Civil Engineering MCQAE Level Civil Engineering
Rankine's coefficient of active earth pressure K_a for a cohesionless soil with friction angle φ is:
Soil MechanicsRankine Active PressureMEDIUM
Choose the correct answer
A
tan²(45° - φ/2)
B
tan²(45° + φ/2)
C
(1 - sinφ)/(1 + sinφ)
D
Both A and C (equivalent)
Correct Answer
D. Both A and C (equivalent)
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K_a = (1 - sinφ)/(1 + sinφ) = tan²(45° - φ/2). Both forms are equivalent trigonometric identities. For φ = 30°: K_a = (1-0.5)/(1+0.5) = 1/3.
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