Question

The shear stress component in xz-plane in Cartesian coordinates for horizontal line load is ___________

(a) \(τ_{xz}=\frac{2Q}{xzsinθcos⁡θ} \)

(b) \(τ_{xz}=\frac{2Qxz^2}{π(x^2+z^2)^2} \)

(c) \(τ_{xz}=\frac{2Qx^3}{π(x^2+z^2)^2} \)

(d) \(τ_{xz}=\frac{2Qx^2 z}{π(x^2+z^2)^2} \)

I got this question in an interview for internship.

This is a very interesting question from Stress Distribution topic in division Stress Distribution of Geotechnical Engineering I

Answer 1

The correct choice is (d) \(τ_{xz}=\frac{2Qx^2 z}{π(x^2+z^2)^2} \)

To explain: On a xz-plane, the relation between the shear stress component in Cartesian coordinates and polar coordinates is,

 \(τ_{xz}=σ_r  sinθcos⁡θ \,where\, σ_r=K \frac{Q cos⁡θ}{r}\)

And \(K=\frac{2}{2α+sin2α}\)

∴\(τ_{xz}=\frac{2Qx^2 z}{π(x^2+z^2)^2}. \)