# 1+#%E302

#$+" 4+14E30# 4+"#E30# 1+#0E30# 1+%#E302 #$+" 4+..E30# 4+99E30# 1+..E302

#4+1 "+10E30# "+""E30# 1+$%E30# 1+"$E302 #4+1 "+.2E30# 9+0.E30# 1+4%E302

#9+$ 9+04E30# 9+99E30# 1+%$E30# 2+04E302 #9+$ 9+..E30# 1+02E302 1+94E302

$1+4 1+01E302 1+12E302 1+"#E30# 2+#1E302 $1+4 1+0%E302 1+1$E302 2+20E302

$$+1 1+12E302 1+2$E302 2+02E30# 2+.%E302 $$+1 1+14E302 1+2%E302 2+$$E302

$%+$ 1+2#E302 1+#4E302 2+2#E30# 2+"2E302 $%+$ 1+29E302 1+#9E302 2+%9E302

$"+4 1+#$E302 1+.0E302 2+$$E30# #+09E302 $"+4 1+$1E302 1+.#E302 2+9.E302

.1+0 1+$%E302 1+%$E302 2+%%E30# #+#4E302 .1+0 1+.$E302 1+%"E302 #+21E302

.#+# 1+.9E302 1+49E302 2+""E30# #+%%E302 .#+# 1+%4E302 1+"2E302 #+$9E302

..+4 1+41E302 1+9$E302 #+12E30# #+94E302 ..+4 1+"0E302 1+9"E302 #+4"E302

."+0 1+"$E302 2+10E302 #+#%E30# $+2"E302 ."+0 1+9$E302 2+1$E302 $+0"E302

%0+# 1+9"E302 2+2%E302 #+%1E30# $+%0E302 %0+# 2+0"E302 2+#1E302 $+#9E302

%2+% 2+12E302 2+$#E302 #+"4E30# $+9#E302 %2+% 2+2#E302 2+$"E302 $+41E302

%$+9 2+2%E302 2+%0E302 $+1#E30# .+24E302 %$+9 2+#"E302 2+%%E302 .+0#E302

%4+# 2+$0E302 2+4"E302 $+$0E30# .+%#E302 %4+# 2+.#E302 2+"$E302 .+#4E302

%9 % 2 ..E 02 2 94E 02 $ %4E 0# . 9"E 02 %9 % 2 %"E 02 # 0#E 02 . 41E 02

$recomposite Deflection from% $ost Composite Deflection from%

-idpt oad Endpt oad &e'! (ei)*t ota' -idpt oad Endpt oad ota'in in in in in in in in in

99+4 $+%4E302 .+"0E302 "+44E30# 1+1$E301 99+4 $+91E302 .+92E302 1+0"E301

102+0 $+"$E302 %+0.E302 9+12E30# 1+1"E301 102+0 .+10E302 %+14E302 1+1#E301

10$+$ .+02E302 %+#1E302 9+$4E30# 1+2#E301 10$+$ .+2"E302 %+$#E302 1+14E301

10%+4 .+19E302 %+.%E302 9+"#E30# 1+24E301 10%+4 .+$4E302 %+%9E302 1+22E301

109+0 .+#4E302 %+"2E302 1+02E302 1+#2E301 109+0 .+%.E302 %+9%E302 1+2%E301

111+# .+..E302 4+09E302 1+0.E302 1+#4E301 111+# .+"$E302 4+2#E302 1+#1E301

11#+% .+42E302 4+#%E302 1+09E302 1+$2E301 11#+% %+02E302 4+.1E302 1+#.E301

11%+0 .+90E302 4+%#E302 1+1#E302 1+$4E301 11%+0 %+21E302 4+4"E302 1+$0E301

11"+# %+0"E302 4+91E302 1+14E302 1+.2E301 11"+# %+$0E302 "+04E302 1+$.E301

120+% %+2%E302 "+19E302 1+20E302 1+.%E301 120+% %+."E302 "+#.E302 1+$9E301122+9 %+$#E302 "+$4E302 1+2$E302 1+%1E301 122+9 %+44E302 "+%$E302 1+.$E301

12.+2 %+%1E302 "+4%E302 1+2"E302 1+%%E301 12.+2 %+9%E302 "+9#E302 1+.9E301

124+. %+49E302 9+0.E302 1+#2E302 1+42E301 124+. 4+1$E302 9+2#E302 1+%$E301

129+9 %+9%E302 9+#$E302 1+#%E302 1+44E301 129+9 4+##E302 9+.#E302 1+%9E301

1#2+2 4+1$E302 9+%$E302 1+$0E302 1+"2E301 1#2+2 4+.1E302 9+"#E302 1+4#E301

1#$+. 4+#2E302 9+9$E302 1+$$E302 1+"4E301 1#$+. 4+40E302 1+01E301 1+4"E301

1#%+" 4+.0E302 1+02E301 1+$4E302 1+92E301 1#%+" 4+"9E302 1+0$E301 1+"#E301

1#9+1 4+%4E302 1+0%E301 1+.1E302 1+94E301 1#9+1 "+04E302 1+0"E301 1+""E301

1$1+. 4+".E302 1+09E301 1+..E302 2+0#E301 1$1+. "+2%E302 1+11E301 1+9#E301

1$#+" "+0#E302 1+12E301 1+.9E302 2+0"E301 1$#+" "+$.E302 1+1$E301 1+9"E301

1$%+1 "+20E302 1+1.E301 1+%#E302 2+1#E301 1$%+1 "+%#E302 1+14E301 2+0#E301

1$"+$ "+#"E302 1+1"E301 1+%4E302 2+19E301 1$"+$ "+"2E302 1+20E301 2+09E301

1.0+4 "+.%E302 1+21E301 1+42E302 2+2$E301 1.0+4 9+00E302 1+2$E301 2+1$E301

1.#+1 "+4#E302 1+2$E301 1+4%E302 2+29E301 1.#+1 9+19E302 1+24E301 2+19E301

1..+$ "+91E302 1+2"E301 1+"0E302 2+#.E301 1..+$ 9+#"E302 1+#0E301 2+2$E301

1.4+4 9+09E302 1+#1E301 1+"$E302 2+$0E301 1.4+4 9+.%E302 1+#$E301 2+29E301

1%0+0 9+24E302 1+#$E301 1+""E302 2+$%E301 1%0+0 9+4.E302 1+#4E301 2+#$E301

1%2+# 9+$$E302 1+#"E301 1+92E302 2+.1E301 1%2+# 9+9$E302 1+$0E301 2+$0E301

1%$+4 9+%2E302 1+$1E301 1+9%E302 2+.4E301 1%$+4 1+01E301 1+$$E301 2+$.E301

1%4+0 9+"0E302 1+$$E301 2+00E302 2+%2E301 1%4+0 1+0#E301 1+$4E301 2+.0E301

1%9+# 9+94E302 1+$"E301 2+0$E302 2+%"E301 1%9+# 1+0.E301 1+.1E301 2+.%E301141+% 1+02E301 1+.1E301 2+09E302 2+4$E301 141+% 1+04E301 1+.$E301 2+%1E301

14#+9 1+0#E301 1+..E301 2+1#E302 2+49E301 14#+9 1+09E301 1+."E301 2+%%E301

14%+2 1+0.E301 1+."E301 2+14E302 2+".E301 14%+2 1+11E301 1+%1E301 2+42E301

14"+% 1+04E301 1+%1E301 2+21E302 2+90E301 14"+% 1+12E301 1+%.E301 2+44E301

1"0+9 1+09E301 1+%.E301 2+2.E302 2+9%E301 1"0+9 1+1$E301 1+%"E301 2+"2E301

1"#+2 1+10E301 1+%"E301 2+#0E302 #+02E301 1"#+2 1+1%E301 1+42E301 2+""E301

1".+. 1+12E301 1+42E301 2+#$E302 #+04E301 1".+. 1+1"E301 1+4.E301 2+9#E301

1"4+" 1+1$E301 1+4.E301 2+#"E302 #+1#E301 1"4+" 1+20E301 1+49E301 2+99E301

190+2 1+1%E301 1+49E301 2+$2E302 #+19E301 190+2 1+22E301 1+"#E301 #+0$E301

192+. 1+14E301 1+"#E301 2+$4E302 #+2.E301 192+. 1+2$E301 1+"%E301 #+10E301

19$+" 1+19E301 1+"%E301 2+.1E302 #+#0E301 19$+" 1+2.E301 1+90E301 #+1.E301194+1 1+21E301 1+90E301 2+..E302 #+#%E301 194+1 1+24E301 1+9#E301 #+21E301

199+$ 1+2#E301 1+9#E301 2+.9E302 #+$2E301 199+$ 1+29E301 1+94E301 #+2%E301

201+" 1+2.E301 1+94E301 2+%#E302 #+$"E301 201+" 1+#1E301 2+01E301 #+#2E301

20$+1 1+2%E301 2+00E301 2+%"E302 #+.$E301 20$+1 1+##E301 2+0$E301 #+#4E301

20%+$ 1+2"E301 2+0$E301 2+42E302 #+.9E301 20%+$ 1+#.E301 2+0"E301 #+$#E301

20"+4 1+#0E301 2+0"E301 2+4%E302 #+%.E301 20"+4 1+#4E301 2+12E301 #+$"E301

211+0 1+#2E301 2+11E301 2+"0E302 #+41E301 211+0 1+#"E301 2+1%E301 #+.$E301

21#+$ 1+##E301 2+1.E301 2+".E302 #+44E301 21#+$ 1+$0E301 2+19E301 #+%0E301

21.+4 1+#.E301 2+19E301 2+"9E302 #+"#E301 21.+4 1+$2E301 2+2#E301 #+%.E301

21"+0 1+#4E301 2+22E301 2+9#E302 #+"9E301 21"+0 1+$$E301 2+24E301 #+41E301

3.3.2.6 HSS Edge Beam Design Created By: DL 11/10/2012

Design tool to validate sellection HSS beam size on the building eterior

!his tool calculates loads a""lied to the section and the section ca"acity

Beam Location Color #ey: $ser %n"ut

10&th 'loor ( )echanical Constant/*revious Calc+

Calc/Loo,u"

-es *asses Chec,.o 'ails Chec,

Summary

Selected Section HSS20121/2

Does section "ass all chec,s -es

Beam Geometries

Side ie Length o3 Beam L 415 in See Diagram Belo$ncurved Length o3 Beam L6 45&+7 in 8 9/50 ; 2<r

=ngle o3 Curvature 9 >0 deg See Diagram Belo

?adius o3 Curvature r &1+& in See Diagram Belo

@ccentricity o3 Curvature b &0+1 in See Diagram Belo

!orAue Coe33icient = 0+02>> regression 3rom Blodgett

=ngular !ist Coe33icient B 0+0020 regression 3rom Blodgett



Applied Loads

Live Load LL 270 "s3

Dead Load DL 77+5 "s3

'actored 'loor Load 3 75 "s3 8 1+LL1+2DL

$n3actored 'loor Load 247+5 "s3 8 LLDL

!ributary =rea =trib 2742 in2

'actored Distributed Load 3 4&+4 lb/in 8 3 ;=trib/L6

$n3actored Distributed Load >4+7 lb/in 8 ;=trib/L6

@nd !orAue !end 2515& lb;in 8 =;r2;3total

=ngular !ist E 0+007 deg 8 B;r5;total/@s;Fb/tG

Bending Moment

)a Shear ma3 72+0 ,i" 8 ;L6/2

)a )oment )ma3 >4& #i"(in 8 ;L62/12

1/7 $ncurved Length L6/7 210 in1/2 $ncurved Length L6/2 720 in

5/7 $ncurved Length 5L6/7 50 in

Bending )oment 1/7 Length )= 5> #i"(in 8 L6;FL6(L62(

2G/12

Bending )oment 1/2 Length )B 2&5& #i"(in 8 L6;FL6(L62(

2G/12

Bending )oment 5/7 Length )C 5> #i"(in 8 L6;FL6(L6 ( G/12

Shear.ominal Steel Strength 'y >0 ,si



Steel ?eduction 'actor y 0+&

'actored Steel Strength y'y 7> ,si 8 y;'y

)inimum ?eAuired Section

)odulusSmin 151 in

5 8 )ma3 /y'y

Section roperties

Selected Section HSS20121/2

Section )odulus FStrongG S 1>> in5

*asses chec, 3or Smin I Sy -es

Sel3 Jeight J 4+1 lb/in

!otal =rea =g 24+5 in2

Slenderness ?atio h/t 71+0

)oment o3 %nertia FStrongG % 1>>0+00 in7

)oment o3 %nertia FJea,G %y 0> in7

Section )odulus FJea,G Sy 11 in5

*lastic Section )odulus 144 in5

?adius o3 Myration FStrongG r +5& in

?adius o3 Myration FJea,G ry 7+&& in

Jeb *late Buc,ling Coe33icient ,v > M>

Limiting !hic,ness ?atio 1 >&+27 8 1+10;F,v;@/'yG1/2

N M2+1FbG

Limiting !hic,ness ?atio 2 5+4 8 1+5;F,v;@/'yG1/2

N M2+1FbG

Jeb Shear Coe33icient Cv 1 M2+1FbG

*olar )oment o3 %nertia O 1>70 in7

!orsional Shear Constant C 20& in5

-oung6s )odulus @ 2&000 ,si

Shear )odulus @s 11200 ,si

!otal Loads

!otal 'actored Load 3total 100+1 lb/in 8 3 1+2;J de3lection 3or 3ied(3ied

!otal $n3actored Load total +00 lb/in 8 3 J

De"lection)a De3lection Pma 1+&5 in 8 total;L6

7/F547;@;%G



=lloable De3lection Palloable 5+>0 in 8 L6/270

*asses 3or Pma I Palloable -es

#ompactness

$ncurved Length o3 Beam L6 45& in

$nbraced Length o3 Beam Lb 8 L6 45& in

Com"actness ?atio Q" 2+0 8 1+12;F@/'yG1/2

N !able B7+1

.oncom"act ?atio Qr 55+ 8 1+70;F@/'yG1/2

N !able B7+1

Com"actness CK)*=C! Section B7

li d d S

#apacity #alculations

.ominal Steel Strength 'y >0+0 ,si

.ominal -ield Ca"acity )n 8 )" &700 #i"(in 8 'y N F'(1G

'lange Local Buc,ling )n ./= #i"(in 8 )"(F)"('ySGF5+>Fb/tGF'y/@G1/2

(7+0 N F'(2G

Jeb Local Buc,ling )n ./= #i"(in

.ominal )oment Ca"acity)

n &700 #i"(in8 )%.Fabove )

n6sG

!hic,ness ?atio >&+0 8 2+7>F@/'yG1/2

N H5FbG

!hic,ness ?atio 5+& 8 5+0F@/'yG1/2

N H5FbG

!orsional Strength 'cr 50+0 ,si

#apacity #alculations

)a Bending Stress 3 b3 5+& ,si 8 )ma/S N 2(&

)a Shear Stress3

v3 2+7 ,si8

ma=

t N 2(21

?eduction 'actor 3or Bending y 0+& Ch 7

?eduction 'actor 3or Shear v 0+& M1

?eduction 'actor 3o !orsion ! 0+& H5

Bending Ca"acity 'b3 >7+ ,si 8 y;)n/S

=vailable Strength in Shear 'v3 2+0 ,si 8 v;0+;'y

!orsional Ca"acity !n >75 #i"(in 8 ! ;'cr;C

$atios o" Applied Loads to Load #apacity

8 )"(F)"('ySGF0+50>Fh/tGF'y/@G1/2

(0+54G N F'(

>G

$tilization 'actor: Bending $b &+>R 8 3 b3 /'b3

$tilization 'actor I 100R -es

$tilization 'actor: Shear $v 4+4R 8 3 v3 /'v3

$tilization 'acotr I 100R -es

$tilization 'actor: !orsion$

t 71+&R8 !

end/!

n


Combined @33ect &>+1R 8 F3 b3 /'b3 GF3 v3 /'v3 !end/!nG2 N FH5(G


3.3.3 Vibration Analysis Created by: SJR 5/9/2012

Estimated Peak Accelerations

Type Bank ap/g ao/g ap/g < ao/g ?

Residential 1 0!!2" 0500" #es

$e%&ani%al 1 0099" 0500" #es

'obby 1 0199" 0500" #es

Residential 2 02()" 0500" #es

$e%&ani%al 2 00(0" 0500" #es

'obby 2 00*)" 0500" #es

Residential ! 019(" 0500" #es$e%&ani%al ! 00(!" 0500" #es

'obby ! 00+!" 0500" #es

Residential ,1 ( 01()" 0500" #es

Residential ,2 ( 01!0" 0500" #es

-ibration o. t&e .loor syste as %&e%ked as a seri%eability re3ireent 4t as .o3nd t&at t&e sele%ted

de%king and oists et t&e re3ireents .or a residential b3ilding as deonstrated belo



Vibration Analysis Calculations Created by: SJR 5/9/2012

Bank Color Key: User Input

Floor Constant/re!"ous Cal#$

%o#at"on Cal#/%ookup&es asses C'e#k

(o Fa"ls C'e#k

)yp"#al Bay:

Consistent Inputs

*##elerat"on %"+"t ao/, 0$5- *ISC .es",n u"de 11 F",ure 2$1

Steel odulus s 29000000 ps"

1

5

%obby

*nalyDes typ"#al res"dent"al +e#'an"#al and lobby =loor bays =or ea#' bank$ Co+pares est"+ated peak

a##elerat"on to a##elerat"on l"+"t =ro+ *ISC .es",n u"de 11 Floor Vibrations Due to Human Activity F",ure

2$1$ a#' ele+ent "s #ons"dered separately and t'en t'e syste+ as a 'ole "s e!aluated$

/"rder

/"rder

J o " s t

J o " s t

J o " s t

s p

Con#rete odulus # 2534000 ps"

.yna+"# odular Rat"o n $65 7 s/81$65# ; *ISC .es",n u"de 11 4$2

ra!"ty *##elerat"on , 6< "n/s2

Constant For#e o <5 lbs <5 lb =or =loors ; *ISC .es",n u"de 11 )able 4$1

odel .a+pen"n, Rat"o > 0$2 *ISC .es",n u"de 11 )able 4$1

Con#rete .ens"ty ?# 110 p#=

Super"+posed .ead %oad S.% 12 ps=

%"!e %oad %% 1 ps=

Joist 1 Details

Joist Length LJ1 183 in

Joist Tributary Area Atr 17,712 in2

Steel Size Chosen W12 x 22

Steel Weight 22 pl

Steel Area As !"#8 in2

Steel $o%ent & 'nertia ($&') 'xx 1*! in#

Steel +epth 12"3 in

Joist 1 Calculations

-nior%ly ist loa . length /l #1"0 lbs.in

-nior%ly ist loa . area /a "#33 lbs.in2

eti4e Conrete With be 73"2 in 5%in(tributary /ith , "#6L J1)

+istane to entroi ybar "78 in belo/ top o or% e

Transor%e $&' 't *!# in#

uses parallel axis theore%

$ispan +eletion 9 "37# in 5 */lLJ1#.38#s't

:atural ;re<ueny n 18"3 .s 5 "186s<rt(g.9) = A'SC +esign >uie 11 3"3

Joist Spaing s ? !"08 t A'SC +esign >uie 11 #"3a

Transor%e Slab $&' +s #"11 in#.t 5 e

3.12n = A'SC +esign >uie 11 #"3a

s e . = g

Transor%e Joist $&' + ? 8"8 in#.t 5 't.S = A'SC +esign >uie 11 #"3a

eti4e With ;ator C ? 1 A'SC +esign >uie 11 #"3a

eti4e @anel With ? 8!"0 in 5 C ?(+s.+ ?)1.#

LJ1 = A'SC +esign >uie 11 #"3a

eti4e @anel Weight W ? !,887 lbs 5 /a ?LJ1 = A'SC +esign >uie 11 #"2

sti%ate @ea Aeleration ap.g "8B 5 @oexp("3* n).W ? = A'SC +esign >uie 11 #"1

Joist 2 Details

Joist Length LJ2 212 in

Joist Tributary Area Atr 21,! in2

Steel Size Chosen W12 x 22

Steel Weight 22 pl

Steel Area As !"#8 in2

Steel $o%ent & 'nertia ($&') 'xx 1*! in#

Steel +epth 12"3 in


-nior%ly ist loa . length /l ##" lbs.in

-nior%ly ist loa . area /a "#32 lbs.in2

eti4e Conrete With be 8#"8 in 5%in(tributary /ith , "#6L J2)

+istane to entroi ybar "**0 in belo/ top o or% e

Transor%e $&' 't *78 in#


$ispan +eletion 9 "!0 in 5 */lLJ2#.38#s't

:atural ;re<ueny n 13"* .s 5 "186s<rt(g.9) = A'SC +esign >uie 11 3"3

Joist Spaing S !"08 t A'SC +esign >uie 11 #"3a

Transor%e Joist $&' + ? 82"8 in#.t 5 't.S = A'SC +esign >uie 11 #"3a


eti4e @anel With ? 1 in 5 C ?(+s.+ ?)1.#


eti4e @anel Weight W ? 0,1!# lbs 5 /a ?LJ2 = A'SC +esign >uie 11 #"2


Joist 3 Details

Joist Length LJ3 2#1 in

Joist Tributary Area Atr 2*,2 in2

Steel Size Chosen W12 x #

Steel Weight # pl

Steel Area As 11"7 in2

Steel $o%ent & 'nertia ($&') 'xx 37 in#

Steel +epth 11"0 in


-nior%ly ist loa . length /l #!"! lbs.in

-nior%ly ist loa . area /a "##! lbs.in2

eti4e Conrete With be 0!"# in 5%in(tributary /ith , "#6L J3)

+istane to entroi ybar 1"2*0 in belo/ top o or% e

Transor%e $&' 't 0*2 in#


$ispan +eletion 9 "7# in 5 */lLJ3#.38#s't

:atural ;re<ueny n 13" .s 5 "186s<rt(g.9) = A'SC +esign >uie 11 3"3

Joist Spaing S !"08 t A'SC +esign >uie 11 #"3a

Transor%e Joist $&' + ? 13!"# in#.t 5 't.S = A'SC +esign >uie 11 #"3a


eti4e @anel With ? 1 in 5 C ?(+s.+ ?)1.#


eti4e @anel Weight W ? 1,70 lbs 5 /a ?LJ3 = A'SC +esign >uie 11 #"2


Girder Details

Joist Length L> 33* in

Steel Size Chosen W1! x !7

Steel Weight !7 pl

Steel Area As 10"7 in2

Steel $o%ent & 'nertia ($&') 'xx 0*# in#

Steel +epth 1!"3 in

Girder Calculations

-nior%ly ist loa . length /l 80"0 lbs.in

-nior%ly ist loa . area /a "#2# lbs.in2

eti4e Conrete With be 13# in 5%in(tributary /ith , "#6L >)

+istane to entroi ybar 2"3# in belo/ top o or% e

Transor%e $&' 't 2,*#* in#


$ispan +eletion 9 "2*# in 5 (#.D)6*/lLJ3#.38#s't

:atural ;re<ueny n 18"3 .s 5 "186s<rt(g.9) = A'SC +esign >uie 11 3"3

A4erage Joist Length L ?a4g 212 t 5 e3.12n = A'SC +esign >uie 11 #"3a

A4erage Joist $&' + ?a4g 81"8 in#.t 5 't.S = A'SC +esign >uie 11 #"3a

Transor%e >irer $&' +g 0"

eti4e With ;ator Cg 1"8 A'SC +esign >uie 11 #"3a

eti4e @anel With g 1#1 in 5 C ?(+s.+ ?)1.#


eti4e @anel Weight Wg 2,!0 lbs 5 /a ?LJ3 = A'SC +esign >uie 11 #"2

sti%ate @ea Aeleration ap.g "3B 5 @oexp("3* n).Wg = A'SC +esign >uie 11 #"1

Combined System Calculations

Total Joist +eletion 9 ? "! in a4erage o all ?oist eletions

Total >irer +eletion 9g "2*# in

Total +eletion 9T "31# in

Total :atural ;re<ueny nT !"31 .s 5 "186s<rt(g.9T) = A'SC +esign >uie 11 3"3

Total eti4e Joist Weight W ? 8,0#7 lbs a4erage o all eeti4e ?oist /eights

Total eti4e >irer Weight Wg 2,!0 lbs

Total eti4e Weight WT 17,030 lbs 5 9 ?.(9T)6W ? E 9g.(9T)6Wg = A'SC +esign >uie 11 #"#

sti%ate @ea Aeleration ap.g "100B 5 @oexp("3* nT).W = A'SC +esign >uie 11 #"1

Aeleration Li%it ao.g "*B

Fesap.g G ao.g H



3.!

Coluns 99

3.!.1

Colun Loa& Take&o'n 100

3.!.2

Co$osite Colun Design 11!

3.!.3

Steel Colun Design 11(



3.4.1 Column Load Takedown Created by: CTM 2/15/2012

General Information

Notes:

• The self weight of the columns has not been addressed

• Lie loads were assumed to be non!reducible

• "afety factors of 1#2 for dead loads and 1#$ for lie loads were used

• %an& ' has been diided into 'a and 'b to corres(ond to the two floor (lans receied#

• Column transfers hae been included as necessary and may not a((ear in the sam(le calculations shown#

This series of s(readsheets calculates the graity loads ia tributary areas on the columns and core segments

summing oer the height of the building to determine the a6ial load each column must resist under graity#

• 7ach ban& has the same loads a((lied oer its height so the alues are in(ut at the bottom of the

ban& and refenerenced on the higher leels#• The tributary area and function of each floor are in(ut into the column s(readsheets the s(readsheets

e6(and to allow for multi(le loads ty(es in which case the (ercentage is in(ut to indicate a fraction of the

tributary area for each ty(e#

• %an& transitions hae been shown on ta&edown sheets omitted leels are identical to those immediately

aboe and below#

• )s the core si8e decreases going u( the building the walls are not aligned a6ially causing an eccentricity fromthe from the walls aboe# The core walls segments were chec&ed as columns using an intaction diagram to

identify area where the ececntricity will cause need for e6tra reinforcing#

• The circular core has been modeled as a tra(e8oidal sha(e to be used in the interaction diagram the (lans

Loads

)rea Loads *L "*L LL

+(sf, +(sf, +(sf,

Core 55 5- 100

Lobby+non core, .2 5- 100

(en 0 0 0 slab o(enings

• The circular core has been modeled as a tra(e8oidal sha(e to be used in the interaction diagram the (lans

and dimensions shown corres(ond to these models#

Column Load Summaries

• %an&s . and ' hae 1' e6terior columns columns 1 and 2#

• Column 1 e6tends the full height of the building

• Column 2 e6ists in ban&s . and ' it then s(lits in two columns for ban& 2 and 1 to become .a and .b

set bac& in the column layout +going towards the core, hae not been considered

3inal Loads at 9round Leel

+factored, *L "*L LL

+&i(s, +&i(s, +&i(s,

Column 1 550 -5$' -'1

Column 2 n/a n/a n/a

Column .a '2'2 500 5.-

Column .b '2'2 500 5.-

• The core is diided into four columns of two sha(es a large and small layout on each ban&#

Core Concrete Columns

Exterior Steel Columns

• <n %an&s 1 and 2 the e6terior ring of 21 columns is com(osed of three columns that re(eat seen

times so there are three load scenarios labeled as columns 1 .a and .b#



• %an& ' core geometry has two columns +To( Core, that transfer loads into the four columns of ban& .#

3inal Loads at 9round Leel

+factored, *L "*L LL

+&i(s, +&i(s, +&i(s,

7!; Core -0$ 1.1-1 2'221

!" Core 120$ 1'20. '..50

To( Core n/a n/a n/a

• The layout of four columns is the same for %an&s 1 through . but the dimensions decrease going u(

the building#

Tributary Area Data Created by: CTM/CYW

Color key: User Input

Used in column load takedown

Bank 1 Bank 2

Number of Columns 2 Number of Columns 2

!on" #uter $adius %&'( ft !on" #uter $adius %('% ft

)*ort #uter $adius +,' ft )*ort #uter $adius -%'% ft

.era"e #uter $adius %(' ft .era"e #uter $adius +0', ft

$adius to Column -0'0 ft $adius to Column &+'0 ft

$adius to Core , ft $adius to Core , ft

Column/Core 1oundary $adius 0+' ft Column/Core 1oundary $adius 0,'+ ft

Ma3imum Trib' .rea (-'& ft2

Ma3imum Trib' .rea -%%'+ ft2

Ma3 e3t' len"t* -'2 ft Ma3 e3t' len"t* '& ft

Minimum Trib' .rea &,&'0 ft2

Minimum Trib' .rea 02&'+ ft2

Min e3t' len"t* 2&'& ft Min e3t' len"t* 2,'0 ft

Core Trib .rea 1oundary !ine & , ft Core Trib .rea 1oundary !ine 0+ % ft

Exterior Steel Columns

2//2(2

T*is information was calculated based on t*e preliminary arc*itectural drawin"s usin" .utoC.4'

.ssociated *and calculations are included'



Core Trib' .rea 1oundary !ine &', ft Core Trib' .rea 1oundary !ine 0+'% ft

Bank 3 Bank 4a

Number of Columns , Number of Columns ,!on" #uter $adius +('& ft !on" #uter $adius -2'( ft

)*ort #uter $adius -'+ ft )*ort #uter $adius &', ft

.era"e #uter $adius -&'2 ft .era"e #uter $adius &-'- ft

$adius to Column & ft $adius to Column 0-'-0 ft

$adius to Core 0',2 ft $adius to Core ,' ft

Column/Core 1oundary $adius ,+'2 ft Column/Core 1oundary $adius ,&'( ft2 2

Bank 4b

Number of Columns ,!on" #uter $adius &0' ft

)*ort #uter $adius 0%', ft

.era"e #uter $adius &2', ft

$adius to Column ,%'&20 ft

$adius to Core '& ft

Column/Core 1oundary $adius ,'& ft

Ma3imum Trib' .rea 0-('0 ft2

Ma3 e3t' len"t* 2' ft

Minimum Trib' .rea ,,' ft2

Min e3t' len"t* ft

Core Trib' .rea 1oundary !ine ,,'( ft

centroid distances are alon" t*e a3is of symmetry5 a3is s*ow in dia"ram to ri"*t

Bank 1

Core Concrete Columns



67W Core .rea Centroid

8ft29 8ft9

Column 2+ ,',(0

$esidential Tributary .rea 0-0 7&'&Mec*anical Tributary .rea 2,0 '%

!obby Tributary .rea ,(% '((

N7) Core .rea Centroid

8ft29 8ft9

Column 2 0'00

Bank 2


8ft29 8ft9

Column ,0'++ ',

$esidential Tributary .rea ( 70'+

Mec*anical Tributary .rea 2,0 %

!obby Tributary .rea 0 2


8ft29 8ft9

Column 2 ,'0-+

$esidential Tributary .rea 0(+ 7,'+0

Mec*anical Tributary .rea ,+ 2',0

!obby Tributary .rea 2, '(0,

#pen to 1elow ,0

Bank 3


8ft29 8ft9

Column &', '

$esidential Tributary .rea +0 70'&



!obby Tributary .rea 222 -


8ft29 8ft9

Column 2,- ,'&

$esidential Tributary .rea (, 7,'++

Mec*anical Tributary .rea -& %'%0

!obby Tributary .rea -& '

#pen to 1elow &(

Bank 4a


8ft29 8ft9

Column '&&+,

$esidential Tributary .rea %0&'2-0 70'&,

!obby Tributary .rea +%'%& +'0(&

N7) Core .rea Centroid8ft

29 8ft9

Column 2'0

$esidential Tributary .rea -2 70'+%

Mec*anical Tributary .rea 0%( '&

!obby Tributary .rea '0-

Bank 4b

Top Core .rea Centroid

8ft29 8ft9

Column 0- ,'0&,%

$esidential Tributary .rea &- 0'-+-,

Mec*anical Tributary .rea -2+ %'%,-0

!obby Tributary .rea %& 22'(+



Column 1

Bank Level Trib Area DL SDL LL Ext. Lng Load Type DL SDL LL DL SDL LL DL+SDL LL Total DL LL

DL + SDL

ft^2 Use !kips" !kips" !kips" !ft" !kips" !kips" !kips" !kips" !kips" !kips" !kips" !kips" !kips" !kips" !kips"

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# $#% &%$ 'e()ani(al $** 22.2 &.% $,.- 2.$ a/ade #.% $*0 2 $% $2- 2% 2$- $% $* $%

# $#, &%$ 'e()ani(al $** 22.2 &.% $,.- 2.$ a/ade #.% $& 2- $% $,$ # 2$- $% $, $%# $#& &%$ 'e()ani(al $** 22.2 &.% $,.- 2 a/ade #.% $,$ # $% $-# #$ 2$- $% $-, $%

# $## &%$ 1esidential $** $0.& $.# $-.# 2.$ a/ade #.% $0& ,, $- 222 %- $ && $- 2&* $-

# $# &%$ 1esidential $** $0.& $.# $-.# 2.$ a/ade #.% 2*0 -% - 2#- $$, ,2 && $- *& -

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# $2 &%$ 1esidential $** $0.& $.# $-.# 2.$ a/ade #.% #, ##2 2&2 &&, &$ #* && $- -*& 2&2

# $$ &%$ 1esidential $** $0.& $.# $-.# 2.$ a/ade #.% #0, #%# 2%2 &0 &,0 ## && $- -,* 2%2

# $* &%$ 1esidential $** $0.& $.# $-.# 2 a/ade #.% &*- &*& 2-$ ,$$ ,*, #,, && $- $*$# 2-$

# $2- ,,- 1esidential $** 2$.0 ,.0 22.0 &. a/ade &.$ &, &#2 $# ,## ,&* &*2 ,# 2 $*%0 $#

# $20 ,,- 1esidential $** 2$.0 ,.0 22.0 &. a/ade &.$ &, &%- , ,%, ,-# &0 ,# 2 $$#2 ,

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# $$# ,,- 1esidential $** 2$.0 ,.0 22.0 &. a/ade &.$ -- $*-# ,&& $$2% $$ $*#0 ,# 2 2* ,&&

# $$ ,,- 1esidential $** 2$.0 ,.0 22.0 &. a/ade &.$ -,, $$$ ,%0 $$,* $&% $*0& ,# 2 2*-% ,%0

# $$2 ,,- 1esidential $** 2$.0 ,.0 22.0 & a/ade &.$ -- $$,0 %*$ $$-2 $#*$ $$2$ ,# 2 2$,$ %*$

$$$ ,,- Lobby!non (ore" $** 2$.# 0.2 ,,.- & a/ade &.$ $*2* $2*, %,0 $22# $##% $220 ,& ,% 222& %,0

$$* -22 3one *.* *.* *.* a/ade #.0 $*2# $2*, %,0 $22- $##% $220 & * 22* %,0

$*- -22 'e()ani(al $** ,.* -.2 22$.# a/ade #.0 $*,& $2$& -0- $2%0 $#&0 $&02 &* 22$ 220* -0-

$*0 -22 1esidential $** *.* &*.% $.# .$ a/ade #.0 $$** $2,, $*2* $2* $&$- $,2 0, $ 2,, $*2*

$*% -22 1esidential $** *.* &*.% $.# .$ a/ade #.0 $$& $$, $*&2 $,2 $&0* $,0 0, $ 2#&$ $*&2

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%% -22 1esidential $** *.* &*.% $.# .$ a/ade #.0 2$%0 200 $--2 2,$# #*, $00 0, $ &*$, $--2

%, -22 1esidential $** *.* &*.% $.# .$ a/ade #.0 22$ 200- 2*2# 2,&, #,% 20 0, $ &$*2 2*2#

%& -22 1esidential $** *.* &*.% $.# a/ade #.0 22#0 2-#* 2*&& 2,-% &20 200 0, $ &$0% 2*&&

2 %# -22 Lobby!non (ore" $** 2-.& &2., -2.2 a/ade #.0 2202 2--2 2$#% 2%0 &-$ #, 0% -2 &2%# 2$#%

2 % 0** 3one $** *.* *.* *.* 2 a/ade #., 220% 2--2 2$#% 2%## &-$ #, & * &2%- 2$#%

2 %2 0** 'e()ani(al $** $.2 0.* $-2.* 2 a/ade #., 222 *** 2- 2%0% ,** %# ## $-2 &2 2-

2 %$ 0** 1esidential $** 2,.* ##.* 2%.2 $., a/ade #., 2& *## 2,% 202# ,& %0, %& 2% &-% 2,%

2 %* 0** 1esidential $** 2,.* ##.* 2%.2 $., a/ade #., 20# *00 2-# 20,* %*, 0* %& 2% &#%2 2-#

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2 # 0** 1esidential $** 2,.* ##.* 2%.2 $., a/ade #., 2*- #2%, $20 0&$ &$$ &**& %& 2% %#0& $20

2 #2 0** 1esidential $** 2,.* ##.* 2%.2 $., a/ade #., 2- #2* $&& 00% &$0# &*#0 %& 2% %&&- $&&

2 #$ 0** 1esidential $** 2,.* ##.* 2%.2 2 a/ade #., 2%* #,# $02 -2# &2% &*-2 %& 2% %,# $02

$ #* 0** Lobby!non (ore" $** 2&., #&., 0*.* 2 a/ade #., ** ##$* 2,2 -,* &2-$ &22* %, 0* %%$* 2,2

$ - $*0 3one $** *.* *.* *.* % a/ade &.# *, ##$* 2,2 -,% &2-$ &22* & * %%$& 2,2

$ 0 $*0 'e()ani(al $** #*.& $*.# 2#-.* % a/ade &.# &$ ##2* &$$ #*22 &*# &,$0 &, 2#- %%%$ &$$

$ % $*0 1esidential $** .% &%.$ &. %.2 a/ade &.# -$ ##%% &#% #*,- &%2 &,%& -, & %0,0 &#%

$ , $*0 1esidential $** .% &%.$ &. %.2 a/ade &.# #* #&# &02 #$$, &##$ &%$ -, & %-,# &02

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$ % $*0 1esidential $** .% &%.$ &. %.2 a/ade &.# #&,# ,$0- #,*& &#%% %#2% %,0 -, & $*%& #,*&

$ , $*0 1esidential $** .% &%.$ &. %.2 a/ade &.# #,* ,2#, #,#* &&2# %#-& %#2# -, & $*0#- #,#*

$ & $*0 1esidential $** .% &%.$ &. % a/ade &.# #,#2 ,* #,%, &&%$ %&,# %#0$ -, & $*-#, #,%,

$ # %.2 a/ade &.# #,#0 ,* #,%, &&%% %&,# %#0$ & * $*-&$ #,%,

$ %.2 a/ade &.# #,& ,* #,%, &&0# %&,# %#0$ & * $*-&, #,%,

$ 2 %.2 a/ade &.# #,&- ,* #,%, &&-* %&,# %#0$ & * $*-,2 #,%,

$ $ #,&- ,* #,%, &&-* %&,# %#0$ $*-,2 #,%,

4nfa(toreds45 of6 above (ol45n transfer

exterior edge and floor loads

7 total

DL8$.2

7 total

SDL8$.2

7 total

LL8$.,

fro5 trib

s)eet loads taken fro5 s455ary s)eet

DL6 fro5

s455ary s)eet

fro5 trib

s)eet

9ol45n Design'idas:en Loads

4n(tion

Total Loads a(tored LoadsLoa ds ro5 T )i s loor E xt er ior E dge Loa ds

3.4.1 Column Load Takedown C-106



Notes: • Baseline point is the left edge along the axis of symmetry, notated with a zero

• Unless otherwise noted eccentricities are measured from the baseline

• Column transfers are extimated based on geometry, some load is going to walls around elevators, not currently considered

Centroid to Side

used as baseline

Bldg

Center to

Centroid b1 b b! b" h1 h h! h"

#ft$ #ft$ #ft$ #ft$ #ft$ #ft$ #ft$ #ft$ #ft$ #ft$ positive eccentricities %&''

Ban( 1 %&% !)&* 1*&+ 1'&1% 1&'' !*&%* !&%) %&'* 1!&'* 1& eccentricities -1&'1

Ban( "&%* !%&! 1+&+ +&)% 1&'' !*&%* !&)% &% 1"&%* '&%

Ban( ! "&)1 !'&* !&'* "&! '&'' !&+% 1&)+ 1)&)"

Ban( "a &!!1% *&* *&*) "&*+ 1&'' !*&)! & 1&'' %&+' +&) levels where column size will be chec(ed.designed

/et

ec ce n n et f ac to red 0 cc en tr ic it y / et a ct &

Ban( 2evel 3rib 4rea 1 ! " 52 S52 22 52 S52 22 52 S52 22 per level loads per level from centroid 2oads

ft6 Use 7

5ist to

Baseline Use 7

5ist to

Baseline Use 7

5ist to

Baseline Use 7

5ist to

Baseline #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #(ips$ #ft$ #(ips$ #ft$ #(ips$

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"a 11" 1*% 8esidential )&% -%&+ 9echanical !1&% 11&) Core )&' 11&) /one '&' '&' 1* ) !! ' )&!1 )& 1+&*" ,!+ ,!+" *,'11 ,*) ,*! 1,*1* "&*! "*1&"% '&')% 1*,%)

"a 11! 1*% 8esidential )&% -%&+ 9echanical !1&% 11&) Core )&' 11&) /one '&' '&' 1* ) !! ' )&!1 )& 1+&*" ,")" ,"1 *,'" ,+% ,+)% 1!,1 "&*! "*1&"% '&')! 1+,'"+

"a 11 1*% 8esidential )&% -%&*+ 9echanical !1&% 11&)!!! Core ) 11&% /one ' ' 1* ) !! ' )&!1 )& 1+&*" ,%! ,%" *,!+ !,'!* !,'% 1!,"!% "&*! "*1&"% '&') 1+,%!'

! 111 1*% 2obby#non core$ )&% -%&*+ 9echanical !1&% 11&)!!! Core ) 11&% /one ' ' !1! ) !! ' ))& +&1 '&1+ ,%+* ,)) *,)) !,11* !,1% 1!,*)* &)1 )'&!1 1&*' ',1!*

! 11' 1)%! :pen ))&) -"&** 9echanical & +&+% Core "&) *&% :pen )&1 ' ' 1)) ' 1*&* *&'+ +&)) ,)1 ,)!% *,)% !,1"1 !,1)1 1",'" +&* 1**&%" '&'"* ',!)

! 1'+ 1)%! 9echanical ))&) -"&** 9echanical & +&+% Core "&) *&% :pen )&1 ' "* 1)) ' )1&% 1+&1' !)1&* ,)+ ,)%" +,1 !,1% !,1*" 1",)'! -'&+ ))&' -'&1" 1,''

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actored 2oads

2oads rom 3his loor

#Unfactored$

N-S Core

3otal 2oads By unction, actored 3otal 2oads

unction 1 unction unction ! unction "

3.4.1 Column Load TakedownC-107



Core Columns to Evaluate Created by: CTM

• These are the levels where we are going to check the columns on the interaction diagram

• We are considering each bank to be one column since it is all the same shape

E-W Core

Eccentricity Load

(t! (kips!

"ank # "ottom $%$$$ &'$)

Top #%*#$ +$*##

"ank * "ottom ,$%$#- *.-'

Top -%)- #-)#)

"ank + "ottom $%$&' #-&+'

Top $%)+& .$.

"ank &a "ottom ,$%#)- -'-)

Top %$+# **#'

N-S Core

Eccentricity Load

• We selected the bottom o each bank where the loads are largest and the top where the eccentricity is

greatest to plot on the interaction diagrams% This gives two points per core section per bank that need to

be plotted%



y

(t! (kips!

"ank # "ottom $%$$$ ..&

Top #%&*. -#++$

"ank * "ottom ,$%$$+ -$..-Top &%+'+ ++).#

"ank + "ottom ,$%$*# +++'

Top #%)'$ *$#+)

"ank &a "ottom $%$.* #-+$

Top &%)+. ##+&.

Column Interaction Diagrams for Core Segments Under Gravity

E-W Bank 1

These diagrams show where the initial wall size estimates need to be increased and reinforced to

address the moments resulting from the eccentricity of the core walls above each bank. The core was

evaluated with little to no rebar to understand the response of the concrete. Lateral loads have no

yet been addressed the sizes will need to be adjusted further after these loads are considered.



E-W Bank 2

E-W Bank



E-W Bank !a

"-S Bank 1



"-S Bank 2

"-S Bank



"-S Bank !a



3.4.2 Composite Column Design

Summary Tables

Bank Level Column 1 C1 Width (in) C1 Length (in) C1 Bar Size C1 # Bars C1 Tie Size C1 Tie Spacing

14 W14!"" 1 1 $ % $ &

1'4 W14!"" 1 1& $ $ &

1' W14!1"' 1$ 1$ $ $ "

111 W14!'4 1$ 1$ $ & $ "

1%% W14!14 4 4 $ & $ 1

$ W14!'4 4 4 11 1 $ 1

4 W14!'4 '% '% " 4 $ 1

&4 W14!"" '& '& 1% 1$ $ 1$

W14!$' '& '& 14 1& $ 1$

4% W14!4& '& '& 1$ 1$ $ 1$

" W14!"% 4 4 1$ 1$ $ 1

1 W14!'4 4 4 1$ 1$ $ 1 W14!1%" 4$ 4$ 1$ 1$ $ 4

Lo* W14!1' 4$ 4$ 1$ 1$ $ 4

This sheet summarizes the dimensions o+ the composite column ,ith an emedded steel shape- .t sho,s the

di++erent sizes +or Column 1/ / and '0 'B-

1

4

'

Column Sizing Column 1



Bank Level Column C Width (in) C Length (in) C Bar Size C # Bars C Tie Size C Tie Spacing14 W14!"" 1 1 $ % $ &

1'4 W14!"" 1 1& $ $ &

1' W14!1"' 1$ 1$ $ $ "

111 W14!'4 1$ 1$ $ & $ "

1%% W14!14 4 4 $ & $ 1

$ W14!'4 4 4 11 1 $ 1

4 W14!'4 '% '% " 4 $ 1

Column Sizing Column

4

'

Bank Level

Column

'0 'B

C'0B

Width(in)

C'0B

Length(in) C' Bar Size C' # Bars C' Tie Size C' Tie Spacing

14

1'4

1'

111

1%%$

4

&4 W14!"" 4 4 " $ 1

W14!'11 4 4 " 4 $ 1

4% W14!4 4 4 " " $ 1

" W14!'"$ '% '% 14 $ 1

1 W14!&% '% '% 14 " $ 1

W14!'11 '& '& 1$ " $ 1$

Lo* W14!'4 '& '& 1$ $ $ 1$

Column Sizing Column '0 'B

1

4

'

Composite Column Design Created by: DF/JL 12/9/2011

2 Color Key: User Input

Floor 40 Constant/Prevous Cal!"

1 Cal!/Loo#up

$es Passes C%e!#Overall Checks &o Fals C%e!#

L'tatons Pass( $)*

+,al Capa!ty Pass( $)*

92"9-

Loading Sheet

14.41 #ps29 #ps

1 #ps

#ps

193 #ps

otal Fa!tored Load Pu 1.4 #ps

Detailing Requirements

3 n +I*C I2516

4 n +I*C I2516

1 n +I*C I2516

1 n +I*C I2516

%s spreads%eet !al!ulates t%e !o'pressve !apa!ty o6 a 75s%ape e'bedded n !on!rete usn8 +I*C

C%apter I2

=an#

7e8%t o6 *teel above 2

7e8%t o6 Con!rete above 2

7e8%t o6 *teel bet@een 2540

Lo!aton

Colu'n

- Capa!ty Used

Fa!tored rbutary Loads

7e8%t o6 Con!rete bet@een 2540

1<en6or!n8 Da'eter

4e Da'eter

0"An D'enson

e *pa!n8

1 n +I*C I2516

Inputs

*teel *e!ton

Colu'n 7dt% b 3 n

Colu'n Len8t% L! 3 n

)66e!tve Len8t% Fa!tor K 1

Unbra!ed e8%t o6 Colu'n 1 n

Con!rete Co'p" *tren8t% 6! 14 #s

Con!rete Densty ; 10 lbs/6t3

An'u' *%ear *tud *pa!n8

714B42

e +rea +tr 0"31 n2

e =ar Da'eter dte 0"2 n*%ear *tud *pa!n8 s 1 n

Cover ! 1" n

Limitations

*teel at least 1-( $)* +I*C I251a

An'u' ransverse ren6or!e'ent o#( $)* +I*C I251a

<en6or!e'ent rato o#( $)* +I*C I251a

Parameters

+rea o6 *teel *e!ton +s 12 n2

+rea o6 <ebar +sr 2 n2

+barnbar

+rea o6 es +tr n2

+tr ntes

Eross +rea +8 1.29 n2

bL!

+rea o6 Con!rete +! 1.099 n2

+8 5 +s

Aodulus o6 )last!ty Con!rete )! .3 #s ;!1"

6!0"

Aodulus o6 )last!ty *teel )s 29.000 #s

An" $eld *tress *teel *e!ton Fy 0 #s

An" $eld *tress =ars Fyr 0 #s

Inerta o6 *teel *e!ton Is 1.110 n4

Inerta o6 *teel =ars Isr 1.03 n4

2nbar dbar4/4 G +bard

2

Inerta o6 Con!rete I! 121.23 n4

bL!3/12 5 Is 5 Isr

C1 0"3 0"1 G 2H+s/ H+! G +s 0"3 +I*C I25

)66e!tve *t66ness )I )G0 #p5n ) I G 0 ) I G C ) I +I*C I25

)66e!tve *t66ness )Ie66 ")G0 #p n )sIs G 0" )s Isr G C1 )C IC +I*C I25

Compressive Strength

+,al *tren8t% o6 *teel *e!ton Ps .20 #ps +sFy

+,al *tren8t% o6 *teel <ebar Psr 4.320 #ps +srFyr

+,al *tren8t% o6 Con!rete P! 13.0 #ps 0" 6! +!

+,al Co'pressve *tren8t% Po 23.4 #ps Ps G Psr G P! +I*C I254

)66e!tve Co'pressve *tren8t% Pe 219.99 #ps 2)Ie66 /HK

2 +I*C I25

&o'nal Co'pressve *tren8t% Pn 22.0 #ps PH0"HPo/Pe

+I*C I252



Load Capacity5llo>able )uas( )tress ,Fy 4 ks#

last#$ Cr#t#$al Bu$kl#n* )tress Fe 1 k#ps 3-4

last#$ Bu$kl#n* &#%#t Fl#% 113 417/Fy81/2

a#%u% 5#al &oad !%a 124 k#ps ? F$r@5

+edu$t#on Fa$tor , 09

Fa$tored a 5#al &oad ,!%a 114 k#ps

C(e$k: ,!%a !uD 'es

I. &e.. E Fl#% use 3-2 else

use 3-3ks#43F$rFleural Bu$kl#n* )tress



4.0 Lateral Design

4.1 Building as a Cantilever 121

4.2 MIDAS Gen FEA Summary 124

4. !reliminary C"re #all $%i&'ness Cal&ulati"n ( )" *utriggers 12+

4.4

Final C"re #all $%i&'ness Cal&ulati"n ( *utriggers 12,

4.+ C"re -ear Design 11

4.+.1 Design "/ C"re -ear /"r erti&al and "ri"ntal S%ear 12

4.+.2 Design "/ C"re -ear /"r Fle3ural Caa&ity 14

4.+. Mat%&ad /"r Ban' 4 Str"ng A3is Bending 1,

4.5 Energy Met%"d *timiati"n 1+5

4.5.1 *timiati"n Cal&ulati"ns 1+,

4.5.2

-esiing "/ Built(6 Memers 151

4.1 Preliminary Deflection Calculations Created by: CYW 5/11/2012

Bank:

Location:

Bank 1 Properties

Wall thickness tc 7 ftCenterline radius R c 40 ft

Centerline circuference Cc 251 ft ! 2"#"$c

%uter radius R o 4&'5 ft ! $c(tc/2

)nner radius R i &*'5 ft ! $c+tc/2

,oent of inertia -100. solid all Ic 141203 ft4

! #/4"-$o2+$i

2

%enin lenth in core/a Log 15 ft

6uber of as Ng 4

otal oen lenth in core Lo *0 ft = Log*Ng

8ercentae of solid all Ps 7*. ! 100. + Lo/Cc

ransfored oent of inertia -ith oenins It 1073*&7 ft4 = Ic*Ps

Bank 1 heiht h 51&'5 ft

Concrete strenth f9c 14000 si

Concrete odulus conc *744&&1 si ! 57000"f9c1/2

; <C) &1+0 '5

otal Bank 1 ind load fro $W=) wtotal 210 kis

=istributed ind load w 4'1 kis/ft ! total/h

Bank 2 Properties

1 to 4

Core

>enerate sectional roerties of the core all for a sile cantile?er deflection check in ,<@<6'

Wall thickness tc 4 ft

Centerline radius R c &3 ft

Centerline circuference Cc 245 ft ! 2"#"$c

%uter radius R o 41'0 ft ! $c(tc/2

)nner radius R i &7'0 ft ! $c+tc/2

,oent of inertia -100. solid all Ic 747&5 ft4

! #/4"-$o2+$i

2


6uber of as Ng 4


Bank 3 Properties

Wall thickness tc & ft

Centerline radius R c & ft

Centerline circuference Cc 2&3 ft ! 2"#"$c

%uter radius R o &3'5 ft ! $c(tc/2

)nner radius R i &*'5 ft ! $c+tc/2

,oent of inertia -100. solid all Ic 5173*2 ft4

! #/4"-$o2+$i

2


6uber of as Ng 4


8ercentae of solid all Ps 75. ! 100. + Lo/Cc

ransfored oent of inertia -ith oenins It &700 ft4 = Ic*Ps

Bank & heiht h 47 ft



; <C) &1+0 '5

otal Bank & ind load fro $W=) wtotal 2544 kis

=istributed ind load w 5'2 kis/ft ! total/h

Bank 4 Properties

Wall thickness tc 2 ft

Centerline radius R c &4 ftCenterline circuference Cc 210 ft ! 2"#"$c

%uter radius R o &4'5 ft ! $c(tc/2

)nner radius R i &2'5 ft ! $c+tc/2

,oent of inertia -100. solid all Ic 2&* 423 ft4

! #/4"-$o2+$i

2

,oent of inertia -100. solid all Ic 2&*423 #/4 -$o $i


6uber of as Ng 2

otal oen lenth in core Lo &0 ft = Log*Ng

8ercentae of solid all Ps *. ! 100. + Lo/Cc

ransfored oent of inertia -ith oenins It 2027&2 ft4 = Ic*Ps

Bank 4 heiht h 44 ft



; <C) &1+0 '5

t l B k 4 i d l d f $W=) 2 &34 ki

MASTAN utput



!n"eforme" Deforme"

4.2 MIDAS Gen FEA Summary Created by: CYW 5/11/2012

Modeling Approach Loading Conditions

• Outriggers are modeled as truss elements.

• All lateral forces are alied along t!e "#a$is at

eac! floor.

• %nfactored dead loads and li&e loads from t!e

column load ta'edo(n (ere alied to nodes at

column ends.

• )!e total unfactored dead load and li&e load for

t!e core (as slit e*ually into nodal forces to t!e

nodes connecting t!e radial girders to t!e core (alls

or lin' beams.

• All belt trusses and outriggers are modeled (it!

in#in end#releases.

• All ot!er structural elements !a&e been alied

fi$ed#fi$ed end#releases.

• Core (alls are modeled as t!ic' late element (it!

drilling +O,.

• -#bracing belt trusses bet(een an' 1 and an' 2

are modeled as beam elements.

A detailed t!ree dimensional structural analysis of t!e ire (as conducted using +A en. All material

roerties and baseline element s!aes (ere ta'en from initial lateral and gra&ity design. 3ertical members4

outriggers and belt trusses4 and core (all t!ic'nesses (ere resi"ed t!roug!out t!e iterati&e modeling rocess

based on element forces and moments4 and ser&iceability re*uirements.

• )!e model sans from t!e lobby at ground

ele&ation to t!e to of le&el 1.• )!e mega#columns and core (all at t!e ground

ele&ation are fi$ed to t!e ground.

• )!e (ind data from (ind tunnel testing is used

directly for strengt! design.• )!e (ind data from (ind tunnel testing is reduced

by a factor of 0.67 for ser&iceability design.

• All ot!er belt trusses are modeled as truss

elements.

• Comosite floor beams are modeled as W#!ae

teel =einforced Concrete >=C? in cross sectionroerties. )!e (idt! c!osen in t!ese =C beams

are based on t!e effecti&e (idt! of t!e comosite

beam from t!e gra&ity design.

• +A en calculates material self#(eig!t in t!e

analysis4 t!us no self#(eig!t is considered in alied

dead loads.

• 2 load combinations are used for ser&iceability

design c!ec's.

• 5 load combinations are used for strengt! designc!ec's.

• Cantile&ers and angled floor girders outside of t!e

e$terior column grid are not modeled.

• 8yot!etical tuned mass damer and mec!anical

floors at t!e ire9s ea' are not modeled.

• Concrete strengt! of fc ; 14000 si is used in all&ertical concrete elements.

• Concrete strengt! of fc ; 4000 si is used in all

!ori"ontal concrete elements.

• A) A<<2 standard (it! ,y ; 504000 si steel is

used.

g

t r i g g e r s

C r e a t e d b y : C J B & A D V

1 / 2 0 / 2 0 1 2

C O L O R S

K ! "

U s e r I n p u t

C o n s t a n t / % r e $ o

u s C a ' c (

, 0 0 0 ! c 3 4 A C I - 1 5 5 (

( 1

C a ' c / 6 o o # u p

8 e s

% a s s e s C h e c #

; o

9 a $ ' s C h e c #

(

4 a

4 )

; o t e s

, "

1 1 1

1 - 0

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2

2

t

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- +

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5

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t 2

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< $ 2

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< $

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a l l T h i c k n e s s C a l c u l a t i o n - O u t r i g g

e r s

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% o a d s a n d @ o @ e n t s " n d u c e d b y

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d & 6 o r o u t r " g g e r s s e e t h e s " s t e r s h e e t t o t h

a t " o n s &

3

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+ K

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h e s e a r e t h

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% e s s t h a n a % % o H a b % e & 9 e d : $ a % u e " s g r e a t e r t h a n a % % o

H a b % e &

4 . 3

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e r s

l l o + a ! l e S t r e s s e s

1

2

C a p p

5 & + = 5

& 1 )

+

a p p

7 2 & 5 +

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7

1 * K

1 0 K

+ 0 K

1 ) K

f c o m p

- $ . 3

! s "

f r

( / $ 0 0

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0

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1 & * ) )

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0

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+ 0 0 2

1 5

6 3 3

1 + 5 1 2

= 5 5 +

5

L c

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1

L

0

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0

+

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+

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1

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1

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7

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+

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7

5 e t & e n s i o n S t r e s s e s a t t ' e ! a s

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, f a < f t

*

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1 * +

1 1 * )

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- s

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3 / A c

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0 & + * 2

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7 0 & + * 2

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, 7 f b

1 & 0 1

0 & = =

0 & 2 =

! s "

, f a < f b

7 0 & = *

7 0 & ) =

7 0 & + 1 )

! s "

, f a < f t

4 . 3

F i n a l C o r e W


e r s



L

0

6 D 3

5 2 + = 5

+ 0 0 2

1

6 s

2 1 ) ) *

5 5 1 5

2

6 3 3

1 + 5 1 2

= 5 5 +

5

f a

2 & + = )

1 & 5

f b

1 & 5 +

1 & + )

f t

7 1 & 5 +

7 1 & + )

7

L c

+ & =

2 & 0

L t

8 / A

8 / A

7

0

6 D 3

+ = 2 = 5 =

2 2 0 2

1

6 H

2 0 = ) 0 0

1 + 2 0 = ) 0 0

)

f a

1 & 2 =

0 & 2 =

f b

+ & = ) *

+ & + + =

f t

7 + & = ) *

7 + & + + =

7

L c

5 & + = 5

& 1 )

L t

7 2 & 5 +

7 2 & 5 1 0

7

0

6 D 3

+ = 2 = 5 =

2 2 0 2

1

6 s

2 1 ) ) *

5 5 1 5

2

f a

1 & 2 =

0 & 2 =

f b

1 & 5 +

1 & + )

f t

7 1 & 5 +

7 1 & + )

7

L c

2 & 1

2 & 2 1 5

L t

7 0 & 0 2

7 0 & 5 5 *

7

s i g n

r e i n f o r c i n g b a r s w e r e s u

f f i c i e n t f o r f l e x u r e a s w e l l .

o r i z o n t a l S h e a r

V e r t i c a l S h e a r

F l e x u r a l

a r S i z e

S p a c i n g

B a r S i z e

S p a c i n g

i n

i n

1 !

"

1 #

1 $ a s v e r t i c a l s h e a r

1 !

"

1 #


1 !

!

1 !

' a s v e r t i c a l s h e a r

1 !

'

1 !

1 # a s v e r t i c a l s h e a r

1 )

1 #

!

1 " a s v e r t i c a l s h e a r

1 )

'

*


1 !

*

"

1 ) a s v e r t i c a l s h e a r

!

1 *

"

1 ) a s v e r t i c a l s h e a r

o t e + i n a

l l

c a s e s , v e r

t i c a l

s h e a r r e b a r w a s

g n e f o r t h e s h e a r i n i t - s p a r t i c u l a r i r e c t i o n t h e o r t h

/ S o u t h 0 o r e S e c t i o n s a r e

o r t h / S o u t h i r e c t i o n , e t c .

c o r e s w o r k i n p a i r s t o r e s i s t o e n t . 2 h e o r t h / S o u t h

c o r e s w o r k t o g e t h e r t o

e x / a x i s , w h i l e t h e % a s t / &

e s t c o r e s w o r k t o g e t h e r t o r e s i s t o e n t a b o u t t h e 3 /

e r e a r e o n l 3 t w o c o r e s ,

o r t h a n S o u t h . 2 h e 3 w o r k t o

g e t h e r t o r e s i s t t h e

s , b u t h a v e t o w o r k i n i v i u a l l 3 t o r e s i s t t h e o e n t a

b o u t t h e 3 / a x i s .

5

4 . 5

C o r e R e b a r D e s i g n



4 . 5 C o r e R e b a r D e s

N o t e s

I n a l l c a s e s , t h e v

e r t i c a l r

R e b a r S u m m a r y

H B

B a n k 1

S

% &

B a n k $

S

% &

B a n k (

S

% &

B a n k )

) . 1 ) . $

% a c h c o r e s e c t i o n i s e s i g

e s i g n f o r s h e a r i n t h e

I n B a n k s 1 , $ , a n ( , t h e

r e s i s t o e n t a b o u t t h e

a x i s . 4 n t h e ) t h B a n k , t h

o e n t a b o u t t h e x / a x i s

C-131

4.5.1 Design of Core Rebar for Vertical and Horizontal Shear

Created by: KMC 5/9/2012

Inputs

Max Horizontal Shear Vu,hor 23,99 !i"#

Max Verti$al Shear Vu, %er 0 !i"#

&xial 'or$e (u 3),521 !i"#

Co*"re##i%e Stren+th o Con$rete -$ 1.,000 "#i

all hi$!ne## h ). in

all en+th l 503 in

all Hei+ht h ,12 in

&""roxi*ate Stru$tural e"th d .02 in 4 0)l6 119.

Mai!u! "er!itted Concrete Shear Strength

7 085 1193

Max Shear Stren+th 7V 299). !i"# 4 710#rt- ;hd6 11 9 3

y"i$al $al$ulation #hon or ?an!1, @orthASouth Core Se$tion

he or* o the hand $al$ a# ta!en ro* (C& @ote# on &CB 31)A0), "a+e 21A28 throu+h

21A296 all reeren$e# are to &CB 31)A0)

S"read#heet ta!e# the load# #hear and axial; ro* MB&S, and, u#in+ the #ize# o MB&S- re"re#entation

o the $ore, $al$ulate# the reuired rebar to re#i#t horizontal #hear

here i# no %erti$al #hear, #o the %erti$al reinor$in+ i# deter*ined "urely ro* the $ode re+ulation# he

#hear# $ho#en are the or#t $a#e, a# are the axial load#

Max Shear Stren+th 7Vn 299). !i"# 4 710#rt $;hd6 1193

7Vn o!ay< 7Vn=Vu, hor< >e#

Shear Strength "ro#ided b$ Concrete

l/2 251 inh/2 3,0)1 in

(o#ition o $riti$al #hear y 251 in 4 *inl/2, h/2;6 1198

Mo*ent at Criti$al Se$tio Mu 1.1,)30,85) !i"#Ain 4 Vu, hor;h A y;

Shear Stren+th (ro%ided b V$ 2,).3 !i"# D#ee belo

Horizontal Shear Reinforce!ent

Horizontal #hear de#i+ned in a$$ordan$e ith 1199

>ield Stren+th o Steel 'y 0 !#i

Steel &rea/S"a$in+ Eatio &%/# 121 in2/in 4 Vu, hor A 7V$;/7'yd;6 e 11A29

?ar Size F 1)

&rea o Cho#en ?ar Size &bar .00 in2

Max S"a$in+ #*ax 2 in 4 *inl/5, 3h, 1);6 11993

Sele$ted S"a$in+ ##ele$ted in

Gro## &rea &+ 50. in 4 hD##ele$ted

Eatio o Steel to Con$rete #teel 0015)8 4 2D&%/&+

#"a$in+ #*all enou+h< ##ele$tedI#*ax< >e#

enou+h rebar< #teelI00025< >e# 11992



Vertical Shear Reinforce!ent

?ar Size F 10

&rea o Cho#en ?ar Size &bar 128 in2

Max S"a$in+ #*ax 1)00 in 4 *inl/3, 3h, 1);6 11995

Sele$ted S"a$in+ ##ele$ted 12 in

4*in00025, 00025 J 05D25 A

h/l;tran# A 00025;;6 e 11A30Eeuired Min #teel *in 000250

4.5.2 Design of Core Rebar for Flexural CapacityCreated by: KMC 5/9/2012

Inputs

h1 19.6 in

h2 80.3 in

h3 102 in

h4 102 in

b1 241 in

b2 65.4 in

b3 12 in

b4 372 in

Distance fr! center f cre t far ed"e f cre d 527 in

C#er c 2 in

$ie%d &tren"th f &tee% 'y 60 (si

C!)ressi#e &tren"th f Cncrete f*c 14000 )si

Desi"n M!ent M+ 45055 ft,(i)s

-his s)readsheet ta(es a "i#en cnfi"+ratin f rebar di!ensins f the cre !ateria% )r)ertiesre+ired !!ent ca)acity and deter!ines hether ca)acity f c%+!n is ade+ate. t des s by

ca%c+%atin" !!ent ca)acity f c%+!n ass+!in" a%% tensin stee% has yie%ded and far ed"e f cncrete

has crac(ed.



1 5

3 4

2

Concrete Equivalent Area Calculations

Calculations

c

art in3

1 641 h1b2/2 514 d,2/3h 329674

2 641 h1b2/2 514 d,2/3h 329674

3 4732 h1b1 517 d,h1/2 2447372

4 29843 h2b4 467 d,h1,h2/ 13944127

5 1213 h3b3 376 d,h1,h2, 456064

6 1213 h3b3 376 d,h1,h2, 456064

&+! 38284 17962974

cn 469 in cr/c

Di!ensions of equivalent pris!atic s"apeen"th % 116 in d,cn2

;idth b 331 in c/%

#train Calculations

c rea

-he cre is an irre"+%ar sha)e that is diffic+%t t r( ith !athe!atica%%y. -h+s a%% f the si@ )arts f the creshn n )re#i+s )a"e*s drain" i%% be added t"ether and then transfr!ed int an e+i#a%ent rectan"+%ar

sha)e. -his rectan"+%ar sha)e i%% ha#e the sa!e area f the cre the sa!e and its far ed"e i%% be in the

sa!e )sitin as the far ed"e f the ri"ina% cre s that e@tre!e cncrete c!)ressin fiber i%% be in the

sa!e )%ace.

in2

in

#train Calculations

< strain in tensin stee% and cncrete is %isted and strain in c!)ressin stee% is ca%c+%ated.

Dist t <ear =d"e f -en &tee% fr! Center dists 427 in d,h4 > c

&train in -ensin &tee% ?s 0.00207

Dist t 'ar =d"e f Cncrete fr! Center distc 527 in d

&train in 'ar =d"e f Cncrete ?c 0 003

#teel Equivalent Area Calculations

in in A in2

in2

in3

2 525 10 1.27 21 26.7 14002

14 513 10 1.27 27 34.3 17591

26 501 10 1.27 31 39.4 19724

38 489 10 1.27 31 39.4 19252

50 477 10 1.27 31 39.4 18779

62 465 10 1.27 31 39.4 18307

74 453 10 1.27 31 39.4 17835

86 441 10 1.27 31 39.4 1736298 429 10 1.27 2 2.54 1090

110 417 10 1.27 2 2.54 1059

122 405 10 1.27 2 2.54 1029

134 393 10 1.27 2 2.54 998

146 381 10 1 27 2 2 54 968

&i!i%ar t cncrete it is diffic+%t t dea% ith each indi#id+a% bar f rebar. -h+s the each cre*s rebar i%% be

transfr!ed int an e+i#a%ent area f stee% ith the sa!e as the ri"ina% %ay+t f stee% in the sa!e ay

that the cncrete as transfr!ed.

Dist fr! 'ar

=d"e f

Cncrete

d , dist

fr! far ed"e

f cncrete barBar &ie

<+!ber

f Bars

s -ta%

rea f

&tee% s



146 381 10 1.27 2 2.54 968

158 369 10 1.27 2 2.54 937

170 357 10 1.27 2 2.54 907

182 345 10 1.27 2 2.54 876

194 333 10 1.27 2 2.54 846

&+! 320.0 151562

st 474 in s/s

$o!ent Calculations

&train in -en &tee% ?s 0.00207

&tress in -en &tee% f s 60 (si !in29000?s 'y

'rce fr! -en &tee% 's ten 19202 (i)s f ss

&train in C!) &tee% ?sce+i# 0.00207

&tress in C!) &tee% f s 60 (si !in29000?sc 'y

'rce fr! C!) &tee% 's c!) 19202 (i)s f ss

&tress B%c( Cefficient 1 0.65

De)th f C!) Ene a 116 in !in1distcc %

#" Cncrete &tress f*c a#" 11.9 (si 0.85f*c/1000

'rce fr! Cncrete 'c 455574 (i)s af*ca#"b

$o!ent Calculation %able

-ensin stee% ,19202 ,'sten 473.6 st

C!)ressin &tee% 19202 'sc!) 473.6 st

Cncrete 455574 'c 469.2 cn

'rce Dist fr! C%+!nCentrid

,9.09=>06

(i)s in

9.09=>06

2.14=>08

M!ent ab+t

C%+!n CentridM'

(i),in

'rce fr! c!)ressin stee% tensin stee% and cncrete is ca%c+%ated

M!ent ca)acity d+e t c!)ressin stee% tensin stee% and cncrete is ca%c+%ated and s+!!ed

incr)rtin" re+ired cncrete crrecti#e frce needed t acc+nt fr cncrete dis)%aced by

c!)ressin stee%. C!)ressin is )siti#e.



455574 c 469.2 cn

&+! 451765

Capacity C"ec&

-ta% M!ent b+t C%+!n Centrid Mn 2.12=>08 (i),in

Mn 1 77=>07 (i),ft

2.=>08

2.14= 08

,2.=>06

Cncrete C!)ressin 'rce

Crrectin ,3808

0.85f*c

s /1000 473.6 st

Individual Strong Axis Bending

Capacity of 4th Bank Cores

Column Geometries

Column Geometriesb1 55.167ft:= h1 0ft:=

b2 0ft:= h2 2ft:=

b3 0ft:= h3 0ft:=

b4 b1 2 b2⋅+:= h4 h1 h2+ h3+:=

b4 55.167 ft⋅= h4 2 ft⋅=

b4 Column

4.5.3 Bank 4 Stong Axis Bending

4.5.3 Bank 4 Strong Axis Bending

y2

:= Column

centroid

y 27.584 ft⋅=

ACI 318-08 10.2.7

Material Properties

fc 14000psi:= fy 60000psi:= Es 29000ksi:=

β1 0.85 fc 4000psi≤if

0.85 0.05 fc 4000psi−

1000psi

⋅−

4000psi fc< 8000psi<if

0.65 fc 8000psi≥if

:=

β1 0.65=

εcu 0.003:= εyfy

Es

:=

εfailure

c

d

cover



steel position

cover

Strain in tension and compression steel found by assuming linear strain profile

through column. Similar triangles are used knowing the failure strain of concrete

in compression, distance from column compression face to neutral axis, and

distance from neutral axis to tension / compression steel.

Positive Bending

Reinforcing Steel Layout

Reinforcing Steel Layoutd is a vector showing the rebar placement starting at the compression face of the column

(the left side in the diagram). n is a vector showing the number of bars at any d-distancefrom the compression face. Size is a vector of the sized of reinforcing bars at a given

d-distance. If different sized bars are used at any given distance,d, one row per bar size

must be included in each of the d, n, and size matrices. d, n, and size vectors are to be

determined by the user to provide adequate column axial and moment capacity.

Areasteel

Asi vlookup sizei BarSizes, 1, 0 1⋅ in

2

←

i 0 length d( ) 1−..∈for

Asreturn

:=

As Areasteel:=

0

0

1

2

3

4

5

6

"

23

3

51

65

"

"3

0

01

2

3

4

5

6

35

4

3

3

3

3

0

01

2

3

4

5

6

66

6

6

6

6

6



d

!

"

10

11

12

13

10

121

135

14"

163

1

1"1

in=n

6

!

"

10

11

12

13

3

22

2

2

2

2

2

= size

6

!

"

10

11

12

13

6

66

6

6

6

6

6

=

Range2Vec Range( ) Count ORIGIN←

VecCount

i←

Count Count 1+←

i Range∈for

Vecreturn

:=

Converts a given range variable into a

vector to be used in later calculations

z11 6 5.999, 6−..:= z21 6.5− 7−, 500−..:=Strain multiplier array. Positive values of Z

correspond to positive (compressive) strainsin extreme layer of tension reinforcement. Two

vectors concatinated to save on computing

timez12 Range2Vec z11( ):= z22 Range2Vec z21( ):=

Z stack z12 z22,( ):=

Cvalues

dt

dlength d( ) 1−

←

Ccoli

0.003

0.003 Zi εy⋅−

dt⋅←

i 0 length Z( ) 1−..∈for

Ccolreturn

:=

Produces an aray of c values (distancefrom compression face to neutral axis)

given a particular strain in the extreme

tension steel (which has a distance of dt

from the compression face

Ccol Cvalues:=

aStressBlock

ai β1 Ccoli

⋅←


areturn

:=Depth of equivalent stress block in

concrete

ACI 318-08 10.2.7.1

a aStressBlock :=

Compressive Concrete

AStressBlock

Asbih2 h3+( ) a

i⋅

ai( )

2h1⋅

2 b2⋅

+← 0 ai

≤ b3<if

Asbi h3 b3⋅ h2 ai⋅+

ai( )

2h1⋅

2 b2⋅+← b3 ai≤ b2<if

Asbih3 b3⋅ h2 a

i⋅+

h1 b2⋅

2+ h1 a

i b2−( )⋅+← b2 a

i≤ b2 b1+<if

Asbih3 b3⋅ h2 a

i⋅+ h1 b1⋅+ h1 b2⋅+

h1 b4 ai

−( )2

⋅

2 b2⋅

−← b2 b1+ ai

≤ b4 b3−<if

Asbih3 b3⋅ h2 a

i⋅+ h1 b1⋅+ h1 b2⋅+

h1 b4 a

i

−( )2

⋅

2 b2⋅− b3 b4− a

i+( ) h3⋅+← b4 b3− a

i< b4≤if


Asbreturn

:=

Asb AStressBlock :=Area of equivalent stress block

ForceConcrete

Cci0.85 fc⋅ Asbi

⋅←


Ccreturn

:=

Cc ForceConcrete:= Compressive force in the concrete

2 105

×

600− 400− 200− 0 2000

5 104

×

1 105

×

1.5 105

×

Z

C . c

( k i p s )

Calculations for Tension and Compression Steel

Strains

εs j i,

Ccolid j

−

Ccoli

0.003⋅←

j 0 length d( ) 1−..∈for


εsreturn

:=Produces an n x m matrix of strain values,

where n = number of values in d and m =

number of values in Z. Thus each column

gives the strain in the steel at distance, d,


tension steel.

εs Strains:=

600− 400− 200− 0 2000.15−

0.1−

0.05−

0

0.05

Z

S t r a i n s

Stresses

f bar εs j i,Es⋅←

f s j i,f bar← fy− f bar≤ fy≤if

f s j i,fy−← fy− f bar>if

f s j i,fy← fy f bar<if



f

:=

Stresses in reinforcing steel.

f sreturng

Each column, i gives the stress

in each bar at distance d j.

f s Stresses:=

600− 400− 200− 0 2001−

10

5×

5− 104

×

0

5 104

×

1 105

×

Z

f . s ( p s i )

Forces

Fs j i,f s j i,

As j⋅← a

i d

j<if

Fs j i,f s j i,

0.85 fc⋅− As j⋅← otherwise



Fsreturn

:= Forces in each bar from

stress defined above

Fs Forces:=

600 400 200 0 20040−

20−

0

20

40

F . s

( k i p s )

600− 400− 200− 0 200

d1

d2

d3

d4

d5

Z

Factors of Φ controlled by strain in exrteme tension reinforcing steel. Areas controlled by

ACI 318 118 9.3.2.2

getPhi

Phii 0.65← εs

Trows εs( ) 1−⟨ ⟩

i εy−>if

Phii

0.90← εsT

rows εs( ) 1−⟨ ⟩

i0.005−<if

Phii

0.65 εsT

rows εs( ) 1−⟨ ⟩

−

iεy−

.25

.005 εy−

⋅+← otherwise


Phireturn

:=

Phi getPhi:=



Summed Forces and Moments

Forcessum

PniCci

Fsi⟨ ⟩

∑+←


Pnreturn

:=

Pn Forcessum:=

600− 400− 200− 0 2005− 10

4

×

0

5 104

×

1 105

×

1.5 105

×

2 105

×

Z

P . n

( k i p s )

ReducePn

ΦPniPni

Phii

⋅←


ΦPnreturn

:=

9.3.2.2

ΦPn ReducePn:=

Momentssum

Msteel j i,Fs j i,

y d j

−( )⋅←


MniCci

y

ai

2−

⋅ Msteel

i⟨ ⟩

∑+←


Mreturn

:=



Mnreturn

Mn Momentssum:=

1 106

×

1.5 106

×

( k i p * f t )

ReduceMn

ΦMniPhi

i Mni⋅←


ΦMnreturn

:=

ΦMn ReduceMn:=

*orces an% Moments

Negative Bending

Reinforcing Steel Layout

dtemp b4 d−:= findn2

n2i

nlength n( ) 1−( ) i−

←

i 0 length n( ) 1−..∈for

n2return

:=findsize2

size2i

sizelength size( ) 1−( ) i−

←

i 0 length size( ) 1−..∈for

size2return

:=

findd2

d2

i

d

temp length d( ) 1−( ) i−

←


d2return

:=

size2 findsize2:=n2 findn2:=

d2 findd2:= This function calculates the distances of reinforcement bars

reltive to right side of the column geometry in order to

calculate moments with the far right face at compression

failure. The resulting "d" vector is flipped, along with the

original "n" and "size" vectors to correspond to these new

distances



distances.

Areasteel2

Asivlookup size

i BarSizes, 1, 0 1⋅ in

2

←

i 0 length d2( ) 1−..∈for

Asreturn

:=

As2 Areasteel2:=

Defined Variables

Cvalues2

dt d2length d2( ) 1−

←

Ccoli

0.003

0.003 Zi εy⋅−

dt⋅←


Ccolreturn

:=

Ccol2 Cvalues2:=

aStressBlock2

ai β1 Ccol2

i

⋅←


areturn

:=

a2 aStressBlock2:=

Strains2

εs j i,

Ccol2id2

j−

Ccol2i

0.003⋅←

j 0 length d2( ) 1−..∈for


εsreturn

:=Produces an n x m matrix of strain values,

where n = number of values in d and m =

number of values in Z. Thus each column

gives the strain in the steel at distance, d,


tension steel.

εs2 Strains2:=

600− 400− 200− 0 2000.15−

0.1−

0.05−

0

0.05

Z

S t

r a i n s

Stresses2

f bar εs2 j i,Es⋅←

f s j i,f bar← fy− f bar≤ fy≤if

f s j i,fy−← fy− f bar>if

f s j i,fy← fy f bar<if



f sreturn

:=

Stresses in reinforcing steel.

Each column, i gives the stress

in each bar at distance d j.

f s2 Stresses2:=

600− 400− 200− 0 2001− 10

5×

5− 104

×

0

5 104

×

1 105

×

Z

f . s ( p s i )

Forces2

Fs j i,f s2 j i,

As2 j⋅← a2

i d2

j<if

Fs j i, f s2 j i, 0.85 fc⋅− As2 j⋅← otherwise



Fsreturn

:=

Forces in each bar fromstress defined above

Fs2 Forces2:=

600− 400− 200− 0 20040−

20−

0

20

40

F . s

( k i p s )

d1

d2

d3

d4

d5

Z

AStressBlock2

Asbih2 h3+( ) a2

i⋅

a2i( )

2h1⋅

2 b2⋅

+← 0 a2i

≤ b3<if

Asbih3 b3⋅ h2 a2

i⋅+

a2i( )

2h1⋅

2 b2⋅

+← b3 a2i

≤ b2<if

Asbi h3 b3⋅ h2 a2i⋅+

h1 b2⋅

2+ h1 a2i b2−( )⋅+← b2 a2i≤ b2 b1+<if

Asbih3 b3⋅ h2 a2

i⋅+ h1 b1⋅+ h1 b2⋅+

h1 b4 a2i

−( )2

⋅

2 b2⋅

−← b2 b1+ a2i

≤ b4 b3−<if

Asbih3 b3⋅ h2 a2

i⋅+ h1 b1⋅+ h1 b2⋅+

h1 b4 a2i

−( )2

⋅

2 b2⋅

− b3 b4− a2i

+( ) h3⋅+← b4 b3− a2i

< b4≤if


Asb

return

:=

Asb2 AStressBlock2:=

ForceConcrete2

Cci0.85 fc⋅ Asb2i

⋅←


Ccreturn

:=

Cc2 ForceConcrete2:=

Compressi(e Concrete

Safety *actors

Factors of Φ controlled by strain in exrteme tension reinforcing steel. Areas controlled by

getPhi2

←T

rows εs2( ) 1−⟨ ⟩

−>

i 0 length Z( ) 1−..∈for:= 318 118 9.3.2.2

Phii 0.65←

εs2 i εy−>

if

Phii

0.90← εs2T

rows εs2( ) 1−⟨ ⟩

i0.005−<if

Phii

0.65 εs2T

rows εs2( ) 1−⟨ ⟩

−

iεy−

.25

.005 εy−

⋅+← otherwise

Phireturn

Forcessum2

PniCc2i

Fs2i⟨ ⟩

∑+←


Pnreturn

:=

Pn2 Forcessum2:=

600− 400− 200− 0 2005− 10

4×

0

5 104

×

1 105

×

1.5 10

5

×

2 105

×

Z

P . n

( k i p s )

ReducePn2

ΦPni Pn2i Phi2i⋅←


ΦPnreturn

:=

ΦPn2 ReducePn2:=

y2 b4 y−:=

Momentssum2

Msteel j i, Fs2 j i, y2 d2 j−( )⋅←


MniCc2i

y2

a2i

2−

⋅ Msteel

i⟨ ⟩

∑+←


Mnreturn

:=

Mn2 Momentssum2−:=

5 105

×

f t )



600− 400− 200− 0 2001.5− 10

6×

1− 106

×

5− 105

×

0

Z

M . n

( k i p * f

ReduceMn2

ΦMniPhi2

i Mn2i⋅←

i 0 length Z( ) 1−..∈for:=

Ag h1 b2 b1+( )⋅ h2 b4⋅+ 2 h4 h1− h2−( )⋅ b3⋅+:=Gross area of the

column

Ast As∑:=Total area of steel in the

column

PhiPn.max

ΦPn.maxi0.80 0.65⋅ 0.85 fc⋅ Ag Ast−( )⋅ fy Ast⋅+⋅←


ΦPn.maxreturn

:=

Maximum compression

force allowed for the

column (ACI 318-08

10.3.6.2)

ΦPn.max PhiPn.max:=

Ma+ Compression *orce

,+ial )ension

Strength of the column under tension is equal to the yield strength of the reinforcement in tension

Ptension

Ptify− Asi⋅←


Ptreturn

:=

Pt Ptension:=

Pnt Pt∑:= Net capacity in pure tension

ΦPnt 0.9 Pnt⋅:= Design compacity in pure tension: Φ = 0.9

Mtension

MtiPti

y di

−( )⋅←

i 0 length d( ) 1−..∈for:=



Mtreturn

Mt Mtension:=

Mnt Mt∑:= Net moment in pure tension

The following vectors are used merely for plotting purposes: plotting a line between the net

tension force / moment point and the points corresponding to the last force / moment pairs

from the P.n, M.n, ΦP.n, and ΦM.n vectors respectively

Pnt1

Pnt

Pnlength Pn( ) 1−

:=

Mnt1

Mnt

Mnlength Mn( ) 1−

:=

Pnt2

Pnt

Pn2length Pn2( ) 1−

:=

Mnt2

Mnt

Mn2length Mn2( ) 1−

:=

ΦPnt1

ΦPnt

ΦPnlength ΦPn( ) 1−

:=

ΦMnt1

ΦMnt

ΦMnlength ΦM

n

( ) 1−

:=

ΦPnt2

ΦPnt

ΦPn2length ΦPn2( ) 1−

:=

ΦMnt2

ΦMnt

ΦMn2length ΦMn2( ) 1−

:=

,+ial )ension

$esign Loa%s

Pg

789kip

636kip

0

:=

Mg

2991ftkip

1600ftkip

0

:=



0

2046.632−

18158.031

38362.694

58567.358

78772.021

98976.684

119181.347

139386.01

159590.674

179795.337

200000

Column Interaction Diagram

Moment

A x i a l L o a d ( k i p s )

427.979−

23.316−

381.347

786.01

1190.674

1595.337

2000

Column Interaction Diagram

i a l L o a d ( k i p s )

-1.50 -1.20 -0.90 -0.60 -0.30 0 0.30 0.60 0.90 1.20 1.50

(kip*ftx10^6)



2046.632−

1641.969−

1237.306−

832.642− A x

-1.50 -1.20 -0.90 -0.60 -0.30 0 0.30 0.60 0.90 1.20 1.50

C r e a t e d b y :

J A C , M Z

5 / 1 / 2 0 1 2

i ! "

( e # 1 0 )

H / 4 0 0

H / 5 0 0

4

1

9

9 2 0

* + 1

4

2 '

9 0 '

9 2 0

* + 1

4

4 0

0 0

0 0

* + 2

4

5 9 9

4

* + '

4

5 4 2

* + 4

4

4 0

5

0

* + 5

2 1 5

1 4 0

1 5

1

1 4 - 0 5

4

4 5

5 1

5

* +

4

4 0

5 0 9

5 1 2

* +

4

4 0 0

5 0 0

5 1 2

* +

4

4 1

0 2

0

* +

2 1 5

1 2 1

1 5 1

1 2

1 4 - 5 5 0

' 4

4

4 0

* + 9

2

' ' 5

' 4

* + 1 0

1 9 5

2 4 4

2 5 0

* + 1 1

1 2

1 5 9

1 2

1 4 - 5 5 0

2 1 5

'

4

5 1 "

1 4 - 1

1 2 '

1 5 '

1 2

1 4 - 5 5 0

1 0

1 ' 5

1 ' 4

1 4 - 4 5 5

9

1 0 1

1 4 - ' 4 2

%

* a k e r 1 9 9 a e r ( $ s i ! e # $ a t i ! 1 0 s 3 ! 3 e r

e ) t 6 % $ t e t i % a & %

e % b e r s e 6 t i ! s r

e s i s t i ! s y s t e % " . 3 e s e a r e a s a r e 6 % a r e d t b a s

e & i ! e a r e a s a ! d b $ i & t 7 $

s e 6 t i ! s s a t i s y i !

O p t i m i z e d

A r e a ( i n 2 )

B a s e l i n e

A r e a ( i n 2 )

O p t i m i z e d

A r e a ( i n 2 )

P r o p o s e d

S e c t i o n

A r e a P r o ! i d e d

( i n 2 )

4 . 6

E n e r g y M e t h o d O p t i m i z a t i o

n



O p t i m i z a t i o n

0 0

Δ = H / 4 0 0 0

1

3 d t i % i a t i ! r %

% b e r s t 3 e & a t e r a & r

% i ! e d "

! s & r s 4 7

s 1 7 4

s 1 7 4

! s & r s 5 7 1

m e r

% ! s & r s 2 7 '

! s & r s 7 9 9

! s & r s 1 0 0 7 1 0

% ! s & r s 1 0 9 7 1 1 0

s & r s 1 1 1 7 1 2 2

! s & r s 1 7 2

! s & r s 2 9 7 '

% ! s & r s ' 7 ' 9

! s & r s 4 0 7 5 2

! s & r s 5 7 '

! s & r s 4 7 1

s & r s 1 2 ' 7 1 ' '

s & r s 1 ' 4 7 1 4 4

e

d

1

, 2

8 > 1

* a ! k

2

8 > 2

* a ! k '

. r a ! s '

8 > '

* a ! k 4

4

2 1 5

4

2 1 5

2 1 5

5 1 2

2 5 0

1 0 1

5 1 2

' 4

1 ' 4

5

4 0

1 2

* +

* + 1 1

1 4 - ' 4 2

+5

* +

* + 1 0

1 4 - 4 5 5

+

* +

* + 9

1 4 - 5 5 0

2

7 1

7 '

7 2 5

7 4

7

7

7 1

1 4 - 1

1 4 - 0 5

1 4 - 5 5 0

1 4 - 5 5 0

0

1

1 2

1 2

5 2

4 . 6

E n e r g y M e t h o d O p t i m i z a t i o

n



& a r e r a & $ e s i ! r e

a

* a ! k 1

. r a ! s 1

4

4

0 0

* + 4

* + '

* + 5

* + 2

* +

7 1 1

7 2

1

0

4.6.1 Optimization Calculations

Steel Reduction Calculation

1 7 754 848 920 2,589 2,809 -220

2 14 754 848 920 5,178 5,618 -440

3 252 158 848 800 19,539 18,433 1,106

4 252 158 848 768 19,539 17,696 1,843

5 189 158 848 688 14,655 11,890 2,7656 21 327 848 608 3,370 2,416 954

7 21 530 215 178 1,386 1,147 239

8 273 158 848 576 21,168 14,378 6,790

9 231 158 848 512 17,911 10,814 7,097

10 168 158 848 512 13,026 7,865 5,161

11 21 342 848 608 3,522 2,526 997

12 21 475 215 162 1,240 934 306

13 196 158 688 480 12,330 8,602 3,72814 154 158 688 347 9,688 4,886 4,802

15 140 158 688 250 8,807 3,200 5,607

16 14 316 688 162 1,763 415 1,348

17 14 432 215 51.8 752 181 571

18 168 158 688 162 10,577 2,491 8,087

19 154 158 688 134 9,696 1,888 7,807

20 154 158 688 101 9,696 1,423 8,273

vol reduction in steel (ft3) 186,432 119,613 66,819

wt reduction in steel (ton) 46,608 29,903 16,705

% reduction 36

!se line "olu#e $ &'

"olu#e !n*e $ !seline - +ti#ied

+ti#ied

"olu#e (ft3)

"olu#e

!n*e (ft3)

u#/er of

le#ents

en*t

(in)

!seline 're!

' (in2)

+ti#ied

're! (in2)

!seline

"olu#e (ft3)



"olu#e !n*e $ !seline +ti#ied

Steel Tonnage for Increased Performance

500 4.0 0 47 30.0

526 3.8 5 47 31.5

556 3.6 10 47 33.2

588 3.4 15 47 35.2

625 3.2 20 47 37.4

rift () !seline

esi*nrift (ft)

% rift

eduction

+ti#ied

esi*n

47

30.0

31.5

33.235.2

37.4

30

35

40

45

50

0 5 10 15 20

S t e e l , 1 0 0 0 t

o n s

Reduction of !rift

!seline esi*n +,ti#i-ed esi*n

Calculations for "ega Column #

' (in2) 848

1 (in.) 709

2 (in) 776

ection 1 eff (in) 754

!teri!l teel (si) 29,000

id!s:

le#ent

u#/er

'i!l ni, "irtu!l

;ind o!d (is)

'i!l <i, 0.7 ;

(is)

=(ni=<i)0.5

(in-

is0.5

)

(ni=<i)0.5

(is0.5

)

're! e>uired

're> (in2)

1 13421 1.49 3,778 56,547 75.03 561

2 13422 0.92 3,110 40,313 53.49 400

3 13424 0.25 499 8,417 11.17 83

4 13425 -1.28 -3,696 51,837 68.78 514

5 13427 -1.49 -4,335 60,569 80.36 601

6 13428 -1.83 -5,108 72,866 96.68 723

7 13430 -1.83 -5,108 72,865 96.68 7238 13431 -1.49 -4,335 60,569 80.36 601

9 13433 -1.28 -3,696 51,837 68.78 514

10 13434 0.25 499 8,417 11.17 83

11 13436 0.92 3,110 40,313 53.49 400

12 13437 1.49 3,778 56,547 75.03 561

13 13439 1.72 4,861 68,918 91.44 683

14 13440 1.72 4,861 68,918 91.44 683

su# 718,932 #! 723

su# !ll 13,004,781 su# 7,129 ? 11,872

@esec: As /!seline !re! *re!terB

13421to13439/C3 13422to13440/C3

le#ent nu#/er fro# !roi!te nodes inid!sDen <' #odel.

+ri*. ection

C r e a t e d

b y :

J A C

5 / 1 / 2 0 1 2

3 8

3 0

4 0

5

9 2 0

8 9 4

Y e s

3 8

3 0

4 0

5

9 2 0

9 0 3

Y e s

3 2

2 4

4 0

5

8 0 0

7 9 8

Y e s

3 2

2 4

3 6

5

7 6 8

7 4 7

Y e s

2 8

2 0

3 6

5

6 8 8

6 7 5

Y e s

2 8

2 0

3 6

4

6 0 8

5 8 5

Y e s

2 8

2 0

3 2

4

5 7 6

5 7 0

Y e s

2 8

2 0

2 4

4

5 1 2

5 0 7

Y e s

2 8

2 0

2 4

4

5 1 2

4 9 8

Y e s

2 8

2 0

2 6

5

6 0 8

6 0 0

Y e s

2 8

2 0

2 0

4

4 8 0

4 6 5

Y e s

3 4 7

3 3 3

Y e s

2 5 0

2 4 3

Y e s

s i d e a r e a

t p i t x b

p ! " s i t e r i # r a r e a

x t p i t x $ d % 2 t p s i d

e &

(

t e r i # r ) ! a t e s

, i d e ) ! a t e

- .

'

# t a ! * e p t +

d $ i &

( t e r i # r

* e p t + d i t

' # t a ! W i d t +

b $ i &

# ( t e r i # r

) ! a t e

s

s x 3

p ! a t e s e ! d e d t # t + e t #

p a d b # t t # ! a e s

x 2

p ! a t e s e ! d e d t # t + e t #

p a d b # t t # ! a e s

+ e

# p t i i ; a t i # s p r e a d s + e e

t & < t + i s t # # ! a b e " s e d t # d e s i a b " i ! t % " p # ! "

" s i s t e e ! p ! a t e s

$ b y

t r i a ! a d e r r # r & =

A r e a ) r # i d e d

A p r #

$ i 2 &

A r e a ? e " i r e d

A r e

$ i 2 &

4 . 6 . 2 R e

s i z i n g o f B u i l t - U p M e m b e r s



4 4 4 4 4 4 4 4 4 4 4

! W i d t +

t - U p M e m b e r s

( t e r i # r

' + i e s s t p i t

i t + 2 2

i t + 2 2

t i # a ! a r e a $ r # t

t + a t r # s s s e t i # $

5.0 Connection Design

5.1 Typical Connections

5.1.1 Welded Column Splice 163

5.1.2

Floor Joist to adial !irder Connection 16"

5.1.3

!irder to Column Connections

5.1.3.1 Fixed Radial Elements to Column Connection 171

5.1.3.2 Pinned Circumferential Girder to Column Connection 175

5.1.#

$SS to Cantile%er Connection 1&&

5.1.5

adial !irder to Concrete Core 1"0

5.1.5.1 Single Plate Connection 181

5.1.5.2 Concrete nc!or "olt #esign 185

5.2 'ase o( )ega*Column Connection 1"+

5.2.1 )ega*Column to Caisson Connection 1+0

5.2.2 Caisson Cap )oment ein(orcement 1+#

5.3 ,utrigger Connections 1+6

5.3.1

'ottom o( ,utrigger to Column Connection 1+&

5.3.2

Top o( ,utrigger to Core 1++

p gg

5.1.1 Welded Column Splice KMC 4/27/2012


Column Location Constant/Preious Calc!

Column "ype Calc/Lookup

#es Passes C$eck

%o &ails C$eck

'(ial &orce P) 1*+,2 kips Column Splice Elevation:

-$ear . y y 2!2 kips

-$ear . 13 kips

"orsion "u .0!4, kip.in

Moment . y My 140 kip.inMoment . M 1!1 kip.in

Column Details

Column -ection Properties

Built.up ept$ 5 23!0 in

Built.up 6i5t$ 8 ,+!0 in

Memer "$ickness t 4!0 in

9ross 'rea ') +33 in2

( . a5ius o8 9yration r( 11!, in

y . a5ius o8 9yration ry 11!0 in Column Plan View:

Create5 y:

2 . ,

"rans8er

BU.2

"$is column splice is use5 8or t$e me)a.column an5 trans8er column connections! "$e connection is ma5e upo8 pre.8aricate5 steel memers t$at are <el5e5 to)et$er on site! In t$is calculation t$e capacity o8 t$e <el5

an5 memers are c$ecke5!

0.9D+1.6Wo!ces "!om #$D%S "o! &oad Case:

#esIs Column -plice =kay>

Welded ColumnSplice

SamplePre-fabricated

Node

depth

plate length

plate width

"op Column Properties

Lateral Unrace5 Len)t$ L 13 in

;88ectie Len)t$ &actor K 0!+

Bottom Column Properties

Welds

Column

width

d h

Plate Details

Plate ' Properties

"$ickness tp 0!7 in6i5t$ <p 14 in ?5imension perpen5icular to column@

Len)t$ lp + in ?5imension parallel to column@

Aproperties <ill e summe5 as necessary

Plate B Properties

"$ickness tp 0!7 in

6i5t$ <p 14 in ?5imension perpen5icular to column@

Len)t$ lp + in ?5imension parallel to column@

Aproperties <ill e summe5 as necessary

-teel Properties . Plate

#iel5 -tren)t$ &y 0 ksi

"ensile -tren)t$ &u + ksi

Weld Details

6el5 Properties

&iller Metal Class! -tren)t$ &; 70 ksi

6el5 -tren)t$ &< 42 ksi 0!+0A&;A?1!0D0!0Asin?E@1!

@ <$ere E 0 F 'I-C G2.

E is assume5 to e 0* as an)le o8 8orce is unkno<n

Plate ' 6el5 Properties

Le) Len)t$ 0!2 in ?same 8or ot$ <el5s* 8or construction purposes@"$roat Len)t$ 0!,4 in le) len)t$ / cos?4

o@

6el5 Len)t$ per -i5e L< 40 in

6el5 'rea '< 14!1 in2

Min! Le) Len)t$ o8 6el5 0!2 in per 'I-C tale G2!4

Ma(! Le) Len)t$ o8 6el5 0!+33 in ?5epen5s on plate t$ickness@F G2.2

Plate B 6el5 PropertiesLe) Len)t$ 0 2 in

Le) Len)t$ 0!2 in

"$roat Len)t$ 0!,,+ in le) len)t$ / cos?4o@

6el5 Len)t$ per -i5e L< 40 in

6el5 'rea '< 14!1 in2

Min! Le) Len)t$ o8 6el5 0!12 in per 'I-C tale G2!4

Ma( Le) Len)t$ o8 6el5 0 +33 in ?5epen5s on plate t$ickness@F G2.2

'ension C(ec)s

Plate ' "ension C$eck

Ma(! "ensile Loa5 "u 41, kipsUlt! #iel5in) "ens! Capacity H"n.yiel5 47, kips 0!0A&yA') F 'I-C 2.1

-$ear La) &actor U 0!1 1.?eccentricty@/?<el5 len)t$@ F 'I-C tale ,!1

;88ectie %et 'rea 'e 10!4 in2

'nU F 'I-C ,.1F 'n ') B4.,F ') tA<

Ult! upture "ens! Capacity H"n.rupture 07 kips 0!0A&uA'e F 'I-C 2.2

Minimum H"n 47, kips min? H"n.yiel5 * H"n.rupture @

"u J"n > #es 1

Plate B "ension C$eck

Ma(! "ensile Loa5 "u 403 kips

Ult! #iel5in) "ens! Capacity H"n.yiel5 47, kips 0!0A&yA') F 'I-C 2.1


;88ectie %et 'rea 'e 10!4 in2

'nU F 'I-C ,.1F 'n ') B4.,F ') tA<

Ult! upture "ens! Capacity H"n.rupture 07 kips 0!0A&uA'e F 'I-C 2.2

Minimum H"n 47, kips min? H"n.yiel5 * H"n.rupture @

"u J"n > #es 1

Col* ' -i5e "ension C$eck

Ma(! "ensile Loa5 "u 1*+,4 kips

Ult! #iel5in) "ens! Capacity H"n.yiel5 ,0*+0 kips 0!0A&yA') F 'I-C 2.1

-$ear La) &actor U 0!+0 1.?eccentricty@/?<el5 len)t$@ F 'I-C tale ,!1;88ectie %et 'rea 'e 447 in

2 'nU F 'I-C ,.1F 'n ') B4.,F ') tA<

Ult! upture "ens! Capacity H"n.rupture 21*301 kips 0!0A&uA'e F 'I-C 2.2

Minimum H"n 21*301 kips min? H"n.yiel5 * H"n.rupture @

"u J"n > #es 1

Col* B -i5e "ension C$eck

Ma(! "ensile Loa5 "u 1*+,4 kipsUlt #iel5in) "ens Capacity H" ,0 +0 kips 0 0A& A' F 'I-C 2 1

Ult! #iel5in) "ens! Capacity H"n.yiel5 ,0*+0 kips 0!0A&yA') F 'I-C 2.1


;88ectie %et 'rea 'e ,73 in2

'nU F 'I-C ,.1F 'n ') B4.,F ') tA<

Ult! upture "ens! Capacity H"n.rupture 13*447 kips 0!0A&uA'e F 'I-C 2.2

Minimum H"n 13*447 kips min? H"n.yiel5 * H"n.rupture @

Comp!ession C(ec)s

"op Column Compression C$ecks

-len5erness atio !,+ KL/rF G4.+KL/r 2 > #es 1

Ma(! Comp! Loa5 Pu 0 kips

Ult! Comp! Capacity HPn ,0*+0 kips 0!0A&yA')F G4.+

Pu JPn > #es 1

Bottom Column Compression C$ecks

-len5erness atio 2!,4 KL/rF G4.+KL/r 2 > #es 1

Ma(! Comp! Loa5 Pu 0 kips

Ult! Comp! Capacity HPn ,0*+0 kips 0!0A&yA')F G4.+

Pu JPn > #es 1

Column Bearin) C$eck

Ma(! Bearin) Loa5 u 0 kipsUlt! Bearin) Capacity Hn 4+*440 kips 0!7A1!3A&yA'p F 'I-C G7.1

u Jn > #es 1

Weld C(ec)s

"otal 6el5 'rea '"=" +!+ in2

2A?'<Plate'D'<PlateB@

Plate ' 6el5 C$eck

'rea o8 <el5 ' '' 14!142 in2

Ma(! ( &orce &( 403 kips ma(?0* ?Pu@A''/'"=" D as?M@/5@

Ma(! y &orce &y 0!7,0 kips as?y@A''/'"="

Ma(! &orce & ,! kips as?@A''/'"=" D as?"@A''/'"="/?5/2@

esultant &orce & 410 kips srt?&(2D&y

2D&

2@

Plate ' 6el5 Capacity Jn.<el5 44 kips '<A&< F 'I-C G2.,

& Jn.<el5 > #es 1

Plate ' Capacity Jn.plate 1*12 kips L<AtpA&y F 'I-C G2.2

& Jn.plate > #es 1

Column -i5e ' Capacity Jn.col si5e +*000 kips L<AtA&y F 'I-C G2.2

& Jn.col si5e > #es 1

Plate B 6el5 C$eck

'rea o8 <el5 B 'B 14!1 in2

2A?'<Plate'D'<PlateB@

Ma(! ( &orce &( 412 kips ma(?0* ?Pu@A'B/'"="D as?My@/8

Ma(! y &orce &y 0!74, kips as?y@A'B/'"=" D as?"@A'B/'"="/?8 /2@

Ma(! &orce & ,! kips as?@A'B/'"="

esultant &orce & 414 kips srt?&(2D&y2D&2@

Plate ' 6el5 Capacity Jn.<el5 44 kips '<A&< F 'I-C G2.,

& Jn.<el5 > #es 1

Plate ' Capacity Jn.plate 1*12 kips L<AtpA&y F 'I-C G2.2

& Jn.plate > #es 1

Column -i5e ' Capacity Jn.col si5e +*000 kips L<AtA&y F 'I-C G2.2

& Jn.col si5e > #es 1

1

5.1.2 Floor Joist to Radial Girder Connection Created by: JDM 3/13/12

Bank: 4 Color Key: User Input

Locaton: !ypcal Lar"est #loor $ost Constant/%re&ous Calc'

Calc/Lookup

(es %asses C)eck

*o #als C)eck

C+bolt Center o, Bolt

Design Adequate?

-ertcal Load at Connecton .u 24 kps

Girder Properties

rder secton 0secton 21

rder ,lan"e 0dt) b, ' n

rder ,lan"e t)ckness t, 5' nrder 0eb t)ckness t0 5'45 n

rder dept) d 21'1 n

rder k1 k1 5'61 n

rder clear space ! 17'46 n

Joist Properties

Jost secton 8secton 12 22

Jost ,lan"e 0dt) b, 4'53 n

J t ,l t) k t 5 42

#ro< Jost Des"n

Des"n tool ,or t)e ,loor $ost to t)e radal "rder connecton usn" a sn"le an"le bolted nto t)e 0eb o, eac)

<e<ber'

PASS

9n"le9n"le

JostJost

/rder

Jost ,lan"e t)ckness t, 5'42 n

Jost 0eb t)ckness t0 5'2 n

Jost dept) d 12'3 n

Jost k1 k1 5'2 n

Jost clear space ! 11'5 n

Bolt Properties

Bolt type 9475

Bolt da<eter db /6 n

=)ear stren"t) >.n 13'6 k/bolt 9I=C !+1

*u<ber o, bolts re;ured ?<n 2@ n 2

Spacing Requireents

1'2 n

5'6 n 9I=C !able J3'4

5'74 n

9n"le ed"e dstance A <nu<u< ed"e dstance (=

3' n

5' n

%late space re<ann" ≥ 5 (=

(=(=

S!ear "ielding

=)ear yeldn" stren"t) >.n kps 5'E#yELpEtp F 9I=C J4+1

>.n ≥ .u (=

S!ear Rupture*et area o, s)ear plane 9n& 1'3 n

2 ?Lp+?nEdbG1/6@@Etp

=)ear rupture stren"t) >.n 34 kps ?5'E5'E#uE9n&@ F 9I=C J4+4

>.n ≥ .u (=

Bloc# S!ear Rupture

ross area o, s)ear plane 9"& 1'62 n2 LpEMI*?tpHt0@

*et area o, tenson plane 9nt 5'6 n2 ?0p+?dbG1/6@@EMI*?tpHt0@

Block s)ear rupture stren"t) ?<n >.n@ >.n 6 kps 5'?5'E#uE9n&G#uE9nt@ F 9I=C J4+

>. 62 kps 5 ?5 E# E9 G# E9 @ F 9I=C J4

C+bolt to ed"e

Mn<u< ed"e dstance

9n"le ed"e dstance

C+bolt spacn"

8dt) o, plate <nus bolt spacn"s

Jost ,ts bet0een "rder ,lan"es9n"le ,ts bet0een $ost ,lan"es

>.n 62 kps 5'?5' #y 9"&G#u 9nt@ F 9I=C J4+

MI* >.n ≥ .u (=

Bearing and $earout at Bolt %oles

Controlln" <ateral ?<n o, t0Htp@ Jost 8eb

&eld' Fillet &eld

lectrode class,caton nu<ber #:: 35 ks

=e o, 0eld ac)e&ed 0t) one pass se /1 n!)roat t)ckness 0t 5'221 n D 5'353Ese

Len"t) o, t)e 0eld L0 '55 n one sde o, plate

8eld stren"t) >.n 42 D 5'3EteEL0E5'E#:: F 9I=C J2+4

>.n ≥ .uB (= kps



5.1.3.1 Fixed Radial Elements to Column Connection


Location: Typical Column Constant/Previous Calc.

Calc/Lookup

Yes Passes Check

o !ails Check

C"#olt Center o$ Bolt

Radial Girder to Column Connection

Design Adequate?

%oment at Connection %u &'&(' Kip"in

%oment )rm *m +,.( in

!orce to #e -esiste* #y !lane Bolts -m 00 Kips 1 %u/*m

2ertical Loa* at Connection -v ++' Kips !rom %i*as 3en %o*el

Girder Properties

3ir*er section section +& 5 ,

Beam $lane 6i*th #$ ,.4 in

Beam $lane thickness t$ '.,0 in

Beam 6e# thickness t6 '.0&0 in

Beam *epth * +& 4 in

Create* #y: 89 4/+&/&+

PA

9esin tool $or the ra*ial an* cantilever ir*ers to the e5terior columns usin t6o anles 6el*e* to the columnan* #olte* to the $lane o$ the ir*er to resist the moment. To resist the shear there are t6o plates 6el*e* to

the column an* #olte* to the 6e# o$ the incomin ir*er.

Plates

:hear !orce Taken #y 4e#

%oment Taken #y !lan.e

Column

3ir*er

Beam *epth * +&.4 in

Beam k& K& '.,, in

Plate Properties

Plate thickness tp &.0' in

!olt Properties

e#Bolt type )4;'

Bolt *iameter *# & &/, in

hear strenth criteria <-n 44.7 k/#olt )IC T7"&

um#er o$ #olts re=uire* >min +? n 0

!lane

Bolt type )4;'

Bolt *iameter *# & &/, in

hear strenth criteria <-n 44.7 k/#olt )IC T7"&

um#er o$ #olts re=uire* >min +? n ,

pacing Requirements

+.4' in

&.7, in

&.70 in )IC Ta#le 8.4

Plate e*e *istance @ minumum e*e *istanceA Y

&.+0 in

+.+' in

Plate space remainin ≥ 'A Y

Plate "ear #ielding $Designed %or Flange &nl'(

hear yiel*in strenth <-n 04' kips 1 '.(!yLptp D )IC 84"&

<-n ≥ -uA Y

Plate "ear Rupture $Designed %or Flange &nl'(

et area o$ shear plane )nv ;.0( in+ 1 >Lp">n*#E&/,??tp

Plate shear rupture strenth <-n +,' kips 1 >'.70'.(!u)nv? D )IC 84"4

<-n ≥ -uA Y

C"#olt to e*e

Plate e*e *istance

%inimum e*e *istance

C"#olt spacin

i*th o$ plate minus #olt spacins

!loc) "ear Rupture *e+

e#3ross area o$ shear plane )v (.&, in

+ 1 Lp%I>tpFt6?

et area o$ tension plane )nt .' in+ 1 >6p">*#E&/,??%I>tpFt6?

Block shear rupture strenth >min <-n? <-n 4+4 kips 1 '.70>'.(!u)nvE!u)nt? D )IC 84"0

<-n +, kips 1 '.70>'.(!y)vE!u)nt? D )IC 84"0

%I <-n ≥ -uA Y

!lane

3ross area o$ shear plane )v &'.'+ in+ 1 Lp%I>tpFt6?

et area o$ tension plane )nt 4., in+ 1 >6p">*#E&/,??%I>tpFt6?

Block shear rupture strenth >min <-n? <-n 0&4 kips 1 '.70>'.(!u)nvE!u)nt? D )IC 84"0

<-n 4'0 kips 1 '.70>'.(!y)vE!u)nt? D )IC 84"0

%I <-n ≥ -uA Y

!earing and ,earout at !olt -oles *e+

e#

Controllin material >min o$ t6Ftp?

C"#olt *istance to e*e +.4' in

Tearout c"#olt to e*e <-n 0 kips 1 '.70&.+Lct!u D )IC 8"(a

Bearin c"#olt to e*e <-n (, kips 1 '.70+.4*#t!u D )IC 8"(a

C"C *istance #et6een holes .'' in

Tearout center #olts <-n 0 kips 1 '.70&.+Lct!u D )IC 8"(a

Bearin center #olts <-n (, kips 1 '.70+.4*#t!u D )IC 8"(a

Total #earin an* tearout capacity <-n +(4 kips

<-n ≥ -uA Y

FlangeControllin material >min o$ t6Ftp?

C #olt *istance to e*e + 4' in

Plate >tpGt6?

Beam e# >t6Gtp?

C"#olt *istance to e*e +.4' in

Tearout c"#olt to e*e <-n ,7 kips 1 '.70&.+Lct!u D )IC 8"(a

Bearin c"#olt to e*e <-n &&' kips 1 '.70+.4*#t!u D )IC 8"(a

C"C *istance #et6een holes .'' in

T t t # lt <- ,0 ki ' 70& +L t! )IC 8 (

*elds Fillet *eld

e#lectro*e classi$ication num#er !HH 7' ksi

ie o$ 6el* 6ith one pass sie & in

Throat thickness 6t '.7'7 in 1 '.7'7sie

Lenth o$ the 6el* L6 &&.'' in one si*e o$ plate

el* strenth <-n +40 kips 1 '.70teL6'.(!HH D )IC 8+"4

<-n ≥ -uA Y

!lane

lectro*e classi$ication num#er !HH 7' ksi

ie o$ 6el* 6ith one pass sie & in

Throat thickness 6t '.7'7 in 1 '.7'7sie

Lenth o$ the 6el* L6 +&.'' in one si*e o$ plate

el* strenth <-n 4(, kips 1 '.70teL6'.(!HH D )IC 8+"4

<-n ≥ -uA Y



5.1.3.2 Pinned Circumferential Girder to Column Connection Created by: JDM 3/13/12


Locaton: !ypcal Colu"n Constant/#re$ous Calc%

Calc/Lookup

&es #asses C'eck

(o )als C'eck

C*bolt Center o+ Bolt

Design Adequate?

,ertcal Load at Connecton -u . Kps )ro" Mdas 0en Model

Girder Properties

0rder secton secton 14 43

Bea" +lane dt' b+ 5%6 n

Bea" +lane t'ckness t+ 6%.3 n

Bea" eb t'ckness t 6%36. n

Bea" dept' d 13% n

Bea" k1 k1 1%66 n

Plate Properties

#late t'ckness tp 6%.6 n

#late lent' Lp 16%6 n

#late dt' p 7%6 n

plate yeldn strent' + y .6 ks

plate ult"ate strent' + u 7. ks

Bolt Properties

Desn tool +or t'e crcu"+erental rders to t'e eteror colu"ns usn a snle plate elded to t'e colu"n andbolted to t'e eb o+ t'e rder%

PASS

#late

0rderColu"n

Bolt type 8496

Bolt da"eter db /5 n

'ear strent' crtera ;-n 2%1 k/bolt 8IC !*1

(u"ber o+ bolts re<ured ="n 2> n 3

Spacing equirements

2%66 n

1%.6 n1%2. n 8IC !able J3%4

#late ede dstance ? "nu"u" ede dstance@ &A

3%66 n

6%66 n

#late space re"ann ≥ 6@ &A

Plate S!ear "ielding

'ear yeldn strent' ;-n 1.6 kps 6%7)yLptp 8IC J4*1

;-n ≥ -u@ &A

Plate S!ear upture

(et area o+ s'ear plane 8n$ 3%. n2 =Lp*=ndbE1/5>>tp

#late s'ear rupture strent' ;-n 116 kps =6%.6%7)u8n$> 8IC J4*4

;-n ≥ -u@ &A

Bloc# S!ear upture

0ross area o+ s'ear plane 8$ 3%6. n2 LpMI(=tpFt>

(et area o+ tenson plane 8nt 1%. n2 =p*=dbE1/5>>MI(=tpFt>

Block s'ear rupture strent' ="n ;-n> ;-n 154 kps 6%.=6%7)u8n$E)u8nt> 8IC J4*.

;-n 143 kps 6%.=6%7)y8$E)u8nt> 8IC J4*.

MI( ;-n ≥ -u@ &A

Bearing and $earout at Bolt %oles

Controlln "ateral ="n o+ tFtp>

C*bolt dstance to ede 2%66 n

!earout c*bolt to ede ;-n 2 kps 6%.1%2Lct)u 8IC J3*7a

Bearn c*bolt to ede ;-n 31 kps 6%.2%4dbt)u 8IC J3*7a

C*C dstance beteen 'oles 3%66 n

!earout center bolts ;-n 37 kps 6%.1%2Lct)u 8IC J3*7a

Bearn center bolts ;-n 31 kps 6%.2%4dbt)u 8IC J3*7a

!otal bearn and tearout capacty ;-n 59 kps

C*bolt to ede

#late ede dstanceMn"u" ede dstance

C*bolt spacn

dt' o+ plate "nus bolt spacns

Bea" eb =ttp>



;-n ≥ -u@ &A

&eld' (illet &eld

Alectrode class+caton nu"ber )AGG 6 ks

5.1.4 HSS to Cantilever Connection Created by: JDM 3/15/2012


o!at"on: #nd o$ typ"!al lon% !ant"le&er Constant/'re&"ous Cal!(

Cal!/ookup

)es 'asses C*e!k

+o ,a"ls C*e!k

C-bolt Center o$ Bolt

Design Adequate?

.ert"!al oad at Conne!t"on u 24 k"ps ,ro Cant"le&er Des"%n

Cantilever Properties

Cant"le&er se!t"on se!t"on 2 14

Cant"le&er $lan%e "dt* b$ 14(0 "n

Cant"le&er $lan%e t*"!kness t$ 1(34 "n

Cant"le&er eb t*"!kness t 0(5 "n

Cant"le&er dept* d 26(1 "n

Cant"le&er k1 k1 1(1 "nCant"le&er !lear spa!e 7 25( "n

HSS Section Properties

899 se!t"on 899se!t"on

899 t*"!kness t 0(21 "n

899 "dt* 6(0 "n

899 *e"%*t * 1(0 "n

Angle Properties

Des"%n tool $or t*e !ant"le&er to 899 se!t"on "t* an an%le bolted to t*e !ant"le&er eb and elded to t*e 899s"de(

899165/1

PASS

899;n%le

Cant"le&er

;n%le type se!t"on <4<1/2

;n%le len%t* a (00 "n

;n%le t*"!kness ta 0(50 "n

;n%le le% lon% len%t* a (00 "n !onne!ted to !ant"le&er

Bolt Properties

Bolt type ;40

Bolt d"aeterd

b 5/6 "n9*ear stren%t* =n 13(6 k/bolt ;I9C 7-1

+uber o$ bolts re>u"red ?"n 2@ n"n 2

+uber o$ bolts used n 4 !onser&at"&e - tor>ue "n 899

se!t"on

Spacing Requirements

1(25 "n

0(65 "n ;I9C 7able J3(4

0(66

;n%le ed%e d"stan!e A "nuu ed%e d"stan!e )#9

3(5 "n

0(5 "n

'late spa!e rea"n"n% ≥ 0 )#9

)#9

Sear !ielding9*ear y"eld"n% stren%t* =n k"ps 0(,yptp E ;I9C J4-1

=n ≥ u )#9

Sear Rupture

+et area o$ s*ear plane ;n& 4(13 "n2 ?p-?ndbF1/6@@tp

9*ear rupture stren%t* =n 3 k"ps ?0(50(,u;n&@ E ;I9C J4-4

=n ≥ u )#9

Bloc" Sear Rupture

Gross area o$ s*ear plane ;%& 5(25 "n2 pMI+?tpHt@

+et area o$ tens"on plane ;nt 3(0 "n2 ?p-?dbF1/6@@MI+?tpHt@

Blo!k s*ear rupture stren%t* ?"n =n@ =n 2 k"ps 0(5?0(,u;n&F,u;nt@ E ;I9C J4-5

=n 24 k"ps 0(5?0(,y;%&F,u;nt@ E ;I9C J4-5

MI+ =n ≥ u )#9

Bearing and #earout at Bolt Holes

C ll" " l ? " $ @

C-bolt to ed%e

M"n"u ed%e d"stan!e

;n%le ed%e d"stan!e

C-bolt spa!"n%

"dt* o$ plate "nus bolt spa!"n%s

;nl%e $"ts beteen !ant"le&er $lan%es

l ? @

Controll"n% ater"al ?"n o$ tHta@

C-bolt d"stan!e to ed%e 1(25 "n

Clear d"stan!e to ed%e 0(66 "n

7earout !-bolt to ed%e =n 2 k"ps 0(51(2!t,u E ;I9C J3-a

;n%le ?tat@

$eld% &illet $eld

#le!trode !lass"$"!at"on nuber ,#<< 0 ks"

9"e o$ eld a!*"e&ed "t* one pass s"e 5/1 "n7*roat t*"!kness t 0(221 "n 0(0s"e

en%t* o$ t*e eld 23(00 "n one s"de o$ plate

eld stren%t* =n 10 k"ps 0(5te0(,#<< E ;I9C J2-4

=n ≥ u )#9



t e

C o r e

C r e a t e d

b y :

J L B

5 / 1 0 / 2 0

1 2

r e b y a s

i m p l e - s

h e a r , s i n g l e p l a t e

c o n n e c t i o n a n d h e a d e d

a n c h o r b o l t s

! h e d e s i g n

o " t h i s c o n n e c t i o n # s e s

s i g n t h e s i n g l e p l a t e s h e a r c o n n e c t i o n t o t h e s t e e l b a s e p l a t e ,

a n d o n e t o d e s i g n t h e h e a d e d a n c h o r b o l t

h e c o n c r e t e c o r e

5 . 1 . 5

R

a d i a l G i r d e r t o C o n c r e t e

C o r e

o

C o n c r e t

e d t o t h e c o

s ,

o n e t o d e s

s e p l a t e t o t h

5.1.5.1 Single Plate Connection Design Created by: JLB 4/5/2012


Location Constant/re!ious Calc"

Bea# Calc/Lookup

asses $inal c%eck& 'es asses C%eck

(o )ails C%eck

Applied Loads

)actored s%ear $orce *u 224 kips

Controllin+ Capacity ,-n 2. kips

Bolt Layout and Properties

bolt type 5 roup B e"+"3 40 bolts3 6%en t%reads are e7cluded $ro# s%ear planes

bolt dia#eter db 5/8 in 9 o$ cols e %ori" ;pacin+

nu#ber o$ colu#ns o$ bolts nb%4 2 . 5"5 8

nu#ber o$ ro6s o$ bolts nb! 4 . . <

!ertical bolt spacin+ sb! < in 4 . 4

%oriontal bolt spacin+ sb% 4 in

Plate Properties and Dimensions

dept% o$ plate d 18 in

6idt% o$ plate b 12 in

plate t%ickness tp 0"<25 in Plate Thickness Eceeds !a Allo"a#le

distance $ro# support $ace to 1st

bolts a . in

%oriontal ed+e distance Le% . in

!ertical ed+e distance Le! . in

speci$ied #ini#u# yield stress o$

plate)y

.< ksi

#ini#u# tensile stren+t% o$ plate )u 58 ksi

Beam Properties and Dimensions

bea# dept% d 21"1 in

distance bet6een 6eld centers = 18".8 in6eb t%ickness t6 0"405 in

speci$ied #ini#u# yield stress )y 50 ksi

)

>esi+n tool t%at calculates t%e capacity o$ a +i!en sin+le plate connection desi+n accordin+ to I;C ;teel

Construction ?anual3 14t% @dition

.

?ec%" )loor

-adial irder

'es

speci$ied #ini#u# tensile stress )u <5 ksi

Bearing Strength at Bolt $oles

, 0"5total nu#ber o$ bolts in +roup n 1< A nb!nb%

clear distance bt6n ed+e o$ %ole

and ed+e o$ #aterial $or botto#

bolts lcbt# . in

nu#ber o$ bolts in botto# ro6 nbt# 4

clear distance bt6n ed+e o$ %ole

and ed+e o$ adacent %ole lc 5"25 in

nu#ber o$ bolts #inus botto# ro6 nb 12

su# o$ bolt clear distance !alues lc 5 in A Icbt#nbt#DIcnb

a!aia e earin+ stren+t at o t

%oles ,-n 13 kips A ,)uE#in1"2lc t63 2"4ndt6 F J.G10

Determine !a Plate Thickness

s%ear stren+t% o$ indi!idual bolt )! 84 psi =able J."2

area o$ indi!idual bolt b 0"2. in2 A H/4dbG0"4./nt

2

coe$" )ro# art $or t%e #o#ent

only case instantaneous center o$rotation at t%e centroid o$ t%e bolt

+roup

C 115 in =able G to G1.

#a7i#u# #o#ent in unbraced

se+#ent?#a7 2342< kipEin

A )!/0"0bEC F 10G4

#a7i#u# plate t%ickness t#a7 1"25 in A <?#a7/)yEd2 F 10G.

Check plate %or limit states o% shear yielding& shear #uckling& and yielding due to %leure

-euired s%ear stren+t% *r A *u 224 kips

,! 1"00

no#inal s%ear stren+t% *n 24. kips A 0"<E)yE+

a!ailable s%ear stren+t% *c 24. kips A ,!E*n

+ross crossGsectional area o$ s%ear

plate+

11". in2 A dEtp

distance $ro# support to center o$

bolt +roupe

in

li#itin+ bucklin+ #o#ent ?r 2301< kipEin A *rEe

,b 0"0

no#inal $le7ural stren+t%?

n .432 kipEinA )

yE

pl

a!ailable $le7ural stren+t% ?c .134. kipEin A ,bE?n

plastic section #odulus o$ s%ear

platepl

2 in. A bEd

2/4

Interaction ok& 0"854 'es A *r/*c2 D ?r/?c

2 A 1"0 F 10G5

Check Plate %or Shear 'ielding

, 1"00

+ross area subect to s%ear +! 1."1 in2

A MLe!Dnb!G1Esb!NEtp

a!ailable s%ear stren+t% $or s%earyieldin+ o$ t%e plate

,-n 284 kips A ,E0"<0E)yE+! F J4G.

Check Plate %or Shear (upture

, 0"5

net area subect to s%ear n! "4 in2

A tpEMdGnb!EdbD0"125inN

a!ailable stren+t% $or s%ear rupture

o$ t%e plate,-n 245 kips A ,E0"<0E)uEn! F J4G4

Check Plate %or Block Shear (uptureblock s%ear rupture reduction

coe$$icientUbs 0"5

, 0"5

+ross area subect to s%ear +! 1."1 in2

A MLe!Dnb!G1Esb!NEtp

net area subect to s%ear n! 11"5 in2

A MLe!Dnb!G1Esb!Gnb!G1/2dbD0"125NEtp

net area subect to tension nt 1"< in2

A MLe%G0"5EdbD0"125NEtp

tension rupture co#ponent ,)unt 1 kips =able G.a

s%ear yieldin+ co#ponent ,0"<)y+! 21. kips =able G.bs%ear rupture co#ponent ,0"<)un! .00 kips =able G.c

a!ailable stren+t% $or block s%ear,U E) E ?I(,0 <0E) E ,0 <0) E

+

rupture alon+ a s%ear $ailure pat% or

pat%s and a perpendicular tension

$ailure pat%

,-n 248 kipsA ,UbsE)uEntD?I(,0"<0E)uEn!3 ,0"<0)yE+!F

J4G5

Check A)aila#le Strength o% *eld

t%ickness o$ t%inner part oined 0"405 in A ?I(t6 3tp#ini#u# 6eld sie ./1< in

#a7i#u# 6eld sie 0".4. in

6eld sie in si7teent%s o$ an inc%> 5/1<

6eld len+t% L6 1 in

$iller #etal classi$ication stren+t%)@OO 0

ksi

, 0"5

a!ailable stren+t% o$ 6elded oint ,-n 2.kips

A 2E,E0"<0E)@OOEsrt2/2E>EL6

Created by: JLB 3/1/2012

Design tool to calculate the capacity of groups of headed anchor bolts in concrete according to AC 31!"0!

Ban# Color $ey: %ser nput

Location Constant/&re'ious Calc(

Bea) Calc/Loo#up

Anchor configuration acceptable* +es &asses Chec#

,o -ails Chec#

Applied Loads

factored tensile force applied to anchor or group of

anchors,ua .2 #ips

factored shear force applied to a single anchor or

group of anchorsua 12 #ips

location of factored tensile force cg, 1!( in )easured fro) center of loest bolt ro

Bolt and Layout Properties

bolt type

nu)ber of colu)ns of bolts per side nbh 2

nu)ber of ros of bolts nb'

nu)ber of anchors in group n !

nu)ber of hoo#ed bolts nL 0 included in the total of anchors4 n

bolt dia)eter db /! in

distance fro) the inner surface of the shaft of a J"

or L"bolt to the outer tip of the J" or L"bolteh 3 in

'ertical bolt spacing sb' . in

hori5ontal bolt spacing sbh in

effecti'e e)bed)ent depth of anchor hef 12 in

'ertical centroid of bolt group cgb 10( in )easured fro) center of loest bolt ro

Concrete Properties

specified co)pressi'e strength of concrete f6c 1000 psi

Results

Design 7ension 8trength 9,n 12 #ips .;

Design 8hear 8trength 9n 1.0 #ips .;

8hear"7ension nteraction 0(0. <,ua/9,n=/3

><ua/9n=/3

Anchor configuration acceptable* +es full strength in tension per)itted if ua ?@ 0(29n

full strength in shear per)itted if ,ua ?@ 0(29,n

shear"tension interaction to be ?@ 1 otherise

5.1.5.2 Concrete Anchor Bolt Design

3

ech( -loor

adial irder

= roup B <e(g(4 A0= bolts4 hen threads are eEcluded fro) shear planes

+es

Design Requirements for ensile Loading !AC" #1$%&$ D.5'

Design (trength

,o)inal 7ension 8trength ,n 1.4.1: lbs ini)u) of ,sa 4 ,cbg4 and ,png

8trength reduction factor 9 0(.0 According to D((

Design 7ension 8trength 9,n 12(! #ips

D.5.1 (teel (trength of Anchor in ension

effecti'e cross"sectional area of single anchor in

tensionAse4, 0(22: in

2

@ <F/=<db"0(.3/nt=2


specified tensile strength of anchor steel -u 124000 psinot greater than s)aller of 1(G-y

and 124000

anchor steel yield strength -y 1134000 psi fro) 7able J3(2

,o)inal strength of group of anchors in tension ,sa 22:4002 lbs @ nGAse4,G-u H <D"3=

D.5.2 Concrete Brea)out (trength of Anchor

proIected concrete failure area of a single anchor

if not li)ited by edge distance or spacingA,co 142: in

2@ Ghef

2 H

<D":=

proIected concrete failure area of a group of

anchorsA,c 242!0 in

2eual to nA,co for anchors spaced K@

3Ghef apart

coefficient for basic concrete brea#out strength in

tension#c 2 2 for cast"on4 1. for post installed

)odification factor reflecting the reduced

)echanical properties of lighteight concrete 1(0 -or nor)al eight concrete

basic concrete brea#out strength in tension of a

single anchor in crac#ed concrete,b 11!40 lbs @ #cGG<f6c=

1/2Ghef

1( H <D".=

distance beteen resultant tension load on a

group of anchors and the centroid of the group of

anchors

e6, ! in

)od( -actor for anchor groups loaded

eccentrically in tensionMec4, 0(. @ <1>2Ge6,/3Ghef =

"1 H <D"=

)od -actor for edge effects of anchors loaded in

)od( -actor for edge effects of anchors loaded in

tensionMed4, 1(0 ,o edge effects hen far fro) edge

)od( -actor for anchors located in region ith no

crac#ing at ser'ice load le'elsMc4, 1(2 for cast"in anchors

D.5.# Pullout (trength of Anchor in ension

)odification factor for an anchor located in a

egion of concrete )e)ber here analysis

indicates no crac#ing at ser'ice load le'els

Mc4& 1(Mc4& @ 1(0 here analysis indicates

crac#ing at ser'ice load le'els

pullout strength in tension of a single headed stud

or headed bolt,ph .413. lb @ !GAbrgGf6c H <D"1=

no)inal pullout strength of a single headed stud

or headed bolt in tension,pnh 10412 lb @ Mc4&G,&h H <D"1=

pullout strength in tension of a single hoo#ed bolt ,pL 234:2 lb@ 0(Gf6cehGdb H <D"1:= for

3Gdb?@eGh?@(Gdb

no)inal pullout strength of a single hoo#ed bolt intension

,pnL3340. lb

@ Mc4&G,&L H <D"1=

net bearing area of the head of stud4 anchor bolt4

or headed defor)ed barAbrg 0(:. in

2 @ <31/2

/2=-2"<F/=db

2H Area of heE

head )inus area of bolt shaft

no)inal pullout strength of a group of anchors ,png !1433 lb @ ,pnlGnL>,pnhG<n"nL=

D.5.* Concrete (ide%+ace Blo,out strength of a -eaded Anchor in ension

,ot applicable for large edge distances

Design Requirements for (hear Loading !AC" #1$%&$ D.'

Design (trength

,o)inal 8hear 8trength n 224002 lbs @ ,<sa4cpg=

8trength reduction factor 9 0(. According to D((

Design 8hear 8trength 9n 1.0 #ips

D..1 (teel (trength of Anchor in (hear

nu)ber of colu)ns of bolts nbh 2

nu)ber of ros of bolts nb'


bolt dia)eter db 0(3 in'ertical bolt spacing sb' .(00 in2

hori5ontal bolt spacing sbh (00 in2

anchor steel yield strength -y !4000 psi fro) 7able J3(2

specified tensile strength of anchor steel -u 124000psi

not greater than s)aller of 1(G-y

and 124000

effect( N"sect( Area of single bolt Ase4 0(23 in2

@ <F/=<db"0(.3/nt=2

,o)inal strength in shear sa 224002 lbs @ nGAse4G-u

D..2 Concrete Brea)out (trength of Anchor in (hear

D..# Concrete Pryout (trength of Anchor in (hear

,o)inal pryout strength <group= cpg 3432 lbs @ #pcG,cbg H <D"31=

coefficient for pryout strength #cp 2(00@ 1(0 for hef ? 2(in4 2(0 for

hef K@ 2(in

O-or anchors far fro) the edge4 D((2(usually ill not go'ern( -or these

cases4 D((1 and D((3 often go'ernO



5.2 Base of Mega-Column Connection

5.2.1 Mega-Column to Caisson Connection 190

5.2.2 Caisson Cap Moment Reinforcement 194

Mega-Columns

Shaft Columns

3 Column Node Beam

Caissons

Caisson Cap

Created by: JL 4/28/2012

Color Key User Input

Constant/Previous Calc

Calc/Loo!up

"es Passes C#ec!

$o %ails C#ec!

Loads Coming Down from Mega-Column

Pu &'(8&2 !ips

)u 2'(488 !ips

*u+, 28(040 !ips

*u+y 2-(10- !ips

.u+, '(48 !ips+t

.u+y +2(02 !ip+t

3ll values ro .idas 5en .odel

dc ' in

b+.C ' in

%y+.C &0 !si

6s+.C 2(000 !si

d ' in

t 40 in

t7 40 in

b 420 in

>uilt Up 1)ype o ection used

?eb )#ic!ness

@verall ;ept# o >ea

%lan<e )#ic!ness

.oent+y

.odulus o 6lasticity

;ept# o .e<a+Coluns

%lan<e ?idt#

"ield tren<t# o teel

)#is preads#eet calculates t#e capacities and c#ec!s t#e connection ro t#e botto o t#e .e<a+Colunto Caissons )#e spreads#eet <oes t#rou<# bearin< c#ec!s and local buc!lin< ro bearin<( as 7ell as 7eld

c#ec!s in tension )#is spreads#eet ollo7s t#e <uidelines outlined in 3IC teel Construction .anuel 1't#

ed C#apter 1

5.2.1 Mega-Column to Caisson Connection

Location

Connection

>t o .e<a+Coluns

)yp Connection

Mega-Column Steel Properties

3 Column Node eam Properties

%lan<e ?idt#

Copression

)ension

#ear+, direction

#ear+y+direction

.oent+,

' Colu4n $ode >ea4

:#a0t Colu4n

.e<a+

Colu4n

Load

%y &0 !si

6s 2(000 !si

<



dsc '0 in

t+sc 40 in

t7+sc 40 in

b+sc 200 in

%y+sc &0 !si

6s+sc 2(000 !si

Lsc 40 t

Concrete Copressive tren<t# =c 14 !si

S!ear Capacit" of 3 Column Node eam

PJP

7t '-& in

%6AA 80 !si

L7 -20 in B b 2

37 810 in2 B 7t 7l

3net 4'2 in2

B t7; n;ts D 52+1

?eld #ear eduction %actor Es+7 0-&

>ase .at #ear eduction %actor Es+>. 100

En+7 2(10 !ips B Es+700%e,,37 D )able J2&

En+>. 12(0 !ips B Es+>.00 3net%yD 52+1

)U 10(&28 !ips

=C 14 !si

Fc 14& pc

6c (&'' !si B 7c1&

G=cH0&

D I'+'

%U & !si

ds 0-& in

3sc 044 in2

B db2/4

n 28-2 !ips B inG0&3sc=c6c ( 3sc%uH D I'+'

$eed #ear tuds

)ensile tren<t# o #ear tud

)ype o ection Used >uilt Up 2

3rea or #ear o ' Colun $ode

Concrete Copress tren<t#

;ensity o Concrete

.odulus o 6lasticity o Conc

@verall ;ept# o >ea

%lan<e )#ic!ness

?eb )#ic!ness

%lan<e ?idt#



)ype o ?eld

?eld 6ective )#roat )#ic!ness

#ear tren<t# o ?eld

#ear tr o >ase .aterial

C#ec! .in En *U9

6lectrode tren<t# o ?eld

?eld len<t#

6ective ?eld 3rea

Len<t# o Colun

S!aft Column Properties

eMuired eainin< )ensile tr

tud ;iaeter

3rea o tud

tren<t# o #ear tud

:#a0t Colu4n :ection

&2& B )u/ n

nro7 10

nuber o s#ear studs reMuired

nuber o ro7s o s#ear studs

Eb 0-&

3pb 1(2in

2 B ;

.Cb

+.C

n 11(40 !ips B 183pb%y D J-+1

Ebn 8-(480 !ips B Ebn

E 10

, 144 in B L12 /2! -00 in

$ ' in B b+.C

En 42(00 !ips B G&! $H%yt7E D J10+2

E 0-&, 14400 in B L12 /2

$ '00 in B b+.C

n 1(&' !ips

En 4(240 !ips

E 0-&

3pb -20 in2

B ;.Cb+.C

n 4(800 !ips B 183pb%y D J-+1

En 48(00 !ips B Ebn

E 100

, 100 in

! -00 in

eduction %actor

Location o orce ro ed<e

;ist ro lan<e to 7eb 7eld

#e$ Local %ielding at 3 Column Node &'op( &)*SC +.1,.1(

%actored ;esi<n tren<t#

>earin< Len<t#

eduction %actor

ProNected >earin< 3rea$oinal tren<t#

;esi<n tren<t#

#e$ local %ielding at ottom from S!aft Column &)*SC +.1,.1(

En Pu/GO stieners 1H 9

En Pn/GO stieners 1H 9

"6

"6

#e$ Crippling at 'op from Mega-Columns &)*SC +.1,.3(

eduction %actorLocation o %orce ro 6d<e

>earin< Len<t#

$oinal tren<t#


B E080t72G1'G$/dHGt7/t H

1&H

GG6%yt H/t7H0&

D J10+4

"6

eduction %actor

ProNected >earin< 3rea

$oinal tren<t#

;esi<n tren<t#

En Pu9

C!ec earing Strengt! at ottom from S!aft Column &)*SC +(

eduction %actor

Location o orce ro ed<e;ist ro lan<e to 7eb 7eld

En Pu9 "6

earing Strengt! at 'op of 3 Column Node eam &'op( &)*SC +(

$ 200 in B b+.C

En ''(000 !ips B G&! $H%yt7E D J10+2

>earin< Len<t#


E 0-&

, 20

$ 0 in B b+.C

n 1(&' !ips

En 4(240 !ips

C!ec S!aft Column #elds in 'ension

P 144 in

L7 144 in

7t 2&0 in

%7 -0 !si

37 '0 in2

B L7

E 080

En 12(0 !ips B E00%6AA37 D )able J2&

eMuired )ension %orce )u 11(-44 !ips

*Compare Against half of the tension since there are !o "haft Columns"

C!ecout S!aft Column for Pullout and 'ension /orces

3 2-2 in2

eduction %actor E 0

Pn 1'(00 !ips B %y3 D ;2+1EtPn 12(240 !ips

eMuired )ensile tren<t# )u 11(-44 !ips

*Compare Against half of the tension since there are !o "haft Columns"

Determine t!e 0m$edment Lengt! of Column in S!aft

d ' in B ;sc

%y &0 !si

=c 14 !si

l -1 in B d /G2&G= H0&

H D 3CI '18 C#apter ;

"6

$oinal tren<t# o ?eld

6ective 3rea o ?eld

tren<t# Capacity o ?eld

eduction %actor

"6

#e$ Crippling at ottom from S!aft Column &)*SC +.1,.3(

En Pn/GO stieners 1H 9 "6

3rea o teel #ape

)ensile tren<t#

B E040t72G1'G$/dHGt7/t H

1&H

GG6%yt H/t7H0&

D J10+4

C#ec! En )u

)#roat )#ic!ness

eduction %actor

Location o %orce ro 6d<e

>earin< Len<t#

$oinal tren<t#


;iaeter o Colun

"ield tren<t# o #at Colun

Concrete Copressive tren<t#

6bedent Len<t#

C#ec! EPn )u

%actored )ensile tren<t#

Pereter o Colun

Len<t# o ?eld

ld -1 in B y db/G2& G cH H D 3CI '18 + C#apter ;

ld '4 t

"6I C 6 b d L # @! 9

6bedent Len<t#

6bedent Len<t#

5.2.2 Caisson Cap Moment Reinforcement JL 4/29/2012

User Input


Calc/Lookup

Moment Coming Down from Mega-Column Yes Passes Check

Moent ! " Mu!# $%4&' kips!(t )o *ails Check

Moent ! " Mu!# 41%&$2 kips!in

Moent ! Y Mu!+ 2%902 kips!(t

Moent ! Y Mu!+ $4%&24 kips!in

Caisson Cap Dimensions and Properties

, 1& (t

L 2& (th 22 (t

(-c 14 ksi

c 10 l,/(t$

c 21$%24 ksi %0003(-c0.

( +r '0 ksi

s 29%000 ksi

1&

5,ar 2.2 in

6,ar 4.00 in2

Calculate the Required Number of ars !long the " Direction #$hort ars%

5# 24 in 7 ! '8 ! $8 ! 5,/2

0.9

6sr!re: $.0 in2 3 ;ee e:uation at the en5 o( sheet

4/$36sr!re: 4.0 in2 4/$ 3 6s!re:

i 1%9& in2 <$3<(-c=

0.3L35#=/( +

Bi5th o( Caisson

Len?th o( Caisson7ei?ht o( Caisson

Concrete Copressive ;tren?th

ensit+ o( Concrete

Mo5ulus o( lasticit+ o( Concrete

@e,ar Yiel5 ;tren?th

Mo5ulus o( lasticit+ o( ;teel

Aar ;iDe o( re,ar

iaeter o( re,ar

6rea o( @ein(orcin? ,ar

Create5 A+E

Calculates the re:uire5 rein(orcin? area ,ase5 on the loa5s ?enerate5 (ro Mi5as Fen. Ghe area o(

steel is calculate5 usin? the Bhitne+ ;tress Alock (or concrete an5 is then checke5 a?ainst iniu

steel e:uations (oun5 in C@;I 200& esi?n Fui5e.

Location

Connection

Aotto o( Me?a!Colun

G+p. Connection

epth to centroi5 o( re,ar

@e5uction *actor (or Moent

@e:uire5 6rea o( ;teel

Color e+

;ha(t Colun

Me?a!

Colun

Loa5$ Colun

)o5e Aea

Caisson

Cap

ii 2&4%$$' in2 <2003L35#=/( +

iii 1'0 in2

0.001&3L37

6sr in Calculations

Calculate the Required Number of ars !long the & direction #'ong ars%

5+ 22 in 7 ! '8 ! $8 ! 5, !5,/2

0.9

6sr!re: 2.' 33 ;ee e:uation at en5 o( sheet

4/$36sr!re: $.42 in2

4/$ 3 6s!re:

i 10%1'& in2

<$3<(-c=0.

3,35+=/( +

ii 2&1%&0& in2

<2003,35+=/( +

iii 10$ in2

0.001&3,37

6sr in 10$ in2

Min<I%ii%iii=

n, 2' 6s!in/6s

s+ $.0 in2

<, ! n,35,= / <5, >1=

3 :uation (or 6s!re: (or Moent a,out " a#is <;hort Aars=

33 :uation (or 6s!re: (or Moent a,out the Y a#is < Lon? Aars=

;pacin? H Min< 5, or 18=

epth to centrio5 o( re,ar in Y

@e5uction *actor (or Moent

@e:uire5 6rea o( ;teel

Controllin? 6s!in

@e:uire5 )u,er o( Aars

;pacin?

6sr in Calculations

Y;

=( ∗ ∗

= K ( ∗ ∗

=2 − 4 ∗ ( ∗ fy

2

2 ∗ 0.85 ∗ f c ∗ )

∗

Mu#

2 ∗ ( ∗ fy2

2 ∗ 0.85 ∗ f c ∗ )

=( ∗ ∗

= K ( ∗ ∗

=2 − 4 ∗ (

∗ fy2

2 ∗ 0.85 ∗ f c ∗ ) ∗ Mu+

2 ∗ ( ∗ fy2

2 ∗ 0.85 ∗ f c ∗ )



5.3 Outrigger Connections

5.3.1 Bottom of Outrigger to Column Connection 197

5.3.2 Top of Outrigger to Core 199

Outriggers



5.3.1 Bottom of Outrigger to Column Connection


Location: Typical Column Constant/Previous Calc.

Calc/Lookup

Yes Passes Check

o !ails Check

Outrigger to Column Connection

Design Adequate?

"ertical Loa# at Connection $u %&'' Kips !rom (i#as )en (o#el

Girder Properties

)ir#er section *section +4 , -'

Beam lan0e 1i#th 2 +-.3 in

Beam lan0e thickness t 4.3+ in

Beam 1e2 thickness t1 .'- in

Beam #epth # %%.4 in

Beam k+ K+ %.-& in

Plate Properties

Plate thickness tp .&' in

Plate len0th Lp %.' in

Plate 1i#th 1p %'.' in

plate yiel#in0 stren0th !y &' ksi

PASS

Create# 2y: ;? 4/%+/+%

?esi0n tool or the outri00er truss to the e,terior columns usin0 1el#s. The ra#ial 0ir#er 1ill 2e #esi0ne# usin0

the moment resistin0 0ir#er connection sprea#sheet.

Column

@utri00er

)ir#er

Plates

plate yiel#in0 stren0th !y &' ksi

plate ultimate stren0th !u & ksi

Plate Sear "upture

et area o shear plane nv 3+.'' in% 7 ALp<An8#2+/DD8tp

Plate shear rupture stren0th 6$n %% kips 7 A'.-&8'.8!u8nvD 9 I5C ;4<4

6$n ≥ $u= Y>5

Bloc# Sear "upture

)ross area o shear plane 0v -3.% in% 7 Lp8(IAtpEt1D

et area o tension plane nt +.4 in% 7 A1p<A#2+/DD8(IAtpEt1D

Block shear rupture stren0th Amin 6$nD 6$n &&& kips 7 '.-&A'.8!u8nv!u8ntD 9 I5C ;4<&

6$n 4-3 kips 7 '.-&A'.8!y80v!u8ntD 9 I5C ;4<&

(I 6$n ≥ $u= Y>5

$eld% &illet $eld

>lectro#e classiication num2er !>FF -' ksi

5iGe o 1el# siGe % in

um2er o *el#s Type + %

Throat thickness 1t +.4+4 in 7 '.-'-8siGe

Len0th o the 1el# type + L1 %&.'' in one si#e o plate

*el# + stren0th 6$n+ %%%- kips 7 '.-&8te8L18'.8!>FF 9 I5C ;%<4

um2er o 1el#s type % %

Len0th o the 1el# type % L1 +'.'' in

*el# % stren0th 6$n% 3+ Kips 7 '.-&8te8L18'.8!>FF 9 I5C ;%<4

Total 1el# stren0th 6$n ++ 7 6$n+6$n%

6$n ≥ $u= Y>5



5.3.2

Top of Outrigger to Core

5.3.2.1

Gusset Plate Design Inputs 200

5.3.2.2 Single Bolt Shear Capacity 203

5.3.2.3 Bolt and Plate Checks or !utrigger Connection 20"

5.3.2." Bolt and Plate Checks or Girder Connection 20#

5.3.2.5

$eld Design or Gusset Plate to %&'edded Steel (ra&e 210

5.3.2.) Steel (ra&e %&'edded in Concrete Core Design 211

5.3.2.# %&'edded Steel (ra&e Shear Stud Spacing 21#

$eld

Gusset Plate

!n %ach Side

*adial Girder



!utrigger

5.3.2.1 Gusset Plate Design Inputs

Input dimensions for gusset plate, outrigger member, column member, floor girder, and bolts

Column Section

selected section W33 x 152

specified minimum yield stress Fy 50 ksi

specified minimum tensile strength Fu 5 ksi

!eb thickness t! 0"35 in

flange thicknesstf 0"#55 in

depth d 33"5 in

!idth bf 11" in

distance from !eb center to line of flange toe of

filletk1 1"125 in

Girder Section

selected section W1$ x %30



!eb thickness t! 3"0% in

flange thickness tf $"&1 in

depth d 22"$ in

!idth bf 1%"& in

distance from !eb center to line of flange toe offillet

k1 2"%5 in

re'uired loads (u 22$ kips

load per gusset plate (u)2 112 kips



number of hori*ontal bolt groups ngh 2

min" spacing bet!een hori*ontal bolt groups % in + 2k1-F

selected spacing bet!een hori*ontal bolt groups sg.

# in

spacing check /es

number of ro!s of bolts per group nb. 1

.ertical bolt spacing sb. 0 in

number of columns of bolts nbh 3

hori*ontal bolt spacing sbh 3 in

Edge Spacing on Platehori*ontal edge distance eh 3 in

.ertical edge distance e. 3 in

Edge Spacing on Girder

hori*ontal edge distance eh $ in

.ertical edge distance e. $"&5 in + bf sg.2nb.1sb.)2

Outrigger Section

selected section W1$ x %30



!eb thickness t! 3"0% in

flange thickness tf $"52 in

depth d 22"$ in

!idth bf 1%"& in

distance from !eb center to line of flange toe of

filletk1 2"%5 in

number of hori*ontal bolt groups ng. 2

min" spacing bet!een hori*ontal bolt groups % in + 2k1-F

selected spacing bet!een hori*ontal bolt groups sg. # in

spacing check /es


ti l b lt i




b f l f b lt

Edge Spacing on Plate

hori*ontal edge distance eh in

.ertical edge distance e. in

Edge Spacing on Outrigger

hori*ontal edge distance eh 3 in

.ertical edge distance e. 1"&5 in +bf sg.2nb.1sb.)2

Plate Dimensions

plate thicknesstp 1"5 in

!idth at outrigger out 2 in

!idth at girder gird 1# in


specified minimum tensile strength Fu %0 ksi

Bolt Properties

bolt type

bolt diameter bd %)# in

bolt head si*e F 1 %)1 in

5 roup 6 e"g", 7$&0 o ts, ! en t rea s are exc u efrom shear planes

5.3.2.2 Single Bolt Shear Capacit

8etermine if the bolts slip and fail in shear

a.ailable slip resistance 9(n 1" kips 9:8uhf ;bns

9 1"00

bolt diameter db %)# in

mean slip coefficient : 0"30 for <lass 7 surfaces

pretension multiplier 8u 1"13

factor for fillersh

f 1 for one filler bt!n connected partsmin" fastener tension ;b $& kips ;able =3"1

number of slip planes

re'uired to permit the

connection to slip

ns 1

a.ailable shear strength 9(n 3%"& kips 9>n7b =31

reduction factor 9 0"%5

nominal shear stress >n #$ ksi

nominal unthreaded body

area of bolt 7b 0"01 in2

?da2)$

shear strength greater than slip resistance@ /es

5.3.2.3 Bolt and Plate Chec!s "or Outrigger Connection

Strength Chec!

re'uired strength 4u 1,0&5 kips

design strength 9(n 1,212 kips

does it pass@ /es

Bolt Chec!

min" A of bolts nmin 2& bolts min A for bolt shear

actual number of bolts nb 32 bolts

does it pass@ /es

Plate Properties

plate thickness tp 1"5 in

!idth at outrigger out 2 in



hori*ontal edge distance eh in

.ertical edge distance e. in

Bolt Group Properties

bolt diameter db %)# in

number of hori*ontal bolt groups ngh 2

selected spacing bet!een hori*ontal bolt gr sg. # in



number of columns of bolts nbh #

hori*ontal bolt spacing sbh $ in

Outrigger Properties

specified minimum yield stress F 50 ksi

<hecking failure modes for bolts and plate at the connection bet!een gusset plate and outrigger

connection




Gross #rea o" Plate

gross area 7g 3&"0 in2

+ min 7!, 7gp

Whitmore Bection !idth l ! $"3 in

Whitmore area 7! &"5 in2

+ l !tp

gross area from plate dimensions 7gp 3&"0 in + outtp

Bolt Shear Strength

design strength 9(n 1,212 kips + 9Fn.7bnb =31

$ensile %ielding o" Gusset Platedesign strength 9(n 1,2$ kips + 9Fy7g =$1

9 0"&0


gross area 7g 3&"0 in

$ensile &upture o" Gusset Plate

design strength 9(n 1,%52 kips + 9Fu7e =$2

9 0"%5


effecti.e net area 7e 33"$ in2

7nC 831

shear lag factor C 1"0 ;able 83"1

net area 7n 33"$ in

Bloc! Shear &upture o" Gusset Plate

a.ailable strength 9(n 1,&2 kips 9CbsFu7nt-90"0minFu7n.,Fy7g.D=$5

9 0"%5

reduction coefficient Cbs 1"0

gross area subEect to shear 7g. 51"0 in2

+ e.-nbh1sbhGtp

net area subEect to shear 7n. 3&"# in2

+ eh-nbh1sbhnbh0"5da-"125Gtp

net area subEect to tension 7nt 1"5 in2

+ 2e.0"5da-0"125Gtp

Bloc! Shear &upture o" 'lange

a.ailable strength 9(n 3,0 kips 9CbsFu7nt-90"0minFu7n.,Fy7g.D =$5

9 0"%5




Bolt Bearing on Gusset Plate

a.ailable bearing strength 9(n 3,1# kips + 9tpFuHIJ 1"51l c,nb3"0da D =3b

9 0"%5

clear distance, in dir" of force, bet!een

edge of hole and edge of materiall c edge 5"5 in


edge of hole and edge adEacent holel c int 3"1 in

J 1"51l c $0"5 in

nb3"0da #$"0 in

Bolt Bearing on 'lange

a.ailable bearing strength 9(n 1,%&# kips + 9tf FuHIJ 1"51l c,nb3"0da D =3b

9 0"%5


edge of hole and edge of materiall c edge 2"5 in


edge of hole and edge adEacent holel c int 3"1 in

J 1"51l c #"2 in

nb3"0da #$"0 in

5.3.2.( Bolt and Plate Chec!s "or Girder Connection

Strength Chec!

re'uired strength (u 112 kips

design strength 9(n 22% kips

does it pass@ /es

Bolt Chec!

min" A of bolts nmin 3 bolts min A for bolt shear

actual number of bolts nb bolts

does it pass@ /es

Plate Properies )"rom Inputs*

plate thickness tp 1"5 in

!idth at girder gird 1# in



hori*ontal edge distance eh 3 in

.ertical edge distance e. 3 in

Bolt Group Properties

bolt diameter da %)# innumber of hori*ontal bolt groups ngh 2

selected spacing bet!een hori*ontal bolt

groups sg. # in



number of columns of bolts nbh 3

hori*ontal bolt spacing sbh 3 in

Girder Properties


specified minimum tensile strength F 5 ksi

<hecking failure modes for bolts and plate at the connection bet!een gusset plate and outrigger




Gross #rea o" Plate

gross area 7g 22"$ in2

+ HI7!, 7gp

Whitmore Bection !idth l ! 1$"& in

Whitmore area 7! 22"$ in2

+ l !tp

gross area from plate dimensions 7gp 2%"0 in + outtp

Bolt Shear Strength

design strength 9(n 22% kips + 9Fn.7bnb =31

$ensile %ielding o" Gusset Platedesign strength 9(n %2 kips + 9Fy7g =$1

9 0"&0


gross area 7g 22"$ in

$ensile &upture o" Gusset Plate

design strength 9(n 12%0 kips + 9Fu7e =$29 0"%5


effecti.e net area 7e 2$"2 in2

+ 7nC 831

shear lag factor C 1"0 ;able 83"1

net area 7n 2$"2 in

Bloc! Shear &upture o" Gusset Plate

a.ailable strength 9(n $$ kips + 9CbsFu7nt-90"0minFu7n.,Fy7g. D =$5

9 0"%5


gross area subEect to shear 7g. 1"5 in2

+ e.-nbh1sbhGtp

net area subEect to shear 7n. 1$"3 in2

+ eh-nbh1sbhnbh0"5da-"125Gtp

net area subEect to tension 7nt 3"# in2

+ 2e.0"5da-0"125Gtp

Bloc! Shear &upture o" 'lange

a.ailable strength 9(n 50 kips + 9CbsFu7nt-90"0minFu7n.,Fy7g. D =$5

9 0"%5

reduction coefficient C 1 0




Bolt Bearing on Gusset Plate

a.ailable bearing strength 9(n %# kips + 9tpFuHIJ 1"51l c,nb3"0da D =3b

9 0"%5

clear distance, in dir" of force, bet!een edge of

hole and edge of materiall c edge 2"5 in


hole and edge adEacent holel c int 2"1 in

J 1"51l c 10"0 in

nb3"0da 15"# in

Bolt Bearing on 'langea.ailable bearing strength 9(n 3%%0 kips + 9tf FuHIJ 1"51l c,nb3"0da D =3b

9 0"%5


hole and edge of materiall c edge $"5 in


hole and edge adEacent holel c int 2"1 in

J 1"51l c

1#"& in

nb3"0da 15"# in

5.3.2.5 +eld Design "or Gusset Plate to Em,edded Steel 'rame

8esign of !eld of gusset plates to embedded steel frame

+eld Speci"ications

Weld Bi*e 8 0"%5 inWeld Bi*e in sixteenths of inch 8 12 1)1 in +! 1

Klectrode K%0

Btrength of Weld FKLL %0 ksi ;able #3

Klectrode <oeffiencient <1 1 ;able #3

-ector #ddition o" oads

Mutrigger Force L <omponent Fx 1,02 kipsMutrigger Force / <omponent Fy 1,$&$ kips

Bhear Force > 22$ kips

et oad L <omponent Fx 1,02 kips

et oad / <omponent >-Fy 1,%1# kips

(esultant oad (u 2,3$# kips + Fx2 - >-Fy

2"5

7ngle of oad %% degrees !ith respect to .ertical

/et oad Design

Mutrigger 7ngle $3 degrees !ith respect to hori*ontal plane

ength of Weld ! &"3 in

8istance 6et!een Welds k! 25"$ in

> l f < ; bl k 0 3% k )

>alue for < ;ables k 0 3% +k )

5.3.2.0 Steel 'rame Em,edded in Concrete Core Design

;ensile oad 21&0 kips applied axially from points !here outrigger connects to frame

'inal Sies

6eams W1$ x 5

<olumns W33 x 152

Ficticious 6races W2$ x 103 act in compression only

ocal <oordinates

(esulting steel si*es from model of steel frame embedded inside concrete core to take load

from outriggers

• #ll mem,ers ere assumed to ,e "ull ,raced, simulating the frameOs embedment in

concrete"

•

7ll beams and columns are connected by moment connections.

•

7ll beams and columns are made of #2 Steel.

• ;he top and bottom nodes of the frame are assumed to be fixed in all directions and

rotations"



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MQ 0"3## 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ $ 2 13 0 1 0"5 %52 $%"5$ 35"#

MQ 0"513 0"012 0 0 1 0"5 2,01 2,0& 25"5

MQ % 2 13 0 1 0"5 & 3"10 #"5%MQ 0"3#1 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ # 2 13 0 1 0"5 #21 2"2 32"01

MQ 0"53& 0"01 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ & 2 13 0 1 0"5 %$$ &"& 3$"11

MQ 0"$## 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ 12 2 13 0 1 0"5 %# 2"1 #"5

MQ 0"3# 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 13 2 13 0 1 0"5 #2$ 5"32 3$"3&MQ 0"55 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 1$ 2 13 0 1 0"5 %51 #"53 3"15

MQ 0"$&% 0"012 0 0 1 0"5 2,01 2,0& 25"5

MQ 1% 2 13 0 1 0"5 #0 2"03 #"3

MQ 0"3# 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 1& 2 13 0 1 0"5 %52 1"0% 35"%

MQ 0"$&3 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ 22 2 13 0 1 0"5 %% 0"55 #"5%MQ 0"3#5 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 23 2 13 0 1 0"5 #2$ 0"20 3$"0

MQ 0"5$% 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 2$ 2 13 0 1 0"5 %50 0"#2 3$"&$

MQ 0"$& 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ 2% 2 13 0 1 0"5 % 0"$3 #"%1

MQ 0"3#$ 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 2# 2 13 0 1 0"5 #2$ 0"%% 33"&MQ 0"5$% 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 2& 2 13 0 1 0"5 %50 0"#& 3$"&0

MQ 0"$#& 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ 32 2 13 0 1 0"5 % 0"&0 #"#

MQ 0"3#5 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 33 2 13 0 1 0 5 #2$ 1 2# 3$ 0%



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MQ 0"$& 0"011 0 0 1 0"5 2,01 2,0& 25"5MQ 52 2 13 0 1 0"5 %% 1"55 #"2

MQ 0"3#5 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 53 2 13 0 1 0"5 #2$ 2"2# 3$"12

MQ 0"5$# 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 5$ 2 13 0 1 0"5 %50 2"32 35"22

MQ 0"$&1 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ 5% 2 13 0 1 0"5 %% 1"55 #"$

MQ 0"3#5 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5MQ 5# 2 13 0 1 0"5 #2$ 1"% 3$"1

MQ 0"5$# 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 5& 2 13 0 1 0"5 %50 1"23 35"20

MQ 0"$&1 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ 2 2 13 0 1 0"5 %% 1"15 #"0

MQ 0"3#5 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 3 2 13 0 1 0"5 #2$ 2"0$ 33"&#

MQ 0"5$% 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5MQ $ 2 13 0 1 0"5 %50 3"$2 3$"$0

MQ 0"$#& 0"011 0 0 1 0"5 2,01 2,0& 25"5

MQ % 2 13 0 1 0"5 #1 1"# #"%3

MQ 0"3#% 0"002 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ # 2 13 0 1 0"5 #2 "05 35"2

MQ 0 55 0 011 0 0 1 0 5 1 &0$ 2 0& 25 5



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MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ &3 1 1"$5% 0 1 0"5 1#2 $5"5 0"32

MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ &$ 1 1"$5% 0 1 0"5 1#2 $5"# 1"1&

MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ &5 1 1"$5% 0 1 0"5 1#3 $5"20 0"5&MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ & 1 1"5#3$ 0 1 0"5 1#3 $&"5% $"55

MQ 0"021 0 0 0 1 0"5 #,#20 5,550 255

MQ &% 1 1"$5% 0 1 0"5 1#0 $$" $"30

MQ 0"02 0 0 0 1 0"5 #,#20 5,550 255

MQ &# 1 1"$5% 0 1 0"5 1#2 $%"$5 2"1$

MQ 0"02 0 0 0 1 0"5 #,#20 5,550 255

MQ && 1 1"$5% 0 1 0"5 1#2 $%"01 1"25MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ 100 1 1"$5% 0 1 0"5 1#2 $$"%5 0"%

MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ 101 1 1"$5% 0 1 0"5 1#2 $3"&3 0"%

MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ 102 1 1"$5% 0 1 0"5 1#2 $$"## 0"33

MQ 0"01& 0 0 0 1 0"5 #,#20 5,550 255

MQ 103 1 1"$5% 0 1 0"5 1#2 $5"1# 0"0MQ 0"01# 0 0 0 1 0"5 #,#20 5,550 255

MQ 10$ 1 1"$5% 0 1 0"5 3,2&5 2"32 0"&3

MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 105 1 1"$5% 0 1 0"5 3,2&5 2"2% 1"11

MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 10 1 1"$5% 0 1 0"5 3,2&5 2"12 1"11

MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 10% 1 1"$5% 0 1 0"5 3,2&5 2"1& 1"1$MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 10# 1 1"$5% 0 1 0"5 3,2&$ 2"$3 1"31

MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 10& 1 1"$5% 0 1 0"5 3,2&3 3"2 10"3$

MQ 0"3%% 0 0 0 1 0"5 #,#20 5,550 255

MQ 110 1 1 51%2 0 1 0 5 3 2&1 % 33 5% 3%



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MQ 11$ 1 1"$5% 0 1 0"5 3,2# 5"31 #"%%

MQ 0"3% 0 0 0 1 0"5 #,#20 5,550 255

MQ 11 1 1"$5% 0 1 0"5 3,2&5 3"1# 0"#

MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 11% 1 1"$5% 0 1 0"5 3,2&5 2"$% 1"31

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MQ 11& 1 1"$5% 0 1 0"5 3,2&5 2"35 1"2$

MQ 0"3%$ 0 0 0 1 0"5 #,#20 5,550 255

MQ 12% 1 0"02$ 0 1 0"5 0 0"00 0"00

MQ 0 0 0 0 1 0"5 #,#20 $,2&# 1%%1"&5

MQ 12& 1 0"02$ 0 1 0"5 1 3"%$ 0"22

MQ 0"001 0"001 0 0 1 0"5 #,330 5,550 255MQ 130 2 13 0 1 0"5 #23 $3"3 33"&

MQ 0"55 0"011 0 0 1 0"5 1,&0$ 2,0& 25"5

MQ 131 2 13 13 1 1 %51 1"30 10"%$

MQ 0"$0& 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 132 2 13 13 1 1 %$ 2"&& 11"$%

MQ 0"$1 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 133 2 13 13 1 1 %51 2"5& 10"##

MQ 0"$1 0"003 13 13 1 1 2,01 1,&1 25"5MQ 13$ 2 13 13 1 1 %51 2"% 10"30

MQ 0"$0& 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 135 2 13 13 1 1 %50 0"3 10"$0

MQ 0"$0% 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 13 2 13 13 1 1 %50 0"02 10"5

MQ 0"$0# 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 13% 2 13 13 1 1 %50 0"%0 10"&

MQ 0"$0# 0"003 13 13 1 1 2,01 1,&1 25"5MQ 13# 2 13 13 1 1 %50 1"2# 10"2

MQ 0"$0# 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 13& 2 13 13 1 1 %50 1"$2 10"0

MQ 0"$0# 0"003 13 13 1 1 2,01 1,&1 25"5

MQ 1$0 2 13 13 1 1 %50 1"51 10"1

MQ 0 $0# 0 003 13 13 1 1 2 01 1 &1 25 5



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MQ 1$5 1 1"$5% 1"$5% 1 1 1$ $$"#% 0"0&

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MQ 1$ 1 1"$5% 1"$5% 1 1 1$ $$"&2 0"00

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MQ 1$% 1 1"$5% 1"$5% 1 1 1$ $5"$3 0"02MQ 0"00& 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 1$# 1 1"$5% 1"$5% 1 1 1$ $5"1$ 0"5&

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MQ 1$& 1 1"$5% 1"$5% 1 1 1$ $$"5 0"3

MQ 0"00& 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 150 1 1"$5% 1"$5% 1 1 1$ $5"#2 2"3&

MQ 0"01 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 151 1 1"51%2 1"51%2 1 1 12 $3"& 2"$0MQ 0"00& 0 0 1"51%2 1 1 #,#20 5,550 255

MQ 152 1 0"02$ 0"02$ 1 1 0 0"00 0"00

MQ 0 0 0 0"02$ 1 1 #,#20 $,2&# 1%%1"&5

MQ 153 1 1"51%2 1"51%2 1 1 1 50"5$ 1"00

MQ 0"01 0 0 1"51%2 1 1 #,#20 5,550 255

MQ 15$ 1 0"02$ 0"02$ 1 1 1 3"%$ 0"22

MQ 0"001 0"001 0 0"02$ 1 1 #,330 5,550 255

MQ 155 1 1"$5% 1"$5% 1 1 1$ $&"#$ 0"#2MQ 0"01 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 15 1 1"$5% 1"$5% 1 1 1$ $"%% 1"%0

MQ 0"01 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 15% 1 1"$5% 1"$5% 1 1 1$ $3"$& 1"%0

MQ 0"00& 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 15# 1 1"$5% 1"$5% 1 1 1$ $3"$0 0"3

MQ 0"00& 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 15& 1 1"$5% 1"$5% 1 1 1$ $$"$1 0"0$MQ 0"00& 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 10 1 1"$5% 1"$5% 1 1 1$ $$"5$ 0"11

MQ 0"00& 0 0 1"$5% 1 1 #,#20 5,550 255

MQ 11 1 0"02$ 0"02$ 1 1 0 0"00 0"00

MQ 0 0 0 0"02$ 1 1 #,#20 $,2&# 1%%1"&5

MQ 12 1 0 02$ 0 02$ 1 1 0 0 00 0 00

5.3.2.9 Em,edded Steel 'rame Shear Stud Spacing

Beam Shear Studs

Belected Bection W1$ x 5

<oncrete <ompressi.e Btrength fRc 1$"0 ksi

8iameter of Bhear Btud d 0"50 in

7rea of Bhear Btud <onnector 7sc 0"20 in2

+ ?d2)$

Weight of <oncrete per Cnit >olume Sc 10 lbs)ft3

Hodulus of Klasticity of <oncrete Kc %,5%3 ksi +Sc1"5

fRc0"5

Hinimum ;ensile Btrength of a Bhear Btud ;u 5 ksi

<oefficient (g 1"00

<oefficient (p 1"00

Shear Stud Speci"ications

Bhear Btrength of Bhear Btud T n1 32"0 kips + 0"5 7scKc fRc0"5

Bhear Btrength of Bhear Btud T n2 12"# kips +7sc (g(p ;u

<ontrolling Bhear Btrength of Bhear Btud T n 12"# kips + HIT 1, T 2

Flange Width bf 1%"% in

umber of (o!s of Bhear Btuds r $ ro!s

Bhear Force > 3,3$ kips 7xial oad in Hember

umber of Bhear Btuds 4er (o! n +>)T nr

Hember ength 1"5 ft

Bpacing s 3"00 in +)

Hinimum Bpacing smin 3"00 in 7IB< I3"2"

Haximum Bpacing smax 3"0 in 7IB< I3"2"

Selected Shear Stud Spacings

ongitudinal Bpacing slong 3"0 in

Bpacing <heck s min U slong U smax @ /es

;rans.erse Bpacing strans 3"0 in

Bpacing <heck s min U strans U smax @ /es

8esign of shear studs for the columns and beams in the embedded steel frame to transfer loads to

concrete

Column Shear Studs

Belected Bection W33 x 152

<oncrete <ompressi.e Btrength fRc 1$"0 ksi

8iameter of Bhear Btud d 0"3# in

7rea of Bhear Btud <onnector 7sc 0"11 in2

+?d2)$

Weight of <oncrete per Cnit >olume !c 10 lbs)ft3

Hodulus of Klasticity of <oncrete Kc %,5%3 ksi +!c1"5

fRc0"5

Hinimum ;ensile Btrength of a Bhear Btud ;u 5 ksi

<oefficient (g 1"00

<oefficient (p 1"00


Bhear Btrength of Bhear Btud T n1 1%"&# kips + 0"5 7scKc fRc0"5

Bhear Btrength of Bhear Btud T n2 %"1# kips +7sc (g(p ;u

<ontrolling Bhear Btrength of Bhear Btud T n %"1# kips + HIT 1, T 2

Flange Width bf 11"0 inumber of (o!s of Bhear Btuds r 3 ro!s

Bhear Force > %%$ kips 7xial oad in Hember

umber of Bhear Btuds n 3 +>)T nr

Hember ength 13"0 ft

Bpacing s $"33 in +)

Hinimum Bpacing smin 2"25 in 7IB< I3"2"

Haximum Bpacing smax 3"0 in 7IB< I3"2"


ongitudinal Bpacing slong $"00 in

Bpacing <heck s min U slong U smax @ /es

;rans.erse Bpacing strans 2"25 in

Bpacing <heck s min U strans U smax @ /es



6.0 Foundation Design

6.1

Retaining Wall 2206.1.1

Soil Profile at Site 221

6.1.2

Effective Soil Pressure Calculations 222

6.1.3

Retaining Wall Design 22

6.1.

Retaining Wall !astan "nal#sis 22$

6.2 Par%ing &arage 230

6.2.1 '(o)Wa# Sla* +sing WWR 231

6.2.2

Par%ing &arage Colu,ns

6.2.2.1

Parking Garage Column with Rebar 247

6.2.2.2

Parking Garage Column with W-Shape 248

6.2.3

-elled Caisson Design 2

6.3 'o(er Foundation 250

6.3.1

"*a/us "nal#sis of Caissons 251

6.3.2 !ega)Colu,n Caisson Design 253

6.3.3 Ring -ea, Design 255

6.3.

Core Caisson Design 25

6.3.5

Caisson Re*ar 25



6.1 Retaining Wall

6.1.1 Soil Profile at Site 221

6.1.2 Effective Soil Pressure Calculations 222

6.1.3 Retaining Wall Design 224

6.1.4 Retaining Wall astan Anal!sis 22"



6 .

1 .

1 S o

i l P r o f i l e a

t S i t e

C r e a t e d B y : N T 5 / 1 1 / 2 0 1 2

T h e j o b s i t e i s l o c a t e d n e x t t o L a k e M i c h i g a n a n d t h e C h i c a g o i ! e r s o t h

e " a t e r t a b l e i s ! e r y h i g h # T h e

s o i l c o n s i s t s o $ a ! a r i t e y o $ s a n d s a n d c l a y s

t h a t " e r e

c a l l e d o % t i n t h e g e o t e c h n i c a l r e & o r t #

6 . 1 . 1

S

o i l P r o f i l e a t S i t e

C-221

6.1.2 Effective Soil Pressure Calculation

Calculating effective pressure and horizontal force to be used in retaining wall design.

ser Input

Density (ρ) (pcf) Effective ressure (psf)! "orizontal #orce (plf$ft run)!!

% % %

&' &*& +*'*

,% &*-& &-

,% &*+' &*

,% &*/* &/-%

,% &-%/ &/,% &-*+ +%&-

,% +%+* &*%+

,% +%' &-

/+. pcf Density of sand &' pcf

Density of clay ,% pcf

%.,%

Fourmulas

orewater pressure () 0 /+.!" "1 height in ft

/

,+

Density of 2ater

Created by 8=: $+,$+%&+

r #ir<$7tiff Clay Earth ressure Coefficient > a

Note: ?round water table is at ft depth as stated in the geotechnical report

!! "orizontal force 0 Effective ressure!>a @ ore ressure

! Effective ressure 0 (D !ρ) @ Effective pressure fro< layers above 1

Depth (d) (ft)

%

+

'

%

,&



7and

Clay

%

&%

+%

'%

.%

(%

/%

,%

*%

% (%% &%%% &(%% +%%% +(%%

D e p t h b e l o !

r o u

n " # f t $

Effective pressure #psf$

6.1.3 Retaining Wall Design Created By: NT 5/11/2012

User Input


Calc/Looup

!es Passes C"ec

No #ails C"ec

$a%i&u& Unsupported 'ei("t L 2) *t Cantilever at top o* +all, 2 -tories 2 -las

$ini&u& all T"icness ts,&in 2 in L/10 3CI )1 Tale 4.5 a6

3ctual all T"icness ts, act )0 in

3t -pansBar -i7e 8 19

3rea o* Bar 3ar 2.25 in2

L

ia&eter o* ar dar 1.;4 in

!ield -tren(t" o* Bars #y ;0 si

Bar -pacin( sspan ; in

Bar -i7e 8 19

3rea o* Bar 3ar 2.25 in2

ia&eter o* ar dar 1.;4 in

!ield -tren(t" o* Bars #y ;0 si

Bar -pacin( ssuport 1; in

$ini&u& steel ratio <( 0.001 per 3CI )1

3rea o* -teel =e>uired 3s 14 in2

<(?L?ts, act

Bar -i7e 8 ;

* 3 i2

esi(n tool *or a retainin( +all to resist soil pressures around t"e

e%terior o* t"e roundation. all "as een desi(ned as a si&ply

supported concrete sla, raced y t"e parin( (ara(e levels. T"e

top t+o storys are &odeled as a cantilever due to uncertainty in

soil conditions.

- u p p o r t s

Dimensions of Wall

Horizontal Shrinkage steel

3t -upports

esi(nin( *or 12 in vertical strip o* +all

Vertical Steel Bar Properties

Area of steel As 4.50 in2

=Abar*12/Sspan

Minimum Steel Required Asmin 0.65 in2

=!*b*" A#$ %1& 0&' (.12.2.1

)

+ension + 2(0 ,ips =As*f -

#ompression # 2(0 ,ips =+

#onrete Stren!t" f 4000 psi

eta 1 1 0.(5

#onrete #o3er 2 in A#$ ' %1&'0& ' (.(.1

Strutural ept" d 2( in = "''dbar

ei!"t of ompression fae a ( in =#/0.&5*f*b7

Moment Arm d'a/27 24 in

8ominal Moment Mn 5%( ,ip'ft =+*d'a/27

Strain in Steel 9s 0.006 :sin! Similar +rian!les

)

Stren!t" Redution ;ator < 0.0 ) o, >"en ?s @ 0.005

4&% ,ip'ft

Maimum Moment on Ball Mm %05 ,ip'ft ;rom MAS+A8

;ator of Safet- for )3erturnin! ;S 1.5

45& ,ip'ft Criniples of ;oundation Dn!ineerin!. -' raEa M. as

)

;S * Mm

< *

Check for Moments At Center of Spans

As F As ma G

As @ As min G

<*Mn @ ;S*Mm G

Area of steel As 1.6 in2 per 12 in >idt"

Minimum Steel Required Asmin 0.65 in2 = !*b*" A#$ %1& 0&' (.12.2.1

)

+ension + 101 ips =As*f -

#ompression # 101 ips =+

#onrete #o3er 2 in

#onrete Stren!t" f 4000 psi

eta 1 1 0.(5

Strutural ept" d 26 in = "''dbar

ei!"t of ompression fae a 2.4& in =#/0.&5*f*b7

Moment Arm d ' a/27 25 in

8ominal Moment Mn 210 ft',ips =+*d'a/27

Strain in Steel Hs 0.021 Similar +rian!les

)

Stren!t" Redution ;ator < 0.0 )

1& ft',ips

Maimum Moment on Ball Mm & ft',ips ;rom MAS+A8

;ator of Safet- for )3erturnin! ;S 1.5

14( ft',ips Criniples of ;oundation Dn!ineerin!. -' raEa M. as

)

Reference ' raEa M. as Criniples of ;oundation Dn!ineerin! Montere- #alif 1&4 p! 1

<*Mn @ ;S*Mm G

;S * Mm

<*Mn

As @ As min G

Hs @ 0.005G

Check for Moments At Supports

Total Retaining Height Ht 84 ft 7 Stories + 8 Slabs

Angle of friction for soil Ω 0.52 radians

Densit !f "la #cla 70 $sf %eotechnical Re$ort

Angle of &ac'fill Abo(e The )all * 0.7 radians

Ran'ine,s "oefficient -or assi(e /arth ressre '$ 0. 1tan45+ 322

Ran'ine,s assi(e /arth ressre $ 25.6 'i$s 10.5#claH2'$

Densit of Reinforced concrete #c 45 $sf

-actored Horiontal Sliding -orce 6 'i$s

9ertical -orce: Self )eight of )all 9 60.5 'i$s $er foot

"alclated -actor of Safet -or Sliding -S 2.2 19 tan2Ω6+$ cos*

!;

)orse "ase -ro< /ffecti(e ressre "alclation: Horiontal -orceHeight

NOTE - "hec'ing for rnning length of feet

Reference = &ra>a ?. Das: rinci$les of -ondation /ngineering: ?ontere: "alif: @84: $g @@

ndrained Shear Strength of 9er Stiff "la S 5 'sf %eotechnical Re$ort

Densit !f "la #cla 70 $sf %eotechnical Re$ort

9ertical Stress in Soil Ad>acent To The )all B C 'sf 1 #claheight

lti<ate &earing "a$acit of "la &" 2 'sf 1B+S

9ertical ressre De To )all 9& 2 'sf 1#co<creteHthh

!;

NOTE - "hec'ing for rnning length of feet

Reference -".R. "laton: E. ?ilitits' and )oods: /arth ressre and /arth=Retaining Strctres: 2nd /d.: "onference

blication FeG or' I A<erican Societ of "i(il /ngineers: @@6: : $g 54

Calculating Factor of Safety For Sliding

Bearing Capacity Check

Designing $er ft.

-S J .5 K

&" J 9& K



6.1.4 Retaining Wall Mastan Analysis

A 2-D Mastan model was created to obtain the induced moments and deflected shape of the parkinggarage retaining wall. Loads on the structure were obtained from the Effective Soil ressure !alculation.

"he# were modeled as resultant point loads of the distributed loads contributed b# each of the different

soil la#ers $sand% cla#% hard pan& from the Soil rofile along the height of the retaining wall. arking

floors provided supports and were modeled as fi'ities resisting the earth pressures. "he bottom of the

wall% on ver# hard cla#% was modeled as fi'ed and the top of the wall acted as a cantilever with a

ma'imum deflection of (.(()*+ in. ,igures of the Mastan output are included below. See also the

etaining all Design spreadsheet.

Retaining Wall Mastan Moment



Retaining Wall Mastan Deformed Shape



6.2

Par#ing $arage

6.2.1

%&o'Wa! Sla( )sing WWR 2316.2.2

Par#ing $arage Colu*ns

6.2.2.1 Parking Garage Column with Rebar 247

6.2.2.2

Parking Garage Column with W-Shape 248

6.2.3

+elled Caisson Design 24,

6.2.1 Two-Way Slab Using WWR Created by: MZ 5/10/2012

Nominal WWR Size Area [in2] Diameter [in]

D11 011 0!"5

D20 020 0500

D!1 0!1 0#25

D$$ 0$$ 0"50

D#0 0#0 0%"5

D"& 0"& 1000

Level 1 Underground

NS Direction !" #t S$an%

Ne'ati(e )o*iti(e Ne'ati(e )o*iti(e

+otal ,a-tored Moment M. [it] %2# $#! 2"5 1$!Widt3 o Stri [t] 1$! 1$! 1$! 1$!

WWR Area er 4inear ,oot A* [in2] 0%% 0%% 0!! 0!!

WWR Sele-ted D$$ D$$ D$$ D$$

ar Sa-in' or WWR me*3 * [in] #0 #0 1#0 1#0

ar* Needed or WWR me*3 2& 2& 11 11

&W Direction 2'.( #t S$an%Ne'ati(e )o*iti(e Ne'ati(e )o*iti(e

+otal ,a-tored Moment M. [it] "1# !%! 21# 115

Widt3 o Stri [t] 1$! 1$! 15% 15%

WWR Area er 4inear ,oot A* [in2] 0%% 0%% 0!! 0!!

6 %

WWR Re#erence Table

ar Size

6 !

6 $

Col.mn Stri Middle Stri


6 5

6 #

6 "

Notes)

7 WWR 8Welded Wire Reinor-ement9 i* .*ed in*tead o traditional rebar* or arin' 'ara'e de*i'n7 n t3e ollo;in' WWR Reenren-e +able< =D= denoted a deormed ;ire +3e n.mber ollo;in' =D= 'i(e*

a -ro***e-tional area in 3.ndredt3* o a *>.are in-3 8AC !1% Aendi? @9

7 ar Size -ol.mn indi-ate* *ize o bar* .*ed to orm WWR *teel me*3



Level 2-* Underground

NS Direction !" #t S$an%


+otal ,a-tored Moment M. [it] !0! 1#5 101 55Widt3 o Stri [t] 1$! 1$! 1$! 1$!

WWR Area er 4inear ,oot A* [in2] 0!1 0!1 0!1 02!

WWR Sele-ted D!1 D!1 D!1 D!1

ar Sa-in' or WWR me*3 * [in] 12 12 12 1#

ar* Needed or WWR me*3 15 15 15 11

&W Direction 2'.( #t S$an%


+otal ,a-tored Moment M. [it] 2%0 1$5 %$ $$

Widt3 o Stri [t] 1$! 1$! 15% 15%

WWR Area er 4inear ,oot A* [in2] 0!1 0!1 0!1 02!

WWR Sele-ted D!1 D!1 D!1 D!1

ar Sa-in' or WWR me*3 * [in] 12 12 12 1#

ar* Needed or WWR me*3 15 15 1# 12



Parking Garage Reinforced Slab Design

Material Properties

Concrete Density ρc 110 pcf

Concrete Strength f'c 4,000 psi

Concrete Modulus Ec 2,410 ksi

WW !ield Strength "y #0 ksi

WW El$stic Modulus Es 2%,000 ksi

Load Cases Summary

Parking Floor

Sl$& Self Weight slf 110 psf ( ρc)h

Superi*posed De$d +o$d SD+ 42 psf

+ie +o$d ++ 40 psf

-ot$l "$ctored +o$d u 24. psf (1/2SWSD31/.++, SCE5610 2/7/2

Parking Roof

Sl$& Self Weight slf 110 psf

Superi*posed De$d +o$d SD 251 psf

+ie +o$d ++ 100 psf

Sno +o$d S+ 20 psf -ot$l "$ctored +o$d u .25 psf (1/2SWSD31/.++0/8S+, SCE5610 2/7/2

Design tool for WW Welded Wire einforce*ent3 of g$r$ge sl$&

(ρc1/8

)77)f'c192

: C 71#60# #/8, #/.

Notes:

; Sl$& for p$rking g$r$ge is designed using e<ui$lent fr$*e *ethod

; =ick positie $nd neg$tie *o*ent $t critic$l sections respectiely in e$ch direction to design

; ll the sl$& p$nels $re split into colu*n strips $nd *iddle strips/ "or e$ch $y>s design ?S $nd EW3, critic$l

*o*ents $re proportion$lly distri&uted to colu*n $nd *iddle strips

; Sl$& is designed ith drop p$nels $nd ithout interior &e$*s or edge &e$*s

asic Dimensions

@rid Sp$n, ?S Direction +?S 70/0 ft

@rid Sp$n, EW Direction +EW 2#/8 ft

Cle$r Sp$n, hicheer s*$ller +n 2./1 ft

Colu*n Strip Width &col 14/7 ft 9 e$ch side 0/28*in+?S, +EW3 C 71#60#

Middle Strip Width, ?S Direction &*,?S 14/7 ft 17/2/1

Middle Strip Width, EW Direction &*,EW 18/# ft

Column

Colu*n Di$*eter dcol 72/0 in

Di$*eter of E<ui/ Section de< 2#/4 in (0/#%)dcol, C 71#60# 17/./2/8

Slab

Sl$& -hickness h 12/0 in

Mini*u* Sl$& -hickness h*in 10/8 in (+n970, C -$&le %/8 c3

hAh*inB !esConcrete Coer on -op $nd t* c 2/0 in

Di$gr$* shoing &re$kdon of sl$& strips

Colu*n Strip

Colu*n @rid

Drop Panel

Drop =$nel -hickness hdr 5/0 in

Mini*u* -hickness hdr,*in 7/0 in (0/28h, C 71#60# 17/2/8 $3

M$i*u* co*puting thickness 11/8 in (0/28det6de<923 C 71#60# 17/7/5

hdrAhdr,*inB !es

+ength of S<u$re Drop =$nel +dr 10/0 ft

Etent dist/ fro* Center Support distet 8/0 ft

distet,*in 4/58 ft (19.3*in+?S,+EW3, C 71#60# 17/2/8 &3

!esdistetAdistet,*inB

deEt

h

hdr

Cut Section of Colu*n 'ith Drop =$nel



Level 1 Underground

EW Direction Span 28.5 ft

Critical Positive Moment

Moment Coefficient under Unit Load 38. unit l!"ft Mastan #nal$sis

%otal Moment at Panel Strip 2 &ip"ft 'u(3)ft

Column Strip Moment Distri!ution Coeff. ).5 #C* 3+8")8 +3.,.-.+

Moment at Column Strip 5-5 &ip"ft %otal Moment().5

Moment at Middle Strip +82 &ip"ft %otal Moment(+").5/

Moment at Column Strip0 Plf 38.3 &ip"ft Moment at Column Strip1! col

Moment at Middle Strip0 Plf ++.5 &ip"ft Moment at Column Strip1! m0EW

Critical eative Moment

Moment Coefficient under Unit Load "2.3 unit l!"ft

%otal Moment at Panel Strip "+354 &ip"ft

Moment at Column Strip "+)2) &ip"ft

Moment at Middle Strip "3-) &ip"ftMoment at Column Strip0 Plf "+., &ip"ft

Moment at Middle Strip0 Plf "2+., &ip"ft

S Direction Span 3).) ft


Moment Coefficient under Unit Load -4.2 unit l!"ft

%otal Moment at Panel Strip 84 &ip"ft 'u(28.5ft

Moment at Column Strip ,54 &ip"ft %otal Moment().5

Moment at Middle Strip 22) &ip"ft %otal Moment(+").5/

Moment at Column Strip0 Plf -,.3 &ip"ft Moment at Column Strip1! col

Moment at Middle Strip Plf +- 3 &ip"ft Moment at Column Strip1! m S

Summary Table for Design Moments at Critical Section

Notes:

Moment Coefficient are from M#S%# anal$sis0 usin one foot sla! applied 'it6 unit load.

Desin for t'o t$pical level0 level + underround and level 2" underround. Use par&in roof load for

level + underround7 par&in floor load for level 2" underround.

or eac6 t$pical level0 desin for EW and S t'o directions.

or eac6 direction0 deisn for column strip and middle strip0 !ased on one foot sla!.



Level 2- Underground

EW Direction Span 28.5 ft


Moment Coefficient under Unit Load 3.3 unit l!"ft

%otal Moment at Panel Strip 2, &ip"ft

Moment at Column Strip 2) &ip"ft

Moment at Middle Strip ,4 &ip"ft

Moment at Column Strip0 Plf +-.5 &ip"ft

Moment at Middle Strip0 Plf -.- &ip"ft


Moment Coefficient under Unit Load "+.4 unit l!"ft

%otal Moment at Panel Strip "53+ &ip"ft

Moment at Column Strip "344 &ip"ft

Moment at Middle Strip "+33 &ip"ft

Moment at Column Strip0 Plf "28.) &ip"ft

Moment at Middle Strip0 Plf "8.- &ip"ft

S Direction Span 3).) ft


Moment Coefficient under Unit Load --. unit l!"ft

%otal Moment at Panel Strip 3+- &ip"ft

Moment at Column Strip 235 &ip"ft

Moment at Middle Strip 8 &ip"ft

Moment at Column Strip0 Plf +,.5 &ip"ft

Moment at Middle Strip0 Plf 5.5 &ip"ft


Moment Coefficient under Unit Load "82.) unit l!"ft

%otal Moment at Panel Strip "5, &ip"ft

Moment at Column Strip "-32 &ip"ftMoment at Middle Strip "+-- &ip"ft

Moment at Column Strip0 Plf "3).3 &ip"ft

Moment at Middle Strip0 Plf "+).+ &ip"ft



M!ST!N "ut#ut

9ne foot 'idt6 of sla! applied 'it6 unit load0 s6o'in critical desin moment coefficients.

38.,5

"2.25

Level + Underround0 EW Direction

"8.83

-4.+

Level + Underround0 S Direction

3.24

"+.4)

Level 2" Underround0 EW Direction

"82.)+



Design Calculations for WWR Concrete Slab Created by: MZ 5/10/2012

• All the reinforcement design are based on one foot slab.

• Leel 1 !orth"#o$th direction calc$lations hae been incl$ded as re%resentatie of the ty%ical calc$lations. &t

consists of %ositie and negatie moment reinforcement design for col$mn and middle stri% res%ectiely.

#hear 'as also chec(ed 'hen eer negatie moment is considered.

• )he *ast"+est direction of leel 1 and both directions of all other leels are calc$lated in the same manner b$t

'ith their indiid$al in%$ts.

Span Length LNS 30 ftCritical Moment Mu 46.3 kip-ft

Material Properties


!erage Concrete Strength f'c,a!g 3400 psi

"ar Si#e for $$% & 6

Nominal $$% Si#e 44

%e(ar rea (ar 0.44 in)

Nominal iameter *(ar 0.+0 in

$$% iel* Strength / 0 ksi

Flexural MMR Calculation (Per Foot Width)

Sla( 1hickness h 2).0 inConcrete Co!er c ).0 in

Sla( ffecti!e epth * .6 in 5h-c-*(ar)

$i*th ( 2).0 in

"ar Spacing s 6.0 in

$$% rea s 0. in) ma7.s526in. C8 32-0 3..3.+

1ension at iel* 1 +0 kips 5/s

epth of 9ui. Comp. Stress "lock a 2.+3 in. 51:(;f'c,a!g<

Nominal Moment Strength Mn 2.4 kip-ft 51:*-a)<

*=ustment actor for Moment > 0.

esign Moment Strength ?Mn 46.3 kip-ft

?Mn@Mu A es

Minimum %e9uire* Steel rea s,min 0.2 in) 50.002(h;60/, for / @ 60 ksi

s@s,minA es C8 32-0 +.2).).2

Level 1 Underground NS irection! Colu"n Strip! Positive Mo"en

Span Length

LNS

30 ftCritical Moment Mu -82.6 kip-ft

Material Properties

Concrete Strength f'c 4000 p!i

"#erage Concrete Strength f'ca#g 3400 p!i

$ar Si%e for && ( 6

Nominal && Si%e )44e*ar "rea "*ar 0.44 in

2

Nominal )iameter +*ar 0.,0 in

&& iel+ Strength / 80 k!i


Sla* 1hickne!! h 2.0 in

Concrete Co#er c 2.0 in

Sla* ffecti#e )epth + .6 in 5h-c-+*ar2

)rop 7anel 1hickne!! h+r ,.0 in

1otal ffecti#e )epth +tot 6.6 in 5+h+r

1otal Sla* 1hickne!! htot .0 in 5hh+r

Sla* $eam &i+th * 2.0 in

$ar Spacing ! 6.0 in

&& "rea "! 0.88 in2 ma9.!56in. "C: 38-08 3..3.,

1en!ion at iel+ 1 ,0 kip! 5/"!

)epth of ;ui. Comp. Stre!! $lock a .,3 in 51<*=f'ca#g>

Nominal Moment Strength Mn 2. kip-ft 51<+-a2>

"+?u!tment /actor for Moment @ 0.

)e!ign Moment Strength AMn 83.2 kip-ft

AMnBMu e!Minimum e;uire+ Steel "rea "!min 0.3 in

2 50.008*h=60/ for / B 60 k!i

"!B"!min e! "C: 38-08 ,.2.2.

Level 1 Underground NS irection! Colu"n Strip! Negative Mo"ent

MMR Shear Chec#

$eam Shear Check1otal /actore+ Loa+ Du 62, p!f

Length of ;ui. Column Section +e; 28.4 in

Shear at +tot )i!tance from Col. face Eu ,.8 kip!ft 5Du<LNS2-+e;2-+tot>

"+?u!tment /actor for Shear A 0., 5A<2=!;rt<f'c>=*=+tot>

Shear Strength AEc 8. kip!ft "C: 38-08 .2..

AEcBEu e!

7unching Shear Check 5Du=LNS=L&

1ri*utar "rea for one Column "tri 8 ft2 5Du<"tri-<+e;+tot>

2>

7unching Shear at +tot2 from Col. face Eu 2, kip! 54<+e;+tot>

7unching Shear 7erimeter *0 80 in

7unching Shear Strength AEc 6, kip! 5A<4=!;rt<f'c>=*0=+tot>

AEcBEu e!

Span Length LNS 30 ftCritical Moment Mu 14.3 kip-ft

Material Properties


!erage Concrete Strength f'c,a!g 3400 psi

"ar Si#e for $$% &

Nominal $$% Si#e (44

%e)ar rea )ar 0.44 in*

Nominal (iameter +)ar 0.0 in

$$% iel+ Strength / 0 ksi


Sla) 2hickness h 1*.0 in

Concrete Co!er c *.0 in

Sla) ffecti!e (epth + . in 5h-c-+)ar6*

$i+th ) 1*.0 in

"ar Spacing s 1.0 in

$$% rea s 0.33 in* ma7.s51in. C8 31-0 3..3.

iel+ 2ension 2 * kips 5/s

(epth of 9ui. Comp. Stress "lock a 0. in. 526:);f'c,a!g<

Nominal Moment Strength Mn *0. kip-ft 52:+-a6*<

+=ustment /actor for Moment > 0.

(esign Moment Strength ?Mn 1.4 kip-ft

?Mn@Mu A es

Minimum %e9uire+ Steel rea s,min 0.1 in* 50.001)h;06/, for / @ 0 ksi

s@s,minA es C8 31-0 .1*.*.1

Level 1 Underground NS irection! Middle Strip! Positive Mo"ent

Span Length

LNS

30 ftCritical Moment Mu -27.5 kip-ft

Material Properties

Concrete Strength f'c 4000 p!i

"#erage Concrete Strength f'ca#g 3400 p!i

$e%ar Si&e for $ ( )

Nominal $ Si&e *44+ne ,ar "rea "%ar 0.44 in

2

Nominal *iameter %ar 0.750 in

$ iel Strength / 10 k!i


Sla% hickne!! h 2.0 in

Concrete Co#er c 2.0 in

Sla% ffecti#e *epth .) in 6h-c-%ar2

*rop 8anel hickne!! hr 7.0 in

otal ffecti#e *epth tot ).) in 69hr

otal Sla% hickne!! htot .0 in 6h9hr

Sla% ,eam ith % 2.0 in

,ar Spacing ! ).0 in

$ "rea "! 0.33 in2 ma:.!6)in. "C; 31-01 3.5.3.7

iel en!ion 2) kip! 6/"!

*epth of <ui. Comp. Stre!! ,lock a 0.)5 in 6=%>f'ca#g?

Nominal Moment Strength Mn 3) kip-ft 6=-a2?

"@u!tment /actor for Moment A 0.

*e!ign Moment Strength BMn 32 kip-ft

BMnMu D e!Minimum $e<uire Steel "rea "!min 0.3 in

2 60.001%h>)0/ for / )0 k!i

"!"!minD e! "C; 31-01 7.2.2.

Level 1 Underground NS irection! Middle Strip! Negative Mo"ent

MMR Shear Chec#

,eam Shear Check

otal /actore Loa Eu

)27 p!f

Length of <ui. Column Section e< 21.4 in

Shear at tot *i!tance from Col. face Fu 7.1 kip!ft 6Eu=LNS2-e<2-tot?

"@u!tment /actor for Shear B 0.75 6B=2>!<rt=f'c?>%>tot?

Shear Strength BFc 1. kip!ft "C; 31-01 .2..

BFcFuD e!

8unching Shear Check 6Eu>LNS>L

ri%utar "rea for one Column "tri 155 ft2

6Eu="tri-=e<9tot?2?

8unching Shear at tot2 from Col. face Fu 527 kip! 64=e<9tot?

8unching Shear 8eremeter %0 10 in

8unching Shear Strength BFc 5)7 kip! 6B=4>!<rt=f'c?>%0>tot?

BFcFuD e!

o f

n

6 . 2 . 2 S u m

m a r y o f P a r k i n g G a r a g e C o l u m n

C r e a t e d b y : K L S

5 / 9 /

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6 . 2 . 2

S u m m a r y o f P a r k i n g G a r a g e C o l u m n s

C-246

6.2.2.1 Parking Garage Column with Rebar Created by: KLS 5/9/2012

Design tool for concrete columns in paring garage reinforced !it" rebar# $

%sed for t"e &oof and Le'els 1() Color ey !it" summary#

Load on Column - Roof

Dead Load DL 1*0 psf L

+errace Li'e Load LL 100 psf

&oof Load ),- psf . 1#2DL1#,LL

+ributary rea )- ft2

Load on Column $ )0- ips

oment 0 ip(ft

Dc

Concrete Properties

Concrete Strengt" f3c -4000 psi

Concrete Density c 0#0 lb/in)

Co'er for Columns ccol 1#5 in

Co'er for Caissons ccais ) in

Column esign - Roof Load

6arage le'el 1 Co'er

Column &adius r 12 in

Column rea g -52 in2

. 7r2

Column 8eig"t " 2*- in

Load on column $ )1- ips includes self(!eig"tuantity of &ebar n ,

&ebar Sie ; , inimum , < C= 10#)

Dc 21#0 in . 2r(2>Co'er?

Steel @ield Stengt" Ay ,0#0 si

Spiral &einforcement ratio s 0#01 . 0#-5>g/>7Dc2/-?(1?f3c/Ay

Spiral &ebar ; ) Sie

Diameter of Spiral &ebar ds 0#)*5 in

rea of single &ebar sr 0#11 in2

Spiral Spacing s 2#2- in . srB7>Dc(ds?/>7Dc2/-?s < C= 10#9#)

0#* C= 10#)#5#1

r

6.2.2.2 Parking Garage Column with W-Shape Created by: KLS 5/9/2012

Design tool for columns wit embedded sa!es under !ure a"ial load

#eference: Ca!ter $ %$SC Steel Construction &anual Color 'ey on

summary(

Loads

)otal Load *u +,-.. 'i!

Section Type

12"1-0

Column Properties

#adius of column r 1 in

%rea of crosssection % 1,01 in2

ield Strengt of Steel Sa!e 3y 50 'si

CrossSectional %rea %s 49(91 in2

Concrete Stengt fc 4 'si

%rea of Concrete %c 9. in2

ield Strengt of #ebar 3ysr .0 'si

CrossSectional %rea of rebar %bar 0(00 in2

&odulus of 6lasticity of Steel 6s 29,000 'si

&oment of $nertia 7Strong8 $" 1,.+9 in4

&oment of $nertia 7ea'8 $y 51- in4

&oment of $nertia of Steel $s 51- in4

&oment of $nertia of rebar $sr 0 in4

6ffectie #igidity C1 0(20 0(+ ; 0(1<27%s/%c<%s8

Density of Concrete =c 145 !sf

&odulus of 6lasticity of Concrete 6c +,492 !si ; wc1(5

s>rt7fc8

&oment of $nertia of Concrete $c 1,9+1 in4

6ffectie 6$ 6$eff -(1.6<0- 'in2

; 6s$s<0(56s$sr<C16c$c

6ffectie Lengt 3actor K 1 ; !in!in connection

Lengt of Column 10 in

Column Capacity

r

/ 12 " 1-0



6.2.3 Belled Caisson Design

Belled caissons distribute the load from the parking garage columns over a larger area to lower the

pressure to below the allowable bearing pressure of the soil, 45 ksf.

Load at boom of caisson

P 3767kip:= Parking arage !olumns."ls

Net Allowable Bearing Pressure on hardan

σ 45ksf := per eotechnical #eport

Area of Belled Caisson

$reaP

σ

%3.7&& ft'

⋅=:=

radius$rea

π

5.&6' ft⋅=:=

radius 5.5ft:=

rshaft &%in:=

# radius rshaft− 4 ft⋅=:=

$ngle must less than or e(ual

to 3) degrees per !hicago Building !ode*

#

tan 3)deg+ 6.-'% ft⋅=:=

* 7ft:=



6.3 %o&er -oundation

6.3.1 Abaqus Analysis of Caissons 251

6.3.2 Mega-Column Caisson Design 253

6.3.3

Ring eam Design 255

6.3.!

Co"e Caisson Design 25#

6.3.5

Caisson Reba" 25$



6.3.1 Abaqus Analysis of Caissons Created By: NT/JAC 5/11/2012

A finite element analysis using Abaqus was perfrmed t btain t!e ma"imum stresses e"perien#ed by t!e

r#$%s#$eted #aissns& T!ere were tw main types f #aissns' ea#! requiring different Abaqus mdels& T!ese

were t!e #aissns transmitting lads frm t!e #n#rete #re dwn t t!e bedr#$ and t!e #aissns

transmitting lads frm t!e mega%#lumns& (n eit!er #ase' t!e #aissns were mdeled as quartered #ylinders

embedded int t!e #rners bedr#$ #ubes' ta$ing ad)antage f t!e symmetry in t!e gemetry& (n t!e Abaqus

results' bluer #lrs indi#ate lwer stresses' w!ereas red #lrs indi#ate !ig!er stresses&

Core Caissons

T!e #re #aissns e"perien#ed nly a"ial lads in t!e frm f gra)ity lads frm t!e #n#rete #re& N s!ear

fr#es were applied n t!ese #aissns& As #an be seen in t!e figure belw' t!ere was a slig!t stress

#n#entratin at t!e tp f t!e #aissn w!ere t!e lad was applied& T!e ma"imum *n%+ises #mpressin

stress was ,&- $si' #rrespnding t a need fr minimum reinfr#ing steel&



Mega-Column Caissons

T!e mega%#lumn #aissns e"perien#ed bt! a"ial lads and s!ear fr#es' in t!e frm f lateral and gra)ity

lads frm t!e mega%#lumns& As su#!' t!e stresses in t!ese #aissns were !ig!er& T!is #an be seen in t!e

figure belw' w!ere dar$er red #lrs indi#ate !ig!er stress #n#entratin at t!e tp surfa#e f t!e #aissn&

T!e ma"imum *n%+ises #mpressin stress was ,&. $si' #rrespnding t a need fr a !ig!er amunt f

reinfr#ing steel&

Abaqus mdel f stresses in t!e r#$%s#$eted #aissns under t!e mega #lumns

6 3 2 Mega Column Caisson Design C t d b KLS 5/9/2012

6.3.2 Mega-Column Caisson Design Created by: KLS 5/9/2012

Design tool for rock-socketed caissons suorting t!e "ega-colu"n

#ccetible$ %&S See botto" of calculation for diagra"'

( )*erdesigned 5'+,(

Concrete Co"ressi*e Strengt! fc 1+ ksi

Steel %ield Strengt! .y 5 ksi C!icago uilding Code

%oungs odulus edrock & 500 ksi ef' 13oissons atio edrock 4 0'2 ef' 2

&"erical Constant n 0'5 ef'

Det! to edrock L 1152 in

Det! in edrock Lo 102 in

Dia"eter of Caisson d 120 inDia"eter of Caisson socket bs 11+ in

Lengt! of Socket Ls 102 in

ini"u" Steel Casing 0'9 in 6 0'00,57d

#ctual Steel Casing Dia"eter dc 1 in

Deduct steel t!ickness for durability dd 0'0825 in

ega Colu"n otal ase eaction 552 kis

;eig!t of Connection 122 kis fro" idas <en

Colu"n Caisson ase eaction 3 5821+ kis

#llo=able Stress in Concrete >c +'81 ksi 6 0'[email protected]'5

@dc-ddAA/d

#llo=able Stress in rock >r +'18 ksi ef' +

#llo=able Stress >all +'18 ksi ini"u" of >c>r

#ctual Stress er Caisson >act 2' ksi 6 3/@Bd2/+A

.actor of Safety .S 2 6 >all/>act

0'+

2

Settlements

Material Properties

Dimensions

Forces and Stresses

plift Check

ai"u" ension eaction "a 2+ ki idas <en

#rea of Steel #s 8,2 in2

;eig!t of Steel +91 ki 1'8 lb/ft for 1 bars#rea of Concrete 108 in

2

Concrete Density Ec 180 cf

;eig!t of Caisson =c 115 ki

Co"ressi*e Strengt! f 0', ksi 6 0'05fc if FuGfc H ef' 5

Socket S!ear Is 255,1'1 kis 6 B7bs7L7f H ef' 8

esistance #gainst Jlift u 28,08 kis

uG"a$ %es 0'12

!eoretical uerbound k 9

oriontal Subgrade odulus k! 2150 ksf/ft

S!ear Strengt! of rock Su +55528 ksf 6 8,7k!7sFrt@d71ftA H ef' +

Lateral 3ressure taken by rock >! +'10&?0, k/ft 6 k7d7Su

S!ear Caacity of ock Ir +'10&?0 kis 6 >!7d

ai"u" S!ear I"a +0000 kis fro" idas <en

.actor of Safety .S +

Design S!ear I 180000 kis 6 I"a7.S

IrGI$ %es

References

+ <eotec!nical eort

1 ec!anics of aterial Ma"es <ere @199,A

Shear Check

Kul!a=y 3!oon and #kbas @199A NDrilled

S!aft Side esisitance in Clau Soil to ockN

<eotec! Sec 3ublications Oo'

2 Coduto N<eotec!nical &ngineering 3rinciles

and 3racticesN@1999A

5 Kul!a=y 3!oon and #kbas @2005A

N&*aluation of Caacity of ock .oundation

SocketsN 3roceddings +0t! JS Sy"osiu" on

ock ec!anics #nc!oarage #laska Mune'

plift Check

9"aC

3 3



6.3.3 Ring Beam Design

A ring beam will be used to connect the core walls to the caissons. This is designed to even distribute

the axial load to the caissons and to resist that shear forces from the core.

Ring Beam Properes

hring 8ft:= Height of Ring Beam

router 47ft:= Outer Radius of Ring Beam

rinner ft:= !nner Radius of Ring Beam

rcaissons "ft:= Radius of #aissons

Aring π router$

⋅ πrinner$

− "%8.& ft$

⋅=:=

Acaissons $' π rcaissons$

⋅⋅ %"7'.8 ft$

⋅=:=

Aslab π rinner$

⋅ 4$%.$ ft$

⋅=:=

A Aring Aslab+ Acaissons− "&( ft$

⋅=:= )*ec+ve Area for ,ric+on

Soil Properes

-u ('''lbf

ft$

:= ndrained -hear -trength / 0eotechnical Re1ort

ρcla2 7'lbf

ft

:= 3enist2 of #la2

3enist2 of aterρw &$.4

lbf

ft

:=

5e 4(.$ft:=

ρe ρcla2 ρw+:= )*ec+ve 3ensit2



Design Base Shear: 49030 kip (from Midas en!

core 4(''i1:=

&$'7." i1⋅=

core> "es

,-

core

%.=:=

Created by: KLS 5/9/20126.3.4 Core Caisson Design

y / /

Design tool for rock-socketed caissons suorting t!e core

See botto" of calculation for diagra"#

Overall Check

$ccetible% &'S

( )*erdesigned 29#+0(

Concrete Co"ressi*e Strengt! f,c 1 ksi

Steel &ield Strengt! .y 5 ksi C!icago uilding Code

&oung,s odulus edrock ' 500 ksi 3ef# 1

4oisson,s 3atio edrock 0#26 3ef# 2

'"erical Constant n 0#5 3ef#

Det! to edrock L 92 in

Det! in edrock Lo 102 in

Dia"eter of Caisson d 120 in

Dia"eter of Caisson socket ds 11 in

Lengt! of Socket Ls 102 in

7u"ber of Caisson 20 8 0#00+5d

ini"u" Steel Casing 0#9 in

$ctual Steel Casing Dia"eter dc 1 in

Deduct steel t!ickness for durability dd 0#025 in

Core 3eaction at 'le*ation80 +601 kis fro" idas ;en

Core <all <eig!t elo= 'le*ation80 219+0 kis

Core Caisson >otal ase 3eaction 4 0069 kis includes self-=eig!t

$llo=able Stress in Concrete ?c #1 ksi 8 0#f,

c@A.

y

1#5Ad

c-d

dBB/d

$llo=able Stress in rock ?r #1 ksi 3ef#

$llo=able Stress ?all #1 ksi ini"u" of ?c?r

$ctual Stress er Caisson ?act 1#++ ksi 8 4/Ad2/B

.actor of Safety .S 2 ? /?

6.3. Co e Ca sso es g

Material Properties

Dimensions

Forces and Stresses

Uplift Check

ai"u" >ension 3eaction >"a 2100 ki 3ef#

$rea of Steel $s 25 in2

<eig!t of Steel 5#+ ki 1# lb/ft for E16 bars

$rea of Concrete 1105 ki

Concrete Density Fc 10 cf

<eig!t of Caisson =c 50# ki

Gnconfined Co"ressi*e Strengt! f 0#+ ksi 8 0#05f,c if HuIf,c J 3ef# 5

Socket S!ear s 255+1 kis

3esistance $gainst Glift 3u 20+5 kis 8 s@<c

3uI>"a% &es 0#92

eferences

;eotec!nical 3eort

;eotec!nical Design of Dee .oundations 20###1

1 ec!anics of aterial a"es ;ere A199+B

2 Coduto M;eotec!nical 'ngineering 4rinciles and 4racticesMA1999B

Kul!a=y 4!oon and $kbas A199B MDrilled S!aft Side 3esisitance in Clau Soil to 3ockM ;eotec! Sec

4ublications 7o# 6

5 Kul!a=y 4!oon and $kbas A2005B M'*aluation of Caacity of 3ock .oundation SocketsM 4roceddings 0t! GS

Sy"osiu" on 3ock ec!anics $nc!oarage $laska une#

8 bsLHu J 3ef#

44>"aD

6.3.5 Caisson Rebar Created by: KLS 5/9/2012

Caisson Properties

Radius r 5 ft User Input

Area A 11,310 in2

Cnstant/!re"ius Ca#$%

Stee# &ie#d Stren't( )y *0 +si Ca#$/L+up

&es !asses C(e$+

Top of Mega-column Caissons )ai#s C(e$+

Stress at -p . %9 +si Abaus de#

aiu -ensin )r$e - 55,14 +ip .6A

Area f Stee# As 92 in2

-/)y

Area f 7bedded Stee# S(ape 282 in2

Area f Rebar eeded *52 in2

ar Sie ; 14

Area f Rebar Abar in2

uber f ars 1*4A$tua# Area f Stee# As<a$tua# 9 in

2

Asa$tua#=As &es

Bottom of Mega-column Caissons

Stress at tt . 1%9 +si Abaus de#


Area f Stee# As 354 in2

-/)y

ar Sie ; 14

Area f Rebar Abar in2

uber f ars 90

A$tua# Area f Stee# As<a$tua# 3*0 in2

Asa$tua#=As &es

Core Caissons

Stress in Cre Caissn . 1%2 +si Abaus de#


Area f Stee# As 22* in2

-/)y

-(is spreads(eet $a#$u#ates t(e aunt f rebar needed inside t(e $aissns

C#r Key

7 0 Creep and Shrinkage



7.0 Creep and Shrinkage

7.1 Steel Column Deformation 261

7.1.1

Steel Column Properties and Loads 262

7.1.2

Steel Column Deformation Calculations 263

7.2 Concrete Core Deformation 26

7.2.1 Concrete Core Properties and Loads 266

7.2.2 Concrete Core Deformation Calculations 267

CONSTRUCTION

ENDS

0

5

10

15

20

25

0 5 10 15 20

C o r e D i s p l a c e m e n t ! i

n c h e s "

#ime !$ears"

Displacement %&er 20 'ears

Concrete Core

Summary

STEEL

COLUMNS

7.1 Steel Column Deformation



Floors

Deflection per

floor

Local Def

per floor

group

Global

Deformation Sum

Lobby 0.979 0.979 0.98 inches

5-! 0.077 0.9" .90 inches

7-"8 0.0!7 0.805 ".7 inches

"9-#9 0.057 0.!# #.#$ inches

$0-5 0.0$9 0.590 #.9# inches

5"-!# 0.0$ 0.$9" $.$" inches

!$-7# 0.0#$ 0.##5 $.75 inches

7$-8! 0.05$ 0.70" 5.$! inches

87-99 0.0$" 0.5$! !.00 inches

00-0 0.0# 0.#$0 !.#$ inches

-"" 0.0" 0."5 !.59 inches

"#-## 0.0" 0.# !.7" inches

#$-$5 0.00$ 0.0$5 !.77 inches

!.77 inches%ltimate Steel Deformation&

t ' " years

7#0

Calculated

Days

(his chart reflects the )eformation of the steel columns for each floor group an) the o*erall steel

)eformation at a time of " years.

7.1.1 Steel Column Properties and Loads

Summary of column an) core )imensions an) the loa)s applie) on each

Column Properties Lobby 5-16 17-28 2-! "#-51 52-6! 6"-7! 7"-86 87- 1##-11# 111-122 12!-1!! 1!"-1"5

+olumn )imensions

)epth ) $0 $0 $0 $0 $0 $0 $0 #! #! #! #! #! #! in

base b $0 $0 $0 $0 $0 $0 $0 #! #! #! #! #! #! inconcrete Strength f,c $000 $000 $000 $000 $000 $000 $000 $000 $000 $000 $000 $000 $000 psi

conc. mo)ulus 57000s/rtf,c1 2c !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ !7$$ 3si

(otal 4rea 4t 9"8 9"8 9"8 9"8 9"8 9"8 9"8 !88 !88 !88 !88 !88 !88 in

+oncrete 4rea c 0 0 0 0 0 0 0 0 0 0 0 0 0

Steel Shape& 6%- 6%- 6%- 6%- 6%- 6%- 6%- 6%-" 6%-" 6%-" 6%-" 6%-" 6%-"

4rea 4 9"8 9"8 9"8 9"8 9"8 9"8 9"8 !88 !88 !88 !88 !88 !88 in"

)epth d #! #! #! #! #! #! #! "8 "8 "8 "8 "8 "8 in

i)th of flange bf #! #! #! #! #! #! #! #! #! #! #! #! #! in

thic3ness of flange tf 0 0 0 0 0 0 0 0 0 0 0 0 0 in

thic3ness of eb tw 0 0 0 0 0 0 0 0 0 0 0 0 0 in

Steel atio ϱg .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

Steel Shape Self eight 87.5 $.# $.# $.# $.# $.# $.# #0.! #0.! #0.! #0.! #0.! #0.! 3ips

((4L +L%:; S2LF 2<G=( 88 $ $ $ $ $ $ # # # # # # 3ips

Core Properties

6an3 " $

a)ius $0 #8 "! ftthic3ness 8 ! #.## ft

(otal >olume ? Floor "!5"7 8900 777 ft#

(otal eight?Floor $"$$ #0"$ $8 3ips

(otal 4rea?Floor "00 $#" 5$$ ft"

@ of +olumns " " $

4rea per core AcolumnA 9! !8 #9 ft"

S per core AcolumnA "0" $$ 8" 3ips

$nfactored %odal Loads

6an3 +ore1 #5.! #$.9 "0 $$.! """9

6an3 2Bt. +olumn1 9!." #5.# "0 "0.8 0#8

6an3 " +ore1 #".7 #0. "0 #7.! 88

6an3 " 2Bt. +olumn1 7$.! "7." "0 !.0 800

6an3 # +ore1 #!.0 "8." "0 "8. $07

6an3 # 2Bt. +olumn1 8!.0 #.0 "0 8.$ 9""

6an3 $ +ore1 #5.! #$.9 "0 "".9 $!

6an3 $ 2Bt. +olumn1 !#.7 "".8 "0 ".$ !"0

!

!

SDL psf1

DL

3ips1

LL

3ips1

S%S LL

psf1

!

!

!

!

!

!

90

#

#!$

9#7

SDL

3ips1

(rib. 4rea

ftC"1

$

90$

#!

!5

7.1.1 Steel Column Properties and Loads

7.1.2 Steel Column Deformation Calculations

(his is a representati*e calculation performe) in the same manner for all floor sets +reep an) Shrin3age calculations per GL"000 :etho) from 4+< "09 " "7

(his is a representati*e calculation performe) in the same manner for all floor sets. +reep an) Shrin3age calculations per GL"000 :etho) from 4+< "09."-"7

6an3

Floor Group

Column Properties

f c "81 psiE' $000 psi ) $0 in s 0.# from table 4.$

f cm"8 4-9$1 !00 psi b $0 in 3 .5 from table 4.$

le*el 0 f,c $000 psi shu 5#8 microstrain 4-991

first le*el 5 2c !7$$ 3si h 0.7$ relati*e humi)ity from ;ational +limatic Data +enter a*erage

last le*el !.0 4t 9"8 in"

Hh 0.!9$ 4-001

total )ef t ' #yr1 0.9 inches 4c 0 in"

tc )ays1 $ time )rying begins

total )ef t ' "0yr1 0.9 inches 6%- t0 )ays1 $ time loa) is applie)

floors )ay en)e) 4s 9"8 in" Itc1 hen t0'tc

6an3 Loa) #7.5 3ips #0 "0 d #! in

6an3 " Loa) 5.9 3ips #$ "5! bf #! in

6an3 # Loa) 77.7 3ips #7 $0$ tf 0 in

6an3 $ Loa) !".9 3ips #$ 5$0 tw 0 in

2s "9000 3si ϱg

4s 9"8 in"

4c 0.0 in"

height 58 in*?s 0.0 in

t g l o

b a l

t l o

c a l

H e 4 - 9 7 1

f c m t t 1 4 - 9 ! 1

2 c 3 s i 1 4 - 9 5 1

H t - t c 1 4 - 0 1

+ o r r e c t e ) S h r i n 3 a

g e

4 - 9 8 1

+ r e e p + o e f f i c i e n t 4 -

0 # 1

J s D L 3

i p 1

J s S D L 3

i p 1

J s t o t a l 3

i p 1

f c 3

s i 1

e l a s t i c s t r a i n

u n r e i n f o r c

e )

6 a

n 3

; u m b e r

o f

+ o l u m n s ? + o l u m n

S t e e l D e f o r m a t i o n

J L ? 4

2 1

) e f o r m a t i o n

"5 9"! 5$9" #$.$ !".# 97 0.097" 0.00000 # 0.00 0.000!

"! " "7# !0" !8.7 !".# # 0.0"9# 0.00000 # 0.00 0.0008

"7 # "#"5 !"7# 0#. !".# !5 0.0#85$ 0.0000 # 0.00 0.000

"8 $ "999 !$"9 #7.5 !".# "00 0.0$77 0.0000 # 0.00 0.00"

"9 5 #$80 !5#7 .00 #7#."# .7 7.8 "$.5 "9! 0.0798 0.0000 # 0.00" 0.007

#0 ! #8$! !!9 .00 #7#."# .9 "0!." "$.5 ## 0.08## 0.0000 # 0.00" 0.009

# 7 $#7 !!8# .00 #7#."# ".0 "$0.! "$.5 #!5 0.090!5 0.0000 # 0.00" 0.00"

#" 8 $#77 !7#5 .00 #7#."# ". "7$.9 "$.5 #99 0.0999! 0.0000 # 0.00" 0.00"#

## 9 $578 !778 .00 #7#."# "." #09.# 8!.8 $9! 0."$9$ 0.0000" # 0.00# 0.00"9

#$ 0 $75 !8! .00 #7#."# "." #$#.! 8!.8 5#0 0.#$## 0.0000" # 0.00# 0.00#

&alues for Creep and S'rin(a)e analysis

5 - !

7.1.2 Steel Column Deformation CalculationsC-263



7.2 Concrete Core Deformation Created by: ADV, JDM, SJR, DSF 4/28/2012

This sheet summaries !a"ues #r$m the %a"%u"ati$& 'a(es i& a& easy t$ read #$rmat a&d %a"%u"ates the t$ta" de#$rmati$&s $# the %$re)



De#$rmati$&

'er F"$$r

De#$rmati$& 'er

F"$$r Se(me&t

Sum $# F"$$r Se(me&t

De#$rmati$&s De#$rmati$& 'er F"$$r

De#$rmati$& 'er

F"$$r Se(me&t


De#$rmati$&s

De#$rmati$& 'er

F"$$r

De#$rmati$& 'er

F"$$r Se(me&t


De#$rmati$&s

De#$rmati$& 'er

F"$$r

De#$rmati$& 'er

F"$$r Se(me&t


De#$rmati$&s

F"$$rs *i&+ *i&+ *i&+ *i&+ *i&+ *i&+ *i&+ *i&+ *i&+ *i&+ *i&+ *i&+

$bby 0)-0. 0)-1 0)- 0)-1. 0)-2 0)- 0)-0 0)- 0)- 0)-1 0)- 0)41 0)0- 0)88 1)2 0)0 0).0 1)2 0)08- 0).. 1)- 0)088 1)0 1)4

128 0)0 0) 2)0 0)0 0)80 2)0 0)04 0)88 2)2 0)08 0).4 2)4

2.-. 0)0 0)2 2) 0)08 0)4 2) 0)04 0)1 2). 0)08 0) -)1

401 0)004 0)04 2) 0)004 0)0 2) 0)004 0)0 -)0 0)00 0)0 -)2

2- 0)00- 0)04 2) 0)00- 0)04 2) 0)004 0)0 -)0 0)004 0)0 -)2

4- 0)00- 0)0- 2) 0)00- 0)0- 2)8 0)00- 0)0- -)1 0)004 0)04 -)-

48 0)11 2)22 4). 0)180 2)-4 )1 0)204 2) ) 0)220 2)8 )1

8.. 0)1-4 1)4 ) 0)142 1)84 )0 0)12 2)11 )8 0)1 2)2 8)4

100110 0)100 1)10 ) 0)10 1)18 8)1 0)12- 1)- .)2 0)1-- 1)4 .).

111122 0)-. )4 14)2 0) ).1 1)0 0)4 ). 1)2 0)1 8). 18)4

12-1-- 0)-0. -)-. 1) 0)--- -) 18) 0)-88 4)2 21)4 0)41. 4)1 2-)1

1-414 0)100 1)20 18)8 0)110 1)-- 20)0 0)1-2 1)8 2-)0 0)14 1)4 24)8

Concrete Core Summary 20-Year Deformation Comparisons Construction Line

C$re De#$rmati$&: 2 4)8 i& Time *yr+ De# *i&+

Time (yr) Def (in) Stee" De#$rmati$&: ) i& 1)4 0

0 0 Di##ere&%e: 18)0 i& 1)4 2

2 18)8 C$m'e&sati$& / #"$$r 0)12 i&

- 20)0 Add ar$u&d 203 t$ a%%$u&t #$r err$r

10 2-)0 3 T$ta" De#$rmati$& at 2 yr ).3 de#*2yr+/de#*20yr+

20 24)8

t = 20 years

Total Deformation

t = 2 years t = 3 years t = 0 years

7.2 Concrete Core DeformationC-265

7.2. Concrete Core !roperties an" Loa"s

This sheet dis'"ays the 'r$'erties #$r the %$re used i& the %ree' a&d shri&5a(e a&a"ysis)

Core !roperties#an$ 2 3 %

Radius R$ 40 -8 - 2 #t

Thi%5&ess t 8 4 -)-- #t

T$ta" V$"ume / F"$$r V% 2-,88 1,41 11,280 ,21 #t-

T$ta" 6ei(ht/F"$$r 6% -,822 2,8 1,80 1,0 5i's

T$ta" Area/F"$$r At 1,810 1,-1. 8 0. #t2

7 $# C$"um&s 21 21 14 14

Stee" Area As 2,8- 10,18 1 12- i&2

Area 'er %$re %$"um& 8 - 1 - #t2

Se"# 6ei(ht 'er %$re %$"um& 182 1-- 12. 5i's

&nfactore" 'o"al Loa"s

Ta$en from (inite )lement *o"el DL LL S&S LL SDL SDL Tri+. ,rea

*5i's+ *5i's+ *'s#+ *'s#+ *5i's+ *#t2

+9a&5 1 *C$re+ 4) -4). 20 44) 2,22.

9a&5 1 *:;t) C$"um&+ .)2 -)- 20 20)8 1,0-8

9a&5 2 *C$re+ 8) -0)1 20 -) 1,881

9a&5 2 *:;t) C$"um&+ 4) 2)2 20 1)0 800

9a&5 - *C$re+ 04 28)2 20 28)1 1,40

9a&5 - *:;t) C$"um&+ 8 -1 20 18)4 .22

9a&5 4 *C$re+ 4.8)4 -4). 20 22). 1,14

9a&5 4 *:;t) C$"um&+ -) 22)8 20 12)4 20

-einforcin Steel ,reas

#an$ 2 3 %

C$re Radius R$ 40 -8 - 2 #t

C$re Thi%5&ess t% 8 4 -)-- #t

C$re Cir%um#ere&%e 21 2-. 22 1- #t

Rebar S'a%i&( *i&+ 12 . 12 14 i&

Rebar S'a%i&( *#t+ s 1 0) 1 1)1 #t

9ar Sie 10 18 8

<umber $# 9ars 'er R$= &b 21 -18 22 140

7.2.2 Concrete Core Deformation Calculations

This sheet 'er#$rms %ree' a&d shri&5a(e %a"%u"ati$&s 'er the @2000 m$de" #r$m AC 20.)2R2) This sheet %a"%u"ates the de#$rmati$&s #$r #"$$r 10, =hi%h is mid"e!e" i& the 1 #"$$r se(me&t)

9a&5 1

F"$$r @r$u' 1

#an$ /nformation Core !roperties

#Bc 14000 'si C$re Radius R$ 40 #t

# %m28 1100 'si 1)1#B% 00 AC20.R *A.4+ C$re Thi%5&ess t% 8 #t

10 C$"um& Area A( 1810 #t2

# 0 C$&%rete Area A% 1.0 #t2

# # 1 Stee" Area As 28- i&2

1)0 i& *# # # 0 1+Ed20yr Stee" Rati$ ρg 0)0110 As/A(

Loa"in alues for Creep an" S1rin$ae ,nalysis

1 2 - 4 Stre&(th De!e"$'me&t >arameter s 0)-- #r$m tab"e A)14

.-0 81. -- 5i's Ceme&t Ty'e C$rre%ti$& Fa%t$r 5 1 #r$m tab"e A)14

7 F"$$rs $# $ad -0 -4 - -4 "timate Shri&5a(e Gshu 48

mi%r$strai& .00E5E*4-0/# %m28+

0) AC 20.R *A..+

Day $adi&( &ded 120 2 404 40 day Re"ati!e Humidity h 0)14 <ati$&a" C"imati% Data Ce&ter a!era(e

Humidity C$rre%ti$& Fa%t$r I*h+ 0).4 *1 1)18Eh4+ AC 20.R *A100+

Curi&( Days t% 4 days time dryi&( be(i&s

*aterial !roperties A(e $# $adi&( t$ 4 days time "$ad is a''"ied

s 2.000 5si Dryi&( C$rre%ti$& Fa%t$r *t%+ 1 AC 20.R *A104+

As 28- i&2

A% 1.0 #t2

h 18 i&

V/S 42) i& V%/*2ER$+

Deformation Summary

>er F"$$r @r$u' u&its

2 years 0)0- 0)8 i&

- years 0)0 0).04 i&

10 years 0)08- 0)..4 i&

20 years 0)088 1)04 i&

V$"ume/Sur#a%e Rati$

Stee" "asti% M$du"us

Stee" Area

C$&%rete Area

F"$$r Hei(ht

9a&5

$ad

S'e%i#ied 28day C$m'ressi!e Stre&(th

Mea& C$&%rete C$m'ressi!e Stre&(th

First F"$$r i& Se(me&t

ast F"$$r i& Se(me&t

F"$$r 7 Mid"e!e"

"timate De#$rmati$& i& Se(me&t

7..2.2 Concrete Core Deformation CalculationsC-267

+

A . 2 +

* A . +

A 1 0 1 +

e d

( e * A . 8 +

$ e # # i % i e & t

a d ,

> s D

a d ,

> s S D

e S t r e s s ,

# %

S t r a i &

$ r % e d

t r a i &

$ r % e d

( e S t r a i &

D e # $ r m a t i $ &

% e d

a t i $ &

$ r % e d

R e i & # $ r % e d

i & # $ r % e d



t ( " $ b a "

t " $ % a "

I e * A .

# c m t * t +

* A

: % * 5 s i + *

I * t t % + * A

C $ r r e % t e

S h r i & 5 a (

C r e e ' C

* A 1 0 - +

S t e e " $

S t e e " $

> s t $ t a "

C $ & % r e t

: " a s t i % S

F & r e i & # $

C r e e ' S t

F & r e i & # $

S h r i & 5 a (

> % * # % +

: " a s t i % D

R e i & # $ r %

: " e a s t i %

D e # $ r m a

F & r e i & # $

R a t i $ $ #

t $ F & r e i

R % # i

9 a & 5

days days 'si 5si mi%r$strai& 5i's 5i's 5i's 5si i& i& i& 5i's *i&+ *i&+2 1 0)48 -,82- -,1 21 124 --. 0)01 0)00000 0)00000 0)00000 2 0)00000 0)0000 0)04 0).20 1

2 2 0)-2 ,42 4,8 422 122 44 0)0-0 0)00001 0)00000 0)00000 0)00001 0)00008 0)0.1 0).- 1

2 - 0)0. 8,088 ,1 2 120 48 0)04 0)00001 0)00000 0)00000 8- 0)00001 0)00010 0)100 0).41 1

28 4 0). .,2 ,08 0)0000 0)000 0)00 8-1 120 .1 0)0- 0)00001 0)00000 0)00000 11- 0)00001 0)00012 0)10 0).4 1

2. 0). 10,18 ,48 0)002 0)8 0)0 1,0-4 2-8 1,22 0)088 0)00002 0)00001 0)00000 1 0)00002 0)0001 0)110 0).4 1

-0 0)82- 10,.1 ,.-- 0)00-8 1)22 0). 1,2- 2- 1,44 0)10 0)00002 0)00001 0)00000 188 0)00002 0)0001 0)11- 0).48 1

K K K K K K K K K K K K K K K K K K K K K

144 120 1)0.0 1.,144 ,. 0)028 .)-2 1)8 2-,.-2 4. 24,-.1 2)2- 0)0002. 0)0002 0)00001 4,0-2 0)000-2 0)0022 0)142 0).0 1

280 2 1)11. 20,14 ,881 0)042- 1-)- 1).0 4,8 -8 48,144 4)4 0)0008 0)00110 0)00001 8,11 0)000- 0)004-8 0)14 0).1 2

428 404 1)1-1 20,0 ,. 0)0-- 1)2. 1). ,4 1.2 ,.4 )4. 0)00082 0)0011 0)00002 11,2 0)0008. 0)001- 0)14 0).1 -

4 40 1)1-8 20,84 8,00. 0)01 20)00 2)02 84,440 0)0 84,440 8)118 0)00101 0)0020 0)00002 14,28 0)00111 0)008 0)14 0).1 4

-0 0 1)144 21,04 8,04 0)00 22)88 2)0 84,440 0)0 84,440 8)1 0)00101 0)00210 0)00002 14,.4 0)00111 0)00 0)14 0).1 4

1,0. 1,01 1)11 21,-20 8,0.- 0)088 28)1 2)1 84,440 0)0 84,440 8)20- 0)00101 0)00218 0)0000- 14,80 0)00111 0)001 0)148 0).2 4

-,0 -,2 1)1 21,84 8,18 0)18 1)44 2)41 84,440 0)0 84,440 8)2.. 0)00101 0)00244 0)0000 14,81 0)00111 0)0044 0)10 0).2 4

,-00 ,2 1)10 22,044 8,221 0)2218 1).8 2)8 84,440 0)0 84,440 8)--2 0)00101 0)0022 0)0000 14,.12 0)00111 0)0041 0)10 0).2 4

"asti%

Strai&

Cree'

Strai&

Shri&5a(e

Strai&

T$ta"

De#$rmati$&

i& i& i& i&

0)00000 0)00000 0)000000 0)0000

0)00000 0)00000 0)000000 0)0000.

0)00000 0)00000 0)000000 0)00014

0)00000 0)00000 0)000000 0)0001.

0)00000 0)00000 0)000000 0)00044

0)00000 0)00000 0)000000 0)000.

K K K K

0)00004 0)0000 0)000001 0)01842

0)00008 0)0001 0)000002 0)0-82

0)00012 0)00024 0)00000- 0)0-8 S=it%h t$ 9a&5 2 $ad

0)0001 0)000-0 0)00000- 0)014 S=it%h t$ 9a&5 - $ad

0)0001 0)000-1 0)00000- 0)0-00 S=it%h t$ 9a&5 4 $ad

0)0001 0)000-2 0)000004 0)0-4 St$' A''"yi&( 9a&5 4 $ad

0)0001 0)000- 0)000008 0)0828

0)0001 0)000-. 0)000011 0)088

7..2.2 Concrete Core Deformation Calculations

8.0 References



8.1 Energy-Based Design of Lateral Systems by W.F. Baker 270

8.2 Geotechnical Report for the Chicago Spire 27

E n e r g y - B a s e d D e s i g n o f L a t e r a l S y s t e m s8.1



W i l l i a m 1 . B a k e r

A s s o c . P a r t n e r

S k i d m o r e , O w i n g s & M e r r i l l

C h i c a g o , I L , U S A

\ V i l l i a m F . B a k e r i s a n A s s o c i a t e P a r t n e r

a n d S e n i o r S t r u c t u r a l E n g i n e e r o f S k i d -

m o r e , O w i n g s & M e r r i l l , C h i c a g o , I l l i n o i s ,

U S A . A s A d j u n c t P r o f e s s o r o f A r c h i t e c t u r e

h e a l s o w o r k s a t t h e I l l i n o i s I n s t i t u t e o f

T e c h n o l o g y . H e w a s i n v o l v e d i n a n u m b e r

o f s i g n i f i c a n t p r o j e c t s , a m o n g s t t h e m t h e

S e a r s T o w e r R e v i t a l i z a t i o n , C h i c a g o ( 1 9 8 5 ) ,

t h e 6 3 s t o r y A T & T C o r p o r a t e C e n t e r ,

C h i c a g o ( 1 9 9 0 ) , a n d m o r e r e c e n t l y , i n 1 9 9 2 ,

t h e U S G B u i l d i n g , a 3 5 s t o r y o f f i c e

b u i l d i n g i n C h i c a g o .

T h e o r e t i c a l B a s i s —

A x i a l M e m b e r s

F r e q u e n t l y i n t h e d e s i g n o f h i g h - r i s e

b u i l d i n g s , t h e s t r u c t u r a l d e s i g n e r w a n t s

t o u s e t h e m i n i m u m m a t e r i a l t o r e s i s t a

p r e s c r i b e d w i n d l o a d w i t h o u t e x c e e d i n g

a d e f l e c t i o n c r i t e r i a ( s u c h a s t i p d e f l e c -

t i o n ) . I n e s s e n c e , t h e e x t e r n a l w o r k d o n e

b y t h e w i n d l o a d h a s b e e n p r e d e f i n e d .

T h e t a s k t h e n i s t o p r o p o r t i o n t h e s t r u c -

t u r e s o t h a t t h e i n t e r n a l w o r k i s a t t a i n e d

w i t h a m i n i m u m v o l u m e s t r u c t u r e . W e

k n o w f r o m v i r t u a l w o r k m e t h o d s t h a t

t h e d e f l e c t i o n a t t h e t o p o f a b r a c e d

s t r u c t u r e ( F i g . 1 ) i s g i v e n b y

A

( 1 )

w h e r e F i s t h e f o r c e i n a m e m b e r d u e t o

t h e l a t e r a l ( w i n d ) l o a d s , L / E A a r e t h e

g e o m e t r i c a n d m a t e r i a l p r o p e r t i e s o f a

m e m b e r , a n d n i s t h e f o r c e i n t h e

m e m b e r d u e t o a u n i t v i r t u a l l a t e r a l l o a d

a p p l i e d a t t h e t o p .

E q u a t i o n ( 1 ) c o n t a i n s s o m e v e r y u s e f u l

B y m o v i n g t h e m a t e r i a l f r o m o n e

m e m b e r t o a n o t h e r , i t i s p o s s i b l e f o r a l l

m e m b e r s o f t h e s t r u c t u r e t o h a v e e q u a l

e n e r g y d e n s i t i e s .

N o w t h e q u e s t i o n i s w h e t h e r t h e r e -

s u l t i n g s t r u c t u r e i s a m i n i m u m v o l u m e

s t r u c t u r e . T h i s c a n b e i n v e s t i g a t e d u s i n g

L a G r a n g e I u l t i p l i e r s . T h e a p p r o a c h i s

t o m i n i m i z e t h e d e f l e c t i o n o f t h e s t r u c -

t u r e a s g i v e n b y

n F L

s u b j e c t t o t h e c o n s t r a i n t t h a t i t h a s a

c o n s t a n t v o l u m e o f m a t e r i a l ( V ) . T h i s

c o n s t r a i n t c a n b e f o r m u l a t e d a s

g = E A L - v = O

A c o n s t r a i n e d d e f l e c t i o n e q u a t i o n m a y

t h e n b e w r i t t e n a s

A = f + A g

S u b s t i t u t i n g f o r f a n g f r o m E q u a t i o n s

( 3 ) a n d ( 4 ) r e s p e c t i v e l y :

A = E

' f _ + A ( L 4 L - )

A b s t r a c t

T h e s i z i n g o f t h e m e m b e r s o f t h e l a t e r a l r e s i s t a n c e s y s t e m f o r m u l t i - s t o r y b u i l d i n g s

i s o f t e n c o n t r o l l e d b y s t i f f n e s s r e q u i r e m e n t s . I n o r d e r t o a c h i e v e e c o n o m i c a l

b u i l d i n g s , i t i s i m p o r t a n t t h a t t h e s e m e m b e r s b e a p p r o p r i a t e l y s i z e d a n d t h a t t h e

s t r u c t u r a l m a t e r i a l s b e e f f i c i e n t l y d i s t r i b u t e d a m o n g t h e v a r i o u s c o m p o n e n t s . T h i s

p a p e r p r e s e n t s a s i z i n g t e c h n i q u e u t i l i z i n g e n e r g y m e t h o d s t h a t i s c u r r e n t l y i n u s e b y

s e v e r a l f i r m s i n v o l v e d i n t h e d e s i g n o f h i g h - r i s e b u i l d i n g s .

W h e n X i s e q u a l f o r a l l m e m b e r s i n a

— '

s t r u c t u r e ,

t h e n t h e d e f l e c t i o n i s a

U n i t

L o a d

m i n i m u m f o r a g i v e n v o l u m e o f s t r u c -

t u r e o r , c o n v e r s e l y , t h e v o l u m e o f s t r u c -

> 1 k b

f o r a s t a t i c a l l y d e t e r m i n a t e s t r u c t u r e ,

w i l l

l e a d

t o a n o p t i m u m m a t e r i a l

d i s t r i b u t i o n f o r c e r t a i n t y p e s o f c r o s s

s e c t i o n s a n d i s a p p r o x i m a t e l y m i n i m a l



F i g . 1

£ Y L

J .

I f a s t r u c t u r e i s s t a t i c a l l y d e t e r m i n a t e , n ,

a n d F 1 a r e c o n s t a n t f o r a g i v e n s t r u c t u r e

a n d l o a d i n g . E q u a t i o n ( 7 ) t h e n r e d u c e s

t o :

- n F L .

E A

t u r e i s a m i n i m u m f o r a g i v e n d e f l e c t i o n .

B y c o m p a r i n g E q u a t i o n s ( 2 ) a n d ( 9 ) , i t

c a n b e s e e n t h a t f o r a s y s t e m o f a x i a l

m e m b e r s , t h e e n e r g y d e n s i t y e , i s i n f a c t

t h e L a G r a n g e M u l t i p l i e r f o r a s t a t i c a l l y

d e t e r m i n a t e s t r u c t u r e .

I t c a n b e d e r i v e d f r o m t h e a b o v e , t h a t

t h e o p t i m u m c r o s s - s e c t i o n a l a r e a s f o r a

s t a t i c a l l y d e t e r m i n a n t t r u s s c a n b e

d e t e r m i n e d f r o m t h e f o l l o w i n g e q u a -

t i o n :

( 8 )

( A i ) r e q = 1 : e q E 1 F 1 ) ° 5 ( E ( L 1 F n F 1

] O . 5 ) )

( 1 0 )

W h e r e A

q

i s t h e t a r g e t d e f l e c t i o n a n d

n , a n d F , a r e t h e v i r t u a l a n d r e a l f o r c e s

( 9 )

i n m e m b e r i , o b t a i n e d f r o m e i t h e r h a n d

c a l c u l a t i o n s o r c o m p u t e r c a l c u l a t i o n s

u s i n g a m o d e l w i t h a r b i t r a r y c r o s s -

s e c t i o n a l a r e a s .


F l e x u r a l M e m b e r s

A p a r a l l e l a p p r o a c h c a n b e a p p l i e d t o

f l e x u r a l s y s t e m s . T h e d e f l e c t i o n c o n -

t r i b u t i o n o f f l e x u r a l d e f o r m a t i o n s i s

g i v e n b y

E l

w h e r e

N I =

M m d u

M = M o m e n t

i n a m e m b e r d u e t o l a t e r a l l o a d

m =

M o m e n t i n a m e m b e r d u e t o u n i t l o a d c a s e

u

= N o n - d i m e n s i o n a l l e n g t h .

T h e i n t e g r a l i s w e l l k n o w n f o r e l e m e n t s

o r

n . F .

F 4

f o r o t h e r c r o s s s e c t i o n s .

T h i s c a n

b e s h o w n b y u s i n g t h e

L a G r a n g e M u l t i p l i e r a p p r o a c h . P a r a l -

l e l i n g t h e e q u a t i o n s f o r a x i a l m e m b e r s

p r o d u c e s —

L M

,

= — _ _ + A ( E A L - v )

1 4 )

T h e l o c a l e x t r e m u m i s f o u n d b y d i f -

f e r e n t i a t i o n .

a

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— =

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0 A 1

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d A 1

o r

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d l .

, . L . _ . . L

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2 - '

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"

F o r a r e c t a n g u l a r s h a p e o f c o n s t a n t

d e p t h ( h ) a n d v a r i a b l e w i d t h ( w ) :

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_ i - w h 3 = i h 2 A

= r 2 A

( 1 7 )

T h e r e f o r e ,

4 - L = 2

( 1 8 )

d A

a n d

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=

( 1 9 )

E i A .

w h i c h m a t c h e s

t h e

e n e r g y

d e n s i t y

( 1 1 )

( E q . 1 3 ) .

F o r r o l l e d U S s t e e l s h a p e s , t h e m o m e n t

o f i n e r t i a c a n b e e x p r e s s e d a s a l i n e a r

f u n c t i o n o f A .

I = a + b A

( 2 0 )

t h e r e f o r e ,

( 2 1 )

d A

N o m e n c l a t u r e

A = C r o s s - s e c t i o n a l

a r e a o f

m e m b e r i

a , b = L i n e a r

r e g r e s s i o n c o n -

s t a n t s

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= M o d u l u s

o f e l a s t i c i t y

e

=

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d e n s i t y

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f o r c e i n m e m b e r i

d u e t o l a t e r a l l o a d c a s e

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h e i g h t

=

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o f m e m b e r i

= M o m e n t

o f i n e r t i a o f

m e m b e r i

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=

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o f m e m b e r i

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= B a y s i z e

=

M o m e n t

i n m e m b e r i

d u e t o l a t e r a l l o a d c a s e

m 1 =

M o m e n t

i n m e m b e r i

d u e t o u n i t l o a d c a s e

=

A x i a l

f o r c e i n m e m b e r i

c a s e ,

a n d

1

d 1 1

F o r r e c t a n g u l a r s h a p e s , a =

1 a n d f o r

( 2 4 )

S e r i e s I = a + b A

R a n g e o f

A v e r a g e

a

a

a

b

i n 4 )

i n 2 )



r o l l e d s h a p e s , a i s g i v e n i n T a b l e I ( a =

1 . 3 i s a r e a s o n a b l e v a l u e f o r t h e d e s i g n o f

c o m m o n l y u s e d s h a p e s i n s t r o n g a x i s

b e n d i n g ) .

A s w a s d o n e f o r a x i a l m e m b e r s , t h e o p -

t i m a l c r o s s - s e c t i o n a l a r e a f o r a s t a t i c a l l y

d e t e r m i n a n t f l e x u r a l m e m b e r c a n b e

d e t e r m i n e d f r o m :

— 0 . 5

0 . 5

— 0 . 5

1

M .

a .

L . M .

( A

=

'

i / r e q

E

r

0 . 5

r e q

i

I X ,

T 1

T h e a b o v e a s s u m e s t h a t t h e r a d i u s o f

g y r a t i o n ( r ) i s c o n s t a n t f o r a m e m b e r a s

t h e m e m b e r s c h a n g e s i z e

( t h i s i s

a

r e a s o n a b l e a s s u m p t i o n a s l o n g a s t h e

m e m b e r s t a y s i n t h e s a m e s e r i e s ) .


G e n e r a l

B e a m E l e m e n t

F o r a g e n e r a l b e a m e l e m e n t , t h e p e r t i -

n e n t d e f o r m a t i o n s a r e a x i a l , m a j o r a x i s

f l e x u r a l , m i n o r a x i s f l e x u r a l , m a j o r a x i s

s h e a r , m i n o r a x i s s h e a r a n d t o r s i o n a l .

T h e a b o v e s i z i n g t e c h n i q u e s c a n b e e x -

t e n d e d t o i n c l u d e a l l o f t h e s e d e f o r m a -

t i o n s . A l t h o u g h i t i s c l e a r t h a t a x i a l

d e f o r m a t i o n s a r e a d i r e c t f u n c t i o n o f

t h e c r o s s - s e c t i o n a l a r e a , t h e o t h e r d e -

f o r m a t i o n s m e r i t s o m e d i s c u s s i o n .

I n r e c t a n g u l a r c r o s s s e c t i o n s o f c o n s t a n t

d e p t h , t h e m a j o r a n d m i n o r a x i s s h e a r

s e c t i o n p r o p e r t i e s a r e l i n e a r f u n c t i o n s

o f c r o s s - s e c t i o n a l a r e a a n d t h e s e f u n c -

t i o n s a p p r o a c h z e r o a s t h e c r o s s - s e c -

t i o n a l a r e a a p p r o a c h e s z e r o . T h e r e f o r e ,

a p r o c e d u r e s i m i l a r t o t h o s e a b o v e

s h o w s t h a t a u n i f o r m e n e r g y d e n s i t y

2 0 0 0 0

1 9 0 0 0

1 8 0 0 0

1 7 0 0 0

1 6 0 0 0

1 5 0 0 0

1 4 0 0 0

1 3 0 0 0

1 2 0 0 0

1 1 0 0 0

1 0 0 0 0

9 0 0 0

8 0 0 0

7 0 0 0

6 0 0 0

5 0 0 0

4 0 0 0

3 0 0 0

2 0 0 0

1 0 0 0

0

F i g . 2

d u c e d f r o m t h e s a m e r o l l e r , t h e m a j o r

a n d m i n o r a x i s m o m e n t o f i n e r t i a s a n d

t h e m a j o r a n d m i n o r a x i s s h e a r a r e a s a r e

a p p r o x i m a t e l y l i n e a r f u n c t i o n s o f a r e a .

T h e s i z i n g t e c h n i q u e s p r e v i o u s l y d e s c r i -

b e d c a n b e u s e d f o r t h e c o r r e s p o n d i n g

A r e a ( i n 2 )

D e s i g n

A k e y p a r t o f t h e a b o v e d i s c u s s i o n i s t h a t

t h i s m e t h o d p r o v i d e s t h e m i n i m u m

v o l u m e o f m a t e r i a l f o r s t a t i c a l l y d e t e r -

m i n a t e s t r u c t u r e s ( s i n c e t h e m e m b e r

W 1 4 x 6 1 — 8 2

— 5 9

3 9 . 1

1 . 0 7 t o 1 . 0 9 1 . 0 8

W 1 4 x 9 0 — 1 3 2

— 1 4 6 4 3 . 2

l . l O t o l . l 5

1 . 1 2

W 1 4 x 1 4 5 — 4 2 6 — 9 3 7 5 8 . 7

l . l l t o 1 . 4 7 1 . 3 0

W l 4 x 4 5 5 — 7 3 0

- 4 6 4 0

8 7 . 4

l . 3 l t o l . 6 3 1 . 4 7

W 1 8

— 2 0 8 6 8 . 2 l . O 9 t o 1 . 3 8

1 . 2 1

W 2 1

— 3 8 5 9 2 . 8 l . l O t o 1 . 4 3

1 . 2 3

W 2 4 — 6 2 6 1 2 1 l . l 2 t o l . 4 5 1 . 2 5

W 2 7

— 9 4 6

1 5 2 l . l 4 t o 1 . 3 2 1 . 2 2

W 3 0 — 1 6 7 4

1 9 3

1 . l 6 t o 1 . 4 1

1 . 2 9

W 3 3 — 2 0 7 5 2 2 9

l . l 4 t o 1 . 3 5 1 . 2 4

W 3 6

— 2 4 4 5

2 5 7

l . l 2 t o 1 . 3 1

1 . 2 0

T a b l e I

( 2 5 )

. ' 1 u u u

W 3 6

+

V A L U E S F R O M S T E E L T A B L E S

—

L E A S T S Q U A R E S F I T F O R

I

= a + b A

W 3 3

W 1 4

0

2 0 4 0 6 0

8 0

1 0 0

1 2 0 1 4 0

1 0 0

1 8 0 2 0 0 2 2 0

1 i n = . 5 4 c m

- 3 . ' '

- 3

A l l o f t h e s e b r a c i n g s y s t e m s c a n b e c o n -

s i d e r e d s t a t i c a l l y d e t e r m i n a t e f o r l a t e r a l

l o a d s . E v e n X - b r a c i n g , w h i c h i s n o r m a l -

l y c o n s i d e r e d t o b e i n d e t e r m i n a t e , i s

b a s i s , i t m a y s t i l l b e v e r y u s e f u l t o a p p l y

t h e t e c h n i q u e t o t h i s t y p e o f s t r u c t u r e .

A s t h e m a t e r i a l a n d l o a d s a r e t r a n s f e r -

r e d f r o m o n e l a t e r a l s y s t e m t o a n o t h e r i t

- 3

- 3

- 3

- 3

- 3

_ _ _ _ _



d e t e r m i n a t e f o r l a t e r a l l o a d s w h e n t h e

d e s i g n e r m a k e s b o t h d i a g o n a l s i n a

s t o r y t h e s a m e s i z e ( w h i c h i s n o r m a l l y

t h e c a s e ) .

A n o t h e r s y s t e m t y p e w h i c h i s m o r e

p r o b l e m a t i c , i s w h e r e t h e r e a r e p a r a l l e l

s y s t e m s o f d i f f e r e n t

t y p e s s u c h a s

p a r a l l e l t r u s s e s o f d i f f e r e n t d e p t h s o r

c o m b i n a t i o n s o f p a r a l l e l t r u s s e s a n d

m o m e n t f r a m e s . F o r t h e s e s y s t e m s t h e

f o r c e l e v e l s i n t h e i n d i v i d u a l m e m b e r s

w i l l c h a n g e a s t h e m e m b e r s i z e s a r e

c h a n g e d . T h e r e f o r e , t h e m e t h o d n o l o n -

g e r c a n b e a s s u r e d o f g i v i n g m i n i m u m

v o l u m e s t r u c t u r e . A l t h o u g h t h e t e c h -

n i q u e n o l o n g e r h a s a c l e a r t h e o r e t i c a l

i s c o m m o n t o h a v e n e g a t i v e e n e r g y d e n -

s i t i e s .

T h i s o f t e n i n d i c a t e s t h a t t h e

m e m b e r s s h o u l d b e r e m o v e d f r o m t h e

s y s t e m . I f t h e i n t e r a c t i o n s c o n v e r g e o n a

r e a s o n a b l e s t r u c t u r e , i t u s u a l l y m u c h

l e s s r e d u n d a n t t h a n t h e i n i t i a l s t r u c t u r e .

T h e L a G r a n g e \ I u I t i p l i e r m e t h o d o l o g y

c a n a l s o b e a p p l i e d t o s u b s y s t e m s s u c h

a s a b e a m a n d c o l u m n a s s e m b l a g e ( F i g .

6 ) .

F o r t h i s s y s t e m , t h e c o n s t r a i n e d

d e f l e c t i o n e q u a t i o n f o r f l e x u r a l d e f o r -

m a t i o n i s a s f o l l o w s :

H 2 I H

i i

P j [ -

+ j +

( A H + A 6 l - v )

— 1

d I g

—

2

c i A

g

F o r r e c t a n g u l a r c r o s s s e c t i o n s

b e c o m e s :

1

r

W h e r e r a n d r a r e t h e r a d i i o f g y r a t i o n

f o r t h e g i r d e r a n d c o l u m n , r e s p e c t i v e l y .

F o r r o l l e d s h a p e s , E q u a t i o n 2 9 b e -

c o m e s :

I

b

0 . 5

. 1 = _ (

( 3 1 )

I

b

W h e r e

b g

a n d

b

c a n

b e t a k e n f r o m

- 3

- 3

- 3

- 3

I

h .

i g . 3

I

I .

.

I . 1 .

. T h e

n e x t c o n d i t i o n t o b e e x a m i n e d i s

w h e n t h e r e a r e m u l t i p l e p a r a l l e l l i n e s o f

b r a c i n g i n a b u i l d i n g ( F i g . 5 ) . T h i s i s t h e

t y p i c a l c a s e f o r b r a c i n g w h i c h i s a d j a -

c e n t t o c o r e e l e m e n t s s u c h a s e l e v a t o r

s h a f t s

a n d s t a i r w e l l s . A l t h o u g h t h e s e

a .

b . c .

d .

e .

f .

e l e m e n t s s h a r e t h e l a t e r a l s h e a r s a n d

F

4

m o m e n t s i n a s t o r y , t h e y o f t e n a r e p r o -

i g .

p o r t i o n e d o n a b a s i s o f t r i b u t a r y w i n d

l o a d . T h e r e f o r e , a s t h e y a r e s i m u l t a -

n e o u s l y r e s i z e d , t h e f o r c e s i n t h e m d i -

B r a c i n g

v i d u a l m e m b e r s d o n o t c h a n g e s i g n i -

( T y p . )

f i c a n t l y a n d b e h a v e a s t h o u g h t h e y w e r e

s t a t i c a l l y d e t e r m i n a t e .

F l o o r

P l a n

F i g . 5

• 1

I C

I l

4 I : -

- - - A . -

F i g . 6

C o l u m n : I , r , b

G i r d e r : ' g ' r g , b g

W h i c h r e d u c e s t o :

1 2 E 1 2 d A l 2 E j 2 d A

C

g

o r

1

d I

2 d A

( 2 7 )

( 2 8 )

( 2 9 )

t h i s

( 3 0 )

D i s p l a c e m e n t

( P r o p e r t y )

f ( A )

d

d A

L a G r a n g e

M u l t i p l i e r

E n e r g y

D e n s i t y

A x i a l

E l o n g a t i o n

( A )

A

1

F n

E A 2

,

F n

E A 2

M a j o r A x i s

F l e x u r e

A h 2

1 2

h 2

1 2

M

E I A

,

M

E J A

8.2 Geotechnical Report for the Chicago Spire



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structural design project of super tall building chicago spire

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