GATE 2017 CE (CE2) – Question 64
Concrete pavements P and Q have the same length, breadth, elastic modulus and Poisson ratio. P has thickness h and subgrade-reaction modulus K; Q has thickness 0.5h and modulus 2K. The ratio of their radii of relative stiffness lP/lQ, to one decimal place, is ______.
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Correct answer: 1.9 to 2.1
Explanation
Westergaard radius is $l=[Eh^3/(12K(1-\mu^2))]^{1/4}$. For Q, halving h and doubling K reduces the quantity under the root by 16. Thus $l_Q=l_P/2$, so $l_P/l_Q=2.0$.