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Fargo Moorhead Metropolitan Area Design Documentation Report Flood Risk Management Project Reach 4 Diversion Channel and Rush River Inlet/Drop Structure Appendix F: Structural Design & Criteria
97% FTR_FMM_R4_Appendix_F_Structural.docx
AppendixF:StructuralDesign&Criteria
FargoMoorheadMetropolitanAreaFloodRiskManagementProject
Reach4DiversionChannelandRushRiver
Inlet/DropStructure
EngineeringandDesignPhase
P2# 370365
Doc Version: POST FTR Submittal
14 November 2013
Fargo Moorhead Metropolitan Area Design Documentation Report Flood Risk Management Project Reach 4 Diversion Channel and Rush River Inlet/Drop Structure Appendix F: Structural Design & Criteria
97% FTR_FMM_R4_Appendix_F_Structural.docx
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AppendixF:StructuralDesign&CriteriaTable of Contents
F.1 Structural Design ................................................................................................................................... 1
F.2 Structural Description ........................................................................................................................... 1
F.3 References ............................................................................................................................................ 1
F.4 Alternatives Considered for Preliminary Engineering Report ............................................................... 1
F.4.1 Headwall Alternative ..................................................................................................................... 2
F.4.2 Flared End Sections Alternative .................................................................................................... 2
F.4.3 Rock Weir Alternative ................................................................................................................... 2
F.4.4 Design Alternative for Design and Construction ........................................................................... 3
F.5 Structural Design Criteria ...................................................................................................................... 3
F.5.1 Reinforced Concrete ..................................................................................................................... 3
F.5.2 Reinforcing Steel ........................................................................................................................... 3
F.5.3 Material Properties ....................................................................................................................... 3
F.5.4 Load and Strength Reduction Factors for Concrete Design .......................................................... 4
F.6 Inlet Headwall Design ........................................................................................................................... 4
F.6.1 Design Loads ................................................................................................................................. 5
F.6.2 Water Loads .................................................................................................................................. 6
F.6.3 Soil Loads ...................................................................................................................................... 6
F.6.4 Self Weight .................................................................................................................................... 7
F.6.5 Uplift ............................................................................................................................................. 7
F.7 Inlet Headwall Concrete Analysis and Design ....................................................................................... 7
F.7.1 Stem Reinforcement ..................................................................................................................... 7
F.7.2 Footing Reinforcement ................................................................................................................. 7
F.8 Inlet Headwall Trash Rack Design ......................................................................................................... 7
F.9 Reinforced Concrete Pipe Design.......................................................................................................... 8
F.9.1 Hydraulic Requirements ................................................................................................................ 8
F.9.2 Soil Loads ...................................................................................................................................... 8
F.9.3 Concrete Strength Design ............................................................................................................. 8
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F.9.4 Concrete Pipe Camber .................................................................................................................. 8
F.10 Outlet Pipe Box Design.......................................................................................................................... 9
F.10.1 Design Loads ............................................................................................................................. 9
F.10.2 Pipe Box Sizing .......................................................................................................................... 9
F.10.3 Water Loads .............................................................................................................................. 9
F.10.4 Soil Loads ................................................................................................................................ 10
F.10.5 Self Weight .............................................................................................................................. 10
F.10.6 Uplift ....................................................................................................................................... 10
F.10.7 Pipe Box Concrete Analysis & Design ...................................................................................... 10
F.10.8 Grating Design ......................................................................................................................... 10
F.11 Outlet Impact Basin Design ................................................................................................................. 11
F.11.1 Design Loads ........................................................................................................................... 11
F.11.2 Impact Basin Sizing .................................................................................................................. 11
F.11.3 Self Weight .............................................................................................................................. 11
F.11.4 Water Loads ............................................................................................................................ 11
F.11.5 Soil Loads ................................................................................................................................ 12
F.11.6 Uplift ....................................................................................................................................... 12
F.12 Outlet Impact Basin Concrete Design and Analysis ............................................................................ 12
F.12.1 Reinforcement Design ............................................................................................................. 12
F.13 Sheet Pile Wall Design ........................................................................................................................ 12
F.13.1 Design Loads ........................................................................................................................... 12
F.13.2 Soil Loads ................................................................................................................................ 13
F.13.3 Water Loads ............................................................................................................................ 13
F.13.4 Wall Sizing ............................................................................................................................... 13
F.14 Attachments ........................................................................................................................................ 15
TABLES
Table F. 1: Load Case Summary…………..……………………………………………………………………………….…………………5
Table F. 2: Sheet Pile Load Case Summary..………………….………………………………..…………………………………….11
Table F.3: Embedment Factors of Safety.………………………………………………….………………………………………….12
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Table F.4: Required Section Moduli….……………………………………………………………………………………………………13
ATTACHMENTS
Attachment F ‐ 1: Inlet Headwall Pipe Section Stability Calculations
Attachment F ‐ 2: Inlet Headwall Typical Section Stability Calculations
Attachment F ‐ 3: Inlet Headwall Wing Wall Section Stability Calculations
Attachment F ‐ 4: Inlet Headwall Pipe Section Reinforcement Design
Attachment F ‐ 5: Inlet Headwall Typical Section Reinforcement Design
Attachment F ‐ 6: Inlet Headwall Wing Wall Section Reinforcement Design
Attachment F ‐ 7: Reinforced Concrete Pipe Design Calculations
Attachment F ‐ 8: Sizing of Outlet Impact Basin Calculations
Attachment F ‐ 9: Inlet Headwall Trash Rack Design
Attachment F ‐ 10: Impact Basin Pipe Box Design
Attachment F ‐ 11: Impact Basin Design
Attachment F ‐ 12: Sheet Pile Wall CWALSHT Design
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AppendixF:StructuralDesign&Criteria
F.1 STRUCTURAL DESIGN
The structural design follows guidelines laid out in the “Fargo‐Moorhead Metropolitan Area Flood Risk Management Project: Project Design Guidelines” along with applicable Corps guidelines and industry standards. Design assumptions and methodology are presented in the following sections.
F.2 Structural Description
The layout of this design consists of 615 linear feet of 72 inch diameter reinforced concrete pipe (three
72 inch pipes side by side). All 615 feet of pipe would need to be Class IV. The inlet structure consists of
a headwall, wing walls and a slab with a trash rack. The impact basin was sized and required a minimum
width, W, of approximately 14 feet per pipe. A width of 16 feet was used for the design. The energy
associated with the pipe flow is dissipated by an internal hanging baffle wall approximately sixteen feet
away from where the three 72 inch pipes enter the impact basin. The impact basin outlet structure will
be constructed with a headwall and extended boxed concrete section allowing for flap gates with the
three 72 inch pipes coming through, a 21 foot‐4 inch long stilling basin, internal hanging baffle wall and
an end sill.
F.3 References
The following design guides and computer programs will be used to design the drainage structure:
EM 1110‐2‐2104 Strength Design of Reinforced Concrete Hydraulic Structures
EM 1110‐2‐2100 Stability Analysis of Concrete Structures
EM 1110‐2‐2502 Retaining and Floodwalls
EM 1110‐2‐2105 Design of Hydraulic Steel Structures
EM 1110‐2‐3104 Structural and Architectural Design of Pumping Stations
EM 1110‐2‐2902 Conduits, Culverts and Pipes
ACI 318‐11 Building Code Requirements for Structural Concrete
USBR Hydraulic Design of Stilling Basin for Pipe or Channel Outlets
Guideline Project Design Guidelines Engineering and Design Phase: Fargo‐ Moorhead Metropolitan Area Flood Risk Management Project
AISC Steel Construction Manual 13th Edition (2005)
F.4 Alternatives Considered for Preliminary Engineering Report
Moore Engineering, under contract with the non‐federal sponsor, modeled the local drainage and
provided a draft memorandum with recommendations for types, sizes, and locations of local drainage
features and drop structures along the diversion channel for Reach 4. This includes station 325+00 to
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521+00 along the overall project alignment. The drainage structure will be located at station 492+20.
According to the memorandum, the flow computed by Moore Engineering for the Reach 4 inlet is
approximately 520 cubic feet per second (cfs). A dual 72 inch pipe drop structure resulted in an increase
in the water surface elevation for the 1% Rush River event due to breakout flow from adjacent river
systems. Therefore, the report recommends a 20ft wide weir structure to achieve minimal change in the
water surface elevation.
Further hydraulic analyses done by MVP showed that a triple 72 inch pipe drop structure would serve as
an adequate drainage structure. Three alternatives were considered; two incorporated the three 72 inch
pipes and the other is a rock weir structure. Each of the two alternatives for the drop pipe structure
included an impact basin at the outlet end of the structure. The three alternatives that were considered
are referred to as the Headwall Alternative, Flared End Sections Alternative and Rock Weir Alternative.
Each alternative is described below.
F.4.1 Headwall Alternative
The Headwall Alternative is conceptually based on the local drainage structure designed for Reach 1 of
this project. The layout of this design consists of 738 linear feet of 72 inch diameter reinforced concrete
pipe (three 72 inch pipes side by side). All 738 feet of pipe would need to be Class IV. The inlet
structure consists of a headwall, wing walls and a slab with a trash rack. For the conceptual design, the
impact basin was sized and required a minimum width, W, of approximately 14 feet per pipe. A width of
16 feet was used for the conceptual design. The energy associated with the pipe flow is dissipated by an
internal hanging baffle wall approximately six feet‐ten inches away from where water flowing though
the pipes enters the impact basin headwall. The impact basin outlet structure would consist of a
headwall with the three 72” pipes coming through, flap gates at the end of each pipe, a 21 foot‐8 inch
long stilling basin and an end sill. The drain plan and profile can be found in the structural drawings
sheet S‐100. The preliminary estimated construction cost of the Headwall Alternative is $1,368,151
including prime contractor profit.
F.4.2 Flared End Sections Alternative
The Flared End Sections Alternative looks to greatly reduce the size of the inlet structure. The layout of
this design consists of 810 linear feet of 72 inch diameter reinforced concrete pipe. Approximately 590
feet of pipe would need to be Class IV and 220 feet of pipe would need to be Class V because the soil
height above the pipe exceeds 11 feet. This design requires three precast concrete flared end sections
for the inlet structure. Each section will have its own trash rack. The Flared End Sections Alternative will
consist of the same outlet structure as described in the Headwall Alternative. The energy associated
with the pipe flow is dissipated by an internal hanging baffle wall approximately six feet‐ten inches away
from where the three 72 inch pipes enter the impact basin headwall. The preliminary estimated
construction cost of the Flared End Sections Alternative is $873,504, including prime contractor profit.
F.4.3 Rock Weir Alternative
The Rock Weir Alternative is the least expensive of the three alternatives. The preliminary estimated construction cost is $504,170, including prime contractor profit. The layout of this design consists of a
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rock weir having a slope of 1:20 and a 20 foot crest width. Rock will be 30 inches of R‐400 riprap for the entire structure.
F.4.4 Design Alternative for Design and Construction
With three viable design alternatives being considered the PDT and Local Sponsors gathered to discuss the engineering merits of each alternative. The Rock Weir Alternative is by far the cheapest of the three alternatives; however, concerns of having a hole in the system that may cause backflow problems may prevent this alternative from moving forward. Both the Headwall Alternative and Flared End Sections Alternative have the advantage of being able to close the system using flap gates. The size of the inlet in the Headwall Alternative may be reduced by using flared end sections presented in the Flared End Sections Alternative. The precast sections for the Flared End Sections Alternative will accomplish the same goal, requiring less concrete to construct. The final decision regarding the alternatives presented was a joint decision between the Corps of Engineers and the Local Sponsor Team. It was decided that the Headwall Alternative is the better option of the three. This alternative allows for a larger trash screen that will reduce the potential of flooding from blocked inlets. A reduced headwall size at the inlet was suggested to cut down costs. Originally, the Headwall Alternative consisted of 738 linear feet of 72 inch diameter Class IV RCP. This alternative was modified after the decision was made to lower the EMB at the drainage structure. Lowering the EMB decreased the pipe length required. The actual design of the Headwall Alternative includes all features discussed in F.4.1, but has 615 linear feet of Class IV RCP instead of 738 linear feet.
F.5 Structural Design Criteria
The design of all structural components follows applicable Corps guidelines and industry standards.
Structural design of the local drainage structure is in accordance with EM 1110‐2‐2104 and EM 1110‐2‐
2105 for reinforced concrete and structural steel, respectively. A single load factor of 1.7 plus a hydraulic
factor of 1.3 are used for reinforced concrete design. Structural design for non‐hydraulic concrete
structures is in accordance with ACI 318‐11. The design of structural steel components is in accordance
with AISC Steel Construction Manual 13th Edition. Designs will be practices and principles that have
proved to be safe and efficient.
F.5.1 Reinforced Concrete
All reinforced concrete shall have a minimum 28 day compressive strength of 4,000 psi.
F.5.2 Reinforcing Steel
Steel reinforcing shall adhere to the requirements of ASTM 615 Grade 60 steel, with a yield strength of
60,000psi. The minimum amount of flexural steel reinforcement should not be less than that required
for shrinkage and temperature in accordance with EM 1110‐2‐2104. The maximum amount of flexural
reinforcement will be 0.25ρb.
F.5.3 Material Properties
Below is a list of material properties used in design:
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Water: 62.5 pcf
Concrete: 150 pcf
Reinforcing Steel: 60 ksi
Frost Free Select Granular Fill: c=o, Φ=32deg; =125 pcf Structural Compacted Backfill: c=o, Φ=31deg; =120 pcf
F.5.4 Load and Strength Reduction Factors for Concrete Design
A single load factor of 1.7 dead and live load factor shall be used along with a hydraulic load factor of 1.3 in accordance with EM 1110‐2‐2104. Combining these two load factors result in a total load factor of 2.21. Overstress factors are permitted for unusual and extreme load cases. Strength reduction factors shall be used to design members subjected to bending, combined bending and axial, and shear. Reduction factors for bending and shear are 0.9 and 0.85, respectively.
F.6 Inlet Headwall Design
In some areas the EMBs will be subject to differential head conditions for the most significant diversion
discharges. Therefore it is likely that a portion of the EMBs will act as levees. There are minimum
vegetation management zone requirements for the levee portion. For Reach 4, the levee will be
embedded in the EMB so no separate stability analyses will be required for the levee.
Figure 1: Inlet Headwall Typical Cross Section
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Figure 2: Inlet Headwall Cross Section at Pipe
F.6.1 Design Loads
Preliminary analysis and design was performed using the guidance outlined in the “Project Design Guidelines Document” dated 9 March 2012. Three load cases were considered for the design of three cross sections: typical section (Figure 1), pipe section (Figure 2) and wing wall section (Figure 3). Table F.1 shows these load cases.
Table F.1: Inlet Headwall Load Case Summary
*Note: Load Case 4 only applies to the wing wall cross section.
Load Case
Usual/UnusualLoad Factor
Hydraulic Factor
Load Case Name
1 Usual 1.7 1.3 Empty Ditch
Case
2 Usual 1.7 1.3 Full Ditch
Case
3 Unusual 1.7 1.3 Lagging Soil
Case
4* Unusual 1.7 1.3 Inundated
Case
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Figure 3: Inlet Headwall Wing Wall Section
F.6.2 Water Loads
Water applies both a lateral and vertical load on the wall. The vertical forces are from the weight of the water on top of the footing. Lateral forces are from hydrostatic pressures on the stem and footing. For the usual load cases, water was placed at the existing ground elevation (EL. 890) or at ½ ft above the top of the footing elevation (EL. 887). For load case 3, water was placed at the top of the wall (EL. 894.5) on the driving side and two feet lower on the toe side to simulate a lagging effect of the water draining form the soil. For load case 4, water was placed at the top of the wall (EL. 894.5) on both sides of the wing wall which causes the wing wall section to be inundated.
F.6.3 Soil Loads
Soil loads are applied laterally and vertically. The weight of the soil acts vertically on the footing of the wall and the soil pressure acts laterally on the stem and footing. The soil is assumed to be sloping to the top of wall having a 1 on 4 slope on the heel of the wall. Soil on the toe side is assumed to be at the top of the footing. Horizontal earth pressure coefficients were calculated referencing EM 1110‐2502, making use of the at‐rest earth pressure Equation 3‐10 along with the strength mobilization factor (SMF).
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F.6.4 Self Weight
This includes the weight of the concrete headwall structure. The weight of the wall applies a vertical force on the soil.
F.6.5 Uplift
Uplift forces are accounted for in each load case.
F.7 Inlet Headwall Concrete Analysis and Design
The design and analysis of the inlet headwall was broken into three components: stem, heel and toe for three different cross sections. The stem is 1.5 foot thick for all sections. The first cross section is a typical section of the wall with toe and heel dimensions of six foot and 8 foot, respectively. The second cross section is for the pipe and trash rack having the same heel dimension and an 8 foot toe dimension. The third section is for the wing walls extending from the headwall. Its dimensions are 6 foot for both the heel and toe. Reinforcement calculations were performed following applicable guidelines, EMs and standards by checking both flexure and shear. Reinforced concrete is designed in accordance with load factors presented in Section F.5.4. Temperature and shrinkage steel was determined based on the requirements presented in EM 1110‐2‐2104.
F.7.1 Stem Reinforcement
The stem was designed as a cantilever beam, fixed at the point where the base and stem connect. Design moments were analyzed at the base of the stem, where the moment would be greatest. Load Case 1 was determined to be the worst case.
F.7.2 Footing Reinforcement
The footing was analyzed in two parts: the heel and the toe. The footing thickness was driven by stability requirements and is to be 24 inches thick. Each load case was considered in designing each of the cross sections; the worst case for each element was used for design. Top flexural steel reinforcement for the footing was determined by analyzing the heel as a cantilever beam, fixed at the point where the heel and stem connect. Bottom flexural steel reinforcement for the footing was determined by analyzing the toe as a cantilever beam, fixed at the point where the toe and stem connect.
F.8 Inlet Headwall Trash Rack Design
The trash rack was designed to be completely submerged with a 5‐ft head differential to account for
debris backup in accordance with EM 1110‐2‐3104. Solid rectangular beams of hot dipped, galvanized
steel make up the trash rack. There are a total of 12 trash rack sections; each section consists of seven,
9.3 foot long simply supported beams with six inches of clear space. Beams are 0.625 inches wide and 4
inches deep. The deflection under the unusual loading condition for these beams was calculated as
0.492 inches; this would be equivalent to L/227. Because large deflections will not adversely affect the
performance of the trash rack, accepting the large deflections is more desirable than increasing the
beams cross‐sectional areas or adding a support beam.
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F.9 Reinforced Concrete Pipe Design
F.9.1 Hydraulic Requirements
Hydraulics sized the pipes to handle 520 cfs. The invert of the pipes at the inlet headwall is 886.5. The
pipes will run through the excavated material berm and down the slope of the main channel until they
reach the outlet impact basin at EL. 874.003. The pipes have a total length of 204.5 feet per pipe. All
sections of the pipe will be Class IV Reinforced Concrete Pipe (RCP).
F.9.2 Soil Loads
Geotechnical investigations have shown that with the weight of the Excavated Material Berm (EMB)
there will be significant settlement of the soil. To limit the loading on the pipes and the amount of
settlement beneath the pipes, the EMB will be constructed approximately six feet above existing
ground. With a nine foot EMB height above existing ground, geotechnical investigations estimate a 12
inch total settlement with two to six inches of total settlement occurring beneath the reinforced
concrete pipes.
F.9.3 Concrete Strength Design
The reinforced concrete pipe was classed using EM 1110‐2‐2902. The maximum soil column anticipated above the pipe is approximately 6 feet. Based on preliminary loading analysis, all reinforced concrete pipes will need to be Class IV. A further look into extra loading due to mowing equipment did not require any length of the pipe to be Class V.
F.10 CONCRETE PIPE CAMBER
The purpose of cambering the pipes would be to get the final flow line of the pipes to settle near the
design flow line when the pipes reach final settlement. The slope of the pipes is approximately 7%. The
pipe settlement‐rebound profile has been predicted as shown below in Figure 4. Pipe bedding will not
be used on this project so low strength concrete material will be used to fill the void beneath the set
pipe and ground for strength.
Two conditions were considered in determining whether the pipes of the structure should be cambered:
(1) In order to maintain sufficient velocities for pipe cleanout (determined by the hydraulic engineer),
the slope needs to be at least 0.2%, and (2) the rotational deflection of the pipe joints is not to exceed 1
degree. Points selected for settlement analysis represented points of greatest anticipated curvature due
to embankment and diversion features. The deflection criterion was applied directly to these points
rather than looking at each individual pipe segments. The above criteria were met without the need to
camber the pipes. Thus, cambering of the pipes isn’t necessary.
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Figure 4: Pipe Settlement Results
F.11 Outlet Pipe Box Design
F.11.1 Design Loads
Analysis and design was performed using the guidance outlined in the “Project Design Guidelines Document,” dated 9 March 2012 (hereafter referred to as the ‘Project Guidelines’).
F.11.2 Pipe Box Sizing
The dimensions of the pipe box are based on the 72 inch RCP and the flap gate that is needed to fit over the end of the pipe. Wall and footing thickness were specified based on the capacities needed by concrete to resist applied loadings. The box is 10 feet by 11 feet 4 inches. There are three pipes; therefore, there will be three pipe box structures centered behind the three impact basins that are side by side.
F.11.3 Water Loads
Water applies both a lateral and vertical load on the wall. The vertical forces are from the weight of the water on top of the footing. Lateral forces are from hydrostatic pressures on the wall and footing.
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F.11.4 Soil Loads
Soil loads are applied both laterally and vertically to the walls. The soil is assumed to be sloping to the top of wall (TOW) with a 1 on 7 channel slope. Soil pressures were calculated assuming an at‐rest condition because the box is constrained with equal soil pressure on all sides.
F.11.5 Self Weight
The weight of the box applies a vertical force on the soil.
F.11.6 Uplift
Uplift of the structure is not a concern. There will not be a difference in water heights across the structure because water is able to enter the structure at grade.
F.11.7 Pipe Box Concrete Analysis & Design
The design and analysis of the pipe box was broken into two parts: wall and footing. The front wall with the pipe cut out hole was considered for load effects. The pressure at the base of the wall per foot of wall width was calculated and was the load that went into Engineering Monograph No. 27 as the Ps. A plate fixed on three sides and free at the top was considered for design. The interior and exterior moment and reactions along the x‐axis at the lower portion of the wall and edge were calculated to determine the wall thickness requirement. A 12 inch thick wall was required and three inches of concrete cover for the rebar was used. Reinforcement calculations were performed per applicable guidance by checking for both flexure and shear. Reinforced concrete is designed in accordance with load factors and resistance factors presented in ACI 318‐11. To simplify the design, all loading is conservatively assumed to be live load making it subject to a 2.21 load factor (1.7 x 1.3). Temperature and shrinkage steel was determined based on EM 1110‐2‐2104. The shear and moment demand on the wall was analyzed at the base of the wall where the moment would be greatest. The wall thickness was adequate for the shear loading; reinforcement was controlled by flexural design. For ease of construction, temperature and shrinkage steel was specified to match that needed for flexure. The footing reinforcement consists of the same rebar required for the wall.
F.11.8 Grating Design
The grating was designed for a live load of 250 pounds per square foot. The live load was estimated from an 8,000 pound tractor mower having one tire on the top of the grating. The grating is to be flat with ¾” by 1/8” steel bars spaced no farther than 11/16” on center. Grating will be divided into four 23.5” sections that will span the entire width of the box. There is a W8x13 steel beam designed to support the grating and the live load that has been designed to reduce the unsupported length of the grating to four feet. The W8x13 beam is connected into the walls of the concrete box with a shear bolt connection. Two ¾” bolts are being bolted through the web of the beam; four manufacturer wedge anchor bolts are being used for the double angle connection to the concrete. On average, the manufacturer specifications for ½” diameter wedge anchor bolts show a minimum shear capacity of 9.38 kips. Analysis showed that the factored shear load requirement is 6.5 kips. Specifying four wedge anchor bolts will provide 37.5 kips of resistance.
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F.12 Outlet Impact Basin Design
Figure 5: Outlet Impact Basin
F.12.1 Design Loads
Preliminary analysis and design was performed using the guidance outlined in the “Project Design Guidelines Document” dated 9 March 2012. Two load cases were considered for the design and are presented in Attachment F.11. Each load case includes hydraulic load factors as specified in the Project Guidelines.
F.12.2 Impact Basin Sizing
Dimensions of the outlet impact basin are based on the “Hydraulic Design of Stilling Basin for Pipe or Channel Outlets” by the Bureau of Reclamation. Dimensions of the impact basin are all based on the hydraulic width. The design width of the impact basin is 16 feet. Since there are three pipes, there will essentially be three basins side by side for a total width of 55 feet. The total length of the structure, including the stilling basin, is 50 feet. The basin is 15 feet tall.
F.12.3 Self Weight
This includes the weight of the impact basin outlet structure. The total weight of the structure is 1202.6 kips.
F.12.4 Water Loads
The force of the water on the baffle wall is based on a design “n” of 0.013, a maximum flow of 173.33 cfs (per pipe), a flow area of 6.23 ft2, and a flow velocity of 27.75 feet per second. Given the density of water, flow area and flow velocity at the outlet, the total force expected to hit the baffle wall is 9.3 kips. This load was input into the STAAD model over a 13.5 ft by 2 ft area, equaling 0.346ksf.
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F.12.5 Soil Loads
Soil pressures are a function of depth of soil and water. Horizontal earth pressure coefficients and surcharge pressures were applied using appropriate load factors. The earth pressure coefficient was calculated referencing EM 1110‐2502, making use of the at‐rest earth pressure Equation 3‐10 along with the strength mobilization factor (SMF). Internal ice loads are not considered because they act in the opposing direction from the soil and water loads. External ice loads do not act directly on the impact basin due to the channel elevation around the structure. Soil pressures were determined and applied to plate elements in STAAD. This can be seen in the structural attachment F‐11.
F.12.6 Uplift
Uplift pressures where accounted for in the stability analysis of the impact basin.
F.13 Outlet Impact Basin Concrete Design and Analysis
The concrete impact basin is 55 feet wide, 50 feet long (including stilling basin) and 15 feet tall. The
structure will be bearing on five feet of select granular fill that will be compacted beneath the structure.
With the weight of the structure and the limited time the structure could be underwater load bearing is
not a concern on these clay soils. Due to the extreme length to height ratio (3.3:1), there is no concern
of the structure overturning. The structure is not closed or able to trap air, so with the little
displacement the structure will have in the soil compared to its weight floatation is not a concern. The
sliding stability is the only concern that was checked considering two load cases. The first load case
assumes all pipes are flowing full and impact forces on the baffle wall are included. Uplift is assumed to
act on both the impact basin slab and the stilling basin slab. The second load case assumes all pipes are
empty, and no impact force acting on the baffle walls. The sliding stability check assumed the entire
structure needed to move including the stilling basin; the key on the end of the stilling basin is not
considered structural.
F.13.1 Reinforcement Design
The wall thickness of the impact baffle wall is 16 inches in accordance with the standards set by USBR. This thickness proved to be adequate based on STAAD results. The wall thickness of the impact basin is 18 inches based on the same standards. Based on the maximum moments and shear stresses given by the STAAD model, the baffle wall requires #5 @ 12” on center each way on each face. Basin walls and footing requires #5 @ 8” on center each way on each face.
F.14 Sheet Pile Wall Design
F.14.1 Design Loads
Three separate load cases were considered for the design of the sheet pile wall. Each load case was analyzed considering a drained and an undrained condition; a total of six cases were analyzed. Since
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greater flow does not affect the sheet pile wall as it does the rest of the drain structure, separate criteria were used to determine the usual, unusual, and extreme events. . A usual loading condition is considered to be the situation where three feet or less of erosion has occurred. An unusual case is when five feet of erosion has occurred, and the extreme case is when all fill on the dredged side of the wall has eroded. The wall is approximately six and a half feet above the channel and completely backfilled on the retained side in each case. In each case a slope of 7:1 was assumed to exist between the top of the fill and the bottom of the channel on the dredged side. Factors of safety associated with each case are governed by Table 5‐1 of EM 1110‐2‐2504. The soil is fine grained and the sheet pile wall is modeled as a retaining wall. The Q‐Case is the undrained case while the S‐Case represents the drained case. A summary of the load cases can be seen in Table F.2.
Table F.2: Sheet Pile Load Case Summary
Load Case Load Condition Factor of Safety
1 Usual (S‐Case) 1.50
2 Unusual (S‐Case) 1.25
3 Extreme (S‐Case) 1.10
4 Usual (Q‐Case) 2.00
5 Unusual (Q‐Case) 1.75
6 Extreme (Q‐Case) 1.50
F.14.2 Soil Loads
The wall was modeled as being placed completely in clay from the Brenna Formation. In each case, a single layer of saturated clay with a unit weight of 106 pounds per cubic foot was used, which is representative of the Brenna formation in which the wall will be placed. The clay was modeled with a friction angle of 19 degrees and cohesion of 50 pounds per square foot in the drained case, and a friction angle of 0 degrees and cohesion of 575 pounds per square foot in the undrained case. A minimum wall friction angle of 54 percent of the friction angle of the soil was used as the wall friction angle, as specified in EM 1110‐2‐2504. Drained and undrained soil conditions were considered for each loading condition.
F.14.3 Water Loads
Water was modeled to the top of the wall on the retained side and at the bottom of the ditch on the dredged side in each case. The effects of seepage under the wall were automatically calculated by the program CWALSHT.
F.14.4 Wall Sizing
The sheet pile wall was designed using the USACE program CWALSHT. For constructability, only readily available sections of z‐shaped sheet pile wall were considered. Further, designs were limited to a maximum ratio of three feet of buried pile to one foot of exposed pile. Since the exposed length was 6.5 feet, the embedded length was first assumed to be 19.5 feet. Factors of safety were not meet with only a 19.5 foot embedment. Keeping in mind that this type of sheet piling normally comes in lengths with multiples of five, a 23.5 foot embedment depth was assumed for design; this requires an overall length
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of sheet pile of 30 feet. Increasing the depth to 23.5 feet met all factor of safety requirements for all load cases. Piling was assumed to be A572 grade steel with 50 ksi yield strength. Using the strength limitations and factors of safety specified by EM 1110‐2‐2504, a PZC 13 section with 23.5 feet buried and 6.5 foot exposed was found to be sufficient under all loading conditions. Embedment was checked based on factors of safety published in table 5‐1 of EM 1110‐2‐2504. Bending and shear strength were checked using strength reduction factors of 50% and 67% respectively, as required by EM 1110‐2‐2504, paragraph 6‐3a. Embedment Factors of Safety were determined by CWALSHT for each case using the fixed surface method, which generally gives less conservative answers than the sweep search method. In each case, the active factor of safety was taken to be one based on EM 1110‐2‐2504 paragraph 5‐2d. The passive factors of safety were required to meet the criteria for stability described in Table F.2. Table F.3 below shows the factors of safety for embedment for each case with an embedment length of 30 feet. Note that the wall would not need to be embedded to retain the soil in the usual and unusual, undrained case because of the high cohesion. In each case, the factor of safety was adequate.
Table F.3: Embedment Factors of Safety
Usual Unusual Extreme
Drained (S‐Case)
9.60 7.40 1.33
Undrained (Q‐Case)
No Embedment
7.20 5.11
After the embedment length was determined to be sufficient, the maximum moments were taken from the output of CWALSHT. The section was assumed to be an A572 grade steel PZC section with yield strength of 50 ksi as described above. The maximum applied moments and minimum section modulus needed to adequately resist each moment are shown below in Table F.4. The values for strength reduction factors and allowable stress increase factors are taken from paragraph 6‐3a of EM 1110‐2‐2504.
Table F.4: Required Section Moduli
Applied Moment (k‐in)
Yield Stress (ksi)
Strength Reduction Factor
Allowable Stress Increase
Allowable Stress (ksi)
Minimum Section Modulus (in3)
Drained
Usual 137.76 50 0.5 1 25 5.51
Unusual 139.55 50 0.5 1.33 33.25 4.20
Extreme 318.5 50 0.5 1.75 43.75 7.28
Undrained
Usual
Unusual 199.25 50 0.5 1.33 33.25 5.99
Extreme 234.55 50 0.5 1.75 43.75 5.36
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97% FTR_FMM_R4_Appendix_F_Structural.docx Page F‐15 of F‐15
A PZC 13 sheet pile has a section modulus of 24.2 in³, which easily satisfies the minimum section modulus in each case. Thus, a PZC 13 will be specified for design.
F.15 Attachments
Attachment F ‐ 1: Inlet Headwall Pipe Section Stability Calculations
Attachment F ‐ 2: Inlet Headwall Typical Section Stability Calculations
Attachment F ‐ 3: Inlet Headwall Wing Wall Section Stability Calculations
Attachment F ‐ 4: Inlet Headwall Pipe Section Reinforcement Design
Attachment F ‐ 5: Inlet Headwall Typical Section Reinforcement Design
Attachment F ‐ 6: Inlet Headwall Wing Wall Section Reinforcement Design
Attachment F ‐ 7: Reinforced Concrete Pipe Design Calculations
Attachment F ‐ 8: Sizing of Outlet Impact Basin Calculations
Attachment F ‐ 9: Inlet Headwall Trash Rack Design
Attachment F ‐ 10: Impact Basin Pipe Box Design
Attachment F ‐ 11: Impact Basin Design
Attachment F ‐ 12: Sheet Pile Wall CWALSHT Design
FMM Reach 4Inlet Headwall Design
Pipe Section
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Inlet Headwall Design: Pipe Section
Project Description
Reach 4 pipe drop structure inlet design for the Fargo Moorhead Metro project. The inlet will consist ofa concrete headwall and base slab, a trash rack for debris and three 7'‐2" openings in the headwall forRCPs.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
The drain will likely be constructed on alluvium, which in the Red River Valley typically occurs as a clayof low or high plasticity. The alluvium will behave differently in short and long‐term loading conditionsdue to its low permeability.
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
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Phi ϕF 32deg
Inputs:
Existing Ground Elevation GR 890ft
Top of Wall Elevation TOW 894.5ft
Top of Footing Elevation TOF 886.5ft
Bottom of Footing Elevation BOF 884.5ft
Water Elevation Water 887ft
Stem Thickness THstem 1.5ft
Toe Length Toe 8ft
Heel Length Heel 8ft
Total Length of Footing B Toe Heel THstem 17.5 ft
EMB Slope EMBs1
4
Slope angle θ atan EMBs 14.036 deg
Strength Mobilization Factor SMF2
3 <‐‐EM 1110‐2‐2502
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg <‐‐EM 1110‐2‐2502
References:U.S. Army Corps of Engineers. (29 September 1989), EM 1110‐2‐2502, Retaining andFlood Walls
U.S. Army Corps of Engineers. (1 December 2005), EM 1110‐2‐2100, StabilityAnalysis of Concrete Structures
U.S. Army Corps of Engineers (February 2012), Project Design Guidelines, FMM AreaFlood Risk Management Project, Engineering and Design Phase, Version 1. St. Paul,MN
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Factors of Safety Requirements (EM 1110‐2‐2100 & EM 1110‐2‐2502):
Loading
Condition
Minimum
Sliding FS
Minimum
Flotation FS
Minimum Bearing
Capacity FS
Minimum Base Area
in Compression
Usual 1.5 1.3 3 100%
Unusual 1.3 1.2 2 75%
Extreme 1.1 1.1 > 1 Resultant within Base
Load Case 1
Assumptions: 1. Sloping Backfill 2. Empty Ditch (water equal on both sides at EL. 887.0) 3. Usual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
1. Determine Critical Slip Plane angle
The soil above the heel of the retaining wall slopes up at a 1V:4H for 8 feet (horizontally), then flattensout (no slope) for 50 feet and then slopes down at a 1V:7H. It is assumed that the critical slip planeintersects the flat surface.
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Prove the assumption, that the critical slip plane intersects the flat surface, by trial and error.
Angle Delta Shown above
Δ atanHeel tan θ( ) TOW BOF( )
50ft
13.496 deg
Limiting angle Angle90 90deg
Assuming the critical plane intersects the flat surface, angle theta now becomes zero. With no verticalsurcharge, coefficients one and two below are calculated using Eqs. 3‐26 and 3‐27 from EM1110‐2‐2502.
Slope of the flat surface θplane atan 0( ) 0 deg
Coeffecient 1(Eq. 3‐26 EM 1110‐2‐2502)
c1 2 tan ϕd 0.801
Coefficient 2(Eq. 3‐27 EM 1110‐2‐2502)
c2 1 tan ϕd tan θplane tan θplane
tan ϕd 1
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α atanc1 c1
24 c2
2
55.915 deg
Does the critical slip plane intersect the flat surface?
Checkangle "Yes" Δ α Angle90if
"No, check another surface" otherwise
"Yes"
Attachment F-1 4 of 27
FMM Reach 4Inlet Headwall Design
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2. Calculate Water Pressures.
Height of water above footing Hw 0 Water TOFif
Water TOF( )( ) otherwise
0.5 ft
ww Hw Toe γw 0.25kip
ft
Weight of Water
AwToe
24 ft
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from B to C LBC TOF BOF 2 ft
Length from C to D LCD B 17.5 ft
Length from D to E LDE Water BOF( ) 2.5 ft
Ls LBC LCD LDE 22 ftSeepage path
Change in water elevation Δh Water Water 0 ft
PB Water TOF( ) γw 31.2 psfPressure at B
PC Water BOF( )Δh LBC
Ls
γw 156 psfPressure at C
PD Water BOF( )Δh LBC LCD
Ls
γw 156 psfPressure at D
PE 0psi <‐‐End of Creep, tail waterPressure at E
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2PB PC TOF BOF( ) 0.187
kip
ft
AcTOF BOF( )
3
2 PB PC PB PC
0.778 ft
Attachment F-1 5 of 27
FMM Reach 4Inlet Headwall Design
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wd1
2PD Water BOF( ) 0.195
kip
ft
Load at D
Ad1
3TOF BOF( ) 0.667 ft
wb1
2PB Water TOF( ) 7.8 10
3
kip
ft
Load at B
Ab1
3Water TOF( ) TOF BOF( ) 2.167 ft
we 0kip
ft <‐‐End of Creep, tail water
Load at E
Ae 0ft <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient above saturationlevel (Equation 3‐14 EM 1110‐2‐2502)
K1
cos ϕd 2
1sin ϕd sin ϕd θplane
cos θplane
20.458
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb
1 tan ϕd cot α( ) 1 tan ϕd tan α( )
1tan α( )
tan α( ) tan θplane 1
γs
γb
0.458
5. Calculate Lateral Driving Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
Heel tan θ( ) TOW BOF( )[ ] γs PD Heel tan θ( ) TOW Water( )[ ] γbf
Water BOF76.6 pcf
Soil Pressure 1 P1 K1 γbf TOW Water( ) Heel tan θ( )[ ] 0.5 ksf
Soil Force 1 F1 .5 P1 TOW Water( ) Heel tan θ( )[ ] 2.376kip
ft
a1 Water BOF( )1
3Heel tan θ( ) TOW Water( )[ ]
Soil Arm 1
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a1 5.667 ft
P2 P1 γprime Kb Water BOF( ) 0.588 ksfSoil Pressure 2
F2 P1 Water BOF( ) 1.251kip
ft
Soil Force 2
Soil Arm 2 a2Water BOF
21.25 ft
F31
2P2 P1 Water BOF( ) 0.11
kip
ft
Soil Force 3
Soil Arm 3 a3Water BOF
30.833 ft
Resultant Force Pa F1 F2 F3 3.736kip
ft
Pah Pa cos θplane 3.736kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F34.047 ft
Pv Pa sin θplane 0kip
ft
Vertical Force
Av B 17.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW Water( ) γbf Heel Water TOF( ) γs 7.38kip
ft
A1 Toe THstemHeel
2 13.5 ft
Section 2 w21
2Heel Heel tan θ( )( ) γbf 0.92
kip
ft
A2 Toe THstem2
3Heel 14.833 ft
Section 3 w3 THstem TOW TOF( ) γc 1.8kip
ft
A3 ToeTHstem
2 8.75 ft
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Section 4 w4 B TOF BOF( ) γc 5.25kip
ft
A4B
28.75 ft
7. Calculate Lateral soil force on resisting side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502) Ko 1 sin ϕ( ) 0.485
Unit weight accounting for buoyancy (EM 1110‐2‐2502) γprime
PB γs TOF BOF( ) PC
TOF BOF( )57.6 pcf
Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Horizontal Force
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift Force U PC B 2.73kip
ft
AuB
28.75 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 12.87kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
137.025 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502)
XR
MR
Vv10.647 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502)
RR
XR
B0.608
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
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Overturning Moment Mo Pah Ah U Au wd Ad 39.137 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao wb Ab
175.164 kipResisting Moment
Factor of Safety FSo
Mr
Mo4.476
Factor of Safety Check CheckFS "Ok" round FSo 1 2if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 17.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 ww U 12.87kip
ft
ΣH Pah wd wc Po wb 3.68kip
ft
Horizontal Forces
Tslide ΣH cos β( ) ΣV sin β( ) 3.68kip
ft
Parallel Resultant(Fig. 4‐11 EM 1110‐‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 12.87kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐‐2502)
FSs
Nslide tan ϕF cF LCD
Tslide2.185
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502)
CheckFS "Ok" round FSs 1 1.5if
"Not Ok" otherwise
"Ok"Factor of Safety Check
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11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
15.96 deg
Eccentricity of Resultant eB
2XR 1.897 ft
Effective Width of Base Bprime B 2e 21.294 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 115.2 psf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.034Eq. 5‐4a EM 1110‐2‐2502
Eq. 5‐4c EM 1110‐2‐2502 ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.017
Eq. 5‐4c EM 1110‐2‐2502 ξγd ξqd 1.017
Inclination Factors
ξqi 1δ
90deg
2
0.677Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.677
Eq. 5‐5b EM 1110‐2‐2502 ξγi 1δ
ϕF
2
0.251
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**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γb Bprime Nγ
2
112.619kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2502)
FSBQ
Nslide8.751
Factor of Safety Check CheckFS "Ok" round FSB 1 3if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2100)
FSF
w1 w2 w3 w4 ww
U5.714
FSCheck "Ok" FSF 1.3if
"Not Ok" otherwise
"Ok"
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Load Case 2
Assumptions: 1. Sloping Backfill 2. Full Ditch (water equal on both sides at EL. 890) 3. Usual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α 55.915 deg <‐‐See Load Case 1 above
2. Calculate Water Pressures.
Height of water above footing Hw GR TOF 3.5 ft
ww Hw Toe γw 1.747kip
ft
Weight of Water
AwToe
24 ft
Attachment F-1 12 of 27
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Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from B to C LBC TOF BOF 2 ft
Length from C to D LCD B 17.5 ft
Length from D to E LDE GR BOF( ) 5.5 ft
Ls LBC LCD LDE 25 ftSeepage path
Change in water elevation Δh GR GR 0 ft
PB GR TOF( ) γw 0.218 ksfPressure at B
PC GR BOF( )Δh LBC
Ls
γw 0.343 ksfPressure at C
PD GR BOF( )Δh LBC LCD
Ls
γw 0.343 ksfPressure at D
PE 0ksf <‐‐End of Creep, tail waterPressure at E
3. Calculate Water Loads and Moment Arms about O.
wc1
2PB PC TOF BOF( ) 0.562
kip
ft
Load at C
AcTOF BOF( )
3
2 PB PC PB PC
0.926 ft
wd1
2PD GR BOF( ) 0.944
kip
ft
Load at D
Ad1
3GR BOF( ) 1.833 ft
wb1
2PB GR TOF( ) 0.382
kip
ft
Load at B
Ab1
3GR TOF( ) TOF BOF( ) 3.167 ft
we 0kip
ft <‐‐End of Creep, tail water
Load at E
Attachment F-1 13 of 27
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Ae 0ft <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficients
Pressure Coefficient(Appendix H EM 1110‐2‐2502)
K1 0.458 <‐‐See Load Case 1 above
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458 <‐‐See Load Case 1 above
5. Calculate Driving Lateral Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
Heel tan θ( ) TOW BOF( )[ ] γs PD Heel tan θ( ) TOW GR( )[ ] γbf
GR BOF63.509 pcf
Soil Pressure 1 P1 K1 γbf TOW GR( ) Heel tan θ( )[ ] 0.342 ksf
Soil Force 1 F1 .5 P1 TOW GR( ) Heel tan θ( )[ ] 1.112kip
ft
a1 GR BOF( )1
3Heel tan θ( ) TOW GR( )[ ] 7.667 ft
Soil Arm 1
P2 P1 γprime Kb GR BOF( ) 0.502 ksfSoil Pressure 2
F2 P1 GR BOF( ) 1.882kip
ft
Soil Force 2
Soil Arm 2 a2GR BOF
22.75 ft
F31
2P2 P1 GR BOF( ) 0.44
kip
ft
Soil Force 3
Soil Arm 3 a3GR BOF
31.833 ft
Pa F1 F2 F3 3.435kip
ft
Resultant Force
Attachment F-1 14 of 27
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Pah Pa cos θplane 3.435kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F34.225 ft
Active Force Arm
Active Vertical Force Pv Pah sin θplane 0kip
ft
Av B 17.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel GR TOF( ) γs 3.36kip
ft
A1 Toe THstemHeel
2 13.5 ft
Section 2 w2 Heel TOW GR( ) γbf 4.14kip
ft
A2 Toe THstem1
2Heel 13.5 ft
w31
2Heel Heel tan θ( )( ) γbf 0.92
kip
ft
Section 3
A3 Toe THstem2
3Heel 14.833 ft
w4 THstem TOW TOF( ) γc 1.8kip
ft
Section 4
A4 ToeTHstem
2 8.75 ft
Section 5 w5 B TOF BOF( ) γc 5.25kip
ft
A5B
28.75 ft
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7. Calculate Soil Force on Resisting Side.
Ko 1 sin ϕ( ) 0.485At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Unit weight accounting for buoyancy (EM 1110‐2‐2502)
γprime
GR BOF( ) γs PD GR BOF( )
57.6 pcf
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B 6.006
kip
ft
AuB
28.75 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 w5 ww U 11.211kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad w5 A5 wb Ab
116.546 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502) XR
MR
Vv10.396 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.594
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 68.794 kip
Attachment F-1 16 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao w5 A5 ww Aw wb Ab
185.341 kipResisting Moment
Factor of Safety FSo
Mr
Mo2.694
Factor of Safety Check CheckFS "Ok" round FSo 1 2if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 17.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 w5 ww U 11.211kip
ft
ΣH Pah wd wc Po wb 3.379kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐‐2502)
Tslide ΣH cos β( ) ΣV sin β( ) 3.379kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 11.211kip
ft
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502) FSs
Nslide tan ϕF cF LCD
Tslide2.073
CheckFS "Ok" round FSs 1 1.5if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
16.772 deg
Attachment F-1 17 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Eccentricity of Resultant eB
2XR 1.646 ft
Effective Width of Base Bprime B 2e 20.791 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502Nγ Nq 1 tan 1.4 ϕF 22.022
Embedment Factors
Eq. 5‐4a EM 1110‐2‐2502 ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.035
Eq. 5‐4c EM 1110‐2‐2502ξqd 1 0.1
TOF BOF( )
Bprimetan 45deg
ϕF
2
1.017
Eq. 5‐4c EM 1110‐2‐2502ξγd ξqd 1.017
Inclination Factors
ξqi 1δ
90deg
2
0.662Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.662
Eq. 5‐5b EM 1110‐2‐2502 ξγi 1δ
ϕF
2
0.226
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Attachment F-1 18 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γb Bprime Nγ
2
100.554kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2502)
FSBQ
Nslide8.969
Factor of Safety Check CheckFS "Ok" round FSB 1 3if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2100)
FSF
w1 w2 w3 w4 w5 ww
U2.867
FSCheck "Ok" FSF 1.5if
"Not Ok" otherwise
"Ok"
Attachment F-1 19 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Load Case 3
Assumptions: 1. Sloping Backfill 2. Lagging soil (Water at EL. 894.5 on Heel side; EL. 892.5 on Toe Side) 3. Unusual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & unequal water pressures.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α 55.915 deg <‐‐See Load Case 1
2. Calculate Water Pressures.
Height of water above footing Hw TOW 2ft( ) TOF[ ] 6 ft
ww Hw Toe γw 2.995kip
ft
Weight of Water
AwToe
24 ft
Attachment F-1 20 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from B to C LBC TOF BOF 2 ft
Length from C to D LCD B 17.5 ft
Length from D to E LDE TOW BOF( ) 10 ft
Ls LBC LCD LDE 29.5 ftSeepage path
Change in water elevation Δh TOW 2ft( ) TOW 2 ft
PB TOW 2ft( ) TOF[ ] γw 0.3744 ksfPressure at B
Pressure at C PC TOW 2ft( ) BOF[ ]Δh LBC
Ls
γw 0.5077 ksf
PD TOW 2ft( ) BOF[ ]Δh LBC LCD
Ls
γw 0.5817 ksfPressure at D
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2TOF BOF( ) PB PC 0.882
kip
ft
AcTOF BOF( )
3
2PB PC PB PC
0.95 ft
wd1
2PD TOW BOF( ) 2.908
kip
ft
Load at D
Ad1
3TOW BOF( ) 3.333 ft
wb1
2PB TOW 2ft( ) TOF[ ] 1.123
kip
ft
Load at B
Ab TOF BOF( )1
3TOW 2ft( ) TOF[ ] 4 ft
Load at E we 0kip
ft <‐‐End of Creep, tail water
Attachment F-1 21 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Ae 0ft 0 <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient(Appendix H EM 1110‐2‐2502) K1 0.458 <‐‐See Load Case 1
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458 <‐‐See Load Case 1
5. Calculate Lateral Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
Heel tan θ( ) TOW BOF( )[ ] γs PD Heel tan θ( )( ) γbf
TOW BOF62.831 pcf
Soil Pressure 1 P1 K1 γbf Heel tan θ( )( ) 0.105 ksf
Soil Force 1 F1 .5 P1 Heel tan θ( )( ) 0.105kip
ft
a1 TOW BOF( )1
3Heel tan θ( )( )( ) 10.667 ft
Soil Arm 1
P2 P1 γprime Kb TOW BOF( ) 0.393 ksfSoil Pressure 2
F2 P1 TOW BOF( ) 1.053kip
ft
Soil Force 2
Soil Arm 2 a2TOW BOF
25 ft
F31
2P2 P1 TOW BOF( ) 1.438
kip
ft
Soil Force 3
Soil Arm 3 a3TOW BOF
33.333 ft
Pa F1 F2 F3 2.597kip
ft
Active Horizontal Force
Attachment F-1 22 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Pah Pa cos θplane 2.597kip
ft
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F34.307 ft
Active Force Arm
Active Vertical Force Pv Pa sin θplane 0kip
ft
Av B 17.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW TOF( ) γs 7.68kip
ft
A1 Toe THstemHeel
2 13.5 ft
w21
2Heel Heel tan θ( )( ) γbf 0.92
kip
ft
Section 2
A2 Toe THstem2
3Heel 14.833 ft
w3 THstem TOW TOF( ) γc 1.8kip
ft
Section 3
A3 ToeTHstem
2 8.75 ft
Section 4 w4 B TOF BOF( ) γc 5.25kip
ft
A4B
28.75 ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
PB γs TOF BOF( ) PC
TOF BOF( )53.369 pcf
Attachment F-1 23 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.052
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B
1
2PD PC B 9.532
kip
ft
Au
PC BB
2
1
2PD PC B
B
3
PC B1
2PD PC B
8.552 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 9.113kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
93.967 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502) XR
MR
Vv10.311 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.589
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 102.393 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao ww Aw wb Ab
196.36 kipResisting Moment
Factor of Safety FSo
Mr
Mo1.918
Attachment F-1 24 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factor of Safety Check CheckFS "Ok" round FSo 1 1.5if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 17.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 ww U 9.113kip
ft
ΣH Pah wd wc Po wb 3.448kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐‐2502) Tslide ΣH cos β( ) ΣV sin β( ) 3.448
kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐‐2502) Nslide ΣV cos β( ) ΣH sin β( ) 9.113
kip
ft
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502)
FSs
Nslide tan ϕF cF LCD
Tslide1.651
CheckFS "Ok" round FSs 2 1.33if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502) δ atan
Tslide
Nslide
20.726 deg
Eccentricity of Resultant eB
2XR 1.561 ft
Effective Width of Base Bprime B 2e 20.622 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Attachment F-1 25 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Embedment Factors
Eq. 5‐4a EM 1110‐2‐2502 ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.035
Eq. 5‐4c EM 1110‐2‐2502ξqd 1 0.1
TOF BOF( )
Bprimetan 45deg
ϕF
2
1.017
Eq. 5‐4c EM 1110‐2‐2502 ξγd ξqd 1.017
Inclination Factors
ξqi 1δ
90deg
2
0.592Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.592
Eq. 5‐5b EM 1110‐2‐2502 ξγi 1δ
ϕF
2
0.124
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γb Bprime Nγ
2
67.256kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2502) FSB
Q
Nslide7.38
Attachment F-1 26 of 27
FMM Reach 4Inlet Headwall Design
Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factor of Safety Check CheckFS "Ok" round FSB 1 2if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2100) FSF
w1 w2 w3 w4 ww
U1.956
FSCheck "Ok" FSF 1.2if
"Not Ok" otherwise
"Ok"
Attachment F-1 27 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Inlet Headwall Design: Typical Section
Project Description
Reach 4 pipe drop structure inlet design for the Fargo Moorhead Metro project. The inlet will consist ofa concrete headwall and base slab, a trash rack for debris and three 7'‐2" openings in the headwall forRCPs.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
The drain will likely be constructed on alluvium, which in the Red River Valley typically occurs as a clayof low or high plasticity. The alluvium will behave differently in short and long‐term loading conditionsdue to its low permeability.
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Attachment F-2 1 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Phi ϕF 32deg
Inputs:
Existing Ground Elevation GR 890ft
Top of Wall Elevation TOW 894.5ft
Top of Footing Elevation TOF 886.5ft
Bottom of Footing Elevation BOF 884.5ft
Water Elevation Water 887ft
Stem Thickness THstem 1.5ft
Toe Length Toe 6ft
Heel Length Heel 8ft
Total Length of Footing B Toe Heel THstem 15.5 ft
EMB Slope EMBs1
4
EMB Slope angle θ atan EMBs 14.036 deg
Strength Mobilization Factor SMF2
3 <‐‐EM 1110‐2‐2502
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg <‐‐EM 1110‐2‐2502
References:U.S. Army Corps of Engineers. (29 September 1989), EM 1110‐2‐2502, Retaining andFlood Walls
U.S. Army Corps of Engineers. (1 December 2005), EM 1110‐2‐2100, StabilityAnalysis of Concrete Structures
U.S. Army Corps of Engineers (February 2012), Project Design Guidelines, FMM AreaFlood Risk Management Project, Engineering and Design Phase, Version 1. St. Paul,MN
Attachment F-2 2 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factors of Safety Requirements (EM 1110‐2‐2100 & EM 1110‐2‐2502):
Loading
Condition
Minimum
Sliding FS
Minimum
Flotation FS
Minimum Bearing
Capacity FS
Minimum Base Area
in Compression
Usual 1.5 1.3 3 100%
Unusual 1.3 1.2 2 75%
Extreme 1.1 1.1 > 1 Resultant within Base
Load Case 1
Assumptions: 1. Sloping Backfill 2. Empty Ditch (water equal on both sides at EL. 887.0) 3. Usual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
1. Determine Critical Slip angle
The soil above the heel of the retaining wall slopes up at a 1V:4H for 8 feet (horizontally), then flattensout (no slope) for 50 feet and then slopes down at a 1V:7H. It is assumed that the critical slip planeintersects the flat surface.
Attachment F-2 3 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Prove the assumption, that the critical slip plane intersects the flat surface, by trial and error.
Angle Delta Shown above
Δ atanHeel tan θ( ) TOW BOF( )
50ft
13.496 deg
Limiting angle Angle90 90deg
Assuming the critical plane intersects the flat surface, angle theta now becomes zero. With no verticalsurcharge, coefficients one and two below are calculated using Eqs. 3‐26 and 3‐27 from EM1110‐2‐2502.
Slope of the flat surface θplane atan 0( ) 0 deg
Coeffecient 1(Eq. 3‐26 EM 1110‐2‐2502)
c1 2 tan ϕd 0.801
Coefficient 2(Eq. 3‐27 EM 1110‐2‐2502)
c2 1 tan ϕd tan θplane tan θplane
tan ϕd 1
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α atanc1 c1
24 c2
2
55.915 deg
Does the critical slip plane intersect the flat surface?
Checkangle "Yes, continue analysis" Δ α Angle90if
"No, check another surface" otherwise
"Yes, continue analysis"
Attachment F-2 4 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
2. Calculate Water Pressures.
Height of water above footing Hw 0 Water TOFif
Water TOF( )( ) otherwise
0.5 ft
ww Hw Toe γw 0.187kip
ft
Weight of Water
AwToe
23 ft
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from B to C LBC TOF BOF 2 ft
Length from C to D LCD B 15.5 ft
Length from D to E LDE Water BOF( ) 2.5 ft
Ls LBC LCD LDE 20 ftSeepage path
Change in water elevation Δh Water Water 0 ft
PB Water TOF( ) γw 31.2 psfPressure at B
PC Water BOF( )Δh LBC
Ls
γw 156 psfPressure at C
PD Water BOF( )Δh LBC LCD
Ls
γw 156 psfPressure at D
PE 0psi <‐‐End of Creep, tail waterPressure at E
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2PB PC TOF BOF( ) 0.187
kip
ft
AcTOF BOF( )
3
2 PB PC PB PC
0.778 ft
Attachment F-2 5 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
wd1
2PD Water BOF( ) 0.195
kip
ft
Load at D
Ad1
3TOF BOF( ) 0.667 ft
wb1
2PB Water TOF( ) 7.8 10
3
kip
ft
Load at B
Ab1
3Water TOF( ) TOF BOF( ) 2.167 ft
we 0kip
ft <‐‐End of Creep, tail water
Load at E
Ae 0ft <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient above saturationlevel (Equation 3‐14 EM 1110‐2‐2502)
K1
cos ϕd 2
1sin ϕd sin ϕd θplane
cos θplane
20.458
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb
1 tan ϕd cot α( ) 1 tan ϕd tan α( )
1tan α( )
tan α( ) tan θplane 1
γs
γb
0.458
5. Calculate Lateral Driving Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
Heel tan θ( ) TOW BOF( )[ ] γs PD Heel tan θ( ) TOW Water( )[ ] γbf
Water BOF76.6 pcf
Soil Pressure 1 P1 K1 γbf TOW Water( ) Heel tan θ( )[ ] 0.5 ksf
Soil Force 1 F1 .5 P1 TOW Water( ) Heel tan θ( )[ ] 2.376kip
ft
a1 Water BOF( )1
3Heel tan θ( ) TOW Water( )[ ]
Soil Arm 1
a1 5.667 ft
Attachment F-2 6 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
P2 P1 γprime Kb Water BOF( ) 0.588 ksfSoil Pressure 2
F2 P1 Water BOF( ) 1.251kip
ft
Soil Force 2
Soil Arm 2 a2Water BOF
21.25 ft
F31
2P2 P1 Water BOF( ) 0.11
kip
ft
Soil Force 3
Soil Arm 3 a3Water BOF
30.833 ft
Resultant Force Pa F1 F2 F3 3.736kip
ft
Horizontal Force Pah Pa cos θplane 3.736kip
ft
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F34.047 ft
Pv Pa sin θplane 0kip
ft
Vertical Force
Av B 15.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW Water( ) γbf Heel Water TOF( ) γs 7.38kip
ft
A1 Toe THstemHeel
2 11.5 ft
Section 2 w21
2Heel Heel tan θ( )( ) γbf 0.92
kip
ft
A2 Toe THstem2
3Heel 12.833 ft
Section 3 w3 THstem TOW TOF( ) γc 1.8kip
ft
A3 ToeTHstem
2 6.75 ft
Attachment F-2 7 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Section 4 w4 B TOF BOF( ) γc 4.65kip
ft
A4B
27.75 ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for buyoant condition (EM 1110‐2‐2502) γprime
PB γs TOF BOF( ) PC
TOF BOF( )57.6 pcf
Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Horizontal Force
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift Force U PC B 2.418kip
ft
AuB
27.75 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 12.519kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
111.637 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502) XR
MR
Vv8.917 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.575
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Attachment F-2 8 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Overturning Moment Mo Pah Ah U Au wd Ad 33.989 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao ww Aw wb Ab
145.626 kipResisting Moment
Factor of Safety FSo
Mr
Mo4.285
Factor of Safety Check CheckFS "Ok" round FSo 1 2if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 15.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 ww U 12.519kip
ft
ΣH Pah wd wc Po wb 3.68kip
ft
Horizontal Forces
Tslide ΣH cos β( ) ΣV sin β( ) 3.68kip
ft
Parallel Resultant
Nslide ΣV cos β( ) ΣH sin β( ) 12.519kip
ft
Normal Resultant
FSs
Nslide tan ϕF cF LCD
Tslide2.126
Factor of Safety(Eq. 4‐6 EM1110‐2‐2502)
CheckFS "Ok" round FSs 1 1.5if
"Not Ok" otherwise
"Ok"Factor of Safety Check
Attachment F-2 9 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
16.383 deg
Eccentricity of Resultant eB
2XR 1.167 ft
Effective Width of Base Bprime B 2e 17.834 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 115.2 psf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.04Eq. 5‐4a EM 1110‐2‐2502
Eq. 5‐4c EM 1110‐2‐2502 ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.02
Eq. 5‐4c EM 1110‐2‐2502 ξγd ξqd 1.02
Inclination Factors
ξqi 1δ
90deg
2
0.669Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.669
ξγi 1δ
ϕF
2
0.238Eq. 5‐5b EM 1110‐2‐2502
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Attachment F-2 10 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γb Bprime Nγ
2
81.526kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2502)
FSBQ
Nslide6.512
Factor of Safety Check CheckFS "Ok" round FSB 1 3if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2100)
FSF
w1 w2 w3 w4 ww
U6.178
FSCheck "Ok" FSF 1.3if
"Not Ok" otherwise
"Ok"
Attachment F-2 11 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Load Case 2
Assumptions: 1. Sloping Backfill 2. Full Ditch (water equal on both sides at EL. 890) 3. Usual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α 55.915 deg <‐‐See Load Case 1 above
2. Calculate Water Pressures.
Height of water above footing Hw GR TOF 3.5 ft
ww Hw Toe γw 1.31kip
ft
Weight of Water
AwToe
23 ft
Attachment F-2 12 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from B to C LBC TOF BOF 2 ft
Length from C to D LCD B 15.5 ft
Length from D to E LDE GR BOF( ) 5.5 ft
Ls LBC LCD LDE 23 ftSeepage path
Change in water elevation Δh GR GR 0 ft
PB GR TOF( ) γw 0.218 ksfPressure at B
PC GR BOF( )Δh LBC
Ls
γw 0.343 ksfPressure at C
PD GR BOF( )Δh LBC LCD
Ls
γw 0.343 ksfPressure at D
PE 0ksf <‐‐End of Creep, tail waterPressure at E
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2PB PC TOF BOF( ) 0.562
kip
ft
AcTOF BOF( )
3
2 PB PC PB PC
0.926 ft
wd1
2PD GR BOF( ) 0.944
kip
ft
Load at D
Ad1
3GR BOF( ) 1.833 ft
wb1
2PB GR TOF( ) 0.382
kip
ft
Load at B
Ab1
3GR TOF( ) TOF BOF( ) 3.167 ft
Attachment F-2 13 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
we 0kip
ft <‐‐End of Creep, tail water
Load at E
Ae 0ft <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficients
Pressure Coefficient(Appendix H EM 1110‐2‐2502) K1 0.458 <‐‐See Load Case 1 above
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458 <‐‐See Load Case 1 above
5. Calculate Lateral Driving Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
Heel tan θ( ) TOW BOF( )[ ] γs PD Heel tan θ( ) TOW GR( )[ ] γbf
GR BOF63.509 pcf
Soil Pressure 1 P1 K1 γbf TOW GR( ) Heel tan θ( )[ ] 0.342 ksf
Soil Force 1 F1 .5 P1 TOW GR( ) Heel tan θ( )[ ] 1.112kip
ft
a1 GR BOF( )1
3Heel tan θ( ) TOW GR( )[ ] 7.667 ft
Soil Arm 1
P2 P1 γprime Kb GR BOF( ) 0.502 ksfSoil Pressure 2
F2 P1 GR BOF( ) 1.882kip
ft
Soil Force 2
Soil Arm 2 a2GR BOF
22.75 ft
F31
2P2 P1 GR BOF( ) 0.44
kip
ft
Soil Force 3
Soil Arm 3 a3GR BOF
31.833 ft
Attachment F-2 14 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Pa F1 F2 F3 3.435kip
ft
Resultant Force
Pah Pa cos θplane 3.435kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F34.225 ft
Active Force Arm
Active Vertical Force Pv Pa sin θ( ) 0.833kip
ft
Av B 15.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel GR TOF( ) γs 3.36kip
ft
A1 Toe THstemHeel
2 11.5 ft
Section 2 w2 Heel TOW GR( ) γbf 4.14kip
ft
A2 Toe THstem1
2Heel 11.5 ft
w31
2Heel Heel tan θ( )( ) γbf 0.92
kip
ft
Section 3
A3 Toe THstem2
3Heel 12.833 ft
w4 THstem TOW TOF( ) γc 1.8kip
ft
Section 4
A4 ToeTHstem
2 6.75 ft
Section 5 w5 B TOF BOF( ) γc 4.65kip
ft
Attachment F-2 15 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
A5B
27.75 ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
GR BOF( ) γs PD GR BOF( )
57.6 pcf
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B 5.32
kip
ft
AuB
27.75 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 w5 ww U 10.861kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad w5 A5 wb Ab
94.474 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502) XR
MR
Vv8.699 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502)
RR
XR
B0.561
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Attachment F-2 16 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Overturning Moment Mo Pah Ah U Au wd Ad 57.469 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao w5 A5 ww Aw wb Ab
151.943 kipResisting Moment
Factor of Safety FSo
Mr
Mo2.644
Factor of Safety Check CheckFS "Ok" round FSo 1 2if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 15.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 w5 ww U 10.861kip
ft
ΣH Pah wd wc Po wb 3.379kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐‐2502)
Tslide ΣH cos β( ) ΣV sin β( ) 3.379kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 10.861kip
ft
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502)
FSs
Nslide tan ϕF cF LCD
Tslide2.009
CheckFS "Ok" round FSs 1 1.5if
"Not Ok" otherwise
"Ok"Factor of Safety Check
Attachment F-2 17 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
17.281 deg
Eccentricity of Resultant eB
2XR 0.949 ft
Effective Width of Base Bprime B 2e 17.397 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Nγ Nq 1 tan 1.4 ϕF 22.022Eq. 5‐3d EM 1110‐2‐2502
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.041Eq. 5‐4a EM 1110‐2‐2502
ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.021Eq. 5‐4c EM 1110‐2‐2502
ξγd ξqd 1.021Eq. 5‐4c EM 1110‐2‐2502
Inclination Factors
ξqi 1δ
90deg
2
0.653Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.653
Eq. 5‐5b EM 1110‐2‐2502 ξγi 1δ
ϕF
2
0.212
Attachment F-2 18 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γb Bprime Nγ
2
72.41kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2502)
FSBQ
Nslide6.667
Factor of Safety Check CheckFS "Ok" round FSB 1 3if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2100)
FSF
w1 w2 w3 w4 w5 ww
U3.042
FSCheck "Ok" FSF 1.3if
"Not Ok" otherwise
"Ok"
Attachment F-2 19 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Load Case 3
Assumptions: 1. Sloping Backfill 2. Lagging soil (Water at EL. 894.5 on Heel side; EL. 892.5 on Toe Side) 3. Unusual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & unequal water pressures.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α 55.915 deg
2. Calculate Water Pressures.
Height of water above footing Hw TOW 2ft( ) TOF[ ] 6 ft
ww Hw Toe γw 2.246kip
ft
Weight of Water
AwToe
23 ft
Attachment F-2 20 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from B to C LBC TOF BOF 2 ft
Length from C to D LCD B 15.5 ft
Length from D to E LDE TOW BOF( ) 10 ft
Ls LBC LCD LDE 27.5 ftSeepage path
Change in water elevation Δh TOW 2ft( ) TOW 2 ft
Pressure at B PB TOW 2ft( ) TOF[ ] γw 0.3744 ksf
Pressure at C PC TOW 2ft( ) BOF[ ]Δh LBC
Ls
γw 0.5083 ksf
PD TOW 2ft( ) BOF[ ]Δh LBC LCD
Ls
γw 0.5786 ksfPressure at D
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2TOF BOF( ) PB PC 0.883
kip
ft
AcTOF BOF( )
3
2PB PC PB PC
0.949 ft
wd1
2PD TOW BOF( ) 2.893
kip
ft
Load at D
Ad1
3TOW BOF( ) 3.333 ft
wb1
2PB TOW 2ft( ) TOF[ ] 1.123
kip
ft
Load at B
Ab TOF BOF( )1
3TOW 2ft( ) TOF[ ] 4 ft
Attachment F-2 21 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Load at E we1
2TOW TOF( ) PE 0
kip
ft
Ae1
3TOW TOF( ) TOF BOF( ) 4.667 ft
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient(Appendix H EM 1110‐2‐2502)
K1 0.458 <‐‐See Load Case 1 above
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458 <‐‐See Load Case 1 above
5. Calculate Lateral Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
Heel tan θ( ) TOW BOF( )[ ] γs PD Heel tan θ( )( ) γbf
TOW BOF63.138 pcf
Soil Pressure 1 P1 K1 γbf Heel tan θ( )( ) 0.105 ksf
Soil Force 1 F1 .5 P1 Heel tan θ( )( ) 0.105kip
ft
a1 TOW BOF( )1
3Heel tan θ( )( )( ) 10.667 ft
Soil Arm 1
P2 P1 γprime Kb TOW BOF( ) 0.394 ksfSoil Pressure 2
F2 P1 TOW BOF( ) 1.053kip
ft
Soil Force 2
Soil Arm 2 a2TOW BOF
25 ft
F31
2P2 P1 TOW BOF( ) 1.446
kip
ft
Soil Force 3
Attachment F-2 22 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Soil Arm 3 a3TOW BOF
33.333 ft
Pa F1 F2 F3 2.604kip
ft
Resultant Force
Pah Pa cos θplane 2.604kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F34.304 ft
Active Force Arm
Pv Pa sin θplane 0kip
ft
Active Vertical Force
Av B 15.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW TOF( ) γs 7.68kip
ft
A1 Toe THstemHeel
2 11.5 ft
w21
2Heel Heel tan θ( )( ) γbf 0.92
kip
ft
Section 2
A2 Toe THstem2
3Heel 12.833 ft
w3 THstem TOW TOF( ) γc 1.8kip
ft
Section 3
A3 ToeTHstem
2 6.75 ft
Section 4 w4 B TOF BOF( ) γc 4.65kip
ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
PB γs TOF BOF( ) PC
TOF BOF( )53.062 pcf
Attachment F-2 23 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.051
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B
1
2PD PC B 8.423
kip
ft
Au
PC BB
2
1
2PD PC B
B
3
PC B1
2PD PC B
7.583 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 8.873kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
71.044 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502)
XR
MR
Vv8.007 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502)
RR
XR
B0.517
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 84.724 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao ww Aw wb Ab
155.769 kipResisting Moment
Factor of Safety FSo
Mr
Mo1.839
Attachment F-2 24 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factor of Safety Check CheckFS "Ok" round FSo 1 1.5if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 15.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 ww U 8.873kip
ft
ΣH Pah wd wc Po wb 3.44kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐‐2502)
Tslide ΣH cos β( ) ΣV sin β( ) 3.44kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 8.873kip
ft
FSs
Nslide tan ϕF cF LCD
Tslide1.612
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502)
CheckFS "Ok" round FSs 1 1.33if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
21.189 deg
Eccentricity of Resultant eB
2XR 0.257 ft
Effective Width of Base Bprime B 2e 16.014 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502) qo γb TOF BOF( ) 0.115 ksf
Attachment F-2 25 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Nγ Nq 1 tan 1.4 ϕF 22.022Eq. 5‐3d EM 1110‐2‐2502
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.045Eq. 5‐4a EM 1110‐2‐2502
Eq. 5‐4c EM 1110‐2‐2502 ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.023
Eq. 5‐4c EM 1110‐2‐2502 ξγd ξqd 1.023
Inclination Factors
ξqi 1δ
90deg
2
0.585Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.585
Eq. 5‐5b EM 1110‐2‐2502 ξγi 1δ
ϕF
2
0.114
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γb Bprime Nγ
2
44.537kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2502)
FSBQ
Nslide5.019
Attachment F-2 26 of 27
FMM Reach 4Inlet Headwall Design
Typical Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factor of Safety Check CheckFS "Ok" round FSB 1 2if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2100)
FSF
w1 w2 w3 w4 ww
U2.053
FSCheck "Ok" FSF 1.2if
"Not Ok" otherwise
"Ok"
Attachment F-2 27 of 27
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Inlet Headwall Design: Wingwall Section
Project Description
Reach 4 pipe drop structure inlet design for the Fargo Moorhead Metro project. The inlet will consist ofa concrete headwall and base slab, a trash rack for debris and three 7'‐2" openings in the headwall forRCPs.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
The drain will likely be constructed on alluvium, which in the Red River Valley typically occurs as a clayof low or high plasticity. The alluvium will behave differently in short and long‐term loading conditionsdue to its low permeability.
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Attachment F-3 1 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Phi ϕF 32deg
Inputs:
Existing Ground Elevation GR 890ft
Top of Wall Elevation TOW 893ft
Top of Footing Elevation TOF 886.5ft
Bottom of Footing Elevation BOF 884.5ft
Water Elevation Water 887ft
Stem Thickness THstem 1.5ft
Toe Length Toe 6ft
Heel Length Heel 6ft
Total Length of Footing B Toe Heel THstem 13.5 ft
EMB Slope EMBs 0
Slope angle θ atan EMBs 0 deg
Strength Mobilization Factor SMF2
3 <‐‐EM 1110‐2‐2502
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg <‐‐EM 1110‐2‐2502
References:U.S. Army Corps of Engineers. (29 September 1989), EM 1110‐2‐2502, Retaining andFlood Walls
U.S. Army Corps of Engineers. (1 December 2005), EM 1110‐2‐2100, StabilityAnalysis of Concrete Structures
U.S. Army Corps of Engineers (February 2012), Project Design Guidelines, FMM AreaFlood Risk Management Project, Engineering and Design Phase, Version 1. St. Paul,MN
Attachment F-3 2 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factors of Safety Requirements (EM 1110‐2‐2100 & EM 1110‐2‐2502):
Loading
Condition
Minimum
Sliding FS
Minimum
Flotation FS
Minimum Bearing
Capacity FS
Minimum Base Area
in Compression
Usual 1.5 1.3 3 100%
Unusual 1.3 1.2 2 75%
Extreme 1.1 1.1 > 1 Resultant within Base
General Note: Since the wingwall slopes down, causing the wall height to vary along it's length, adesign section is taken 1/3 of the distance down the wall.
Load Case 1
Assumptions: 1. Horizontal Backfill 2. Empty Ditch (water equal on both sides at EL. 887.0) 3. Usual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
Attachment F-3 3 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
1. Determine Critical Slip Plane angle
Coeffecient 1(Eq. 3‐26 EM 1110‐2‐2502) c1 2 tan ϕd 0.801
Coefficient 2(Eq. 3‐27 EM 1110‐2‐2502) c2 1 tan ϕd tan θ( )
tan θ( )
tan ϕd 1
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502) α atan
c1 c12
4 c2
2
55.915 deg
2. Calculate Water Pressures.
Height of water above footing Hw 0 Water TOFif
Water TOF( )( ) otherwise
0.5 ft
ww Hw Toe γw 0.187kip
ft
Weight of Water
AwToe
23 ft
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length top of water to BOF L1 TOF BOF 2 ft
Length from C to D LCD B 13.5 ft
Length from D to E LDE Water BOF( ) 2.5 ft
Ls L1 LCD LDE 18 ftSeepage path
Change in water elevation Δh Water Water 0 ft
PB Water TOF( ) γw 31.2 psfPressure at B
PC Water BOF( )Δh L1
Ls
γw 156 psfPressure at C
Attachment F-3 4 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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PD Water BOF( )Δh L1 LCD
Ls
γw 156 psfPressure at D
PE 0psi <‐‐End of Creep, tail waterPressure at E
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2PB PC TOF BOF( ) 0.187
kip
ft
AcTOF BOF( )
3
2 PB PC PB PC
0.778 ft
wd1
2PD Water BOF( ) 0.195
kip
ft
Load at D
Ad1
3TOF BOF( ) 0.667 ft
wb1
2PB Water TOF( ) 7.8 10
3
kip
ft
Load at B
Ab1
3Water TOF( ) TOF BOF( ) 2.167 ft
we 0kip
ft <‐‐End of Creep, tail water
Load at E
Ae 0ft <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient(Appendix H EM 1110‐2‐2502)
K1
1 tan ϕd cot α( ) 1 tan ϕd tan α( )
tan α( )
tan α( ) tan θ( ) 0.458
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb
1 tan ϕd cot α( ) 1 tan ϕd tan α( )
1tan α( )
tan α( ) tan θ( )1
γs
γb
0.458
Attachment F-3 5 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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5. Calculate Lateral Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
TOW BOF( )( ) γs PD TOW Water( )( ) γbf
Water BOF69.6 pcf
Soil Pressure 1 P1 K1 γbf TOW Water( )( ) 0.316 ksf
Soil Force 1 F1 .5 P1 TOW Water( )( ) 0.948kip
ft
a1 Water BOF( )1
3TOW Water( )( )
Soil Arm 1
a1 4.5 ft
P2 P1 γprime Kb Water BOF( ) 0.396 ksfSoil Pressure 2
F2 P1 Water BOF( ) 0.79kip
ft
Soil Force 2
Soil Arm 2 a2Water BOF
21.25 ft
F31
2P2 P1 Water BOF( ) 0.1
kip
ft
Soil Force 3
Soil Arm 3 a3Water BOF
30.833 ft
Resultant Force Pa F1 F2 F3 1.837kip
ft
Pah Pa cos θ( ) 1.837kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F32.904 ft
Pv Pa sin θ( ) 0kip
ft
Vertical Force
Av B 13.5 ft
Attachment F-3 6 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW Water( ) γbf Heel Water TOF( ) γs 4.5kip
ft
A1 Toe THstemHeel
2 10.5 ft
Section 2 w21
2Heel Heel tan θ( )( ) γs 0
kip
ft
A2 Toe THstem2
3Heel 11.5 ft
Section 3 w3 THstem TOW TOF( ) γc 1.463kip
ft
A3 ToeTHstem
2 6.75 ft
Section 4 w4 B TOF BOF( ) γc 4.05kip
ft
A4B
26.75 ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for buyoant condition (EM 1110‐2‐2502) γprime
PB γs TOF BOF( ) PC
TOF BOF( )57.6 pcf
Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Horizontal Force
Ao TOF BOF( )1
3 0.667 ft
Attachment F-3 7 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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8. Calculate Uplift Force.
Uplift Force U PC B 2.106kip
ft
AuB
26.75 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 8.094kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
65.54 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2‐2502) XR
MR
Vv8.098 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.6
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 19.681 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao wb Ab
84.659 kipResisting Moment
Factor of Safety FSo
Mr
Mo4.302
Factor of Safety Check CheckFS "Ok" round FSo 1 2if
"Not Ok" otherwise
"Ok"
Attachment F-3 8 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 13.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 ww U 8.094kip
ft
ΣH Pah wd wc Po wb 1.781kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐2‐2502) Tslide ΣH cos β( ) ΣV sin β( ) 1.781
kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐2‐2502) Nslide ΣV cos β( ) ΣH sin β( ) 8.094
kip
ft
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502)
FSs
Nslide tan ϕF cF LCD
Tslide2.839
CheckFS "Ok" round FSs 1 1.5if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
12.413 deg
Eccentricity of Resultant eB
2XR 1.348 ft
Effective Width of Base Bprime B 2e 16.195 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Attachment F-3 9 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.045Eq. 5‐4a EM 1110‐2‐2502
Eq. 5‐4c EM 1110‐2‐2502 ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.022
Eq. 5‐4c EM 1110‐2‐2502 ξγd ξqd 1.022
Inclination Factors
ξqi 1δ
90deg
2
0.743Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.743
ξγi 1δ
ϕF
2
0.375Eq. 5‐5b EM 1110‐2‐2502
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γprime Bprime Nγ
2
96.568kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2‐2502) FSB
Q
Nslide11.931
Factor of Safety Check CheckFS "Ok" round FSB 1 3if
"Not Ok" otherwise
"Ok"
Attachment F-3 10 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2‐2100)
FSF
w1 w2 w3 w4 ww
U4.843
FSCheck "Ok" FSF 1.3if
"Not Ok" otherwise
"Ok"
Load Case 2
Assumptions: 1. Horizontal Backfill 2. Full Ditch (water equal on both sides at EL. 890) 3. Usual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α 55.915 deg <‐‐See Load Case 1 above
Attachment F-3 11 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
2. Calculate Water Pressures.
Height of water above footing Hw GR TOF 3.5 ft
Weight of Water ww Hw Toe γw 1.31kip
ft
AwToe
23 ft
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
L1 TOF BOF 2 ftLength from top of water to BOF
Length from C to D LCD B 13.5 ft
Length from D to E LDE GR BOF( ) 5.5 ft
Ls L1 LCD LDE 21 ftSeepage path
Change in water elevation Δh GR GR 0 ft
PB GR TOF( ) γw 0.218 ksfPressure at B
PC GR BOF( )Δh L1
Ls
γw 0.343 ksfPressure at C
PD GR BOF( )Δh L1 LCD
Ls
γw 0.343 ksfPressure at D
PE 0ksf <‐‐End of Creep, tail waterPressure at E
3. Calculate Water Loads and Moment Arms about O.
Load at C wc1
2PB PC TOF BOF( ) 0.562
kip
ft
AcTOF BOF( )
3
2 PB PC PB PC
0.926 ft
Attachment F-3 12 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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wd1
2PD GR BOF( ) 0.944
kip
ft
Load at D
Ad1
3GR BOF( ) 1.833 ft
wb1
2PB GR TOF( ) 0.382
kip
ft
Load at B
Ab1
3GR TOF( ) TOF BOF( ) 3.167 ft
we 0kip
ft <‐‐End of Creep, tail water
Load at E
Ae 0ft <‐‐End of Creep, tail water
4. Calculate Lateral Pressure Coefficients
Pressure Coefficient(Appendix H EM 1110‐2‐2502)
K1 0.458 <‐‐See Load Case 1 above
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458 <‐‐See Load Case 1 above
5. Calculate Lateral Driving Force
**Since there is soil above and below the water table, two pressures are computed and then convertedto forces.
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime
TOW BOF( )( ) γs PD TOW GR( )( ) γbf
GR BOF60.327 pcf
Soil Pressure 1 P1 K1 γbf TOW GR( )( ) 0.158 ksf
Soil Force 1 F1 .5 P1 TOW GR( )( ) 0.237kip
ft
a1 GR BOF( )1
3Heel tan θ( ) TOW GR( )[ ] 6.5 ft
Soil Arm 1
Attachment F-3 13 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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P2 P1 γprime Kb GR BOF( ) 0.31 ksfSoil Pressure 2
F2 P1 GR BOF( ) 0.869kip
ft
Soil Force 2
Soil Arm 2 a2GR BOF
22.75 ft
F31
2P2 P1 GR BOF( ) 0.418
kip
ft
Soil Force 3
Soil Arm 3 a3GR BOF
31.833 ft
Pah F1 F2 F3 1.524kip
ft
Active Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F33.082 ft
Active Force Arm
Pv Pah sin θ( ) 0kip
ft
Av B 13.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel GR TOF( ) γs 2.52kip
ft
A1 Toe THstemHeel
2 10.5 ft
Section 2 w2 Heel TOW GR( ) γbf 2.07kip
ft
A2 Toe THstem1
2Heel 10.5 ft
w31
2Heel Heel tan θ( )( ) γbf 0
kip
ft
Section 3
A3 Toe THstem2
3Heel 11.5 ft
w4 THstem TOW TOF( ) γc 1.463kip
ft
Section 4
Attachment F-3 14 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
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A4 ToeTHstem
2 6.75 ft
Section 5 w5 B TOF BOF( ) γc 4.05kip
ft
A5B
26.75 ft
7. Calculate Soil Force on Resisting Side.
Ko 1 sin ϕ( ) 0.485At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
GR BOF( ) γs PD GR BOF( )
57.6 pcf
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B 4.633
kip
ft
AuB
26.75 ft
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 w5 ww U 6.78kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad w5 A5 wb Ab
53.403 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502) XR
MR
Vv7.877 ft
Attachment F-3 15 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.583
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 37.7 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao w5 A5 ww Aw wb Ab
91.103 kipResisting Moment
Factor of Safety FSo
Mr
Mo2.417
Factor of Safety Check CheckFS "Ok" round FSo 1 2if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 13.5 ftLength of Sliding Plane
Vertical Forces ΣV w1 w2 w3 w4 w5 ww U 6.78kip
ft
ΣH Pah wd wc Po wb 1.468kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐2‐2502)
Tslide ΣH cos β( ) ΣV sin β( ) 1.468kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐2‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 6.78kip
ft
Attachment F-3 16 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502) FSs
Nslide tan ϕF cF LCD
Tslide2.886
CheckFS "Ok" round FSs 1 1.5if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
12.215 deg
Eccentricity of Resultant eB
2XR 1.127 ft
Effective Width of Base Bprime B 2e 15.754 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.046Eq. 5‐4a EM 1110‐2‐2502
Eq. 5‐4c EM 1110‐2‐2502 ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.023
Eq. 5‐4c EM 1110‐2‐2502 ξγd ξqd 1.023
Inclination Factors
ξqi 1δ
90deg
2
0.747Eq. 5‐5a EM 1110‐2‐2502
Attachment F-3 17 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.747
ξγi 1δ
ϕF
2
0.382Eq. 5‐5b EM 1110‐2‐2502
**Base Tilt and Ground Slope Factors are al equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γprime Bprime Nγ
2
93.688kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2‐2502)
FSBQ
Nslide13.819
Factor of Safety Check CheckFS "Ok" round FSB 1 3if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2‐2100)
FSF
w1 w2 w3 w4 w5 ww
U2.463
FSCheck "Ok" FSF 1.5if
"Not Ok" otherwise
"Ok"
Attachment F-3 18 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Load Case 3
Assumptions: 1. Horizontal Backfill 2. Lagging soil (Water at EL. 893.0 on Heel side; EL. 891.0 on Toe Side) 3. Unusual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & unequal water pressures.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502) α 55.915 deg
2. Calculate Water Pressures.
Height of water above footing Hw TOW 2ft( ) TOF[ ] 4.5 ft
ww Hw Toe γw 1.685kip
ft
Weight of Water
AwToe
23 ft
Attachment F-3 19 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from ground to C L1 TOF BOF 2 ft
Length from C to DLCD B 13.5 ft
Length from D to ELDE TOW BOF( ) 8.5 ft
Seepage path Ls L1 LCD LDE 24 ft
Change in water elevation Δh TOW 2ft( ) TOW 2 ft
Pressure at B PB TOW 2ft( ) TOF[ ] γw 0.2808 ksf
PC TOW 2ft( ) BOF[ ]Δh L1
Ls
γw 0.416 ksfPressure at C
Pressure at D PD TOW 2ft( ) BOF[ ]Δh L1 LCD
Ls
γw 0.486 ksf
3. Calculate Water Loads and Moment Arms about O.
wc1
2TOF BOF( ) PB PC 0.697
kip
ft
Load at C
AcTOF BOF( )
3
2PB PC PB PC
0.935 ft
wd1
2PD TOW BOF( ) 2.066
kip
ft
Load at D
Ad1
3TOW BOF( ) 2.833 ft
wb1
2PB TOW 2ft( ) TOF[ ] 0.632
kip
ft
Load at B
Ab TOF BOF( )1
3TOW 2ft( ) TOF[ ] 3.5 ft
Attachment F-3 20 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
we 0kip
ft <‐‐End of Creep, tail water
Load at E
<‐‐End of Creep, tail waterAe 0ft
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient(Appendix H EM 1110‐2‐2502) K1 0.458
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458
5. Calculate Lateral Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
TOW BOF( )( ) γs PD
TOW BOF62.8 pcf
Soil Pressure 1 P1 K1 γprime TOW BOF( ) 0.244 ksf
Soil Force 1 F1 .5 P1 TOW BOF( ) 1.039kip
ft
a11
3TOW BOF( ) 2.833 ft
Soil Arm 1
Pah F1 1.039kip
ft
Active Horizontal Force
Ah a1 2.833 ftActive Force Arm
Pv Pah sin θ( ) 0kip
ft
Av B 13.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW TOF( ) γs 4.68kip
ft
Attachment F-3 21 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
A1 Toe THstemHeel
2 10.5 ft
w21
2Heel Heel tan θ( )( ) γs 0
kip
ft
Section 2
A2 Toe THstem2
3Heel 11.5 ft
w3 THstem TOW TOF( ) γc 1.463kip
ft
Section 3
A3 ToeTHstem
2 6.75 ft
Section 4 w4 B TOF BOF( ) γc 4.05kip
ft
A4B
26.75 ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
PB γs TOF BOF( ) PC
TOF BOF( )52.4 pcf
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.051
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B
1
2PD PC B 6.09
kip
ft
Au
PC BB
2
1
2PD PC B
B
3
PC B1
2PD PC B
6.575 ft
Attachment F-3 22 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 5.787kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
45.462 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2502) XR
MR
Vv7.855 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.582
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 48.838 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao ww Aw wb Ab
94.301 kipResisting Moment
Factor of Safety FSo
Mr
Mo1.931
Factor of Safety Check CheckFS "Ok" round FSo 1 1.5if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 13.5 ftLength of Sliding Plane
Attachment F-3 23 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Vertical Forces ΣV w1 w2 w3 w4 ww U 5.787kip
ft
ΣH Pah wd wc Po wb 1.726kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐2‐2502)
Tslide ΣH cos β( ) ΣV sin β( ) 1.726kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐2‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 5.787kip
ft
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502) FSs
Nslide tan ϕF cF LCD
Tslide2.096
CheckFS "Ok" round FSs 1 1.33if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
16.604 deg
Eccentricity of Resultant eB
2XR 1.105 ft
Effective Width of Base Bprime B 2e 15.711 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Attachment F-3 24 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.046Eq. 5‐4a EM 1110‐2‐2502
ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.023Eq. 5‐4c EM 1110‐2‐2502
ξγd ξqd 1.023Eq. 5‐4c EM 1110‐2‐2502
Inclination Factors
ξqi 1δ
90deg
2
0.665Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.665
ξγi 1δ
ϕF
2
0.231Eq. 5‐5b EM 1110‐2‐2502
**Base Tilt and Ground Slope Factors are all equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γprime Bprime Nγ
2
62.264kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2‐2502)
FSBQ
Nslide10.758
Factor of Safety Check CheckFS "Ok" round FSB 1 2if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2‐2100) FSF
w1 w2 w3 w4 ww
U1.95
FSCheck "Ok" FSF 1.2if
"Not Ok" otherwise
"Ok"
Attachment F-3 25 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Load Case 4
Assumptions: 1. Horizontal Backfill 2. Wall is completely submerged (water @ EL. 894.5) ‐ Flotation is the primary concern for this LC 3. Unusual Condition
The loading on the strcture consists of the structure dead load, the weight of the soil above the heel, theweight of the water above the toe, lateral earth pressures & water pressures equal on both sides.
1. Determine Critical Slip angle
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502) α 55.915 deg
2. Calculate Water Pressures.
Height of water above footing Hw TOW 1.5ft( ) TOF 8 ft
ww Hw Toe γw 2.995kip
ft
Weight of Water
AwToe
23 ft
Attachment F-3 26 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Water pressures are computed using the line of creep method from EM 1110‐2‐2502. The seepage pathis assumed to start at the top of the soil and ends at Point E.
Length from ground to C L1 TOF BOF 2 ft
Length from C to DLCD B 13.5 ft
Length from D to ELDE TOW 1.5ft( ) BOF[ ] 10 ft
Seepage path Ls L1 LCD LDE 25.5 ft
Change in water elevation Δh TOW 1.5ft( ) TOW 1.5ft( ) 0 ft
Pressure at B PB TOW 1.5ft( ) TOF[ ] γw 0.4992 ksf
PC TOW 1.5ft BOF( )Δh L1
Ls
γw 0.624 ksfPressure at C
Pressure at D PD TOW 1.5ft BOF( )Δh L1 LCD
Ls
γw 0.624 ksf
3. Calculate Water Loads and Moment Arms about O.
wc1
2TOF BOF( ) PB PC 1.123
kip
ft
Load at C
AcTOF BOF( )
3
2PB PC PB PC
0.963 ft
wd1
2PD 1.5ft TOW( ) BOF[ ] 3.12
kip
ft
Load at D
Ad1
3TOW 1.5ft( ) BOF[ ] 3.333 ft
wb1
2PB TOW 1.5ft TOF( ) 1.997
kip
ft
Load at B
Ab TOF BOF( )1
3TOW 1.5ft TOF( ) 4.667 ft
Attachment F-3 27 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
we 0kip
ft <‐‐End of Creep, tail water
Load at E
<‐‐End of Creep, tail waterAe 0ft
4. Calculate Lateral Pressure Coefficient
Pressure Coefficient(Appendix H EM 1110‐2‐2502) K1 0.458
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb 0.458
5. Calculate Lateral Force
**Since there is soil above and below the water table, three pressures and computed and thenconverted to forces.
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
TOW 1.5ft( ) BOF[ ] γs PD
TOW 1.5ft( ) BOF57.6 pcf
Soil Pressure 1 P1 K1 γprime TOW BOF( ) 0.224 ksf
Soil Force 1 F1 .5 P1 TOW BOF( ) 0.953kip
ft
a11
3TOW BOF( ) 2.833 ft
Soil Arm 1
Pah F1 0.953kip
ft
Active Horizontal Force
Ah a1 2.833 ftActive Force Arm
Pv Pah sin θ( ) 0kip
ft
Av B 13.5 ft
6. Calculate Structure and Soil Weights and Moments Arms about O.
Section 1 w1 Heel TOW TOF( ) γs 4.68kip
ft
Attachment F-3 28 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
A1 Toe THstemHeel
2 10.5 ft
w2 Heel THstem TOW 1.5ft( ) TOW[ ] γw 0.702kip
ft
Section 2(water weight)
A2 ToeHeel THstem
2
9.75 ft
w3 THstem TOW TOF( ) γc 1.463kip
ft
Section 3
A3 ToeTHstem
2 6.75 ft
Section 4 w4 B TOF BOF( ) γc 4.05kip
ft
A4B
26.75 ft
7. Calculate Soil Force on Resisting Side.
At Rest Coefficient(Eq. 3‐4 EM 1110‐2‐2502)
Ko 1 sin ϕ( ) 0.485
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime
PB γs TOF BOF( ) PC
TOF BOF( )57.6 pcf
Horizontal Force Po1
2Ko γprime TOF BOF( )
2 0.056
kip
ft
Ao TOF BOF( )1
3 0.667 ft
8. Calculate Uplift Force.
Uplift ForceU PC B
1
2PD PC B 8.424
kip
ft
Au
PC BB
2
1
2PD PC B
B
3
PC B1
2PD PC B
6.75 ft
Attachment F-3 29 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
9. Check Overturning about O.
Sum of Vertical Forces Vv w1 w2 w3 w4 ww U 5.466kip
ft
MR w1 A1 w2 A2 w3 A3 w4 A4
ww Aw U Au Pah Ah Po Ao
wc Ac wd Ad wb Ab
42.655 kipSum of All Moments
Resultant Location(Eq. 4‐1 EM 1110‐2‐2502) XR
MR
Vv7.804 ft
Resultant Ratio(Eq. 4‐2 EM 1110‐2‐2502) RR
XR
B0.578
Base Compression Check CheckBase "Ok" .667 RR .333if
"Not Ok" otherwise
"Ok"
Overturning Moment Mo Pah Ah U Au wd Ad 69.962 kip
Mr w1 A1 w2 A2 w3 A3 w4 A4
wc Ac Po Ao ww Aw wb Ab
112.617 kipResisting Moment
Factor of Safety FSo
Mr
Mo1.61
Factor of Safety Check CheckFS "Ok" round FSo 1 1.5if
"Not Ok" otherwise
"Ok"
10. Check Slidng using EM1110‐2‐2502 "Single Wedge Analysis".
Slip angle β 0
cF 0 psfShear strength of foundation
ϕF 32 degPhi angle for foundation
LCD 13.5 ftLength of Sliding Plane
Attachment F-3 30 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Vertical Forces ΣV w1 w2 w3 w4 ww U 5.466kip
ft
ΣH Pah wd wc Po wb 0.897kip
ft
Horizontal Forces
Parallel Resultant(Fig. 4‐11 EM 1110‐2‐2502)
Tslide ΣH cos β( ) ΣV sin β( ) 0.897kip
ft
Normal Resultant(Fig. 4‐11 EM 1110‐2‐2502)
Nslide ΣV cos β( ) ΣH sin β( ) 5.466kip
ft
Factor of Safety(Eq. 4‐12 EM 1110‐2‐2502) FSs
Nslide tan ϕF cF LCD
Tslide3.808
CheckFS "Ok" round FSs 1 1.33if
"Not Ok" otherwise
"Ok"Factor of Safety Check
11. Check Bearing Capacity.
Angle of Wall Friction(Fig. 5‐1 EM 1110‐2‐2502)
δ atanTslide
Nslide
9.319 deg
Eccentricity of Resultant eB
2XR 1.054 ft
Effective Width of Base Bprime B 2e 15.608 ft
Effective Overburden Stress(Eq. 5‐8a EM 1110‐2‐2502)
qo γb TOF BOF( ) 0.115 ksf
Bearing Capacity Factors for strip load
Nq exp π tan ϕF tan 45degϕF
2
2
23.177Eq. 5‐3a EM 1110‐2‐2502
Eq. 5‐3b EM 1110‐2‐2502 Nc Nq 1 cot ϕF 35.49
Eq. 5‐3d EM 1110‐2‐2502 Nγ Nq 1 tan 1.4 ϕF 22.022
Attachment F-3 31 of 32
FMM Reach 4Inlet Headwall Design
Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Embedment Factors
ξcd 1 0.2TOF BOF( )
Bprimetan 45deg
ϕF
2
1.046Eq. 5‐4a EM 1110‐2‐2502
ξqd 1 0.1TOF BOF( )
Bprimetan 45deg
ϕF
2
1.023Eq. 5‐4c EM 1110‐2‐2502
ξγd ξqd 1.023Eq. 5‐4c EM 1110‐2‐2502
Inclination Factors
ξqi 1δ
90deg
2
0.804Eq. 5‐5a EM 1110‐2‐2502
Eq. 5‐5a EM 1110‐2‐2502 ξci ξqi 0.804
ξγi 1δ
ϕF
2
0.502Eq. 5‐5b EM 1110‐2‐2502
**Base Tilt and Ground Slope Factors are all equal to 1 since there is not a base tilt nor sloped groundover the toe.
Ultimate Bearing Capacity (Eq. 5‐2 EM 1110‐2‐2502):
Q Bprime ξcd ξci cd Nc ξqd ξqi qo Nqξγd ξγi γprime Bprime Nγ
2
113.683kip
ft
Factor of Safety(Eq. 5‐1 EM 1110‐2‐2502)
FSBQ
Nslide20.799
Factor of Safety Check CheckFS "Ok" round FSB 1 2if
"Not Ok" otherwise
"Ok"
12. Check Flotation Criteria.
Factor of Safety(Eq. 3‐2 EM 1110‐2‐2100) FSF
w1 w2 w3 w4 ww
U1.649
FSCheck "Ok" FSF 1.2if
"Not Ok" otherwise
"Ok"
Attachment F-3 32 of 32
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Inlet Headwall Reinforcement Design for Pipe Section
Project Description
Reach 4 pipe drop structure inlet design for the Fargo Moorhead Metro project. The inlet will consist ofa concrete headwall and base slab, a trash rack for debris and three 7'‐2" openings in the headwall forRCPs.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Phi ϕF 32deg
Attachment F-4 1 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Inputs:
Existing Ground Elevation GR 890ft
Top of Wall Elevation TOW 894.5ft
Top of Footing Elevation TOF 886.5ft
Bottom of Footing Elevation BOF 884.5ft
Water Elevation Water 887ft
Stem Thickness THstem 1.5ft
Toe Length Toe 8ft
Heel Length Heel 8ft
Total Length of Footing B Toe Heel THstem 17.5 ft
EMB Slope EMBs1
4
Slope angle θ atan EMBs 14.036 deg
Strength Mobilization Factor SMF2
3
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg
Load Factors and Reduction Factors:
Load Factor Lf 1.7
Hydraulic Factor Hf 1.3
Bending Reduction Factor ϕb 0.90
Shear Reduction Factor ϕv 0.75
Reinforcement Parameters:
#6 Bar Diameter Dia6 0.75in <‐‐Assume #6 bar
#7 Bar Diameter Dia7 0.875in <‐‐Assume #7 bar
#8 Bar Diameter Dia8 1.00in <‐‐Assume #8 bar
Attachment F-4 2 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Section Width b 12in
Concrete Cover cover 4in coverstem 3in
tp 7inPipe Thickness
Stem Design
From inspection, it can be determined that the worst design case for the stem will be Load Case 1. Soilis compacted on one side of the stem and water at EL. 887.0 on the other (empty ditch).
The stem will be designed as a cantilever beam, fixed at the point where the base and stem connect.
1. Calculate forces acting on stem.
Pressure Coefficient K1 0.458 <‐‐Taken from Inlet Headwall Design
Pressure Coefficient Kb 0.458 <‐‐Taken from Inlet Headwall Design
Unit weight accounting for seepage (EM 1110‐2‐2502)
γprime 76.6pcf <‐‐Taken from Inlet Headwall Design
θplane 0deg <‐‐Taken from Inlet Headwall Design
Soil Pressure 1 P1 K1 γbf TOW Water( ) Heel tan θ( )[ ] 0.5 ksf
Soil Force 1 F1 .5 P1 TOW Water( ) Heel tan θ( )[ ] 2.377kip
ft
a1 Water TOF( )1
3Heel tan θ( ) TOW Water( )[ ]
Soil Arm 1
a1 3.667 ft
P2 P1 γprime Kb Water TOF( ) 0.518 ksfSoil Pressure 2
F2 P1 Water TOF( ) 0.25kip
ft
Soil Force 2
Soil Arm 2 a2Water TOF
20.25 ft
F31
2P2 P1 Water TOF( ) 4.385 10
3
kip
ft
Soil Force 3
Soil Arm 3 a3Water TOF
30.167 ft
Attachment F-4 3 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Resultant Force Pa F1 F2 F3 2.631kip
ft
Pah Pa cos θplane 2.631kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F33.336 ft
Surcharge Load surcharge 200psf
Ps K1 surcharge TOW TOF( ) Heel tan θ( )[ ] 0.916kip
ft
Surcharge Horizontal Force
As1
2TOW TOF( ) Heel tan θ( )[ ] 5 ft
Surcharge Force Arm
Resisting Water Load Pr .5 γw Water TOF( )2
0.008kip
ft
Water Load Arm Ar1
3Water TOF( ) 0.167 ft
MD Lf Hf Pah Ah 1 ft Ps As 1 ft
Pr Ar 1 ft
29.518 kip ftDesign Moment
2. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b THstem 0.302 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
3. Determine area of flexural steel required.
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Attachment F-4 4 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Distance to reinforcement d THstem coverstem1
2Dia8 14.5 in
Steel ratio Ru
MD
b d2
140.396 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0027
Required Area of Reinforcement Ast ρ b d 0.463 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.58 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.616 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.58 in2
4. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Attachment F-4 5 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
5. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.58 in2
Area of Reinforcement Provided Asf 0.60in2
<‐‐Input the area of steel that will be provided
Specify #7 @ 12" for Flexural Reinforcement
6. Verify Steel Yields.
Tension Force T Asf fy 36 kip
Depth of compression zone aAsf fy
0.85 fc b0.882 in
ca
β11.038 in
Distance to neutral axis
εcd c
c
0.003 0.039Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
Attachment F-4 6 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
7. Calculate Moment Capacity Provided by Steel Reinforcment .
ϕb 0.9 εc .005if
0.65 εc .002if
0.65 εc .002 250
3
.002 εc .005if
0.9Verify Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
37.959 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MDif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
8. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
16.507 kip
Ultimate Shear Strength Vu Lf Pah 1 ft Ps 1 ft Pr 1 ft 6.017 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Heel and Toe Design
Each Load Case will be evaluated to determine the maximum moments in both the heel and toe.Forces will include bearing pressures underneath the footing, uplift pressures underneath the footingand water and soil loads above the footing.Both the Heel and the Toe are designed as cantileverbeams subjected to soil and water loads.
Load Case 1 Summary
Eccentricity e 1.897 ft <‐‐Taken from Inlet Headwall Design
Attachment F-4 7 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Vertical Loads Vv 12.87kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 17.5 ft2
Moment of Inertia I1ft B
3
12446.615 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.257 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 1.214 ksf
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 1
Soil above footing Ws 7.38kip
asHeel
24 ft
Wst 0.92kip
Attachment F-4 8 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
ast2
3Heel 5.333 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 2.4 kip
ahHeel
2
Weight of Surcharge Wsusurcharge
γsHeel 1 ft γs 1.6 kip
asuHeel
24 ft
Uplift Pressure Uplift 0.156ksf
fu Uplift Heel 1 ft 1.248 kip
auHeel
2
Pressure underneath Heel(Uniform Section)
p1 Toe THstem q2 q1
B q1 0.776 ksf
f1 p1 Heel 1 ft 6.211 kip
a1Heel
2
Pressure underneath Heel(Triangular Section)
p2 q2 p1 0.437 ksf
f2 0.5 Heel p2 1 ft 1.749 kip
a22
3Heel 5.333 ft
Attachment F-4 9 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu 4.799 kipTotal Weight
Moment in Heel Muh1 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu au
24.883 kip ft
Vuh1 Wtotal 4.799 kipShear in Heel
Toe Loads for Load Case 1
Pressure underneath toe(Uniform Section)
p1 q1 0.257 ksf
f1 p1 Toe 1 ft 2.057 kip
Attachment F-4 10 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
a1Toe
24 ft
Pressure underneath toe(Triangular Section)
p2 Toeq2
B
0.555 ksf
f21
2p2 Toe 1 ft 2.219 kip
a21
3Toe 2.667 ft
The figure below shows the bearing pressure distribution underneath the toe.
Wtoe TOF BOF( ) Toe 1 ft γc 2.4 kipWeight of Toe
atToe
24 ft
Weight of water over toe Ww Toe Water TOF( ) 1ft γw 0.25 kip
Attachment F-4 11 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
awToe
24 ft
Uplift Pressure underneath toe Uplift 0.156ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 1.248 kip
auToe
24 ft
Moment in Toe Mut1 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
18.872 kip ft
Vut1 2.21 f1 f1 fu Wtoe Ww 5.994 kipShear in Toe
Load Case 2 Summary
Eccentricity e 1.646 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 11.211kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 17.5 ft2
Moment of Inertia I1ft B
3
12446.615 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.279 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 1.002 ksf
Attachment F-4 12 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 2
Soil above footing Ws 7.5kip
asHeel
24 ft
Wst 0.92kip <‐‐Triangular region
ast2
3Heel 5.333 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 2.4 kip
ahHeel
24 ft
Attachment F-4 13 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Weight of Surcharge Wsusurcharge
γsHeel 1 ft γs 1.6 kip
asuHeel
24 ft
Uplift Pressure Uplift 0.343ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Heel 1 ft 2.744 kip
auHeel
24 ft
p1 Toe THstem q2 q1
B q1 0.672 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 5.373 kip
a1Heel
24 ft
p2 q2 p1 0.331 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 1.322 kip
a22
3Heel( ) 5.333 ft
Attachment F-4 14 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu 4.555 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh2 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu au
25.166 kip ft
Vuh2 Wtotal 4.555 kipShear in Heel
Toe Loads for Load Case 1
Pressure underneath toe(Uniform Section)
p1 q1 0.279 ksf
f1 Toe p1 1 ft 2.233 kip
Attachment F-4 15 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
a1Toe
24 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.458 ksf
f21
2p2 Toe 1 ft 1.833 kip
a21
3Toe 2.667 ft
The figure below shows the bearing pressure distribution underneath the toe.
Wtoe TOF BOF( ) Toe 1 ft γc 2.4 kipWeight of Toe
atToe
24 ft
Attachment F-4 16 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Weight of water over toe Ww Toe GR TOF( ) 1ft γw 1.747 kip
awToe
24 ft
Uplift Pressure underneath toe Uplift 0.343ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 2.744 kip
auToe
24 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut2 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
18.133 kip ft
Vut2 2.21 f1 f2 fu Wtoe Ww 5.883 kipShear in Toe
Load Case 3 Summary
Eccentricity e 1.561 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 9.113kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 17.5 ft2
Moment of Inertia I1ft B
3
12446.615 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.242 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.799 ksf
Attachment F-4 17 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 3
Soil above footing Ws 7.68kip
asHeel
24 ft
Wst 0.92kip
ast2
3Heel 5.333 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 2.4 kip
Attachment F-4 18 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
ahHeel
24 ft
Weight of Surcharge Wsu 0kip <‐‐With water to the top of wall, nosurcharge will be considered in this load case
asuHeel
24 ft
Uplift Pressure underneath heel Uplift1 0.5817ksf <‐‐Taken from Inlet Headwall Design
Uplift Pressure underneath toe Uplift2 0.5077ksf <‐‐Taken from Inlet Headwall Design
pu1 HeelUplift1 Uplift2
B Uplift2 0.542 ksf
fu1 pu1 Heel 1 ft 4.332 kip
au1Heel
24 ft
pu2 Uplift1 pu1 0.04 ksf
fu21
2Heel pu2 1 ft 0.161 kip
au22
3Toe 5.333 ft
p1 Toe THstem q2 q1
B q1 0.545 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 4.357 kip
a1Heel
24 ft
p2 q2 p1 0.255 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 1.019 kip
a22
3Heel( ) 5.333 ft
Attachment F-4 19 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the heel.
Total Weight Wtotal Lf Hf Ws Wh Wsu f1 f2 fu1 fu2 0.466 kip
Moment in Heel(Counterclockwisemoment is positive)
Muh3 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu1 au1 fu2 au2
9.23 kip ft
Vuh3 Wtotal 0.466 kipShear in Heel
Toe Loads for Load Case 3
Pressure underneath toe(Uniform Section)
p1 q1 0.242 ksf
Attachment F-4 20 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
f1 Toe p1 1 ft 1.936 kip
a1Toe
24 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.365 ksf
f21
2p2 Toe 1 ft 1.462 kip
a21
3Toe 2.667 ft
The figure below shows the bearing pressure distribution underneath the toe.
Wtoe TOF BOF( ) Toe 1 ft γc 2.4 kipWeight of Toe
atToe
24 ft
Attachment F-4 21 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Weight of water over toe Ww Toe Water TOF( ) 1ft γw 0.25 kip
awToe
24 ft
Uplift Pressure underneath heel Uplift1 0.579ksf <‐‐Taken from Inlet Headwall Design
Uplift Pressure underneath toe Uplift2 0.508ksf <‐‐Taken from Inlet Headwall Design
fu1 Uplift2 Toe 1 ft 4.064 kip
auToe
24 ft
fu21
2Toe Toe
Uplift1
B
1 ft 1.059 kip
au21
3Toe 2.667 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut3 2.21 Wtoe at Ww aw
fu1 au1 fu2 au2
18.743 kip ft
Vut3 2.21 f1 f2 fu1 fu2 Wtoe Ww 12.976 kipShear in Toe
Design Load Summary for Heel
Maximum Moment from all load cases MDH min Muh1 Muh2 Muh3 25.166 ft kip
Since I've chosen counterclockwise moments to be positive, a negative moment here represents thetop of the heel being in tension.
Design Moment MH MDH 25.166 ft kip
Maximum Shear from all load cases VH max Vuh1 Vuh2 Vuh3 4.799 kip
Design Load Summary for Toe
Maximum Moment from all load cases MTH min Mut1 Mut2 Mut3 18.872 ft kip
Since I've chosen counterclockwise moments to be positive, a negative moment here represents thebottom of the toe the being in tension.
MT MTH 18.872 ft kipDesign Moment
Attachment F-4 22 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Maximum Shear from all load cases VT max Vut1 Vut2 Vut3 12.976 kip
Reinforcement Design of the Heel
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b TOF BOF( ) 0.403 in2
Area of Reinforcement Provided Ast .44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.85
Distance to reinforcement d TOF BOF( ) tp cover1
2Dia6 12.625 in
Steel ratio Ru
MH
b d2
157.888 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.003
Required Area of Reinforcement Ast ρ b d 0.455 in2
Attachment F-4 23 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.505 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.605 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.505 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.505 in2
Area of Reinforcement Provided Asf 0.53in2
<‐‐Input the area of steel that will be provided
Attachment F-4 24 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Specify #6 @ 10" for Flexural Reinforcement.
5. Verify Steel Yields.
Tension Force T Asf fy 31.8 kip
Depth of compression zone aAsf fy
0.85 fc b0.779 in
ca
β10.917 in
Distance to neutral axis
εcd c
c
0.003 0.038Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 εc .005if
0.65 εc .002if
0.65 εc .002 250
3
.002 εc .005if
0.9Verify Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
29.181 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MHif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
Attachment F-4 25 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
14.373 kip
Ultimate Shear Strength Vu VH 4.799 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Reinforcement Design of the Toe
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b TOF BOF( ) 0.403 in2
Area of Reinforcement Provided Ast 0.44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.85
Distance to reinforcement d TOF BOF( ) cover1
2Dia6 19.625 in
Steel ratio Ru
MT
b d2
49.001 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0009
Attachment F-4 26 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Required Area of Reinforcement Ast ρ b d 0.215 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.785 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.287 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.403 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
Attachment F-4 27 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.403 in2
Area of Reinforcement Provided Asf 0.44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Flexural Reinforcement
5. Verify Steel Yields.
Tension Force T Asf fy 26.4 kip
Depth of compression zone aAsf fy
0.85 fc b0.647 in
ca
β10.761 in
Distance to neutral axis
εcd c
c
0.003 0.074Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 εc .005if
0.65 εc .002if
0.65 εc .002 250
3
.002 εc .005if
0.9Verify Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
38.217 kip ft
Attachment F-4 28 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Pipe Section
05/21/2013Comp by: MVR
97% FTR Submittal
Capacity Check Check "Adequate Moment Capacity" ϕMn MTif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
22.341 kip
Ultimate Shear Strength Vu VT 12.976 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Attachment F-4 29 of 29
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Inlet Headwall Reinforcement Design for Typical Section
Project Description
Reach 4 pipe drop structure inlet design for the Fargo Moorhead Metro project. The inlet will consist ofa concrete headwall and base slab, a trash rack for debris and three 7'‐2" openings in the headwall forRCPs.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Phi ϕF 32deg
Attachment F-5 1 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Inputs:
Existing Ground Elevation GR 890ft
Top of Wall Elevation TOW 894.5ft
Top of Footing Elevation TOF 886.5ft
Bottom of Footing Elevation BOF 884.5ft
Water Elevation Water 887ft
Stem Thickness THstem 1.5ft
Toe Length Toe 6ft
Heel Length Heel 8ft
Total Length of Footing B Toe Heel THstem 15.5 ft
EMB Slope EMBs1
4
Slope angle θ atan EMBs 14.036 deg
Strength Mobilization Factor SMF2
3
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg
Load Factors and Reduction Factors:
Load Factor Lf 1.7
Hydraulic Factor Hf 1.3
Bending Reduction Factor ϕb 0.90
Shear Reduction Factor ϕv 0.75
Reinforcement Parameters:
#6 Bar Diameter Dia6 0.75in <‐‐Assume #6 bar
#7 Bar Diameter Dia7 0.875in <‐‐Assume #7 bar
#8 Bar Diameter Dia8 1.00in <‐‐Assume #8 bar
Attachment F-5 2 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Section Width b 12in
Concrete Cover cover 4in coverstem 3in
Stem Design
From inspection, it can be determined that the worst design case for the stem will be Load Case 1. Soilis compacted on one side of the stem and water at EL. 887.0 on the other (empty ditch).
The stem will be designed as a cantilever beam, fixed at the point where the base and stem connect.
1. Calculate forces acting on stem.
Pressure Coefficient K1 0.458 <‐‐Taken from Inlet Headwall Design
Kb 0.458 <‐‐Taken from Inlet Headwall Design
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime 76.6pcf <‐‐Taken from Inlet Headwall Design
θplane 0deg <‐‐Taken from Inlet Headwall Design
Soil Pressure 1 P1 K1 γbf TOW Water( ) Heel tan θ( )[ ] 0.5 ksf
Soil Force 1 F1 .5 P1 TOW Water( ) Heel tan θ( )[ ] 2.377kip
ft
a1 Water TOF( )1
3Heel tan θ( ) TOW Water( )[ ]
Soil Arm 1
a1 3.667 ft
P2 P1 γprime Kb Water TOF( ) 0.518 ksfSoil Pressure 2
F2 P1 Water TOF( ) 0.25kip
ft
Soil Force 2
Soil Arm 2 a2Water TOF
20.25 ft
F31
2P2 P1 Water TOF( ) 0.004
kip
ft
Soil Force 3
Soil Arm 3 a3Water TOF
30.167 ft
Resultant Force Pa F1 F2 F3 2.631kip
ft
Attachment F-5 3 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Horizontal Force Pah Pa cos θplane 2.631kip
ft
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F33.336 ft
Resisting Water Load Pr .5 γw Water TOF( )2
0.008kip
ft
Water Load Arm Ar1
3Water TOF( ) 0.167 ft
Surcharge Load surcharge 200psf
Ps K1 surcharge TOW TOF( ) Heel tan θ( )[ ] 0.916kip
ft
Surcharge Horizontal Force
As1
2TOW TOF( ) Heel tan θ( )[ ] 5 ft
Surcharge Force Arm
MD Lf Hf Pah Ah 1 ft Ps As 1 ft Pr Ar 1 ft
29.518 kip ftDesign Moment
2. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b THstem 0.302 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
3. Determine area of flexural steel required.
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Distance to reinforcement d THstem coverstem1
2Dia8 14.5 in
Attachment F-5 4 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Steel ratio Ru
MD
b d2
140.396 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0027
Required Area of Reinforcement Ast ρ b d 0.463 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.58 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.616 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.58 in2
4. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Attachment F-5 5 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
5. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.58 in2
Area of Reinforcement Provided Asf 0.60in2
<‐‐Input the area of steel that will be provided
Specify #7 @ 12" for Flexural Reinforcement
6. Verify Steel Yields.
Tension Force T Asf fy 36 kip
Depth of compression zone aAsf fy
0.85 fc b0.882 in
ca
β11.038 in
Distance to neutral axis
εcd c
c
0.003 0.039Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
7. Calculate Moment Capacity Provided by Steel Reinforcment .
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
37.959 kip ft
Attachment F-5 6 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Capacity Check Check "Adequate Moment Capacity" ϕMn MDif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
8. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
16.507 kip
Ultimate Shear Strength Vu Lf Pah 1 ft Ps 1 ft Pr 1 ft 6.017 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Heel and Toe Design
Each Load Case will be evaluated to determine the maximum moments in both the heel and toe.Forces will include bearing pressures underneath the footing, uplift pressures underneath the footingand water and soil loads above the footing.Both the Heel and the Toe are designed as cantileverbeams subjected to soil and water loads.
Load Case 1 Summary
Eccentricity e 1.167 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 12.519kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 15.5 ft2
Moment of Inertia I1ft B
3
12310.323 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.443 ksf
Attachment F-5 7 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 1.173 ksf
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 1
Soil above footing Ws 7.38kip <‐‐Taken from Inlet Headwall Design
asHeel
24 ft
Wst 0.92kip
ast2
3Heel 5.333 ft
Attachment F-5 8 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 2.4 kip
ahHeel
24 ft
Weight of Surcharge Wsusurcharge
γsHeel 1 ft γs 1.6 kip
asuHeel
24 ft
Uplift Pressure Uplift 0.156ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Heel 1 ft 1.248 kip
auHeel
24 ft
p1 Toe THstem q2 q1
B q1 0.796 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 6.367 kip
a1Heel
24 ft
p2 q2 p1 0.377 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 1.507 kip
a22
3Heel( ) 5.333 ft
Attachment F-5 9 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu
Wst
7.024 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh1 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu au
26.367 kip ft
Vuh1 Wtotal 7.024 kipShear in Heel
Toe Loads for Load Case 1
Pressure underneath toe(Uniform Section)
p1 q1 0.443 ksf
f1 Toe p1 1 ft 2.657 kip
Attachment F-5 10 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
a1Toe
23 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.454 ksf
f21
2p2 Toe 1 ft 1.362 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the toe.
Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kipWeight of Toe
atToe
23 ft
Weight of water over toe Ww Toe Water TOF( ) 1ft γw 0.187 kip
Attachment F-5 11 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
awToe
23 ft
Uplift Pressure underneath toe Uplift 0.156ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 0.936 kip
auToe
23 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut1 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
16.664 kip ft
Vut1 2.21 f1 f2 fu Wtoe Ww 6.558 kipShear in Toe
Load Case 2 Summary
Eccentricity e 0.949 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 10.861kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 15.5 ft2
Moment of Inertia I1ft B
3
12310.323 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.443 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.958 ksf
Attachment F-5 12 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 2
Soil above footing Ws 7.5kip
asHeel
24 ft
Wst 0.92kip <‐‐Triangular region
ast2
3Heel 5.333 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 2.4 kip
ahHeel
24 ft
Attachment F-5 13 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Weight of Surcharge Wsusurcharge
γsHeel 1 ft γs 1.6 kip
asuHeel
24 ft
Uplift Pressure Uplift 0.343ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Heel 1 ft 2.744 kip
auHeel
24 ft
p1 Toe THstem q2 q1
B q1 0.692 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 5.539 kip
a1Heel
24 ft
p2 q2 p1 0.266 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 1.063 kip
a22
3Heel( ) 5.333 ft
Attachment F-5 14 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu
Wst
6.793 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh2 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu au
26.752 kip ft
Vuh2 Wtotal 6.793 kipShear in Heel
Toe Loads for Load Case 2
Pressure underneath toe(Uniform Section)
p1 q1 0.443 ksf
Attachment F-5 15 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
f1 Toe p1 1 ft 2.66 kip
a1Toe
23 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.371 ksf
f21
2p2 Toe 1 ft 1.113 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the toe.
Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kipWeight of Toe
atToe
23 ft
Attachment F-5 16 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Weight of water over toe Ww Toe GR TOF( ) 1ft γw 1.31 kip
awToe
23 ft
Uplift Pressure underneath toe Uplift 0.343ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 2.058 kip
auToe
23 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut2 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
15.575 kip ft
Vut2 2.21 f1 f2 fu Wtoe Ww 6.011 kipShear in Toe
Load Case 3 Summary
Eccentricity e 0.257 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 8.873kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 15.5 ft2
Moment of Inertia I1ft B
3
12310.323 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.516 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.629 ksf
Attachment F-5 17 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 3
Soil above footing Ws 7.68kip
asHeel
24 ft
Wst 0.92kip
ast2
3Heel 5.333 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 2.4 kip
ahHeel
24 ft
Attachment F-5 18 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Weight of Surcharge Wsu 0kip <‐‐With water to the top of wall, nosurcharge will be considered in this load case
asuHeel
24 ft
Uplift Pressure underneath heel Uplift1 0.5786ksf <‐‐Taken from Inlet Headwall Design
Uplift Pressure underneath toe Uplift2 0.5083ksf <‐‐Taken from Inlet Headwall Design
pu1 HeelUplift1 Uplift2
B Uplift2 0.545 ksf
fu1 pu1 Heel 1 ft 4.357 kip
au1Heel
24 ft
pu2 Uplift1 pu1 0.034 ksf
fu21
2Heel pu2 1 ft 0.136 kip
au22
3Toe 4 ft
p1 Toe THstem q2 q1
B q1 0.571 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 4.565 kip
a1Heel
24 ft
p2 q2 p1 0.059 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 0.235 kip
a22
3Heel( ) 5.333 ft
Attachment F-5 19 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu1 fu2
Wst
3.773 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh3 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu1 au1 fu2 au2
17.11 kip ft
Vuh3 Wtotal 3.773 kipShear in Heel
Toe Loads for Load Case 3
Pressure underneath toe(Uniform Section)
p1 q1 0.516 ksf
Attachment F-5 20 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
f1 Toe p1 1 ft 3.093 kip
a1Toe
23 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.244 ksf
f21
2p2 Toe 1 ft 0.731 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the toe.
Weight of Toe Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kip
atToe
23 ft
Attachment F-5 21 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Weight of water over toe Ww Toe TOW 2ft( ) TOF[ ] 1ft γw 2.246 kip
awToe
23 ft
Uplift Pressure underneath heel Uplift1 0.5786ksf <‐‐Taken from Inlet Headwall Design
Uplift Pressure underneath toe Uplift2 0.5083ksf <‐‐Taken from Inlet Headwall Design
fu1 Uplift2 Toe 1 ft 3.05 kip
auToe
23 ft
fu21
2Toe Toe
Uplift1
B
1 ft 0.672 kip
au21
3Toe 2 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut3 2.21 Wtoe at Ww aw f1 a1 f2 a2
fu1 au1 fu2 au2
26.84 kip ft
Vut3 2.21 f1 f2 fu1 fu2 Wtoe Ww 7.733 kipShear in Toe
Design Load Summary for Heel
Maximum Moment from all load cases MDH min Muh1 Muh2 Muh3 26.752 ft kip
Since I've chosen counterclockwise moments to be positive, a negative moment here represents thetop of the heel being in tension.
Design Moment MH MDH 26.752 ft kip
Maximum Shear from all load cases VH max Vuh1 Vuh2 Vuh3 7.024 kip
Design Load Summary for Toe
Maximum Moment from all load cases MTH min Mut1 Mut2 Mut3 26.84 ft kip
Since I've chosen counterclockwise moments to be positive, a negative moment here represents thebottom of the toe the being in tension.
MT MTH 26.84 ft kipDesign Moment
Attachment F-5 22 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Maximum Shear from all load cases VT max Vut1 Vut2 Vut3 7.733 kip
Reinforcement Design of the Heel
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b TOF BOF( ) 0.403 in2
Area of Reinforcement Provided Ast .44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.85
Distance to reinforcement d TOF BOF( ) cover1
2Dia6 19.625 in
Steel ratio Ru
MH
b d2
69.461 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0013
Required Area of Reinforcement Ast ρ b d 0.306 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.785 in2
Attachment F-5 23 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.408 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.408 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.408 in2
Area of Reinforcement Provided Asf .44in2
<‐‐Input the area of steel that will be provided
Specify #6 @12" for Flexural Reinforcement
5. Verify Steel Yields.
Tension Force T Asf fy 26.4 kip
Depth of compression zone aAsf fy
0.85 fc b0.647 in
Attachment F-5 24 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
ca
β10.761 in
Distance to neutral axis
εcd c
c
0.003 0.074Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
38.217 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MHif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
22.341 kip
Ultimate Shear Strength Vu VH 7.024 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Attachment F-5 25 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Reinforcement Design of the Toe
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b TOF BOF( ) 0.403 in2
Area of Reinforcement Provided Ast .44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.85
Distance to reinforcement d TOF BOF( ) cover1
2Dia6 19.625 in
Steel ratio Ru
MT
b d2
69.688 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0013
Required Area of Reinforcement Ast ρ b d 0.307 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.785 in2
Attachment F-5 26 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.409 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.409 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.409 in2
Area of Reinforcement Provided Asf 0.44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Flexural Reinforcement
5. Verify Steel Yields.
Tension Force T Asf fy 26.4 kip
Depth of compression zone aAsf fy
0.85 fc b0.647 in
Attachment F-5 27 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Typical Section
5/21/2013Comp by: MVR
97% FTR Submittal
ca
β10.761 in
Distance to neutral axis
εcd c
c
0.003 0.074Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
38.217 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MTif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
22.341 kip
Ultimate Shear Strength Vu VT 7.733 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Attachment F-5 28 of 28
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Inlet Headwall Reinforcement Design for Wingwall Section
Project Description
Reach 4 pipe drop structre inlet design for the Fargo Moorhead Metro project. The inlet will consist of aconcrete headwall and base slab, a trash rack for debris and three 7'‐2" openings in the headwall forRCPs.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Phi ϕF 32deg
Attachment F-6 1 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Inputs:
Existing Ground Elevation GR 890ft
Top of Wall Elevation TOW 893ft
Top of Footing Elevation TOF 886.5ft
Bottom of Footing Elevation BOF 884.5ft
Water Elevation Water 887ft
Stem Thickness THstem 1.5ft
Toe Length Toe 6ft
Heel Length Heel 6ft
Total Length of Footing B Toe Heel THstem 13.5 ft
EMB Slope EMBs 0
Slope angle θ atan EMBs 0 deg
Strength Mobilization Factor SMF2
3
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg
Load Factors and Reduction Factors:
Load Factor Lf 1.7
Hydraulic Factor Hf 1.3
Bending Reduction Factor ϕb 0.90
Shear Reduction Factor ϕv 0.75
Reinforcement Parameters:
Bar Diameter Dia5 0.625in <‐‐Assume #5 bar
Bar Diameter Dia6 0.75in <‐‐Assume #6 bar
Bar Diameter Dia7 0.875in <‐‐Assume #7 bar
Attachment F-6 2 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Bar Diameter Dia8 1.00in <‐‐Assume #8 bar
Section Width b 12in
Concrete Cover cover 4in coverstem 3in
Stem Design
The design section of the stem was taken at the one‐third distance along the wingwall. Frominspection, it can be determined that the worst design case for the stem will be Load Case 1. Soil iscompacted on one side of the stem and water at EL. 887.0 on the other (empty ditch).
The stem will be designed as a cantilever beam, fixed at the point where the base and stem connect.
1. Calculate forces acting on stem for Load Case 1.
Pressure Coefficient K1 .458 Ko .485 Kb K1 <‐‐Taken from Inlet Headwall Design
Unit weight accounting for seepage (EM 1110‐2‐2502) γprime 69.6pcf <‐‐Taken from Inlet Headwall Design
Soil Pressure 1 P1 K1 γbf TOW Water( )( ) 0.316 ksf
Soil Force 1 F1 .5 P1 TOW Water( )( ) 0.948kip
ft
a1 Water TOF( )1
3TOW Water( )( )
Soil Arm 1
a1 2.5 ft
P2 P1 γprime Kb Water TOF( ) 0.332 ksfSoil Pressure 2
F2 P1 Water TOF( ) 0.158kip
ft
Soil Force 2
Soil Arm 2 a2Water TOF
20.25 ft
F31
2P2 P1 Water TOF( ) 3.985 10
3
kip
ft
Soil Force 3
Soil Arm 3 a3Water TOF
30.167 ft
Attachment F-6 3 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Resultant Force Pa F1 F2 F3 1.11kip
ft
Pah Pa cos θ( ) 1.11kip
ft
Horizontal Force
Ah
F1 a1 F2 a2 F3 a3
F1 F2 F32.171 ft
Pw1
2γw Water TOF( )
2 0.008
kip
ft
Water Force
Aw1
3Water TOF( ) 0.167 ft
Water Force Arm
Surcharge Load surcharge 200psf
Ps K1 surcharge TOW TOF( )( ) 0.595kip
ft
Surcharge Horizontal Force
As1
2TOW TOF( )( ) 3.25 ft
Surcharge Force Arm
MD1 Lf Hf Pah Ah Ps As
Pw Aw
1 ft 9.6 kip ftDesign Moment
2. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐ACI 318‐11 Section 7.12.2
Required Area of Reinforcement At ρt b THstem 0.302 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
3. Determine area of flexural steel required.
Desgin Moment MD MD1 9.6 kip ft
Attachment F-6 4 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Distance to reinforcement d THstem coverstem1
2Dia5 14.688 in
Steel ratio Ru
MD
b d2
44.503 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0008
Required Area of Reinforcement Ast ρ b d 0.146 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.588 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.195 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.302 in2
Attachment F-6 5 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
4. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
5. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.302 in2
Area of Reinforcement Provided Asf .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Flexural Reinforcement
6. Verify Steel Yields.
Tension Force T Asf fy 18.6 kip
Depth of compression zone aAsf fy
0.85 fc b0.456 in
ca
β10.536 in
Distance to neutral axis
εcd c
c
0.003 0.079Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
Attachment F-6 6 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
7. Calculate Moment Capacity Provided by Steel Reinforcment .
ϕb 0.9 εc .005if
0.65 εc .002if
0.65 εc .002 250
3
.002 εc .005if
0.9Verify Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
20.171 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MDif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
8. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
16.721 kip
Ultimate Shear Strength Vu Lf Pah 1 ft Ps 1 ft 2.899 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Heel and Toe Design
Each Load Case will be evaluated to determine the maximum moments in both the heel and toe.Forces will include bearing pressures underneath the footing, uplift pressures underneath the footingand water and soil loads above the footing.Both the Heel and the Toe are designed as cantileverbeams subjected to soil and water loads.
Load Case 1 Summary
Eccentricity e 1.348 ft <‐‐Taken from Wingwall Design
Attachment F-6 7 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Vertical Loads Vv 8.094kip <‐‐Taken from Wingwall Design
Area for 1‐ft length of footing A B 1 ft 13.5 ft2
Moment of Inertia I1ft B
3
12205.031 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.24 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.959 ksf
Heel Loads for Load Case 1
The figure below shows the bearing pressure distribution underneath the footing.
Attachment F-6 8 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Soil above footing Ws 4.5kip <‐‐Taken from Wingwall Design
asHeel
23 ft
Wst 0kip <‐‐Taken from Wingwall Design
ast2
3Heel 4 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 1.8 kip
ahHeel
2
Weight of Surcharge Wsusurcharge
γsHeel 1 ft γs 1.2 kip
asuHeel
23 ft
Uplift Pressure Uplift 0.156ksf <‐‐Taken from Wingwall Design
fu Uplift Heel 1 ft 0.936 kip
auHeel
23 ft
p1 Toe THstem q2 q1
B q1 0.639 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 3.837 kip
a1Heel
23 ft
p2 q2 p1 0.319 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 0.958 kip
a22
3Heel( ) 4 ft
Attachment F-6 9 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu 3.91 kipTotal Weight
Moment in Heel Muh1 Lf Hf Ws as Wh ah Wsu asu
f1 a1 f2 a2 fu au
9.614 kip ft
Vuh1 Wtotal 3.91 kipShear in Heel
Toe Loads for Load Case 1
Pressure underneath toe(Uniform Section)
p1 q1 0.24 ksf
f1 Toe p1 1 ft 1.442 kip
Attachment F-6 10 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
a1Toe
23 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.426 ksf
f21
2p2 Toe 1 ft 1.278 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the heel.
Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kipWeight of Toe
atToe
23 ft
Weight of water over toe Ww Toe Water TOF( ) 1ft γw 0.187 kip
Attachment F-6 11 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
awToe
23 ft
Uplift Pressure underneath toe Uplift 0.156ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 0.936 kip
auToe
23 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut1 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
8.242 kip ft
Vut1 2.21 f1 f2 fu Wtoe Ww 3.689 kipShear in Toe
Load Case 2 Summary
Eccentricity e 1.127 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 6.78kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 13.5 ft2
Moment of Inertia I1ft B
3
12205.031 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.251 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.754 ksf
Attachment F-6 12 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 2
Soil above footing Ws 4.59kip <‐‐Taken from Wingwall Design
asHeel
23 ft
Wst 0kip <‐‐Triangular region
ast2
3Heel 4 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 1.8 kip
ahHeel
23 ft
Attachment F-6 13 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Weight of Surcharge Wsusurcharge
γsHeel 1 ft γs 1.2 kip
asuHeel
23 ft
Uplift Pressure Uplift 0.343ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Heel 1 ft 2.058 kip
auHeel
23 ft
p1 Toe THstem q2 q1
B q1 0.53 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 3.181 kip
a1Heel
23 ft
p2 q2 p1 0.224 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 0.671 kip
a22
3Heel( ) 4 ft
Attachment F-6 14 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu 3.713 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh2 Lf Hf Ws as Wh ah
Wsu asu f1 a1 f2 a2
fu au
9.657 kip ft
Vuh2 Wtotal 3.713 kipShear in Heel
Toe Loads for Load Case 2
Pressure underneath toe(Uniform Section)
p1 q1 0.251 ksf
f1 Toe p1 1 ft 1.504 kip
Attachment F-6 15 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
a1Toe
23 ft
Pressure under heel(Triangular Section)
p2 Toeq2
B
0.335 ksf
f21
2p2 Toe 1 ft 1.005 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the heel.
Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kipWeight of Toe
atToe
23 ft
Weight of water over toe Ww Toe GR TOF( ) 1ft γw 1.31 kip
awToe
23 ft
Attachment F-6 16 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Uplift Pressure underneath toe Uplift 0.343ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 2.058 kip
auToe
23 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut2 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
7.436 kip ft
Vut2 2.21 f1 f2 fu Wtoe Ww 3.219 kipShear in Toe
Load Case 3 Summary
Eccentricity e 1.105 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 5.787kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 13.5 ft2
Moment of Inertia I1ft B
3
12205.031 ft
4
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.218 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.639 ksf
Attachment F-6 17 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 3
Soil above footing Ws 4.68kip
asHeel
23 ft
Wst 0kip
ast2
3Heel 4 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 1.8 kip
Attachment F-6 18 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
ahHeel
23 ft
Weight of Surcharge Wsu 0kip <‐‐With water to the top ofwall, no surcharge will beconsidered in this load case
asuHeel
23 ft
Uplift Pressure underneath heel Uplift1 0.486ksf <‐‐Taken from Inlet Headwall Design
Uplift Pressure underneath toe Uplift2 0.416ksf <‐‐Taken from Inlet Headwall Design
pu1 HeelUplift1 Uplift2
B Uplift2 0.447 ksf
fu1 pu1 Heel 1 ft 2.683 kip
au1Heel
23 ft
pu2 Uplift1 pu1 0.039 ksf
fu21
2Heel pu2 1 ft 0.117 kip
au22
3Toe 4 ft
p1 Toe THstem q2 q1
B q1 0.452 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 2.712 kip
a1Heel
23 ft
p2 q2 p1 0.187 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 0.561 kip
Attachment F-6 19 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
a22
3Heel( ) 4 ft
The figure below shows the bearing pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu f1 f2 fu1 fu2
Wst
0.899 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh3 Lf Hf Ws as Wst ast Wh ah
Wsu asu f1 a1 f2 a2
fu1 au1 fu2 au2
1.199 kip ft
Vuh3 Wtotal 0.899 kipShear in Heel
Attachment F-6 20 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Toe Loads for Load Case 3
Pressure underneath toe(Uniform Section)
p1 q1 0.218 ksf
f1 Toe p1 1 ft 1.309 kip
a1Toe
23 ft
Pressure under toe(Triangular Section)
p2 Toeq2
B
0.284 ksf
f21
2p2 Toe 1 ft 0.852 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the heel.
Attachment F-6 21 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kipWeight of Toe
atToe
23 ft
Weight of water over toe Ww Toe TOW 2ft( ) TOF[ ] 1ft γw 1.685 kip
awToe
23 ft
Uplift Pressure underneath heel Uplift1 0.486ksf <‐‐Taken from Inlet Headwall Design
Uplift Pressure underneath toe Uplift2 0.416ksf <‐‐Taken from Inlet Headwall Design
fu1 Uplift2 Toe 1 ft 2.496 kip
auToe
23 ft
fu21
2Toe Toe
Uplift1
B
1 ft 0.648 kip
au21
3Toe 2 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut3 2.21 Wtoe at Ww aw f1 a1
fu1 au1 fu2 au2 f2 a2
8.753 kip ft
Vut3 2.21 f1 f2 fu1 fu2 Wtoe Ww 4.023 kipShear in Toe
Load Case 4 Summary
Eccentricity e 1.054 ft <‐‐Taken from Inlet Headwall Design
Vertical Loads Vv 5.466kip <‐‐Taken from Inlet Headwall Design
Area for 1‐ft length of footing A B 1 ft 13.5 ft2
Moment of Inertia I1ft B
3
12205.031 ft
4
Attachment F-6 22 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Pressure under toe q1
Vv
A
Vv e 0.5 B( )
I 0.215 ksf
Pressure under heel q2
Vv
A
Vv e 0.5 B( )
I 0.595 ksf
The figure below shows the bearing pressure distribution underneath the footing.
Heel Loads for Load Case 4
Soil above footing Ws 4.68kip <‐‐Taken from Wingwall Design
asHeel
23 ft
Attachment F-6 23 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Wst 0.562kip <‐‐Weight of water over the heel
astHeel
23 ft
Weight of Heel Wh Heel TOF BOF( ) 1 ft γc 1.8 kip
ahHeel
23 ft
Weight of Surcharge Wsu 0kip <‐‐With water to the top ofwall, no surcharge will beconsidered in this load case
asuHeel
23 ft
Uplift Pressure Uplift 0.624ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Heel 1 ft 3.744 kip
auHeel
23 ft
p1 Toe THstem q2 q1
B q1 0.426 ksf
Pressure underneath Heel(Uniform Section)
f1 p1 Heel 1 ft 2.556 kip
a1Heel
23 ft
p2 q2 p1 0.169 ksfPressure underneath Heel(Triangular Section)
f2 .5 Heel p2 1 ft 0.506 kip
a22
3Heel( ) 4 ft
Attachment F-6 24 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
The figure below shows the bearing pressure distribution underneath the heel.
Wtotal Lf Hf Ws Wh Wsu Ws f1 f2 fu 9.623 kipTotal Weight
Moment in Heel(Counterclockwisemoment is positive)
Muh4 Lf Hf Ws as Wh ah Wst ast
Wsu asu f1 a1 f2 a2
fu au
0.45 kip ft
Vuh4 Wtotal 9.623 kipShear in Heel
Toe Loads for Load Case 4
Pressure underneath toe(Uniform Section)
p1 q1 0.215 ksf
f1 Toe p1 1 ft 1.291 kip
Attachment F-6 25 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
a1Toe
23 ft
Pressure under heel(Triangular Section)
p2 Toeq2
B
0.264 ksf
f21
2p2 Toe 1 ft 0.793 kip
a21
3Toe 2 ft
The figure below shows the bearing pressure distribution underneath the heel.
Wtoe TOF BOF( ) Toe 1 ft γc 1.8 kipWeight of Toe
atToe
23 ft
Weight of water over toe Ww 2.995kip
awToe
23 ft
Attachment F-6 26 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Uplift Pressure underneath toe Uplift 0.624ksf <‐‐Taken from Inlet Headwall Design
fu Uplift Toe 1 ft 3.744 kip
auToe
23 ft
Moment in Toe(Counterclockwisemoment is positive)
Mut4 2.21 Wtoe at Ww aw
f1 a1 f2 a2 fu au
5.097 kip ft
Vut4 2.21 f1 f2 fu Wtoe Ww 2.283 kipShear in Toe
Design Load Summary for Heel
Maximum Moment from all load cases MDH min Muh1 Muh2 Muh3 Muh4 9.657 ft kip
Since I've chosen counterclockwise moments to be positive, a negative moment here represents thetop of the heel being in tension.
Design Moment MH MDH 9.657 ft kip
Maximum Shear from all load cases VH max Vuh1 Vuh2 Vuh3 Vuh4 9.623 kip
Design Load Summary for Toe
Maximum Moment from all load cases MTH min Mut1 Mut2 Mut3 Mut4 8.753 ft kip
Since I've chosen counterclockwise moments to be positive, a negative moment here represents thebottom of the toe the being in tension.
MT MTH 8.753 ft kipDesign Moment
Maximum Shear from all load cases VT max Vut1 Vut2 Vut3 Vut4 4.023 kip
Reinforcement Design of the Heel
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐ACI 318‐11 Section 7.12.2
Required Area of Reinforcement At ρt b TOF BOF( ) 0.403 in2
Attachment F-6 27 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Area of Reinforcement Provided Ast 0.44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.85
Distance to reinforcement d TOF BOF( )( ) cover1
2Dia6 19.625 in
Steel ratio Ru
MH
b d2
25.074 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0005
Required Area of Reinforcement Ast ρ b d 0.11 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.785 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.146 in2
Attachment F-6 28 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.403 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.403 in2
Area of Reinforcement Provided Asf 0.44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Flexural Reinforcement.
5. Verify Steel Yields.
Tension Force T Asf fy 26.4 kip
Depth of compression zone aAsf fy
0.85 fc b0.647 in
ca
β10.761 in
Distance to neutral axis
εcd c
c
0.003 0.074Concrete Strain
Attachment F-6 29 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 εc .005if
0.65 εc .002if
0.65 εc .002 250
3
.002 εc .005if
0.9Verify Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
38.217 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MHif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
22.341 kip
Ultimate Shear Strength Vu VH 9.623 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Attachment F-6 30 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Reinforcement Design of the Toe
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b TOF BOF( ) 0.403 in2
Area of Reinforcement Provided Ast .44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.85
Distance to reinforcement d TOF BOF( ) cover1
2Dia6 19.625 in
Steel ratio Ru
MT
b d2
22.727 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0004
Required Area of Reinforcement Ast ρ b d 0.099 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.785 in2
Attachment F-6 31 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.132 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.403 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.403 in2
Area of Reinforcement Provided Asf 0.44in2
<‐‐Input the area of steel that will be provided
Specify #6 @ 12" for Flexural Reinforcement
5. Verify Steel Yields.
Tension Force T Asf fy 26.4 kip
Depth of compression zone aAsf fy
0.85 fc b0.647 in
Attachment F-6 32 of 33
FMM Reach 4Inlet Headwall Reinforcement
Design - Wingwall Section
05/21/2013Comp by: MVR
97% FTR Submittal
ca
β10.761 in
Distance to neutral axis
εcd c
c
0.003 0.074Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
38.217 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn MTif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
22.341 kip
Ultimate Shear Strength Vu VT 4.023 kip
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Attachment F-6 33 of 33
FMM Reach 4RCP Class Determination
9/06/2012Comp by: MVR
97% FTR Submittal
Class Determination for Reinforced Concrete Pipe
References: 1. EM 1110‐2‐2902 "Conduits, Culverts and Pipes" 2. ASTM C76
Units: kip 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
kips kip
Inputs:
Unit Weight of Fill γf 123pcf
Unit Weight of Water γw 62.4pcf
Inside Diameter Di 6ft
t 7inWall Thickness
Do Di 2t 7.167 ftOutside Diameter
ELEMB 896.0ftTop of EMB EL.
Max Soil Cover Over Pipe Hc 7.333ft
ELPipe ELEMB Hc 888.667 ftTop of Pipe EL.
Existing Ground EL. ELGr 890ft
Equipment Surcharge surcharge 200psf
Assumptions: 1. Design follows EM 1110‐2‐2902 2. All pipe bedding is considered "ordinary". 3. Pipes are spaced far enough apart so that one pipe excavation will not be affected by the adjacent excavation. Loading is considered as a single pipe. 4. Trench width limits specified in Figure 2‐4 of Ref.1 will likely be exceeded in the field; thus, Fill Condition will be a considered an embankment condition (Condition III). 5. Pipe Strength 5,000psi; Wall B from ASTM C76
Attachment F-7 1 of 4
FMM Reach 4RCP Class Determination
9/06/2012Comp by: MVR
97% FTR Submittal
Figure 2‐4. Loading conditions for conduits (Reference 1)
Outputs:
Outside Pipe Dimension bc Do 7.167 ft
Height of Fill above natural ground Hf ELEMB ELGr 6 ft
Height of Fill above pipe Hc 7.333 ft
Height of Fill above pipe CL Hh Hc
Do
2 10.916 ft
Height of Pipe above level foundation Hp bc max 8in 0.04 Hc 6.5 ft
I. Loading Determination
Soil Load on Pipe
We 1.5 γf bc Hh 1 ft 14.434 kip <‐‐Equation 2‐12 Ref. 1
Live Load on Pipe
WL 0kip <‐‐No Live Load assumed
Water Load in Pipe
Ww
π Di2
4γw 1 ft 1.764 kip
Attachment F-7 2 of 4
FMM Reach 4RCP Class Determination
9/06/2012Comp by: MVR
97% FTR Submittal
Equipment Surchage Load in Pipe
Wssurcharge
γfDo 1 ft γf 1.433 kip
II. Bedding Factor Determination
Projection ratio ρHp
bc0.907 <‐‐Defined on Figure 3‐2 Ref.1
Bedding Factor Constant, Xa Xa .654 <‐‐Input value from Table 3‐2
Xp .840 <‐‐Input value from Table 3‐2Bedding Factor Constant, Xp
Bedding Factor Bf1.431
Xp
Xa
3
2.301
III. D‐Load Analysis
Total Load WT We WL Ww Ws 17.632 kip
Hydraulic Load Factor LF 1.3
D‐Load D0.01
LF WT
Di Bf1.66
kip
ft <‐‐Paragraph 3‐7 Ref. 1
III. Determine Pipe Class
Class "Class IV" 1.35kip
ftD0.01 2
kip
ftif
"Class V" 2kip
ftD0.01 3
kip
ftif
"Class IV"
Attachment F-7 3 of 4
FMM Reach 4RCP Class Determination
9/06/2012Comp by: MVR
97% FTR Submittal
IV. Determine height requiring Class V pipe
Limiting D0.01 D0.01 2kip
ft
Solve for the maximum Hh
Hh_max
D0.01 Di Bf
LFWw WL
1.5 γf bc 1 ft14.727 ft <‐‐Max distance from centerline of pipe to top of
embankment.
Solve for maximum EMB Height
EMBmax Hh_max
bc
2 ELPipe 899.81 ft
Solve for maximum height above pipe
Hmax EMBmax ELPipe 11.143 ft <‐‐All sections of pipe that have more fill above it than this value will require a Class V precast concrete pipe.
Attachment F-7 4 of 4
FMM Reach 4Sizing Impact Stilling Basin
05/10/2013Comp by: MVR
97% FTR Submittal
Initial Sizing Design of USBR Type VI Impact Stilling Basin
References:1. "Hydraulic Design of Stilling Basin for Pipe or Channel Outlets" by U.S. Bureau of Reclamation2. "Design of Small Canal Structures" by U.S. Bureau of Reclamation
Inputs:cfs
ft3
s
Total Design Flow QT 520cfs
Number of Pipes Pipetotal 3
Pipe Diameter Dpipe 6ft
Pipe Inlet Invert Elevation Invertinlet 886.5ft
Pipe Outlet Invert Elevation Invertoutlet 874.003ft
Acceleration due to gravity g 32.174ft
s2
Outputs:
Apipe
π Dpipe2
428.274 ft
2
Pipe Area
Design Flow per Pipe Qp
QT
Pipetotal173.333 cfs
Entrance Velocity Ve 2 g Invertinlet Invertoutlet 28.358ft
s
Flow Area Af
Qp
Ve6.112 ft
2
Depth of Flow Depthflow Af 2.472 ft
FrVe
g Depthflow3.18
Froude Number
Attachment F-8 1 of 3
FMM Reach 4Sizing Impact Stilling Basin
05/10/2013Comp by: MVR
97% FTR Submittal
**Use Froude Number calculated above to obtain W/D in Figure 8 below.
W/D ratio RatioWD 5.4 <‐‐Input W/D ratio from Figure 8 of Ref. 1 below
Wmin Depthflow RatioWD 13.351 ftMinimum Inside Width of Basin
Rounded Inside Width of Basin W round ceilWmin
ft
1
ft 14.00 ft
WD 16.00ft <‐‐Input Design width of basinDesign Width of Basin
Attachment F-8 2 of 3
FMM Reach 4Sizing Impact Stilling Basin
05/10/2013Comp by: MVR
97% FTR Submittal
**Use Figure 1 below and WD from above to obtain the remaining dimensions of the Stilling Basin.
β
H3 WD
412 ft c
WD
28 ft r
WD
200.8 ft <‐‐Riprap Dia.
L4 WD
321.333 ft d
WD
62.667 ft
aWD
28 ft e
WD
121.333 ft
b3 WD
86 ft t
WD
121.333 ft
Attachment F-8 3 of 3
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Inlet Headwall Design: Trash Rack Section
Trash rack will be located on the inlet headwall of the Reach 4 draingage structure. There will be a totalof 12 trash rack sections. Each section is made up of 7 beams with six inches of clear space betweeneach beam.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Unit weight of steel γs 490pcf
Steel Yield Strength fy 50ksi
Strength of Concrete fc 4000psi
Young's Modulus E 29000ksi
General Inputs:
Bottom of Trash Rack Elevation BOT 886.5ft
Top of Trash Rack Elevation TOT 893.29ft
Water 894.5ftWater Elevation
ϕb 0.90Moment Reduction Factor
Shear Reduction Factor ϕv 0.90
Connection Bolt Diameter D .75in
Trash Rack Angle θ 45deg
Beam Properties:
wb .625inBeam Width
db 4inBeam Depth
Lb 9.3ftBeam Length
Attachment F-9 1 of 7
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Ab wb db 2.5 in2
Beam Area
Center‐to‐Center Spacing spacing 6in wb 6.625 in
Section Modulus Sx
wb db2
61.667 in
3
Plastic Modulus Zx
wb db2
42.5 in
3
Moment of Inertia Ix
wb db3
123.333 in
4
Beam Loads
The trashrack will be designed to be completely submerged with a 5‐ft head differential resulting fromdebris backup. (EM 1110‐2‐3104 pg. 4‐16)
Assumptions:
1. Trash Rack beam is assumed to be simply supported with a uniform loading.2. Trash Rack beam has a rectangular bar cross section and will be checked for yielding and lateraltorsional buckling flexural limit states.3. Analysis follows the LRFD design method used in AISC Steel Construction Manual 13th edition.4. Load combination 1.2DL + 1.6LL will be used for design.5. Larger than normal deflections will be accepted at the discretion of designer.
Driving Pressure PD γw Water BOT( ) 0.499 ksf
Driving Normal Uniform Force wud PD spacing 0.276kip
ft
Resisting Pressure PR γw Water BOT( ) 5ft[ ] 0.187 ksf
wur PR spacing 0.103kip
ft
Resisting Normal Uniform Force
Beam Self Weight wsf γs Ab sin θ( ) 0.00602kip
ft
Total Beam Load wT 1.2 wsf 1.6 wud wur 0.283kip
ft
Design Moment Mu
wT Lb2
83.058 kip ft
Design Shear Vu
wT Lb
21.315 kip
Attachment F-9 2 of 7
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Design Checks
Flexural Capacity ‐ AISC Steel Manual Chapter F
1. Yielding Check
Fully Plastic Moment(Eq. F11‐1 AISC Steel Manual)
Mp min fy Zx 1.6 fy Sx 10.417 kip ft
2.Lateral Torsional Buckling Check
Nominal Flexural Strength (Eqs. F11‐2 & F11‐3 AISC Steel Manual)
Taking Cb 1
Mn Cb 1.52 0.274Lb db
wb2
fy
E
fy Sx
0.08 E
fy
Lb db
wb2
1.9 E
fyif
min Mp Sx
1.9 E Cb
Lb db
wb2
otherwise
6.697 kip ft
3. Flexural Design Strength
Flexural Design Strength ϕMn ϕb min Mp Mn 6.027 kip ft
Check1 "Adequate Flexural Capacity" ϕMn Muif
"Inadequate Flexural Capacity" ϕMn Muif
"Adequate Flexural Capacity"
Shear Capacity ‐ AISC Steel Manual Chapter G
Taking Cv 1
Nominal Shear Strength(Eq. G2‐1 AISC Steel Manual)
Vn 0.6 fy Ab Cv 75 kip
Shear Design Strength ϕVn ϕv Vn 67.5 kip
Check2 "Adequate Shear Capacity" ϕVn Vuif
"Inadequate Shear Capacity" ϕVn Vuif
"Adequate Shear Capacity"
Attachment F-9 3 of 7
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Serviceability Check ‐ Deflection
Max Deflection for simplysupported beam
Δmax
5 wT Lb4
384 E Ix0.492 in
Deflection Ratio RatioLb
Δmax226.631
This maximum deflection of Lb/227 will be accepted for design.
Bolted Connection Design ‐ AISC Steel Manual Chapter J
Assumptions:
1. Bolts shall be 3/4" in diameter.2. ASTM A325 Bolts in Standard Holes.3. Bolt threads are not exclued from shear planes.4. Each trash rack has 2 bolts on the top and bottom of the trash rack which bolts into the concreteheadwall; it will be conservatively assumed that the entire shear loading from the section isconcentrated on one bolt. There are 7 beams in each section; thus, the design shear will be multipliedby seven and conservatively applied to one bolt.
Design Bolt Shear Vbolt 7 Vu cos θ( ) 6.509 kip
Nominal Shear Stress in Bearing Fnv 48ksi
Reduction Factor ϕbv 0.75
Shear Strength of Bolt(Eq. J3‐1 AISC Steel Manual)
ϕRn ϕbv Fnvπ D
2
4
15.904 kip
Check3 "Adequate Bolt Shear Capacity" ϕRn Vboltif
"Inadequate Bolt Shear Capacity" ϕRn Vboltif
"Adequate Bolt Shear Capacity"
Bearing Strength at Bolt Holes (Angle to Base Connection)
Edge of angle to edge of hole Lc 3in <‐‐Input edge distance
Angle thickness tp .5in
Angle Leg Length Lp 6in
Minimum Tensile Strength of plate Fu 58ksi <‐‐Assumes A50 Steel
Attachment F-9 4 of 7
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Plate Yield Strength Fy 36ksi
Available Bearing Strength(Eq. J3‐6a AISC Steel Manual)
ϕRnb min ϕbv 1.2 Lc tp Fu ϕbv 2.4 D tp Fu
ϕRnb 39.15 kip
Check4 "Adequate Bearing Strength" ϕRnb Vboltif
"Inadequate Bearing Strength" ϕRnb Vboltif
"Adequate Bearing Strength"
Check Beam to End Section Welds
Weld Strength FEXX 70ksi
Reduction Factor ϕw 0.75
Beam and end section width wb 0.625 in
Miniumum Weld Size Weldmin1
8in
wb .25inif
3
16in
.25in wb .5inif
1
4in
.5in wb .75inif
5
16in
wb .75inif
Weldmin1
4in
Weld Size (multiples of 1/16") Weld1
4in
Effective Area Ae2
2Weld 1 in 0.177 in
2
ϕrwL ϕw 0.6 FEXX Ae 5.568 kipShear resistance per inch of weld
Vu 1.315 kipDesign Shear
Attachment F-9 5 of 7
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Lmin1
Vu
2 ϕrwLin 0.118 in
Minium Effective Length
Minimum Effective Length Lmin2 4 Weld 1 in
Minimum Effective Length Lmin max Lmin1 Lmin2 1 in
One inch of 1/4" fillet weld should be welded on each side of the bar.
Check End Section to Plate Welds
It will be assumed that the shear force from the seven beam sections will be concentrated on oneconnection.
Since the plate, end section and beam all have the same thickness, the minumum weld size is thesame as above.
Minimum Weld Size Weldmin 0.25 in
Weld21
4in
Weld Size (multiples of 1/16")
Ae22
2Weld2 1 in 0.177 in
2
Effective Area
ϕrwL ϕw 0.6 FEXX Ae2 5.568 kipShear resistance per inch of weld
VT 7 Vu 9.206 kipDesign Shear
Lmin1
VT
2 ϕrwLin 0.827 in
Minium Effective Length
Lmin2 4 Weld 1 in <‐‐AISC Steel Manual pg. 16.1‐96
Minimum Effective Length
Lmin max Lmin1 Lmin2 1 inMinimum Effective Length
One and a half inch of 1/4" fillet weld should be welded on each side of the bar.
Attachment F-9 6 of 7
FMM Reach 4Inlet Headwall Trash Rack Design
Updated 10/08/2013Comp by: MVR
97% FTR Submittal
Check Shear Strength of Concrete ACI
Shear force resisted by Concrete Vuc 7 Vu sin θ( ) 6.509 kip
Shear Strength of Concrete Vc ϕbv 2fc
psi 12 in 24in 4in .5 0.75 in( )
The above equation assumes a 24in base, 4inches of clearconcrete cover and #6 bars.
Vc Vclb
in2
22.341 kipShear Strength of Concrete
Check5 "Adequate Concrete Capacity" Vc Vucif
"Inadequate Concrete Capacity" Vc Vucif
"Adequate Concrete Capacity"
Section Weight Calculation
Each section of trash rack will consist of 7 beams at 9ft‐4in with a 40.375 inch beam attached to theend. There are a total of 12 sections required.
Trash Rack Single Section Weight TRw Ab 7 Lb 2 40.375 in γs 0.611 kip
Trash Rack Total Weight TRT 12 TRw 7.333 kip
Attachment F-9 7 of 7
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Impact Basin Design: Pipe Box Section
The impact basin structure has a concrete box extending from the front of the basin that the RCP willsit in, along with a flap gate.
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Phi ϕF 32deg
Attachment F-10 1 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Inputs:
Top of Box Elevation GR 883.6ft
Bottom of Box Elevation BOB 872.3ft
Water Elevation Water 883.6ft
Footing Thickness THfoot 1ft
Wall Thickness THwall 1ft
Wall Opening for Pipe Dp 6ft
Total Width of Box wi 10ft
Total Length of Box Li 11.33ft
EMB Slope EMBs1
7
Slope angle θ atan EMBs 8.13 deg
Strength Mobilization Factor SMF2
3
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg
qs 250psfSurcharge Load
Load Factors and Reduction Factors:
Load Factor Lf 1.7
Hydraulic Factor Hf 1.3
Bending Reduction Factor ϕb 0.90
Shear Reduction Factor ϕv 0.75
Reinforcement Parameters:
Bar Diameter Dia .75in <‐‐Assume #6 bar
Section Width bw 12in
Concrete Cover cover 4in
Attachment F-10 2 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Lateral Forces on Walls and Base of Box Section
Assumptions:
1. Design follows USBR Monograph 27. Plate fixed along 3 edges with the top free; uniformly varyingload.2. Soil and Water are assumed to be at the top of the box.3. At‐Rest soil conditions.
At‐Rest Pressure Coefficient Ko 1 sin ϕd 1 sin θ( )( ) 0.717 <‐‐Equation 3‐6 EM 1110‐2‐2502
Lateral Soil Pressure on Walls Psoil Ko γb GR BOB( ) 0.467 ksf
Pwater γw GR BOB( ) 0.705 ksfLateral Water Pressure on Walls
Psurcharge Ko qs 0.179 ksfLateral Surcharge Pressure on Walls
Because there are two different types of loads applied to the wall, the figures and coefficients taken fromUSBR Monagraph 27 will be combined to determine design moments and reactions. See Figures below.
Attachment F-10 3 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Dimension a awi
25 ft
Dimension b b Li
THfoot
2 10.83 ft
a/b ratio Ratioa
b0.462
The charts on pgs. 7 & 10 of USBR Monograph 27 gives values of a/b for .375 and .5; thus, interpolationwill be used to determine coefficient values for the above ratio.
54.77 82.69
x/a y/b Psoil Pwater Msoil Mwater
0.0 1.0 0.012516 0.012516 0.68555 1.03493 3.80226
0.0 0.8 0.01859 0.01859 1.01825 1.53718 5.6475
0.0 0.6 0.024351 0.024351 1.3338 2.01355 7.39765
0.0 0.4 0.025602 0.025602 1.40232 2.117 7.77769
0.0 0.2 0.015544 0.015544 0.85141 1.28531 4.72215
0.0 0.0 0 0 0 0 0
1.0 1.0 ‐0.00812 ‐0.00812 ‐0.4448 ‐0.6714 ‐2.4668
1.0 0.8 ‐0.00968 ‐0.00968 ‐0.5302 ‐0.8004 ‐2.9407
1.0 0.6 ‐0.01186 ‐0.01186 ‐0.6496 ‐0.9807 ‐3.603
1.0 0.4 ‐0.01171 ‐0.01171 ‐0.6414 ‐0.9683 ‐3.5574
1.0 0.2 ‐0.00589 ‐0.00589 ‐0.3226 ‐0.487 ‐1.7893
1.0 0.0 0.00574 0.00574 0.3144 0.47463 1.74377
7.77769
Mx for Wall
.
Maximum Moment
Values of pb2‐‐‐>>
Moment CoefficientsMoments (ft‐kips)
Total
Moment
(ft‐kip)
5.06 7.64
y/b Psoil Pwater Psoil Pwater
1.0 0.028435 0.028435 0.14381 0.21711 0.79763
0.8 0.118428 0.118428 0.59896 0.90422 3.32202
0.6 0.184098 0.184098 0.9311 1.40562 5.16413
0.4 0.232554 0.232554 1.17617 1.77558 6.52337
0.2 0.163254 0.163254 0.82568 1.24647 4.57944
6.52337Maximum Reaction
Rx for Wall
Reaction CoefficientsReactions (kips)
Total
Reaction
(kips)
Values of
pb ‐‐‐>
NOTE: Both Tables above contain a load factor of 2.21 for design. The load case considerswater and soil to the top of the box with no surcharge loading.
Attachment F-10 4 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Walls Reinforcement Design
Design Moment Mu 7.78kip ft <‐‐Input Moment from Table above
Design Shear Vu 6.52kips <‐‐Input Shear from Table above
1. Determine area of temperature and shrinkage steel required.
Minimum reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt bw THwall 0.202 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Distance to reinforcement d THwall cover1
2Dia 7.625 in
Steel ratio Ru
Mu
bw d2
133.813 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0025
Required Area of Reinforcement Ast ρ bw d 0.232 in2
Attachment F-10 5 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fybw d psi
3fc
psi
fybw d psi
200
fy1
psi
bw dif
200
fy1
psi
bw d
otherwise
0.305 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.308 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.305 in2
3. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.305 in2
Area of Reinforcement Provided Asf 0.31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Flexural Reinforcement
4. Check Maximum Steel ratio.
Actual Steel Ratio ρa
Asf
bw d0.0034
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Attachment F-10 6 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Asmax "Less than or equal to recommended limit (OK)" ρa 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρa .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
5. Verify Steel Yields.
Tension Force T Asf fy 18.6 kip
Depth of compression zone aAsf fy
0.85 fc b0.042 in
ca
β10.05 in
Distance to neutral axis
εcd c
c
0.003 0.459Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 εc .005if
0.65 εc .002if
0.65 εc .002 250
3
.002 εc .005if
0.9Verify Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
10.608 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn Muif
"Inadequate Moment Capacity" otherwise
Attachment F-10 7 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi bw d
lb
in2
8.68 kip
Vu 6.52 kipUltimate Shear Strength
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Box Grating Design
The box dimensions are 9' X 10'. Grating will span 8' across the width of the box and 8' along the lengthof the box. An I‐beam will be placed at midspan to make the unsupported length 4ft; beam is consideredsimply supported. Grating is assumed to be W‐11‐4 type with 3/4" X 1/8" bar sizes. Dead load for thistype of grating is approximately 6.4 psf (Grating Pacific manufacturer). The assumed live load over thegrating is a tractor mower. A total of 4 small 23.5" grating sections with 2/3" spacing between eachsection will be used for design.
Check capacity of Grating (23.5" section)
Live Load from Tractor LT 250psf
Grating Dead Load DG 6.4psf
Grating Bar Thickness th .125in
Grating Bar Depth depth .75in
Grating Bar Spacing spacing .6875in
Grating Span span 4ft
Unit Panel Width panel12 12in
Actual Panel Width panel22 23.5in
Number of bars in unit panel width Kpanel12
spacing17.455
Allowable Fiber Stress F 18ksi
Attachment F-10 8 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
E 29000ksiElastic Modulus
Section Modulus SwK th depth
2
60.205 in
3
Moment of InertiaIw
K th depth3
120.077 in
4
Max. Allowable Moment per unit width Mw
F Sw
ft3.682 10
3
lb in
ft
Max. Allowable Uniform Load Unit U8 Mw
span2
153.409 psf
Max. Allowable Uniform Load Actual U22 Upanel22
panel12
300.426 psf
Check "Grating Adequate" U22 LT DGif
"Grating Not Adequate" otherwise
"Grating Adequate"
Grating Support Beam Design
Beam Tributary Width wtrib span 4 ft
Lbeam 8.00ftBeam Length
Design Moment per ft of beam Mu
1.2 DG wtrib 1.6 LT wtrib Lbeam2
813.046 kip ft
Design Shear per ft of beam Vu
1.2DG wtrib 1.6 LT wtrib Lbeam
26.523 kip
Fy 50ksiYield Strength
Bending Reduction Factor ϕb 0.90
ϕv 0.90Shear Reduction Factor
Initial Beam Size Based on Yielding
Zrequired
Mu
Fy3.131 in
3
Attachment F-10 9 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Zspecify 11.4in3
<‐‐Input Z for W‐shape Chosen (W8X13)from AISC Steel Manual Table 3‐2.
Lb Lbeam 8 ft
Selected Beam Properites
Lp 2.98ft <‐‐AISC Steel Manual Table 3‐2
Lr 9.30ft <‐‐AISC Steel Manual Table 3‐2
Sx 9.91in3
<‐‐AISC Steel Manual Table 1‐1
rts 1.03in <‐‐AISC Steel Manual Table 1‐1
Cb 1 <‐‐Conservatively taken as 1
J .0871in4
<‐‐AISC Steel Manual Table 1‐1
c 1 <‐‐Doubly symmetric shape
ho 7.74in <‐‐AISC Steel Manual Table 1‐1
d 8in <‐‐AISC Steel Manual Table 1‐1
tw 0.23in <‐‐AISC Steel Manual Table 1‐1
Check Beam Flexural Strength ‐ AISC Steel Manual Chapter F
Moment based on Yielding(Eq. F2‐1 AISC Steel Manual)
Mp Fy Zspecify 47.5 kip ft
Moment based on Lateral Torsional Buckling (Eqs. F2‐2 & F2‐3 AISC Steel Manual)
MLTB 1000000ft kip Lb Lpif
min Cb Mp Mp 0.7 Fy Sx Lb Lp
Lr Lp
Mp
Lp Lb Lrif
Cb π E
Lb
rts
21 0.078
J c
Sx ho
Lb
rts
2
Sx Lb Lrif
32.729 kip ft
Attachment F-10 10 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Design Strength ϕMn ϕb Mp MLTB 1000000kip ft=if
ϕb min Mp MLTB otherwise
29.456 kip ft
Design Strength Check CheckM "Adequate Moment Capacity" ϕMn Muif
"Inadequate, choose another beam" otherwise
CheckM "Adequate Moment Capacity"
Check Beam Shear Strength ‐ AISC Steel Manual Chapter G
Web Shear Coefficient(Eq. G2‐2 AISC Steel Manual)
Cv 1
Design Strength(Eq. G2‐2 AISC Steel Manual)
ϕVn ϕv 0.6 Fy d tw Cv 49.68 kip
CheckV "Adequate Shear Capacity" ϕVn Vuif
"Inadequate Shear Capacity" otherwise
CheckV "Adequate Shear Capacity"
The grating beam will be connected to the concrete box by 2‐ L3X3X5/16. Angles will be anchored to theconcrete by 2 ‐ 3/4" diameter bolts. Angles will also be bolted to the grating beam. Shear strength of theangle and bolts in standardar holes will be checked in the following sections.
Check Shear Strength of connecting element (Angle) ‐ AISC Steel Manual Chapter J
Angle Thickness ta .3125in
La 6inAngle Length
Fya 36ksiAngle Yield Strength
Fua 50ksiAngle Ultimate Strength
ϕbolt .75inBolt Diameter
ϕbolt_hole ϕbolt1
16in 0.812 in
Bolt Hole Diameter (Standard Hole)
Attachment F-10 11 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
Edge of angle to center of bolt hole distance Ledge 1.5in
Shear Yielding of the Angle(Eq. J4‐3 AISC Steel Manual)
ϕRua_yield 0.60 Fya ta La 40.5 kip
Shear Rupture of the Angle(Eq. J4‐4 AISC Steel Manual)
ϕRua_rupture 0.75 0.6 Fua La ta 2π ϕbolt
2
4
22.307 kip
Shear Strength of the Angle ϕRua min ϕRua_yield ϕRua_rupture 22.307 kip
Check "Adequate Shear Strength" Vu ϕRuaif
"Inadequate Shear Strength" otherwise
Check "Adequate Shear Strength"
Check Block Shear Strength of connecting element (Angle) ‐ AISC Chapter J
Gross area subject to shear Agv La ta 1.875 in2
Net area subject to shear Anv La ta 2π ϕbolt
2
4
0.991 in2
Eq. J4‐5 AISC Steel Manual ϕRblock min 0.75 0.6 Fua Anv 0.75 0.6 Fya Agv
ϕRblock 22.307 kip
Checkblock "Adequate" ϕRblock Vuif
"Inadequate" otherwise
Checkblock "Adequate"
Check Bearing Strength at bolt holes ‐ AISC Steel Manual Chapter J
Edge distance Lc Ledge
ϕbolt_hole
2 1.094 in
Number of Bolts Nbolts 2
Available Bearing Strength(Eq. J3‐6a AISC Steel Manual)
ϕRbearing Nbolts min 1.2 Lc ta Fua 2.4 ϕbolt ta Fua
Attachment F-10 12 of 13
FMM Reach 4Impact Basin Design
Pipe Box Section
04/29/2013Comp by: MVR
97% FTR Submittal
ϕRbearing 41.016 kip
Checkbearing "Adequate" ϕRbearing Vuif
"Inadequate" otherwise
Checkbearing "Adequate"
Check Shear Strength of Bolts ‐ AISC Steel Manual Chapter J
Bolts shall be conform to ASTM A325 with 3/4" diameter. Bolts will be placed in standard holes. It wil beassumed that threads are not excluded from shear planes.
Nominal Shear Stress Fnv 48ksi <‐‐Table J3.2 AISC Steel Manual
Shear Strength of bolts(Eq. J3‐1 AISC Steel Manual)
ϕRbolt Nbolts 0.75 Fnvπ ϕbolt
2
4
31.809 kips
Checkbolt "Adequate" ϕRbolt Vuif
"Inadequate" otherwise
Checkbolt "Adequate"
Attachment F-10 13 of 13
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Outlet Impact Basin Design
Units: kips 1000lbf pcflbf
ft3
lb lbf lbf lb psflbf
ft2
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Inputs:
ρ 1000kg
m3
Pipe Inlet Invert Elevation ELinlet 886.5ft Rho of water
Pipe Outlet Invert Elevation ELoutlet 874.003ft Top of Basin TOW 15ft
Bottom of Basin BOW 0ft Q 173.33ft
3
s
Design Discharge
Footing Thickness TH 1.5ftDp 6ft
Pipe DiameterBaffle Thickness THb 16in
Strength Mobilization Factor SMF2
3
Wall Thickness THw 1.5ft
Baffle Span L 16ftSoil Slope S
1
7
Slope Angle β atan S( ) 8.13 deg
Material Properties:
Unit weight of water γw 62.4pcf
Unit weight of concrete γc 150pcf
Reinforcing Steel fy 60000psi
Strength of Concrete fc 4000psi
Attachment F-11 1 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Unit weight of soil, saturated γs 120pcf
Unit weight of soil, compacted γbf 115pcf
Unit weight of soil, bouyant γb γs γw 57.6 pcf
Undrained shear strength
Cohesion cu 900psf
Phi ϕu 0deg
Drained Shear Strength
Cohesion cd 0psf
Phi ϕ 31deg
Unit weight, select granular fill γF 125pcf
Cohesion cF 0psf
Phi ϕF 32deg
Developed angle of internal friction ϕd atan SMF tan ϕ( )( ) 21.83 deg
Load Factors and Reduction Factors:
Load Factor Lf 1.7
Hydraulic Factor Hf 1.3
Bending Reduction Factor ϕb 0.90
Shear Reduction Factor ϕv 0.75
Reinforcement Parameters:
Bar Diameter Dia .625in <‐‐Assume #5 bar
Section Width b 12in
Concrete Cover cover 3in
Attachment F-11 2 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
The following calculations are for the impact basin in Reach 4 of the Fargo Moorhead Metro project.The impact basin is a concrete structure consisting of two wing walls, two base slabs, a hanging impactbaffle wall, head wall and a box structure that connects to the RCP. A finite element model of the basinwas done is STAAD to determine maximum shear and moments. The overall dimensions weredetermined by the U.S. Bureau of Reclamation, "Hydraulic Design of Stilling Basin for Pipe or ChannelOutlets."
Hanging Baffle Wall Water Load Determination
1. Calculate entrance velocity into the basin
Pipe Area Ap
π Dp2
428.274 ft
2
Initial Velocity viQ
Ap6.13
ft
s
Theorectical Entrance Velocity ve vi2
2g ELinlet ELoutlet 29.013ft
s
Flow Area AfQ
ve5.974 ft
2
Depthflow Af 2.444 ft <‐‐Assumes square area for impact basin design
Depth of Flow
2. Calculate entrance velocity accounting for friction losses using Bernoulli Equation and Manning's Equation
fhzg
Vpz
g
Vp 2
222
1
211
22 <‐‐Bernoulli Equation
Attachment F-11 3 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
2
3/249.1
pp
p
fRA
nQS <‐‐Manning's Equation
(a) Results from Excel:
*Solver was used to determine the flow depth and angle. Other variables were determined after thesetwo values had been determined for a given flow, slope, pipe diameter and friction coefficient.
Angle
Flow_Depth
Flow_Area
Wetted_Perimeter
Hydraulic_Radius
Flow_Velocity
Q 173.33 cfs
k 1.49
n 0.013
S 0.06111 ft/ft
D 6 ft
Theta 2.207373 radians
Theta 126.4732 degrees
y 1.649077 ft
A 6.314569 ft^2
P 6.622119 ft
R 0.953557 ft
V 27.44922 ft/s
Qend 173.3301 ft^3/s
θ Angle deg θ 126.473 deg <‐‐Central Angle
yd Flow_Depth ft yd 1.649 ft <‐‐Flow Depth
Aflow Flow_Area ft2
Aflow 6.315 ft2
<‐‐Flow Area
P Wetted_Perimeter ft P 6.622 ft <‐‐Wetted Perimeter
Rh Hydraulic_Radius ft Rh 0.954 ft <‐‐Hydraulic Radius
Attachment F-11 4 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
ve Flow_Velocityft
s ve 27.449
ft
s <‐‐Flow velocity entering
the stilling basin
5. Calculate impact force on baffle wall
Impact Force F ρ Aflow ve ve 9.232 kip
Effective Length of Impact Force E 13.5ft
W 2ft
Abaffle E W 27 ft2
Impact Pressure per square foot FpF
Abaffle0.342 ksf
This impact force will be applied to the bottom two feet of the baffle over a 13.5ft width. This converts toan pressure of 0.346 psf applied to plate elements.
Impact Basin Side and Head Wall Load Determination
Assumptions 1. Soil and Water is assumed to be at the top of the impact basin.2.Two load cases will be considered for design:
LC1 ‐ Basin walls are loaded all around by soil and water; no load is applied to baffle wall; surcharge load applied to walls; impact basin emptyLC2 ‐ Basin walls are loaded all around by soil and water; impact water force is applied to baffle wall; surcharge load applied to walls; impact basin empty
3. Soil modulus of reaction for input into STAAD is assumed to be 10 kip/ft2/ft.
1. Calculate earth pressure coefficient for at‐rest condition.
At Rest Earth Pressure Coefficient Ko
cos ϕd 2
1sin ϕd sin ϕd β
cos β( )
20.511
2. Calculate soil and water pressure on head wall to be used as STAAD inputs.
The slopes down to meet the headwall approximately 4.5 ft from the top of the headwall; thus, aheight of 10.5 will be used to calculate the soil and water pressures acting on the head wall.
Attachment F-11 5 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Soil Pressure Psoil Ko γb TOW 4.5ft( ) 0.309 ksf
Pwater γw TOW 4.5ft( ) 0.655 ksfWater Pressure
PT Psoil Pwater 0.964 ksfTotal Pressure
3. Calculate soil and water pressure on side wall to be used as STAAD inputs.
Since the side wall slopes down, two different pressures will be applied along the length of the wall.The soil slopes from 10.5 ft to about 9 ft for the first 10'‐10" (moving away from the head wall). Thesoil and water pressures will be calculated for an average height of 9.75 ft and applied to the first10'‐10" of the wall up to a height of 9.75 ft. The soil slopes from approximately 9ft to 7.5 ft. The soiland water pressures will be calculated for an average height of 8.25 ft and applied to this portion of thewall up to a height of 8.25 ft.
Soil Pressure 1 Psoil_1 Ko γb 9.75ft( ) 0.287 ksf
Water Pressure 1 Pwater_1 γw 9.75ft( ) 0.608 ksf
Soil Pressure 2 Psoil_2 Ko γb 8.25ft( ) 0.243 ksf
Water Pressure 2 Pwater_2 γw 8.25ft( ) 0.515 ksf
4. Calculate soil surcharge pressure to be used as STAAD input.
Soil surcharge loads will be applied at the same heights, over the same areas as the above pressures forthe head wall and side walls.
Soil Surcharge qsur 250psf
Psurcharge Ko qsur 0.128 ksfSoil Surcharge Pressure
Finite Element Model of Structure
The calculated soil and water loads were applied to a finite element model of the impact stilling basin.The loads where applied as pressure loads on the walls of the structure. Soil and water pressure loadswere reduced linearly to zero at the top of the soil/water elevation. A load factor of 2.21 was added toall loads and considered in the model.
A snapshot of the STAAD model is shown on the next page. Plate elements were used to model theimpact basin. Each plate is modeled as 4000 psi concrete with a unit weight of 150 pcf. The base of the
structure is supported by a plate mat with a soil modulus equal to 10 kip/ft2/ft.
Attachment F-11 6 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
The results from STAAD are presented at the end document, after the stability analysis. A general threedimensional view of the structure is shown below. The Y‐direction is vertical, the Z‐direction is parallelto water flow and the X‐direction runs along the width of the structure.
Attachment F-11 7 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Baffle Wall Design Shear and Moment
The diagrams below show the results of the STAAD analysis. The maximum moment occurs at eachinterface of the baffle and side wall/end wall. The maximum Shear occurs at the bottom corners of thebaffle at the interface of the baffle and side wall/end wall.
The diagram tothe left showsthe areas ofmax moment.
Max momentis equal to 8.43ft‐kip.
The diagram tothe left showsthe areas ofmax shearstress.
Max ShearStress is equalto 33.81 psi.
Attachment F-11 8 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Based on the results, the baffle wall wil be designed to resist a moment of 8.52 ft‐kip. Since the bafflewall is 16 inches thick, a shear force of 6.8 kips will be used for design.
Vbaffle 6.5kips Mu_baffle 8.43kip ft
Reinforcement Design for Baffle Wall:
1. Determine area of temperature and shrinkage steel required.
Reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b THb 0.269 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Distance to reinforcement d THb cover1
2Dia 12.688 in
Factored Moment Mu Mu_baffle 8.43 kip ft
Steel ratio Ru
Mu
b d2
52.369 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.001
Required Area of Reinforcement Ast ρ b d 0.149 in2
Attachment F-11 9 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.507 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.198 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.269 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.269 in2
Area of Reinforcement Provided Asf 0.31in2
<‐‐Input the area of steel that will be provided
Attachment F-11 10 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Specify #5 @ 12" for Flexural Reinforcement
5. Verify Steel Yields.
Tension Force T Asf fy 18.6 kip
Depth of compression zone aAsf fy
0.85 fc b0.456 in
ca
β10.536 in
Distance to neutral axis
εcd c
c
0.003 0.068Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 Check "Tension Controlled"=if
0.65 Check "Compression Controlled"=if
0.65 εc .002 250
3
otherwise
0.9Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
17.381 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn Muif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
Attachment F-11 11 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
14.444 kip
Ultimate Shear Strength Vu Vbaffle 6.5 kips
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Impact Basin Wall Design Shear and Moment
The diagrams below show the results of the STAAD analysis. The maximum moments in the "X" and "Y"directions were controlled by the end walls. The maximum shear stress also occurred in the end walls.
The diagram above shows the maximum moment in the headwall in the Y‐direction (12.8 ft‐kip).
Attachment F-11 12 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
The diagram above shows the maximum shear stress in the headwall in the Y‐direction (34.7 psi).
The diagram above shows the maximum moment in the side wall in the Y‐direction (18.5 ft‐kip).
Attachment F-11 13 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
The diagram above shows the maximum shear stress in the side wall in the Y‐direction (50.4 psi).
Attachment F-11 14 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
The diagram above shows the maximum moments in the end wall in the X‐direction. The maximummoment occured at the interface between the headwall and the side wall (M=4.7 kip‐ft). The maximummoment at the interface of the baffle wall and side all is 3.6 kip‐ft.
Based on the results, the side walls, head wall and interior walls will be designed to resist a moment of18.5 ft‐kip and a shear force of 11 kips will be used for design.
Vbasin 11kips Mu_basin 18.5kip ft
Impact Basin Wall Reinforcement Design:
1. Determine area of temperature and shrinkage steel required.
Reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b THw 0.302 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Distance to reinforcement d THw cover1
2Dia 14.688 in
Factored Moment Mu Mu_basin 18.5 kip ft
Steel ratio Ru
Mu
b d2
85.758 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0016
Required Area of Reinforcement Ast ρ b d 0.284 in2
Attachment F-11 15 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.588 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.378 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.378 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.378 in2
Area of Reinforcement Provided Asf 0.61in2
<‐‐Input the area of steel that will be provided
Attachment F-11 16 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Specify #5 @ 6" for Flexural Reinforcement
5. Verify Steel Yields.
Tension Force T Asf fy 36.6 kip
Depth of compression zone aAsf fy
0.85 fc b0.897 in
ca
β11.055 in
Distance to neutral axis
εcd c
c
0.003 0.039Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 Check "Tension Controlled"=if
0.65 Check "Compression Controlled"=if
0.65 εc .002 250
3
otherwise
0.9Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
39.086 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn Mu_basinif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
Attachment F-11 17 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
16.721 kip
Ultimate Shear Strength Vu Vbasin 11 kips
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Impact Basin Slab Design Shear and Moment
The diagrams below show the results of the STAAD analysis. The maximum positive moment occurs atthe interior and exterior wall and slab interface. The maximum shear stress also occurrs at this interface.
The diagram above shows the maximum moment in the X‐direction (24 ft‐kip).
Attachment F-11 18 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
The diagram above shows the maximum shear stress (SQX) in the X‐direction (47 psi).
The diagram above shows the maximum shear stress (SQY) in the Y‐direction (37 psi).
Based on the results, the base slab will be designed to resist a moment of 24 ft‐kip in the X‐directionand 13 ft‐kip in the Y‐direction. Also, a shear force of 17.3 kips will be used for design of the base slab.
Vu_base 10.2kips Mu_base 24kip ft
Attachment F-11 19 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Impact Basin Slab Reinforcement Design
1. Determine area of temperature and shrinkage steel required.
Reinforcement ratio ρt .0014 <‐‐EM 1110‐2‐2104
Required Area of Reinforcement At ρt b TH 0.302 in2
Area of Reinforcement Provided Ast .31in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 12" for Temperature and Shrinkage
2. Determine area of flexural steel required.
Fraction β1 β1 0.854ksi
ksi
fc
ksi
.05 0.85
Distance to reinforcement d TH cover1
2Dia 14.688 in
Factored Moment Mu Mu_base 24 kip ft
Steel ratio Ru
Mu
b d2
111.254 psi
ρ0.85 fc
fy1 1
2 Ru
ϕb 0.85( ) fc
0.0021
Required Area of Reinforcement Ast ρ b d 0.37 in2
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.1)
Asmin
3fc
psi
fyb d psi
3fc
psi
fyb d psi
200
fy1
psi
b dif
200
fy1
psi
b d
otherwise
0.588 in2
Attachment F-11 20 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Minimum Flexural Steel Required (ACI 318‐11 Section 10.5.3)
Asmin2 1.33 Ast 0.492 in2
Required Area of Reinforcment Check
Ast max min Asmin Asmin2 Ast At 0.492 in2
3. Check Maximum Steel ratio.
Balanced Steel ratio ρb 0.85 β1fc
fy
87
87fy
1000psi
0.029
Asmax "Less than or equal to recommended limit (OK)" ρ 0.25 ρbif
"Doesn't require special investigation (OK)" 0.25 ρb ρ .375 ρbif
"Consider other options (NOT OK)" otherwise
Asmax "Less than or equal to recommended limit (OK)"
4. Specify Flexural Steel Reinforcement.
Required Area of Flexural Steel Ast 0.492 in2
Area of Reinforcement Provided Asf 0.61in2
<‐‐Input the area of steel that will be provided
Specify #5 @ 6" for Flexural Reinforcement in
X‐direction; Specify #5 @ 10" for Flexural Reinforcement in Y‐direction.
5. Verify Steel Yields.
Tension Force T Asf fy 36.6 kip
Depth of compression zone aAsf fy
0.85 fc b0.897 in
Attachment F-11 21 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
ca
β11.055 in
Distance to neutral axis
εcd c
c
0.003 0.039Concrete Strain
Check "Tension Controlled" εc .005if
"Compression Controlled" εc .002if
"Transition Zone" .002 εc .005if
Steel Yield Check
Check "Tension Controlled"
6. Calculate Moment Capacity Provided by Steel Reinforcment.
ϕb 0.9 Check "Tension Controlled"=if
0.65 Check "Compression Controlled"=if
0.65 εc .002 250
3
otherwise
0.9Reduction Factor
Moment Capacity ϕMn ϕb Asf fy d1
2
Asf fy
0.85 fc b
39.086 kip ft
Capacity Check Check "Adequate Moment Capacity" ϕMn Mu_baseif
"Inadequate Moment Capacity" otherwise
Check "Adequate Moment Capacity"
7. Check Shear Capacity.
Shear Strength of Concrete ϕVc ϕv 2fc
psi b d
lb
in2
16.721 kip
Ultimate Shear Strength Vu Vu_base 10.2 kips
Check "Adequate Shear Capacity" ϕVc Vuif
"Inadequate Shear Capacity" otherwise
Check "Adequate Shear Capacity"
Attachment F-11 22 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Stability Analysis of Impact Basin
The impact basin is 55 feet wide, 49 feet ‐ 10 inches long (including the stilling basin) and 15 feet tall.Due to the extreme length to height ratio (3.3:1), there is not concern of the structure overturning.Bearing is not of concern because of the weight of the structure, it's footprint, and the limited timethe structure could be underwater.
Sliding stability and flotation of the structure will be checked for two load cases:
1. Load Case 1 assumes all pipes are flowing full and impact forces on the baffle walls are included inthe analysis. The impact basin is assumed to be filled up to the end sill with uplift assumed to act onboth concrete slabs (impact basin and stilling basin).2. Load Case 2 assumes all pipes are empty, and not impact forces acting on the baffle walls areincluded in the analysis. Water is assumed to be at the elevation of the impact basin slab with upliftonly acting on the impact basin slab.
The stability check will assume that the entire structure needs to move (including the stilling basin);but, the key at the end of the stilling basin is not a structural element.
Stability check follows EM 1110‐2‐2502.
Load Case 1 ‐ Stability Checks
At Rest Pressure CoefficientKo 0.511 <‐‐Taken from above calculations
Slope Angle β 8.13 deg <‐‐Taken from above
Coeffecient 1(Eq. 3‐26 EM 1110‐2‐2502)
c1 2 tan ϕd 0.801
Attachment F-11 23 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Coefficient 2(Eq. 3‐27 EM 1110‐2‐2502)
c2 1 tan ϕd tan β( )tan β( )
tan ϕd 0.586
Critical Slip‐Plane Angle(Eq. 3‐25 EM 1110‐2‐2502)
α atanc1 c1
24 c2
2
51.665 deg
Pressure Coefficient forfill below the saturationlevel (EM 1110‐2‐2502)
Kb
1 tan ϕd cot α( ) 1 tan ϕd tan α( )
1tan α( )
tan α( ) tan β( )1
γs
γb
0.574
Critical Slip Angle βc 0
Height of the water Hw 4.167ft
Height of soil Hs 10.771ft
Length of stilling basin Basin 25.5ft
Width of structure Widths 55ft
Thickness of Slab THslab 1.5ft
Wimpact 21ft 4in 21.333 ftInside Width of impact basin
Weight of the Impact Basin WS 938.6kips <‐‐Taken from STAAD
Weight of the Stilling Basin WSB Basin THslab Widths γc 315.563 kips
Total Weight of the Structure WT WS WSB 1254.16 kips
Soil Pressure 1 P1 Ko γs Hs Hw 0.405 ksf
Soil Force 1 F1 .5 P1 Hs Hw Widths 73.582 kip
P2 P1 γb Kb Hw 0.543 ksfSoil Pressure 2
F2 P1 Hw Widths 92.858 kipSoil Force 2
F31
2P2 P1 Hw Widths 15.783 kip
Soil Force 3
Attachment F-11 24 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Driving Water Force Fw1
2Hw 2 γw Widths 29.796 kip
F41
2Hw 2 γw Widths 29.796 kip
Resisting Water Force
Force on Baffle Wall Fbaffle F 9.232 kip
Uplift Force Uplift γw Basin Wimpact 3ft Hw Widths 712.674 kips
Weight of water insideimpact basin
Ww γw Hw THslab Widths 7ft Wimpact 170.415 kips
Sum of Vertical Forces ΣV WT Ww Uplift 711.904 kips
Sum of Horizontal Forces ΣH F1 F2 F3 Fw F4 3 F 209.92 kips
Parallel Resultant Tslide ΣH cos βc ΣV sin βc 209.92 kips
Normal Resultant N ΣV cos βc ΣH sin βc 711.9 kips
Factor of Safety, Sliding FSslide
N tan ϕF
Tslide2.119
Factor of Safety Check CheckFS "Ok" FSslide 1.5if
"Not Ok" otherwise
"Ok"
Factor of Safety, Flotation FSFloat
WT Ww
Uplift1.999
CheckFS "Ok" FSFloat 1.3if
"Not Ok" otherwise
"Ok"Factor of Safety Check
Attachment F-11 25 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Load Case 2 ‐ Stability Checks
Height of water Hw 1.5ft
Soil Pressure 1 P1 Ko γs Hs Hw 0.569 ksf
Soil Force 1 F1 .5 P1 Hs Hw Widths 145.015 kip
P2 P1 γb Kb Hw 0.618 ksfSoil Pressure 2
F2 P1 Hw Widths 46.925 kipSoil Force 2
F31
2P2 P1 Hw Widths 2.045 kip
Soil Force 3
Driving Water Force Fw1
2Hw 2 γw Widths 3.861 kip
F41
2Hw 2 γw Widths 3.861 kip
Resisting Water Force
Uplift Force Uplift γw Wimpact 3ft Hw Widths 125.268 kips
Weight of water insideimpact basin
Ww γw Hw THslab Widths 7ft Wimpact 0 kips
Attachment F-11 26 of 27
FMM Reach 4Impact Basin Design
Updated 10/10/2013Comp by: MVR
97% FTR Submittal
Sum of Vertical Forces ΣV WT Ww Uplift 1128.894 kips
Sum of Horizontal Forces ΣH F1 F2 F3 Fw F4 193.99 kips
Parallel Resultant Tslide ΣH cos βc ΣV sin βc 193.99 kips
Normal Resultant N ΣV cos βc ΣH sin βc 1128.89 kips
Factor of Safety, Sliding FSslide
N tan ϕF
Tslide3.636
Factor of Safety Check CheckFS "Ok" FSslide 1.5if
"Not Ok" otherwise
"Ok"
Factor of Safety, Flotation FSFloat
WT Ww
Uplift10.012
CheckFS "Ok" FSFloat 1.3if
"Not Ok" otherwise
"Ok"Factor of Safety Check
Attachment F-11 27 of 27
CWALSHT Calculations
The output files shown are for six individual cases. The first three are the usual, unusual, and extreme events for the drained case, and the last three are the usual, unusual, and extreme events for the undrained case. Note that the applied moments are reported in pound – feet and translated to kip‐inches in the DDR document.
Case 1: Usual Event, Drained Soil. PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:03:15 **************** * INPUT DATA * **************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. USUAL EVENT, DRAINED SOIL II.‐‐CONTROL CANTILEVER WALL ANALYSIS FACTOR OF SAFETY FOR ACTIVE PRESSURES = 1.00 III.‐‐WALL DATA ELEVATION AT TOP OF WALL = 871.16 FT. ELEVATION AT BOTTOM OF WALL = 841.16 FT. WALL MODULUS OF ELLASTACITY = 2.900E+07 PSI. WALL MOMENT OF INERTIA = 152.00 IN^4. IV.‐‐SURFACE POINT DATA IV.A.‐‐RIGHTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 871.16 100.00 871.16 IV.B.‐‐LEFTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 868.16 24.65 864.64 100.00 864.64 V.‐‐SOIL LAYER DATA
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 1 of 22
V.A.‐‐RIGHTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 19.00 50.00 10.26 0.00 DEF DEF V.B.‐‐LEFTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 19.00 50.00 10.26 0.00 DEF DEF VI.‐‐WATER DATA UNIT WEIGHT = 62.40 (PCF) RIGHTSIDE ELEVATION = 871.16 (FT) LEFTSIDE ELEVATION = 864.64 (FT) NO SEEPAGE VII.‐‐VERTICAL SURCHARGE LOADS NONE VIII.‐‐HORIZONTAL LOADS NONE PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:03:21 **************************** * SUMMARY OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. USUAL EVENT, DRAINED SOIL II.‐‐SUMMARY RIGHTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 2 of 22
LEFTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. PASSIVE FACTOR OF SAFETY : 9.60 MAX. BEND. MOMENT (LB‐FT) : 1.1480E+04 AT ELEVATION (FT) : 851.60 MAXIMUM DEFLECTION (IN.) : 1.2252E+00 AT ELEVATION (FT) : 871.16 PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHOREDOR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:03:21 **************************** * COMPLETE OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. USUAL EVENT, DRAINED SOIL II.‐‐RESULTS BENDING NET ELEVATION MOMENT SHEAR DEFLECTION PRESSURE (FT) (LB‐FT) (LB) (IN) (PSF) 871.16 0.0000E+00 0. 1.2252E+00 0.00 870.16 1.0400E+01 31. 1.1564E+00 62.40 869.16 8.3200E+01 125. 1.0875E+00 124.80 868.16+ 2.8080E+02 281. 1.0187E+00 187.20 868.16‐ 2.8080E+02 281. 1.0187E+00 175.21 867.94 3.4533E+02 318. 1.0039E+00 169.25 867.16 6.4528E+02 445. 9.5003E‐01 154.25 866.84 7.9595E+02 488. 9.2794E‐01 113.74 866.16 1.1544E+03 572. 8.8159E‐01 135.02 865.16 1.7902E+03 695. 8.1361E‐01 111.11 864.64 2.1678E+03 750. 7.7839E‐01 98.60 864.16 2.5372E+03 794. 7.4634E‐01 87.15 863.16 3.3712E+03 870. 6.8006E‐01 63.20 862.16 4.2685E+03 921. 6.1510E‐01 39.25 861.16 5.2050E+03 948. 5.5182E‐01 15.29 860.52 5.8124E+03 953. 5.1247E‐01 0.00 860.16 6.1568E+03 951. 4.9058E‐01 ‐8.66 859.16 7.0999E+03 931. 4.3176E‐01 ‐32.61 858.16 8.0105E+03 886. 3.7571E‐01 ‐56.57 857.16 8.8644E+03 818. 3.2281E‐01 ‐80.52 856.16 9.6379E+03 725. 2.7338E‐01 ‐104.48
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 3 of 22
855.16 1.0307E+04 609. 2.2772E‐01 ‐128.43 854.16 1.0847E+04 468. 1.8610E‐01 ‐152.38 853.16 1.1236E+04 304. 1.4872E‐01 ‐176.34 852.16 1.1447E+04 116. 1.1574E‐01 ‐200.29 851.16 1.1459E+04 ‐97. 8.7250E‐02 ‐224.24 850.16 1.1246E+04 ‐333. 6.3239E‐02 ‐248.20 849.16 1.0785E+04 ‐593. 4.3630E‐02 ‐272.15 848.16 1.0052E+04 ‐877. 2.8239E‐02 ‐296.10 847.16 9.0230E+03 ‐1185. 1.6779E‐02 ‐320.06 846.16 7.6738E+03 ‐1517. 8.8461E‐03 ‐344.01 845.16 5.9806E+03 ‐1873. 3.9101E‐03 ‐367.96 845.02 5.7080E+03 ‐1926. 3.4105E‐03 ‐371.40 844.16 3.9710E+03 ‐2072. 1.3072E‐03 30.77 843.16 1.9925E+03 ‐1807. 2.6209E‐04 500.31 842.16 5.1434E+02 ‐1072. 1.4391E‐05 969.85 841.25 0.0000E+00 0. 0.0000E+00 1395.30 III.‐‐WATER AND SOIL PRESSURES <‐‐‐‐‐‐‐‐‐‐‐‐‐SOIL PRESSURES‐‐‐‐‐‐‐‐‐‐‐‐‐‐> WATER <‐‐‐‐LEFTSIDE‐‐‐‐‐> <‐‐‐RIGHTSIDE‐‐‐‐> ELEVATION PRESSURE PASSIVE ACTIVE ACTIVE PASSIVE (FT) (PSF) (PSF) (PSF) (PSF) (PSF) 871.16 0. 0. 0. 0. 12. 870.16 62. 0. 0. 0. 59. 869.16 125. 0. 0. 0. 107. 868.16+ 187. 0. 0. 0. 154. 868.16‐ 187. 12. 0. 0. 154. 867.94+ 201. 31. 0. 0. 202. 867.94‐ 201. 31. 0. 0. 165. 867.16 250. 111. 0. 15. 202. 866.84+ 270. 212. 0. 22. 218. 866.84‐ 270. 143. 0. 22. 218. 866.16 312. 212. 29. 35. 250. 865.16 374. 318. 73. 55. 298. 864.64 407. 373. 92. 65. 323. 864.16 407. 394. 103. 74. 345. 863.16 407. 438. 118. 94. 393. 862.16 407. 481. 133. 114. 441. 861.16 407. 525. 148. 133. 489. 860.52 407. 553. 158. 146. 519. 860.16 407. 569. 164. 153. 537. 859.16 407. 612. 179. 173. 584. 858.16 407. 656. 194. 192. 632. 857.16 407. 699. 209. 212. 680. 856.16 407. 743. 224. 232. 728. 855.16 407. 787. 240. 251. 775. 854.16 407. 830. 255. 271. 823.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 4 of 22
853.16 407. 874. 270. 290. 871. 852.16 407. 917. 285. 310. 919. 851.16 407. 961. 301. 330. 967. 850.16 407. 1005. 316. 349. 1014. 849.16 407. 1048. 331. 369. 1062. 848.16 407. 1092. 346. 389. 1110. 847.16 407. 1135. 362. 408. 1158. 846.16 407. 1179. 377. 428. 1205. 845.16 407. 1223. 392. 448. 1253. 845.02 407. 1229. 394. 450. 1260. 844.16 407. 1266. 407. 467. 1301. 843.16 407. 1310. 422. 487. 1349. 842.16 407. 1353. 438. 507. 1397. 841.25 407. 1397. 453. 526. 1444. 840.16 407. 1441. 468. 546. 1492.
Case 2: Unusual Event, Drained Soil. PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:04:05 **************** * INPUT DATA * **************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. UNUSUAL EVENT, DRAINED SOIL II.‐‐CONTROL CANTILEVER WALL ANALYSIS FACTOR OF SAFETY FOR ACTIVE PRESSURES = 1.00 III.‐‐WALL DATA ELEVATION AT TOP OF WALL = 871.16 FT. ELEVATION AT BOTTOM OF WALL = 841.16 FT. WALL MODULUS OF ELLASTACITY = 2.900E+07 PSI. WALL MOMENT OF INERTIA = 152.00 IN^4. IV.‐‐SURFACE POINT DATA IV.A.‐‐RIGHTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 871.16 100.00 871.16 IV.B.‐‐LEFTSIDE
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 5 of 22
DIST. FROM ELEVATION WALL (FT) (FT) 0.00 868.16 10.65 864.64 100.00 864.64 V.‐‐SOIL LAYER DATA V.A.‐‐RIGHTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 19.00 50.00 10.26 0.00 DEF DEF V.B.‐‐LEFTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 19.00 50.00 10.26 0.00 DEF DEF VI.‐‐WATER DATA UNIT WEIGHT = 62.40 (PCF) RIGHTSIDE ELEVATION = 871.16 (FT) LEFTSIDE ELEVATION = 864.64 (FT) NO SEEPAGE VII.‐‐VERTICAL SURCHARGE LOADS NONE VIII.‐‐HORIZONTAL LOADS NONE PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:04:08 **************************** * SUMMARY OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * ****************************
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 6 of 22
I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. UNUSUAL EVENT, DRAINED SOIL II.‐‐SUMMARY RIGHTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. LEFTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. PASSIVE FACTOR OF SAFETY : 7.40 MAX. BEND. MOMENT (LB‐FT) : 1.1629E+04 AT ELEVATION (FT) : 851.56 MAXIMUM DEFLECTION (IN.) : 1.2471E+00 AT ELEVATION (FT) : 871.16 PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHOREDOR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:04:08 **************************** * COMPLETE OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. UNUSUAL EVENT, DRAINED SOIL II.‐‐RESULTS BENDING NET ELEVATION MOMENT SHEAR DEFLECTION PRESSURE (FT) (LB‐FT) (LB) (IN) (PSF) 871.16 0.0000E+00 0. 1.2471E+00 0.00 870.16 1.0400E+01 31. 1.1771E+00 62.40 869.16 8.3200E+01 125. 1.1072E+00 124.80 868.16+ 2.8080E+02 281. 1.0373E+00 187.20 868.16‐ 2.8080E+02 281. 1.0373E+00 171.28 867.94 3.4528E+02 318. 1.0222E+00 170.75 867.16 6.4582E+02 447. 9.6752E‐01 159.01 866.84 7.9757E+02 493. 9.4508E‐01 127.24 866.16 1.1616E+03 582. 8.9800E‐01 135.06 865.16 1.8072E+03 705. 8.2894E‐01 111.11
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 7 of 22
864.64 2.1898E+03 760. 7.9315E‐01 98.60 864.16 2.5638E+03 804. 7.6059E‐01 87.15 863.16 3.4076E+03 879. 6.9325E‐01 63.20 862.16 4.3146E+03 931. 6.2725E‐01 39.25 861.16 5.2609E+03 958. 5.6294E‐01 15.29 860.52 5.8745E+03 963. 5.2294E‐01 0.00 860.16 6.2224E+03 961. 5.0069E‐01 ‐8.66 859.16 7.1753E+03 941. 4.4088E‐01 ‐32.61 858.16 8.0956E+03 896. 3.8389E‐01 ‐56.57 857.16 8.9593E+03 827. 3.3006E‐01 ‐80.52 856.16 9.7425E+03 735. 2.7975E‐01 ‐104.48 855.16 1.0421E+04 618. 2.3325E‐01 ‐128.43 854.16 1.0971E+04 478. 1.9083E‐01 ‐152.38 853.16 1.1369E+04 314. 1.5271E‐01 ‐176.34 852.16 1.1591E+04 125. 1.1904E‐01 ‐200.29 851.16 1.1612E+04 ‐87. 8.9905E‐02 ‐224.24 850.16 1.1409E+04 ‐323. 6.5316E‐02 ‐248.20 849.16 1.0958E+04 ‐583. 4.5192E‐02 ‐272.15 848.16 1.0235E+04 ‐867. 2.9354E‐02 ‐296.10 847.16 9.2152E+03 ‐1175. 1.7519E‐02 ‐320.06 846.16 7.8758E+03 ‐1507. 9.2865E‐03 ‐344.01 845.16 6.1923E+03 ‐1863. 4.1299E‐03 ‐367.96 844.82 5.5281E+03 ‐1992. 2.9501E‐03 ‐376.22 844.16 4.1666E+03 ‐2126. 1.3888E‐03 ‐32.28 843.16 2.1123E+03 ‐1895. 2.8010E‐04 492.51 842.16 5.5057E+02 ‐1141. 1.5519E‐05 1017.30 841.25 0.0000E+00 0. 0.0000E+00 1493.99 III.‐‐WATER AND SOIL PRESSURES <‐‐‐‐‐‐‐‐‐‐‐‐‐SOIL PRESSURES‐‐‐‐‐‐‐‐‐‐‐‐‐‐> WATER <‐‐‐‐LEFTSIDE‐‐‐‐‐> <‐‐‐RIGHTSIDE‐‐‐‐> ELEVATION PRESSURE PASSIVE ACTIVE ACTIVE PASSIVE (FT) (PSF) (PSF) (PSF) (PSF) (PSF) 871.16 0. 0. 0. 0. 15. 870.16 62. 0. 0. 0. 64. 869.16 125. 0. 0. 0. 113. 868.16+ 187. 0. 0. 0. 162. 868.16‐ 187. 16. 0. 0. 162. 867.94+ 201. 30. 0. 0. 211. 867.94‐ 201. 30. 0. 0. 172. 867.16 250. 106. 0. 15. 211. 866.84+ 270. 188. 0. 22. 227. 866.84‐ 270. 140. 0. 22. 227. 866.16 312. 212. 26. 35. 260. 865.16 374. 318. 65. 55. 309. 864.64 407. 373. 81. 65. 335. 864.16 407. 394. 90. 74. 358.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 8 of 22
863.16 407. 438. 101. 94. 407. 862.16 407. 481. 111. 114. 457. 861.16 407. 525. 122. 133. 506. 860.52 407. 553. 128. 146. 537. 860.16 407. 569. 132. 153. 555. 859.16 407. 612. 143. 173. 604. 858.16 407. 656. 153. 192. 653. 857.16 407. 699. 164. 212. 702. 856.16 407. 743. 174. 232. 751. 855.16 407. 787. 185. 251. 800. 854.16 407. 830. 195. 271. 849. 853.16 407. 874. 206. 290. 898. 852.16 407. 917. 216. 310. 948. 851.16 407. 961. 227. 330. 997. 850.16 407. 1005. 235. 349. 1046. 849.16 407. 1048. 244. 369. 1095. 848.16 407. 1092. 260. 389. 1144. 847.16 407. 1135. 280. 408. 1193. 846.16 407. 1179. 300. 428. 1242. 845.16 407. 1223. 320. 448. 1291. 844.82 407. 1238. 326. 454. 1308. 844.16 407. 1266. 339. 467. 1340. 843.16 407. 1310. 359. 487. 1390. 842.16 407. 1353. 378. 507. 1439. 841.25 407. 1397. 398. 526. 1488. 840.16 407. 1441. 418. 546. 1537.
Case 3: Extreme Event, Drained Soil. PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 14:13:48 **************** * INPUT DATA * **************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. EXTREME EVENT, DRAINED SOIL II.‐‐CONTROL CANTILEVER WALL ANALYSIS FACTOR OF SAFETY FOR ACTIVE PRESSURES = 1.00 III.‐‐WALL DATA ELEVATION AT TOP OF WALL = 871.16 FT.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 9 of 22
ELEVATION AT BOTTOM OF WALL = 841.16 FT. WALL MODULUS OF ELLASTACITY = 2.900E+07 PSI. WALL MOMENT OF INERTIA = 152.00 IN^4. IV.‐‐SURFACE POINT DATA IV.A.‐‐RIGHTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 871.16 100.00 871.16 IV.B.‐‐LEFTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 864.64 100.00 864.64 V.‐‐SOIL LAYER DATA V.A.‐‐RIGHTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 19.00 50.00 10.26 0.00 DEF DEF V.B.‐‐LEFTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 19.00 50.00 10.26 0.00 DEF DEF VI.‐‐WATER DATA UNIT WEIGHT = 62.40 (PCF) RIGHTSIDE ELEVATION = 871.16 (FT) LEFTSIDE ELEVATION = 864.64 (FT) NO SEEPAGE VII.‐‐VERTICAL SURCHARGE LOADS NONE
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 10 of 22
VIII.‐‐HORIZONTAL LOADS NONE PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 14:13:51 **************************** * SUMMARY OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. EXTREME EVENT, DRAINED SOIL II.‐‐SUMMARY RIGHTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. LEFTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. PASSIVE FACTOR OF SAFETY : 1.33 MAX. BEND. MOMENT (LB‐FT) : 2.6542E+04 AT ELEVATION (FT) : 851.19 MAXIMUM DEFLECTION (IN.) : 2.7464E+00 AT ELEVATION (FT) : 871.16 PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHOREDOR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 14:13:51 **************************** * COMPLETE OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. EXTREME EVENT, DRAINED SOIL II.‐‐RESULTS BENDING NET ELEVATION MOMENT SHEAR DEFLECTION PRESSURE (FT) (LB‐FT) (LB) (IN) (PSF) 871.16 0.0000E+00 0. 2.7464E+00 0.00 870.16 1.0400E+01 31. 2.5965E+00 62.40
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 11 of 22
869.16 8.3200E+01 125. 2.4466E+00 124.80 868.16 2.8080E+02 281. 2.2967E+00 187.20 867.94 3.4576E+02 323. 2.2645E+00 200.65 867.16 6.6718E+02 505. 2.1470E+00 265.01 866.16 1.3186E+03 811. 1.9975E+00 347.06 865.16 2.3171E+03 1199. 1.8486E+00 429.11 864.64+ 3.0036E+03 1435. 1.7712E+00 471.93 864.64‐ 3.0036E+03 1435. 1.7712E+00 363.22 864.16 3.7292E+03 1598. 1.7006E+00 321.68 863.64 4.6057E+03 1757. 1.6239E+00 285.92 863.16 5.4768E+03 1886. 1.5541E+00 253.17 862.16 7.4777E+03 2105. 1.4097E+00 184.66 861.42 9.0743E+03 2218. 1.3050E+00 122.56 861.16 9.6607E+03 2249. 1.2682E+00 116.15 860.16 1.1957E+04 2331. 1.1306E+00 47.64 859.46 1.3585E+04 2348. 1.0376E+00 0.00 859.16 1.4300E+04 2344. 9.9759E‐01 ‐20.87 858.16 1.6623E+04 2289. 8.7023E‐01 ‐89.38 857.16 1.8856E+04 2166. 7.4938E‐01 ‐157.89 856.16 2.0931E+04 1974. 6.3592E‐01 ‐226.40 855.16 2.2780E+04 1713. 5.3065E‐01 ‐294.91 854.16 2.4334E+04 1384. 4.3431E‐01 ‐363.42 853.16 2.5525E+04 986. 3.4749E‐01 ‐431.93 852.16 2.6283E+04 520. 2.7066E‐01 ‐500.44 851.16 2.6542E+04 ‐15. 2.0413E‐01 ‐568.95 850.16 2.6231E+04 ‐618. 1.4797E‐01 ‐637.46 849.16 2.5283E+04 ‐1290. 1.0208E‐01 ‐705.97 848.16 2.3628E+04 ‐2030. 6.6081E‐02 ‐774.48 847.16 2.1200E+04 ‐2839. 3.9317E‐02 ‐842.99 846.16 1.7928E+04 ‐3716. 2.0835E‐02 ‐911.50 845.67 1.5980E+04 ‐4175. 1.4382E‐02 ‐945.34 845.16 1.3764E+04 ‐4549. 9.3520E‐03 ‐532.79 844.16 9.0850E+03 ‐4674. 3.2472E‐03 282.50 843.16 4.6885E+03 ‐3984. 7.1321E‐04 1097.79 842.16 1.3896E+03 ‐2478. 5.2976E‐05 1913.07 841.16 3.9163E+00 ‐157. 9.9030E‐11 2728.36 841.10 0.0000E+00 0. 0.0000E+00 2775.01 III.‐‐WATER AND SOIL PRESSURES <‐‐‐‐‐‐‐‐‐‐‐‐‐SOIL PRESSURES‐‐‐‐‐‐‐‐‐‐‐‐‐‐> WATER <‐‐‐‐LEFTSIDE‐‐‐‐‐> <‐‐‐RIGHTSIDE‐‐‐‐> ELEVATION PRESSURE PASSIVE ACTIVE ACTIVE PASSIVE (FT) (PSF) (PSF) (PSF) (PSF) (PSF) 871.16 0. 0. 0. 0. 109. 870.16 62. 0. 0. 0. 206. 869.16 125. 0. 0. 0. 294. 868.16 187. 0. 0. 0. 382.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 12 of 22
867.94+ 201. 0. 0. 0. 470. 867.94‐ 201. 0. 0. 0. 401. 867.16 250. 0. 0. 15. 470. 866.16 312. 0. 0. 35. 558. 865.16 374. 0. 0. 55. 646. 864.64+ 407. 0. 0. 65. 692. 864.64‐ 407. 109. 0. 65. 692. 864.16 407. 160. 0. 74. 735. 863.64 407. 206. 0. 85. 781. 863.16 407. 248. 0. 94. 823. 862.16 407. 336. 0. 114. 911. 861.42+ 407. 424. 0. 128. 976. 861.42‐ 407. 401. 0. 128. 976. 861.16 407. 424. 5. 133. 999. 860.16 407. 512. 25. 153. 1087. 859.46 407. 574. 38. 167. 1149. 859.16 407. 600. 44. 173. 1175. 858.16 407. 689. 64. 192. 1264. 857.16 407. 777. 84. 212. 1352. 856.16 407. 865. 103. 232. 1440. 855.16 407. 953. 123. 251. 1528. 854.16 407. 1041. 143. 271. 1616. 853.16 407. 1129. 162. 290. 1704. 852.16 407. 1218. 182. 310. 1792. 851.16 407. 1306. 202. 330. 1881. 850.16 407. 1394. 221. 349. 1969. 849.16 407. 1482. 241. 369. 2057. 848.16 407. 1570. 261. 389. 2145. 847.16 407. 1658. 280. 408. 2233. 846.16 407. 1746. 300. 428. 2321. 845.67 407. 1790. 310. 438. 2365. 845.16 407. 1835. 320. 448. 2410. 844.16 407. 1923. 339. 467. 2498. 843.16 407. 2011. 359. 487. 2586. 842.16 407. 2099. 378. 507. 2674. 841.16 407. 2187. 398. 526. 2762. 841.10 407. 2275. 418. 546. 2850. 839.16 407. 2364. 437. 566. 2939.
Case 4: Usual Event, Undrained Soil. CWALSHT will not solve this case because no embedment of the wall is necessary. Case 5: Unusual Event, Undrained Soil. PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 13 of 22
BY CLASSICAL METHODS DATE: 6‐MAY‐2013 TIME: 8:15:59 **************** * INPUT DATA * **************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. UNUSUAL EVENT, DRAINED SOIL II.‐‐CONTROL CANTILEVER WALL ANALYSIS FACTOR OF SAFETY FOR ACTIVE PRESSURES = 1.00 III.‐‐WALL DATA ELEVATION AT TOP OF WALL = 871.16 FT. ELEVATION AT BOTTOM OF WALL = 841.16 FT. WALL MODULUS OF ELLASTACITY = 2.900E+07 PSI. WALL MOMENT OF INERTIA = 152.00 IN^4. IV.‐‐SURFACE POINT DATA IV.A.‐‐RIGHTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 871.16 100.00 871.16 IV.B.‐‐LEFTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 866.16 10.65 864.64 100.00 864.64 V.‐‐SOIL LAYER DATA V.A.‐‐RIGHTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 0.00 575.00 0.00 0.00 DEF DEF V.B.‐‐LEFTSIDE
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 14 of 22
LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 0.00 575.00 0.00 0.00 DEF DEF VI.‐‐WATER DATA UNIT WEIGHT = 62.40 (PCF) RIGHTSIDE ELEVATION = 871.16 (FT) LEFTSIDE ELEVATION = 864.64 (FT) NO SEEPAGE VII.‐‐VERTICAL SURCHARGE LOADS NONE VIII.‐‐HORIZONTAL LOADS NONE PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 6‐MAY‐2013 TIME: 8:16:19 **************************** * SUMMARY OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. UNUSUAL EVENT, DRAINED SOIL II.‐‐SUMMARY RIGHTSIDE SOIL PRESSURES DETERMINED BY SWEEP SEARCH WEDGE METHOD. LEFTSIDE SOIL PRESSURES DETERMINED BY SWEEP SEARCH WEDGE METHOD. PASSIVE FACTOR OF SAFETY : 7.20 MAX. BEND. MOMENT (LB‐FT) : 1.6604E+04 AT ELEVATION (FT) : 851.29 MAXIMUM DEFLECTION (IN.) : 1.7367E+00 AT ELEVATION (FT) : 871.16
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 15 of 22
PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHOREDOR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 6‐MAY‐2013 TIME: 8:16:19 **************************** * COMPLETE OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. UNUSUAL EVENT, DRAINED SOIL II.‐‐RESULTS BENDING NET ELEVATION MOMENT SHEAR DEFLECTION PRESSURE (FT) (LB‐FT) (LB) (IN) (PSF) 871.16 0.0000E+00 0. 1.7367E+00 0.00 870.16 1.0400E+01 31. 1.6404E+00 62.40 869.16 8.3200E+01 125. 1.5440E+00 124.80 868.16 2.8080E+02 281. 1.4477E+00 187.20 867.16 6.6560E+02 499. 1.3515E+00 249.60 866.16+ 1.3000E+03 780. 1.2556E+00 312.00 866.16‐ 1.3000E+03 780. 1.2556E+00 152.28 865.16 2.1550E+03 929. 1.1602E+00 145.49 864.64 2.6594E+03 1003. 1.1107E+00 139.08 864.16 3.1540E+03 1065. 1.0656E+00 118.76 863.16 4.2740E+03 1171. 9.7231E‐01 93.82 862.16 5.4882E+03 1253. 8.8068E‐01 70.83 861.16 6.7736E+03 1314. 7.9119E‐01 50.49 860.16 8.1098E+03 1355. 7.0437E‐01 32.09 859.16 9.4759E+03 1372. 6.2072E‐01 0.30 859.15 9.4845E+03 1372. 6.2021E‐01 0.00 858.16 1.0839E+04 1347. 5.4079E‐01 ‐48.54 857.16 1.2155E+04 1276. 4.6510E‐01 ‐95.14 856.16 1.3376E+04 1160. 3.9418E‐01 ‐136.28 855.16 1.4461E+04 1003. 3.2849E‐01 ‐177.45 854.16 1.5368E+04 804. 2.6847E‐01 ‐219.84 853.16 1.6055E+04 563. 2.1447E‐01 ‐262.57 852.16 1.6480E+04 280. 1.6675E‐01 ‐304.26 851.16 1.6601E+04 ‐46. 1.2548E‐01 ‐346.83 850.16 1.6374E+04 ‐414. 9.0713E‐02 ‐390.43 849.16 1.5757E+04 ‐827. 6.2348E‐02 ‐434.03 848.16 1.4707E+04 ‐1282. 4.0146E‐02 ‐476.72 847.16 1.3179E+04 ‐1780. 2.3694E‐02 ‐518.89 846.16 1.1133E+04 ‐2320. 1.2391E‐02 ‐561.96 845.48 9.4292E+03 ‐2711. 7.2600E‐03 ‐591.50 845.16 8.5277E+03 ‐2872. 5.4341E‐03 ‐404.18
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 16 of 22
844.16 5.5509E+03 ‐2985. 1.8072E‐03 176.92 843.16 2.7510E+03 ‐2518. 3.6207E‐04 758.01 842.16 7.0913E+02 ‐1469. 2.0168E‐05 1339.11 841.24 0.0000E+00 0. 0.0000E+00 1871.00 III.‐‐WATER AND SOIL PRESSURES <‐‐‐‐‐‐‐‐‐‐‐‐‐SOIL PRESSURES‐‐‐‐‐‐‐‐‐‐‐‐‐‐> WATER <‐‐‐‐LEFTSIDE‐‐‐‐‐> <‐‐‐RIGHTSIDE‐‐‐‐> ELEVATION PRESSURE PASSIVE ACTIVE ACTIVE PASSIVE (FT) (PSF) (PSF) (PSF) (PSF) (PSF) 871.16 0. 0. 0. 0. 160. 870.16 62. 0. 0. 0. 203. 869.16 125. 0. 0. 0. 247. 868.16 187. 0. 0. 0. 291. 867.16 250. 0. 0. 0. 334. 866.16+ 312. 0. 0. 0. 378. 866.16‐ 312. 160. 0. 0. 378. 865.16 374. 229. 0. 0. 421. 864.64 407. 268. 0. 0. 444. 864.16 407. 288. 0. 0. 465. 863.16 407. 313. 0. 0. 509. 862.16 407. 336. 0. 0. 552. 861.16 407. 356. 0. 0. 596. 860.16 407. 375. 0. 0. 639. 859.16 407. 407. 0. 0. 683. 859.15 407. 407. 0. 0. 683. 858.16 407. 456. 0. 0. 727. 857.16 407. 502. 0. 0. 770. 856.16 407. 543. 0. 0. 814. 855.16 407. 584. 0. 0. 857. 854.16 407. 627. 0. 0. 901. 853.16 407. 670. 0. 0. 945. 852.16 407. 711. 0. 0. 988. 851.16 407. 754. 0. 0. 1032. 850.16 407. 797. 0. 0. 1075. 849.16 407. 841. 0. 0. 1119. 848.16 407. 884. 0. 0. 1163. 847.16 407. 926. 0. 0. 1206. 846.16 407. 969. 0. 0. 1250. 845.48 407. 998. 0. 0. 1279. 845.16 407. 1013. 0. 0. 1293. 844.16 407. 1056. 0. 0. 1337. 843.16 407. 1100. 0. 0. 1381. 842.16 407. 1143. 0. 0. 1424. 841.24 407. 1187. 0. 0. 1468. 840.16 407. 1231. 0. 0. 1511.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 17 of 22
Case 6: Extreme Event, Undrained Soil. PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:35:43 **************** * INPUT DATA * **************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. EXTREME EVENT, UNDRAINED SOIL II.‐‐CONTROL CANTILEVER WALL ANALYSIS FACTOR OF SAFETY FOR ACTIVE PRESSURES = 1.00 III.‐‐WALL DATA ELEVATION AT TOP OF WALL = 871.16 FT. ELEVATION AT BOTTOM OF WALL = 841.16 FT. WALL MODULUS OF ELLASTACITY = 2.900E+07 PSI. WALL MOMENT OF INERTIA = 152.00 IN^4. IV.‐‐SURFACE POINT DATA IV.A.‐‐RIGHTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 871.16 100.00 871.16 IV.B.‐‐LEFTSIDE DIST. FROM ELEVATION WALL (FT) (FT) 0.00 864.64 100.00 864.64 V.‐‐SOIL LAYER DATA V.A.‐‐RIGHTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 0.00 575.00 0.00 0.00 DEF DEF
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 18 of 22
V.B.‐‐LEFTSIDE LEVEL 2 FACTOR OF SAFETY FOR ACTIVE PRESSURE = DEFAULT LEVEL 2 FACTOR OF SAFETY FOR PASSIVE PRESSURE = DEFAULT ANGLE OF ANGLE OF <‐SAFETY‐> SAT. MOIST INTERNAL COH‐ WALL ADH‐ <‐‐BOTTOM‐‐> <‐FACTOR‐> WGHT. WGHT. FRICTION ESION FRICTION ESION ELEV. SLOPE ACT. PASS. (PCF) (PCF) (DEG) (PSF) (DEG) (PSF) (FT) (FT/FT) 106.00 106.00 0.00 575.00 0.00 0.00 DEF DEF VI.‐‐WATER DATA UNIT WEIGHT = 62.40 (PCF) RIGHTSIDE ELEVATION = 871.16 (FT) LEFTSIDE ELEVATION = 864.64 (FT) NO SEEPAGE VII.‐‐VERTICAL SURCHARGE LOADS NONE VIII.‐‐HORIZONTAL LOADS NONE PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHORED OR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:35:46 **************************** * SUMMARY OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. EXTREME EVENT, UNDRAINED SOIL II.‐‐SUMMARY RIGHTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. LEFTSIDE SOIL PRESSURES DETERMINED BY FIXED SURFACE WEDGE METHOD. PASSIVE FACTOR OF SAFETY : 5.11 MAX. BEND. MOMENT (LB‐FT) : 1.9546E+04 AT ELEVATION (FT) : 851.62 MAXIMUM DEFLECTION (IN.) : 2.0400E+00 AT ELEVATION (FT) : 871.16
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 19 of 22
PROGRAM CWALSHT‐DESIGN/ANALYSIS OF ANCHOREDOR CANTILEVER SHEET PILE WALLS BY CLASSICAL METHODS DATE: 11‐MARCH‐2013 TIME: 15:35:46 **************************** * COMPLETE OF RESULTS FOR * * CANTILEVER WALL ANALYSIS * **************************** I.‐‐HEADING 'SHEET PILE WALL IN BRENNA FOUNDATION. EXTREME EVENT, UNDRAINED SOIL II.‐‐RESULTS BENDING NET ELEVATION MOMENT SHEAR DEFLECTION PRESSURE (FT) (LB‐FT) (LB) (IN) (PSF) 871.16 0.0000E+00 0. 2.0400E+00 0.00 870.16 1.0400E+01 31. 1.9263E+00 62.40 869.16 8.3200E+01 125. 1.8126E+00 124.80 868.16 2.8080E+02 281. 1.6990E+00 187.20 867.16 6.6560E+02 499. 1.5854E+00 249.60 866.16 1.3000E+03 780. 1.4722E+00 312.00 865.16 2.2464E+03 1123. 1.3595E+00 374.40 864.64+ 2.8852E+03 1327. 1.3009E+00 406.97 864.64‐ 2.8852E+03 1327. 1.3009E+00 181.92 864.16 3.5396E+03 1409. 1.2476E+00 161.08 863.64 4.2960E+03 1487. 1.1898E+00 138.32 863.16 5.0219E+03 1548. 1.1372E+00 117.48 862.16 6.6218E+03 1644. 1.0287E+00 73.88 861.16 8.2956E+03 1696. 9.2281E‐01 30.28 860.47 9.4784E+03 1707. 8.5115E‐01 0.00 860.16 9.9996E+03 1705. 8.2019E‐01 ‐13.32 859.16 1.1690E+04 1670. 7.2148E‐01 ‐56.92 858.16 1.3324E+04 1591. 6.2736E‐01 ‐100.52 857.16 1.4857E+04 1468. 5.3846E‐01 ‐144.12 856.16 1.6247E+04 1303. 4.5537E‐01 ‐187.72 855.16 1.7448E+04 1093. 3.7865E‐01 ‐231.32 854.16 1.8418E+04 840. 3.0876E‐01 ‐274.92 853.16 1.9113E+04 543. 2.4608E‐01 ‐318.52 852.16 1.9490E+04 203. 1.9089E‐01 ‐362.12 851.16 1.9504E+04 ‐181. 1.4332E‐01 ‐405.72 850.16 1.9113E+04 ‐609. 1.0338E‐01 ‐449.32 849.16 1.8273E+04 ‐1080. 7.0927E‐02 ‐492.92 848.16 1.6939E+04 ‐1594. 4.5618E‐02 ‐536.52 847.16 1.5070E+04 ‐2153. 2.6931E‐02 ‐580.12 846.16 1.2619E+04 ‐2755. 1.4133E‐02 ‐623.72 845.77 1.1505E+04 ‐2999. 1.0561E‐02 ‐640.60
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 20 of 22
845.16 9.5688E+03 ‐3287. 6.2619E‐03 ‐298.04 844.78 8.3163E+03 ‐3360. 4.3388E‐03 ‐87.74 844.16 6.2260E+03 ‐3306. 2.1321E‐03 261.05 843.16 3.1441E+03 ‐2765. 4.5151E‐04 820.13 842.16 8.8246E+02 ‐1665. 3.0256E‐05 1379.21 841.16 ‐1.2732E‐02 ‐7. ‐4.8148E‐14 1938.30 841.16 0.0000E+00 0. 0.0000E+00 1940.17 III.‐‐WATER AND SOIL PRESSURES <‐‐‐‐‐‐‐‐‐‐‐‐‐SOIL PRESSURES‐‐‐‐‐‐‐‐‐‐‐‐‐‐> WATER <‐‐‐‐LEFTSIDE‐‐‐‐‐> <‐‐‐RIGHTSIDE‐‐‐‐> ELEVATION PRESSURE PASSIVE ACTIVE ACTIVE PASSIVE (FT) (PSF) (PSF) (PSF) (PSF) (PSF) 871.16 0. 0. 0. 0. 225. 870.16 62. 0. 0. 0. 269. 869.16 125. 0. 0. 0. 312. 868.16 187. 0. 0. 0. 356. 867.16 250. 0. 0. 0. 399. 866.16 312. 0. 0. 0. 443. 865.16 374. 0. 0. 0. 487. 864.64+ 407. 0. 0. 0. 509. 864.64‐ 407. 225. 0. 0. 509. 864.16 407. 246. 0. 0. 530. 863.64 407. 269. 0. 0. 553. 863.16 407. 289. 0. 0. 574. 862.16 407. 333. 0. 0. 617. 861.16 407. 377. 0. 0. 661. 860.47 407. 407. 0. 0. 691. 860.16 407. 420. 0. 0. 705. 859.16 407. 464. 0. 0. 748. 858.16 407. 507. 0. 0. 792. 857.16 407. 551. 0. 0. 835. 856.16 407. 595. 0. 0. 879. 855.16 407. 638. 0. 0. 923. 854.16 407. 682. 0. 0. 966. 853.16 407. 725. 0. 0. 1010. 852.16 407. 769. 0. 0. 1053. 851.16 407. 813. 0. 0. 1097. 850.16 407. 856. 0. 0. 1141. 849.16 407. 900. 0. 0. 1184. 848.16 407. 943. 0. 0. 1228. 847.16 407. 987. 0. 0. 1271. 846.16 407. 1031. 0. 0. 1315. 845.77 407. 1048. 0. 0. 1332. 845.16 407. 1074. 0. 0. 1359. 844.78+ 407. 1091. 0. 0. 1402. 844.78‐ 407. 1091. 0. 0. 1375.
FMM Reach 4 Sheet Pile Wall Design
03/11/2013 Comp by: MVR
97% FTR Submittal
Attachment F-12 21 of 22
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