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Figure 1: Typical Floor Layout for Design Purposes ...................................................................................... 5

Figure 2: Area Considered in Wind Load Calculations .................................................................................. 7

Figure 3: Price Comparison of Floor Systems – from PCA ............................................................................ 8

Figure 4: Drop Panel Dimensions for 1st and 2nd Interior Columns ............................................................ 9

Figure 5: SAP Model .................................................................................................................................... 12

Figure 6: Effective Slab Dimensions ............................................................................................................ 13

Figure 7: Location of Wind Load Application .............................................................................................. 14

Figure 8: Distributed Dead Load Application .............................................................................................. 15

Figure 9: Point Dead Load Application ........................................................................................................ 15

Figure 10: Live Load Application ................................................................................................................. 15

Figure 11: Deflection Envelope (at 100x mag.) ........................................................................................... 16

Figure 12: Labeled Locations of Critical Moment ....................................................................................... 17

Figure 13. Location of Edge Beam Along Grid BC ....................................................................................... 19

Figure 14. Frame Design Locations ............................................................................................................. 20

Figure 15. Frame 3 SAP Model Moment Diagram ...................................................................................... 24

Figure 16. Labeled Locations of Critical Moment ....................................................................................... 27

Figure 17: Illustration of columns to be designed .....................................................................................40

Figure 18: Interior Column Longitudinal Reinforcement ...........................................................................43

Figure 19: Exterior Column Longitudinal Reinforcement ...........................................................................43

Figure 20: Interior Column P-M Interaction Diagram ................................................................................44

Figure 21: Exterior Column P-M Interaction Diagram ................................................................................45

Figure 17: Shear Wall Cross-Section ........................................................................................................... 45

Figure 18: Shear Wall P-M Interaction Diagram ......................................................................................... 46

Drawing 1: East-West Negative (Top) Reinforcement ................................................................................ 31

Drawing 2: East-West Positive (Bottom) Reinforcement ........................................................................... 32

Drawing 3: North-South Negative (Top) Reinforcement ............................................................................ 33

Drawing 4: North-South Positive (Bottom) Reinforcement ........................................................................ 34

Drawing 5: Cantilever Beam Reinforcement in Column Strip ..................................................................... 35

Drawing 6: Cantilever Beam Reinforcement in Middle Strip ...................................................................... 36

Drawing 7: Beam Elevation ......................................................................................................................... 37

Drawing 8: Beam Section ............................................................................................................................ 38

Drawing 9: Reinforcement Interaction in Column Core ............................................................................. 39

Drawing 10: Interior Column Reinforcement ............................................................................................. 43

Drawing 11: Exterior Column Reinforcement ............................................................................................. 44

Drawing 12: Shear Wall Plan View Reinforcement ..................................................................................... 47

Drawing 13: Shear Wall Corner Reinforcement .......................................................................................... 48

Drawing 14: Shear Wall Section View Reinforcement ................................................................................ 49

Table 1: System Cost Comparison ............................................................................................................... 10

Table 2: Effective Width and Moment of Inertia in Regions of Negative and Positive Moments .............. 13

Table 3: Wind Loads Applied to Frame ....................................................................................................... 14

Table 4: Dead and Live Loads Applied to Structure .................................................................................... 14

Table 5: Load Combinations Considered .................................................................................................... 15

Table 6: Maximum Moment Values at 3rd Story ........................................................................................ 17

Table 7: Column Axial Loads and Moments ................................................................................................ 17

Table 8: Shear Wall Axial Loads and Moments ........................................................................................... 18

Table 9. Frame 1 Column and Middle Strip Moment Values ...................................................................... 21

Table 10. Frame 1 Reinforcement Requirements ....................................................................................... 22

Table 11. Frame 2 Column and Middle Strip Moment Values .................................................................... 23


Table 13. Frame 3 Column and Middle Strip Moment Values .................................................................... 25

Table 14. Frame 3 Column Strip Distribution to Slab and Beam ................................................................ 25


Table 16. Maximum Moment Values at 3rd Story ...................................................................................... 27

Table 17. Frame 4 Moment Distribution .................................................................................................... 28


Table 28: Maximum Axial Loads and Moments .........................................................................................41

Table 29: P-M Interaction Values ...............................................................................................................44

Table 30: Final Column Design Summation ...............................................................................................45

Introduction

We were given the task of designing the new Engineering Education Research Center (EERC) South

Tower. This building has two concrete towers that are connected by a steel framed atrium in the middle.

This building is to be located south of the Ernest Cockrell Jr. Hall (ECJ) and north of W.R. Woolrich

Laboratories (WRW) on the north side of the University of Texas at Austin campus. The south tower is

separated from the rest of the structure by expansion joints, therefore allowing the design for this

structure to be separate from the rest of the EERC. The objective of this project is to design a regular

slab system portion of the floor, one regular exterior and interior column as well as the shear wall, all

designed at the third floor. The portion of the floor to be designed is shown below in red in Figure 1.

This slab pattern repeats throughout the rest of the floor and the rest of the tower. The shear wall to be

designed is in green at the center of the building as shown in Figure 1.

Figure : Typical Floor Layout for Design Purposes

For the scope of this project, wind loads were only applied in the North-South direction, which is the

weak direction of the building since those are the largest sides of the tower. Also, the analysis of the

structure was allowed to be done using 2D frames in the North-South direction. Since the steel structure

that connects the North and South towers is sensitive to deflections, the largest deflection allowed is

h/800, where h is the height of the building. To better investigate framing options, two options were

researched and priced to compare and yield a final system to then analyze using SAP and prepare a

complete design. There were several codes used to help aid in the final design of the South tower. The

ACI 318-14 was used for the reinforced concrete design, and ASCE 7-10 and IBC 12 were referenced for

the wind loads and live loads. As an addition, the UT Austin Structural Criteria was used to supplement

the live loads so we also met their requirements since UT is the owner.

The following sections describe the design steps the team took to arrive to the final solution.

Loads

To begin the analysis of loads on the building, we looked at the live loads as well as wind loads being

applied to our framing section. For both loading cases, we took a more conservative approach to end up

with a more conservative design.

Live Loads

To consider the live loads acting across our floor, we looked at IBC 2012 and ASCE 7-10 to find the live

loads that corresponded with the usage of the space within our section. In addition to these sources,

we found that The University of Texas has its own building code as well, which is more conservative than

either of the previously considered codes. Since this is a building for the university, and the loads are

more conservative, we will be using the loads from The University of Texas’ building codes. From this,

we yield a live load of 80 psf on the office space, one of 100 psf on the corridor, and one of 80 psf on the

lab space.

Within the project description, it was specified that an additional live load of 25 psf be added to any

space that did not already have a live load of 100 psf or greater. As a result, we decided to add a portion

of the partition load to both the 80 psf office space and 80 psf lab space. We increased the load being

analyzed in these section to create an even load across the floor of 100 psf. We chose not to add the

entire partition load due to our use of an already conservative load as well as having the same load

across the entire floor makes the analysis simpler.

In the end, we ended up with an overall live load across the floor of 100 psf.

Wind Loads

In our problem statement, we were to consider wind loads only acting in the N-S direction, which we did

using specifications from ASCE 7-10. The first step towards calculating the wind loads was to determine

the tributary area acting on the frame of the buildings. This was done by taking half of the height of the

elevation below in combination with half the height from the elevation above, and multiplying by the

width of one of the 21’ bays. The next step was assessing the risk category of the building. Since the

EERC is an adult educational facility (college), the building was found to be of risk category III. Once the

risk category was determined, the next step was to find the basic wind speed for Austin, Tx. This was

found to be 120 mph.

The EERC design we used was a Main Wind Force Resisting System, therefore we had a Wind

Directionality factor of 0.85. The following wind load parameter considered was the surface roughness

category. The EERC is located in an urban area so it was fond to be classified as surface roughness B,

which in turn lead to an exposure category of B.

The default condition of the topographic factor is 1, and considering our building to be a rigid structure,

we had a gust effect factor of 0.85. Our design was also considered to be for an enclosed structure,

leading to an internal pressure coefficient of ± 0.18.

To analyze the wind load, we assumed the ground line to be horizontal at the building's lowest

point. The ground is actually sloped, so by considering it flat at the lowest point we calculate a more

conservative wind load, and account for the largest open face of the building. A representation of the

area we considered is outlined in red in Figure 2.

Considering a flat ground, we calculated the velocity pressure exposure coefficient at each floor of the

building we were to design. Using the Kz value found for each floor, the velocity pressure for each floor

was calculated. Using L/B to calculate the wall pressure coefficient acting on the leeward wall, it was

found that Cp was -0.5, with a constant windward wall pressure coefficient of 0.8 (standard).

Then, following the code of ASCE 7-10, the wind pressure being applied at each floor was found. Using

the wind pressure found and multiplying it across the tributary area of the wall we found the total force

being applied to our frame.

We ended up with a total windward force of approximately 55 kips, and a leeward force of -41 kips. The

spreadsheet for this design can be found in Appendix A.

Figure : Area Considered in Wind Load Calculations

Framing Selection

To pick the final flooring system, the team had to first research system options and select two to

prepare an initial design to use to compare them. The purpose of this process was to find the most

effective framing system. We relied on a paper published by the Portland Cement Association that

compared the price of different framing systems across multiple spans for a live load of 100 psf, which is

exactly what is going to be applied to our system. Our original hypothesis was that 1-way joists and 2-

way flat slab were going to be the cheapest options. The paper proved that our hypothesis was half

right. Joists are mainly economical in longer spans of around 30 ft, which took them out as an option

since none of the spans are that long. The paper also explained that flat plate is not possible since it is

only economical in small spans of 20 ft, which are smaller than any of the spans in this project. Once

these two were eliminated as options, only flat slab and 2-way slab with drop beams were left as

options. Pictured below in Figure 3, is an image taken from the PCA publication. The graph depicts the

cost comparison between the each of the framing options per span length.

Figure : Price Comparison of Floor Systems – from PCA

The preliminary sizing of the two options was done using ACI 318-14. For both options, a 4000 psi

strength concrete was originally chosen, although it was changed later in the design process to 5000 psi.

To calculate preliminary column dimensions, this equation was used: . This yielded an initial column

dimension of 28 inches. It was very apparent that this dimension was too large, but was later refined

based on more rigorous structural analysis and calculations.

For the drop beam option, the beam depth was calculated to be 8 inches according to clause 7.3.1.1.

Even though this table is for one-way slabs, it gave an estimate of the depth that could be used to

calculate an initial αfm. Using this depth and the calculated αfm, Table 8.3.1.2 yielded a slab depth of 7

inches. The beam width was chosen to match the column width according to the architectural drawings

since the calculated column dimensions seemed inappropriately large.

For the flat slab with drop panels, the minimum slab depth was 10 inches according to 8.3.1.1 as well.

For the drop panel dimensions and depth, clause 8.2.4 was used. The drop panel depth came out to be

2.5 inches. The preliminary dimensions of the drop panels were calculated using 8.2.4.

These original dimensions are the minimum dimensions needed for each option. They do not represent

what the member needs in terms of strength or deflection since no analysis had been done at that

point. Using these minimum dimensions and RSMeans, a preliminary cost estimate was made to

compare the effectiveness of the two floor systems as will be outlined later in this section. The initial

cost analysis results showed that the flat slab with drop panel was the cheapest option, even though

later calculations showed otherwise. For this reason though, we chose to go with the flat slab with drop

panels.

Initial Sizing: After selecting a flat slab system with drop panels, the next step was to perform punching

shear calculations in order to determine the actual required depth and dimensions of the drop panels.

During preliminary design we had used the minimum dimensions required by ACI 8.2.4 in order to be

considered a drop panel.

In order to provide adequate resistance to two-way punching shear without drop panels using 4000 psi

concrete a slab thickness of 12 inches would be required. Increasing the concrete strength to 5000 psi

would allow us to reduce the slab thickness to 11 inches. As expected a flat plate system without drop

panels would require a slab thickness much greater than the 10 inch (ln/33) slab allowed by ACI 8.3.1.1

for a beam with drop panels but without edge beams. The addition of an edge beam would allow the

slab thickness to be further reduced to 9 inches (ln/36).

A 9 inch slab depth was selected. The required drop panel dimensions to resist two-way shear were

then determined. The minimum drop panel dimensions are required to be at least 1/6th of the center to

center span by ACI 8.2.4. We rounded the required dimensions to the nearest foot for ease of design

and construction. The resulting dimensions for the first interior column and second interior column are

shown in Figure 4 respectively.

Figure : Drop Panel Dimensions for 1st and 2nd Interior Columns

Two way shear calculations were then performed at both critical locations. The first critical location is

the perimeter of the rectangle d/2 away from the face of the column. The second critical location is the

perimeter of the rectangle d/2 away from the drop panel where the drop panel comes into contact with

the slab.

Adequate shear resistance is provided by the slab at the first critical location; therefore, a 9 inch slab will

suffice. A drop panel depth of 3.5” will provide adequate shear resistance to resist two-way shear at the

second critical location. This exceeds the minimum depth of 2.5” (slab thickness/4) required by ACI

8.2.4. See Appendix page C for detailed calculations.

Initial Cost Analysis

Preliminary cost analysis was performed on the two most likely eligible floor system options; Flat slab

with drop panels, and two-way slab and beam systems. The cost analysis described in this section is a

summary of only our preliminary estimations. A more detailed cost calculation for our final system can

be found later in the report with a more detailed methodology of calculation.

For each of these options, RS Means was used to estimate the cost of each system by dividing them

between the costs of their concrete, steel, and formwork. The spreadsheet for each of these systems’

cost estimation can be found in Appendix L. Overall, the cost of concrete and formwork were the driving

costs of both systems. An overall cost breakdown of each of these options can be found in Table 1.

Table : System Cost Comparison

As can be seen, the preliminary data shows that the two-way slab and beam system is the cheaper

option.

Unfortunately, this conclusion was drawn after we found various mistakes in our cost estimation and

were already well down the path of designing for a flat slab with drop panels. As such, we decided to

continue our pursuit of a flat slab with drop panels and consider our initial cost mistakes as lessons

learned.

Practical Consideration in Framing Selection

While the flat slab with drop panel system may not be exactly the most cost efficient option, there are a

number of other benefits for a flat slab with drop panels. Namely, the constant which relates beam

stiffness to slab thickness, , is zero because of having no interior beams. This allows for an easier

interpolation of Tables 8.10.5 which determine how much of a moment enter the column strip versus

the middle strip. Additionally, having no interior beams means that the column strip moment is resisted

solely by the slab which entails less flexural design than if there were a beam. So overall, there is an

increased ease of design for a flat slab with drop panels.

Structural Analysis

We determined the design axial, shear, and moment values for all design calculations using analysis

performed in SAP2000. In the following section, we will discuss the assumptions made in creating our

SAP model and the resulting output.

SAP Model

We modeled all nine stories of the building in SAP assuming the base of the structure to be fixed, as

shown in Figure 5. The first three floors were pinned against lateral translation due to rigid walls in the

building’s substructure. Levels three and above are assumed to be laterally independent of the

substructure. In addition to modeling the spans that we were specifically outlined in our scope, we also

modeled one additional span to ensure that the interior span would be treated as an interior span by

SAP.

Figure : SAP Model

Because we are using a flat slab system without beams we are modeling the slab as a line element with

a depth of 9 inches, and a width equivalent to the portion of the slab acting as a beam. The moment of

inertia of this slab-beam section was also reduced to more accurately reflect the actual stiffness of the

structure. The effective slab width and associated effective moment of inertia were based on

suggestions from Wight and MacGregor, and are outlined in Table 2. The effective slab dimensions are

outlined in red in Figure 6.

Region Effective

Width

Effective Moment

of Inertia

M- Exterior 0.2L 0.33*Ig

M+ 0.5L 0.5*Ig

M- Interior 0.5L 0.33*Ig

Table : Effective Width and Moment of Inertia in Regions of Negative and Positive Moments

Figure : Effective Slab Dimensions

Nodes were placed in the effective slab beam indicating the exterior bounds of each drop panel. The

member thicknesses in the regions bounded by these nodes were increased to 12.5 inches to reflect the

added depth created by the drop panel. The boundary between negative and positive moment used in

defining the effective width and effective moment of inertia were assumed to occur at the boundary of

each drop panel.

The shear wall was modeled as a column line element. The specific cross-section was defined using the

section designer. Only the exterior box surrounding the elevator core was used to resist lateral loads for

reasons that will be described in the shear wall design section of this report. Diaphragm constraints

were applied to the beam-column intersection nodes at each level in order to create a rigid diaphragm

that axially transfers the lateral load through the slab. To ensure that the lateral load would be

transferred from the slab to the shear wall, a rigid beam with a stiffness modification factor of 2000 was

used to attach the frame to the shear wall. End releases were applied to the rigid beam to ensure that

only lateral forces, not moments, would be transferred to the shear wall. Only the lateral wind loads

acting on the frame, as opposed to all ten frames along the length of the structure, were applied to the

SAP model. As a result, the stiffness of the shear wall was reduced to 10% of its total stiffness. The wind

loads applied to the structure for analysis purposes are tabulated in Table 3.

Story Load

9 12.09

8 16.14

7 12.31

6 12.01

5 11.67

4 11.21

3 10.74

2 10.09

1 9.16

0 4.55

Table : Wind Loads Applied to Frame

The magnitude and location of all dead and live loads applied to the model have been summarized in

Table 4. See Appendix B to see all corresponding calculations. Figures 8 and 9 depicts the distributed

and concentrated dead loads being applied to the structure respectively. Figure 10 depicts the live load

being applied to the structure. The self-weight multiplier for all load cases was set to zero to avoid

double counting the structure’s self-weight.

Load Type Description Magnitude of Load

Dead Self-weight of slab + additional DL (25 psf) 2.889 k/ft

Dead Self-weight of slab & drop panel + additional DL (25 psf) 3.193 k/ft

Dead Self-weight of edge beam 4.725 k

Dead Self-weight of interior column 8.975 k

Dead Self-weight of exterior column 5.048 k

Dead Exterior façade load 3.150 k

Live Occupancy LL (100 psf) 2.100 k/ft

Table : Dead and Live Loads Applied to Structure

Figure : Distributed Dead Load Application

Figure : Point Dead Load Application

Figure : Live Load Application

The load combinations tabulated in Table 5 from ACI 5.3.1 were considered in our analysis:

Load Combinations

U = 1.4D

U = 1.2D + 1.6L

U = 1.2D + 1.0W + 1.0L

U = 0.9D + 1.0W

Table : Load Combinations Considered

Patterned loading was not considered. As per provision 6.4.3.2 of ACI 318-14, the maximum moments

can be assumed to occur when the live load is applied simultaneously across all spans if 75% of the dead

load is greater than 100% of the live load. This condition was satisfied as shown:

P-delta effects were considered by converting the analysis type for each load case to nonlinear and

selecting P-delta as the geometric non-linearity parameter in the load case data window.

Analysis Output

The 0.9D + 1.0W load combination was found to control in regards to deflection. The total maximum

deflection over the height of the building was 0.45 inches, as shown in Figure 11. This lies well within

the h/800 total deflection requirement, where h is the height of the structure from the base of the 3rd

story to the top of the building.

Figure : Deflection Envelope (at 100x mag.)

The maximum positive moment was found to occur on the exterior span (location 3, Figure 12) and

correspond with the 1.2D + 1.6L load combination. The maximum negative moment was found to occur

at the exterior face of the first interior column (location 4, Figure 12) and was also found to correspond

with the 1.2D + 1.6L load combination. The maximum moment at each critical location shown in Figure

12 is tabulated in Table 6. These were the values that were used in flexural design.

Figure : Labeled Locations of Critical Moment

Location 1 2 3 4 5 6 7

Moment (k-ft) 44.10 255.56 268.10 589.58 338.40 127.39 298.54

Shear (k) 20.44 -83.66 - 105.76 -76.71 - 72.40

Table : Maximum Moment Values at 3rd Story

The maximum axial load and moment on both the exterior and interior columns for each load

combination were determined through SAP analysis. Table 7 summarizes the output obtained from SAP.

Notice that the maximum axial load occurs for both the exterior and interior columns corresponds with

the 1.2D + 1.6L load combination. Likewise the maximum moment also corresponds with the 1.2D +

1.6L load combination. These axial loads and moments were then utilized in the design of each column.

Their use will be described in depth in the column design section of this report.

1st Story

Interior Exterior

Load Combination Axial Load [k] Moment [k-ft] Axial Load [k] Moment [k-ft]

1.4D 970 65 546 53

1.2D + 1.6L 1444 106 812 90

1.2D + 1.0W + 1.0L 1214 88 683 73

0.9D + 1.0W 624 43 351 34

3rd Story

Interior Exterior


1.4D 649 78 365 64

1.2D + 1.6L 965 127 543 110

1.2D + 1.0W + 1.0L 812 107 456 89

0.9D + 1.0W 417 52 235 41

Table : Column Axial Loads and Moments

The maximum axial load and moment acting on the shear wall were also determined using SAP analysis.

Table 8 summarizes the output obtained from SAP. The maximum axial load corresponds to the 1.4D

load combination, while the maximum moment corresponds to the 0.9D + 1.0W load combination.

These axial loads and moments were utilized in the design of the shear wall. Their use will be described

in greater depth in the shear wall design portion of this report.

1st Story 3rd Story


1.4D 2040 1 1400 1037

1.2D + 1.6L 1748 1 1200 1620

1.2D + 1.0W + 1.0L 1748 2 1200 2557

0.9D + 1.0W 1311 2 900 3236

Table : Shear Wall Axial Loads and Moments

Floor System Design

From the comparison of different floor systems, we felt confident moving forward with a flat slab with

drop panels, but added an edge beam along Grid BC in order to assist with the large perimeter cladding

load. The location of the edge beam is shown in red in Figure 13. The following section will outline the

design process for the two-way slab and perimeter beam.

Figure . Location of Edge Beam along Grid BC

Two-Way Slab Design

Slab Thickness: The minimum slab thickness was first estimated using the minimum thickness for one-

way slabs without interior beams as outlined in ACI Table 7.3.1.1. Considering the longest span, 28’3”,

and the smallest column dimension, 18”, Ln/36 yielded 8.92” as a minimum thickness.

Using this criteria, a trial thickness of 9” was used to more clearly calculate the minimum thickness at

the edge beam. With a slab thickness of 9”, more complete calculations for could be calculated for the

interaction between the edge beam along Grid BC and the slab. was calculated to be 0.846 so the

minimum thickness was the maximum of equations (b) and (c) from ACI Table 8.3.1.2. Equation (b)

controlled with a minimum thickness of 7.21 inches. The calculations for and the minimum thickness

can be found in Appendix D.

After calculating a minimum thickness of 8.9” from Table 8.3.1.1, and 7.21” from Table 8.3.1.2, 9” was

taken as the final slab thickness.

Edge Beam Dimensions: The edge beam along Grid BC was dimensioned using ACI Table 9.3.1.1 with the

depth being limited to Ln/21. This gave a depth of 18”. Additionally, because the value (=0.846) is

greater than 0.8, the beam is allowed to be considered an edge beam per ACI Table 8.3.1.1, Footnote 4.

The beam width was also taken as 18” in order to match the width of the column and limit formwork.

Frame Layout: For the floor slab design, the direct design method was employed in order to design four

separate two-way slab frames. The frames designed for, as outlined in Figure 14, include three frames in

the East-West direction, as well as one frame in the North-South direction. Three frames were designed

for in the East-West direction due to their varying perpendicular spans causing different geometry and

loading conditions.

Figure . Frame Design Locations

For purposes of this report, the frames will be referred to as follows:

Frame 1 – E-W frame shown in yellow in Figure 14.

Frame 2 – E-W frame shown in green in Figure 14.

Frame 3 – E-W frame shown in blue in Figure 14.

Frame 4 – N-S frame shown in red in Figure 14.

The direct design method was used for the design of Frames 1 and 2 because they met the following

criteria as outlined in ACI 8.10.2:

• Minimum of three spans in each direction (assuming the North-South frame is continuous).

• Span lengths differed by less than 1/3 the longer span in each direction.

• Panels are rectangular with perpendicular span ratios being less than two.

• There are not column offsets within scope.

• All loads are distributed gravity loads.

• Unfactored live load is less than twice the unfactored dead load.

• There is not a given panels with beams on all sides (ACI 8.10.2.7 does not apply).

Frame 1

The spread sheet for this design can be found in Appendix E.

Loading: For the design of Frame 1, the direct design method was used. The first step is to determine

the loading conditions on this frame. In order to do so, the statical moment, Mo, was calculated. This

statical moment was then multiplied by coefficients from ACI Table 8.10.4.2. Because this frame is

entirely interior spans with no interior beams or an edge beam at the end of this span, the coefficients

were 0.7 for the negative moment (at supports), and 0.52 for the positive moment (at midspan).

The moment at each location was then divided between the column and middle strips. was found to be

0.94 for this frame. As such, ACI Tables 8.10.5.5 and 8.10.5.1 were interpolated to find the percentage of

the moment transferred to the column strip at each location. A summary of these forces can be found in

Table 9.

Table . Frame 1 Column and Middle Strip Moment Values

Geometry: Because of the different perpendicular spans on both sides of the centerline of Frame 1, the

perpendicular span, L2, was taken as the average of the two spans. This wound up controlling in the

determination of the strip geometry. The maximum column strip width for Frame 1 was found to be 1/4

of twice L2 at 107.5” (about 9’). The middle strip was taken as the remainder of the perpendicular span

which was the same width.

Flexural Design: The next step was the flexural design of the slab. For Frame 1, four separate flexural

designs were performed. For simplification purposes, the additional flexural capacity at the supports

from the increased depth of the drop panel was not considered.

For the flexural design, the minimum reinforcement for flexural capacity was found and reinforcement

was prescribed. This reinforcement was then checked to ensure that the design met all requirements for

ensuring tension control (As max) and cracking control (As min). The final factored moment capacity

(including the phi factor) was then checked against the moment acting on the given area to ensure

strength capacity.

In general, the spacing was limited to factors of 2” for ensure constructability. Also, the middle strip

reinforcement design was chosen considering the middle strip for both adjacent frames to ensure clarity

in detailing and constructability.

For Frame 1, the final needed reinforcement can be found in Table 10.

Table . Frame 1 Reinforcement Requirements

Detailing: Once the reinforcement is designed, the detailing was calculated to cut down on the amount

of reinforcement needed, reducing the overall cost of the building. Since Frame 1 runs in the E-W

direction, the portion we considered is continuous at both ends, allowing us to use Figure 8.7.4.1.3a

from ACI 318-14. In doing so, we found the minimum lengths of reinforcement. Since the negative

reinforcement in the middle strip is 10” longer than the shorter reinforcement in the column strip (these

details can be found in Appendix I), we made both bars cut off at 10’ – 6” for ease of construction, as

shown in Table 11 below. The detail for Frame 1 can be found on Drawing 1 and Drawing 2 for negative

and positive flexure, respectively.

Table : Frame 1 Reinforcement Lengths

Additionally, in accordance with ACI 8.7.4.2.2, two of the bottom (positive) reinforcement bars pass

through the region of the column bounded by the longitudinal reinforcement of the column. The detail

for this parameter can be found in Drawing 9, and the example calculations for the reinforcement

detailing for Frame 1 can be found in Appendix I.

The lap splice lengths for the bottom bar sizes in Frame 1 can be found in Table 12 below, and

calculations along with an excel sheet for this can be found in Appendix I. When splicing, we stayed

within the boundaries given by the size of the negative reinforcement per Figure 8.7.4.1.3a in ACI 318-

14 as well as staggered the splicing every other bar to avoid creating critical stresses within the slab.

However, we maintained a central location for the staggered splicing so that splices of different lengths

have the same central location and still abide by specifications set in ACI. This splicing strategy is the

same for Frame 1 and Frame 2.

Table : Frame 1 Lap Splice Length

Frame 2

The spreadsheet for the design of Frame 2 can be found in Appendix F.

Loading: Overall, the design process for Frame 2 was very similar to Frame 1. Using the direct design

method, the loading analysis began with the calculation of the statical moment which was then

multiplied by 0.7 for the negative moments at supports and 0.52 for the positive moments at midspan.

The moments were then distributed to the column and middle strips per ACI Tables 8.10.5.5 and

8.10.5.1. This distribution is outlined in Table 13.


Geometry: The strip geometry is the major aspect in which Frame 2 differed from Frame 1. Similar to

Frame 1, the differing perpendicular spans lead to L2 being taken as the average of the two spans.

Because this was relatively short, the maximum column width was controlled as 1/4 of twice the span

along the frame at 114” (about 9 ½’). The middle strip was the remainder of L2 at 156.5” (about 13’).

Flexural Design: Flexural design was performed for each moment location along the frame’s column and

middle strips similar to Frame 1. The required strength reinforcement was required and checked against

cracking control, tension control, and actual moment capacity.

One location of unique design was the column strip of the internal negative moment. Here, the required

As for strength was greater than the maximum As to ensure the section is tension controlled. In order to

alleviate this, the additional depth of concrete from the drop panel was considered in the flexural design

which decreased the As required for strength which is outlined as permissible in ACI 8.5.2.2. A summary

of the required reinforcement for Frame 2 can be found in Table 14.


Detailing: The design of the detailing for Frame 2 was designed to be the same as Frame 1. Since the

governing factor for bar cutoff is the clear span, and the clear span is the same between Frame 1 and

Frame 2, we ended up with the same detailing. The minimum requirement for bar length can be found

in Appendix I, and the bar length we ended up using can be shown in Table 15 below.


Similar to frame 1, instead of using the 9’ – 8” bar length for the shorter reinforcement, we again

increased the length of those bars to be 10’ – 6” to match the middle strip bar length for ease of

constructability. Additionally, we needed two of the bottom (positive) reinforcement bars to pass

through the region of the column bounded by the longitudinal reinforcement of the column per ACI

8.7.4.2.2. An example of this can be found in Drawing 9. Example calculations of the detailing can be

found in Appendix I.

The lap splice lengths for Frame 2 abide by the same parameters stated for Frame 1. The splice lengths

for Frame 2 based on bar size are given in Table 16 below, while excel sheets for the calculations can be

found in Appendix I.

Table : Frame 2 Lap Splice Lengths

Frame 3

The spreadsheet for the design of Frame 3 can be found in Appendix G.

Geometry: The irregular geometry of Frame 3 was a driving factor in its loading determination. Because

of the cantilever, edge beam along its length, and the large perimeter cladding load, the direct design

method could not be used. Instead the Equivalent Frame Design Method was used. In order to analyze

this frame, a SAP model was created from which to determine the flexural moments acting on the

frame. The geometry input into SAP was that of an effective T-beam for modelling purposes.

For the actual frame geometry, L2 was taken as the distance from half way to Frame 2 plus the 3’

cantilever at approximately 17.2’, with L1 being 21’. As such, the controlling column strip width was L2/4

at 4.3’ leaving the middle strip at 12.9’.

Loading: When creating the SAP model, the edge beam was modelled as an effective T-beam with the

appropriate distributed live and dead load as well as the perimeter dead load and slab self-weight.

Additionally, while the frame is three spans, two additional spans were modelled on each side of the

spans to ensure the frame behaved as interior spans rather than exterior spans.

The moment diagram shape can be seen in Figure 16. The spans shown in the red brackets are the spans

under consideration.

Figure . Frame 3 SAP Model Moment Diagram

The maximum interior negative moment was found to be 223.45k-ft and the maximum positive moment

was found to be 105.26k-ft.

As previously described, = 0.845 causing = 0.75. After double interpolating ACI Tables 8.10.5.5 and

8.10.5.1, the percentage of moment transferred to the column strip was determined. These results are

summarized in Table 17.


Additionally, the column strip moment at both the interior negative moment and positive moment

needed to be distributed to the slab and beam. This was done by interpolating ACI Table 8.10.5.7.1. A

summary of this moment distribution can be seen in Table 18.

Table . Frame 3 Column Strip Distribution to Slab and Beam

Flexural Design: The flexural design of Frame 3 was performed similarly to Frames 1 and 2. Flexural

design was performed at six locations; the middle strip slab, the column strip slab, and the column strip

beam, at both the interior negative and positive moment locations.

To design for flexure, the minimum area of steel was found for strength and then reinforcing was

prescribed. This was then checked against As max to ensure the section is tension controlled and against

As min to ensure cracking control. The final reinforcement for Frame 3 can be found in Table 19.


Shear Design of Beam: The edge beam required its own shear design. In order to do so, the normal

simplified method of shear design for a beam was employed. The spreadsheet for this design can be

found in Appendix G.

First, the shear envelope was gotten from the SAP model for Frame 3. The factored shear force, Vf, at

distance “d” from the support was determined to be 43k. From here, the concrete shear capacity, Vc,

was calculated to be 41.7k. Because was found to be less than Vf, shear reinforcement stirrups were

required. The required shear capacity from steel, Vs, was found from .

Once the required Vs was found, the spacing of #3 stirrups was found to reach this shear capacity as

13.7”. This spacing was then checked against S max and S’. It was determined that S’, which accounts for

Av min, controlled the spacing at 7.4”. As such, the final spacing of #3 stirrups was taken as 7” o.c. To

confirm the shear design, the factored shear strength, ØVn, was found to be 54.4k which is greater than

Vf at 43k. The final beam shear design is to provide #3 stirrups at 7” o.c. across the length of the beam.

Frame 3 Detailing: The detailing for Frame 3 is designed the same as for Frame 1 and Frame 2.

However, the columns in Frame 3 are 18” instead of 24”, which increased the span length, and therefore

increased the length of the bar from the face of the support. However, the slight addition to the span

length proved to add less length to the bar than what was taken away in the change in column size. This

means the overall bar length of Frame 3 ended up being slightly less than the overall bar length for

Frames 1 and 2, as shown in Appendix I. Since the reinforcement length of Frame 3 varied no more than

4” at any given time, and the required reinforcement length in Frame 1 and Frame 2 were larger than

those for Frame 3, we conformed to the same reinforcement length as Frame 1 and 2 for ease of

constructability, as shown in Table 20 below. The specifications for this are shown in Drawing 1 and

Drawing 2.


The lap splice lengths conform to the same parameters as Frame 1 and Frame 2, and the splice lengths

for Frame 3 can be found in Table 21 below, and excel sheets for the calculations can be found in

Appendix I.

Table : Frame 3 Lap Splice Lengths

Perimeter Beam Detailing: For the perimeter beam, we used standards laid out in MacGregor and

Wight’s Reinforced Concrete Mechanics & Design book. Using Figure A-5 (b) for standards, we designed

for splice location based on the splice lengths calculated in Appendix I, continuity, bar cutoffs, and

embedment lengths. Since the beam runs in the E-W direction, we are analyzed it as discontinuous,

which meant anchorage need not be considered. The Macgregor and Wight book references ACI 318-

11, and so we used details from ACI 318-11 in the design of the perimeter beam so long as it did not

conflict with codes in ACI 318-14, which it did not. The details for the bar are given in Table 22 below.

Table : Perimeter Beam Reinforcement Details

The splice locations conform with Figure A-5 (b) and are shown in Drawing 7. According to ACI, a

minimum of 2 bars must be continuous in both the positive and negative reinforcement, and the rest

can be cut as long as it meets the ratios given in A-5 (b). Our ratio of cut bars to continuous bars was ½,

which is greater than any ratio given in the chart, therefore the other 2 negative reinforcements and

positive reinforcements were cut according to Table 22. Details for these calculations can be found in

Appendix I.

Frame 4

Frame 4 was the only North-South frame designed for. Because of the consistent perpendicular spans,

this single frame design can be applied across all North-South frames within our scope. Using the

Equivalent Frame Design Method, the flexural design of this frame is based off the SAP model described

previously. The spreadsheet for the design of Frame 4 can be found in Appendix H.

Loading: The flexural design was based off the following moments described in the previous SAP

section:

Figure . Labeled Locations of Critical Moment

Location 1 2 3 4 5 6 7

Moment (k-ft) 44.10 255.56 268.10 589.58 338.40 127.39 298.54

Table . Maximum Moment Values at 3rd Story

These moments then needed to be distributed to the column and middle strips at each critical moment

location.

For points 4,5, and 7, the interior negative moment was distributed according to Table 8.10.5.1 with

75% going to the column strip.

For points 3 and 6, the positive moment was distributed according to Table 8.10.5.5 with 60% going to

the column strip.

For points 1 and 2, the exterior negative moment was distributed according to Table 8.10.5.2. In order

to interpolate from this table, the torsional stiffness parameter t had to be calculated. In order to do

this, the constant, C, and the moment of inertia of the slab, Is, were calculated and used to calculate t.

This calculation can be found within the Frame 4 excel sheets in Appendix H. With t determined, the

table was double interpolated and found that 96% of the moment is transferred to the column strip at

points 1 and 2.

A summary of these moment distributions can be found in Table 24.

Table . Frame 4 Moment Distribution

Geometry: While the perpendicular span, L2, for both of the spans in this frame are the same at 21’, the

span length themselves, L1 vary between spans. Because of this, each span has a different minimum

column width. For the long span, the controlling column width is 117”, while the controlling column

width for the short span in 58.5”. For detailing continuity and looking at the required reinforcing for

these spans in the flexural design, the column width for both spans was taken as 58.5” as it is

conservative to concentrate the force into a smaller width. This assumption allowed for more efficient

flexural design, easier detailing, and would be less complicated to construct.

Flexural Design: Flexural design was done similarly to other frames, designing for the required column

and middle strip reinforcing at all critical moments. To design for flexure, the minimum area of steel was

found for strength and then reinforcing was prescribed. This was then checked against As max to ensure

the section is tension controlled and against As min to ensure cracking control. The final reinforcement

for Frame 3 can be found in Table 25.


Notably, the moments at points 4 and 5 were taken as the larger of the two, being point 4, to ease the

continuity of the interior negative bars. Also, the bars for the cantilever at point 1 in the middle strip

were oversized to #4’s at 12” o.c. to allow for the bars from Point 2 to be continuous to the end of the

cantilever. This is explained further in the following detailing section.

Detailing: For comprehension of spans to be discussed in the N-S direction, we maintained the critical

section numbering. We labeled the critical section on Drawings 3 and 4 so it is more clear where within

the N-S section we are discussing reinforcement detailing.

When considering the cantilever, we noticed it had a significantly smaller moment at critical section 1

than at critical section 2. Initially we had planned to continue our negative and positive reinforcement

through to the end of the cantilever at a minimum spacing to account for the moment. However, in

order to hook into the end of the cantilever, we needed a smaller bar than a No. 9 since the inside

diameter of a 180 degree hook is 9”, and the hook length of a 90 degree hook is 13.5”. These are both

too large to fit within the slab, and therefore we had to look at alternate solutions.

In order to develop the strength in our negative reinforcement, and to account for the No. 9 bar being

too large, we hooked the No. 9 bar into the beam and developed the strength of a No. 5 bar to account

for the moment on the cantilever. The No. 9 bar development length needed for the 90 degree hook

was initially sized as longer than the width of the beam. However, when accounting for a clear cover

from the edge of 2.5”, and a depth clearance of 2”, we were able to use a Ѱc of .7 (per ACI 25.4.3.2)

instead of 1. This lowered the development length to 14 inches, which allowed for a clear cover of 2.5”,

meeting the requirements to use the modification factor. However, the No. 5 bar does not hook into the

beam, but rather develops its strength by continuing straight into the slab. The dimensions of the

negative reinforcement detailing can be found in Table 26 and a section view for the cantilever and

development lengths is given in Drawing 5.

For the negative reinforcement spanning critical sections 2 (axis BC), 4-5 (axis BD), and 7 (axis BE), we

made the shorter column strip reinforcement longer than the calculated minimum such that it would

equal the length of the middle strip bars. This is noticeable in Drawing 3. We chose to do this because it

had a difference of 6” in bar length for both sides of the reinforcement. By adding the extra

reinforcement across the already slender column strip, we are able to make constructability easier.

Additionally, for the negative reinforcement crossing critical section 4-5 the length of the bar from the

face of support is determined by the large clear span. For critical section 7, the controlling span is the

span within our area of analysis, and therefore it ends up with a smaller bar length from face of support.

For the positive reinforcement, ACI does not state a requirement to have equal spacing from the

centerline in the event of uneven spans on either side of the column. This yielded a 3’ – 2” space in the

south direction of critical section 4-5, and a space of 4’ – 0” in the north direction. The overall

dimensions for the positive reinforcement can be found in Table 27.

The middle strip cantilever hook reinforcement shown in Drawing 6 has no development length (shown

in Table 27) for the negative reinforcement. This is due to continuing the negative reinforcement from

critical section 2 into the cantilever. The length of the bar is much larger than the development length,

so no development length was considered.

All sections continue reinforcement into the cantilever except for the negative reinforcement in the

column strip, as specified above.

Table : Frame 4 Column Strip Detailing Lengths

Table : Frame 4 Middle Strip Detailing Lengths

Slab Drawings

The following section represents the detailed drawings of the flat slab reinforcement and beam

reinforcement.

Drawing : East-West Negative (Top) Reinforcement

Drawing : East-West Positive (Bottom) Reinforcement

Drawing : North-South Negative (Top) Reinforcement

Drawing : North-South Positive (Bottom) Reinforcement

Drawing : Cantilever Beam Reinforcement in Column Strip

Drawing : Cantilever Beam Reinforcement in Middle Strip

Drawing : Beam Elevation

Drawing : Beam Section

Drawing : Reinforcement Interaction in Column Core

Column Design

Two columns were considered as part of our project scope. Highlighted in Figure 17, these columns

consisted of both an interior and exterior square column in the center of our slab area. Each column was

to be designed at the first story in order to take into account maximum axial loading, and intended to

have a sufficient margin of safety against both instability and material failure.

Figure 17: Illustration of columns to be designed

Initial material and spatial considerations:

• f’c = 5 ksi

• = 60 ksi

• Story Height =

• Interior Column, = 536.375 ft²

• Exterior Column, = 361.375 ft²

Load Considerations: Four load combinations were considered in determining the axial loading and

moments being applied on the two columns. These four load combinations were selected because, as

detailed in the “Structural Analysis” section of this report, patterned loading is not being analyzed in this

design.

• 1.4D

• 1.2D + 1.6L

• 1.2D + 1.0W +1.0L

• 0.9D

Using the SAP model detailed previously, the maximum axial force and moment applied to either

column were evaluated for each load combination. Although our project scope calls only for the

consideration of the columns at the first story, all four load combinations were assessed at both the first

and third stories to account for all maximum values. Maximum axial loads occurred at the first story, but

maximum moments occurred at the third story because the first three stories are rigid. The outputs of

this evaluation are illustrated in Table 28. From these outputs, we were able to determine that the 1.2D

+ 1.6L loading combination controls. For our final design of the interior and exterior columns, we

considered the maximum axial loads and moments for the controlling load combination at the first

story.

1st Story

Interior Exterior

Load Combination Axial Load, P [k] Moment, M [k-ft] Axial Load, P [k] Moment, M [k-ft]

1.4D 970 65 546 53

1.2D + 1.6L 1444 106 812 90

1.2D + 1.0W + 1.0L 1214 88 683 73

0.9D + 1.0W 624 43 351 34

3rd Story

Interior Exterior

Load Combination Axial Load, P [k] Moment, M [k-ft] Axial Load, P [k] Moment, M [k-ft]

1.4D 649 78 365 64

1.2D + 1.6L 965 127 543 110

1.2D + 1.0W + 1.0L 812 107 456 89

0.9D + 1.0W 417 52 235 41

Table 28: Maximum Axial Forces and Moments

Slenderness: As the interior and exterior columns are laterally unbraced, they will have lateral joint

movements that depend on all lateral resisting element stiffness. As a result, the sway frame column

slenderness effects needed to be evaluated. These slenderness effects resulted from P-∆ moments. In

accordance with ACI 318-14 6.2.5, the P-∆ moments were considered for each column as a result of the

lateral deflections of the beam-column joints from their original un-deflected locations. We accounted

for these P-∆ effects by converting the load combinations to non-linear in our SAP analysis.

Dimensioning and Reinforcing: The sizing of each column section was determined based on the axial

loads found at the first story for the controlling gravity load case, 1.2D + 1.6L, as outlined in Table 28.

These loads, in accordance with the tributary areas of the interior and exterior columns, 536.375 in² and

361.375 in² respectively, and the dead and live loads outlined in Appendix B, the initial dimensions for

each column were determined.

• Interior Column, 24” x 24”

• Exterior Column, 18” x 18”

The interior column, given its larger tributary area, has greater and more conservative dimensions in

comparison to the exterior column. The smaller tributary area and axial loading on the exterior column

allowed for the use of smaller column. We tried to minimize the column dimensions, especially for the

exterior column, to ensure efficiency and cost effectiveness in our design.

Once sizing was determined, the longitudinal and transverse reinforcement for each column were

calculated. The controlling load combination used in the design process for both columns was 1.2D +

1.6L. The longitudinal reinforcement for each column was designed in accordance with ACI 318-14 10.6,

and the transverse reinforcement for each column was determined in accordance with ACI 318-14

10.7.6 and 25.7.2. For the exterior column, consideration of shear reinforcement was required; reducing

the tie spacing from 16 inches at no shear reinforcement to 7 inches. The reinforcing design process for

each column can be followed via the hand calculations in Appendix J, and the cross-sections and

elevations for each column design can be found in Drawings 10 and 11.

Longitudinal Reinforcement (Figures 18 and 19)

• Interior Column, 12 #7 Bars

• Exterior Column, 8 #8 Bars

Transverse Reinforcement

• Interior Column, #3 Bars at 14 inches

• Exterior Column, #3 Bars at 7 inches

Figure 18: Interior Column Longitudinal Reinforcement

Figure 19: Exterior Column Longitudinal Reinforcement

These column sizes and reinforcement details were applied to our SAP model to produce the P-M

interactions presented in Table 29. The axial load and moments for each column, taken from the SAP

model and tabulated in Table 28, were then plotted on the interaction diagrams resulting in the graphs

shown in Figures 18 and 19. All maximum P-M combinations fall within the interaction diagrams,

however, as expected, the 1.2D + 1.6L load combination controls and both stories.

P-M Interaction Diagrams

Interior Exterior

Axial Load, P [k] Moment, M [k-ft] Axial Load, P [k] Moment, M [k-ft]

1504 0 899 0

1504 222 899 104

1396 358 820 161

1175 457 683 205

940 522 532 236

674 562 360 259

594 623 304 282

469 659 189 291

196 510 39 223

-85 296 -180 103

-429 0 -341 0

Table 29: P-M Interaction Diagram Values

Figure 20: Interior Column Interaction Diagram

1st Floor

3rd Floor

Figure 21: Exterior Column Interaction Diagram

1st Floor

3rd Floor

Summation of Final Design: The final interior and exterior designs are presented in Table 30. In

accordance with ACI 318-14 Chapter 10, these columns were designed to maximize efficiency and cost

effectiveness whilst maintaining a sufficient margin of safety against both instability and material failure.

Dimensions Longitudinal Reinforcement Transverse Reinforcement

Interior Column 24” x 24” 12 No. 7 bars No. 3 bars @ 14”

Exterior Column 18” x 18” 8 No. 8 bars No. 3 bars @ 7”

Table 30. Column Design Summation

Column Drawings

Drawing : Interior Column Reinforcement

Drawing : Exterior Column Reinforcement

Shear Wall Design

To design the shear wall, hand calculations as well as SAP modeling were used. At first, all 5 walls (3 in

the strong direction, 2 in the weak direction) were used to maximize the strength of the wall. Once the

first design was finished, the wall had a large excess capacity that led to the middle wall being taken out.

The new wall configuration is shown below (Figure ____). All the exterior walls were kept, with two

walls located in the strong direction and two walls located in the weak direction. This configuration was

used for the final design calculations and SAP modeling:

Figure : Shear Wall Cross-Section

Figure ____: Shear Wall Cross Section

Using table 11.3.1.1, the minimum wall thickness is 9 inches. The concrete cover, specified by table

20.6.1.3.1, was ¾ inch. The total shear was originally the sum of all of the wind forces on the building,

which got evenly divided between the 2 walls positioned in the strong direction. From the SAP model,

the maximum axial loads were obtained. From these values, a maximum moment was calculated using

the critical height of 8 feet, which is half of the story height. From the wall dimensions, a nominal shear

capacity and concrete shear capacity were calculated. Vc was calculated according to table 11.5.4.6 in

the ACI code.

Once it was clear that the ultimate shear was more than half of the factored concrete shear capacity,

the reinforcement ratios were calculated according to clause 11.6.2. From these reinforcement ratios,

the horizontal reinforcement came out to be two layers of #4’s spaced at 18 inches according to

11.7.2.1. The vertical reinforcement was calculated to be two layers of #4’s spaced at 18 inches

according to 11.7.2.2.

The flexural design of the wall calls for a calculation of the ultimate moment according to the moments

imposed by the wind loads. This value came out to be much larger than the moments shown in the SAP

model. Also, the calculated Mu did not take into account the effects of any axial load or the stiffness of

the framing system, making it a very conservative value to use in the calculations. This process yielded a

flexural design that uses four #7 bars. Since the ends are being treated like a column, the flexural bars

need to be tied according to the column clause 25.7.2.1. The ties would be #3 bars spaced at 14 inches.

Once the wall cross section and reinforcement was laid out in SAP, the PM diagram was obtained. The

points on the diagram were also obtained from SAP and not from the hand calculated values from the

design process. There were two locations that were considered, each with four different load

combinations. The first floor was considered to obtain the location with the maximum axial load. The

second location that was considered was the third floor since that is the location with the maximum

moment. The completed PM diagram is shown below:

Figure : Shear Wall P-M Interaction Diagram

Figure _____: Shear Wall PM Diagram

The PM diagram shows that the design has sufficient capacity. It is clear that the axial capacity is well

beyond what is necessary, but the design was not changed since it is safe.

Shear Wall Drawings

Drawing : Shear Wall Plan View Reinforcement

Drawing : Shear Wall Corner Reinforcement

Drawing : Shear Wall Section View Reinforcement

Conclusion

Final Cost Analysis

The final cost analysis was performed utilizing cost data for R.S.Means, 2015. The unit cost per

item, not considering overhead and profit, was used in determining the final cost. This value was

multiplied by the quantity of units required of each item. This value was then adjusted by the Austin

multiplier in order to normalize the cost for Austin’s market. The multiplier used for each category is

listed in Table ###.

Category Austin Multiplier

Concrete 82.30

Steel 72.10

Formwork 64.50

Table 30: Austin Multipliers by Category

Initial cost estimates were performed for the shaded in red in Figure ###.

Figure 22: Area Used for Initial Cost Calculations

This area accounts for approximately 16% of a given floor’s area. The total cost per floor was

determined by extrapolating this cost across the entire area of the floor as follows:

The cost of the shear wall per floor was assumed to be the total cost of the shear wall across the

floor and was not divided by 0.16. The total cost of the south tower was then determined by multiplying

the cost per floor by the number of stories in the tower which is 6.

The final building design yielded a total cost of $2,089,003.96, with an estimated cost per square

foot of $16.30. This includes the cost of story three through the top of the building. Total costs for

concrete, steel reinforcement, and formwork are shown below in Table ###. Formwork was found to be

the most expensive component which would be expected for a slab system with drop panels.

Total Cost Cost per Square Foot

Concrete $702,290.18 $5.48

Steel $599,722.78 $4.68

Formwork $786,991.00 $6.14

Total $2,089,003.96 $16.30

Table 31: Total Project Cost by Category

The total cost of concrete includes the cost of the concrete ready mix (5 ksi), the placement of

each structural member, as well as the cost of finishing and curing. The total cost of steel includes the

cost of all steel reinforcement for all structural members. The total weight of steel was determined by

multiplying the weight of each bar per unit length by the total length of each bar. The cost of formwork

was included for all members and was determined based on the total contact surface area. See

Appendix page ### for a more detailed cost breakdown.

Overall Project Discussion

Changes Made During Design: Initially, we were using 4 ksi concrete for the entire building. As we

started actually designing, we found various benefits in increasing the concrete strength to 5 ksi, namely

for the increased resistance to punching shear and the increased axial strength in the columns.

Additionally, while we initially thought that a flat plate with drop panel system would be the least

expensive option, we found that a two-way slab with beams were actually more cost efficient.

Lessons Learned:

This project gave many lessons to the group, both in aspects of structural design and in group

work. In terms of structural design, we learned that where flexural design capacity needs to be

increased, increasing concrete strength is not necessarily the most efficient solution. Instead we found

that considering the increased concrete depth at the negative moment near the column was much more

efficient. Also, when designing shear walls, it is beneficial to consider an overall, built-up geometry of

multiple walls rather than designing for single walls individually. This was something that took place late

in our design, but added significantly to our structural strength as well and overall building deflection

control. We also found that stringency is a must when using structural analysis software. In our case,

using SAP, we ran into issues with diaphragm constraints, accounting for the various dead load

application, and understanding how to properly input the geometric configurations of structural

members.

Additionally, we learned various lessons about how to maneuver the design process as a whole

and how to work efficiently as a group. We learned the hard way that unknown topics should be

thoroughly investigated early in the design process. Additionally, one must be stringent with initial cost

estimation as these early calculations can have radical effects on the direction of the design process.

Also, design items must be checked periodically throughout the design process. Errors should be found

as soon as possible to avoid compounding effects as different assumptions are made off these

calculations. Plus, the process of explaining your work to another person allows you to ensure to the

clarity of your design as well as check for errors.

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