Question

Westergaard's formula for vertical stress gives greater value of stress than that by the Boussinesq's formula, when r/z exceeds

• A. 1.5
• B. 2.5
• C. 3.5
• D. 4.0

Answer 1

The correct option is A 1.5

The Boussinesq's equation gives vertical stress
${\sigma }_z=K_B\frac{Q}{z^2}$
$where{K}_B=\frac{3/2\pi }{{[1+(r/z{)}^2]}^{5/2}}...\left(i\right)$
$\text{For}\mu =0,\text{the Westergaard's solution is}$
${\sigma }_z=K_W\frac{Q}{z^2}$
$K_W=\frac{1/\pi }{[1+2(r/z{)}^2{]}^{3/2}}...\left(ii\right)$
Equating(i) and (ii),we get,
$r/z=1.524$
$forr/z<1.524;K_w<K_B$
Westergaard's formula gives lesser value of vertical stress. For $r/z>1.524,K_w>K_B$ i.e., Westergaard's formula gives greater value of stress.