Question

A three-hinged symmetrical arch is loaded as shown in figure below. Which one of the following is the magnitude of the correct horizontal thrust?

• A. $\frac{4}{3}P$
• B. $\frac{3}{4}P$
• C. $P$
• D. $\frac{3}{8}P$

Answer 1

The correct option is C $P$

Let the vertical reaction at A and B be $V_A$ and $V_B$ respectively.

Also let the horizontal thrust be H.
Taking moment about A, we get

$V_B\times 8-P\times 5=0$
$\Rightarrow V_B=0.625P$
$\therefore V_A=P-0.625P$
$=0.375P$
Taking moments about C, from right, we get
$0.625P\times 4-P\times 1-H\times 1.5=0$
$\Rightarrow H=P$