Q1. Select a suitable site and design are Gravity Retaining Wall, your design an
ID: 1730281 • Letter: Q
Question
Q1. Select a suitable site and design are Gravity Retaining Wall, your design and retain judgement; vis-à-vis height of the soil to be retained, stability analysis, cost, available space and ing wall proportioning should be based on sound engineering aesthetic. Rules: i. Background/ Introduction of the Problem ii. Uniqueness of design and decisions/Objectives ii Retaining wall proportioning iv. Clear drawing and steps or procedures v. Analysis and design vi. Conclusions and recommendations vii. References (0.5 Mark) (1 Marks) (1 Marks) (2 Marks) (3 Marks) (2 Marks) (0.5Mark)Explanation / Answer
Design of Cantilever Retaining Wall for culvert wall
Height of culvert as retaining wall= 4.57m (15 feet)
SBC of Soil= 100 KN/m2
a= 0.3
Height of back fill h 4.57m m
Provide a retaining wall section shown in fig.
Earth fill Side
h=4.572
heel side Corrections in RED only
0.75 1
Toe 0.55 0.5
0.5
Stability calculations B = 2.3
for unit length
Sl. No. Portion Height Thickness Weight Lever arm Moment
m m KN about heal (m) KNm
1 Stem(rect) 4.572 0.3 34.29 1.15 39.434
2 Stem(tri) 4.3 0.25 13.44 1.38 18.589
3 Base slab 2.3 0.5 28.75 1.15 33.063 Surcharge height 0.0 m above top
4 Wt. of soil 4.57 1 82.30 0.50 41.148 Surcharge pressure at top 0.0 kN/m2
5 0 0 0.00 0 0.000 Lateral load due to surcharge 0 kN
Total ?W= 158.77 KN ?M= 132.23 KNm Moment due to surcharge 0 kNm
Check for Base Overturning
Distance of resultant vertical force from heel , z = ?M/?W = 0.83 m
Stabilising Moment about Toe, Mr = ?W(B-z) 232.95 kNm or provide load from column at respective level and take the moment about base, then add to total momnet
Coefficient of active earth pressure for ? = 30 deg , Ka 0.333
Earth ht on toe h0= 0 m
Lateral Earth pressure, P= KaYh2/2 61.12 KN
Moment of Lateral earth pressure about base, Mo= Pxh/3+Ms 93.14 KNm
Factor of safety against overturning = 0.90Mr/Mo 2.251 safe
Check for Base pressure
Total Vertical Load= 158.77 kN
Total moment about heal= ?M+Mo = 225.37 kN
Distance of net reaction about Heal, Z1= net mom./net load= 1.42 m
Eccentricity= e = Z1-B/2 = 0.27 m <B/6, Safe
Max. pressure at base Pmax =W/B(1+6e/B) 117.56 KN/m2 > SBC, redesign
Min. pressure at base Pmin =W/B(1-6e/B) 20.51 KN/m2 no Tension, safe
Check for Sliding
Frictional Resistance f W 87.33 KN
Provide a key of 0.5 m width x 0.5 m ht. in the base slab
Passive pressure on Key 18xh12/2Ka 27.03
Factor of safety against sliding 0.9fW/P 1.684 safe
Design of Stem :
Adopt M20 mix and use HYSD (tor steel) bars 1.319972196
Adopting, Limit State method, 4.8
At bottom of stem,M 93140.0 Nm 61.77 1.431186284
Provided Bottom depth 55 cm 1.288067655
Mu, Factoref moment = 1.5M = 139.71 KNm
b= 1000 mm
d= 492 mm
Xu/d= 0.48
fy= 415 MPa
fck= 20 MPa
Clear Cover= 50 mm
Bar Dia= 16 mm
M= 0.138fckbd2
dreqd.= 225.02 mm safe
b 23710.84337
C 18648416.85
Ast 814 mm2
min. Ast= 0.12%= 660 mm2
Main rft. Provide for 814 mm2
Spacing using 16 mm bars= 247 mm
Max. spacing= 3d or 1476 mm
300 mm
Hence max spacing = 247 mm 240 mm 200
rounded to 200 mm
Provide 16 mm bars @ 200 mm c/c at bottom
Distribution steel per face= 330 mm2
Spacing using 8mm bars= 153 mm
Max. allowable= 153 mm 140 mm 200
rounded to 140 mm
Provide 8mm bars @ 140 mm c/chorizontal for bottom 1.0m height
Provide 8mm bars @ 220 mm c/c verticals on outer face
1
Design of Heel slab Pmax Pmin
117.56 62.7 20.5
Base pressure diagram
Moment at critical section -26.497 KNm
Effective depth = 120 mm
Provide an overall depth of 500 mm
Mu, Factoref moment = 1.5M = 39.75 KNm
d= 442 mm
Xu/d= 0.48
fy= 415 MPa
fck= 20 MPa
Clear Cover= 50 mm
Bar Dia= 16 mm
Ast 252 mm2
min. Ast= 0.12%= 600 mm2
Main rft. Provide for 600 mm2
Spacing using 16 mm bars= 336 mm
Max. spacing= 3d or 1326 mm
300 mm
Hence max spacing = 300 mm 300 mm 200
rounded to 200 mm
Provide 16 mm bars @ 200 mm c/c at top of heel or 12mm at 150mm C/C
Distribution steel = 600 mm2
Spacing using 10mm bars= 131 mm
Max. allowable= 131 mm 120 mm 220
rounded to 120 mm
Provide 10mm bars @ 120 mm c/c as distributors in Heel and Toe
Design of Toe slab Toe projection 0.75 m
Moment at critical section 33.06 KNm
Effective depth = 134 mm
Provided overall depth 500 mm
Mu, Factoref moment = 1.5M = 49.59 KNm
b= 1000 mm
d= 442 mm
Xu/d= 0.48
fy= 415 MPa
fck= 20 MPa
Clear Cover= 50 mm 1.777777778
Bar Dia= 12 mm
Ast 315 mm2
Spacing using 12 mm bars= 189 mm 168.5393258
Max. spacing= 3d or 1326 mm
300 mm
Hence max spacing = 189 mm 180 mm 200
rounded to 180 mm
Provide 12 mm bars @ 180 mm c/c at bottom of Toe
use 12mm Dia bar at 150mm C/C
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