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Counterfort Retaining Wall Design

This document contains calculations for the design of a counterfort retaining wall. It provides details of the wall geometry, soil properties, and calculations of forces including active earth pressure, water pressure, seismic loads, soil and structural weights, and moments. Key values calculated include an active earth pressure of 7.0 kPa/m, an overturning force of 56.5 kN/m, and an overturning moment of 65.2 kN-m/m. Structural components are then checked against these demands.

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Bassa Jean-Daniel
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558 views9 pages

Counterfort Retaining Wall Design

This document contains calculations for the design of a counterfort retaining wall. It provides details of the wall geometry, soil properties, and calculations of forces including active earth pressure, water pressure, seismic loads, soil and structural weights, and moments. Key values calculated include an active earth pressure of 7.0 kPa/m, an overturning force of 56.5 kN/m, and an overturning moment of 65.2 kN-m/m. Structural components are then checked against these demands.

Uploaded by

Bassa Jean-Daniel
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 9

Test Project: Page # ___

Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Conc. Stem Height ................ m Uniform Surcharge ................ KPa


Stem Thickness Top ............. cm Strip Pressure ....................... KPa
Stem Thickness Bot .............. cm
Footing Thickness ................. cm Stem Vertical (Dead) ............. KN/m
Toe Length ............................ m Stem Vertical (Live) ............... KN/m
Heel Length ........................... m Vertical Load Eccentricity ..... cm
Soil Cover @ Toe .................. m Wind Load on Stem ............... KPa
Backfill Height ....................... m OK Wind Height from Top ........... m
Backfill Slope Angle .............. deg

Wall taper aTan ((30.5 - 30.5) / 100 / 5.00) = 0.000 rad


Backfill slope 10.0 * 3.14 / 180 = 0.175 rad
Internal friction 28.0 * 3.14 / 180 = 0.489 rad
Wall-soil friction 0.489 / 2 = 0.244 rad
Seismic angle aTan (0.00 / (1 - 0.00)) = 0.000 rad
Footing length 1.22 + 30.5 / 100 + 1.52 = 3.05 m
Height for Stability 0.27 + 3.00 + 50.8 / 100 = 3.78 m
Earth pressure theory = Coulomb Active Moist density = 19 KN/m³ Saturated density = 20 KN/m³

Active coefficient = 0.37

Active pressure 0.37 * 18.8 = 7.0 KPa/m of height


- For stability analysis (non-seismic)
Active force 0.37 * 18.8 * 3.78² / 2 = 50.2 KN/m
50.2 * Cos(0.244 + 0.000) = 48.7 KN/m
50.2 * Sin(0.244 + 0.000) = 12.1 KN/m
Water force
Pw = (0.37 * (20.4 - 9.8 - 18.8) + 9.8) * 1.52² / 2 = 7.8 KN/m

1 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

- For stem design (non-seismic)


Active force 0.37 * 18.8 * 3.00² / 2 = 31.7 KN/m
31.7 * Cos (0.244 + 0.000) = 30.7 KN/m
31.7 * Sin (0.175) = 5.5 KN/m
Water force
Pw = (0.37 * (20.4 - 9.8 - 18.8) + 9.8) * (1.52 - 50.8 / 100)² / 2 = 3.4 KN/m
Hor. seismic coeff. kh = 0.00 Ver. seismic coeff. kv = 0.00

Active seismic coeff. = 0.37

- For stability analysis (seismic)


Seismic force 0.37 * 18.8 * 3.78² / 2 * (1 - 0.0 ) = 50.2 KN/m
50.2 * Cos (0.244 + 0.000) = 48.7 KN/m
50.2 * Sin (0.244 + 0.000) = 12.1 KN/m
Water force
Pwe = 0.00 * (20.4 - 18.8) * (1.52)² / 2 = 0.0 KN/m
- For stem design (seismic)
Seismic force 0.37 * 18.8 * 3.00² / 2 = 31.7 KN/m
31.7 * Cos (0.244 + 0.000) = 30.7 KN/m
31.7 * Sin (0.244 + 0.000) = 7.7 KN/m
Water force
Pwe = 0.00 * (20.4 - 18.8) * (1.52 - 50.8 / 100)² / 2 = 0.0 KN/m

Backfill = 1.0 * 48.7 = 48.7 KN/m


Arm = 3.78 / 3 = 1.26 m Moment = 48.7 * 1.26 = 61.3 KN-m/m
Water table = 1.0 * 7.8 = 7.8 KN/m
Arm = 1.52 / 3 = 0.51 m Moment = 7.8 * 0.51 = 3.9 KN-m/m
Surcharge = 1.0 * 0.37 * 0.0 * 3.78 = 0.0 KN/m
Arm = 3.78 / 2 = 1.89 m Moment = 0.0 * 1.89 = 0.0 KN-m/m
Strip load = 0.0 KN/m
Arm = 0.00 m Moment = 0.0 * 0.00 = 0.0 KN-m/m
Wind load = 0.6 * 0.0 * 1.52 = 0.0 KN/m
Arm = 50.8 / 100 + 5.00 - 1.52 / 2 = 4.75 m
Moment =0.0 * 4.75 = 0.0 KN-m/m
Backfill seismic = 0.0 * (48.7 - 48.7) = 0.0 KN/m
Arm = 0.6 * 3.78 = 2.27 m Moment = 0.0 * 2.27 = 0.0 KN-m/m
Water seismic = 0.0 * 0.0 = 0.0 KN/m
Arm = 1.52 / 3 = 0.51 m Moment = 0.0 * 0.51 = 0.0 KN-m/m

2 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Wall seismic = 0 KN
Moment = 0 KN-m/m
Passive force = 1.0 * (0.00 + 39.04) / 2 * 1.42 = 0.0 KN/m
Arm = 0.37 m Moment = 0.0 * 0.37 = 0.0 KN-m/m
Overturning force Rh = 48.7 + 7.8 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 - 0.0 = 56.5 KN/m
Overturning moment OTM = 61.3 + 3.9 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 - 0.0 = 65.2 KN-m/m
Arm of hor. resultant = 65.2 / 56.5 = 1.16 m

Stem weight 1.0 * 30.5 / 100 * 5.00 * 24.00 = 36.6 KN/m


Arm = 1.22 + 30.5 / 100 / 2 = 1.37 m Moment = 36.6 * 1.37 = 50.2 KN-m/m
Counterfort weight
= 1.0 * (0.30 + 1.22) / 2 * 30.5 / 100 * 5.00 * 24.00 / 2.44 = 11.4 KN/m
Arm = 1.22 + 30.5 / 100 + 1.22 / 3 = 1.93 m Moment = 11.4 * 1.93 = 22.0 KN-m/m
Ftg. weight 1.0 * 3.05 * 50.8 / 100 * 24.00 = 37.1 KN/m
Arm = 3.05 / 2 = 1.52 m Moment = 37.1 * 1.52 = 56.5 KN-m/m
Key weight 1.0 * 30.50 / 100 * 30.5 / 100 * 24.00 = 2.2 KN/m
Arm = 1.22 + 30.5 / 100 / 2 = 1.37 m Moment = 2.2 * 1.37 = 3.1 KN-m/m
Soil cover = 1.0 * 1.22 * 0.61 * 18.8 = 14.0 KN/m
Arm = 1.22 / 2 = 0.61 m Moment = 14.0 * 0.61 = 8.5 KN-m/m
Stem wedge = 1.0 * (30.5 - 30.5) / 100 * 3.00 / 2 * 18.8 = 0.0 KN/m
Arm = 1.22 + 30.5 / 100 - (30.5 - 30.5) / 100 / 3 = 1.53 m
Moment =0.0 * 1.53 = 0.0 KN-m/m
Backfill weight = 1.0 * 1.52 * 3.00 * 18.8 = 76.8 KN/m
Arm = 3.05 - 1.52 / 2 = 2.29 m Moment = 76.8 * 2.29 = 175.5 KN-m/m
Backfill slope =
= 1.0 * (1.5 + (30.5 - 30.5) / 100) * 0.27 / 2 * 18.8 = 3.8 KN/m
Arm = 3.05 - (1.52 + (30.5 - 30.5) / 100) / 3 = 2.54 m
Moment =3.8 * 2.54 = 9.7 KN-m/m
Water = 1.0 * 1.52 * (1.52 - 50.8 / 100) * (20.4 - 18.8) = 2.5 KN/m
Arm = 3.05 - 1.52 / 2 = 2.29 m Moment = 2.5 * 2.29 = 5.6 KN-m/m
Seismic backfill = 0.0 * (12.1 - 12.1) = 0.0 KN/m
Arm = 3.05 m Moment = 0.0 * 3.05 = 0.0 KN-m/m
Backfill Pav = 1.0 * 12.1 = 12.1 KN/m
Arm = 3.05 m Moment = 12.1 * 3.05 = 37.0 KN-m/m
Concentrated = 1.0 * 0.0 + 0.0 * 0.0 = 0.0 KN/m
Arm = 1.22 + (30.5 - 15.2) / 100 = 1.37 m
Moment =0.0 * 1.37 = 0.0 KN-m/m

3 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Surcharge = 1.0 * (1.5 + (30.5 - 30.5) / 100) * 0.0 = 0.0 KN/m


Arm = 3.05 - (1.52 + (30.5 - 30.5) / 100) / 2 = 2.29 m
Moment =0.0 * 2.29 = 0.0 KN-m/m
Strip = 1.0 * 0.0 * 1.52 = 0.0 KN/m
Arm = 3.05 - 1.52 / 2 = 2.29 m Moment =0.0 * 2.29 = 0.0 KN-m/m
Buoyancy = 1.0 * 9.8 * 1.52 * 3.05 = -45.4 KN/m
Arm = 3.05 / 2 = 1.52 m Moment =-45.4 * 1.52 = -69.1 KN-m/m
Ver. resultant Rv = 151.2 KN/m
Resisting moment RM = 299.0 KN-m/m
Arm of ver. resultant = 299.0 / 151.2 = 1.98 m
Overturning ratio = 299.0 / 65.2 = 4.59 > 1.50 OK

3.05 284.2 - 39.1


Eccentricity = - = - = -0.15 m
2 146.3
Bearing length = Min (3.05, 3 * (3.05 / 2 - -0.15)) = 3.05 m
146.3 6 * 146.3 * -0.15
Toe bearing = - = - = 33.6 KN/m²
3.05 3.05²

146.3 6 * 146.3 * -0.15


Heel bearing = + = + = 62.5 KN/m² < 191.6 OK
3.05 3.05²

4 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Sliding force Rh = 48.7 + 7.8 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 = 59.9 KN/m
Passive coefficient 1 / 0.42 = 2.37
Passive depth 0.61 + (50.8 + 30.5) / 100 - 0.00 = 1.42 m
Passive pressure top = 2.37 * 18.8 * 0.00 + 0.00 = 0.00 KN/m²
Passive pressure bot = 2.37 * 18.8 * (1.42 + 0.00) + -13.74 = 49.69 KN/m²
Passive force = (0.00 + 49.69) / 2 * 1.42 = 35.4 KN/m
Friction force = Max (0, 151.2 * 0.50) = 75.6 KN/m
Sliding ratio = (35.4 + 75.6) / 59.9 = 1.85 > 1.50 OK

Max horizontal load at bottom = 43.7 KN/m²


Max shear at support = 43.7 * 2.44 / 2 = 53.3 KN/m
Shear at crit. section = 53.3 (1 - 30.5 / (2.44 * 100) = 46.6 KN/m
-Moment at support = 43.7 * 2.44² / 12 = -21.7 KN-m/m
+Moment at center = 43.7 * 2.44² / 24 = 10.8 KN-m/m
Shear strength ACI Eq. (22.5.5.1)
φ Vn = 0.75 * 0.17 * (28)½ * 10 * 24.8 = 162.2 KN/m> 46.6 KN/m OK
Use #6 @ 30.5 cm Cont + #6 @ 30.5 cm (Back) 18.61 / (100 * 24.4) = 0.0076
Bending strength ACI 22.2.2
-φ Mn = 0.90 * 24.4² * 27.6 * 0.114 * (1 - 0.59 * 0.114) = -158.0 KN-m/m
> -21.7 KN-m/m OK
Use D12 @ 30.5 cm Cont + #6 @ 30.5 cm (Ext) 13.01 / (100 * 24.8) = 0.0052
Bending strength ACI 22.2.2
+φ Mn = 0.90 * 24.8² * 27.6 * 0.079 * (1 - 0.59 * 0.079) = 114.6 KN-m/m
> 10.8 KN-m/m OK
0.0018 * 100.0 * 30.5 = 5.49 cm²/m ACI 24.4.3.2
Min. steel area ratio = 5.49 / 3.70 = 1.48 > 1.0 NG

5 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Bearing force = 0.0 KN/m (Neglect bearing pressure for heel design)
Concrete weight = 1.4 * 50.8 / 100 * 1.52 * 24.00 = 25.9 KN/m
Backfill weight = 1.4 * 1.52 * 3.00 * 18.8 = 107.5 KN/m
Backfill slope =
= 1.4 * (1.5 + (30.5 - 30.5) / 100) * 0.27 / 2 * 18.8 = 5.4 KN/m
Water = 1.4 * 1.52 * (1.52 - 50.8 / 100) * (20.4 - 18.8) = 3.4 KN/m
Surcharge = 1.4 * (1.5 + (30.5 - 30.5) / 100) * 0.0 = 0.0 KN/m
Strip = 1.4 * 0.0 * 1.22 = 0.0 KN/m
Vertical load = -0.0 + 25.9 + 107.5 + 5.4 + 3.4 + 0.0 + 0.0 = 93.6 KN/m²
Max shear at support = 93.6 * 2.44 / 2 = 114.2 KN/m
Shear at crit. section = 114.2 (1 - 30.5 / (2.44 * 100) = 99.9 KN/m
-Moment at support = 93.6 * 2.44² / 12 = 39.8 KN-m/m
+Moment at center = 93.6 * 2.44² / 24 = 19.9 KN-m/m
Shear strength ACI Eq. (22.5.5.1)
φ Vn = 0.75 * 0.17 * (28)½ * 10 * 44.7 = 292.7 KN/m> Vu = 114.2 KN/mOK
Use #4 @ 30.5 cm As = 4.23 cm²/m 4.23 / (100 * 44.7) = 0.0009
Bending strength ACI 22.2.2
φ Mn = 0.90 * 44.7² * 27.6 * 0.014 * (1 - 0.59 * 0.014) = 69.9 KN-m/m > Mu = 46.4 KN-m/m OK
Cover factor = Min (2.5, (5.1 + 1.91 / 2, 30.5 / 2) / 1.91) = 2.5
Straight ACI 25.4.2.3
= Max (30, 413.7 / 1.1 / (28)½ * 0.8 * 1.3 / 2.5 * 1.91 * 0.66) = 37.7 cm
Hooked 0.24 * 413.7 / (27.6)½ * 1.91 * 0.7 * 0.66 = 16.7 cm ACI 25.4.3
Dev. length at toe side = = (3.05 - 1.52) * 100 - 5.1 = 147.4 cm
> 37.7 cm OK
Dev. length at heel side = = 1.52 * 100 - 5.1 = 146.9 >cm37.7 cm OK
ACI 9.6.1.1
= Min (Max ((1.4 / 414, 0.25 * (27.6)½ / 414) * 100 * 44.7, 1.33 * 2.8) = 3.7 cm²/m
0.0018 * 100.0 * 50.8 = 9.14 cm²/m ACI 24.4.3.2
Min. steel area ratio = Max(3.74 / 9.31, 9.14 / 23.29, 9.14 / 8.46) = 1.08
> 1.0 NG
6 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Bearing force = (70.4 + 63.0) / 2 * 1.22 = 81.4 KN/m


Arm =
= (63.0 * 1.22² / 2 + (70.4 - 63.0) * 1.22² / 3) / 81.4 = 0.62 m
Moment = 81.4 * 0.62 = 50.6 KN-m/m
Water Buoyancy = 1.2 * 9.8 * 1.52 * 1.22 = 21.8 KN/m
Arm = = 1.22 / 2 = 0.61 m Moment =21.8 * 0.61 = 13.3 KN-m/m
Concrete weight = 1.2 * 50.8 / 100 * 1.22 * 24.00 = 17.8 KN/m
Arm = = 1.22 / 2 = 0.61 m Moment =17.8 * 0.61 = 10.9 KN-m/m
Soil cover = 1.2 * 1.22 * 13.99 * 18.8 = 16.8 KN/m
Arm = = 1.22 / 2 = 0.61 m Moment = 16.8 * 0.61 = 10.2 KN-m/m
Max. Shear Vu = 81.4 + 21.8 - 17.8 - 16.8 = 68.6 KN/m (1.2D+1.6(L+H))
Shear at crit. section Vu = 68.6 * (1.22 - 42.2 / 100) / 1.22 = 44.8 KN/m
Max. Moment Mu = 50.6 + 13.3 - 10.9 - 10.2 = 42.8 KN/m
Shear strength ACI Eq. (22.5.5.1)
φ Vn = 0.75 * 0.17 * (28)½ * 10 * 42.2 = 276.3 KN/m > Vu = 44.8 KN/m OK
Use #6 @ 20.3 cm As = 13.98 cm²/m 13.98 / (100 * 42.2) = 0.0033
Bending strength ACI 22.2.2
φ Mn = 0.90 * 42.2² * 27.6 * 0.050 * (1 - 0.59 * 0.050) = 213.5 KN-m/m > Mu = 42.8 KN-m/m OK
Cover factor = Min (2.5, (7.6 + 1.91 / 2, 20.3 / 2) / 1.91) = 2.5
Straight ACI 25.4.2.3
= Max (30, 413.7 / 1.1 / (28)½ * 0.8 * 1.0 / 2.5 * 1.91 * 0.20) = 30.0 cm
Hooked 0.24 * 413.7 / (27.6)½ * 1.91 * 0.7 * 0.20 = 15.2 cm ACI 25.4.3
Dev. length at heel side = = (3.05 - 1.22) * 100 - 7.6 = 174.9 cm
> 30.0 cm OK
Dev. length at toe side = = 1.22 * 100 - 7.6 = 114.4 >cm30.0 cm OK
ACI 9.6.1.1
= Min (Max ((1.4 / 414, 0.25 * (27.6)½ / 414) * 100 * 42.2, 1.33 * 2.7) = 3.6 cm²/m
0.0018 * 100.0 * 50.8 = 9.14 cm²/m ACI 24.4.3.2
Min. steel area ratio = Max(3.64 / 13.98, 9.14 / 23.29, 9.14 / 8.46) = 1.08
> 1.0 NG

Max. Shear at bottom Vu = 133.4 KN


Shear at crit. section = 133.4 * (3.00 - 115.9 / 100) / 3.00 = 81.8 KN
Use #4 @ 30.5 cm Horizontal stirrups
0.75 * 0.17 * (28)½ / 10 * 30.5 * 94.6 = 188.7 KN ACI Eq. (22.5.5.1)
0.75 * 2 * 0.20 * 413.7 / 10 * 94.6 / 30.5 = 248.4 KN
Shear strength 188.7 + 248.4 = 437.1 KN > Vu = 81.8 KN OK
Horizontal tension = 43.7 * 2.44 = 106.6 KN/m < 0.9 * 8.46 * 413.7 / 10 = 315.0 KN/m OK
Max. Moment at bottom Mu = 124.5 KN-m
Use 4 #6 Cont + 4 #6 As = 22.71 cm²/m 22.71 / (30.5 * 115.9) = 0.0064
Bending strength ACI 22.2.2
φ Mn = 0.90 * 115.9² * 27.6 * 0.096 * (1 - 0.59 * 0.096) = 924.7 KN-m > Mu = 124.5 KN-m/m OK
7 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

Use #4 @ 30.5 cm Vertical stirrups


Vertical tension = 2 * 114.2 = 228.4 KN/m < 0.9 * 8.46 * 413.7 / 10 = 315.0 KN/m OK
Cover factor = Min (2.5, (5.1 + 1.91 / 2) / 1.91) = 2.5
Straight ACI 25.4.2.3
= Max (30, 413.7 / 1.1 / (28)½ * 0.8 * 1.0 / 2.5 * 1.91 * 0.13) = 30.0 cm
Hooked 0.24 * 413.7 / (27.6)½ * 1.91 * 0.7 * 0.13 = 15.2 cm ACI 25.4.3
ACI 9.6.1.1
= Min (Max ((1.4 / 414, 0.25 * (27.6)½ / 414) * 30.5 * 115.9, 1.33 * 2.9) = 3.9 cm²/m
Min. steel area ratio = 3.87 / 22.71 = 0.17 < 1.0 OK

Shear key depth = 30.5 cm Shear key thickness = 30.5 cm


Passive force = 1.6 * (49.7 + 49.8) / 2 * 30.5 / 100 = 24.3 KN/m
Shear at crit. section Vu = 24.3 * (30.5 - 22.2) / 30.5 = 6.6 KN/m
Arm =
= (49.8 * 30.50² / 2 + (49.7 - 49.8) * 30.50² / 3) / 15.2 = 0.15 m
Max. moment Mu = 24.3 * 0.15 = 3.7 KN-m/m
Shear strength ACI Eq. (22.5.5.1)
φ Vn = 0.75 * 0.17 * (28)½ * 10 * 22.2 = 145.5 KN/m > Vu = 6.6 KN/m OK
Use #4 @ 30.5 cm As = 4.23 cm²/m 4.23 / (100 * 22.2) = 0.0019
Bending strength ACI 22.2.2
φ Mn = 0.90 * 22.2² * 27.6 * 0.029 * (1 - 0.59 * 0.029) = 34.5 KN-m/m > Mu = 3.7 KN-m/m OK

8 of 9
Test Project: Page # ___
Engineer: 08/05/2021
Descrip: Mur avec contreforts
ASDIP Retain 4.7.6 COUNTERFORT RETAINING WALL DESIGN www.asdipsoft.com

General Analysis .............. IBC 2018


Concrete Design .............. ACI 318-14 1 D+L+0.6H 1 1.4D+0.9H
Load Combinations .......... ASCE 7-10/16 2 D+H+0.6W 2 1.2D+1.6(L+H)
3 D+L+H+0.6W 3 1.2D+0.9H+0.5W
4 D+H+0.7E 4 1.2D+L+0.9H+W
5 D+L+H+0.7E 5 1.2D+L+0.9H+E
Stem Footing 6 0.9D+1.6H+W
Concrete f'c ......... MPa 7 0.9D+1.6H+E
Rebars fy ............. MPa

Bending 0.20 < 1.00 (1.2D+1.6(L+H)) Bending 0.66 < 1.00 (1.4D+0.9H)
Shear 0.16 < 1.00 (1.2D+1.6(L+H)) Shear 0.34 < 1.00 (1.4D+0.9H)

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