If the pressure sustained by 75 cm dia rigid plate at 0.125 cm deflection is 0.4 kg/cm2 and thickness of slab is 20 cm with modulus of elasticity = 210000 kg/cm2, then the radius of relative stiffness is (assume Poissons ratio as 0.13)

58 cm

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81.67 cm

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42.64 cm

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53.3 cm

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Solution

The correct option is B 81.67 cm
Modulus of subgrade reaction,
$= 0.4 / 0.125 = 3.2 k g / c m^{3}$
Radius of relative stiffness,
$l = {[\frac{E h^{3}}{12 K (1 - μ^{2})}]}^{\frac{1}{4}}$
$l = {[\frac{210000 \times 20^{3}}{12 \times 3.2 (1 - {0.13}^{2})}]}^{\frac{1}{4}}$
$= 81.67 c m$

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