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210

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Mechanical Engineering

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Oct 30, 2023

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1. A Ultimate bearing capacity = qf = CnxNc + γDf 5.14 × 40 + 150 × 1 = 320.6 kpa b. 2. qf = CNu+yDNq+0.5yBNy 150 x 20.72 + 0.5 x 120 x 10.88 = 963 c. the second case is is used for design because it is the worst-case scenario. The two cases are so different because of the soil type and drainage conditions differences. 2. Q = 3000 + 400 = 3400 kN qna = Q A = 3400 2 × 2 = 850 Ka = 1 sin 40 1 + sin 40 = 0.217 Pa = ka.γ .h = 0.217 x 14 x 1 = 3.038 Description Forces Lever arm moments Vertical Horizontal clockwise Counterclockwise 1=0.3 x 0.7 x 24 5.04 1 5.04 2=0.85 x 0.7 14 8.33 1.575 13.12 3=2 x 0.3 x 24 14.4 1 14.4 pa 3.038 0.67 2.04 sum 27.78 3.038 32.56 2.04 Pmax = v B ( 1 + 6 e B ) But since e = 0, Pmax = 27.78 2 = 13.89 Fb = 850 13.89 = 61 3.
Given vertical force, V=1.8kips Lateral fore, p=9.6kips Overturning moment Mo = 9.6 ft .ki ps Factor of safety 3 Factor of safety against bearing , Fb = qna / pmax Pmax = v B ( 1 + 6 e B ) e = B 2 −´ x ´ x = Mr Mo V Mr = pxA = ( 1.8 ) x ( 9 x 1 ) = 16.2 ft kips ´ x = 16.2 9.6 11. 4 = 0.579 e = B 2 −´ x = 4.5 1.6 = 3.92 Pmax = 11.2 9 ( 1 + 6 x 2.9 9 ) = 4.5778 q na = F b xPmax = 4.5778 × 3 = 13.7 ksf 4. the total loads = 1634+1393=3027kn AREA= π r 2 = π 10 2 =100 π Bearing pressure =force/area = 3027 100 π = 9.63 kpa 9.63kpa is less than the assumed bearing capacity of soil hence sufficient.
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