Question

When the maximum vertical stress \((σ_z)_{max}=\frac{0.0888Q}{r^2}\)  at a point, the shear stress at that point is ____________

(a) \(τ_{rz}=\frac{0.0888Q}{r^2} \)

(b) \(τ_{rz}=\frac{0.0725Q}{r^2} \)

(c) \(τ_{rz}=\frac{0.234Q}{r^2} \)

(d) \(τ_{rz}=\frac{0.328Q}{r^2} \)

The question was asked in unit test.

The doubt is from Stress Distribution in division Stress Distribution of Geotechnical Engineering I

Answer 1

Correct answer is (b) \(τ_{rz}=\frac{0.0725Q}{r^2} \)

To explain: Since the shear stress is given by the relation,

\(τ_{rz}=\frac{(σ_z)_{max} r}{z}\)

For maximum vertical stress,

r/z=0.817

∴ \(τ_{rz}=\frac{0.0888Q}{r^2}*0.817\)

∴ \(τ_{rz}=\frac{0.0725Q}{r^2}. \)