appendix f – structural...young, et al., roark’s formulas for stress and strain (8 th edition),...

WP-43D Oxbow-Hickson-Bakke Ring Levee System

WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Structural

APPENDIX F – STRUCTURAL

WP-43D Oxbow-Hickson-Bakke Ring Levee System i


F1 TABLE OF CONTENTS

Appendix F – Structural ............................................................................................... 1

F2 Introduction ...................................................................................................... 1

F3 Technical Guidance and Reference Standards ..................................................... 2

F4 General ............................................................................................................. 3

F4.1 Gravity Drain Inlet .................................................................................................3

F4.2 Pump Station ........................................................................................................3

F4.3 Gatewell ...............................................................................................................4

F4.4 Gravity Drain Outlet ..............................................................................................5

F5 Materials ........................................................................................................... 7

F5.1 Structural Steel .....................................................................................................7

F5.2 Reinforced Concrete ..............................................................................................7

F6 Design Loads ..................................................................................................... 9

F6.1 Risk Category ........................................................................................................9

F6.2 Dead Loads ...........................................................................................................9

F6.3 Hydrostatic Loading ...............................................................................................9

F6.4 Hydraulic Pump Self-Weight and Thrust Force ...................................................... 10

F6.5 Live Loads ........................................................................................................... 10

F6.5.1 Minimum Floor Loads ........................................................................................................... 10

F6.5.2 Moving Live Loads ................................................................................................................ 11

F6.6 Earth Loads ......................................................................................................... 11

F6.7 Wind Loads ......................................................................................................... 12

F6.8 Snow Loads ......................................................................................................... 13

F6.9 Ice Loads ............................................................................................................. 13

F6.10 Earthquake Loads ................................................................................................ 13

F7 Stability Analysis ............................................................................................. 14

WP-43D Oxbow-Hickson-Bakke Ring Levee System ii


F7.1 Load Combinations .............................................................................................. 14

F7.2 Stability Criteria .................................................................................................. 15

F7.2.1 Sliding Stability...................................................................................................................... 15

F7.2.2 Flotation Stability .................................................................................................................. 16

F7.2.3 Bearing Capacity and Resultant Location ............................................................................. 17

F7.3 Pump Station Stability Analysis ............................................................................ 18

F7.4 Gatewell Stability Analysis ................................................................................... 18

F8 Structural Evaluation and Capacity .................................................................. 18

F8.1 Load Factors ........................................................................................................ 18

F8.2 Load Combinations .............................................................................................. 18

F8.3 Resistance Factors ............................................................................................... 19

F9 Structural Capacity .......................................................................................... 20

F9.1 Concrete Design Capacity Methodology ............................................................... 20

F9.1.1 Shear ..................................................................................................................................... 20

F9.1.2 Flexure .................................................................................................................................. 20

F9.2 Structural Analysis .............................................................................................. 21

F9.3 Gravity Drain Inlet Design Capacity ...................................................................... 21

F9.4 Pump Station Design Capacity ............................................................................. 22

F9.4.1 Base Slab ............................................................................................................................... 22

F9.4.2 Exterior Vertical Walls .......................................................................................................... 23

F9.4.3 Interior Vertical Wall ............................................................................................................ 23

F9.4.4 Top Slab ................................................................................................................................ 23

F9.5 Gatewell Design Capacity .................................................................................... 24

F9.6 Gravity Drain Outlet Design Capacity ................................................................... 25

F10 Design Quality Control ..................................................................................... 26

F10.1 Quality Control .................................................................................................... 26

WP-43D Oxbow-Hickson-Bakke Ring Levee System iii


Figures

Figure 4-1 Gravity Drain Inlet Structure ................................................................................................... 3

Figure 4-2 Pump Station .......................................................................................................................... 4

Figure 4-3 Gatewell .................................................................................................................................. 5

Figure 4-4 Gravity Drain Outlet ................................................................................................................ 6

Tables

Table 5-1 Structural Steel Material Properties ........................................................................................... 7

Table 5-2 Reinforced Concrete Material Properties ................................................................................... 7

Table 5-3 Minimum Concrete Clear Cover ................................................................................................. 8

Table 6-1 Dead-Load Unit Weights ............................................................................................................. 9

Table 6-2 Hydraulic Thrust Force .............................................................................................................. 10

Table 6-3 Minimum Floor Loads ............................................................................................................... 10

Table 6-4 Soil Parameters ......................................................................................................................... 11

Table 7-1 Pump Station Load Combinations ............................................................................................ 14

Table 7-2 Gatewell Load Combinations .................................................................................................... 14

Table 7-3 Sliding Stability Minimum Factors of Safety ............................................................................. 16

Table 7-4 Flotation Stability Minimum Factors of Safety ......................................................................... 17

Table 7-5 Limits of Resultant Location ..................................................................................................... 18

Table 7-6 Pump Station Stability Analysis Results .................................................................................... 18

Table 7-7 Gatewell Stability Analysis Results ........................................................................................... 18

Table 8-1 Load Combinations ................................................................................................................... 18

Table 8-2 Applicable Load Combinations ................................................................................................. 18

Table 8-3 Resistance Factors .................................................................................................................... 19

Table 9-1 Gravity Drain Inlet Calculated and Design Capacity Values ...................................................... 22

WP-43D Oxbow-Hickson-Bakke Ring Levee System iv


Table 9-2 Pump Station Base Slab Calculated and Design Capacity Values ............................................. 22

Table 9-3 Pump Station Exterior Vertical Walls Calculated and Design Capacity Values ......................... 23

Table 9-4 Pump Station Interior Vertical Walls Calculated and Design Capacity Values.......................... 23

Table 9-5 Pump Station Top Slab Calculated and Design Capacity Values ............................................... 24

Table 9-6 Gatewell Design Capacity Values .............................................................................................. 25

Table 9-7 Gravity Drain Outlet Design Capacity Values ............................................................................ 25

Attachments

Attachment F1 Gravity Drain Inlet, Gravity Drain Outlet, and Gatewell Computations

Attachment F2 Pump Station Computations

WP-43D Oxbow-Hickson-Bakke Ring Levee System F-1

WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Introduction

F2 INTRODUCTION

Appendix F provides support for the structural design assumptions and methods for the gravity drain inlet

and trashrack, pump station, gatewell, and gravity drain outlet for the OHB Ring Levee. The north interior

drainage pond (North Pond) is located in Pleasant Township along the interior of the north levee to the

west of Highway 81, which will be drained by a gravity drain system except during flood events when the

gravity system will be closed and a pump station will be required. Major structural components of the

drainage system consist of a gravity drain inlet and trashrack located at the edge of the North Pond, pump

station located near the northeast corner of the North Pond, a gatewell structure located in the levee

north of the pump station structures, and a gravity drain outlet structure to discharge the water into the

Red River of the North. These structures are connected by piping that extends from the North Pond,

through the pump station and gatewell passing through the levee, and then turns east along the northern

exterior of the levee, underneath Highway 18 to the outflow structure and river.

At the time of this report, the following elements were evaluated for both the pump station and gatewell

structures: overall load combinations, design methodology, global stability, and member sizing.


WP-43D BCOE 4/1/2/2016 DDR Pump Station, Volume 2 – Appendix F – Technical Guidance

F3 TECHNICAL GUIDANCE AND REFERENCE STANDARDS

The following listed technical guidance and reference standards were used to complete the structural

evaluation within this appendix.

1. International Building Code (IBC) 2006, International Code Council, March 2006.

2. North Dakota State Building code, North Dakota Department of Commerce, Division of

Community Services; Effective November 1, 2007.

3. American Concrete Institute (ACI) 318-11, Building Code Requirements for Structural Concrete,

ACI Committee 318, 2011.

4. American Institute of Steel Construction (AISC) 325, Steel Construction Manual, Fourteenth

Edition, American Institute of Steel Construction, March 2011.

5. AISC 360, Specification for Structural Steel Buildings, American Institute of Steel Construction,

March 2011.

6. Engineer Manual (EM) 1110-2-2100, Stability Analysis of Concrete Structures, U.S. Army Corps of

Engineers, Washington DC, 1 December 2005.

7. EM 1110-2-2104, Strength Design for Reinforced-Concrete Hydraulic Structures, U.S. Army Corps

of Engineers, Washington DC, 20 August 2003.

8. EM 1110-2-2502, Retaining and Flood Walls, U.S. Army Corps of Engineers, Washington DC, 29

September 1989.

9. EM 1110-2-3102, General Principles of Pumping Station Design and Layout, U.S. Army Corps of

Engineers, Washington DC, 28 February 1995.

10. EM 1110-2-3104, Structural and Architectural Design of Pumping Stations, U.S. Army Corps of

Engineers, Washington DC, 30 June 1989.

11. EM 1110-2-3105, Mechanical and Electrical Design of Pumping Stations, U.S. Army Corps of

Engineers, Washington DC, 30 November 1999.

12. Young, et al., Roark’s Formulas for Stress and Strain (8th

Edition), McGraw Hill, New York, 2012.


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – General

F4 GENERAL

The structural features required to transport water from the interior of the OHB Ring Levee system to the

Red River of the North include an inlet, pump station, gatewell, and gravity drain outlet.

F4.1 GRAVITY DRAIN INLET

The gravity drain inlet is shown in Figure 4-1. It consists of a precast concrete 7-foot-rise box culvert

sloped-end section which is to be doweled into the interior drainage low-flow channel. The width of the

box-culvert section is 10 feet, which matches the width of the low-flow channel. A cast-in-place concrete

head wall provides the transition from the 60-inch reinforced-concrete pipe (RCP) to the precast concrete

box-culvert sloped-end section. Three HSS beams spanning between the box-culvert end-section walls

support the ¼-inch x 2-inch trashrack grates. The top section of trashrack grating is called out to be

hinged to enable flow during emergency plugged conditions.

FIGURE 4-1 GRAVITY DRAIN INLET STRUCTURE

F4.2 PUMP STATION

The pump station (Figure 4-2) is a cast-in-place, reinforced-concrete structure that will pump water

resulting from interior drainage to the gatewell structure. Water enters the pump station through a 66-

inch-diameter pipe where it is distributed through an interior baffle wall. The baffle wall also acts to slow

water flow and reduce turbulence of the flow to the pumps. The pump station houses four pumps which

are able to pump water from the ponds to a point beyond the protection line. The valves for the pumps

are located in a smaller attached structure to allow easier access for maintenance. A sluice gate on the 66-

inch pipe, along with valves on the pipes from the pumps, will allow for maintenance. A total of six access

hatches will be placed in the top slab, four for the pumps, one for the valves, and the last for general

personal access.



FIGURE 4-2 PUMP STATION

F4.3 GATEWELL

The gatewell provides passage for water in the pump station to the gravity drain outlet and connects the

gravity drain through the line of protection. The gatewell is shown in Figure 4-3. The sluice gate on the

south wall of the gatewell provides secondary backflow protection. The gatewell is a cast-in-place

reinforced-concrete structure; it is rectangular in shape and contains two chambers. There is a 16-inch

wall that separates the two chamber with a 7’x7’ gated opening centered at the base. This gate’s

intended function is to force water out of the gatewell through the emergency overflow in the north gate

is jammed close and the south gate is jammed open. Four 16-inch-diameter ductile iron pipes connect to

the gatewell at elevation 904.0 and discharge to the first chamber. The second chamber is the gravity

pass-through chamber. During non-flood times this permits gravity drainage through a 60-inch-diameter

RCP inlet and outlet in opposite walls. Passing of the pumped water to the flood side of the levee is

allowed by pump flows entering the pass-through chamber. Each wall has a sluice gate to allow total



dewatering of the gatewell or closure of the flood side from the gatewell. Access to the gatewell is

achieved through the top slab in the gravity pass-through chamber and a metal ladder.

FIGURE 4-3 GATEWELL

F4.4 GRAVITY DRAIN OUTLET

The ultimate gravity drain outlet design will be a function of cost and environmental impacts. For reasons

discussed in the geotechnical portion of this report, the pipe outlet must be recessed approximately 180

feet back from the shoreline. Currently, the drawings show a significant excavation exposing this outlet

location and allowing flow to the river.

The gravity drain outlet structure is shown in Figure 4-4 and consists of a head wall with a duck bill valve,

two wing walls, and a stilling basin slab. The downstream end of the gravity drain outlet is to be formed

against sheet pile that extends to a sufficient depth to provide backup scour protection in addition to the

riprap erosion protection. The wing walls are restrained against overturning by their connection to the

stilling basin base slab.



FIGURE 4-4 GRAVITY DRAIN OUTLET

The cast-in-place concrete gravity drain outlet consists of two wing walls, a head wall, and base slab

stilling basin.


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Materials

F5 MATERIALS

Below is a discussion of the material property assumptions used in the design of all structural

components.

F5.1 STRUCTURAL STEEL

All structural steel within the structural components will be per the specifications of the American

Institute of Steel Construction (AISC). The minimum yield strength for structural steel is listed in Table 5-1.

TABLE 5-1 STRUCTURAL STEEL MATERIAL PROPERTIES

Structural Material Minimum Yield

Stress (ksi)

Minimum Tensile

Stress (ksi) Reference

W-shapes (ASTM A992) 50 65 AISC Table 2-4

Channels (ASTM A36) 36 58 AISC Table 2-4

Plates (ASTM A36) 36 58 AISC Table 2-4

Bolts (ASTM 325) N/A 105 AISC Table 2-6

F5.2 REINFORCED CONCRETE

As determined by Chapter 4, Durability Requirements, ACI 318, reinforced concrete with a minimum 28-

day compressive strength of 4,500 pounds per square inch (psi) will be used for all structural components.

Concrete mix design requirements (per Chapter 4, ACI 318) are listed in Table 5-2. All reinforcing steel will

be per ASTM A615: Grade 60, undeformed, uncoated. Minimum concrete clear cover is listed in Table 5-3;

this is dependent on location, per EM 1110-2-2104 and ACI 318.

TABLE 5-2 REINFORCED CONCRETE MATERIAL PROPERTIES

Component Designation Reference

Exposure category and class F2 (severe) ACI 318, Table 4.2.1

Maximum water-to-cement ratio 0.45 ACI 318, Table 4.3.1

Minimum 28-day compressive strength 4,500 psi ACI 318, Table 4.3.1

Nominal maximum aggregate size ¾ inch ACI 318, Table 4.4.1

Air content 6% ± 1.5% ACI 318, Table 4.4.1


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Materials

TABLE 5-3 MINIMUM CONCRETE CLEAR COVER

Concrete Location Applicable Pump Station and

Gatewell Features

Minimum

Clear Cover

(inches)

Reference

Surfaces subject to

abrasion erosion

• Top of bottom slab

• Inside of exterior walls

• Both sides of interior walls

6 EM 1110-2-2104, Section 2-6

Unformed surfaces in

contact with foundation • Bottom of bottom slab 4 EM 1110-2-2104, Section 2-6

Equal to or greater than 24

inches in thickness • Exterior of exterior walls 4 EM 1110-2-2104, Section 2-6

Greater than 12 inches and

less than 24 inches in

thickness

• Top and bottom of top slab 3 EM 1110-2-2104, Section 2-6

Equal to or less than 12

inches in thickness • Gatewell top slab 3 ACI 318, Section 7.7.1


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Design Loads

F6 DESIGN LOADS

F6.1 RISK CATEGORY

All structures are determined to be risk/occupancy category IV per ASCE 7. This category was selected

because the structures are considered essential facilities and could pose substantial hazard to the

community.

F6.2 DEAD LOADS

Dead-load unit weights for materials used are located in Table 6-1. The soil self-weight properties are

taken directly from the geotechnical data within Appendix D.

TABLE 6-1 DEAD-LOAD UNIT WEIGHTS

Dead Load Unit Weight (pcf)

Reinforced concrete self-weight 150

Structural steel self-weight 490

Water self-weight 62.4

Soil, clay, moist self-weight 110

Soil, clay, saturated self-weight 115

Soil, structural backfill self-weight 120

F6.3 HYDROSTATIC LOADING

Hydrostatic loading is linear and increases with the fluid depth. Hydrostatic pressure is applied

perpendicular to all surfaces regardless of orientation. For the structures in this system, hydrostatic

pressures occur laterally on vertical walls or vertically on base slabs. Each is described in the following

sections.

The design fluid depth is a function of the structure’s location relative to the free-water surfaces on each

side of the line of protection and the load case considered.

Since the pump station and gatewell are located at or inside the protection line, the hydrostatic pressure

is related to the hydraulic gradient between the free-water surfaces inside and outside the line of

protection. Using linear interpolation between the free-water surfaces inside and outside the line of

protection, the hydrostatic pressure head was determined at the pump station and gatewell. Because of

the large distance between the two free-water surfaces, the difference between hydrostatic pressure

head on the flood side and protected side of each structure was negligible. Therefore, the hydrostatic

pressure head was determined at the centroid of each structure.



F6.4 HYDRAULIC PUMP SELF-WEIGHT AND THRUST FORCE

Hydraulic thrust loads caused by the pumps are based on the hydrostatic pumping head in addition to a

50-percent increase for dynamic effects (per EM 1110-2-3104). This load is applied to the bottom slab of

the pump station at the location of each pump. The assumed loading used for design is shown in Table

6-2, which is based off of information from a pump manufacturer. The actual pump self-weight and thrust

forces will be dependent on the pump manufacturer; a maximum load was computed for comparison to

the actual loads from the pump manufacturer. Since bearing pressure controls the slab design, the

maximum hydraulic thrust loads must be less than the bearing pressure at that location. This is shown as

the maximum allowable hydraulic thrust load below, which will be compared to the actual loads from the

manufacturer.

TABLE 6-2 HYDRAULIC THRUST FORCE

Pump Identification Assumed Hydraulic

Thrust Load (kip)

Maximum

Hydraulic Thrust

Load (kip)

6010 Motor, Type K impeller 4.7 10.0

F6.5 LIVE LOADS

Live loads for the structures were evaluated. These include minimum floor loads for both base and top

slabs, along with moving live loads created by vehicular traffic. The section below summarizes the live

loads used for the evaluation of the hydraulic structures.

Live loads shall not be applied to concrete surfaces prior to completion of the specified 28-day

compressive strength of the concrete without prior approval.

F6.5.1 MINIMUM FLOOR LOADS

The minimum floor live loads were determined based on the North Dakota State Building Code for 2006

International Building Code Amendments and EM 1110-2-3104. Table 6-3 lists the maximum for minimum

floor live-load values, dependent on floor classification.

TABLE 6-3 MINIMUM FLOOR LOADS

Description Live Load Reference

Pump station operating floor 300 psf or H20 vehicle EM 1110-2-3104, Table 4-1

Gatewell top slab 300 psf EM 1110-2-3104, Table 4-1



F6.5.2 MOVING LIVE LOADS

There is potential for vehicular traffic adjacent to the vertical walls of the pump station and gatewell. A

vehicular surcharge load equivalent to an HS-20 vehicle of 300 pounds per square foot (psf), per ASSHTO

and EM 1110-2-3104, was used. For preliminary analysis, a surcharge load value was conservatively

applied perpendicular to the entire height of the vertical walls equal to the at-rest lateral earth pressure

coefficient (Ko) times the applicable vehicular live load. During final design Boussinesq method for point

load distribution through soil will be computed for a more accurate and reasonable surcharge loading.

The top slab of the pump station will allow access for vehicular traffic for maintenance. A vehicular load

equivalent to an HS-20 vehicle will apply either as a 300 psf uniform load or as point loads per AASHTO.

For the preliminary analysis, a uniform load was applied to the entire slab. Final design will evaluate both

uniform and point loads of the vehicle at locations that create maximum design forces. The top slab of the

gatewell will be located far enough above the surrounding grade to prevent vehicular access. Therefore, it

will not be considered.

F6.6 EARTH LOADS

The soil parameters used for both stability and capacity were determined from the Geotechnical

information provided in Appendix D. Below in Table 6-4 is a summary of the soil parameter values used.

TABLE 6-4 SOIL PARAMETERS

Soil Type Condition Moist Unit

Weight (pcf)

Saturated Unit

Weight (pcf)

Cohesion (psf) Coefficient of

Friction (degrees)

Levee Fill Undrained 105 115 900 N/A

Levee Fill Drained 105 115 N/A 28

Structural Fill Drained 115 120 N/A 32

For the purposes of lateral earth pressure acting on structures and structural features, soils were assumed

to behave as predicted by Mohr-Coulomb active/passive pressure theory as shown in Eq. 1 and Eq. 2.

The pump station is to be surrounded by select granular structural fill. Therefore, cohesion is assumed to

be 0. For stability analysis, active and passive pressure coefficients are quantified as shown in Eq. 3 and

Eq. 4, respectively. For strength analysis of wall elements, the at rest pressure coefficient shown in Eq. 5 is

assumed.

The gatewell is to be surrounded by soils exhibiting both cohesive and cohesionless properties. The soil

acts more cohesively when undrained and less cohesively when drained. Therefore, both states of the soil

were conservatively computed in which Φ was assumed to equal 0 for the cohesive (or undrained)

condition and is represented by Eq. 5 and c was assumed to equal 0 for the cohesionless (or drained)

condition and is represented by Eq. 6.



All Soils:

�� =�tan� �45° − ∅�� + 2�tan(45° − ∅

�) Eq. 1 (Bowles 1996, Eq. 2-54)

�� =�tan� �45° + ∅�� + 2�tan(45° + ∅

�) Eq. 2 (Bowles 1996, Eq. 2-55)

Where: �=�ℎ and �� =tan� �45° − ∅

��= !"#$(∅) %"#$(∅)

��=tan� &45° + ∅2'=

1 + sin(∅)1 − sin(∅)

Cohesionless Soils where c is assumed to = 0 psf (pump station, gatewell – drained case):

Stability analysis of global structure:

Active pressure coefficient: �� = !"#$(∅) %"#$(∅) Eq. 3

Passive pressure coefficient: �� = %"#$(∅) !"#$(∅) Eq. 4

Strength analysis of vertical structural elements (walls):

At rest soil pressure: �+ = 1 + sin(∅) Eq. 5

Cohesive Soils where Φ is assumed to = 0º (gatewell – undrained case):

Stability analysis of global structure: (not applicable):

Strength analysis of vertical structural elements (walls):

Since: tan �45° + ∅�� = 1

�� =ℎ�,��- − 2� Eq. 6

Earth loads shall not be applied to concrete surfaces prior to completion of the specified 28-day

compressive strength of the concrete without prior approval.

F6.7 WIND LOADS

Wind loads were applied to the building over the pump station (see architectural section).



F6.8 SNOW LOADS

Snow loads were applied to the building over the pump station wet well (see architectural section).

F6.9 ICE LOADS

Ice debris loads were not applicable for the structures in this project.

F6.10 EARTHQUAKE LOADS

Earthquake loading was not applicable for the structures in this project.


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Stability Analysis

F7 STABILITY ANALYSIS

F7.1 LOAD COMBINATIONS

Load combinations for stability analyses performed on the structures are listed in Table 7-1 and Table 7-2

for the pump station and gatewell, respectively.

TABLE 7-1 PUMP STATION LOAD COMBINATIONS

Load Combinations Category

Flood Side Water

Elevation (feet)

Protected Side Water

Elevation (feet)

Interior Water Elevation

(feet)

a Construction Unusual 4-feet differential in soil

b Normal operating Usual 916.0 916.0 898.0

c Pump start-up Usual Not applicable, normal operation controls

d Pump stop Usual Not applicable, normal operation controls

e MDF Usual Not applicable for pump station because it is inside line of protection

f Maximum pump thrust Unusual Not applicable, inundated controls

g Maintenance Unusual Not applicable see note 3

h Rapid drawdown Unusual Not applicable see note 2

i Blocked trashrack Unusual Not applicable for pump station

j Inundated Extreme 916.0 916.0 914.0

k Coincident pool + OBE Not applicable for this project

l Coincident pool + MDE Not applicable for this project

TABLE 7-2 GATEWELL LOAD COMBINATIONS


Flood Side Water

Elevation (feet)

Protected Side Water

Elevation (feet)

Interior Water Elevation

(feet)

a Construction Unusual 4-feet differential in soil

b Normal operating Usual Not applicable see note 2

c Pump start-up Not applicable for gatewell

d Pump stop Not applicable for gatewell

e MDF Usual 922.00 895.50 895.50

f Maximum pump thrust Not applicable for gatewell

g Maintenance Not applicable see note 3

h Rapid drawdown Not applicable see note 2

i Blocked trashrack Not applicable for gatewell

j Inundated Extreme 922.00 895.50 922.0

k Coincident pool + OBE Not applicable for this project

l Coincident pool + MDE Not applicable for this project

Notes:

1. During construction fill will be placed in lifts around the pump station and gatewell with a differential lift on any side not

more than 4 feet. The influence from compaction equipment on stability is negligible in comparison to the size of the

structures

2. Will result in equal lateral loads on all sides thereby resulting in global equilibrium around the pump station and gatewell.

3. Maintenance on these structures will not be performed during an event



Construction = pumping station complete with and without fill

in place; no water loads

Normal operating = plant operating at discharge routine local floods

over a range of exterior flood levels for which

the pumps are operating at approximately 100%

efficiency

Pump start-up = station empty with water at pump start

elevation or maximum pump level

Pump stop = water below pump start elevation on intake

side, levee design flood on discharge side

MDF = maximum design water level outside protection

line, minimum pumping level inside

Max. pump thrust = maximum design water level condition –

maximum operating floods both inside and

outside protection line, maximum pump thrust

Maintenance = maximum design water level inside with one,

more, or all intake bays unwatered

Rapid drawdown = water at pump stop elevation, sumps dewatered

Blocked trashrack = five foot head differential across trashracks

Inundated = maximum flood levels inside and outside

protection line, pumping station inoperative,

foundation drains inoperative, protection line

intact

F7.2 STABILITY CRITERIA

Stability criteria for structures are in accordance with EM1110-2-3104 and EM1110-2-2502. The minimum

factors of safety for stability for critical structures with ordinary site information are listed. Refer to the

Geotechnical Appendix D of this report for soil properties and bearing capacity calculations. Per EM 1110-

2-2100, Section 3-10, the bearing capacity for the usual case is increased by fifteen percent for the

unusual case and fifty percent for the extreme case.

F7.2.1 SLIDING STABILITY

Sliding along a horizontal plane is caused by a differential in hydrostatic elevation and/or soil elevation on

each side of the structure. Sliding forces are resisted by shear-friction forces between the potential sliding

surfaces and passive soil pressure. The shear-friction forces are developed between the vertical load

caused by gravity of the material and the shear interface resistance between the horizontal plane of the

concrete slab and soil. The factor of safety against sliding is the ratio of the total resisting force to the

forces tending to cause sliding from the net unbalanced horizontal lateral forces. This factor of safety is

determined by Equation 7 in accordance with EM 1110-2-2502. Table 7-3 shows the minimum factors of

safety against sliding for each classification in accordance with EM 1110-2-3104.



./�0�1�23 = (4!5)∗7%�8∑: Eq. 7

Where: W = total weight of structure (kip)

U = total uplift force (kip)

µ = friction coefficient along sliding plane

c = cohesion (ksf)

A = area of uncracked sliding surface (feet)

H = total horizontal force causing sliding (kip)

TABLE 7-3 SLIDING STABILITY MINIMUM FACTORS OF SAFETY

Classification Minimum Factor

of Safety Reference

Usual 2 EM 1110-2-3104, Table 4-2

Unusual 2 EM 1110-2-3104, Table 4-2

Extreme 1.33 EM 1110-2-3104, Table 4-2

F7.2.2 FLOTATION STABILITY

Flotation of the structure is due to the uplift pressure on the base slab caused from the hydrostatic

pressure from the water elevation. Under balanced water condition, the uplift pressure is a uniform

rectangular pressure. While the unbalanced water condition causes a linearly varying pressure dependent

on the water elevation. The factor of safety against flotation is the ratio of total downward forces to the

total upward forces. This factor of safety is determined by Equation 8 in accordance with EM 1110-2-

2502.

./;0+��+2 = 4<%4=%>5!4? Eq. 8

Where: WS = total weight of structure (kip)

WC = weight of water contained in structure (kip)

S = surcharge loads (kip)

U = uplift forces active on the base of the structure (kip)

WG = weight of water above top surface of the structure (kip)

Flotation stability of the structures was checked in accordance with EM 1110-2-3104. The minimum

factors of safety required for flotation are listed in Table 7-4.



TABLE 7-4 FLOTATION STABILITY MINIMUM FACTORS OF SAFETY

Classification Minimum Factor

of Safety Reference

Usual 1.5 EM 1110-2-3104, Table 4-2

Unusual 1.3 EM 1110-2-3104, Table 4-2

Extreme 1.1 EM 1110-2-3104, Table 4-2

F7.2.3 BEARING CAPACITY AND RESULTANT LOCATION

Overturning of the structure is checked by limiting the eccentricity of the resultant force with respect to

the analyzed surface(s). The overturning forces are the horizontal resultants of lateral loads from

differential hydrostatic and soil pressures and uplift forces. Resisting forces are the horizontal resultants

of vertical self-weight loads that are multiplied by the frictional angle factor with respect to the sliding

plane. The at-rest lateral earth pressure coefficient was used in bearing and overturning stability analysis.

The overturning stability and bearing pressures of the structure were checked in accordance with EM

1110-2-3104 and EM 1110-2-2100. The eccentric distance is determined by Equation 9 and the resulting

maximum and minimum bearing pressure by Equations 10 and 11 based on the resultant eccentricity

location. Equation 10 is applicable when the eccentricity falls within the middle one-third of the base and

Equation 11 is used to compute the maximum bearing when the eccentricity falls outside the middle one-

third.

The resulting percent of base in compression due to the calculated eccentricity is calculated and

compared to the minimum percent of the base in compression requirements dependent on classification

per Table 7-5.

@ = A� + B

C Eq. 9

DE�F/E�2 = CA H1 ± �

�IJ�K Eq. 10

DE�F = LM � C

A!�� Eq. 11

Where: e = Eccentricity of resultant from center of base (in)

B = Width of base of structure (in)

M = Sum of the Moments (in-kip)

N = Effective normal force on the base of the structure (kip)



TABLE 7-5 LIMITS OF RESULTANT LOCATION

Classification Percent of Base

in Compression Reference

Usual 100 EM 1110-2-3104, Table 4-2

Unusual 75 EM 1110-2-3104, Table 4-2

Extreme Within base EM 1110-2-3104, Table 4-2

F7.3 PUMP STATION STABILITY ANALYSIS

Below is a summary of the stability analysis completed for the pump station in accordance with EM 1110-

2-3104 and EM 1110-2-2502. Load combinations a, b and j were evaluated. As can be seen below in Table

7-6, of the load combinations evaluated, the pump station exceeds all the minimum factors of safety

required. The basic rectangular box pump station was utilized for preliminary stability analysis. During the

next phase of design, the valve box area will be included in the evaluation.

TABLE 7-6 PUMP STATION STABILITY ANALYSIS RESULTS


FOS Sliding

Stability

FOS Flotation

Stability

Percent of Base

in Compression

Maximum Bearing

Pressure (ksf)

a Construction Unusual 6.1 N/A 100% 2.45

b Normal operating Usual 2.4 1.5 100% 3.52

j Inundated Extreme 5.2 1.8 100% 2.96

F7.4 GATEWELL STABILITY ANALYSIS

The only stability failure mode considered controlling in the design of the gatewell was MDF water levels

surrounding an empty gatewell and causing floatation. There is not a significant enough difference in

flood side and protected side soil and water elevations to cause a reasonable sliding or overturning

stability issue. Therefore, these modes will not be computed. The results for the single checked load

combination and stability failure mode are presented in Table 7-7.

TABLE 7-7 GATEWELL STABILITY ANALYSIS RESULTS


FOS Flotation

Stability

Maximum Bearing

Pressure (ksf)

a Construction Unusual NA 3.8

e.1 MDF – No Water in Chamber Usual 1.84 3.8

e.2 MDF –Water in Chamber Usual 2.51 5.2


WP-43D 100% DDR Pump Station, Volume 2 – Appendix F – Structural Evaluation and Capacity

F8 STRUCTURAL EVALUATION AND CAPACITY

F8.1 LOAD FACTORS

Load factors for concrete structures were based on EM 1110-2-2104. A dead load factor (DL) of 1.4 was

applied to all self-weight items; concrete, steel, pumps, soil and water. A live load factor (LL) of 1.7 was

applied to hydrostatic, ice and soil loading. The factored dead and live loads are then factored by 1.3, the

hydraulic factor (HL). The 1.3 hydraulic factor is required by EM 1110-2-2104 to increase reinforcing

requirements, reduce stress level, and minimize cracking in concrete hydraulic structures.

F8.2 LOAD COMBINATIONS

Load combinations were used in accordance with EM 1110-2-2104 and as applicable from ASCE 7. Table

8-1 summarizes the load combinations evaluated for each structure. Table 8-2 shows the load

combinations that have been and will be evaluated for each design phase as well as what structural

element is controlled by each load combination.

TABLE 8-1 LOAD COMBINATIONS

Load

Condition Description Load Combination Reference

Ultimate Non-hydraulic 1.4DL+1.7LL EM 1110-2-2104, Section 3-3

Hydraulic 1.3(1.4DL+1.7LL) EM 1110-2-2104, Section 3-3

Where: DL = dead load

LL = live load

TABLE 8-2 APPLICABLE LOAD COMBINATIONS

Load Combinations Applicability Description Design

Phase

a Construction Controls outwards flexure on walls when tested with fluid Controls bottom slab 95%

b Normal operating Will not control – not accounted for in concrete capacity design NA

c Pump start-up Will not control – not accounted for in concrete capacity design NA

d Pump stop Will not control – not accounted for in concrete capacity design NA

e MDF Controls inwards flexure on walls (for gatewell) 35%

f Maximum pump thrust May control isolated locations in bottom slab (for pump station) 95%

g Maintenance

Controls downward flexure on top slab when subject to maintenance

vehicle loading 35%

h Rapid drawdown Controls inwards flexure on walls (for pump station) 35%

i Blocked trashrack Controls trashrack design 95%

j Inundated Will not control – not accounted for in concrete capacity design NA

k Coincident pool + OBE <0.1 G NA

l Coincident pool + MDE <0.1 G NA


WP-43D 100% DDR Pump Station, Volume 2 – Appendix F – Structural Evaluation and Capacity

F8.3 RESISTANCE FACTORS

For the design of both concrete and steel items, the calculated capacity of the section must be reduced by

the associated resistance factor. Below in Table 8-3 is a summary of the typical resistance factors used for

both concrete and steel per ACI 318 and AISC, respectively.

For hydraulic structural steel items, the calculated capacity is reduced by the reliability factor listed in EM

1110-2-2105 Section 3-4. All steel components involved in this project are assumed to be exposed for

inspections and not subject to brackish water. Therefore, the AISC resistance factors are multiplied by 0.9

resulting in a resistance factor of 0.81. This is reflected in Table 8-3.

TABLE 8-3 RESISTANCE FACTORS

Material Design Resistance Factor Reference

Concrete

Axial – compression 0.70 ACI, C9.3.2

Axial – tension 0.90 ACI, C9.3.2

Shear and Torsion 0.85 ACI, C9.3.2

Flexure – tension 0.90 ACI, C9.3.2

Flexure - compression 0.65 – 0.90 ACI, C9.3.2

Steel

Axial – tension 0.81 AISC, Chapter D

Axial – compression 0.81 AISC, Chapter E

Flexure 0.81 AISC, Chapter F

Shear 0.81 AISC, Chapter G


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Structural Capacity

F9 STRUCTURAL CAPACITY

Structural design of the hydraulic structures is in accordance with EM 1110-2-2104, EM 1110-2-2105 for

concrete and steel, respectively. ACI 318 was used to determine the ultimate design capacity for concrete

and steel, respectively. The following sections provide design capacity methodology and discussion of the

analytical process for each hydraulic structure design.

F9.1 CONCRETE DESIGN CAPACITY METHODOLOGY

F9.1.1 SHEAR

The shear strength of the concrete was calculated using ACI 318, Chapter 11. Unless necessary, the

concrete depth of the section was designed to be adequate to resist the maximum calculated shear force.

In case where the concrete depth was not adequate, such as concrete beams between hatch openings,

shear reinforcement was provided to resist the maximum calculated shear force. All concrete flexural

elements were considered to be two-way flexural systems with a high level of redundancy. Therefore, the

provisions of ACI 11.4.6.1 requiring a minimum area of shear reinforcing when Vu exceeds 0.5ΦVn were

neglected. The shear capacity for concrete, reinforcement, and combined concrete and reinforcement are

provided below in Equations 12, 13 and 14, respectively.

N� = 2OP�QR,S Eq. 12 (ACI 318, Eq. 11-3)

N� =8T;UVW�T Eq. 13 (ACI 318)

N2 = N� + N� Eq. 14 (ACI 318, Eq. 11-2)

Where: Vn = nominal shear strength (kip)

VC = nominal concrete shear strength (kip)

Vs = nominal steel reinforcement shear strength (kip)

f’c = minimum 28 day concrete compressive strength (ksi)

bw = width of analysis (inch)

d = distance from extreme compression fiber to centroid of tension

reinforcement (inch)

Av = shear reinforcement area (square inch)

fy = shear reinforcement minimum yield strength (ksi)

sv = spacing of shear reinforcement (inch)

F9.1.2 FLEXURE

Flexure capacity of concrete members was calculated using ACI 318, Chapter 10. The flexure capability for

all slabs, walls and beams were evaluated. Elements were evaluated as one-way slabs that were simply

supported for a 1 foot width of analysis. Capacity was determined for each orthogonal direction in line



with the reinforcing steel for that direction. The flexure capacity for concrete are provided below in

Equations 15 and 16.

X = 8<;UYZ;=[VW Eq. 15 (ACI 318, Chapter 10)

\2 = ]�P̂ _S − ��` Eq. 16 (ACI 318, Chapter 10)

Where: Mn = nominal flexure strength (kip)

a = depth of equivalent rectangular stress block (inch)

As = flexure reinforcement area (square inch)

fy = flexure reinforcement minimum yield strength (ksi)

β1 = compression block reduction factor

f’c = minimum 28 day concrete compressive strength (ksi)

bw = width of analysis (inch)

d = distance from extreme compression fiber to centroid of tension

reinforcement (inch)

F9.2 STRUCTURAL ANALYSIS

While the walls and slabs that constitute a majority of the pump station and gatewell structures are two-

way concrete systems, for a majority, the bi-directional distribution of force was ignored for the 35%

design. Instead, the design force was assumed to distribute through flexure along the shortest span. All

connections with perpendicular structural walls and slabs are assumed to be fixed.

For the design, bi-directional moment behavior was accounted for through the use of distribution factors

presented in Roark’s Formulas for Stress and Strain. Bi-directional behavior was only accounted for in wall

elements. Typical single-directional moment behavior was assumed for base and top slab elements.

F9.3 GRAVITY DRAIN INLET DESIGN CAPACITY

The concrete design for the gravity drain inlet will be the responsibility of the precast concrete supplier.

All external forces are assumed to be equal and opposite resulting in no significant stability issues.

The trashrack support beams and rails were designed assuming an 80% blocked condition with the head

water to the interior drainage design water elevation and a back pressure at 80% of that height.

Trashrack rails were assumed to be braced against lateral torsional buckling at 6 inches, the spacing of the

horizontal 1-inch rails. HSS beams are to be post-installed into the box culvert wall with ¾-inch-diameter

epoxy-grouted anchors. These beams were assumed to be unbraced for their entire 10 foot length.

Gravity drain inlet calculated and design capacity values are shown in Table 9-1.



TABLE 9-1 GRAVITY DRAIN INLET CALCULATED AND DESIGN CAPACITY VALUES

Design Element

Description

Calculated Maximum Design Capacity Utilization

Shear

Force

Moment

Force

Shear

Force

Moment

Force Shear Moment

(kip) (kip-ft) (kip) (kip-ft) (%) (%)

Trashrack Rails 0.19 0.43 9.7 0.69 2 72

Trashrack support beams 18.6 46.3 152.5 69.0 13 67

F9.4 PUMP STATION DESIGN CAPACITY

Below is a discussion of each design element that was evaluated for the design. The pump station base

slab is supported by native soil and the backfill around the structure vertically is assumed to be native soil

that was removed during excavation of the pump station.

F9.4.1 BASE SLAB

The maximum force was determined to be the upward force caused by bearing pressure forces and uplift

forces from the design hydrostatic pressure, with only the concrete slab self-weight resisting the force.

The uplift force was calculated based on the worst hydrostatic pressure that could be placed on the base

slab. This uplift force was applied as a uniform load across the entire area of the slab.

The exterior portion of the base slab that cantilevers from the exterior edge of the vertical walls was

evaluated. This portion was evaluated as one-way slab strips of 1 foot of width that is supported on the

fixed end by the exterior edge of the vertical walls. On the bottom of the slab, the same hydrostatic and

bearing pressures calculated for the interior base slab was used. Unlike the interior base slab, there are

downward forces on this portion of the cantilevered base slab section due to the buoyant soil, water, and

concrete slab weights. The force due to these three items was calculated and applied as a uniform load to

resist the uplift force.

The design approach discussed above is conservative. The calculated maximum shear and moment forces,

design shear and moment forces and utilizations are listed below in Table 9-2. As can be seen, the base

slab has adequate capacity to resist the calculated forces.

TABLE 9-2 PUMP STATION BASE SLAB CALCULATED AND DESIGN CAPACITY VALUES

Design Element

Description


Shear

Force

Moment

Force

Shear

Force

Moment

Force Shear Moment


Interior base slab 36.4 232.1 38.1 277.0 95 84



F9.4.2 EXTERIOR VERTICAL WALLS

The exterior vertical walls of the pump station were designed for the base maximum hydrostatic head and

buoyant soil pressure acting perpendicular to the wall. The maximum forces were calculated using Roark’s

plate equations due to distribution of the wall section since the bottom and vertical sides are a fixed

condition and the top is free.

The design approach discussed above is conservative. The calculated maximum shear and moment forces,

design capacity shear and moment forces, and utilizations are listed below in Table 9-3. As can be seen,

the exterior vertical walls have adequate capacity to resist the calculated forces.

TABLE 9-3 PUMP STATION EXTERIOR VERTICAL WALLS CALCULATED AND DESIGN CAPACITY VALUES

Design Element

Description


Shear

Force

Moment

Force

Shear

Force

Moment

Force Shear Moment


Pump station walls 36.9 96.8 37.9 138.5 97 70

Valve walls 14.0 11.3 37.9 138.5 37 28

F9.4.3 INTERIOR VERTICAL WALL

The baffle wall was evaluated based on the hydrostatic pressure and force from the flowing water. The

maximum forces were calculated using Roark’s plate equations due to distribution of the wall section

since the bottom and vertical sides are a fixed condition and the top is free.

The design approach discussed above is conservative. The calculated maximum forces, design capacities

and utilizations are listed below in Table 9-4. As shown below, the interior vertical walls have adequate

capacity to resist the calculated forces.

TABLE 9-4 PUMP STATION INTERIOR VERTICAL WALLS CALCULATED AND DESIGN CAPACITY VALUES

Design Element

Description


Shear

Force

Moment

Force

Shear

Force

Moment

Force Shear Moment


Baffle wall 5.7 11.2 6.1 14.1 92 79

Valve separation wall 15.5 38 19.8 71 78 54

F9.4.4 TOP SLAB

The top slab was evaluated for two loading conditions design. The maximum force was determined to be

the uniform load across the entire top slab due to vehicular traffic, 300 psf along with the inclusion of the



concrete self-weight of the slab. The portion of the slab that is continuous without discontinuities from

hatch openings was evaluated as a one-way slab strip of 1 foot of width that is simply supported by the

exterior vertical walls. The beam between adjacent hatches was evaluated for the uniform vehicular load

along with the inclusion of the triangular distribution that is carried by the hatch. The controlling case,

uniform slab or beam between hatches, was used to determine preliminary thickness of the top slab. The

preliminary design approach discussed above is conservative. The calculated maximum forces, design

capacities and utilizations are listed in Table 9-5. The table shows that the top slab has adequate capacity

resist the calculated forces.

TABLE 9-5 PUMP STATION TOP SLAB CALCULATED AND DESIGN CAPACITY VALUES

Design Element

Description


Shear

Force

Moment

Force

Shear

Force

Moment

Force Shear Moment


Slab 11.9 37.7 22.3 63.9 53 59

Beam – between hatches 19.0 85.0 22.3 94.4 85 90

F9.5 GATEWELL DESIGN CAPACITY

The gatewell is supported by compacted native soil. Levee material surrounds the gatewell on all four

sides. The controlling force occurs on the exterior walls when the gatewell is empty and the MDE flood

condition exists in the soil surrounding the gatewell. The “East Wall” is the controlling wall based on span

and aspect ratio. Under this loading situation, the resulting maximum forces are reported in Table 9-6. A

3-foot-thick slab with #8 bars @ 12” o.c. was selected to resist the shear force without the use of shear

reinforcing. Identical reinforcing was used on both faces to simplify construction and improve quality

assurance. The wall was assumed to span both horizontally and vertically in two-way flexure. Methods of

tabulated coefficients presented in Roark’s Formulas for Stress and Strain were used to account for the

two-way flexure. Shear friction per ACI 11.6.4 was confirmed at the construction joints at the top and

bottom of the wall elements to provide shear capacity at those interfaces. See the detailed computations

in the remainder of this appendix for additional methods and assumptions.

The interior wall is loaded by way of thrust force from four 16-inch pipes and by static loading in the event

the middle gate is closed. The wall spans both horizontally and vertically in two-way flexure and was

designed using the method explained in the previous paragraph. See the detailed computations in the

remainder of this appendix for additional methods and assumptions. A 2-foot 6-inch-thick wall with #8

bars @ 12” o.c. each way was selected to resist the shear force without the use of shear reinforcing.

The top slab was discretized into three assumed one-way flexural elements as identified in the

computations later in this appendix. Identical reinforcing was used on both faces to simplify construction

and quality assurance. See the detailed computations in the remainder of this appendix for additional

methods and assumptions



The controlling force occurs on the base slab when the gatewell is empty and thus the largest bearing

pressure results in the largest flexure. Under this loading situation, the resulting maximum forces are

reported in Table 9-6. A 3-foot-thick slab with #8 bars @ 12” o.c. was selected to resist the shear force

without the use of shear reinforcing. Identical reinforcing was used on both faces to simplify construction

and quality assurance. The slab was conservatively assumed to span in the long direction in one-way

flexure. See the detailed computations in the remainder of this appendix for additional methods and

assumptions.

TABLE 9-6 GATEWELL DESIGN CAPACITY VALUES

Design Element

Description


Vu Mu ΦVn ΦMn Shear Moment


East wall 37.9 57.9 38.0 110.0 100 53

Middle wall 22.6 36.3 22.7 58.8 100 62

Top slab 3.7 11.4 13.2 27.5 28 41

Bottom slab 25.4 72.2 39.0 99.4 65 72

F9.6 GRAVITY DRAIN OUTLET DESIGN CAPACITY

The structure will exhibit equivalent lateral pressures resulting in negligible overturning and sliding

stability issues. Flotation will not be possible as there is no loading condition where high water would

exist with an empty stilling basin. The overturning of the wing walls is resisting by the base slab.

A two-dimensional frame model was composed for the controlling section of wing wall and slab with

compression-only soil springs as boundary conditions along the base. The base slab and wing walls were

designed using the enveloped and factored moment and shear values from this model. See the detailed

computations in the remainder of this appendix for additional methods and assumptions. Gravity drain

outlet design capacity values are shown in Table 9-7, below.

TABLE 9-7 GRAVITY DRAIN OUTLET DESIGN CAPACITY VALUES

Design Element

Description


Vu Mu ΦVn ΦMn Shear Moment


Wing wall 13.0 49.8 13.0 51.4 100 97

Base slab 13.6 49.8 29.6 83.6 46 60


WP-43D BCOE 4/1/2016 DDR Pump Station, Volume 2 – Appendix F – Design Quality Control

F10 DESIGN QUALITY CONTROL

F10.1 QUALITY CONTROL

Quality control for all structural components was completed in accordance with the project quality

control plan.

There were multiple designers working on the structural components of this project. Some design

methodology may vary slightly between components. The table below shows a summary breakdown of

the quality-control personnel for each structural component.

Structural Component Designer Calculations Check Engineer of Record

Gravity Drain Inlet BJ Siljenberg Chris Toulouse Adéle Braun

Pump Station Allison Lunde Chris Toulouse Adéle Braun

Gatewell BJ Siljenberg Chris Toulouse Adéle Braun

Gatewell Middle Wall Darren Preiner BJ Siljenberg Adéle Braun

Gravity Drain Outlet BJ Siljenberg Chris Toulouse Adéle Braun

Oxbow-Hickson-Bakke Ring Levee System

Attachment F1 – Gravity Drain Inlet Calculations

ATTACHMENT F1 – GRAVITY DRAIN INLET CALCULATIONS

Drawing Ref(s):

SK102 Sheet No. 1 of 11

Computed Checked Submitted

Project Name: OHB Levee – Inlet Trashrack

Model

By: BJS By: CJT By: BJS Project Number: 34091004.10

Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015

10 - Inlet Model Summary.docx

1.0 Contents

1.1 Overall Design Philosophy .......................................................................................................................................... 2

1.2 Risa Inputs ......................................................................................................................................................................... 3

1.2.1 Load Cases and Combinations ............................................................................................................................ 3

1.2.2 Fluid Loading .............................................................................................................................................................. 4

1.3 Staad Results .................................................................................................................................................................... 6

1.3.1 Bars ................................................................................................................................................................................. 6

1.3.2 HSS Support Beams ................................................................................................................................................. 9

Figure 1: Isometric Views (a) Revit and (b) Risa Isometric Views ....................................................................................................................... 2

Figure 2: Bar Loading – Fluid Pressure from 80% assumed blockage ............................................................................................................. 4

Figure 3: HSS Support Beam Loading – Reactions from bars ............................................................................................................................. 5

Figure 4: Bar Deflected Shape – Fluid Loading ......................................................................................................................................................... 6

Figure 5: Bar Reactions (Service Level FL, Loading to HSS Support Beams) .................................................................................................. 7

Figure 6: Bar Factored & Enveloped Utilizations (<0.9) ......................................................................................................................................... 8

Figure 7: HSS Support Beam Deflected Shape – Fluid Loading ......................................................................................................................... 9

Figure 8: HSS Support Beam Reactions (Enveloped and Factored, Reactions at post-installed embeds) ...................................... 10

Figure 9: HSS Support Beam Factored & Enveloped Utilizations (<0.9) ....................................................................................................... 11

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.1 Overall Design Philosophy

The inlet system will be specified as a precast box section with a custom fabricated trash rack attached to the face. The

design of the precast box section will be the responsibility of the precast supplier and will be specified as such on the

drawings and in the specifications. The trash rack will be called out in detail on the drawings and the design is detailed

herein.

The trash rack is composed of ¼” x 2” bars spanning vertically and spaced at 3” o/c. These vertical bars have are braced

against lateral torsional buckling via ¼” x 1” bars @ 6” o/c. The bars run continuous from the top HSS to the cantilevered

portion near the invert of the channel/box section. The bars between the top HSS and the top of the box section will be

specified as part of a hing-gate section which can be opened in emergency situations; these bars are pinned at both ends.

The bars were modeled and designed in RISA. The results of that Analysis/Desgin are presented below.

The reactions from these bars load the horizontally spanning HSS sections. These sections were analyzed and designed in

the same model. Their results are also presented below.

.

(a) (b)

Figure 1: Isometric Views (a) Revit and (b) Risa Isometric Views

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.2 Risa Inputs

1.2.1 Load Cases and Combinations

Basic Load Cases:

Load Combinations:

The only dead load which acts on the trashrack system is the self-weight which is computed internally in Risa.

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.2.2 Fluid Loading

1.2.2.1 Bars

Figure 2: Bar Loading – Fluid Pressure from 80% assumed blockage

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.2.2.2 HSS Support Beams

Figure 3: HSS Support Beam Loading – Reactions from bars

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.3 Risa Results

1.3.1 Bars

Figure 4: Bar Deflected Shape – Fluid Loading

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


Figure 5: Bar Reactions (Service Level FL, Loading to HSS Support Beams)

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


Figure 6: Bar Factored & Enveloped Utilizations (<0.9)

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.3.2 HSS Support Beams

Figure 7: HSS Support Beam Deflected Shape – Fluid Loading

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


Figure 8: HSS Support Beam Reactions (Enveloped and Factored, Reactions at post-installed embeds)

Drawing Ref(s):




Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


.

Figure 9: HSS Support Beam Factored & Enveloped Utilizations (<0.9)

Inlet Structure Trash Rack OHB Flood Control ProjectComputed By: BJS, 1/27/15Checked By: CJT, 2/5/15Submit Date: 2/9/2015

1.0 Description, Assumptions, and References

1.1 Description

This worksheet computes the applied loading and capacities of the wall and slab

elements which compose the outlet structure

1.2 Assumptions

1. Grillage is anchored horizontally and vertically resulting in two-way action

2. All pinned reactions and interaction between members (3/4" bars vertically at 3" OC,

1/2" bars horizontally at 6" OC)

3. 5' Head differential (90% blocked)

1.3 References

- ACI 318-08 Building Code Requirements for Structural Concrete and Commentary, ACI,

2008

- ASCE/SEI 7-05 Minimum Design Loads for Buildings and Other Structures , ASCE,

2005

- AISC Manual for Steel Construction (14th ed.), AISC, 2010

- Gere, James R.; "Mechanics of Materials (6th ed.)", Thomson Brooks/Cole, 2004

- Lindeburg, Michael R.; "Civil Engineering Reference Manual (11th ed.)", Proffessional

Publications, 2008

- USACE, "EM-1110-2-2105 Design of Hydraulic Steel Structures." USACE, 1993,

Washington DC.

11 - Inlet Trashrack Model Loading.xmcd

1


2.0 Geometry and Materials

2.1 Geometry

2.1.1 Water Elevations

EL1 0 ft⋅:= Elevation: Top of Base Slab

EL2 12.15 ft⋅:= Elevation: Top of Downstream Pressure Head

EL3 2.43 ft⋅:= Elevation: Top of Upstream Pressure Head

2.1.2 Support Beam Elevations

ELA 2.29 ft⋅:=Elevation of first horizontal beam

ELB 5.03 ft⋅:=Elevation of second horizontal beam

ELC 7.09 ft⋅:=Elevation of third horizontal beam

2.1.3 Bars

Sp 3 in⋅:=Spacing of vertical bars

2.2 Materials

γw 62.4pcf:=Density of water


2


2.3 Loading for Structural Model Input

3.1 Area Loads Tributary to HSS Supports

P1 γw EL2 EL1−( )⋅ 0.758 ksf⋅=:=

PA γw EL2 ELA−( )⋅ 0.615 ksf⋅=:=

PB γw EL2 ELB−( )⋅ 0.444 ksf⋅=:=

PC γw EL2 ELC−( )⋅ 0.316 ksf⋅=:=

P3 γw EL3 EL1−( )⋅ 0.152 ksf⋅=:=

3.2 Linear Loads Tributary to Vertical Bars

Pbar.1

P1 Sp⋅ 0.19 klf⋅=:=Pbar.1

Pbar.A PA Sp⋅ 0.154 klf⋅=:=

Pbar.B PB Sp⋅ 0.111 klf⋅=:=

Pbar.C PC Sp⋅ 0.079 klf⋅=:=

Pbar.3 P3 Sp⋅ 0.038 klf⋅=:=


3


3.3 Linear Loads Tributary to Vertical Bars

RA.X .546− k⋅:=

RA.Y .021− k⋅:=

RB.X .181− k⋅:=

RB.Y .55− k⋅:=

RC.X .204− k⋅:=

RC.Y .374− k⋅:=

RA.X.Linear

12 in⋅Sp

RA.X⋅

ft:=

RA.Y.Linear

12 in⋅Sp

RA.Y⋅

ft:=

RB.X.Linear

12 in⋅Sp

RB.X⋅

ft:=

RB.Y.Linear

12 in⋅Sp

RB.Y⋅

ft:=

RC.X.Linear

12 in⋅Sp

RC.X⋅

ft:=

RC.Y.Linear

12 in⋅Sp

RC.Y⋅

ft:=


4


RA.X.Linear 2.184− klf⋅=

RA.Y.Linear 0.084− klf⋅=

RB.X.Linear 0.724− klf⋅=

RB.Y.Linear 2.2− klf⋅=

RC.X.Linear 0.816− klf⋅=

RC.Y.Linear 1.496− klf⋅=


5


Attachment F2 – Pump Station Calculations

ATTACHMENT F2 – PUMP STATION CALCULATIONS

PROJECT: Oxbow Pump Station TO13

SUBJECT: Stabiltiy Analysis Summary

COMPUTED BY: AAL2, 02/05/2015

CHECKED BY: CJT2, 02/09/2015

Stability Analysis Minimum RequirementsSliding Requirements: for normal structures, ordinary site information category per EM 1110‐2‐3104 per Table 4‐2

Usual Unusual Extreme

Sliding Safety Factor 2 2 1.33

SFs=(N*tan()+cL)/T Eq. 3‐1

N =

=c =

L = Length of the structure in contact with the foundation

T = Shear force acting parallel to the base of the structure

Flotation Requirements: per EM 1110‐2‐2100 per Table 3‐4


Flotation Safety Factor 1.3 1.2 1.1

SFf=(Ws+Wc+S)/(U‐Wg) Eq. 3‐2

Ws =

Wc =

Wg =

S = Surcharge loads

U = Uplift forces acting on the base of the structure

Overturning Requirements : per EM 1110‐2‐2100 per Table 3‐5


% Base in Compression 100% 75%Resultant

within base

Stability Summary Results

7.16 N/A 100% 2.50

2.0 1.5 100% 3.66

7.0 1.8 100% 3.08

Weight of the water above the top surface of the structure which is controlled by gravity flow

Force acting normal to the sliding failure plane under the structure

angle of internal friction of the foundation material

Cohesive strength of the foundation material

Weight of the structure, including weights of fixed equipment and soil above the top surface of the structure

Weight of the water contained within the structure

e. MDF

f. Maximum pump thrust

FOS Sliding

Stability

FOS Flotation

Stability

Percent of Base in

Compression

d. Pump stop

N/A

N/A

N/A

N/A

Summary Results

Load Combinations

a. Construction

b. Normal operating

c. Pump start‐up

Maximum Bearing

Pressure (ksf)

l. Coincident pool + MDE

N/A

N/A

g. Maintenance

h. Rapid downdown

i. Blocked trash rack

j. Inundated

k. Coincident pool + OBE

N/A

N/A

N/A

F2.1 OF F2.83


SUBJECT: Stability Material Properties



Table 1.1: Material Property Inputs

NameEquation/Variable

Value

Density of concrete c 0.150 kcf

Density of water w 0.0624 kcf

Density of soil moist m 0.115 kcf

Density of soil saturated s 0.125 kcf

Density of soil buoyant b 0.063 kcf

Friction angle 28 degrees

Friction angle shear interface v 28 degrees

cohesion c 900 psf

Friction angle for sliding =(2/3)* tan(v) 0.35

At‐rest lateral earth pressure coefficent Ko=1‐sin() 0.53

Active lateral earth pressure coefficent Ka=(1‐sin())/(1+sin()) 0.36

Passive lateral earth pressure coefficient Kp=(1+sin())/(1‐sin()) 2.77

Table 1.2: Loading Conditions

Name Equation/Variable Value

Net Wind Horizontal ASCE 7 19.8 psf

Net Wind Vertical ASCE 7 23.9 psf

Snow ASCE 7 40.3 psf

F2.2 OF F2.83


SUBJECT: Pump Station Geometry



Elevation: Pump Station

Section: Pump Station

F2.3 OF F2.83


SUBJECT: Stability Analysis ‐ Construction



Loading: Construction Condition ‐ 4‐foot soil compation difference

Category: Unusual

Table 1: Geometry Inputs

Value

feet

Top slab thickness A 2

Wall Height B 22

Bottom slab thickness C 3

Bottom slab overhang D 1

Wall thickness E 3

Interior length F 18

Interior width G 25.5

Inlet pipe diameter H 5.5

Pump outlet pipe diameter I 1.33

Interior separation wall thickness J 2.00

Interior wet well length K 6.00

Elevation top of slab M 916.50

Elevation top of grade ‐F.S. N 916.00

Elevation water ‐ F.S. O 889.50

Elevation pipe invert Q 898.00

Elevation bottom of slab R 889.50

Elevation top of grade ‐ P.S. S 912.00

Elevation water ‐ P.S. T 889.50

Length of Base L 34.00

Width of Base W 33.50

Table 2: Vertical/Gravity Weight

Length Height Thickness Volume Weight

feet feet feet feet3 kips

Superstructure 22.54 1 483.0 KLJ estimate of superstructure weight

Wall "F" 24.00 22.0 3 2 3168 475.2

Wall "G" 25.50 22.0 3 2 3366 504.9

Edge Overhang Soil "G" River Side 27.50 23.5 1 1 646.25 74.3

Edge Overhang Soil "F" Side 18.00 23.5 1 2 846 97.3

Edge Overhang Soil "G" Land Side 27.50 23.5 1 1 646.25 74.3

Interior Wall 25.50 22.0 2 1 1122 168.3

Top Slab 24.00 31.5 2 1 1512 226.8

Top Opening 4 4 ‐2 4 ‐128 ‐19.2

Bottom Slab 34.00 33.5 3 1 3417 512.6

Baffle Wall 25.50 7.08 1 1 180.63 27.1

Baffle Wall Supports 6.00 4.00 1 3 72 10.8

Invert Pipe Cutout 5.50 1.00 ‐3 1 ‐71.27 ‐10.7

Pump Outlet Invert Pipe Cutout 1.33 1.00 ‐3 4 ‐16.76 ‐2.5

Front Sloped under Baffle Wall 7.85 25.50 1.33 1 133.52 20.0

Fillet 5.42 25.50 4.75 1 328.05 49.2

Pump 1 1 1 4 4.7 18.80

Water ‐ normal operating 26.00 25.50 0.00 1 0 0.00

2710.20

Table 3: Loading

Height Length Width Horizontal Vertical Arm Moment

feet feet feet kip kip feet kip‐feet

Wind (building) (‐1)*wind horiz*W*H 22.54 ‐‐ 0 0.00 (1/2)H +(M‐R) 38.27 0.00

Soil ‐ moist (‐0.5)*m*H2*Ko*W 26.50 ‐‐ 31.50 ‐674.81 ‐‐ (1/3)*(N‐O)+(O‐R) 8.83 ‐5960.78

Soil ‐ saturated rect. (‐1)*b*H2*Ko*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/2)*(O‐R) 0.00 0.00

Soil ‐ saturated tri. (‐0.5)*b*H2*Ko*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/3)*(O‐R) 0.00 0.00

Hydrostatic (‐0.5)*w*H2*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/3)*(O‐R) 0.00 0.00

Uplift ‐ rect. (‐1)*w*H*L*W 0.00 34.00 33.50 ‐‐ 0.00 L/2 17.00 0.00

Uplift ‐ tri. (‐0.5)*w*H*L*W 0.00 34.00 33.50 ‐‐ 0.00 L/3 11.33 0.00

Surcharge (vehicle) (‐0.300)*H*L*W*Ko 26.50 1.00 34.00 ‐143.40 (M‐R_)/2 13.50 ‐1935.92

Structure Weight Ws ‐‐ 34.00 33.50 ‐‐ 2710.20 L/2 17.00 46073.43

Soil ‐ moist1 0.5*m*H2*Kp*W 22.50 ‐‐ 31.50 0.375 952.42 ‐‐ (1/3)*(S‐T)+(T‐R) 7.50 7143.13

Soil ‐ saturated rect.1 b*H2*Kp*W 0.00 ‐‐ 31.50 0.375 0.00 ‐‐ (1/2)*(T‐R) 0.00 0.00

Soil ‐ saturated tri.1 0.5*b*H2*Kp*W 0.00 ‐‐ 31.50 0.375 0.00 ‐‐ (1/3)*(T‐R) 0.00 0.00

Hydrostatic 0.5*w*H2*L 0.00 ‐‐ 31.50 0.00 ‐‐ (1/3)*(T‐R) 0.00 0.00

134.21 2710.20 ‐‐ ‐‐ 45319.85

1. Maximum passive earth pressure that can be used is 1/2 of the total calculated passive lateral earth pressure. The passive lateral earth pressure can not be more than the active, thus a reduction factor is used.

Name Equation/Variable

Component Quantity

Total weight of the structure (Ws)

Component Element Force Equation

Driving Forces

Reduction Factor Arm Equation

Resisting Forces

Total Forces

F2.4 OF F2.83


SUBJECT: Stability Analysis ‐ Construction



Table 4: Sliding Analysis:

Evaluate the sliding stability of the structure due to lateral forces of soil and hydrostatic head

Force

kips

960.7

134.21

1. Ignore the shear resistance provided by the cohesion of the soil

Sliding Safety Factor Required 2.0Sliding Safety Factor (SFs = N/T) 7.16

Check OK

Table 5 ‐ Uplift Analysis:

Evaluate the uplift base pressure applied to the bottom of the base slab of the structure due to hydrostatic head

Force

kips

0.0

0.0

0.0

Flotation Safety Factor Required 1.2Flotation Safety Factor (SFf = Ws/U) N/A

Check OK Water elevation assumed to be at base of slab, thus no uplift forces applied to structure

Table 6: Bearing Pressure Analysis:

Evaluate the overturning moment applied to the structure from lateral forces due to soil and hydrostatic head

Equation Value

Resultant Location X_R=SM/SV 16.72

Eccentricity* ecc = abs((L/2)‐X_R) 0.28 feet

Max Eccentricity eccmax=L/6 5.67 feet

Area Area = L*W 1139.00 sq. feet

Bearing pressure q1 = ((V/A)‐U)*(1+((6*ecc)/L) 2.50 ksf

Bearing pressure q2 = ((V/A)‐U)*(1‐((6*ecc)/L) 2.26 ksf

*Weight of structure and uplift force resultants add at the centroid of the structure.

Overturning Percent Base in Comp. Req. 75%

Percent Bearing 100%

Check OK

Overturning Evaluation

Lateral Force Evaluation

Equation

Normal force acting at sliding failure plane N=V*Shear force acting parallel to structure base T=H

Flotation Safety Factor Evaluation

Sliding Safety Factor Evaluation

Uplift Force ‐ from Table 2.3

Rectangular portion

Triangular portion

Total uplift force ‐ applied on base of the structure (U)

F2.5 OF F2.83


SUBJECT: Stability Analysis ‐ Normal Operating



Loading: Normal Operation

Category: Usual


Value

feet


Wall Height B 22



Wall thickness E 3




















Wall "F" 24.00 22.0 3 2 3168 475.2

Wall "G" 25.50 22.0 3 2 3366 504.9




Edge Overhang Water "G" River Side 27.50 23.5 1 1 646.25 40.3

Edge Overhang Water "F" Side 18.00 23.5 1 2 846 52.8

Edge Overhang Water "G" Land Side 27.50 23.5 1 1 646.25 40.3

Interior Wall 25.50 22.0 2 1 1122 168.3

Top Slab 24.00 31.5 2 1 1512 226.8

Top Opening 4 4 ‐2 4 ‐128 ‐19.2

Bottom Slab 34.00 33.5 3 1 3417 512.6

Baffle Wall 25.50 7.08 1 1 180.63 27.1





Fillet 5.42 25.50 4.75 1 328.05 49.2

Pump 1 1 1 4 4.7 18.80

Water ‐ normal operating 26.00 25.50 2.50 1 1657.5 103.43

2835.01

Table 3: Loading



Wind (building) wind horiz*W*H 22.54 ‐‐ 33.5 14.95 (1/2)H +(M‐R) 38.27 572.22

Soil ‐ moist 0.5*m*H2*Ko*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/3)*(N‐O)+(O‐R) 26.50 0.00

Soil ‐ saturated rect. b*H2*Ko*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/2)*(O‐R) 13.25 0.00

Soil ‐ saturated tri. 0.5*b*H2*Ko*W 26.50 ‐‐ 31.50 367.33 ‐‐ (1/3)*(O‐R) 8.83 3244.74

Hydrostatic 0.5*w*H2*W 26.50 ‐‐ 31.50 690.17 ‐‐ (1/3)*(O‐R) 8.83 6096.51

Uplift ‐ rect. (‐1)*w*H*L*W 26.50 34.00 33.50 ‐‐ ‐1883.45 L/2 17.00 ‐32018.66

Uplift ‐ tri. (‐0.5)*w*H*L*W 26.50 34.00 33.50 ‐‐ 0.00 L/3 11.33 0.00

Surcharge (vehicle) 0.300*H*L*W*Ko 26.50 1.00 34.00 143.40 (N‐R_)/2 13.25 1900.07


Soil ‐ moist1 (‐0.5)*m*H2*Kp*W 0.00 ‐‐ 31.50 0.1875 0.00 ‐‐ (1/3)*(S‐T)+(T‐R) 26.50 0.00

Soil ‐ saturated rect.1 (‐1)*b*H2*Kp*W 0.00 ‐‐ 31.50 0.1875 0.00 ‐‐ (1/2)*(T‐R) 13.25 0.00

Soil ‐ saturated tri.1 (‐0.5)*b*H2*Kp*W 26.50 ‐‐ 31.50 0.1875 ‐359.58 ‐‐ (1/3)*(T‐R) 8.83 ‐3176.33

Hydrostatic (‐0.5)*w*H2*W 26.50 ‐‐ 31.50 ‐690.17 ‐‐ (1/3)*(T‐R) 8.83 ‐6096.51

166.10 951.56 ‐‐ ‐‐ 18717.31



Component Quantity


Component Element Force Equation Reduction Factor Arm Equation

Driving Forces

Resisting Forces

Total Forces

F2.6 OF F2.83


SUBJECT: Stability Analysis ‐ Normal Operating





Force

kips

337.3

166.10



Check OK



Force

kips

1883.5

0.0

1883.5

Flotation Safety Factor Required 1.3Flotation Safety Factor (SFf = Ws/U) 1.51

Check OK



Equation Value








Overturning Percent Base in Comp. Req. 100%


Check OK




Rectangular portion

Triangular portion




Equation


F2.7 OF F2.83


SUBJECT: Stability Analysis ‐ Inundated



Loading: Inundated

Category: Extreme


Value

feet


Wall Height B 22



Wall thickness E 3




















Wall "F" 24.00 22.0 3 2 3168 475.2

Wall "G" 25.50 22.0 3 2 3366 504.9




Edge Overhang Water "G" River Side 27.50 23.5 1 1 646.25 40.3

Edge Overhang Water "F" Side 18.00 23.5 1 2 846 52.8

Edge Overhang Water "G" Land Side 27.50 23.5 1 1 646.25 40.3

Interior Wall 25.50 22.0 2 1 1122 168.3

Top Slab 24.00 31.5 2 1 1512 226.8

Top Opening 4 4 ‐2 4 ‐128 ‐19.2

Bottom Slab 34.00 33.5 3 1 3417 512.6

Baffle Wall 25.50 7.08 1 1 180.63 27.1





Fillet 5.42 25.50 4.75 1 328.05 49.2

Pump 1 1 1 4 4.7 18.80

Water ‐ inundated 18.00 25.50 22.00 1 10098 630.12

Water ‐ subtract baffle wall 1.00 1.00 1.00 1 ‐180.63 ‐11.27

Water ‐ subtract baffle wall supports 1.00 1.00 1.00 1 ‐72.00 ‐4.49

Water ‐ subtract front sloped concrete 1.00 1.00 1.00 1 ‐133.52 ‐8.33

Water ‐ subtract fillet 1.00 1.00 1.00 1 ‐328.05 ‐20.47

3317.14

Table 3: Loading



Wind (building) (‐1)*wind horiz*W*H 22.54 ‐‐ 33.5 ‐14.95 (1/2)H +(M‐R) 38.27 ‐572.22

Soil ‐ moist (‐0.5)*m*H2*Ko*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/3)*(N‐O)+(O‐R) 26.50 0.00

Soil ‐ saturated rect. (‐1)*b*H2*Ko*W 0.00 ‐‐ 31.50 0.00 ‐‐ (1/2)*(O‐R) 13.25 0.00

Soil ‐ saturated tri. (‐0.5)*b*H2*Ko*W 26.50 ‐‐ 31.50 ‐367.33 ‐‐ (1/3)*(O‐R) 8.83 ‐3244.74

Hydrostatic (‐0.5)*w*H2*W 26.50 ‐‐ 31.50 ‐690.17 ‐‐ (1/3)*(O‐R) 8.83 ‐6096.51

Uplift ‐ rect. (‐1)*w*H*L*W 26.50 34.00 33.50 ‐‐ ‐1883.45 L/2 17.00 ‐32018.66

Uplift ‐ tri. (‐0.5)*w*H*L*W 26.50 34.00 33.50 ‐‐ 0.00 L/3 11.33 0.00

Surcharge (vehicle) (‐0.300)*H*L*W*Ko 27.00 1.00 33.50 ‐143.96 (M‐R_)/2 13.50 ‐1943.45


Soil ‐ moist1 0.5*m*H2*Kp*W 0.00 ‐‐ 31.50 0.3125 0.00 ‐‐ (1/3)*(S‐T)+(T‐R) 26.50 0.00

Soil ‐ saturated rect.1 b*H2*Kp*W 0.00 ‐‐ 31.50 0.3125 0.00 ‐‐ (1/2)*(T‐R) 13.25 0.00

Soil ‐ saturated tri.1 0.5*b*H2*Kp*W 26.50 ‐‐ 31.50 0.3125 599.31 ‐‐ (1/3)*(T‐R) 8.83 5293.88

Hydrostatic 0.5*w*H2*W 26.50 ‐‐ 31.50 690.17 ‐‐ (1/3)*(T‐R) 8.83 6096.51

73.07 1433.69 ‐‐ ‐‐ 23906.13



Component Quantity


Component Element Force Equation Reduction Factor Arm Equation

Driving Forces

Resisting Forces

Total Forces

F2.8 OF F2.83


SUBJECT: Stability Analysis ‐ Inundated





Force

kips

508.2

73.07



Check OK



Force

kips

1883.5

0.0

1883.5

Flotation Safety Factor Required 1.1Flotation Safety Factor (SFf = Ws/U) 1.76

Check OK



Equation Value








Overturning Percent Base in Comp. Req. Resultant within base


Check OK




Rectangular portion

Triangular portion




Equation


F2.9 OF F2.83

Pump Station EvaluationTop Slab

24" Section, #8 @ 12" o.c.

Oxbow Pump Station - TO 13Computed By: AAL2Checked By: CJT2Date: 2/10/2015

I. Description and References

This worksheet computes the factured design loads, forces and capacity for the designelement.

- EM 1110-2-3104 Structural and Architectural Design of Pumping Stations, US Army Corpsof Engineers, June 30, 1989.

- EM 1110-2-2104 Strength Design for Reinforced-Concrete Hydraulic Structures, US ArmyCorps of Engineers, Aug. 20, 2003.

- ACI 318-08 Building Code Requirements for Structural Concrete and Commentary, ACI,2008

- ASCE 7 Minimum Design Loads for Buildings and other Structures.

II. Material Properties and Geometry

1. Design Element Geometry

Slab thickness ts 2ft

Slab elevation - top ELtop 916.5ft

Slab elevation - bottom ELbot ELtop ts 914.5 ft

Slab length ls 25.5ft

Slab interior width w 18ft

Hatch length hatl 8.5ft

Hatch width hatw 4ft

2. Concrete Properties

Width of analysis bw 1ft

Concrete compressive strength - 28 day fc 4500 psi

Concrete clear cover cc 4in

Elastic modulus Ec 57000 fc psi 3823.68 ksi

ACI Section 8.5

01 - Top Slab Design.xmcd 1

F2.10 OF F2.83


24" Section, #8 @ 12" o.c.


3. Reinforcement Properties

Yield strength fy 60ksi

Longitudinal reinforcement bar area albi 0.79in2

#8@12" oc

Longitudinal reinforcement bar diameter dlb 1.00in

slb 12inLongitudinal reinforcement spacing

Asl albi12in

slb

0.79 in2

Longitudinal reinforcement area

Transverse reinforcement bar area atbi 0.79in2

#8@12" oc

Transverse reinforcement bar diameter dtb 1.00in

stb 12inTransverse reinforcement spacing

Ast atbi12in

stb

0.79 in2

Transverse reinforcement area

4. One or Two Way Slab Analysis

Two way slab evaluation per ACI Chapter 18 and PCA Notes Chapter 19.

Slab length l 0.003 m2

ft

Slab width w 18 ft

Length to width ratiol

w0 m

2

One or Two Way Check Check ifls

w2 "Two Way" "One Way"

Check "Two Way"

The top slab will more than likely act as a two way slab. To be conservative for preliminarydesign, the top slab was evaluated as a one way, simply supported beam. Also, it is difficultto esimate the load distribution of interior floors, walls, pump selfweights and pump thrustbased on preliminary layout.

5. Deep Beam Check

Deep beam properties checkl

ts0.002 m

2

Checkdb ifls

ts

4 "Deep Beam" "Beam"

Checkdb "Beam"

Evaluate the section as a beam.


F2.11 OF F2.83


24" Section, #8 @ 12" o.c.


6. Free Body Diagram


F2.12 OF F2.83

Aal2

Stamp


24" Section, #8 @ 12" o.c.


III. Loading

1. Load Factors

Dead load factor DL 1.4

EM 1110-2-2104, Section 3-3

Live load factor LL 1.7

EM 1110-2-2104, Section 3-3

Hydraulic load factor HL 1.3

EM 1110-2-2104, Section 3-3

2. Dead Weight

tslab ts 2 ftSlab thickness

γconc 150pcfConcrete selfweight

Width of analysis b 1ft

Concrete weight wc γconc tslab

wc 300 psf

3. Live Load

Floor live load wlive 100psf

EM 1110-2-3104, Table 4-1

3. Truck Loadwveh 300psfVehicular uniform live load

EM 1110-2-3104, Table 4-1

Vehicular point live load pveh 16kip

EM 1110-2-3104, Table 4-1, AASHTO Section 3.6.1.2.2 and 3.6.1.2.3


F2.13 OF F2.83


24" Section, #8 @ 12" o.c.


4. Unfactored Loads

Case 1 - Uniform slab, no hatches

Unfactored maximum pressure ptot1 wc 0.75 max wlive wveh

ptot1 525.00 psf

Case 2 - Beam, hatches

Unfactored triangle pressure dueto hatches

Wtri 21

2

hatw hatl 0.75 max wlive wveh

Wtri 7650 lbf

Unfactored pressure on slab beam puni.a wc 0.75 max wlive wveh

puni.a 525.00 psf

Case 3 - Beam, hatches, point live load Pveh pveh 16 kip

6. Factored Loads


Factored maximum pressure ptot1u DL wc LL max wlive wveh

ptot1u 0.93kip

ft2

Case 2 - Beam, hatches, uniform live load

Factored triangle pressure due to hatches

Wtriu 21

2

hatw hatl LL max wlive wveh

Wtriu 17.34 kip

Factored pressure on slab beam puniu DL wc LL max wlive wveh

puniu 0.28 mkip

ft3

Case 3 - Beam, hatches, point live load Puveh LL pveh 27.2 kip


F2.14 OF F2.83


24" Section, #8 @ 12" o.c.


7. Shear Force

Evaluate as a one way slab that is 1 foot wide and simply supported beam


Shear force - simple beam Vu1

ptot1u max ls w b

2

AISC Table 3-23, Case 1Vu1 11.86 kip

Case 2 - Beam hatches Vu2a

puniu max ls w b

2Shear force - simple beam

AISC Table 3-23, Case 1Vu2a 11.857 kip

Shear force - simple beam, triangle distributionVu2b

Wtri

2AISC Table 3-23, Case 3

Vu2b 3.825 kip

Total shear force Vu2 Vu2a Vu2b

Vu2 15.68 kip

Maximum shear force Vu max Vu1 Vu2

Vu 15.68 kip


F2.15 OF F2.83


24" Section, #8 @ 12" o.c.


8. Moment Force

Evaluate as a one way slab that is 1 foot wide and simply supported beam.


Moment force - simple beamMu1

ptot1u min ls w 2 b

8

AISC Table 3-23, Case 1

Mu1 37.66 kip ft

Case 2 - Beam hatches

Moment force - simple beamMu2a

puniu min ls w 2 b

8


Mu2a 37.66 kip ft

Moment force - simple beam, triangle distribution

AISC Table 3-23, Case 3 Mu2b

Wtri hatl

6

Mu2b 10.84 kip ft

Total moment force Mu2 Mu2a Mu2b

Mu2 48.502 kip ft

Maximum moment force Mu max Mu1 Mu2

Mu 48.5 kip ft


F2.16 OF F2.83


24" Section, #8 @ 12" o.c.


IV. Computations

1. Reduction Factors

Flexure, tension controlled ϕf 0.90

ACI Section 9.3.2.1

Flexure, compression controlled, non-spiral ϕc 0.65

ACI Section 9.3.2.2

Shear and torsion ϕv 0.75

ACI Appendix C Section 9.3.2.3


F2.17 OF F2.83


24" Section, #8 @ 12" o.c.


2. Ultimate Moment Capacity - Longitudinal

Depth of analysis section dl ts ccdlb

2 19.5 in

Reduction factor β1a 0.85

ACI Section 10.2.7.3β1b 0.85 0.05

fc 4000 1000

0.825

β1c 0.65

β1 β1a fc 4000if

max β1b β1c

β1 0.825

al

Asl fy

β1 fc psi bw1.06 inDepth of equivalent stress block

ACI Section 10.2.7.1

Nominal moment capacity Mnl Asl fy dl

al

2

74.92 ft kip

Ratio of tensile steel areaρtl 0.319 β1

fc psi

fy 0.02

Ratio of steel area to section areaρl

Asl

bw dl0.003

ACI Section 10.3.4.

ϕf1 if ρtl ρl ϕc ϕf Controlling reduction factor

ϕf1 0.9

Ultimate moment capacity ϕMn.l ϕf1 Mnl

ϕMn.l 67.43 kip ft

Check moment capacity Checkultl if ϕMn.l Mu "OK" "NG"

Checkultl "OK"

Utilization of moment capacityUtilultl

Mu

ϕMn.l

Utilultl 0.72


F2.18 OF F2.83


24" Section, #8 @ 12" o.c.


3. Ultimate Moment Capacity - Transverse

Depth of analysis section dt ts cc dlbdtb

2 18.5 in


ACI Section 10.2.7.3β1b 0.85 0.05

fc 4000 1000

0.825

β1c 0.65

β1 β1a fc 4000if

max β1b β1c

β1 0.825

at

Ast fy



Nominal moment capacity Mnt Ast fy dt

at

2

70.97 ft kip

Ratio of tensile steel areaρtt 0.319 β1

fc psi

fy 0.02

Ratio of steel area to section areaρt

Ast

bw dt0.004

ACI Section 10.3.4.

ϕft if ρtt ρt ϕc ϕf Controlling reduction factor

ϕft 0.9

Ultimate moment capacity ϕMn.t ϕf1 Mnt

ϕMn.t 63.88 kip ft

Check moment capacity Checkultt if ϕMn.t Mu "OK" "NG"

Checkultt "OK"

Utilization of moment capacityUtilultt

Mu

ϕMn.t

Utilultt 0.76


F2.19 OF F2.83


24" Section, #8 @ 12" o.c.


5. Shear Capacity

Nominal concrete shear capacity Vc 2 fc psi bw min dl dt

ACI Section 11.2.1.1Vc 29.78 kip

ϕVn ϕv VcUltimate shear capacity

ϕVn 22.34 kip

Check shear capacity Checkv if ϕVn Vu "OK" "NG"

Checkv "OK"

Utilization of shear capacityUtilv

Vu

ϕVn

Utilv 0.7


F2.20 OF F2.83

Pump Station EvaluationBase Slab

36" Section, #10 @ 12" o.c.




- EM 1110-2-2104 Strength Design for Reinforced Concrete Hydraulic Strucutres, US ArmyCorps of Engineers, Aug. 20, 2003.


-ACI 318-11 Building Code Requirements for Structural Concrete and Commentary, ACI2011



ts 3.0ftSlab thickness

Slab interior length ls 18ft

Slab interior width ws 25.5ft

lover 1ftSlab overhang length

tw 3.0ftWall thickness

ELtop 916.5ftWall elevation - top

ELbot 892.5ft ts 889.5 ftWall elevation - bottom

Structure height Hw ELtop ELbot 27 ft





Ec 57000 fc psi 3823.68 ksiElastic modulus

ACI Section 8.5

03 - Base Slab Design.xmcd 1

F2.21 OF F2.83


36" Section, #10 @ 12" o.c.



fy 60ksiYield strength


#11@8" oc



Asl albi12in

slb

2.34 in2



#11@8" oc



Ast atbi12in

stb

2.34 in2



F2.22 OF F2.83


36" Section, #10 @ 12" o.c.


4. One or Two Way Slab Analysis

Two way slab evaluation per ACI Chapter 18 and Portland Cement Association Notes Chapter19.Slab interior length ls 18 ft

Slab interior width ws 25.5 ft

Length to width ratiols

ws0.706

One or Two Way Check Check ifls

ws2 "Two Way" "One Way"

Check "Two Way"

The base slab will more than likely act as a two way slab. To be conservative, the base slabwas evaluated as a one way, simply supported beam.

5. Deep Beam Check

Deep beam properties checkls

tw6

Checkdb ifls

tw


Checkdb "Beam"

Evaluate the section as a beam.


F2.23 OF F2.83


36" Section, #10 @ 12" o.c.


6. Free Body Diagram


F2.24 OF F2.83

aal2

Stamp

aal2

Stamp


36" Section, #10 @ 12" o.c.


III. Loading

1. Load Factors


EM 1110-2-2104, Section 3-3


EM 1110-2-2104, Section 3-3


EM 1110-2-2104, Section 3-3

2. Dead Weight

Density of concrete γc 150pcf

Slab selfweight - per foot pc γc ts bw 0.45kip

ft

3. Bearing Pressure

Average bearing pressure pb

3.66 1.32( )kip

ft

22.49

kip

ft

From stability analysis


F2.25 OF F2.83


36" Section, #10 @ 12" o.c.


4. Hydrostatic Pressure - Inside Pump Station

To be conservative, ignored any downward forces caused by water within the Pump Stationsince this downward force will counteract the uplift force reducing the total force acting onthe slab.

5. Pump Weights

To be conservative, ignored any downward forces caused by the pump selfweight or pumpthrust loads since this will counteract the uplift force reducing the total force acting on theslab.

6. Unfactored Loads

Case 1 - uniform load, simply supported

Unfactored maximum pressure - per feet ptot1 pb pc

ptot1 2.04kip

ft

8. Factored Loads

Case 1 - uniform load, simply supported

Factored maximum pressure - per feet ptotu1 DL pb pc

ptotu1 2.86kip

ft


F2.26 OF F2.83


36" Section, #10 @ 12" o.c.


9. Shear Force


Shear force - simple beamVu1

ptotu1 ws

2


Vu1 36.41 kip

Evaluate as a on way slab that is 1 foot wide and cantilever beam.

Shear force - cantilever beam Vu2 ptotu1 lover

AISC Table 3-23, Case 22 Vu2 2.86 kip

Maximum shear force Vu max Vu1 Vu2

Vu 36.41 kip

10. Moment Force


Moment force - simple beamMu1

ptotu1 ws2

8


Mu1 232.14 kip ft

Evaluate as a on way slab that is 1 foot wide and cantilever beam.

Moment force - cantilever beam Mu2

ptotu1 lover2

2

AISC Table 3-23, Case 22 Mu2 1.43 kip ft

Maximum moment force Mu max Mu1 Mu2

Mu 232.14 kip ft


F2.27 OF F2.83


36" Section, #10 @ 12" o.c.


IV. Computations



ACI Section 9.3.2.1


ACI Section 9.3.2.2


ACI Section 9.3.2.3, Appendic C


F2.28 OF F2.83


36" Section, #10 @ 12" o.c.



Depth of analysis section dl ts ccdlb

2 29.3 in


ACI Section 10.2.7.3β1b 0.85 0.05

fc 4000 1000

0.825

β1c 0.65

β1 β1a fc 4000if

max β1b β1c

β1 0.825

al

Asl fy



Nominal moment capacity Mn Asl fy dl

al

2

324.32 ft kip


fc psi

fy 0.02


Asl

bw dl0.007

ACI Section 10.3.4.


ϕf1 0.9

Ultimate moment capacity ϕMn.l ϕf1 Mn

ϕMn.l 291.88 kip ft


Checkultl "OK"


Mu

ϕMn.l

Utilultl 0.8


F2.29 OF F2.83


36" Section, #10 @ 12" o.c.



Depth of analysis section dt ts cc dlbdtb

2 27.89 in


ACI Section 10.2.7.3β1b 0.85 0.05

fc 4000 1000

0.825

β1c 0.65

β1 β1a fc 4000if

max β1b β1c

β1 0.825

at

Ast fy



Nominal moment capacity Mn Ast fy dt

at

2

307.82 ft kip


fc psi

fy 0.02


Ast

bw dt0.007

ACI Section 10.3.4.


ϕft 0.9

Ultimate moment capacity ϕMn.t ϕf1 Mn

ϕMn.t 277.04 kip ft


Checkultt "OK"


Mu

ϕMn.t

Utilultt 0.84


F2.30 OF F2.83


36" Section, #10 @ 12" o.c.


4. Shear Capacity



ϕVn ϕv VcUltimate shear capacity

ϕVn 38.16 kip

Check shear capacity Checkv if ϕVn Vu "OK" "NG"

Checkv "OK"


Vu

ϕVn

Utilv 0.95


F2.31 OF F2.83

Pump Station EvaluationInterior Baffle Wall

14" Section, #8 @ 12" o.c.




- EM 1110-2-2104 Strength Design for Reinforced Concrete Hydraulic Strucutres, US ArmyCorps of Engineers, Aug. 20, 2003.


-ACI 318-11 Building Code Requirements for Structural Concrete and Commentary, ACI2011.

-ASCE 7 Minimum Design Loads for Buildings and Other Structures.

-Handbook of Concrete Culvert Pipe Hydraulics, Portland Cement Association (PCA).



Wall thickness - vertical twv 1ft

Wall thickness - horizontal twh 1ft

Wall height Hwall 7ft 1in 7.08 ft

Wall length - unsupported length lwall 6ft

Wall length - horizontal unsupported length lwallh 3ft





Elastic modulus Ec 57000 fc psi 3823.68 ksi

ACI Section 8.5

04 - Baffle Wall_reduce velocity.xmcd

1

F2.32 OF F2.83


14" Section, #8 @ 12" o.c.



Yield strength fy 60ksi


#8@12" oc



Asl albi12in

slb

0.79 in2



#8@12" oc



Ast atbi12in

stb

0.79 in2



2

F2.33 OF F2.83


14" Section, #8 @ 12" o.c.


III. Loading

1. Load Factors


EM 1110-2-2104, Section 3-3


EM 1110-2-2104, Section 3-3


EM 1110-2-2104, Section 3-3

2. Dead Weight

Density of concrete γc 150pcf

Interior wall selfweight - per footpc γc

twv Hwall bw

lwallhtwh bw

0.5kip

ft

3. Water Selfweight

Density of water γw 62.4pcf

Water height Hw Hwall 7.08 ft

Water selfweight - per foot pwh γw Hw bw 0.44kip

ft

4. Hydrostatic Lateral Pressure

Hydrostatic pressure - per foot pwv γw Hw bw 0.44kip

ft

5. Lateral Pressure due to Flow

The lateral force applied to the vertical interior wall due to water flowing from the pipe.

Flow Qwt 50ft

3

sec

Velcoity of water - existing pipe Vwt 2ft

sec

Gravity gc 32.17ft

sec2

Lateral water force Fw

Qwt Vwt γw

gc0.19 kip

Assumed to act as a point load perpendicular to the interior veritcal wall at the top, mid-spanof the wall.


3

F2.34 OF F2.83


14" Section, #8 @ 12" o.c.


6. Unfactored Loads

Load Case 1 - vertical wall

Unfactored vertical total pressure load ptotv 0.5 pwv Hwall 1.57 kip

Unfactored vertical point load Ptotv Fw 0.194 kip

Load Case 2 - horizontal wall

Unfactored horizontal maximum pressure ptoth pwh pc 0.95kip

ft

7. Factored Loads


Factored vertical force ptotvu HL LL ptotv 3.46 kip

Factored vertical point load Ftotvu HL LL Ptotv 0.43 kip


Factored horizontal maximum pressure ptothu HL LL pwh DL pc 1.89kip

ft

8. Shear Force

Vertical Wall - evaluate as a one way slab that is 1 foot wide and cantilever.

Horizontal Wall - evaluate as a one way slab that is 1 foot wide and simply supported.


Shear force - beam Vuv ptotvu Ftotvu

AISC Table 3-23, Case 1AISC Table 3-23, Case 7 Vuv 3.89 kip


Shear force - beam Vuh

ptothu lwall

2

AISC Table 3-23, Case 1Vuh 5.68 kip

Maximum Design Force Vu max Vuv Vuh

Vu 5.68 kip


4

F2.35 OF F2.83


14" Section, #8 @ 12" o.c.


9. Moment Force

Evaluate as a one way slab that is 1 feet wide and cantilever.


Moment force - beamMuv

ptotvu Hwall

3

Ftotvu Hwall AISC Table 3-23, Case 1AISC Table 3-23, Case 7

Muv 11.2 kip ft

Load Case 2- horizontal wall

Moment force - beam Muh

ptothu lwall2

8

AISC Table 3-23, Case 1Muh 8.52 kip ft

Maximum Design Force Mu max Muv Muh

Mu 11.2 kip ft


5

F2.36 OF F2.83


14" Section, #8 @ 12" o.c.


IV. Computations



ACI Section 9.3.2.1


ACI Section 9.3.2.2


ACI Appendix C Section 9.3.2.3

2. Deep Beam Evaluation

lwall

twv6Deep beam properties check

Checkdb iflwall

twv


Checkdb "Beam"

Evaluate section as a beam.


6

F2.37 OF F2.83


14" Section, #8 @ 12" o.c.



Depth of analysis section dl twv ccdlb

2 5.5 in


ACI Section 10.2.7.3β1b 0.85 0.05

fc 4000 1000

0.825

β1c 0.65

β1 β1a fc 4000if

max β1b β1c

β1 0.825

al

Asl fy



Nominal moment capacity Mn Asl fy dl

al

2

19.62 ft kip


fc psi

fy 0.02


Asl

bw dl0.012

ACI Section 10.3.4.


ϕf1 0.9

Ultimate moment capacity ϕMn.l ϕf1 Mn

ϕMn.l 17.66 kip ft


Checkultl "OK"


Mu

ϕMn.l

Utilultl 0.63


7

F2.38 OF F2.83


14" Section, #8 @ 12" o.c.



Depth of analysis section dt twv cc dlbdtb

2 4.5 in


ACI Section 10.2.7.3β1b 0.85 0.05

fc 4000 1000

0.825

β1c 0.65

β1 β1a fc 4000if

max β1b β1c

β1 0.825

at

Ast fy



Nominal moment capacity Mn Ast fy dt

at

2

15.67 ft kip


fc psi

fy 0.02


Ast

bw dt0.015

ACI Section 10.3.4.


ϕft 0.9

Ultimate moment capacity ϕMn.t ϕf1 Mn

ϕMn.t 14.11 kip ft


Checkultt "OK"


Mu

ϕMn.t

Utilultt 0.79


8

F2.39 OF F2.83


14" Section, #8 @ 12" o.c.


4. Shear Capacity - Vertical Wall



ϕVn ϕv Vc Ultimate shear capacity

ϕVn 6.16 kip

Check shear capacity Checkv if ϕVn Vuv "OK" "NG"

Checkv "OK"


Vuv

ϕVn

Utilv 0.63


9

F2.40 OF F2.83


14" Section, #8 @ 12" o.c.


5. Shear Capacity - Horizontal Wall

Depth of analysis section dlh twh ccdlb

2 5.5 in

Depth of analysis section dth twh cc dlbdtb

2 4.5 in

Nominal concrete shear capacity Vch 2 fc psi bw min dlh dth

ACI Section 11.2.1.1Vch 7.24 kip

ϕVnh ϕv Vch Ultimate shear capacity

ϕVnh 6.16 kip

Check shear capacity Checkvh if ϕVnh Vuh "OK" "NG"

Checkvh "OK"

Utilization of shear capacityUtilvh

Vuh

ϕVnh

Utilvh 0.92


10

F2.41 OF F2.83


SUBJECT: Pump Station Vertical Walls

Interior Separation Wall ‐ Interior Loading



1. Project Description

2. References

‐ Roark's Formulas for Stress and Strains, Seventh Edition

3. Important Geometric Inputs

a.X: ft, panel width

b.X: ft, panel height

Thickness: 20 inches

#9 Bars @ 12 Inches O.C.



Loaded Side Clear Cover: 3 inches

Non Loaded Side Clear Cover: 6 inches

4. Design Result Summary

Vertical Shear Utilization: 0.78

Horizontal Shear Utilization: 0.22

0.54

0.38

0.00

1.00 0.34 1.94

25.50

16.58

1.00

1.00

0.66

0.49

0.34

0.34

As Provided

As

minimum

(T&S)

As minimum

(Flexure)

Vertical Reinforcing ‐ Loaded

Side:Horizontal Reinforcing ‐ Loaded

Side:Horizontal Reinforcing ‐ Non ‐

Loaded Side:


Side:

Horizontal Reinforcing ‐ Loaded

Side:

Horizontal Reinforcing ‐ Non ‐

Loaded Side:

0.00

As maximum

(0.25 A.bal)

2.37

2.37

SHEET 1 OF 6F2.42 OF F2.83







Description

Unit weight of concrete

Concrete Strength ASTM A612, Grade 60

Reinforcement Yield Strength

Concrete Density Factor

Modulus of Elasticity Ec = 57000 x sqrt(fc)/1000

Resistance Factor Shear ACI 318 9.3.2.3

Resistance Factor Bending ACI 318, 9.3.2.1

Load Factor Due to Soil

4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion

At‐Rest Coefficient Ko.i = 1 ‐ sin(Phi.i)

5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Unit

fc 4500 psi

fy 60000 psi

Gn 1

deg

c.i

Ko.i

pcf

psf

0

0 pcf

0

0

N/A

Thickness

t.Xi (in)

N/A

306.0

q.s

Value Unit

20.0

N/A

Ec 3823.68 ksi

0 psf

Phi.i 0

0

G.i

Gsat.i

Variable Native Sand i = 1

Variable

0

0

0

00

1.000

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

0

Description

Description

q.w 62.4 psf

199.0Wall A1

1.000 1.000

Native Clay i = 2Design

i = d

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

800.0

Section Modulus,

Sb.Ai (in3)

800.0

LFs 2.21







7. Wall Design using Roark.

7.1 Rectangular plate; three edes fixed, one edge free (Roark Table 11.4)

Uniform load over entire plate

Vertical:

Horizontal:

Horizontal:

Uniformly decreasing from fixed edge to zero at free edge

7.2. Roark Coefficinets based on 3 Edges Fixed, 1 Edge Free

0.493 1.110

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

N/A

2

0.151

Linearly interpolate the values presented in 6.1.a and 6.1.b above to obtain coefficients. Conservatively assume that the loads

on B1, B2, and B3 extend the entire wall. Therefore the same equations would apply

0.363 0.255

N/A 0.686

1 0.018 0.064

0.019

N/A N/A 0.410

Loading

Uniform

1.538

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

0.120 0.195

0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173

Fixed

Fixed

Free

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

1.538 0.765

0.113

20.886

10.0752

10.1480.0660.0162

0.25a/b

Sections 7‐9 of this sheet includes computations for the moments, reactions, and required reinforcement to resist the flexure and shear based

on Roark

0.510

b

a

x

z







7.3. Loading on the walls using Roark Coefficients

Load ‐ Full Height (A1)

Lateral Soil Load

Lateral Surcharge Load

Lateral Hydrostatic Load

7.4. Plate stresses and reactions per equations in Roark's Formulas for Stress and Strains

7.5. Combined Stress and Reactions with calcualted moments

Loading on both sides of the pump station is similar for wall of similar height. Assume the lower walls (A2) are designed the same as

the full height walls A1 and B1

q.SL

psi

psi

0.00 psi

Value Unit

N/A

0.00

q.PL qPL = Ko.d*q.s/144 0.00

q.HL qHL = q.w*b.A1/144 7.19

N/A

0 0 0.00 0.00 N/A

0

qSL = Ko.d*G.d*b.A1/144

Variable Equation

Location

X Z

Mb

(kip*in)/LF

R

(lb/LF)b (psi) a (psi)

Uniform

Surcharge

Loading

0

153

X

153 199 0.00 N/A

0 0 7034.40 ‐258.08

Location

Z

Triangular

Soil

Ma

(kip*in)/LF

N/A

N/A

‐181.26

0.00

b

(psi)

N/A N/A

‐258.08

a

(psi)

‐206.47

R

(lb/ft)

N/A

0.00

a/b

N/A 0.00

‐145.01

0 199 N/A N/A 0.00

153 199 1939.30 N/A ‐181.26

0.00N/A

0

N/A

0.00

1.538

Triangular

Hydrostatic

0

153

0

199

7034.40

1939.30

199

199 0.00







8. Reinforcement Design based on reactions and moments using Roark

8.1 Vertical Reinforcement Design

Description

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF

0

0.00

1.31

767

690

13.44

21,632

16,224

60,000

in

kip*in

kip*in

kip*in

lb

Unit

852 852

Factored Moment:

Mu.Ai = abs(LFs*max(Mb.Ai))456 320

Flexural Check:

If Mu.Ai / ΦMn.Ai0.54 0.38

Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/1000947 947

Nominal Moment Resistance: Mn.Ai =

Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

Shear Resistance:

Vc.Ai= 2*sqrt(fc)*d.Ai*bw.Ai26,461

depth the tension steel:

d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/216.44 16.44

26,461

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

19,846

Factored Shear Load:

Vu.Ai = LFs*max(R.Ai)4,286

Nominal Shear Resistance:

Vc.Ai = Phi.v*Vc.Ai19,846

15,546

0.22Shear Check:

Vu.Ai / ΦVc.Ai0.78

3.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side

12.00

Area Steel Prov, As.Ai*

Diameter Steel, db.Ai*

Clear Cover, Cc.Ai

Width Stress Block, bw.Ai

Vertical

Loaded Side

12.00

3.00

1.13

1.00

Horizontal Non‐

Loaded Side







8.2. Vertical Reinforcement Area Verification

Description

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.00

35,294

‐725,544

0

0.0000

0.00

0.0321

5.17

1.94

0.54

0.54

0.54

0.00

0.34

Unit

in2

in2

in2

in2

in2

0.66

0.66

Temp & Shrinkage Req. TS.Req.Ai =

0.0014*bw.Ai*t.Ai0.34 0.34

0.0027

Quadratic "A" = Phi.b*fy^2/(1.7*fc*bw.Ai) 35,294

pReq.Ai = As.Req.Ai/(bw.Ai*d.Ai) 0.0019

Quadratic "B" = ‐Phi.b*fy*d ‐887,544

2.37

As.design.Ai =

Based on above0.66 0.49

As.bal = pbal*bw.Ai*d.Ai 6.33 6.33

Minimum Steel (1): AsMin.1.Ai =

3*sqrt(fc)/fy*bw.Ai*d.Ai (ACI 10.5)0.66 0.66


200*bw.Ai*d.Ai/fy (ACI 10.5)0.66

As.max = 0.375*As.bal 2.37

Minimum Steel AsMin.Ai =

Max(AsMin.1.Ai,AsMin.2.Ai)0.66

pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐887,544

As.Req.Ai =

Use quadratic where A, B, C are:0.53 0.37

0.70 0.49

Quadratic "C" = Mu*1000 456,289 320,469




Width of Pump Station ‐ Exterior Loading




2. References














0.70

0.61

0.07

1.00 0.60 4.25

25.50

22.00

1.00

1.00

0.93

0.81

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)




Loaded Side:


Side:


Side:


Loaded Side:

0.09

As maximum

(0.25 A.bal)

4.54

4.54








Description






Resistance Factor Shear ACI 318 9.3.2.3, ACI Appendic C



4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Unit

fc 4500 psi

fy 60000 psi

Gn 1

deg

c.i

Ko.i

pcf

psf

110

115 pcf

110

115

N/A

Thickness

t.Xi (in)

N/A

306.0

q.s

Value Unit

Description Variable Native Sand i = 1

Variable

q.w 62.4 psf

264.0

47.6

57.6

28

0

Wall A1

0

0.531 0.531 0.531


i = d

N/A

Ec 3823.68 ksi

300 psf

Phi.i 28

0

G.i

Gsat.i

36.0

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

28

Description

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21










Vertical:

Horizontal:

Horizontal:



0.331 0.690

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

N/A

2

0.151

Linearly interpolate the values presented in 6.1.a and 6.1.b above to obtain coefficients. Conservatively assume that the

loads on B1, B2, and B3 extend the entire wall. Therefore the same equations would apply

0.245 0.191

N/A 0.526

1 0.018 0.064

0.019

N/A N/A 0.350

Loading

Uniform

1.159

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

0.120 0.195

0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173

Fixed

Fixed

Free

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

1.159 0.450

0.199

20.621

10.0752

10.1480.0660.0162

0.25a/b

Sections 7‐9 of this sheet includes computations for the moments, reactions, and required reinforcement to resist the flexure and shear

based on Roark

0.510

b

a

x

z









Lateral Soil Load







q.SL

psi

psi

3.86 psi

Value Unit

N/A

‐39.59

q.PL qPL = Ko.d*q.s/144 1.11

q.HL qHL = q.w*b.A1/144 9.53

N/A

0 0 4279.00 ‐50.76 N/A

0


Variable Equation

Location

X Z

Mb

(kip*in)/LF

R


X

153 264 2428.95 N/A

0 0 16693.13 ‐202.94

Ma

(kip*in)/LF

N/A

N/A

‐97.83

19.65

b

(psi)

N/A N/A

‐125.42

a

(psi)

Location

‐526.01

Z

Uniform

Surcharge

LoadingR

(lb/ft)

N/A

0

153

Triangular

Soil

‐26.76

a/b

N/A 50.93

‐462.47

0 264 N/A N/A 19.65

153 264 10605.41 N/A ‐178.42

‐41.00N/A

0

N/A

1840.83

1.159

Triangular

Hydrostatic

0

153

0

264

10573.31

6001.88

264

264 2174.58









Description

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF

113

0.07

1.31

1,727

1,554

29.44

47,391

35,543

60,000

in

kip*in

kip*in

kip*in

lb

Unit

1,662 1,662

Factored Moment:

Mu.Ai = abs(LFs*max(Mb.Ai))1,162 1,022

Flexural Check:


Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/10001,847 1,847

Nominal Moment Resistance: Mn.Ai

= Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/231.44 31.44

50,611

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

37,958





36,892

0.62Shear Check:

Vu.Ai / ΦVc.Ai0.97

4.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

1.13

1.00

Horizontal Non‐

Loaded Side

12.00








Description

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.07

35,294

‐1,589,544

112,561

0.0002

0.09

0.0321

11.33

4.25

1.18

1.18

1.18

0.09

0.60

Unit

in2

in2

in2

in2

in2

1.26

1.27


0.0014*bw.Ai*t.Ai0.60 0.60

0.0018



Quadratic "B" = ‐Phi.b*fy*d ‐1,697,544

4.54

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26

As.max = 0.375*As.bal 4.54



pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐1,697,544

As.Req.Ai =


0.93 0.81

Quadratic "C" = Mu*1000 1,162,484 1,022,059




Width of Pump Station ‐ Interior Loading




2. References














0.49

0.40

0.00

4.54

4.54

As maximum

(0.25 A.bal)


Loaded Side:


Side:


Side:


Loaded Side:

0.00

25.50

24.00

1.00

1.00

0.65

0.53

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)



Side:

1.00 0.60 4.25








Description









4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

0

Description

N/A

Ec 3823.68 ksi

0 psf

Phi.i 0

0

G.i

Gsat.i


Variable

q.w 62.4 psf

288.0

0

0

0

0

Wall A1

0

1.000 1.000 1.000


i = d

N/A

306.0

q.s

Value Unit

36.0

Thickness

t.Xi (in)

pcf

psf

0

0 pcf

0

0

N/A

deg

c.i

Ko.i

Unit

fc 4500 psi

fy 60000 psi

Gn 1










Vertical:

Horizontal:

Horizontal:



10.1480.0660.0162

0.25a/b


based on Roark

0.510

10.0752

0.5541.063 0.372

0.225

2

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50

Fixed

Fixed

Free

0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173 0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.120 0.195

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

N/A

2

0.151



0.215 0.176

N/A 0.484

1 0.018 0.064

0.019

N/A N/A 0.334

Loading

Uniform

1.063

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.287 0.581

b

a

x

z









Lateral Soil Load





0.00N/A

0

N/A

0.00

1.063

Triangular

Hydrostatic

0

153

0

288

12013.75

8087.04

288

288 0.00

a/b

N/A 0.00

‐303.21

0 288 N/A N/A 0.00

153 288 8087.04 N/A ‐116.98

Ma

(kip*in)/LF

N/A

N/A

‐116.98

0.00

b

(psi)

N/A N/A

‐142.77

a

(psi)

‐370.06

R

(lb/ft)

N/A

0.00

X

153 288 0.00 N/A

0 0 12013.75 ‐142.77

Location

Z

Triangular

Soil

X Z

Mb

(kip*in)/LF

R


Uniform

Surcharge

Loading

0

153

N/A

0 0 0.00 0.00 N/A

0


Variable Equation

Location

0.00

q.PL qPL = Ko.d*q.s/144 0.00

q.HL qHL = q.w*b.A1/144 10.40

N/A

Loading on both sides of the pump station is similar for wall of similar height. Assume the lower walls (A2) are designed the same

as the full height walls A1 and B1

q.SL

psi

psi

0.00 psi

Value Unit









Description



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

1.13

1.00

Horizontal Non‐

Loaded Side

4.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side

12.00

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/231.44 31.44

50,611

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

37,958





26,550

0.47Shear Check:

Vu.Ai / ΦVc.Ai0.70

Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/10001,847 1,847


= Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

1,662 1,662

Factored Moment:


Flexural Check:


0

0.00

1.31

1,727

1,554

29.44

47,391

35,543

60,000

in

kip*in

kip*in

kip*in

lb

Unit

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF








Description

817,839 670,094

pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐1,697,544

As.Req.Ai =


0.65 0.53

Quadratic "C" = Mu*1000

4.54


Max(AsMin.1.Ai,AsMin.2.Ai)1.27 1.27


0.0014*bw.Ai*t.Ai0.60 0.60

0.0013

Quadratic "A" =

Phi.b*fy^2/(1.7*fc*bw.Ai)35,294



4.54

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26

As.max = 0.375*As.bal in2

in2

in2

in2

in2

1.26

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.00

35,294

‐1,589,544

0

0.0000

0.00

0.0321

11.33

4.25

1.18

1.18

1.18

0.00

0.60

Unit




Length of Pump Station ‐ Exterior Loading




2. References














0.39

0.41

0.04

4.54

4.54

As maximum

(0.25 A.bal)


Loaded Side:


Side:


Side:


Loaded Side:

0.05

18.00

22.00

1.00

1.00

0.52

0.54

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)



Side:

1.00 0.60 4.25








Description









4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

28

Description

N/A

Ec 3823.68 ksi

300 psf

Phi.i 28

0

G.i

Gsat.i


Variable

q.w 62.4 psf

264.0

47.6

57.6

28

0

Wall A1

0

0.531 0.531 0.531


i = d

N/A

216.0

q.s

Value Unit

36.0

Thickness

t.Xi (in)

pcf

psf

110

115 pcf

110

115

N/A

deg

c.i

Ko.i

Unit

fc 4500 psi

fy 60000 psi

Gn 1










Vertical:

Horizontal:

Horizontal:



10.1480.0660.0162

0.25a/b


based on Roark

0.510

10.0752

0.4090.818 0.213

0.219

2

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50

Fixed

Fixed

Free

0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173 0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.120 0.195

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

N/A

2

0.151



0.140 0.136

N/A 0.373

1 0.018 0.064

0.019

N/A N/A 0.281

Loading

Uniform

0.818

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.178 0.347

b

a

x

z









Lateral Soil Load





‐20.65N/A

0

N/A

1304.78

0.818

Triangular

Hydrostatic

0

108

0

105.6

8489.40

6627.88

264

264 1431.79

a/b

N/A 27.47

‐307.72

0 264 N/A N/A 10.60

108 264 10741.96 N/A ‐118.72

Ma

(kip*in)/LF

N/A

N/A

‐69.82

10.60

b

(psi)

N/A N/A

‐72.01

a

(psi)

‐295.05

R

(lb/ft)

N/A

‐12.68

X

108 105.6 2682.29 N/A

0 0 13229.82 ‐113.83

Location

Z

Triangular

Soil

X Z

Mb

(kip*in)/LF

R


Uniform

Surcharge

Loading

0

108

N/A

0 0 3435.64 ‐29.14 N/A

0


Variable Equation

Location

‐28.26

q.PL qPL = Ko.d*q.s/144 1.11

q.HL qHL = q.w*b.A1/144 9.53

N/A



q.SL

psi

psi

3.86 psi

Value Unit









Description



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

1.13

1.00

Horizontal Non‐

Loaded Side

4.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side

12.00

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/231.44 31.44

50,611

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

37,958





29,238

0.63Shear Check:

Vu.Ai / ΦVc.Ai0.77

Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/10001,847 1,847


= Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

1,662 1,662

Factored Moment:


Flexural Check:


61

0.04

1.31

1,727

1,554

29.44

47,391

35,543

60,000

in

kip*in

kip*in

kip*in

lb

Unit

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF








Description

652,067 680,066

pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐1,697,544

As.Req.Ai =


0.52 0.54


4.54




0.0014*bw.Ai*t.Ai0.60 0.60

0.0010




4.54

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26


in2

in2

in2

in2

1.26

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.04

35,294

‐1,589,544

60,699

0.0001

0.05

0.0321

11.33

4.25

1.18

1.18

1.18

0.05

0.60

Unit




Length of Pump Station ‐ Interior Loading




2. References














0.25

0.24

0.00

4.54

4.54

As maximum

(0.25 A.bal)


Loaded Side:


Side:


Side:


Loaded Side:

0.00

18.00

22.00

1.00

1.00

0.33

0.32

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)



Side:

1.00 0.60 4.25








Description









4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

0

Description

N/A

Ec 3823.68 ksi

0 psf

Phi.i 0

0

G.i

Gsat.i


Variable

q.w 62.4 psf

264.0

0

0

0

0

Wall A1

0

1.000 1.000 1.000


i = d

N/A

216.0

q.s

Value Unit

36.0

Thickness

t.Xi (in)

pcf

psf

0

0 pcf

0

0

N/A

deg

c.i

Ko.i

Unit

fc 4500 psi

fy 60000 psi

Gn 1










Vertical:

Horizontal:

Horizontal:



10.1480.0660.0162

0.25a/b


based on Roark

0.510

10.0752

0.4090.818 0.213

0.219

2

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50

Fixed

Fixed

Free

0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173 0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.120 0.195

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

N/A

2

0.151



0.140 0.136

N/A 0.373

1 0.018 0.064

0.019

N/A N/A 0.281

Loading

Uniform

0.818

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.178 0.347

b

a

x

z









Lateral Soil Load





0.00N/A

0

N/A

0.00

0.818

Triangular

Hydrostatic

0

108

0

105.6

8489.40

6627.88

264

264 0.00

a/b

N/A 0.00

‐180.97

0 264 N/A N/A 0.00

108 264 6627.88 N/A ‐69.82

Ma

(kip*in)/LF

N/A

N/A

‐69.82

0.00

b

(psi)

N/A N/A

‐72.01

a

(psi)

‐186.65

R

(lb/ft)

N/A

0.00

X

108 105.6 0.00 N/A

0 0 8489.40 ‐72.01

Location

Z

Triangular

Soil

X Z

Mb

(kip*in)/LF

R


Uniform

Surcharge

Loading

0

108

N/A

0 0 0.00 0.00 N/A

0


Variable Equation

Location

0.00

q.PL qPL = Ko.d*q.s/144 0.00

q.HL qHL = q.w*b.A1/144 9.53

N/A



q.SL

psi

psi

0.00 psi

Value Unit









Description



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

1.13

1.00

Horizontal Non‐

Loaded Side

4.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side

12.00

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/231.44 31.44

50,611

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

37,958





18,762

0.39Shear Check:

Vu.Ai / ΦVc.Ai0.49

Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/10001,847 1,847


= Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

1,662 1,662

Factored Moment:


Flexural Check:


0

0.00

1.31

1,727

1,554

29.44

47,391

35,543

60,000

in

kip*in

kip*in

kip*in

lb

Unit

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF








Description

412,487 399,939

pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐1,697,544

As.Req.Ai =


0.33 0.32


4.54




0.0014*bw.Ai*t.Ai0.60 0.60

0.0006




4.54

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26


in2

in2

in2

in2

1.26

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.00

35,294

‐1,589,544

0

0.0000

0.00

0.0321

11.33

4.25

1.18

1.18

1.18

0.00

0.60

Unit




Dry Well ‐ Exterior Loading




2. References














0.08

0.09

0.01

1.00 0.60 4.25

6.67

24.00

1.00

1.00

0.11

0.12

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)




Loaded Side:


Side:


Side:


Loaded Side:

0.01

As maximum

(0.25 A.bal)

4.54

4.54








Description









4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Unit

fc 4500 psi

fy 60000 psi

Gn 1

deg

c.i

Ko.i

pcf

psf

110

115 pcf

110

115

N/A

Thickness

t.Xi (in)

N/A

80.0

q.s

Value Unit

36.0

N/A

Ec 3823.68 ksi

300 psf

Phi.i 28

0

G.i

Gsat.i

Variable Native Sand i = 1

Variable

47.6

57.6

28

00

0.531

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

28

Description

Description

q.w 62.4 psf

288.0Wall A1

0.531 0.531


i = d

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21










Vertical:

Horizontal:

Horizontal:



0.022 0.042

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

N/A

2

0.151



0.023 0.024

N/A 0.127

1 0.018 0.064

0.019

N/A N/A 0.116

Loading

Uniform

0.278

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

0.120 0.195

0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173

Fixed

Fixed

Free

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

0.278 0.027

0.083

20.139

10.0752

10.1480.0660.0162

0.25a/b


based on Roark

0.510

b

a

x

z









Lateral Soil Load







q.SL

psi

psi

4.21 psi

Value Unit

N/A

‐6.58

q.PL qPL = Ko.d*q.s/144 1.11

q.HL qHL = q.w*b.A1/144 10.40

N/A

0 0 1685.70 ‐6.23 N/A

0


Variable Equation

Location

X Z

Mb

(kip*in)/LF

R


Uniform

Surcharge

Loading

0

40

X

40 115.2 1213.77 N/A

0 0 6335.71 ‐23.50

Location

Z

Triangular

Soil

Ma

(kip*in)/LF

N/A

N/A

‐16.27

1.52

b

(psi)

N/A N/A

‐15.38

a

(psi)

‐60.92

R

(lb/ft)

N/A

‐1.89

a/b

N/A 3.95

‐66.86

0 288 N/A N/A 1.52

40 288 4742.64 N/A ‐25.79

‐2.94N/A

0

N/A

484.69

0.278

Triangular

Hydrostatic

0

40

0

115.2

4165.32

2999.19

288

288 529.68









Description

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF

9

0.01

1.31

1,727

1,554

29.44

47,391

35,543

60,000

in

kip*in

kip*in

kip*in

lb

Unit

1,662 1,662

Factored Moment:


Flexural Check:


Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/10001,847 1,847


= Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/231.44 31.44

50,611

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

37,958





14,002

0.28Shear Check:

Vu.Ai / ΦVc.Ai0.37

4.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side

12.00



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

1.13

1.00

Horizontal Non‐

Loaded Side








Description

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.01

35,294

‐1,589,544

8,734

0.0000

0.01

0.0321

11.33

4.25

1.18

1.18

1.18

0.01

0.60

Unit

in2

in2

in2

in2

in2

1.26

1.27


0.0014*bw.Ai*t.Ai0.60 0.60

0.0002




4.54

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26

As.max = 0.375*As.bal 4.54



pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐1,697,544

As.Req.Ai =


0.11 0.12

Quadratic "C" = Mu*1000 134,629 147,758




Dry Well ‐ Interior Loading




2. References














0.05

0.06

0.00

4.54

4.54

As maximum

(0.25 A.bal)


Loaded Side:


Side:


Side:


Loaded Side:

0.00

6.67

24.00

1.00

1.00

0.07

0.07

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)



Side:

1.00 0.60 4.25








Description









4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6

Height

b.Xi

(in)

Length

a.Xi

(in)

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21

Description

36.0

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

0

N/A

Ec 3823.68 ksi

0 psf

Phi.i 0

0

G.i

Gsat.i


Variable

q.w 62.4 psf

288.0

0

0

0

0

Wall A1

0

1.000 1.000 1.000


i = d

N/A

80.0

q.s

Value Unit

Thickness

t.Xi (in)

pcf

psf

0

0 pcf

0

0

N/A

deg

c.i

Ko.i

Unit

fc 4500 psi

fy 60000 psi

Gn 1










Vertical:

Horizontal:

Horizontal:



10.1480.0660.0162

0.25a/b


based on Roark

0.510

10.0752

0.1390.278 0.027

0.083

2

0.211 0.242 0.106 0.199

0.75 1.00

1.50 2.00

0.387

1.212

0.265

1.50

0.351

0.166 0.244

0.859

0.511 1.073

2.00

1.568

0.341 0.457 0.673

Fixed

Fixed

Free

Fixed

0.50

1

7.1.b

3 0.031 0.126

0.114 0.230

0.25 0.50 0.75

0.507

2 0.125 0.248 0.371

1.00

0.020

0.845

0.173 0.727 1.226

0.259 0.484 0.605

0.321

0.324 0.406 0.458

N/A

0.120 0.195

0.081

3.00

2.105

0.519

1.9820.286

7.1.a

a/b

N/A

2

0.151



0.023 0.024

N/A 0.127

1 0.018 0.064

0.019

N/A N/A 0.116

Loading

Uniform

0.278

0.1950.106

0.1250.068

Triangular

a/b 1 2 3 1

3.00

0.758

0.514

0.505

0.313

1.012

1.627

0.022 0.042

b

a

x

z









Lateral Soil Load





0.00N/A

0

N/A

0.00

0.278

Triangular

Hydrostatic

0

40

0

115.2

4165.32

2999.19

288

288 0.00

N/A 0.00

‐42.17

0 288 N/A N/A 0.00

40 288 2999.19 N/A ‐16.27

Location

‐39.87

Z

Uniform

Surcharge

LoadingR

(lb/ft)

N/A

0

40

Triangular

Soil

0.00

a/b

Ma

(kip*in)/LF

N/A

N/A

‐16.27

0.00

b

(psi)

N/A N/A

‐15.38

a

(psi)X Z

Mb

(kip*in)/LF

R


X

40 115.2 0.00 N/A

0 0 4165.32 ‐15.38

N/A

0 0 0.00 0.00 N/A

0


Variable Equation

Location

0.00

q.PL qPL = Ko.d*q.s/144 0.00

q.HL qHL = q.w*b.A1/144 10.40

N/A

Loading on both sides of the pump station is similar for wall of similar height. Assume the lower walls (A2) are designed the same

as the full height walls A1 and B1

q.SL

psi

psi

0.00 psi

Value Unit









Description



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

1.13

1.00

Horizontal Non‐

Loaded Side

12.00

4.00

1.13

1.00 1.00

1.13

12.00

Horizontal Loaded

Side

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/231.44 31.44

50,611

Yield Force Bars

T.Ai = Bars.Ai*fy*As60,000 60,000

37,958





9,205

0.17Shear Check:

Vu.Ai / ΦVc.Ai0.24

Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/10001,847 1,847


= Phi.b*Mn.Ai

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.31 1.31

1,662 1,662

Factored Moment:


Flexural Check:


0

0.00

1.31

1,727

1,554

29.44

47,391

35,543

60,000

in

kip*in

kip*in

kip*in

lb

Unit

6.00

in

in

in

in2

in

lb/LF

lb/LF

lb/LF








Description

88,117 93,201

pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

‐1,697,544

As.Req.Ai =


0.07 0.07


4.54




0.0014*bw.Ai*t.Ai0.60 0.60

0.0001

Quadratic "A" =

Phi.b*fy^2/(1.7*fc*bw.Ai)35,294



4.54

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26


in2

in2

in2

in2

1.26

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.00

35,294

‐1,589,544

0

0.0000

0.00

0.0321

11.33

4.25

1.18

1.18

1.18

0.00

0.60

Unit



Attachment F3 – Gatewell Calculations

ATTACHMENT F3 – GATEWELL CALCULATIONS

Drawing Ref(s): SK101, SK301 Sheet No. 1 of 2

Computed Checked Submitted Project Name: OHB Levee – Gatewell By: BJS By: CJT2 By: BJS Project Number: 34091004.10 Date: 1/27/2015 Date: 1/30/2015 Date: 3/27/2015

00 - Gatewell Analysis and Design Approach.docx

Overall Design Philosophy The gatewell is composed of various concrete members with differing levels of static determinacy, force flow, and boundary conditions. Figure 1 shows the various critical elements who’s capacities where specifically verified in the following computations. The assumed force flow and boundary conditions are also reflected in Figure 1. Details on the load of each element are presented in the following computations.

Drawing Ref(s): SK101, SK301 Sheet No. 2 of 2

Computed Checked Submitted Project Name: OHB Levee – Gatewell By: BJS By: CJT2 By: BJS Project Number: 34091004.10 Date: 1/27/2015 Date: 1/30/2015 Date: 3/27/2015

00 - Gatewell Analysis and Design Approach.docx

Figure 1: Gatewell Concrete Design Elements

1-Way Strip #1 (pin-pin)


1-Way Strip #3 (fixed-cantilevered)

2-Way Panel #2 (“Middle Wall”) (fixed-fixed-fixed-free)

2-Way Panel #1 (“East Wall”) (fixed-fixed-fixed-free)


Project Name: Oxbow Pump Station

Project Number: 34091004

Subject Gatewell Structural Loading

By: BJS

Date: 08/14/14

File:

Shade Indicates: Input Required

1.0 Description, Assumptions, References

1.1 Description

1.2 Assumptions

1.2.1 Stability

4. High surrounding water elevation and empty gatewell controls:

a. Stability (floatation)

b. Strength (concrete shear and flexure)

**

** Conservatively assume chamber is empty for uplift & bottom slab design

2. Design event as 'unusual'

3. For 65%, only check Load Case 4-4L

This worksheet computes the factor of safety of flotation for a gatewell structure and critical

design forces in the lower portions of the wall and bottom slab.

P:\Mpls\34 ND\09\34091004 Fargo Moorhead Metropolitan Feas. Study\WorkFiles\Design_FY2013-

2014\Task_Order_13\600_OxbowPumpSta\Design_Structural\02_Gatewell\[01 - Gatewell - Stability & Design

Forces.xls]Computation

Gatewell Stability & Design Force Computations

1. Conservatively ignore intermediate walls and top slab in weight computation

Page 1 of 6




By: BJS

Date: 08/14/14

File:





5. Overturning and sliding are not possible due to soil height on both sides

6. Flotation factor of safety as shown below

1.2.2 Strength

1.3 References

- ACI 318-08 Building Code Requirements for Structural Concrete and Commentary, ACI, 2011

- Bowles, Joseph E.;"Foundation Analysis and Design (5th ed.)", McGraw-Hill Companies, Inc., 1996

- Lindeburg, Michael R.; "Civil Engineering Reference Manual (11th ed.)", Proffessional Publications, 2008

- USACE;"EM 1110-2-2100: Stability of Concrete Structures", USACE, December 2005.

- USACE;"EM 1110-2-2104: Strength Design of Concrete Hydraulic Structures", USACE, August 2003.

- USACE;"EM 1110-2-3104: Structural and Architectural Design of Pumping Stations", USACE, June 1989.

4. Drained and undrained soil conditions are treated independantly (i.e. c=0 when Φ≠0, and

Φ=0 when c≠0)

3. Slab elements treated as one-way flexural elements spanning in the short direction

1. Provisions of ACI 318-14 Section 11.1.3.3 permitting shear at d away from support edge

ignored

2. Wall elements treated as one-way flexural elements spanning horizontally

Page 2 of 6




By: BJS

Date: 08/14/14

File:





2.0 Inputs

1.1 Geometry

Eltop slab: 929.25 ft

Elbot slab: 895.45 ft

Elbot slab: 892.45 ft

Elsoil: 928.50 ft

Elwater: 922.50 ft

Wshaft: 18.50 ft

Bshaft: 20.50 ft

tshaft: 3.00 ft

Wfooting: 20.50 ft

Bfooting: 22.50 ft

ttop slab: 1.00 ft

tbot slab: 3.00 ft

dpump pipes: 1.33 ft

npump pipes: 4

dpass pipe: 5.00 ft

npass pipes: 2

Page 3 of 6




By: BJS

Date: 08/14/14

File:





1.2 Materials

Φ: 28 º For 'drained' loading

Ko: 0.53 1-sin(Φ) Lindeburg Eq. XX-XX

c: 900 psf For 'undrained' loading

γsoil,moist: 125.0 pcf

γwater: 62.4 pcf

γconc: 150.0 pcf

3.0 Comptuations

3.1 Loading

3.1.1 Stability

Filled Chamber: 641 kips only used for bearing pressure below

Concrete Volume: 8,432 ft3 (from Revit)

Weight (Revit): 1,265 kips Does not include soil

Base Slab 207.6 kips Bfooting*Wfooting*tbot slab*γconc/1000

Walls1 1042.5 kips

Soil 338.8 kips

Σ = 1,589 kips

1,748 kips

Hydrostatic Uplift: 1,875 psf (B.O. Bot Slab)

865 kips

F.S.uplift = 1.84 > 1.3

Chamber conservatively assumed to be empty

tshaft*((2*Bshaft+2*Wshaft-2*tshaft)*(Bfooting-

ttop slab-Elbot slab)-npump pipes*π*dpump pipes^2/4-

npass pipes*π*dpass pipe^2/4)*γconc/1000

(Bfooting*Wfooting-Bshaft*Wshaft)*(Elsoil-Elbot

slab)*γsoil/1000

(includes 10% for middle wall & gates)

Page 4 of 6




By: BJS

Date: 08/14/14

File:





3.1.2 Strength

3.1.2.1 Lateral Earth Pressure

LFLRFD: 2.21 1.3 x 1.7 per USACE EM 1110-2-2104

Bowles eq. 2-54:

Drained (psf) Undrained (psf)

T.O. Soil: 0 -1,800

T.O. Water: 398 -1,424

T.O. Bot Slab: 2,984 1,957

T.O. Bot

Slab:

T.O. Water:

T.O. Soil:

T.O. Water + Ko*(Elwater -

Elbot slab) * (γsoil-

γwater)+γwater*(Elwater-Elbot slab)

(Elsoil-Elbot slab)*(γsoil-γwater)+(Elwater-Elbot

slab)*(γwater)-2*c

(Elsoil-Elwater)*Ko*γsoil (Elsoil-Elwater)*(γsoil-γwater)-2*c

for c=0 (drained) for Φ=0 (undrained)

0 -2*c

890.00

895.00

900.00

905.00

910.00

915.00

920.00

925.00

930.00

935.00

-3,500 -2,500 -1,500 -500 500 1,500 2,500 3,500

Ele

va

tio

n,

ft

Lateral Pressure, psf

Drained (psf)

Undrained (psf)

Page 5 of 6




By: BJS

Date: 08/14/14

File:





3.1.2.3 Controlling Base Slab Design Forces

Assume fixed end moment for design at corner

Assume pinned end moment for midspan design

Shear values are the same reguardless of fixity condition

Wbase = 3.79 ksf Service Level, Deadload Only

Wbase = 5.18 ksf Service Level, Deadload + Filled Chamber

Wremoved soil = 4.51 ksf Service Level, Removed Soil Pressure

"unloaded pressure"

Page 6 of 6

PROJECT: Oxbow Gatewell

SUBJECT: Gatewell East Vertical Wall

COMPUTED BY: BJS, 01/27/15

CHECKED BY: CJT, 02/05/15


2. References

- Roark's Formulas for Stress and Strains, Seventh Edition



b.X: ft, panel height Top El. 929.3 - TO Bot Slab El. 895.45' = 33.85










0.53

0.57

0.03

0.79 0.60 0.02 4.26

Vertical Reinforcing - Loaded

Side:

Horizontal Reinforcing - Loaded

Side:

Horizontal Reinforcing - Non -

Loaded Side:

Vertical Reinforcing - Loaded

Side:

Horizontal Reinforcing - Loaded

Side:

Horizontal Reinforcing - Non -

Loaded Side:

12.50

33.85

0.79

0.79

0.41

0.45

0.60

0.60

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)

As maximum

(0.25 A.bal)

4.55

4.55

SHEET 1 OF 4






Description









4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion

At-Rest Coefficient Ko.i = 1 - sin(Phi.i)

5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6




Vertical:

Horizontal:

Horizontal:

3.00

####

####

####

####

####

Unit

pcf

psf

125

120 pcf

125

120

N/A

Thickness

t.Xi (in)

0.727 1.226

0.259 0.484 0.605

0.321

7.1.a

a/b 0.25 0.50 0.75

150.0

q.s

Value Unit


i = d

0.845

0.1730.081

deg

c.i

Ko.i

Gsat.i

28

0

0.531 0.531 0.531 N/A

γ2 0.125 0.248 0.371


Variable

q.w 62.4 psf

406.2

62.6

57.6

28

0

Wall A1

1.00

fc 4500 psi

fy 60000 psi

Gn 1 N/A

Ec 3823.68 ksi

300 psf

Phi.i 28

0

36.0

Section Modulus,

Sa.Ai (in3)

Phi.v 0.75 N/A

Phi.b 0.90 N/A

G.i

0.020

Fix

ed

Fix

ed

Free

Fixed

γ1

β3 0.031 0.126 0.286

0.114 0.230

1.50 2.00

1.2120.859

0.511 1.073 1.568

0.341 0.457 0.673

Description

β1

0.1480.0660.016β2

Sections 7-9 of this sheet includes computations for the moments, reactions, and required reinforcement to resist the flexure and shear

based on Roark

Height

b.Xi

(in)

Length

a.Xi

(in)

0.510

Variable Value Unit

wc 150 pcf

2592.0

Section Modulus,

Sb.Ai (in3)

2592.0

LFs 2.21

b

a

x

z

SHEET 2 OF 4






3.00

####

####

####

####



Load - Full Height (A1)

Lateral Soil Load







q.SL

0.040 0.076 N/A 0.169 0.184

σa

(psi)

psi

psi

7.81 psi

Value

Location

Unit

0.1950.106

0.1250.068

0.120 0.195

-42.12

0.324 0.406 0.458

N/A

γ3

q.PL qPL = Ko.d*q.s/144 1.11

q.HL qHL = q.w*b.A1/144 14.67

N/A


Variable Equation

0.507

0.50

7.1.b

β2

β1 0.018 0.064

0.019

0.211 0.242 0.106 0.199

0.75 1.00

0.387

0.265

1.50

0.351

0.166 0.244

2.00

0.151



0.040 0.042 N/A N/A 0.148

Loading

Uniform

0.369Triangular 0.111

a/b β1 β2 β3 β4 γ1 γ2

0.369 0.049

N/A

0 0 5649.59 -39.70 N/A

0Uniform

Surcharge

LoadingR

(lb/ft)

N/A

0

75

Triangular

Soil

-6.91

75 162.48 4233.89 N/A

0 0 17176.89 -121.21

Location

-314.19

406.2 13178.50 N/A -132.00

N/A

-74.60

X Z

Mb

(kip*in)/LF

R

(lb/LF)σb (psi) σa (psi)

X Z

N/A

Ma

(kip*in)/LF

N/A

N/A

-79.14

5.61

σb

(psi)

N/A

N/A 14.54

-342.15

0 406.2 N/A N/A 5.61

75

a/b

γ1

0.075γ2

-10.74N/A

0

N/A

912.34

0.369

Triangular

Hydrostatic

0

75

0

162.48

10614.96

7955.01

406.2

406.2 989.60

0.25a/b

SHEET 3 OF 4







Description

110.1

57.86


Description

in2

in2

in2

in2

in2

in2

Horizontal Non-

Loaded Side

0.02

35,294

-1,593,000

32,126

0.0001

0.03

0.0321

11.35

4.26

1.19

1.18

1.19

0.03

0.60

Unit

in2

in2

in2

in

kip*in

kip*in

kip*in32

0.03

1.03

1,374

1,236

lb

Unit

in

in

in

in2

in

lb/LF

lb/LF

lb/LF

29.50

47,494

35,621

47,400

Horizontal Non-

Loaded Side

12.00

6.00

1.27


0.0014*bw.Ai*t.Ai0.60 0.60

0.0011



Quadratic "B" = -Phi.b*fy*d -1,701,000

4.55

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)1.26 1.26

As.max = 0.375*As.bal 4.55



pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

1,322 1,322

Factored Moment:


-1,701,000

Flexural Check:


As.Req.Ai =


0.55 0.60

Quadratic "C" = Mu*1000 694,350 756,145

Moment Capacity

Mn.Ai = T.Ai*(d.Ai-aAi/2)/10001,469 1,469

Nominal Moment Resistance: φMn.Ai =

Phi.b*Mn.Ai

Yield Force Bars

T.Ai = Bars.Ai*fy*As47,400 47,400

38,036




φVc.Ai = Phi.v*Vc.Ai38,036

37,961

0.77Shear Check:

Vu.Ai / ΦVc.Ai1.00

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.03 1.03

Shear Resistance:



d.Ai = t.Ai - Cc.Ai -db.Ai/231.50 31.50

50,714

1.00

0.79

4.00

1.00

0.79 0.79

1.00

12.00

Horizontal Loaded

Side



Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

4.00

SHEET 4 OF 4


SUBJECT: Gatewell Middle Wall

COMPUTED BY: DCP, 02/03/16

CHECKED BY: BJS, xx/xx/16


2. References




b.X: ft, panel height Top El. 928.3' ‐ TO Bot Slab El. 895.45' = 32.85'










0.60

0.64

0.00

2.38

2.38

As maximum

(0.25 A.bal)

12.50

32.85

0.79

0.79

0.47

0.50

0.34

0.34

As Provided

As

minimum

(T&S)

As

minimum

(Flexure)

2.38




Loaded Side:


Side:


Side:


Loaded Side:

0.79 0.34 0.00

SHEET 1 OF 4






Description






Resistance Factor Shear

Resistance Factor Bending ACI 318 9.3.2.1


4. Soil Properties

Moist unit weight

Sat. unit weight

Friction Angle

Cohesion


5. Additional Loads

Description

Surcharge Load

Hydrostatic Load

6. Geometry

Sa.Ai = (12in*t.Xi^2)/6

Sb.Ai = (12in*t.Ai^2)/6


7.1 Rectangular plate; three edges fixed, one edge free (Roark Table 11.4)


Vertical:

Horizontal:

Horizontal:

3.00

2.105

0.519

1.982

1.012

1.627

10.1480.0660.0162

Sections 7 and 8 of this sheet includes computations for the moments, reactions, and required reinforcement to resist the flexure and shear

based on Roark

Height

b.Xi

(in)

Length

a.Xi

(in)

0.510

Variable Value Unit

wc 150 pcf

800.0

Section Modulus, Sb.Ai

(in3)

800.0

LFs 2.21

Description

1.50 2.00

1.2120.859

0.511 1.073 1.568

0.341 0.457 0.673

3 0.031 0.126 0.286

0.114 0.230

0.020

Fixed

Fixed

Free

Fixed

1

Ec 3823.68 ksi

0 psf

Phi.i 0

0

20.0

Section Modulus,

Sa.Ai (in3)

Phi.v 0.85 N/A

Phi.b 0.90 N/A

G.i

fc 4500 psi

fy 60000 psi

Gn 1 N/A

2 0.125 0.248 0.371


Variable

q.w 62.4 psf

394.2

0

0

0

0

Wall A1

1.00

deg

c.i

Ko.i

Gsat.i

0

0

1.000 1.000 1.000 N/A

150.0

q.s

Value Unit

Native Clay i = 2Design i

= d

0.845

0.1730.081

7.1.a

a/b 0.25 0.50 0.75

Thickness

t.Xi (in)

0.727 1.226

0.259 0.484 0.605

0.321

pcf

psf

0

0 pcf

0

0

N/A

Unit

ba

x

z

SHEET 2 OF 4






3.00

0.758

0.514

0.505

0.313




Lateral Soil Load





0.25a/b

10.0752

0.00N/A

0

N/A

0.00

0.381

Triangular

Hydrostatic

0

75

0

157.68

10266.52

7722.05

394.2

394.2 0.00

N/A

N/A

‐246.54

0.00

b

(psi)

N/A

N/A 0.00

‐197.23

0 394.2 N/A N/A 0.00

75

a/bX Z

Mb

(kip*in)/LF

R


X Z

N/A

Ma

(kip*in)/LF

75 157.68 0.00 N/A

0 0 10266.52 ‐232.35

Location

‐185.88

394.2 7722.05 N/A ‐246.54

N/A

‐232.35

N/A

0 0 0.00 0.00 N/A

0Uniform

Surcharge

LoadingR

(lb/ft)

N/A

0

75

Triangular

Soil

0.00

0.151

Linearly interpolate the values presented in 7.1.a and 7.1.b above to obtain coefficients.

0.042 0.045 N/A N/A 0.152

Loading

Uniform

0.381Triangular 0.115

a/b 1 2 3 1 20.381 0.052

0.211 0.242 0.106 0.199

0.75 1.00

0.387

0.265

1.50

0.351

0.166 0.244

2.00

2

1 0.018 0.064

0.019

0.50

7.1.b

0.507


Variable Equation

0.00

0.324 0.406 0.458

N/A

q.PL qPL = Ko.d*q.s/144 0.00

q.HL qHL = q.w*b.A1/144 14.24

N/A

0.120 0.195

0.1950.106

0.1250.068

Middle wall designed for hydrostatic loading along the entire height of one side. This load case could occur on either side, so the

reinforcement will be the same on both sides.

q.SL

0.042 0.081 N/A 0.175 0.189

a

(psi)

psi

psi

0.00 psi

Value

Location

Unit

SHEET 3 OF 4







Description

56.82

34.23


Description

Area Steel Prov, As.Ai

Diameter Steel, db.Ai

Clear Cover, Cc.Ai


Vertical

Loaded Side

12.00

3.003.00

1.00

0.79 0.79

1.00

12.00

Horizontal Loaded

Side

Shear Resistance:



d.Ai = t.Ai ‐ Cc.Ai ‐db.Ai/216.50 16.50

26,564

1.00

0.79

Moment Capacity

Mn.Ai = T.Ai*(d.Ai‐aAi/2)/1000758 758

Nominal Moment Resistance: Mn.Ai =

Phi.b*Mn.Ai

Yield Force Bars

T.Ai = As.Ai*fy47,400 47,400

22,580





22,689

0.76Shear Check:

Vu.Ai / ΦVc.Ai1.00

Location of N.A

aAi = T.Ai/(0.85*fc*bw.Ai)1.03 1.03

pbal = 0.85*0.85*fc/fy *87000/(87000+fy) 0.0321 0.0321

35,294

Vertical

Loaded Side

Horizontal Loaded

Side

4/3*As.Req

682 682

Factored Moment:


‐891,000

Flexural Check:


As.Req.Ai =


0.63 0.67

Quadratic "C" = Mu*1000 410,790 435,880

As.max = 0.375*As.bal 2.38




0.0014*bw.Ai*t.Ai0.34 0.34

0.0024



Quadratic "B" = ‐Phi.b*fy*d ‐891,000

2.38

As.design.Ai =






200*bw.Ai*d.Ai/fy (ACI 10.5)0.66 0.66

Horizontal Non‐

Loaded Side

12.00

3.00

lb

Unit

in

in

in

in2

in

lb/LF

lb/LF

lb/LF

16.50

26,564

22,580

47,400

in2

in2

in

kip*in

kip*in

kip*in0

0.00

1.03

758

682

in2

in2

in2

in2

in2

in2

Horizontal Non‐

Loaded Side

0.00

35,294

‐891,000

0

0.0000

0.00

0.0321

6.35

2.38

0.66

0.66

0.66

0.00

0.34

Unit

in2

SHEET 4 OF 4

Shear CapacityInteface Friction of Wall @ Slab

Oxbow Pump StationComputed By: BJS, 1/27/15Checked By: CJT, 2/9/15

1.0 Description and References

This worksheet computes the shear-friction capacity for concrete surfaces


2008

2.0 Input parameters

2.1. Materials

Concrete:

fc 4000:= psi

fy 60 ksi⋅:=

Avf 0.79 in2⋅ 0.79 in

2⋅=:= (2) #8 bars @ 12" o.c.

2.2. Resistance

(ACI C.9.2)

ϕf 0.9:=

ϕv 0.85:=

2.3. Loading

Vu 38 k⋅:= see Roark Analysis of East wall

3. Computations

3.1. Interface Shear Friction (ACI 11.6.4)

μ 1.0:= Assume "intentionally roughened" ... standard construction procedure

Vs Avf fy⋅ μ⋅ 47.4 k⋅=:= ACI eq. 11-25

ϕVn.force ϕv Vs⋅ 40.29 k⋅=:=

ϕVn.stress ϕv

Vs

12 in⋅ 36⋅ in⋅⋅ 93.264 psi⋅=:=

Vu

ϕVn.force

0.943= < 1.0

03 - Shear Interface Capacity at Exterior Wall Base.xmcd

1

GatewellOne Way Strip #1

Top Slab Flexural Capacity

OHB Flood Control ProjectComputed By: BJS, 1/27/15Checked By: CJT, 2/9/15


1.1 Description

This worksheet computes the applied loading and capacity of one-way strip #1 in the

top slab.

1.2 Assumptions

1. Span is pin-pin

2. Assume slab is poured over walls and thus interface friction cannot control shear

capacity

3. Assume there is significant redundancy such that concrete shear capacity need not

be reduced for non-shear reinforced concrete sections per ACI 11.4.6.1

1.3 References


2008


2005

- Liu, Cheng; Evett, Jack; "Soils and Foundations (7th ed.)", Pearson Prentice Hall 2008


Publications, 2008

2.0 Loading & Boundary Conditions

2.1 Geometry

L 8.25 ft⋅:= Assume one-way span

04 - One Way Strip #1.xmcd 1




3.0 Capacity

3.1 Geometry

H 12 in⋅:=

Bw 12 in⋅:=

d H 2 in⋅−0.625 in⋅2

− 9.687 in⋅=:= Assume inside bar

As 0.31 in2⋅12

12⋅:= #5's @ 12" o.c.

3.1.1 Temperature & Shrinkage Reinf (EM 1110-2-2104, SECTION 2-8)

This reinforcing is on one face

AsTS 0.31 in2⋅12

12⋅:= #5's @ 12" o.c.

ATS .0014 H⋅ Bw⋅ 0.202 in2⋅=:=

AsTS

ATS

1.538= > 1.0

3.2 Materials

fc 4500:= psi

fy 60 ksi⋅:=

β1 0.85:=

γc 150 pcf⋅:=

3.3 Design Factors (EM 1110-2-2104, ACI App. C)

ϕf 0.9:= Flexure, tension controlled

ϕv 0.85:= Shear

ϕc 0.65:= Flexure - Compression Controlled, Compression





3.4 Loading

LL 250 psf⋅ Bw⋅ 0.25 klf⋅=:=

DL γc H⋅ Bw⋅ 0.15 klf⋅=:=

Wu 1.2 DL⋅ 1.6 LL⋅+ 0.58 klf⋅=:=

Vu WuL

2⋅ 2.392 k⋅=:=

Mu WuL2

8⋅ 4.935 k ft⋅⋅=:=

3.5 Ultimate Moment Capacity based on Cracked Section (ACI 10.2, Williams 1.2)

aAs fy⋅

0.85 fc⋅ psi⋅ Bw⋅0.405 in⋅=:=

Mn As fy⋅ da

2−

⋅ 14.702 ft kip⋅⋅=:=

therefore, section is

tension controlledρt 0.319 β1⋅

fc psi⋅

fy

⋅ 0.02=:= > ρAs

Bw d⋅0.003=:=

ϕMn.ultimate ϕf Mn⋅ 13.231 ft kip⋅⋅=:= per foot width

Mu

ϕMn.ultimate

0.373= < 1.0





3.6. Concrete Shear Capacity (ACI 11.3)

Vc 2 fc⋅ psi⋅ Bw⋅ d⋅ 15.597 k⋅=:= (ACI eq. 11-2)

ϕVn ϕv Vc( )⋅ 13.257 k⋅=:=

Vu

ϕVn

0.18= < 1.0






1.1 Description

This worksheet computes the applied loading and capacity of one-way strip #2 in the

top slab.

1.2 Assumptions

1. Span is pin-pin


capacity



1.3 References


2008


2005



Publications, 2008


2.1 Geometry






3.0 Capacity

3.1 Geometry

H 12 in⋅:=

Bw 12 in⋅:=

d H 2.0 in⋅−0.625 in⋅2


As 0.66 in2⋅12

12⋅:= #5's @ 12" o.c.



AsTS 0.31 in2⋅12

12⋅:= #5's @ 12" o.c.

ATS .0014 H⋅ Bw⋅ 0.202 in2⋅=:=

AsTS

ATS

1.538= > 1.0

3.2 Materials

fc 4500:= psi

fy 60 ksi⋅:=

β1 0.85:=

γc 150 pcf⋅:=



ϕv 0.85:= Shear






3.4 Loading

LL 250 psf⋅ Bw⋅ 0.25 klf⋅=:=


Wu 1.2 DL⋅ 1.6 LL⋅+ 0.58 klf⋅=:=

Vu WuL

2⋅ 3.625 k⋅=:=

Mu WuL2

8⋅ 11.328 k ft⋅⋅=:=


aAs fy⋅

0.85 fc⋅ psi⋅ Bw⋅0.863 in⋅=:=

Mn As fy⋅ da

2−

⋅ 30.545 ft kip⋅⋅=:=



fc psi⋅

fy

⋅ 0.02=:= > ρAs

Bw d⋅0.006=:=


Mu

ϕMn.ultimate

0.412= < 1.0







ϕVn ϕv Vc( )⋅ 13.257 k⋅=:=

Vu

ϕVn

0.273= < 1.0




OHB Flood Control ProjectComputed By: BJS, 1/27/15Checked By: CJT, 2/5/15Submit Date: 2/9/2015


1.1 Description

This worksheet computes the applied loading and capacity of the cantilevered one-way

top slab element extending West from the middle wall over the flap valve chamber.

1.2 Assumptions

1. Span is pin-pin


capacity



1.3 References


2008


2005



Publications, 2008


2.1 Geometry






3.0 Capacity

3.1 Geometry

H 12 in⋅:=

Bw 12 in⋅:=

d H 2 in⋅−0.625 in⋅2

− 9.687 in⋅=:= Assume top bar (2" clr.)

As 0.31 in2⋅12

12⋅:= #5's @ 12" o.c.



AsTS 0.31 in2⋅12

12⋅:= #5's @ 12" o.c.

ATS .0014 H⋅ Bw⋅ 0.202 in2⋅=:=

AsTS

ATS

1.538= > 1.0

3.2 Materials

fc 4500:= psi

fy 60 ksi⋅:=

β1 0.85:=

γc 150 pcf⋅:=



ϕv 0.85:= Shear






3.4 Loading

LL 250 psf⋅ Bw⋅ 0.25 klf⋅=:=


Wu 1.2 DL⋅ 1.6 LL⋅+ 0.58 klf⋅=:=

Vu Wu L⋅ 1.305 k⋅=:=

Mu VuL

2⋅ 1.468 k ft⋅⋅=:=


aAs fy⋅

0.85 fc⋅ psi⋅ Bw⋅0.405 in⋅=:=

Mn As fy⋅ da

2−

⋅ 14.702 ft kip⋅⋅=:=



fc psi⋅

fy

⋅ 0.02=:= > ρAs

Bw d⋅0.003=:=


Mu

ϕMn.ultimate

0.111= < 1.0







ϕVn ϕv Vc( )⋅ 13.257 k⋅=:=

Vu

ϕVn

0.098= < 1.0



Bottom Slab Capacity



1.1 Description

This worksheet computes the applied loading and capacity of one-way strip #5, the

base slab when subjected to self weight of the empty structure (ignoring slab weight)

1.2 Assumptions

1. Span is pin-pin


capacity



1.3 References


2008


2005



Publications, 2008


2.1 Geometry






3.0 Capacity

3.1 Geometry

H 36 in⋅:=

Bw 12 in⋅:=

d H 6 in⋅−1 in⋅2

− 29.5 in⋅=:= Assume top bar (6" clr.)

As 0.79 in2⋅12

12⋅:= #8's @ 12" o.c.



AsTS 0.79 in2⋅12

12⋅:= #8's @ 12" o.c.

ATS .0014 H⋅ Bw⋅ 0.605 in2⋅=:=

AsTS

ATS

1.306= > 1.0

3.2 Materials

fc 4500:= psi

fy 60 ksi⋅:=

β1 0.85:=



ϕv 0.85:= Shear






3.4 Loading

DL 3.79 klf⋅ 3.79 klf⋅=:= Obtained from structure bearing weight

when water is not in the chamber, self

weight of slab is neglected, see up-front

stability computations.Wu 1.2 DL⋅ 4.548 klf⋅=:=

Vu WuL

2⋅ 28.425 k⋅=:=

Mu WuL2

8⋅ 88.828 k ft⋅⋅=:=


aAs fy⋅

0.85 fc⋅ psi⋅ Bw⋅1.033 in⋅=:=

Mn As fy⋅ da

2−

⋅ 114.485 ft kip⋅⋅=:=



fc psi⋅

fy

⋅ 0.02=:= > ρAs

Bw d⋅0.002=:=


Mu

ϕMn.ultimate

0.862= < 1.0







ϕVn ϕv Vc( )⋅ 40.37 k⋅=:=

Vu

ϕVn

0.704= < 1.0



Attachment F4 – Gravity Drain Outlet Calculations

ATTACHMENT F4 – GRAVITY DRAIN OUTLET CALCULATIONS

Drawing Ref(s):

SK103, SK302 Sheet No. 1 of 7

Computed Checked Submitted Project Name: OHB Levee – Outlet Model


Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015

20 - Outlet Model Summary.docx

1.0 Contents

1.1 Overall Design Philosophy .......................................................................................................................................... 2

1.2 Risa Inputs ......................................................................................................................................................................... 3

1.2.1 Load Cases and Combinations ............................................................................................................................ 3

1.2.2 Loading ......................................................................................................................................................................... 3

1.3 Risa Results ....................................................................................................................................................................... 5

Figure 1: Isometric Views (a) Revit and (b) Risa Isometric Views ....................................................................................................................... 2

Figure 2: HL (soil) ................................................................................................................................................................................................................... 3

Figure 3: LL ..................................................................................................................................................................................................................... 4

Figure 4: Deflected Shape & Factored/Enveloped Moment ................................................................................................................................ 5

Figure 5: Deflected Shape & Factored/Enveloped Moment ................................................................................................................................ 6

Figure 6: Deflected Shape .................................................................................................................................................................................................. 7

Drawing Ref(s):




Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.1 Overall Design Philosophy

The outlet structure will be composed of a slab (stilling basin) with vertical earth retaining walls on three sides. The open

river side of the structure ensures there is no unequal water pressures significant enough to produce flotation. The

unequal sliding and overturning forces acting on the structure from the hillside above are small relative to the structures

length of 28’, therefore, there are no stability concerns from earth pressure.

The earth retaining walls will be subject to flexural forces from saturated soil. These walls are assumed to span vertically

be restrained by the base slab. A Risa structural model was composed to compute these internal forces in the wall and

base slab. The model assumptions are described herein. All details on loading and capacity computations are presented

following this section.

The highest internal moment and shear would result from the tallest wall segment just down flow of the drop into the

stilling basin. A 2-D frame model was composed at this location. Because the section is loaded equally on both sides of

the structure, the only external boundary conditions which act on the section result from the soil bearing pressure.

Assumed compression only springs were placed at 1’ o/c along the base slab element.

(a) (b)

Figure 1: Isometric Views (a) Revit and (b) Risa Isometric Views

Drawing Ref(s):




Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.2 Risa Inputs

1.2.1 Load Cases and Combinations

Basic Load Cases:

Load Combinations (USACE EM 1110-2-2104):

1.2.2 Loading

Figure 2: HL (soil)

Drawing Ref(s):




Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


Figure 3: LL

Drawing Ref(s):




Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


1.3 Risa Results

Figure 4: Deflected Shape & Factored/Enveloped Moment

Drawing Ref(s):




Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


Figure 5: Deflected Shape & Factored/Enveloped Moment

Drawing Ref(s):




Date: 1/27/2015 Date: 2/5/2015 Date: 2/9/2015


Figure 6: Deflected Shape

Outlet Structure at the Red River OHB Flood Control ProjectComputed By: BJS, 1/27/15Checked By: CJT, 2/9/15Submit Date: 2/9/2015


1.1 Description



1.2 Assumptions

1. Side walls act as vertical cantilevers supported by the base slab.

2. Saturated soil will be used for lateral earth pressure. The water level will

conservatively be assumed to act to the top of the wall.

3. Wall and slab moment and shear forces will be obtained from a frame finite element

model (Risa)

4. Loading and capacity per USACE EM-1110-2-2104 (ACI 318-14 Appendix C with a 1.3

hydraulic factor)

5. Wall and slab thickness and reinforcing will be assumed to be consistent, therefore,

critical section is just below the slab step

1.3 References


2008


2005



Publications, 2008

21 - Outlet Loading and Wall Capacity.xmcd

1



2.1 Geometry

EL1 0 ft⋅:= Elevation: Top of Base Slab

EL2 10.5 ft⋅:= Elevation: Top of Soil

2.2 Materials

γw 62.4pcf:= Density of water

γsat 125pcf:= Soil unit weight

Ko 0.53:= At-Rest Pressure Coefficient, per Geotechnical Report


2


2.3 Surcharge Loading

WLL 100 psf⋅:= Per ASCE 7-05 Table 4-1, classify as exterior

balcony

WSL 50 psf⋅:= Per ASCE 7-05 Figure 7-1, ignore since LL

exceeds SL

2.4 Lateral Earth Loading on West Wall

Psoil EL2 EL1−( ) Ko γsat γw−( )⋅ γw+ ⋅ 1.004 ksf⋅=:=

PLL Ko WLL⋅ 0.053 ksf⋅=:=

2.5 Subgrade Modulous

AreaK 12 in⋅ 12⋅ in⋅:= Nodal Tributary Area

K 75psi

in⋅:= Assumed stiffness of highly platic clay

Klinear K AreaK⋅ 10.8k

in⋅=:=


3


3.0 Capacity

3.1 Geometry

H 12 in⋅:=

Bw 12 in⋅:=

d H 2 in⋅−1.128 in⋅2


As 1 in2⋅12

9⋅:= #9's @ 9" o.c.


This reinforcing is on the compressed face of the cantilevered wall and base slab

AsTS 0.31 in2⋅12

12⋅:= #5's @ 12" o.c.

ATS .0014 H⋅ Bw⋅ 0.202 in2⋅=:=

AsTS

ATS

1.538= > 1.0

3.2 Materials

fc 4500:= psi

fy 60 ksi⋅:=

β1 0.85:=



ϕv 0.85:= Shear



4


3.4 Loading

Vu 13 k⋅ 13 k⋅=:=

Mu 49.8 ft⋅ k⋅ 49.8 k ft⋅⋅=:=


5



aAs fy⋅

0.85 fc⋅ psi⋅ Bw⋅1.743 in⋅=:=

Mn As fy⋅ da

2−

⋅ 57.097 ft kip⋅⋅=:=



fc psi⋅

fy

⋅ 0.02=:= > ρAs

Bw d⋅0.012=:=


Mu

ϕMn.ultimate

0.969= < 1.0



ϕVn ϕv Vc( )⋅ 12.913 k⋅=:=

Vu

ϕVn

1.007= < 1.0

3.7. Interface Shear Friction (ACI 11.6.4)

μ 1.0:= Assume "intentionally roughened" ... standard construction procedure

Vs As AsTS+( ) fy⋅ μ⋅ 98.6 k⋅=:= ACI eq. 11-25

ϕVn.force ϕv Vs⋅ 83.81 k⋅=:=

ϕVn.interface ϕv Vs⋅ 83.81 k⋅=:=

Vu

ϕVn.interface

0.155= < 1.0


6



1.1 Description



1.2 Assumptions

1. Side walls act as vertical cantilevers supported by the base slab.

2. Saturated soil will be used for lateral earth pressure. The water level will

conservatively be assumed to act to the top of the wall.

3. Wall and slab moment and shear forces will be obtained from a frame finite element

model (Risa)

4. Loading and capacity per USACE EM-1110-2-2104 (ACI 318-14 Appendix C with a 1.3

hydraulic factor)

5. Wall and slab thickness and reinforcing will be assumed to be consistent, therefore,

critical section is just below the slab step

1.3 References


2008


2005



Publications, 2008

22 - Outlet Slab Capacity.xmcd 1



2.1 Geometry



3.0 Capacity

3.1 Geometry

H 24 in⋅:=

Bw 12 in⋅:=

d H 2 in⋅−0.625 in⋅

2− 21.687 in⋅=:= Assume inside bar

As 0.66 in2⋅12

9⋅:= #9's @ 9" o.c.


This reinforcing is on the compressed face of the cantilevered wall and base slab

AsTS 0.44 in2⋅12

12⋅:= #5's @ 12" o.c.

ATS .0014 H⋅ Bw⋅ 0.403 in2⋅=:=

AsTS

ATS

1.091= > 1.0

3.2 Materials

fc 4500:= psi

fy 60 ksi⋅:=

β1 0.85:=



ϕv 0.85:= Shear




3.4 Loading

Vu 13.6 k⋅ 13.6 k⋅=:=

Mu 49.8 ft⋅ k⋅ 49.8 k ft⋅⋅=:=




aAs fy⋅

0.85 fc⋅ psi⋅ Bw⋅1.15 in⋅=:=

Mn As fy⋅ da

2−

⋅ 92.894 ft kip⋅⋅=:=



fc psi⋅

fy

⋅ 0.02=:= > ρAs

Bw d⋅0.003=:=


Mu

ϕMn.ultimate

0.596= < 1.0



ϕVn ϕv Vc( )⋅ 29.679 k⋅=:=

Vu

ϕVn

0.458= < 1.0


appendix f – structural...young, et al., roark’s formulas for stress and strain (8 th edition),...

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