Practice Question: Resultant Force on a Gravity Wall

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Solution

Answer: D) 5 Kips

According to Rankine theory the active earth pressure coefficient is as follows:

\[K_{a}  =  \frac{[1 - sin  \phi ]}{[1  +  sin  \phi ]}   = \frac{[1- sin 27 ]}{[1 + sin 27 ]} = 0.375\]

Stress at wall bottom:
\[=  \gamma   \times  h  \times   K_{a}  = 120  \times  15  \times  0.375 = 675\ PSF\]

Force acting on the wall:

\[=0.5  \times  γ  \times  h^2  \times   K_{a} = 0.5  \times  120  \times  15^2  \times  0.375 = 5062.5\ lb = 5.06\ kip\]

 

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