Question

A three hinged arch shown in figure is quarter of a circle. If the vertical and horizontal components of reaction at A are equal, the value of $\theta$ is

Answer 1

$\sum M_B=0\text{from left of 'B'}$
$\therefore V_A\left(R\cos \theta \right)+H_A(R-Rsin\theta )=0$
$V_A\cos \theta =H_A(sin\theta -1)$
$V_A=H_A\left(given\right)$
$sin\theta -1=cos\theta$
$\therefore \theta ={90}^{\circ }$