Question

The Boussinesq equation representing the tangential stress is ___________

(a) \(τ_{rz}=\frac{3}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{5/2}\)

(b) \(τ_{rz}=\frac{3Qr}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^5\)

(c) \(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)

(d) \(τ_{rz}=\frac{3Q}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^2\)

This question was posed to me in an interview for job.

I want to ask this question from Stress Distribution topic in division Stress Distribution of Geotechnical Engineering I

Answer 1

The correct choice is (c) \(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)

For explanation I would say: Boussinesq showed that the polar radial stress is given by,

\(σ_R=\frac{3Q}{2π}   \frac{cos⁡β}{R^2}\)

 Boussinesq’s tangential stress σz is given by,

\(τ_{rz}=\frac{1}{2} σ_R sin2β\)

∴ \(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{5/2} \) where, τrz is the tangential stress

Q is the point load acting at the ground surface

r is the radial horizontal distance

z is the vertical distance.