Mathcad - Final Version_Vertical Cantilever Retaining Wall _CTA 95th Street_Typical SE_Without Column Canopy Pedestal

Title: Proposed Retaining Wall (Typical SE Wall Without Canopy Column Pedestal)

PROJECT NUMBER: HBM1301-568 PROJECT NAME: CTA-95th St Terminal Improvement

CALC BY: MA, LAB DATE: 03/21/2014CHECK BY: MI, MAI DATE: 03/28/2014

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PROJECT NUMBER: HBM1301-568PROJECT NAME: CTA-95th Terminal Improvement

T ypical SE Wall Without Canopy Column Pedestal

1. Obtain Design CriteriaThe analysis and design procedures for the retaining wall will be those outlined in the 2012 IDOT BridgeManual English, AASHTO 2012 LRFD Bridge Design Specifications (Sixth Edition) through 2013 Interims.Seismic Performance Zone (SPZ) = 1Design Spectral Acceleration at 1.0s (SD1) = 0.086gDesign Spectral Acceleration at 0.2s (SDS) = 0.144gSoil Site Class = D

1.1 Material Properties

conc 150pcf Concrete unit weight

f'c 5000psi Concrete strength at 28 days ageCorrection factor for source of aggregate(to be taken as 1.0 unless determined byphysical test and as approved by theauthority of jurisdiction)(AASHTO LRFD Article 5.4.2.4)

K1 1.0

ag 0.75in coarse aggregate size

Concrete elastic modulus(AASHTO LRFD Eqn. 5.4.2.4-1)Ec 33000 K1

conc1000pcf

1.5

f'c ksi 4.29 103 ksi

1 0.85 f'c 4.0ksiif

0.850.05ksi

f'c 4ksi 4ksi f'c 8ksiif0.65 otherwise

Ratio of the depth of equivalent uniformlystressed compression zone assumed inthe strength limit state to the depth of theactual compression zone (LRFD 5.7.2.2)

1 0.8fy 60000psi Steel yield stress

Es 29000ksi Steel elastic modulus (AASHTO LRFDArticle 5.4.3.2)




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1.2 Reinforcement Steel Cover Requirements

Covers 2in Stem back cover

Coverft 2in Footing top cover

Coverfb 3in Footing bottom cover 1.3 Soil Properties

Water 62.4pcf Unit weight of water

Soil unit weight (use average of loose andcompacted gravel)Soil 120pcf

SoilLS 125pcf Soil unit weight of Live load surcharge

Obtained from geotechnical informationand in accordance with IDOT BridgeManual Article 3.11.2.2 for "T-type" walls,using an angle of internal friction of 30degrees.

Ka 0.53

1.4 Footing Bed Properties (Clay)

Su 6ksf Undrained shear strength

Kp 0 Passive pressure coefficient

qall 10ksf Allowable bearing capacityquall 15ksf Ultimate bearing capacity 2. Retaining Wall Dimensions 2.1 Retaining Wall Stem Dimensions

Hstem 21.75ft Stem wall height

Tstem_bot 2.50ft Stem wall thickness at foundation

Tstem_top 1ft 3in 1.25 ft Stem wall thickness at top

Tformliner 0in Formliner thickness

Hkey 0ft Shear key height




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2.2 Footing Dimensions

Wpcap 19.75ft Footing width

Dpcap 4ft Footing depth

Wpctoe 2ft Footing toe width

Wpcheel Wpcap Tstem_bot Wpctoe 15.25 ft Footing heel width

2.3 Sidewalk, Approach Slab, Parapet and Railing Loads

Tappslab 15in Approach slab thickness

Lappslab 30ft Approach slab lengthweight of approach slab transferred to thewall stem per footDCappslab Tappslab conc

Lappslab2

2.81 kipft

Tsidewalk 8in Sidewalk thickness

Lsidewalk 8ft Sidewalk width

DCsidewalk Tsidewalk conc Lsidewalk 0.8kipft

Weight of sidewalk per foot

Weight of New Jersey parapet per footDCNJparap 0.413

kipft




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Figure 1. Retaining Wall Dimensions




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3. Applied Loads CalculationsDC1: Self-weight of sidewalk, moment slab, parapet and railingDC2: Self-weight of rectangular portion of wall stemDC3: Self-weight of triangular portion of wall stemDC4: Self-weight of base footingEV1: Vertical earth pressure on the base heelEV2: Vertical earth pressure above the truncated wall stemEV3: Vertical earth pressure on the base toeESv: Vertical surcharge load due to moment slab at time of construction (before concrete cures)LSv: Vertical live load surchargeLLped: Pedestrian live load

EH: Horizontal earth pressureESh: Horizontal surcharge load due to moment slab at time of construction (before concrete cures)LSh: Horizontal live load surcharge

DC2

DC3

DC4

EV2

EV1

EV3

DC1

EHfoot EShfoot LShfootA

B

C

HR

W/3

Wpcap/2

ESvLSv

Heel

LLped

Toe

Leffqu_Bearing

R eR: Resultant of vertical loadse: eccentricity of resultant

EHstem EShstem LShstem

(Tstem_bot-Tstem_top)/3

WpcheelTstem_top/2

Tstem_top/2

Wpctoe/2


HR

W/2

qu_Bearing: equivalent bearing pressure from R distributed over effective Base Area




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3.1 Retaining Wall Dead Loads [DC] (Per 1 Foot Linear Strip of Wall):3.1.1 Sidewalk, Moment Slab, Parapet and Railing Dead Load [DC1]:

Dead load due to approach slab, sidewalk,parapet and railing [DC1]DCtotslab DCappslab DCsidewalk DCNJparap 4.03

kipft

3.1.2 Retaining Wall Stem Dead Load

Rectangular Portion of Retaining Wall Stem Dead Load [DC2]:

Rectangular portion of retaining wall stemvertical [DC2] dead loadDCstemrect Hstem Tstem_top conc 4.08

kipft

Triangular Portion of Retaining Wall Stem Dead Load [DC3]:

Triangular portion of retaining wall stemvertical [DC3] dead loadDCstemtriang Hstem

Tstem_bot Tstem_top2

conc 2.04kipft

3.1.3 Footing Dead Load [DC4]:

DCpcap Wpcap Dpcap conc 11.85kipft

Footing vertical [DC4] dead load

3.2 Earth Loads 3.2.1 Vertical Earth Loads

3.2.1.1 Soil Pressure above Heel [EV]

Rectangular Portion of Soil Above Heel Dead Load [EV1]

HSoilheel Hstem 21.75 ft Soil height above footing heel

EVSoilheelrect Wpcheel HSoilheel Soil 39.8kipft

Rectangular portion of soil above heelvertical dead load [EV]

Triangular Portion of Soil Above Heel Dead Load [EV2]

Triangular portion of soil above heel verticaldead load [EV2] due to wall batterEVSoilheeltriang

12

HSoilheel Tstem_botTstem_top

Soil 1.63kipft

3.2.1.2 Soil Pressure above Toe [EV3]:

HSoiltoe 2.ft Soil height above footing toe

EVSoiltoe Wpctoe HSoiltoe Soil 0.48kipft

Soil above toe vertical dead load




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3.2.2 Horizontal Earth Loads [EH]

3.2.2.1 Horizontal Earth Load at bottom of Stem [EHstem]

PStem Ka Soil HSoilheel 1.38 ksf Lateral earth pressure at bottom of stem

The lateral load effects due to soil above the wall footing applied to the stem is:

Lateral load due to earth pressure behindstem with soil backfill [EH]REHstem

12

PStem HSoilheel 15.04

kipft

3.2.2.2 Horizontal Earth Load at bottom of Footing [EHfoot]

HRW Hstem Dpcap 25.75 ft Total height of retaining wall

Ppc Ka Soil HRW 1.64 ksf Lateral earth pressure at bottom of footingThe lateral load effects due to soil above the bott. of wall footing and applied to the wall footing is:

Lateral load due to earth pressure behindstem and footing with soil backfill [EH] atHRW/3 from the bottom

REHpc12

Ppc HRW 21.09

kipft

3.2.2.3 Horizontal Surcharge Loads due to Sidewalk and Moment Slab [ES]

ES conc Tappslab 0.19 ksf Uniform surcharge load due to momentslab

Note: Two load cases will be considered regarding the moment slab effect on the retaining wall. Case 1: before the concrete cures, includes surcharges for the slab and live loads. Case 2: after the concrete cures, assumes that dead and live loads are applied from the moment slab to thetop of the wall, so no surcharges are included.

3.2.2.3.1 Uniform Vertical Surcharge at bottom of Stem [ESv]

Vertical load due to uniform surchargefrom moment slab applied per linear footof wall [ESv]

ESvert ES Tstem_bot Tstem_top Wpcheel 3.09 kipft3.2.2.3.2 Uniform Horizontal Surcharge at bottom of Stem [EShstem]

pES Ka ES 0.1 ksf Maximum lateral surcharge load due to1'-thick RC pavement (AASHTO 3.11.6.1)

RESstem pES HSoilheel 2.16kipft

Lateral load due to uniform surcharge atbottom of stem [EH]

3.2.2.3.3 Uniform Horizontal Surcharge at bottom of Footing [EShfoot]

Lateral load due to uniform surcharge atbottom of footing [EH]RESpc pES HRW 2.56

kipft




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3.3 Live Loads3.3.1 Pedestrian Live Load [LLped]

According to Article 3.6.1.6 A pedestrian load of 0.075 ksf shall be applied to all sidewalks wider than 2.0 ftand considered simultaneously with the vehicular design live load in the vehicle lane. Where vehicles canmount the sidewalk, sidewalk pedestrian load shall not be considered concurrently. If a sidewalk may beremoved in the future, the vehicular live loads shall be applied at 1 ft from edge-of-deck for design of theoverhang, and 2 ft from edge-of-deck for design of all other components. The pedestrian load shall not beconsidered to act concurrently with vehicles. The dynamic load allowance need not be considered forvehicles.Bridges intended for only pedestrian, equestrian, light maintenance vehicle, and/or bicycle traffic should bedesigned in accordance with AASHTO's LRFD Guide Specifications for the Design of Pedestrian Bridges.

LLped 0.075ksf Wpcheel 1.14kipft

Pedestrian live load (conservative)

3.3.2 Live Load Surcharge [LSv]

heqLS 4ft Hstem 5ftif

3ft10ft Hstem

5 5ft Hstem 10ftif

2ft20ft Hstem

10 10ft Hstem 20ftif

2ft otherwise

Equivalent height of soil for vehicularloading based on AASHTO LRFD Table3.11.6.4-2

heqLS 2 ftAccording to Article 3.11.6.5 If the vehicular loading is transmitted through a structural slab, which is alsosupported by means other than earth, a corresponding reduction in the surcharge loads may be permitted.

3.3.2.1 Vertical Live Load Surcharge [LSv]

LSvert SoilLS heqLS Tstem_bot Tstem_top Wpcheel 4.13 kipft Vertical component of live loadsurcharge [LSv]3.3.2.1 Horizontal Live Load Surcharge at bottom of Stem [LShstem]

pStem Ka SoilLS heqLS 0.13 ksf Horizontal pressure increase due to liveload surcharge at bottom of stem

Lateral load due to Live Load surcharge atbottom of stem [LShstem] applied atHsoilheel/2

RLSstem pStem HSoilheel 2.88kipft

3.3.2.2 Horizontal Live Load Surcharge at bottom of Footing [LShfoot]

ppc Ka SoilLS heqLS 0.13 ksf Horizontal pressure increase due to liveload surcharge at bottom of footingLateral load due to Live Load surcharge atbottom of footing [LShfoot] applied at HRW/2RLSpc ppc HRW 3.41

kipft




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4. Limit States Design Method 4.1 Resistance and Load Modification FactorsThe resistance factors, , for reinforced concrete Retaining walls for the Strength Limit State perAASHTO LRFD Article 5.5.4.2 are as shown below:

f 0.9 Resistance factor for flexure

v 0.9 Resistance factor for shear

4.2 Load FactorsIn accordance with LRFD (Table 3.4.1-1) the following Strength I load factors shall be used for retainingwall design

DCstrmax 1.25 DCstrmin 0.9 Strength I Load factor for DC load case

LLstrmax 1.75 LLstrmin 1.75 Strength I Load factor for LL + IM loadcase

LSstrmax 1.75 LSstrmin 1.75 Strength I Load factor for live loadsurcharge

EVstrmax 1.35 EVstrmin 1.0 Strength I Load factor for vertical earthpressure

EHstrmax 1.50 EHstrmin 0.9 Strength I Load factor for horizontal earthpressure (active)

ESstrmax 1.50 ESstrmin 0.75 Strength I Load factor for earth surcharge

In accordance with LRFD (Table 3.4.1-2) the following Service I load factors shall be used for retaining walldesign

DCsv 1.0 Service I Load factor for DC load case

LLsv 1.0 Service I Load factor for LL + IM load case

LSsv 1.0 Service I Load factor for live load surcharge

EVsv 1.0 Service I Load factor for vertical earthpressure

EHsv 1.0 Service I Load factor for horizontal earthpressure

ESsv 1.0 Service I Load factor for earth surcharge




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5. Stability Analysis for Retaining Wall 5.1 Moment Arms CalculationsNote: Moment arms are calculated from the toe at the bottom of the footing

DCtotslab 4.03kipft

H1 WpctoeTstem_top

2 2.63 ft

DCstemrect 4.08kipft

H5 WpctoeTstem_top

2 2.63 ft

DCstemtriang 2.04kipft

H6 Wpctoe Tstem_topTstem_bot Tstem_top

3 3.67 ft

DCpcap 11.85kipft

H7Wpcap

29.88 ft

EVSoilheelrect 39.8kipft

H8 Wpctoe Tstem_botWpcheel

2 12.12 ft

EVSoilheeltriang 1.63kipft

H9 Wpctoe Tstem_top23

Tstem_bot Tstem_top 4.08 ft

EVSoiltoe 0.48kipft

H10Wpctoe

21 ft

LLped 1.14kipft

H11 WpctoeTstem_top

2 2.63 ft

LSvert 4.131ft

kip H12 Wpctoe Tstem_botWpcheel

2 12.12 ft

ESvert 3.09kipft

H13 Wpctoe Tstem_botWpcheel

2 12.12 ft

REHpc 21.09kipft

d1HSoilheel Dpcap

38.58 ft

RESpc 2.56kipft

d2HRW

212.88 ft

RLSpc 3.41kipft

d3HRW

212.88 ft




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5.3 Stability Checks and Bearing Capacity under Service I Limit State per Article 11.6.2 Four Loads Cases are Considered:Case 1: Includes vertical and horizontal surcharge due to approach slab and horizontal live load surchargeCase 2: Includes horizontal surcharge due to live loadCase 3: Includes vertical and horizontal live load surcharge and surcharge due to approach SlabCase 4: Includes vertical and horizontal live load surcharge and weight of approach slab and sidewalk

Table 1: Load Cases Required for Check for Stability and Bearing Capacity at Service Limit State

Case 1 Case 2 Case 3 Case 4

DC1moment slab, sidewalk, parapet and railing 4.03 2.63 10.57 1.0

DC2 Rectangular portion of wall stem 4.08 2.63 10.71 1.0 1.0 1.0 1.0

DC3Triangular portion of wall stem DC dead load 2.04 3.67 7.48 1.0 1.0 1.0 1.0

DC4 Footing weight 11.85 9.88 117.02 1.0 1.0 1.0 1.0

EV1Rectangular portion of soil above heel 39.80 12.13 482.61 1.0 1.0 1.0 1.0

EV2Triangular portion of soil above heel 1.63 4.08 6.66 1.0 1.0 1.0 1.0

EV3 Soil above toe 0.48 1.00 0.48 1.0 1.0 1.0 1.0

EHstemHorizontal earth pressure at bottom of stem 15.04 1.0

EHfootHorizontal earth pressure at bottom of footing 21.09 -8.58 -180.98 1.0 1.0 1.0 1.0

ESvVertical surcharge due to moment slab and sidewalk 3.09 12.13 37.51 1.0 1.0

EShstemHoriz. surch. at bot. of stem due to moment slab & sidewalk 2.16

EShfootHoriz. surch. at bot. of footing due to moment slab & sidewalk 2.56 -12.88 -32.95 1.0 1.0

LSv Vertical surcharge live load 4.13 12.13 50.02 1.0 1.0

LShstemHorizontal live load surcharge at bottom of footing 2.88

LShfootHorizontal live load surcharge at bottom of stem 3.41 -12.88 -43.93 1.0 1.0 1.0 1.0

LLped Pedestrian Live Load 1.14 2.63 3.00 1.0

1.20 2.63 3.15 404.6 400.0 454.6 463.61.20 2.63 3.15 63.0 59.9 67.1 69.2

Load typeVert.

Loads, Kips

Horiz. Loads, Kips

Arm, ft

Moment at the Toe, Kip-ft

MaximumVertical Load, Kip

Service I FactorsStability Bearing

Net Moment Capacity, Kip-ft




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5.3.1 Stability Checks against Overturning, Sliding, and Eccentricity

DC2

DC3

DC3

EV2

EV1

EV3

HR

W/2

Wpcap/2

HR

W/3

EHfoot

A

Wpctoe/2

Tstem_top/2



Wpcheel

Tstem_top/2

Heel

Toe

ESv LSv

EShfootLShfoot

Case 1

DC2

DC3

DC3

EV2

EV1

EV3

EHfoot LShfoot

A

Heel

Toe

Wpctoe/2

Tstem_top/2



Wpcheel

Tstem_top/2

HR

W/3

Wpcap/2

Case 2




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5.3.1.1 Factor of Safety Against Overturning (Service I)

5.3.1.1.1 Case 1: Includes vertical and horizontal surcharge due to approach slab and horizontal live loadsurcharge

Mresist1 DCsv DCstemrect H5DCstemtriang H6 DCpcap H7

EVsv EVSoilheelrect H8 EVSoilheeltriang H9EVSoiltoe H10

ESsv ESvert H13

Resisting Moment arms are calculatedfrom the toe (Point A) at the bottom of thefooting.

Mresist1 662.46kip ft

ft Resisting Moment due to Vertical Loads

Movert1 EHsv REHpc d1 ESsv RESpc d2 LSsv RLSpc d3 Overturning Moment due to HorizontalLoads

Movert1 257.86kip ft

ft

FSovert1Mresist1Movert1

Overturning Factor of Safety

FSovert1 2.57CheckFSovert if FSovert1 2 "OK" "N.G." CheckFSovert "OK" Check Overturning5.3.1.1.2 Case 2: Includes horizontal surcharge due to live load

Mresist2 DCsv DCstemrect H5DCstemtriang H6 DCpcap H7

EVsv EVSoilheelrect H8 EVSoilheeltriang H9EVSoiltoe H10

Resisting Moment arms are calculatedfrom the toe (Point A) at the bottom of thefooting.


ft Resisting Moment due to Vertical Loads

Movert2 EHsv REHpc d1 LSsv RLSpc d3 Overturning Moment due to HorizontalLoads

Movert2 224.91kip ft

ft

Overturning Factor of SafetyFSovert2

Mresist2Movert2

FSovert2 2.78CheckFSovert if FSovert2 2 "OK" "N.G." CheckFSovert "OK" Check Overturning




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5.3.1.2 Factor of Safety Against Sliding (Service I) per Article 10.6.3.4 (Case 2)

As per IDOT Bridge Manual, Article 3.10.3.2 Sliding resistance is determined differently depending onwhether the spread footing is setting on granular soil, cohesive soil, or rock. For granular soils, the slidingresistance is calculated as the vertical resultant, P, times the tangent of the friction angle for footings cast onin-place aggregate. Shear keys are not recommended for granular soils due to constructability concerns. Forcohesive soils, sliding resistance is calculated as cohesion times the effective footing width B. Lower strengthclays require special attention to ensure adequate sliding resistance and, in some cases, have successfullyutilized shear keys.

Su 6 ksf Undrained shear strength


Pp Kp Soil Hkey 0 ksf Passive pressure due to shear key

Lateral Load due to passive pressure onshear keyRp

12

Pp Hkey 0kipft

5.3.1.2.1 Case 1: Includes vertical and horizontal surcharge due to approach slab and horizontal live loadsurchargeDLvert1 DCsv DCstemrect DCstemtriang DCpcap

EVsv EVSoilheelrect EVSoilheeltriang EVSoiltoe

ESsv ESvert

Total Vertical Load

DLvert1 62.97kipft

Assume 50Y for replacing compact soil in front of footing

v1DLvert1Wpcap

3.19 ksf Vertical effective stress

qsmin1 min Su 0.5 v1 1.59 ksf Shear resistance (LRFD 10.6.3.4) Assume qs1 Su 6 ksf

Fresist_fric1 qs1 Wpcap Rp 118.5kipft

Friction force resisting sliding

Fsliding1 EHsv REHpc ESsv RESpc LSsv RLSpc 27.06kipft

Force causing sliding

FSsliding1Fresist_fric1

Fsliding14.38 Sliding Factor of Safety

CheckFSsliding1 if FSsliding1 1.5 "OK" "N.G." CheckFSsliding1 "OK"




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5.3.1.2.2 Case 2: Includes horizontal surcharge due to live load

DLvert2 DCsv DCstemrect DCstemtriang DCpcap EVsv EVSoilheelrect EVSoilheeltriang EVSoiltoe

Total Vertical Load not Including LLped

DLvert2 59.88kipft

v2DLvert2Wpcap





Fsliding2 EHsv REHpc LSsv RLSpc 24.5kipft





5.3.1.3 Check Eccentricity

AASHTO LRFD 11.6.3.3-Eccentricity LimitsFor foundations on soil, the location of the resultant of the reaction forces shall be within the middle two thirdsof the base width.

Net moment at bottom of toefor Case 1 loadingMnet1 Mresist1 Movert1 404.6

kip ftft

Vvert1 DLvert1 62.97kipft

Total Vertical Load for Case 1 loadingNet moment at bottom of toefor Case 2 loadingMnet2 Mresist2 Movert2 400.04

kip ftft

Vvert2 DLvert2 59.88kipft

Total Vertical Load for Case 2 loadingHence the maximum eccentricity due to either Case 1 or Case 2 load configuration is:

eccWpcap

2min

Mnet1Vvert1

Mnet2Vvert2

3.45 ft Maximum eccentricity from the centerlineof the base




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Checkuplift if eccWpcap

3 "OK" "N.G."

Checkuplift "OK"Wpcap

36.58 ft

5.3.2 Factor of Safety Against Bearing Capacity Failure (Service I)

EShfootLShfootA

Wpctoe/2

Tstem_top/2



Wpcheel

Tstem_top/2

HR

W/3

HR

W/2

Wpcap/2

Heel

ToeC

ESv

DC2

DC3

DC3

EV2

EV1

EV3

EHfoot

Leffqu_Bearing

R eR: Resultant of vertical loadse: eccentricity of resultant


Case 3




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DC2

DC3

DC3

EV2

EV1

EV3

Leffqu_Bearing

R eR: Resultant of vertical loads


EHfootLShfoot

A

Wpctoe/2

Tstem_top/2



Wpcheel

Tstem_top/2

HR

W/3

HR

W/2

Wpcap/2

Heel

ToeC

LSv

DC1

Case 4

qall 10 ksf Allowable bearing capacity5.3.2.1 Case 3: Includes vertical and horizontal live load surcharge and surcharge dueto approach Slab

Mresist3 DCsv DCstemrect H5 DCstemtriang H6 DCpcap H7 EVsv EVSoilheelrect H8 EVSoilheeltriang H9 EVSoiltoe H10

ESsv ESvert H13 LSsv LSvert H12

Mresist3 712.47 kipftft

Movert3 EHsv REHpc d1 ESsv RESpc d2 LSsv RLSpc d3

Mnet3 Mresist3 Movert3 454.62kip ft

ft

Net moment at bottom of toe




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Vvert3 DCsv DCstemrect DCstemtriang DCpcap EVsv EVSoilheelrect EVSoilheeltriang EVSoiltoe

ESsv ESvert LSsv LSvert

Total Vertical Load

Vvert3 67.1kipft

Hence the eccentricity of the resultant, R, may be expressed as:

ecc3Wpcap

2

Mnet3Vvert3

3.1 ft Eccentricity from the centerline of the base

Find effective stress on the bottom of the base due to the applied vertical loads

Per AASHTO LRFD 11.6.3.2, where the wall is supported by a soil foundation, the vertical stress shall becalculated assuming a uniformly distributed pressure over an effective base length of (B - 2e) where e =distance from resultant to center of base

qeff3Vvert3

Wpcap 2 ecc34.95 ksf vertical stress on bottom of base per LRFD

Eq. 11.6.3.2-1

qtoe3Vvert3Wpcap

16 ecc3Wpcap

6.6 ksf Applied bearing pressure at toe due toCase 3 loading

qheel3Vvert3Wpcap

16 ecc3Wpcap

0.2 ksf Applied bearing pressure at heel due toCase 3 loading

5.3.2.2 Case 4: Includes vertical and horizontal live load surcharge and weight of approach slab andsidewalk transferred to the wall stem

Mresist4 DCsv DCtotslab H1 DCstemrect H5 DCstemtriang H6 DCpcap H7 EVsv EVSoilheelrect H8 EVSoilheeltriang H9 EVSoiltoe H10

LLsv LLped H11 LSsv LSvert H12


ft

Movert4 EHsv REHpc d1 LSsv RLSpc d3

Mnet4 Mresist4 Movert4 463.62kip ft

ft Net moment at bottom of toe

Vvert4 DCsv DCtotslab DCstemrect DCstemtriang DCpcap EVsv EVSoilheelrect EVSoilheeltriang EVSoiltoe

LLsv LLped LSsv LSvert

Total Vertical Load

Vvert4 69.18kipft




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Hence the eccentricity of the resultant, R, may be expressed as:

ecc4Wpcap

2

Mnet4Vvert4

3.17 ft Eccentricity from the centerline of the base



qeff4Vvert4

Wpcap 2 ecc45.16 ksf vertical stress on bottom of base per LRFD

Eq. 11.6.3.2-1

qtoe4Vvert4Wpcap

16 ecc4Wpcap

6.88 ksf Applied bearing pressure at toe due toCase 4 loading

qheel4Vvert4Wpcap

16 ecc4Wpcap

0.13 ksf Applied bearing pressure at heel due toCase 4 loading

qmax max qtoe4 qheel4 6.88 ksf Maximum applied bearing pressure5.3.2.3 Check against Bearing Capacity

qeff max qeff3 qeff4 5.16 ksf Maximum vertical stressCheckqall if qall qeff "OK" "N.G." Check bearing capacityCheckqall "OK"qtoe qtoe3 qeff3 qeff4if

qtoe4 otherwise

6.88 ksf Applied bearing pressure at toe

qheel qheel3 qeff3 qeff4ifqheel4 otherwise

0.13 ksf Applied bearing pressure at heel




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5.5 Stability Checks under Strength Limit StateFour Loads Cases are Considered:Case 1: Includes vertical and horizontal surcharge due to approach slab and horizontal live load surchargeCase 2: Includes horizontal surcharge due to live loadCase 3: Includes vertical and horizontal live load surcharge and surcharge due to approach SlabCase 4: Includes vertical and horizontal live load surcharge and weight of approach slab and sidewalktransferred to the wall stem

Table 2: Load Cases Required for Check for Stability and Bearing Capacity at Strength Limit State

Case 1 Case 2 Case 3 Case 4

DC1moment slab, sidewalk, parapet and railing 4.03 2.63 10.57 1.25

DC2 Rectangular portion of wall stem 4.08 2.63 10.71 0.90 0.90 1.25 1.25

DC3Triangular portion of wall stem DC dead load 2.04 3.67 7.48 0.90 0.90 1.25 1.25

DC4 Footing weight 11.85 9.88 117.02 0.90 0.90 1.25 1.25

EV1Rectangular portion of soil above heel 39.80 12.13 482.61 1.00 1.00 1.35 1.35

EV2Triangular portion of soil above heel 1.63 4.08 6.66 1.00 1.00 1.35 1.35

EV3 Soil above toe 0.48 1.00 0.48 1.00 1.00 1.35 1.35

EHstemHorizontal earth pressure at bottom of stem 15.04

EHfootHorizontal earth pressure at bottom of footing 21.09 -8.58 -180.98 1.50 1.50 1.50 1.50

ESvVertical surcharge due to moment slab and sidewalk 3.09 12.13 37.51 0.75 1.50

EShstemHoriz. surch. at bot. of stem due to moment slab & sidewalk 2.16

EShfootHoriz. surch. at bot. of footing due to moment slab & sidewalk 2.56 -12.88 -32.95 1.50 1.50

LSv Vertical surcharge live load 4.13 12.13 50.02 1.75 1.75

LShstemHorizontal live load surcharge at bottom of footing 2.88

LShfootHorizontal live load surcharge at bottom of stem 3.41 -12.88 -43.93 1.75 1.75 1.75 1.75

LLped Pedestrian Live Load 1.14 2.63 3.00 1.75

1.20 2.63 3.15 241.8 263.1 576.2 587.81.20 2.63 3.15 60.4 58.1 90.9 93.3

Net Moment Capacity, Kip-ft

MaximumVertical Load, Kips

Strength I FactorsStability BearingApplied Loads

Vert. Loads, Kips

Horiz. Loads, Kips

Arm, ft

Moment at the Toe, Kip-ft




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5.5.1 Check Eccentricity at Strength Limit State per AASHTO LRFD 11.6.3.3

5.5.1.1 Case 1: Includes vertical and horizontal surcharge due to approach slab and horizontal liveload surchargePu_ecc1 DCstrmin DCstemrect DCstemtriang DCpcap

EVstrmin EVSoilheelrect EVSoilheeltriang EVSoiltoe ESstrmin ESvert

Pu_ecc1 60.4kipft

Factored vertical load for eccentricity

Muresist_ecc1 DCstrmin DCstemrect H5 DCstemtriang H6 DCpcap H7 EVstrmin EVSoilheelrect H8 EVSoilheeltriang H9 EVSoiltoe H10

ESstrmin ESvert H13

Muresist_ecc1 639.56kip ft

ft

Muovert_ecc1 EHstrmax REHpc d1 ESstrmax RESpc d2 LSstrmax RLSpc d2 397.77kip ft

ft

Munet_ecc1 Muresist_ecc1 Muovert_ecc1 241.79kip ft

ft Factored moment for eccentricity

5.5.1.2 Case 2: Includes horizontal surcharge due to live load

Pu_ecc2 DCstrmin DCstemrect DCstemtriang DCpcap EVstrmin EVSoilheelrect EVSoilheeltriang EVSoiltoe

Pu_ecc2 58.08kipft

Factored vertical load for eccentricity




SHEET: 22 OF 59

Muresist_ecc2 DCstrmin DCstemrect H5 DCstemtriang H6 DCpcap H7 EVstrmin EVSoilheelrect H8 EVSoilheeltriang H9 EVSoiltoe H10

Muresist_ecc2 611.43kip ft

ft

Muovert_ecc2 EHstrmax REHpc d1 LSstrmax RLSpc d3 348.35kip ft

ft

Munet_ecc2 Muresist_ecc2 Muovert_ecc2 263.08kip ft

ft Factored moment for eccentricity

5.5.1.3 Check for Eccentricity

ecceccWpcap

2min

Munet_ecc1Pu_ecc1

Munet_ecc2Pu_ecc2

5.87 ft Eccentricity

Checkuplift if ecceccWpcap

3 "OK" "N.G."

Check eccentricity per AASHTO LRFD11.6.3.3Checkuplift "OK"

5.5.2 Factor of Safety Against Sliding at Strength Limit State per Article 11.6.3.6

Su 6 ksf Undrained shear strength


Pp Kp Soil Hkey 0 ksf Passive pressure due to shear key

Lateral Load due to passive pressure onshear keyRp

12

Pp Hkey 0kipft

5.5.2.1 Case 1: Includes vertical and horizontal surcharge due to approach slab and horizontal liveload surcharge

Pu_s1 Pu_ecc1 60.4kipft

Factored vertical load for sliding

v1Pu_s1Wpcap








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Fsliding1 EHstrmax REHpc ESstrmax RESpc LSstrmax RLSpc 41.44kipft




CheckFSsliding1 if FSsliding1 1.5 "OK" "N.G." CheckFSsliding1 "OK"5.5.2.2 Case 2: Includes horizontal surcharge due to live load

Pu_s2 Pu_ecc2 58.08kipft

Factored vertical load for sliding

v2Pu_s2Wpcap





Fsliding2 EHstrmax REHpc LSstrmax RLSpc 37.6kipft








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5.5.3 Factor of Safety Against Bearing Capacity Failure at Strength Limit State per AASHTO LRFD11.6.3.2quall 15 ksf

5.5.3.1 Case 3: Includes vertical and horizontal live load surcharge and surcharge due to approachSlabPu_b3 DCstrmax DCstemrect DCstemtriang DCpcap

EVstrmax EVSoilheelrect EVSoilheeltriang EVSoiltoe

ESstrmax ESvert LSstrmax LSvert

Pu_b3 90.9kipft

Factored vertical load for bearingresistance

Muresist_b3 DCstrmax DCstemrect H5 DCstemtriang H6 DCpcap H7 EVstrmax EVSoilheelrect H8 EVSoilheeltriang H9 EVSoiltoe H10

ESstrmax ESvert H13 LSstrmax LSvert H12

Muresist_b3 973.95kip ft

ft

Muovert_b3 EHstrmax REHpc d1 ESstrmax RESpc d2 LSstrmax RLSpc d3 397.77kip ft

ft

Munet_b3 Muresist_b3 Muovert_b3 576.19kip ft

ft Factored net moment for bearing

resistance

eccb3Wpcap

2

Munet_b3Pu_b3





SHEET: 25 OF 59



queff3Pu_b3

Wpcap 2 eccb37.17 ksf vertical stress on bottom of base per LRFD

Eq. 11.6.3.2-1

qutoe3Pu_b3Wpcap

16 eccb3Wpcap

9.55 ksf Maximum factored soil pressure at toe forCase 2 loading

quheel3Pu_b3Wpcap

16 eccb3Wpcap

0.34 ksf Minimum factored soil pressure at toe forCase 2 loading

5.5.3.2 Case 4: Includes vertical and horizontal live load surcharge and weight of approach slab andsidewalk transferred to the wall stemPu_b4 DCstrmax DCtotslab DCstemrect DCstemtriang DCpcap

EVstrmax EVSoilheelrect EVSoilheeltriang EVSoiltoe

LSstrmax LSvert LLstrmax LLped

Pu_b4 93.29kipft

Factored vertical load for bearingresistance

Muresist_b4 DCstrmax DCtotslab H1 DCstemrect H5 DCstemtriang H6 DCpcap H7 EVstrmax EVSoilheelrect H8 EVSoilheeltriang H9 EVSoiltoe H10

LSstrmax LSvert H12 LLstrmax LLped H11

Muresist_b4 936.15kip ft

ft

Muovert_b4 EHstrmax REHpc d1 LSstrmax RLSpc d3 348.35kip ft

ft

Munet_b4 Muresist_b4 Muovert_b4 587.8kip ft

ft Factored net moment for bearing

resistance

eccb4Wpcap

2

Munet_b4Pu_b4





SHEET: 26 OF 59



queff4Pu_b4

Wpcap 2 eccb47.4 ksf vertical stress on bottom of base per LRFD

Eq. 11.6.3.2-1

qutoe4Pu_b4Wpcap

16 eccb4Wpcap

9.85 ksf Maximum factored soil pressure at toe forCase 2 loading

quheel4Pu_b4Wpcap

16 eccb4Wpcap

0.41 ksf Minimum factored soil pressure at toe forCase 2 loading

5.5.3.3 Check against Bearing Capacity

queff max queff3 queff4 7.4 ksf Maximum vertical stressCheckqall if qall queff "OK" "N.G." Check bearing capacityCheckqall "OK"qutoe qutoe3 queff3 queff4if

qutoe4 otherwise

9.85 ksf Applied bearing pressure at toe

quheel quheel3 queff3 queff4ifquheel4 otherwise

0.41 ksf Applied bearing pressure at heel




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6. Design of Retaining Wall StemThe service and ultimate factored moment calculations for the Wall stem are taken at the bottom at point B,at the center of gravity of the Wall Stem in the horizontal direction

A

HeelB

TruncatedWall Stem

6.1 Combination Factors for Forces applied on the Bottom of Wall StemThe stem loads that are required include:Horizontal distances "H" are measured from the c.g. of the stem at the bottom

The c.g. of the stem from its exterior face is:

xcstemTstem_top

2 Tstem_top Tstem_bot Tstem_bot23 Tstem_top Tstem_bot

Center of gravity of the truncated wall stemfrom the exterior face of the wallxcstem 0.97 ft

DCtotslab 4.03kipft

H1 xcstemTstem_top

2 0.35 ft

DCstemrect 4.08kipft

H5 xcstemTstem_top

2 0.35 ft

DCstemtriang 2.04kipft

H6 xcstem Tstem_topTstem_bot Tstem_top

3

0.69 ft

LLped 1.14kipft

H11 xcstemTstem_top

2 0.35 ft

ESvert 3.09kipft

H12 Tstem_topTstem_bot Wpcheel Tstem_top

2 xcstem 8.53 ft

LSvert 4.13kipft

H13 H12 8.53 ft




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REHstem 15.04kipft

d1HSoilheel

37.25 ft

RESstem 2.16kipft

d2HSoilheel

210.88 ft

RLSstem 2.88kipft

d3HSoilheel

210.88 ft

6.1.1 Retaining Wall Stem Strength I Force Effects

The factored longitudinal shear force at the critical section of the stem is:

VustemstrI EHstrmax REHstem ESstrmax RESstem LSstrmax RLSstemFactored shear at bottom of wall stem(Strength I)VustemstrI 30.85

kipft

The factored moment at the base of the stem is:

MustemstrI DCstrmax DCstemrect H5 DCstemtriang H6 EHstrmax REHstem d1 ESstrmax RESstem d2 LSstrmax RLSstem d3

MustemstrI 253.7kip ft

ft Factored Moment at bottom of wall stem

(Strength I)

6.1.2 Retaining Wall Stem Extreme Event II Force Effects

The following load factors will be used to calculate the force effects for Extreme Event II (AASHTO LRFDTables 3.4.1-1 and 3.4.1-2):

DCEEII 1.25 EHEEII 1.50 ESEEII 1.50 LSEEII 0.5 CTEEII 1.00The factored longitudinal shear force at the base of the stem is (maximum of Case 1 and Case 2):

VustemEEII EHEEII REHstem ESEEII RESstem LSEEII RLSstem

VustemEEII 27.25kipft

The factored moment at the base of the stem is (Case 1):

MustemEEII DCEEII DCstemrect H5 DCstemtriang H6 EHEEII REHstem d1 ESEEII RESstem d2 LSEEII RLSstem d3

MustemEEII 214.52kip ft

ft




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6.1.3 Retaining Wall Stem Service I Force Effects

The service longitudinal shear force at the base of the stem is:

VustemservI EHsv REHstem ESsv RESstem LSsv RLSstem

VustemservI 20.09kipft

The service moment at the base of the stem is:

Mustem_servI DCsv DCstemrect H5 DCstemtriang H6 EHsv REHstem d1 ESsv RESstem d2 LSsv RLSstem d2

Mustem_servI 163.91kip ft

ft

6.1.4 Maximum Force Effects

The maximum factored stem shear force and moment are:

Vustem_max max VustemstrI VustemEEII Maximum factored stem shear forceVustem_max 30.85

kipft

Mustem_max max MustemstrI MustemEEII Maximum factored stem momentMustem_max 253.7

kip ftft

6.2 Design the Reinforcement for Retaining Wall Stem6.2.1 Applied Loads:

Applied Service limit state factoredmomentMustem_servI Mustem_servI 1 ft 163.91 ft kipApplied maximum Strength limit statefactored momentMustem_max Mustem_max 1 ft 253.7 kip ftApplied maximum Strength limit statefactored shearVustem_max Vustem_max 1 ft 30.85 kip




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6.2.2 Design for Flexure

6.2.2.1 Primary Flexural ReinforcementNote: The use of epoxy coated reinforcement is requiredAccording to AASHTO 5.7.3.3.2 unless otherwise specified, at any section of a flexural component, theamount of flexural reinforcement shall be adequate to develop a factored flexural resistance, Mr, at least equalto the lesser of:

The cracking moment (Mcr) determined from Equation 5.7.3.3.2-11.33 times the factored moment required by the applicable strength load combinations specified inAASHTO Table 3.4.1-1

Mustem_max 253.7 kip ft Applied maximum Strength limit statefactored moment at wall stem per foot

b 12in Width of concrete strip

Igb Tstem_bot Tformliner 3

12 Ig 27000 in4 Moment of inertia

ytTstem_bot Tformliner

2 yt 15 in Depth at mid-section

Section modulus for the extreme fiber ofthe composite section where tensile stressis caused by externally applied loads(AASHTO 5.7.3.3.2)

ScIgyt

1.8 103 in3

Flexural cracking variability factor(AASHTO 5.7.3.3.2)1 1.6Modulus of rupture for cracking momentcalculations (AASHTO 5.4.2.6)fr 0.24 f'c ksi 0.54 ksiRatio of specified minimum yield strengthto ultimate tensile strength for A615 Grade60 reinforcement (AASHTO 5.7.3.3.2)

3 0.75

Cracking moment (simplified equation -neglects prestressing and noncompositeterms) (AASHTO LRFD Eqn. 5.7.3.3.2-1)

Mcr 3 1 fr Sc 96.6 kip ftMustem_des Mcr Mustem_max Mcrif

Mustem_max otherwise

Mustem_des 253.7 kip ft Minimum design momentDepth to tensile steel reinforcementmeasured from extreme compression fiberof structural wall. For the calculation ofeffective depth, d, assume #10 bar.

dws Tstem_bot12

1.27in Tformliner Covers dws 27.37 in

RnMustem_des

0.9 b dws20.38 ksi Coefficient of resistance




SHEET: 31 OF 59

Calculated ratio of steel for the ultimatemoment in the wall stem 0.85

f'cfy

1 12Rn

0.85f'c

0.0066

Calculated amount of steel for the ultimatemoment in the wall stemAs b dws 2.16 in

2

bal 0.851 f'c

fy 87 ksi

87 ksi fy

0.0335 Balanced ratio of steel reinforcement

max 0.75 bal 0.0252 Maximum ratio of steelFor practical purposes a steel ratio up to1/2max = 1/2x0.75xbal = 0.375bal canalso be used

pract12max 0.0126

Standard reinforcing bar number providedfrom AASHTO Appendix B, Table B.4,selected for the wall stem

Barws 10

Bar# Dia(in) Area(in2)3 0.375 0.114 0.5 0.205 0.625 0.316 0.75 0.447 0.875 0.68 1.00 0.799 1.128 1.0010 1.27 1.2711 1.41 1.56

dbws db1 in 1.27 in Diameter of primary reinforcement

Abws Ab1 in2 1.27 in2 Area of primary reinforcement

Calculated spacing of momentreinforcementSws 12

AbwsAs

in 7.05 in

Sws 6in Selected spacing of moment reinforcement

AswsAbwsSws

12 in 2.54 in2 Area of primary reinforcement

Approximate depth of compression blockaws

Asws fy0.85 f'c b

2.99 inEquivalent rectangular stress blockreduction factor = 0.85 for f`c




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6.2.2.2 Check Moment StrengthTensile strain in concrete section at tensilesteel reinforcement where a strain of 0.005is the limiting strain to ensure the concretemember in flexure will be tensioncontrolled (AASHTO Figure C5.5.4.2.1-1)

t 0.003dws cws

cws

0.019

checkstrain "Tension Controlled" t 0.005if"Not Tension Controlled" otherwise

checkstrain "Tension Controlled"

f 0.90 t 0.005if

0.65 0.15dwscws

1

0.002 t 0.005if

0.75 otherwise

LRFD reduction factor for bending fornon-prestressed members (AASHTO Eqn.5.5.4.2.1-2)

f 0.9Flexural resistance for an equivalent 1ftwidth of deck (AASHTO 5.7.3.2)Mnstem f Asws fy dws

aws2

295.7 kip ft

Mustem_des 253.7 kip ft Minimum design moment

checkflexure "O.K." Mnstem Mustem_desif"N.G." otherwise

checkflexure "O.K."

6.2.2.3 Check for Minimum Reinforcement

Mustem_max 253.7 kip ft Total Factored moment at Toe per FootCracking moment (simplified equation -neglects prestressing and noncompositeterms) (AASHTO LRFD Eqn. 5.7.3.3.2-1)

Mcr 96.6 kip ft

checkminflexure "O.K." Mnstem min 1.33Mustem_max Mcr if"N.G." otherwise

checkminflexure "O.K."




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6.2.2.4 Crack Control

6.2.2.4.1 Stress at Tensile ReinforcementThe control of cracking by distribution of reinforcement must be checked. According to AASHTOLRFD Article 5.7.3.4, crack control reinforcement is required where tension in the cross-sectionexceeds 80% of the modulus of rupture.

Applied Service limit state factoredmomentMustem_servI 163.91 kip ftModular ratio of steel to concrete moduli ofelasticityn

EsEc

6.76

Depth to tension steel measured fromextreme compressive fiber of the concretesection

dws 27.37 in

Area of steel in compression. Assume #6at 12 in spacing CTCAsneg 0.44in

2 Barshtempvert 6Depth to compressive reinforcing steelmeasured from extreme compressive fiberof the concrete section

d' Covers12

0.75 in 2.38 in Sshtempvert 12in

Sum of the statical momentsabout the neutral axisf c( )

b c22

n Asws n 1( ) Asneg c n Asws dws n 1( ) Asneg d'Depth to the neutral axis from extremecompressive fiber of structural slabc root f c( ) c 0in Tstem_bot Tformliner 7.42 in

Moment of inertia of the doublyreinforced transformed cracked sectionIcr

b c33

n Asneg d' c( )2 n Asws dws c 2 8.55 103 in4Distance from neutral axis to tensile steelreinforcementyws dws c 19.95 in

Tensile stress at tensile steelreinforcements n

Mustem_servI ywsIcr

31.06 ksi

6.2.2.4.2 Required Spacing for Crack Control

Maximum Spacing per LRFD 5.7.3.4

Note: AASHTO LRFD 5.7.3.4 states that when tension in the cross-section exceeds 80% of the modulus of rupture, specified in Article 5.4.2.6, at applicable service limit state load combination, the concrete deck slab main reinforcement must meet the following spacing limitations.

Equivalent deck section modulus atmidspanS Sc 1.8 10

3 in3

Tensile stress at extreme deck due toService I Load combinationsfMserv

Mustem_servIS

1.09 ksi




SHEET: 34 OF 59

Checkvalidity "LRFD 5.7.3.4 is Valid" fMserv 0.8 0.24 f'c ksi if"LRFD 5.7.3.4 is Not Valid" otherwise

Checkvalidity "LRFD 5.7.3.4 is Valid"

Thickness of concrete cover measuredfrom extreme tension fiber to center of theflexural reinforcement located closestthereto (AASHTO 5.7.3.4)

dc Coversdbws

2 2.64 in

Class 2 exposure factor for decks andsubstructures exposed to water (AASHTO5.7.3.4)

cf 0.75

s 1dc

0.7 Tstem_bot Tformliner dc 1.14Maximum spacing of tensile reinforcingbars allowed to control flexural cracking ofconcrete for service loads (AASHTO Eq.5.7.3.4-1)

Smax1700 cf

ssksi

2

dcin

in 9.59 in


Note: AASHTO LRFD 5.10.3.2 states that the spacing of the reinforcement in walls and slabs shall notexceed 1.5 times the thickness of the member or 18 in.

Smax2 min Tstem_bot Tformliner 18in 18 in Maximum spacing of steel reinforcing barsallowed per AASHTO LRFD 5.10.3.2

Smax min Smax1 Smax2 9.59 in Maximum allowable spacing of steelreinforcing bars

Check that the provided spacing is less than the maximum allowable spacing:

checklim "OK" Sws Smaxif"NG" otherwise

checklim "OK"




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6.2.3 Shrinkage and Temperature Reinforcement per AASHTO LRFD Article 5.10.8

b Tstem_bot Tformliner 30 in thickness of stem wall at bottom

h Hstem 261 in total height of stem wall Amount of steel reinforcement required fortemperature and shrinkage located at bothsides of the stem

As_shtemp max 0.11in2 min

1.3 b h2 b h( ) fy

kipin

0.6in2

0.291 in2

Barshtempws 5 Selected steel bar size for temperatureand shrinkage reinforcement

Bar# Dia(in) Area(in2)3 0.375 0.114 0.5 0.205 0.625 0.316 0.75 0.447 0.875 0.68 1.00 0.799 1.128 1.0010 1.27 1.27

Abshtempws Ab1 in2 0.31 in2 Area of single reinforcement

Maximum spacing fortemperature and shrinkagereinforcement in the stem

Sshtempws min 18in 3 Tstem_top Tformliner 12in AbshtempwsAs_shtemp

12.76 in

Selected spacing for temperature andshrinkage reinforcement at both sides ofthe stem

Sshtempws 12in




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6.3 Design for Shear:The critical section for shear is located at the bottom of the wall stem (top face of footing) but not at distancedv since the primary flexural reinforcement are located in the face of the stem wall where the load is applied

6.3.1 Simplified procedure for nonprestressed sections according to AASHTO LRFD 5.8.3.4.1

tv Tstem_bot Tformliner Thickness of the wall stem value for sections less than 16" inthickness LRFD [5.8.3.4.1] 2.0

tv 30 in if tv less than 16 in, then 45deg value for sections less than 16" in

thickness LRFD [5.8.3.4.1]

bv 12in width of concrete stripEffective shear depth (AASHTO LRFDArticle 5.8.2.9)dvstem max dws

aws2

0.9dws 0.72 tv

25.87 in

Nominal shear resistance (1) (AASHTOLRFD Eqns. 5.8.3.3-3 and 5.8.3.3-1)Vn1 0.0316 f'c ksi bv dvstem Vn1 43.87 kip

Vn2 0.25 f'c bv dvstem Vn2 388.06 kip Nominal shear resistance (2) (AASHTOLRFD Eqn. 5.8.3.3-2)

The nominal shear resistance is the lesser of:

Nominal shear resistance (AASHTO LRFDArticle 5.8.3.3)Vn min Vn1 Vn2 Vn 43.87 kipResistance factor for shear (AASHTOLRFD Article 5.5.4.2.1)v 0.9Factored shear resistance (AASHTOLRFD Eqn. 5.8.2.1-2)Vr v Vn Vr 39.49 kip

Factored shear at critical section of wallstem (Strength I)Vustem_max 30.85 ft

kipft

checklim "OK" Vr Vustem_maxif"N.G." otherwise

checklim "OK"

Note:If the Nominal shear resistance is not adequate using =2 and =45 deg, or the concrete section does notmeet the requirements for simplified procedure, use the General procedure of AASHTO LRFD Article 5.8.3.4.2




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6.3.2 General Procedure according to AASHTO LRFD 5.8.3.4.2

As Asws 2.54 in2 Area of nonprestressed steel on the

flexural tension side of the memberNu 0 Factored axial load taken as positive if

tensile and negative if compressive (kip)

Vu Vustem_max 30.85 kip Factored shear at critical section of wallstem (kip)

See LRFD Figure 5.8.3.4.2-3: Definition ofcrack spacing parametersx dvstem 25.87 in

Mucs Mustem_maxAbsolute value of factored moment atcritical section for shearMucs 253.7 kip ft

Mu max Mucs Vu dvstem 253.7 kip ftNet longitudinal tensile strain in thesection at the centroid of tensionreinforcement per LRFD Eq. 5.8.3.4.2-4ss

Mudvstem

0.5Nu Vu

Es As2.02 10 3

If the value of s calculated from Eq.5.8.3.4.2-4 is negative, it should be takenas zero or the value should be recalculatedwith the denominator of Eq. 5.8.3.4.2-4replaced by (EAs + EpAps + EoAc,).However, s should not be taken as lessthan -0.40 x 10-3.

s 0 ss 0ifss otherwise

2.02 10 3

sxe max 12in min sx1.38

agin

0.63 80in

25.87 in crack spacing parameter per LRFD Eq.

5.8.3.4.2-5

29 3500s 36.06

4.8

1 750 s 51

39sxein

1.5 for sections not containing at least theminimum amount of transversereinforcement (LRFD Eq. 5.8.3.4.2-2)

Vn1 0.0316 f'c ksi bv dvstem 32.95 kip Nominal shear resistance of a concretemember LRFD [5.8.3.3]

Vn2 0.25 f'c bv dvstem 388.06 kip




SHEET: 38 OF 59


Vn min Vn1 Vn2 Vn 32.95 kipVr v Vn Vr 29.66 kip Factored shear resistance

Vustem_max 30.85 kip Factored shear resistance (AASHTOLRFD Eqn. 5.8.2.1-2)

checklim "OK" Vr Vustem_maxif"N.G." otherwise

checklim "N.G."

Designer note: V of 29.66 is approximately equal to V of 30.85 kip. By inspection, it is OK.

7. Design of Retaining Wall FootingThe flexural reinforcement must be designed at two critical sections for retaining wall footing. The twosections include the back and front faces of the stem (AASHTO LRFD Article 5.13.3.4).The service and ultimate factored shear and moment of the Heel and Toe are calculated at the rear and frontface of the Wall Stem, respectively.

Neglect abovesoil pressure

Toe Heel

wtoe1qmin

qmaxqheel 0.13 ksfquheel 0.41 ksf

qtoe 6.88 ksfqutoe 9.85 ksf

7.1 Heel Design for Flexure:7.1.1 Applied Moment at Heel

The applied vertical loads on the heel of the footing are::

Rectangular portion of soil above heelvertical dead load [EV]EVSoilheelrect 39.8

kipft

Vertical load due to uniform surchargefrom moment slab applied per linear foot ofwall [ESv]

ESvert 3.09kipft




SHEET: 39 OF 59

LSvert 4.13kipft

Vertical component of live load surcharge[LSv]

The bearing pressure at the back face of the stem is calculated as:

qbfwall qheelqtoe qheel

WpcapWpcheel Bearing pressure in the heel at the face of

the wall stem (Service I)

qbfwall 5.34 ksf

qubfwall quheelqutoe quheel

WpcapWpcheel Factored Bearing pressure in the heel t the

face of the wall stem (Strength I)

qubfwall 7.52 ksf

The maximum factored moment applied due to Strength I Limit State on the Heel Footing is:

Muheel_strI DCstrmax conc Dpcap Wpcheel EVstrmax EVSoilheelrect


Wpcheel2

ft

quheel Wpcheel 12qubfwall quheel

2

Wpcheel3

Wpcheel ft

Muheel_strI 327.5 kip ftThe maximum service moment applied due to Service I Limit State on the Heel Footing is:

Muheel_servI DCsv conc Dpcap Wpcheel EVsv EVSoilheelrect

ESsv ESvert LSsv LSvert

Wpcheel2

ft

qheel Wpcheel 12qbfwall qheel

2

Wpcheel3

Wpcheel ft

Muheel_servI 211.52 kip ft


Muheel_strI 327.505 kip ft Total Factored Moment at Heel per Foot

Muheel_servI 211.519 kip ft Total Service Moment at Heel per Foot




SHEET: 40 OF 59

7.1.2.1 Primary Flexural Reinforcement (Top of Heel Footing)

Note: The use of epoxy coated reinforcement is required

According to AASHTO 5.7.3.3.2 unless otherwise specified, at any section of a flexural component, theamount of flexural reinforcement shall be adequate to develop a factored flexural resistance, Mr, at least equalto the lesser of:


Muheel_strI 327.5 kip ft Total Factored Moment at Heel per Foot b 12in Width of concrete striptft Dpcap 48 in

Igb tft

312

Ig 110592 in4 Moment of inertia

yttft2

yt 24 in Depth at mid-sectionSection modulus for the extreme fiber ofthe composite section where tensile stressis caused by externally applied loads(AASHTO 5.7.3.3.2)

ScIgyt

4.61 103 in3

Flexural cracking variability factor(AASHTO 5.7.3.3.2)1 1.6

fr 0.24 f'c ksi 0.54 ksi Modulus of rupture for cracking momentcalculations (AASHTO 5.4.2.6)

Ratio of specified minimum yield strengthto ultimate tensile strength for A615 Grade60 reinforcement (AASHTO 5.7.3.3.2)

3 0.75


Mcr 3 1 fr Sc 247.29 kip ftMuheel_des Mcr Muheel_strI Mcrif

Muheel_strI otherwise

Muheel_des 327.5 kip ft Minimum design moment

Depth to tensile steel reinforcementmeasured from extreme compression fiberof concrete section. For the calculation ofeffective depth, d, assume #10 bar.

dheel tft12

1.27 in Coverft 45.37 in




SHEET: 41 OF 59

RnMuheel_strI

0.9 b dheel20.18 ksi Coefficient of resistance

Calculated ratio of steel for the ultimatemoment in the heel footing 0.85

f'cfy

1 12Rn

0.85f'c

0.003

Calculated amount of steel for the ultimatemoment in the heel footingAs b dheel 1.64 in

2

bal 0.0335 Balanced ratio of steel reinforcement


pract12max 0.0126


Barheel 10

Bar# Dia(in) Area(in2)3 0.375 0.114 0.5 0.205 0.625 0.316 0.75 0.447 0.875 0.68 1.00 0.799 1.128 1.0010 1.27 1.2711 1.41 1.56

dbheel db1 in 1.27 in Diameter of primary reinforcement in theheel

Abheel Ab1 in2 1.27 in2 Area of single primary reinforcement in the

heel

Calculated spacing of momentreinforcementSheel 12

AbheelAs

in 9.3 in

Sheel 6in Selected Spacing of momentreinforcement

AsheelAbheelSheel

12 in 2.54 in2 Area of primary reinforcement in the heel

Approximate depth of compression blockaheel

Asheel fy0.85 f'c b

2.99 in

Equivalent rectangular stress blockreduction factor = 0.85 for f`c




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Depth to neutral section in concretesection (AASHTO 5.5.4.2.1)cheel

aheel1

3.74 in

Depth to tensile steel reinforcementmeasured from extreme compression fiberof concrete section

dheel tftdbheel

2 Coverft 45.37 in

7.1.2.2 Check Moment StrengthTensile strain in concrete section at tensilesteel reinforcement where a strain of 0.005is the limiting strain to ensure the concretemember in flexure will be tensioncontrolled (AASHTO Figure C5.5.4.2.1-1)

t 0.003dheel cheel

cheel

0.0334

checkstrain "Tension Controlled" t 0.005if"Not Tension Controlled" otherwise

checkstrain "Tension Controlled"

f 0.90 t 0.005if

0.65 0.15dheelcheel

1

0.002 t 0.005if

0.75 otherwise

LRFD reduction factor for bending fornon-prestressed members (AASHTO Eqn.5.5.4.2.1-2)

f 0.9Flexural resistance for an equivalent 1ftwidth of deck (AASHTO 5.7.3.2)Mnheel f Asheel fy dheel

aheel2

501.44 kip ft

Muheel_des 327.5 kip ft Minimum design moment

checkflexure "O.K." Mnheel Muheel_desif"N.G." otherwise

checkflexure "O.K."

7.1.2.3 Check for Minimum Reinforcement per AASHTO 5.7.3.3.2

Muheel_strI 327.5 kip ft Total Factored moment at Toe per FootCracking moment (simplified equation -neglects prestressing and noncompositeterms) (AASHTO LRFD Eqn. 5.7.3.3.2-1)

Mcr 247.29 kip ft

checkminflexure "O.K." Mnheel min 1.33Muheel_strI Mcr if"N.G." otherwise





SHEET: 43 OF 59


7.1.2.4.1 Stress at Tensile ReinforcementThe control of cracking by distribution of reinforcement must be checked. According to AASHTO LRFDArticle 5.7.3.4, crack control reinforcement is required where tension in the cross-section exceeds 80% of themodulus of rupture.

Applied Service limit state factoredmomentMuheel_servI 211.52 kip ft

Modular ratio of steel to concrete moduli ofelasticityn

EsEc

6.76Depth to tension steel measured fromextreme compressive fiber of concretesection

dheel 45.37 in

Asneg 0 Area of steel in compression. Notconsidered in the calculations.

Depth to compressive reinforcing steelmeasured from extreme compressive fiberof the concrete section

d' Coverfb12

1.27 in


b c22

n Asheel n 1( ) Asneg c n Asheel dheel n 1( ) Asneg d'

Depth to the neutral axis from extremecompressive fiber of structural slabc root f c( ) c 0in tft 10.06 in

Moment of inertia of the doublyreinforced transformed crackedsection

Icrb c3

3n Asneg d' c( )2 n Asheel dheel c 2 2.55 104 in4

Distance from neutral axis to tensile steelreinforcementyheel dheel c 35.31 in


Muheel_servI yheelIcr

23.79 ksi




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7.1.2.4.2 Required Spacing for Crack ControlMaximum Spacing per LRFD 5.7.3.4

Note: AASHTO LRFD 5.7.3.4 states that when tension in the cross-section exceeds 80% of the modulus ofrupture, specified in Article 5.4.2.6, at applicable service limit state load combination, the concretedeck slab main reinforcement must meet the following spacing limitations.


3 in3

Tensile stress at extreme deck due toService I Load combinationsfMserv

Muheel_servIS

0.55 ksi


Checkvalidity "LRFD 5.7.3.4 is Valid"

Thickness of concrete cover measuredfrom extreme tension fiber to center of theflexural reinforcement located closestthereto (AASHTO 5.7.3.4)

dc Coverftdbheel

2 2.64 in


cf 0.75

s 1dc

0.7 tft dc 1.08Maximum spacing of tensile reinforcingbars allowed to control flexural cracking ofconcrete for service loads (AASHTO Eq.5.7.3.4-1)

Smax1700 cf

ssksi

2

dcin

in 15.11 in



Smax2 min tft 18in 18 in Maximum spacing of steel reinforcing barsallowed per AASHTO LRFD 5.10.3.2

Smax min Smax1 Smax2 15.11 in Maximum allowable spacing of steelreinforcing bars


checklim "OK" Sheel Smaxif"N.G." otherwise

checklim "OK"




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7.2 Toe Design for Flexure7.2.1 Applied Moment at Toe

The bearing pressure at the front face of the stem is:

Bearing pressure in the toe at the face ofthe wall stem (Service I)qffwall

qheel qtoeWpcap

Wpctoe qtoe 6.19 ksfFactored Bearing pressure in the toe t theface of the wall stem (Strength I)quffwall

quheel qutoeWpcap

Wpctoe qutoe 8.81 ksfThe loads that are required include:

DLpcap_toe conc Dpcap Wpctoe 1.2kipft

self-weight of toe footing

The maximum factored moment applied due to Strength I Limit State on the Toe Footing is:

Mutoe_strI 1ft DCstrmin DLpcap_toeWpctoe

2

quffwall Wpctoe 12qutoe quffwall

2

2Wpctoe3

Wpctoe

Mutoe_strI 17.93 kip ftThe maximum service moment applied due to Service I Limit State on the Toe Footing is:

Mutoe_servI 1ft DCsv DLpcap_toeWpctoe

2

qffwall Wpctoe 12qtoe qffwall

2

2Wpctoe3

Wpctoe

Mutoe_servI 12.1 kip ft

Once the maximum moment at the critical section is known, the same procedure that was used for the stemto calculate the flexural reinforcement must be followed. The footing toe flexural reinforcement is locatedlongitudinally in the bottom of the footing since the bottom of footing is in tension at the critical section.These bars will extend from the back of the heel to the front of the toe taking into account the clear cover.


Mutoe_strI 17.934 kip ft Total Factored Moment at Toe per Foot

Mutoe_servI 12.102 kip ft Total Service Moment at Toe per Foot




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7.2.2.1 Primary Flexural Reinforcement (Bottom of Toe Footing)

Note: The use of epoxy coated reinforcement is required

According to AASHTO 5.7.3.3.2 unless otherwise specified, at any section of a flexural component, theamount of flexural reinforcement shall be adequate to develop a factored flexural resistance, Mr, at least equalto the lesser of:


Mutoe_strI 17.934 kip ft Total Factored Moment at Toe per Foot

b 12in Width of concrete strip

tft Dpcap 48 in Thickness of the footing

Igb tft

312

Ig 110592 in4 Moment of inertia

yttft2

yt 24 in Depth at mid-sectionSection modulus for the extreme fiber ofthe composite section where tensile stressis caused by externally applied loads(AASHTO 5.7.3.3.2)

ScIgyt

in3

Flexural cracking variability factor(AASHTO 5.7.3.3.2)1 1.6

fr 0.24 f'c ksi 0.54 ksi Modulus of rupture for cracking momentcalculations (AASHTO 5.4.2.6)

Ratio of specified minimum yield strengthto ultimate tensile strength for A615 Grade60 reinforcement (AASHTO 5.7.3.3.2)

3 0.75


Mcr 3 1 fr Sc 247.29 kip ft

Mutoe_des Mcr Mutoe_strI McrifMutoe_strI otherwise

Mutoe_des 247.29 kip ft Minimum design moment




SHEET: 47 OF 59

Depth to tensile steel reinforcementmeasured from extreme compression fiberof concrete section. For the calculation ofeffective depth, d, assume #10 bar.

dtoe tft12

1.27in Coverfb 3.7 ft

RnMutoe_des

0.9 b dtoe20.14 ksi Coefficient of resistance

Calculated ratio of steel for the ultimatemoment in the toe footing 0.85

f'cfy

1 12Rn

0.85f'c

0.00237

Calculated amount of steel for the ultimatemoment in the toe footingAs b dtoe 1.26 in

2

bal 0.0335 Balanced ratio of steel reinforcement


pract12max 0.0126


Bartoe 10

Bar# Dia(in) Area(in2)3 0.375 0.114 0.5 0.205 0.625 0.316 0.75 0.447 0.875 0.68 1.00 0.799 1.128 1.0010 1.27 1.2711 1.41 1.56

dbtoe db1 in 1.27 in Diameter of primary reinforcement in thetoe footing

Abtoe Ab1 in2 1.27 in2 Area of single primary reinforcement

Calculated spacing of momentreinforcement Stoe 12

AbtoeAs

in 12.1 in

Stoe 6in Selected Spacing of momentreinforcement

Area of primary reinforcement in the toefootingAstoe

AbtoeStoe

12 in 2.54 in2




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atoeAstoe fy0.85 f'c b

2.99 in Approximate depth of compression blockEquivalent rectangular stress blockreduction factor = 0.85 for f`c




SHEET: 49 OF 59

7.2.2.3 Check for Minimum Reinforcement per AASHTO 5.7.3.3.2

Mutoe_strI 17.93 kip ft Total Factored moment at Toe per Foot


Mcr 247.29 kip ft

checkminflexure "O.K." Mntoe min 1.33Mutoe_strI Mcr if"N.G." otherwise



7.2.2.4.1 Stress at Tensile ReinforcementThe control of cracking by distribution of reinforcement must be checked. According to AASHTO LRFDArticle 5.7.3.4, crack control reinforcement is required where tension in the cross-section exceeds 80% of themodulus of rupture.

Mutoe_servI 12.1 kip ft Applied Service limit state factoredmoment

Modular ratio of steel to concrete moduli ofelasticityn

EsEc

6.76Depth to tension steel measured fromextreme compressive fiber of concretesection

dtoe 44.37 in

Area of steel in compression. Notconsidered in the calculationAsneg 0

Depth to compressive reinforcing steelmeasured from extreme compressive fiberof the concrete section

d' Coverft12

1.27in 2.64 in


b c22

n Astoe n 1( ) Asneg c n Astoe dtoe n 1( ) Asneg d'Depth to the neutral axis from extremecompressive fiber of structural slabc root f c( ) c 0in tft 9.93 in

Moment of inertia of the doublyreinforced transformed cracked sectionIcr

b c33

n Asneg d' c( )2 n Astoe dtoe c 2 2.43 104 in4Distance from neutral axis to tensile steelreinforcementytoe dtoe c 34.43 in


Mutoe_servI ytoeIcr

1.39 ksi




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7.2.2.4.2 Required Spacing for Crack Control


Note: AASHTO LRFD 5.7.3.4 states that when tension in the cross-section exceeds 80% of the modulus ofrupture, specified in Article 5.4.2.6, at applicable service limit state load combination, the concretedeck slab main reinforcement must meet the following spacing limitations.


3 in3Tensile stress at extreme deck due toService I Load combinationsfMserv

Mutoe_servIS

0.03 ksi


Checkvalidity "LRFD 5.7.3.4 is Not Valid"Thickness of concrete cover measuredfrom extreme tension fiber to center of theflexural reinforcement located closestthereto (AASHTO 5.7.3.4)

dc Coverfbdbtoe

2 3.63 in


cf 0.75

s 1dc

0.7 tft dc 1.12Maximum spacing of tensile reinforcingbars allowed to control flexural cracking ofconcrete for service loads (AASHTO Eq.5.7.3.4-1)

Smax1700 cf

ssksi

2

dcin

in 330.22 in



Smax2 min tft 18in 18 in Maximum spacing of steel reinforcing barsallowed per AASHTO LRFD 5.10.3.2

Smax min Smax1 Smax2 18 in Maximum allowable spacing of steelreinforcing bars


checklim "OK" Stoe Smaxif"N.G." otherwise

checklim "OK"




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7.3 Shrinkage and Temperature Reinforcement per AASHTO LRFD Article 5.10.8

b Wpcap 237 in total width of footing from outside tooutside

h tft 48 in thickness of footingAmount of steel reinforcement required fortemperature and shrinkageAs_shtemp max 0.11in

2 min1.3 b h

2 b h( ) fykipin

0.6in2

0.432 in2

Selected steel bar size for temperatureand shrinkage reinforcement located in thetransverse top and bottom of footing

Barshtempft 7

Bar# Dia(in) Area(in2)3 0.375 0.114 0.5 0.205 0.625 0.316 0.75 0.447 0.875 0.68 1.00 0.799 1.128 1.0010 1.27 1.27

Abshtemp Ab1 in2 0.6 in2 Area of single reinforcement

Maximum spacing for temperature andshrinkage reinforcementSshtempft min 18in 3 tft 12in

AbshtempAs_shtemp

16.65 in

Selected spacing for temperature andshrinkage reinforcementSshtempft 12in




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7.4 Design for ShearShear design in retaining wall footings consists of having adequate resistance against one-way andtwo-way actions. (Two-way shear does not apply for the spread footing). The design shear is taken at acritical section. For retaining walls, one-way action is checked in the toe and heel. The factored shearforce at the critical section is computed by cutting the footing at the critical section and summing theloads that are outside the critical section.

7.4.1 One-Way Shear Force at Footing Heel

For one-way action in the retaining wall footing heel the critical section is taken as follows:

dheel tft Coverftdbheel

2 dheel 45.37 in Assumed effective depth

aheel 2.99 in Depth of equivalent stress block at heel

bv 12in Effective web width per 1ft strip

dvheel max dheelaheel

2 0.9dheel 0.72 tft

Effective shear depth (AASHTO LRFDArticle 5.8.2.9)

The bearing pressure at distance dv from the back face of the stem is calculated as:

Bearing stress in the heel at the face of thewall stem (Service I)qbfwall 5.34 ksfBearing stress in the heel at the face ofthe wall stem (Strength I)qubfwall 7.52 ksf

The factored one-way shear force and Moment at the retaining wall footing heel critical section on a per footbasis is:

Vuheel DCstrmax conc Dpcap Wpcheel EVstrmax EVSoilheelrect


qubfwall quheel2

Wpcheel

1 ft

Vuheel 22.82 kipMuheel_strI 327.5 kip ft




SHEET: 53 OF 59

7.4.2 One-Way Shear Force at Footing Toe

For one-way action in the retaining wall footing toe, the critical section is taken as follows:

dtoe tft Coverfbdbtoe

2 dtoe 44.37 in Assumed effective depth

atoe 2.99 in Depth of equivalent stress block at toe

Effective shear depth (AASHTO LRFDArticle 5.8.2.9)dvtoe max dtoe

atoe2

0.9dtoe 0.72 tft

dvtoe 42.87 in

bv 12in Effective web width per 1ft stripThe factored one-way shear force at the retaining wall footing toe critical section on a per foot basis is:

Vutoe 1ft DCstrmin DLpcap_toequtoe quffwall

2Wpctoe

Vutoe 17.59 kip

7.4.3 Check for Shear in Footing Heel

The critical section for shear in the heel is located at the interior face of the wall stem but not at distance dvsince the primary flexural reinforcement are located in the top face of the heel where the load is applied 7.4.3.1 Simplified procedure for nonprestressed sections according to AASHTO LRFD 5.8.3.4.1

dv dvheel value for sections less than 16" inthickness LRFD [5.8.3.4.1] 2.0

tv tft 48 in if tv less than 16 in, then 45deg value for sections less than 16" in


Nominal shear resistance (1) (AASHTOLRFD Eqns. 5.8.3.3-3 and 5.8.3.3-1)Vn1 0.0316 f'c ksi bv dv Vn1 74.4 kip

Vn2 0.25 f'c bv dv Vn2 658.06 kip Nominal shear resistance (2) (AASHTOLRFD Eqn. 5.8.3.3-2)

The nominal shear resistance is the lesser of:Nominal shear resistance (AASHTO LRFDArticle 5.8.3.3)Vn min Vn1 Vn2 Vn 74.4 kipResistance factor for shear (AASHTOLRFD Article 5.5.4.2.1)v 0.9Factored shear resistance (AASHTOLRFD Eqn. 5.8.2.1-2)Vr v Vn Vr 66.96 kip




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Vuheel 22.82 kip Factored shear at critical section of heel(AASHTO LRFD Eqn. 5.8.2.1-2)

checklim "OK" Vr Vuheelif"N.G." otherwise

checklim "OK"

Note:If the Nominal shear resistance is not adequate using =2 and =45 deg, or the concrete section does notmeet the requirements for simplified procedure, use the General procedure of AASHTO LRFD Article 5.8.3.4.2

7.4.3.2 General Procedure according to AASHTO LRFD 5.8.3.4.2

Area of nonprestressed steel on theflexural tension side of the memberAs Astoe 2.54 in

2

Nu 0 Factored axial load taken as positive iftensile and negative if compressive (kip)

Vu Vuheel 22.82 kip Factored shear force (kip)

See LRFD Figure 5.8.3.4.2-3: Definition ofcrack spacing parametersx dv 43.87 in

Mucs Muheel_strI

Absolute value of factored moment atcritical section for shearMucs 327.5 kip ft

Mu max Mucs Vu dv 327.5 kip ftNet longitudinal tensile strain in thesection at the centroid of tensionreinforcement per LRFD Eq. 5.8.3.4.2-4ss

Mudv

0.5Nu Vu

Es As1.53 10 3

If the value of s calculated from Eq.5.8.3.4.2-4 is negative, it should be takenas zero or the value should be recalculatedwith the denominator of Eq. 5.8.3.4.2-4replaced by (EAs + EpAps + EoAc,).However, s should not be taken as lessthan -0.40 x 10-3.

s 0 ss 0ifss otherwise

1.53 10 3

sxe max 12in min sx1.38

agin

0.63 80in

43.87 in crack spacing parameter per LRFD Eq.

5.8.3.4.2-5




SHEET: 55 OF 59

29 3500s 34.34

4.8

1 750 s 51

39sxein

1.38 for sections not containing at least theminimum amount of transversereinforcement (LRFD Eq. 5.8.3.4.2-2)

Vn1 0.0316 f'c ksi bv dv 51.24 kip Nominal shear resistance of a concretemember LRFD [5.8.3.3]

Vn2 0.25 f'c bv dv 658.06 kipThe nominal shear resistance is the lesser of:

Vn min Vn1 Vn2 Vn 51.24 kipVr v Vn Vr 46.12 kip Factored shear resistance

Vuheel 22.82 kip Factored shear at critical section of heel(AASHTO LRFD Eqn. 5.8.2.1-2)

checklim "OK" Vr Vuheelif"N.G." otherwise

checklim "OK"

7.4.4 Check for Shear in Footing Toe:

7.4.4.1 Simplified procedure for nonprestressed sections according to AASHTO LRFD 5.8.3.4.1

dv dvtoe value for sections less than 16" inthickness LRFD [5.8.3.4.1] 2.0

tv tft 48 in if tv less than 16 in, then 45deg value for sections less than 16" in


Nominal shear resistance (1) (AASHTOLRFD Eqns. 5.8.3.3-3 and 5.8.3.3-1)Vn1 0.0316 f'c ksi bv dv Vn1 72.7 kip

Vn2 0.25 f'c bv dv Vn2 643.06 kip Nominal shear resistance (2) (AASHTOLRFD Eqn. 5.8.3.3-2)


Vn min Vn1 Vn2 Vn 72.7 kipNominal shear resistance (AASHTO LRFDArticle 5.8.3.3)




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Resistance factor for shear (AASHTOLRFD Article 5.5.4.2.1)v 0.9

Factored shear resistance (AASHTOLRFD Eqn. 5.8.2.1-2)Vr v Vn Vr 65.43 kip

Vutoe 17.59 kip Factored shear r

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