Question

Consider the following three hinged arch



If this arch is carrying uniformly distributed horizontal load of 5 kN/m on left side, then magnitude of horizontal thrust at A is _____ kN.

• A. 22.5

Answer 1

The correct option is A 22.5
$Taking\Sigma M_B=0$

$\Rightarrow V_A\times 18-H_A\times 6-\frac{5\times 6^2}{2}=0$

$\Rightarrow V_A\times 18=90+6H_A$

$\Rightarrow V_A=5+\frac{H_A}{3}$

$Taking,\Sigma M_C=0$

$\Rightarrow V_A\times 36+5\times 6\times 3=0$

$\Rightarrow V_A=\frac{-5\times 6\times 3}{36}=-25kN$

$\therefore H_A=(-2.5-5)\times 3$

$=-7.5\times 3=-22.5kN$