Question

A concentrated load W moves on the span of a three-hinged arch. The horizontal thrust at the supports is maximum when the load is at which one of the following?

• A. Quarter span
• B. The springing
• C. One-sixth of the span from one end
• D. The crown

Answer 1

The correct option is D The crown


When a unit load moves on the span from left to right, the reactions will change each and every section on the span. Let the unit load be at a distance x from A, then

$V_A=\frac{L-x}{L}and{V}_B=\frac{x}{L}$

Let H be the horizontal thrust;
Taking moments about hinge C from right, we get

$Hh=\frac{x}{L}\times \frac{L}{2}[0\le x\le \frac{L}{2}]$

$\Rightarrow H=\frac{x}{2h}$

Horizontal thrust will be maximum when

$x=\frac{L}{2}\text{i.e., at the crown.}$

$\therefore H_{max}=\frac{L}{4h}$