GATE 2017 CE (CE1) – Question 17
A two-hinged parabolic arch of span $L$ carries a uniformly distributed load of intensity $q$ per unit horizontal length over its entire span, as shown. Its maximum bending moment equals
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Correct answer: (C) zero
Explanation
For this loading the funicular shape is a parabola. If the arch rise is $h$, horizontal thrust is $H=qL^2/(8h)$. At coordinate $x$, the simply supported beam moment is $qx(L-x)/2$, and the arch ordinate is $y=4hx(L-x)/L^2$. Thus $M=M_{beam}-Hy=0$ at every section. Its maximum bending moment is zero, C.