Question

The Boussinesq equation representing the polar radial stress is ___________

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

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

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

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

I had been asked this question during a job interview.

Enquiry is from Stress Distribution topic in section Stress Distribution of Geotechnical Engineering I

Answer 1

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

Best explanation: Boussinesq showed that the polar radial stress is given by,

\(σ_R=\frac{3Q}{2π}   \frac{cos⁡β}{R^2} \) where σR is the polar radial stress

\(cos⁡β=\frac{z}{R} \)

R is the polar radial coordinate=√(r^2+z^2).