Question

For a loaded circular area of radius ‘a’, μ=Poisson’s ratio, the horizontal radial stress is ________

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

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

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

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

I have been asked this question in examination.

I'm obligated to ask this question of Stresses in Flexible Pavements topic in section Design of Flexible & Rigid Pavement of Geotechnical Engineering II

Answer 1

The correct option is (d) \(σ_r=\frac{p}{2} \left[1+2μ-\frac{2(1+μ)z}{(a^2+z^2)^\frac{1}{2}}+\frac{z^3}{(a^2+z^2)^\frac{3}{2}}\right]\)

Easy explanation: For a loaded circular area of radius ‘a’, the horizontal radial stress is given by,

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

where, σr= horizontal radial stress

p=load intensity per unit area

μ=Poisson’s ratio.