Question

If θ is the apex angle which the line joining the apex makes with the outer edge of the loading of a circular area, then the Boussinesq’s vertical pressure σz under a uniformly loaded circular area is given by ______________

(a) σz=q[1-sin^3θ]

(b) σz=q[1-cos^3θ]

(c) σz=q[1-tan^3θ]

(d) σz=q[1-cos^2θ]

I got this question in exam.

Query is from Stress Distribution in division Stress Distribution of Geotechnical Engineering I

Answer 1

The correct option is (b) σz=q[1-cos^3θ]

The explanation: The Boussinesq’s vertical pressure σ_z under a uniformly loaded circular area is given by,

\(σ_z=q\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right]. \) If θ is the apex angle which the line joining the apex makes with the outer edge of the loading of a circular area, then the term,

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

∴ σz=q[1-cos^3θ].