Question

A three hinge arch consisting two quadrantal parts $AC$ and $CB$ of radii $R_1$ and $R_2$ is shown in figure below. If it is subjected to a central point load $W$ at crown then horizontal thrust at each support is__________W.

• A. 0.5

Answer 1

The correct option is A 0.5


Taking moments about C from left hand side of C,
$V_A\times R_1=H{R}_1$
$\Rightarrow V_A\times R_1=H{R}_1$
$\Rightarrow V_A=H$
Taking moment about C on the right hand side of C,
$V_B\times R_2=H\times R_2$
$\Rightarrow V_B=H$
$Now,V_A+V_B=W$
$\therefore V_A=V_B=\frac{W}{2}=H$
$\therefore H=\frac{W}{2}=0.5W$