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1. Cantilever Retaining
WallDesign of Cantilever Retaining wall
Prepared by
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Design of Cantilever Retaining wall 1
DESIGN AND DRAWING
OF STEEL STRUCTURES
B-Tech
Civil Engineering
Kerala University

2. Question No 1
• Design a candilever retaining wall for a height of 5m above the ground.
• Density of Soil = 18kN/m^2
• Bearing Capacity = 200 kN/m^2
• Angle of internal friction =20^0
• Level of Earth = Horizontal
• Use Fe415 Grade Steel and M20 concrete
• Coefficient of friction between soil and concrete = 0.55
Draw the Sectional Elevation through the vertical wall , Sectional Bottom plan through base slab and
Cross Sectional Elevation.
Design of Cantilever Retaining wall 2

3. Step 1 : Given Data
• Height of wall = 5m
• Density of Soil = 18kN/m ² (𝞬)
• Bearing Capacity = 200 kN/m ²
• Angle of internal friction =20°
• Level of Earth = Horizontal
• Fy = 415
• Fck = 20
• μ = 0.55
Design of Cantilever Retaining wall 3

4. Step 2 : Preliminary Dimensioning
• Depth of Foundation =
𝑆𝐵𝐶
𝞬
[
(1−𝑠𝑖𝑛ф)
(1+𝑠𝑖𝑛ф)
]² =
200
18
[
(1−sin 30)
(1+sin 30)
]² = 1.234 ≈ 1.2m
• Total Height of retaining wall = 5+1.2 = 6.2m
• Assume Thickness of vertical wall at the top = 200m (Std values between 200m to 400m)
• Assume Width of base slab (b) = 0.6m (Std values between 0.4h to 0.6h)
= 0.6*6.2 = 3.72m
• Total Projection = tp = (Std values between (⅓ to ¼)*b )= 0.25*b = 0.25*3.72 = 0.93m
• Thickness of base slab = (Std values between
𝐻
10
to
𝐻
14
)=
𝐻
10
=
6.2
10
= 0.62m = 600mm
Design of Cantilever Retaining wall 4

5. Design of Cantilever Retaining wall 5

6. • Pressure ordinate from the critical section = ka 𝞬 (H-h) = 0.33*18*(6.3-0.6) = 33.264kN/m²
• Ka =
(1−𝑠𝑖𝑛ф)
(1+𝑠𝑖𝑛ф)
---- for cases without surcharge
• Ka = cosϴ [
(cosϴ−⎷(cos²ϴ−cos²ϴ))
(cosϴ+⎷(cos²ϴ−cos²ϴ))
] ---- for cases with surcharge
• Ka =
(1−𝑠𝑖𝑛 30)
(1+𝑠𝑖𝑛 30)
= 0.333
• Pressure(P) = ka 𝞬 (H-h)² = 0.33*18*(6.3-0.6)² = 93.13 kN/m
• Maximum Bending Moment about base = P*
(𝐻)
(3)
= 93.13*
(5.9)
(3)
= 173.84 kNm
• Factored Moment = 1.5*173.84 = 260.7 kNm
Equating the Factored moment with limiting moment of resistance -----
• BM = Qfckbd²
Design of Cantilever Retaining wall 6

7. • BM = 0.138*20*1000*d² = 260.78*10⁶
Via calculations we get d = 307.38mm ≈ 315mm
• Take cover = 35mm
• D = 350mm
• Heel = 3.7-0.9-0.35 = 2.45mm
Fe Value Q
Fe250 0.148
Fe415 0.138
Fe500 0.133
Design of Cantilever Retaining wall 7

8. Step 3 : Check for Overall Stability
• Sliding Force =
1
2
ka𝞬H ² =
1
2
*0.33*18*6.2² = 114.1668 kN
Segment Magnitude(kN) Distance from A (m) BM About A
(kNm)
Stem Segment 1 (W1) 0.2*5.6*1*25=28 0.9+0.15+0.1=1.15 32.2
Stem Segment 2 (W2) 0.5*0.15*5.6*25=10.5 0.9+(0.5*0.15)=1 10.5
Base Slab (W3) 25*0.6*3.7=55.5 1.88 102.67
Soil (W4) 2.45*5.6*18=246.96 0.9+0.15+0.2+(2.45*0.5)=2.45 609.99
∑ ∑W=340.96 ∑M=755.36
Design of Cantilever Retaining wall 8

9. • Earth Pressure = 114kN
• M = 235.6kNm
1. Check against Sliding
FOS =
μ∑ 𝑊
𝑃ℎ
=
0.55∗340.96
114
= 1.644 > 1.55 → SAFE
2. Check against Overturning
FOS = ∑ 𝑀𝑟
∑ 𝑀𝑜
=
736
245
= 3.2 > 1.55 → SAFE
3. Check against Subsidence
FOS = ∑ 𝑀
∑ 𝑊
=
∑(𝑀𝑟−𝑀𝑜)
∑ 𝑊
=
755−235
340.96
= 1.5
e =
b
2
− x = 3.7
2
=1.5 = 0.3
Design of Cantilever Retaining wall 9

10. • Pmax (toe’s end) = W
b
𝟏 +
6e
b
=
340
3.7
𝟏 +
6∗𝟎.𝟑𝟓
3.7
= 144.04 < 200 → SAFE
• Pmin =
W
b
𝟏 −
6e
b
= 39 > 0 → SAFE
Design of Cantilever Retaining wall 10

11. Step 4 : Structural Design(Vertical Wall)
• Design of Vertical Wall
Total Pressure = 93.13kN/m
Max BM = 173.84kNm
Factored BM = 260.74kNm
d = 315
d+35mm = D = 315 + 35 = 350mm
Area of tension steel
Factored BM = 0.87*fy*Ast*d*[1-
Ast∗fy
Fck∗b∗d
]
Design of Cantilever Retaining wall 11

12. 260.74*10⁶ = 0.87*415*Ast*314[1-
Ast∗415
20∗1000∗350
]
Via calculations Ast = 2804mm²
Assume 16mm dia bars
Spacing = 1000 *
Area(1 bar)
𝐴𝑠𝑡
= 1000*
π
𝟒
(16²)
2804
= 71.7mm
Provide 16mm фbars at 70mm ᶜ/c spacing
• Curtailment of Reinforcement
50% of rift needs to be curtailed from the top
(
ℎ1
ℎ2
)² =
50
100
= 0.5
H2 = 5.6
(
ℎ1
5.6
)² = 0.5
H1 = 3.95 = 4m
Design of Cantilever Retaining wall 12

13. • Actual Point of Cutoff = 3.95-Ld = 3.95-
фσ𝑠
4ʈ𝑏𝑑
← ← IS 456 Page 43
ʈ𝑏𝑑 ← Page 4
= 3.95 -
16 ∗ 0.87∗fy
4∗1.6∗1.2
= 3197mm
=3.2m from the top
Check for Shear Force
Max Factored SF = 1.5*[0.5*Ka* 𝞬H²] = 1.5 ∗ 0.5 ∗ 0.33 ∗ 18 ∗ 5.6²=140kN
Nominal Shear Strength
ʈv=
𝑉𝑢
bd
=
140∗10³
1000∗315
= 0.444N/mm²
ʈc= 0.6
From Page 73 :
100 𝐴𝑠
bd
=
100∗2804
1000∗315
= 0.9
Design of Cantilever Retaining wall 13

14. Via interpolation
0.75 → 0.56
1.00 → 0.62
ʈ𝑣 > ʈc → Hence Safe
• Distribution Steel
Minimum Area of Distribution Steel = 0.12%(area of concrete)
=
0.12
100
∗ 1000 ∗
200∗350
2
= 330mm²
→ Assume 8mm фbars
Spacing = 1000 *
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑖𝑛𝑔𝑙𝑒 𝐵𝑎𝑟
𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎
= 1000*
π
4
∗8²
330
=152.31 = 150mm
Provide 8mm фbar with a spacing of 300mm on both faces
Design of Cantilever Retaining wall 14

15. Design of Cantilever Retaining wall 15

16. Step 5 : Structural Design(Heel Slab)
• Moment and Weight Calculation
Let the weight at C be x
x−39
2.75
=
144−39
3.7
X = 3.9 + 2.75 (
144−39
3.7
)
Area = 2.45*39 + (0.5*2.45*(108-39)) = 180.075
Design of Cantilever Retaining wall 16

17. Design of Cantilever Retaining wall 17
Sl.No LOAD Magnitude (kN) Distance from C
(m)
BM About C
(kNm)
1 Backfill 246 1.225 301.35
2 Heel Slab 25*0.6*2.45= 36.75 1.225 45.01275
3 Pressure Distribution 39*2.45= 95.55 1.225 117.04
4 Pressure Distribution 0.5*2.45*69= 84.525 0.8 0.6533
∑ 102.68 163.99
BM = 163.99kNm
Factored BM = 244kNm
244*10⁶ = 0.138*20*1000*d²
dreq = 297.33mm
dprov = 600-40 = 560mm
dprov> dreq → SAFE

18. • Area of tension steel
Factored BM = 0.87*fy*Ast*d*[1-
Ast∗fy
Fck∗b∗d
]
244*10⁶ = 0.87*415*Ast*560*[1-
Ast∗ 415
20∗1000∗560
]
→ Ast = 1266mm²
→ Assume 12mm фbars
Spacing = 1000 *
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑖𝑛𝑔𝑙𝑒 𝐵𝑎𝑟
𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎
= 1000*
π
4
∗12²
1266
=89.33 = 90mm
Provide 12mm фbar with a spacing of 90mm on both faces
• Check for Shear Force
Max Factored SF = 1.5 ∗ 102.68=159.02kN
• Nominal Shear Strength
ʈv=
𝑉𝑢
bd
=
159∗10³
1000∗560
= 0.275N/mm²
Design of Cantilever Retaining wall 18

19. 100 𝐴𝑠
bd
= 0.226
From IS 456:2000 Page 73 :
Via interpolation
0.15 → 0.28
0.25 → 0.36
0.22 → 0.3N/mm²
ʈ𝑣 > ʈc → Hence Safe
• Distribution Steel
Minimum Area of Distribution Steel = 0.12%(area of concrete)
=
0.12
100
∗ 1000 ∗ 600
= 720mm²
→ Assume 10mm фbars
Spacing = 1000 *
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑖𝑛𝑔𝑙𝑒 𝐵𝑎𝑟
𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎
= 1000*
π
4
∗10²
720
=109.05 = 100mm
Provide 10mm фbar with a spacing of 100mm on both faces
Design of Cantilever Retaining wall 19

20. Step 6 : Structural Design(Toe Slab)
• Moment and Weight Calculation
Let the weight at C be x
•
x
3.75−0.9
=
144−39
3.7
• X = 3.75 + 0.9 (
144−39
3.7
)
Design of Cantilever Retaining wall 20

21. Design of Cantilever Retaining wall 21
Sl.No LOAD Magnitude (kN) Distance from C
(m)
BM About C
(kNm)
1 Self Weight 25*0.9*0.6= 13.5 0.45 6.075
2 Pressure Distribution 0.9*119= 107.1 0.45 48.195
3 Pressure Distribution 0.5*0.9*25= 11.25 0.6 6.78
∑ 104 49
BM = 49 kNm
Factored BM = 73.5 kNm
73.5*10⁶ = 0.138*20*1000*d²
dreq = 162 mm
dprov = 600-40 = 560mm
dprov> dreq → SAFE

22. • Area of tension steel
Factored BM = 0.87*fy*Ast*d*[1-
Ast∗fy
Fck∗b∗d
]
73.5*10⁶ = 0.87*415*Ast*560*[1-
Ast∗ 415
20∗1000∗560
]
→ Ast =368.55= 370mm²
→ Assume 12mm фbars
Spacing = 1000 *
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑖𝑛𝑔𝑙𝑒 𝐵𝑎𝑟
𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎
= 1000*
π
4
∗12²
370
=305.66 = 300mm
Provide 12mm фbar with a spacing of 300mm on both faces
• Check for Shear Force
Max Factored SF = 1.5 ∗ 104=156kN
Nominal Shear Strength
ʈv=
𝑉𝑢
bd
=
156∗10³
1000∗560
= 0.27N/mm²
Design of Cantilever Retaining wall 22

23. 100 𝐴𝑠
bd
= 0.066
From IS 456:2000 Page 73 :
0.066<0.15 → ʈc = 0.28
ʈ𝑣 > ʈc → Hence Safe
• Distribution Steel
Minimum Area of Distribution Steel = 0.12%(area of concrete)
=
0.12
100
∗ 1000 ∗ 600
= 720mm²
→ Assume 10mm фbars
Spacing = 1000 *
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑖𝑛𝑔𝑙𝑒 𝐵𝑎𝑟
𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎
= 1000*
π
4
∗10²
720
=109.05 = 100mm
Provide 10mm фbar with a spacing of 100mm on both faces
Design of Cantilever Retaining wall 23

24. There may be errors/variations is the above solution for which I apologize but the
methodology is correct and some variations can be expected as designing is mixture of
art and science.
This is just a guide line to understand the problem and not a solid reference.
Find More at https://www.slideshare.net/achuthanium
Thankyou for your time. 
Design of Cantilever Retaining wall 24