Question

If the influence value \(i_f=\frac{1}{35} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \) for a uniformly loaded circular area, then the circular area is divided into _________ sectors.

(a) 20

(b) 35

(c) 7

(d) 14

I had been asked this question in an international level competition.

Question is taken from Stress Distribution in portion Stress Distribution of Geotechnical Engineering I

Answer 1

Correct answer is (b) 35

To explain: let the vertical stress be σz.

The Boussinesq’s vertical pressure σz 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 the area is divided into 35 area units, then the stress in each unit is given by,

\(\frac{σ_z}{35}=\frac{q}{35}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \)

Therefore for \(i_f=\frac{1}{35} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right], \)

The circular area is divided into 35 sectors.