Practice Question: Active Earth Pressure on Cantilever Retaining Wall

Answer: D) 486 kip

Calculate the Rankine coefficient of active earth pressure:

$$ K_a=\cos{\alpha}\ast\frac{\cos{\alpha}-\sqrt{\cos^2{\alpha}-\cos^2{\phi}}}{\cos{\alpha}+\sqrt{\cos^2{\alpha}-\cos^2{\phi}}} $$

$$ K_a=\cos{15°}\ast\frac{\cos{15°}-\sqrt{\cos^2{15°}-\cos^2{30°}}}{\cos{15°}+\sqrt{\cos^2{15°}-\cos^2{30°}}}=0.37 $$

Calculate the horizontal component of the coefficient:

$$ K_{ah}\ =K_{ah}\ast\cos{\alpha}\ =\ 0.37 \ast \cos{15°} =\ 0.36 $$

Calculate the horizontal component of the resultant force:

$$ R_{ah}=\frac{1}{2}\gamma\ H^2K_{ah}L=\ \frac{1}{2}\ast120\ pcf\ast\left(30\ ft\right)^2\ast0.36\ast(25\ ft)=486,000\ lb $$