Question

Using Westergaard's equation, the stress at the edge region of a cement concrete pavement based on following data will be ____
Wheel laod $=4100kg$
Modulus of elasticity of cement concrete
$=3\times {10}^{5}kg/c{m}^2$
Pavement thickness = 15 cm
Modulus of subgrade reaction = 3 kg/cm${}^3$
Radius of contact area = 15 cm
Poisson's ratio = 0.15

• A. $42.42kg/c{m}^2$
• B. $38.42kg/c{m}^2$
• C. $33.63kg/c{m}^2$
• D. $48.82kg/c{m}^2$

Answer 1

The correct option is C $33.63kg/c{m}^2$

$\text{Radius of relative stiffness,}l={\left[\frac{E{h}^3}{12k(1-{\mu }^2)}\right]}^{1/4}={\left[\frac{3\times {10}^5\times {15}^3}{12\times 3(1-{0.15}^2)}\right]}^{1/4}$
$\Rightarrow l=73.24cm$
For the equivalent radius of resisting section
$\because \frac{a}{h}=\frac{15}{15}=1<1.724$
$\therefore b=\sqrt{1.6a^2+h^2}-0.675h$
$=\sqrt{1.6\times {15}^2+{15}^2}-0.675\times 15$
$=14.06cm$
Stress at the edge, $S_c=\frac{0.572P}{h^2}[4lo{g}_{10}\frac{l}{b}+0.359]$
$=\frac{0.572\times 4100}{{15}^2}\times [4lo{g}_{10}\left(\frac{73.24}{14.06}\right)+0.359]$
$=33.63kg/c{m}^2$