Question

The relation between the stress component in x-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

(a) σx=σr  tan^2⁡θ

(b) σx=σr  cosec^2⁡θ

(c) σx=σr  cos⁡θ

(d) σx=σr  sin^2⁡θ

The question was posed to me in an interview for internship.

The origin of the question is Stress Distribution in chapter Stress Distribution of Geotechnical Engineering I

Answer 1

Right option is (d) σx=σr  sin^2⁡θ

Easiest explanation: From the figure,

On a horizontal plane, the relation between the stress component in x-direction in Cartesian coordinates and polar coordinates is,

σx=σr  sin^2⁡θ.