Question

The intensities of pressure below a point load where r=0 on axis of loading is ____________

(a) \(σ_z=\frac{0.4775Q}{z^2} \)

(b) \(σ_z=\frac{0.7Q}{z^2} \)

(c) \(σ_z=\frac{0.4775Q}{z^3} \)

(d) \(σ_z=\frac{0.8Q}{z}\)

The question was posed to me in examination.

Origin of the question is Stress Distribution topic in portion Stress Distribution of Geotechnical Engineering I

Answer 1

Right answer is (a) \(σ_z=\frac{0.4775Q}{z^2} \)

Easy explanation: Boussinesq’s vertical stress σz is given by,

\(σ_z=\frac{3Q}{2πz^2} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)

Substituting r=0,

We get,

\(σ_z=\frac{0.4775Q}{z^2}.\)