Question

On simplifying the compatibility equation in terms of stresses with respect to Poisson’s ratio is given by _________

(a) σz=γz

(b) σx=σy=\(\frac{μ}{1-μ}γz\)

(c) σx=σy=\(\frac{1}{μ} γz\)

(d) σx=σy=μγz

This question was addressed to me in final exam.

The above asked question is from Stresses due to Self Weight in division Stress Distribution of Geotechnical Engineering I

Answer 1

Right answer is (b) σx=σy=\(\frac{μ}{1-μ}γz\)

For explanation: On simplifying the compatibility equation in terms of stresses with respect to Poisson’s ratio is given by

 σx=σy=\(\frac{μ}{1-μ}γz\)

Where σx,σy are the normal stresses in x and y direction respectively

μ= Poisson’s ratio

\(K_o=\frac{μ}{1-μ}\)  is the coefficient of lateral pressure at rest.