Question

For the loaded circular area of radius a, the vertical stress on a vertical line passing through the center of the loaded area is __________

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

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

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

(d) \(σ_z=p\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2}\right]\)

The question was posed to me during an internship interview.

My question is based upon Stresses in Flexible Pavements in section Design of Flexible & Rigid Pavement of Geotechnical Engineering II

Answer 1

Correct choice is (a) \(σ_z=p\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\)

To elaborate: The vertical pressure σz under a uniformly loaded circular area is given by,

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

where, p=load intensity per unit area

a=radius of circle

z= depth of point.