Question

The Westergaard’s equation is given by ___________

(a) \(σ_z=\frac{1}{\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \)

(b) \(σ_z=\frac{1}{2\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \)

(c) \(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}}\frac{Q}{z^2} \)

(d) \(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}} \)

This question was posed to me in unit test.

This interesting question is from Stress Distribution topic in section Stress Distribution of Geotechnical Engineering I

Answer 1

Correct answer is (c) \(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}}\frac{Q}{z^2} \)

For explanation I would say: The Westergaard’s equation is given by,

\(σ_z=\frac{1}{π\left[1+2(\frac{r}{z})^2 \right]^\frac{3}{2}}\frac{Q}{z^2} \)

Where Q=load

Z= depth of point at which load is found

r=radial distance.