Design of Cantilever retaining wall

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1. Cantilever Retain ing Wall Design of Cantilever Retaining wall Prepared by ↘ 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 ( ) 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 = ]² = ]² = 1.234 ≈ 1.2m T otal 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 to ) = = = 0.62m = 600mm   Design of Cantilever Retaining wall 4 ∆<

5. Initial Dimensioned Figure Design of Cantilever Retaining wall 5 ∆<

6. Pressure ordinate from the critical section = ka (H-h) = 0.33*18*(6.3-0.6) = 33.264 kN/m ² Ka = ---- for cases without surcharge K a = cos ϴ [ ] ---- for cases with surcharge K a = = 0.333 P ressure ( P) = ka (H-h) ² = 0.33*18*(6.3-0.6) ² = 93.13 kN /m Maximum Bending Moment about base = P* = 93.13* = 173.84 kNm Factored Moment = 1.5*173.84 = 260.7 kNm Equating the Factored moment with limiting moment of resistance ----- BM = Qfckbd ²   Design of Cantilever Retaining wall 6 ∆<

7. BM = 0.138*20*1000*d ² = 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 = ka H 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 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 = 114 kN M = 235.6 kNm Check against Sliding FOS = = = 1.644 > 1.55 → SAFE 2. Check against Overturning FOS = = = 3.2 > 1.55 → SAFE 3. Check against Subsidence FOS = = = = 1.5 e = = =1.5 = 0.3   Design of Cantilever Retaining wall 9 ∆<

10. Pmax (toe’s end) = = = 144.04 < 200 → SAFE P min = = 39 > 0 → SAFE   Design of Cantilever Retaining wall 10 ∆<

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

12. 260.74*10⁶ = 0.87*415* Ast *314[1- Via calculations Ast = 2804 mm² Assume 16mm dia bars Spacing = 1000 * = 1000* = 71.7 mm Provide 16mm ф bars at 70mm ᶜ/c spacing Curtailment of Reinforcement 50% of rift needs to be curtailed from the top )² = = 0.5 H2 = 5.6 )² = 0.5 H1 = 3.95 = 4 m   Design of Cantilever Retaining wall 12 ∆<

13. Actual Point of Cutoff = 3.95-Ld = 3.95- ← ← IS 456 Page 43 ← Page 4 = 3.95 - = 3197 mm = 3.2 m from the top C heck for Shear Force M ax Factored SF = 1.5*[0.5*Ka* = 140 kN N ominal Shear Strength = = 0.444 N/mm² c= 0.6 From Page 73 : = = 0.9   Design of Cantilever Retaining wall 13 ∆<

14. Via interpolation 0.75 → 0.56 1.00 → 0.62 > c → Hence Safe Distribution Steel Minimum Area of Distribution Steel = 0.12%(area of concrete) = = 330 mm² → Assume 8mm ф bars Spacing = 1000 * = 1000* =152.31 = 150 mm Provide 8mm ф bar with a spacing of 300mm on both faces   Design of Cantilever Retaining wall 14 ∆<

15. Design of Cantilever Retaining wall 15 Details of the reinforcement in the vertical wall ∆<

16. Step 5 : Structural Design(Heel Slab) Moment and Weight Calculation Let the weight at C be x X = 3.9 + 2.75 ( A rea = 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 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 = 163.99 kNm Factored BM = 244 kNm 244*10⁶ = 0.138*20*1000*d² d req = 297.33 mm d prov = 600-40 = 560 mm d prov > d req → SAFE ∆<

18. Area of tension steel Factored BM = 0.87* fy * Ast *d*[1- 244*10⁶ = 0.87*415* Ast *560*[1- → Ast = 1266 mm² → Assume 12mm ф bars Spacing = 1000 * = 1000* =89.33 = 90 mm Provide 12mm ф bar with a spacing of 90mm on both faces C heck for Shear Force M ax Factored SF = = 159.02 kN N ominal Shear Strength = = 0.275 N/mm²   Design of Cantilever Retaining wall 18 ∆<

19. = 0.226 From IS 456:2000 Page 73 : Via interpolation 0.15 → 0.28 0.25 → 0.36 0.22 → 0.3N/mm² > c → Hence Safe Distribution Steel Minimum Area of Distribution Steel = 0.12%(area of concrete) = = 720 mm² → Assume 10mm ф bars Spacing = 1000 * = 1000* =109.05 = 100 mm Provide 10mm ф bar 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 (   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 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 d req = 162 mm d prov = 600-40 = 560 mm d prov > d req → SAFE ∆<

22. Area of tension steel Factored BM = 0.87* fy * Ast *d*[1- 73.5*10⁶ = 0.87*415* Ast *560*[1- → Ast =368.55= 370 mm² → Assume 12mm ф bars Spacing = 1000 * = 1000* =305.66 = 300 mm Provide 12mm ф bar with a spacing of 300mm on both faces C heck for Shear Force M ax Factored SF = = 156 kN N ominal Shear Strength = = 0.27 N/mm²   Design of Cantilever Retaining wall 22 ∆<

23. = 0.066 From IS 456:2000 Page 73 : 0.066<0.15 → c = 0.28 > c → Hence Safe Distribution Steel Minimum Area of Distribution Steel = 0.12%(area of concrete) = = 720 mm² → Assume 10mm ф bars Spacing = 1000 * = 1000* =109.05 = 100 mm Provide 10mm ф bar 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 ∆<