Question

A three-hinged parabolic arch of span 'l' and rise 'h' is subjected to a u.d.l. of intensity 'w'. Then the horizontal thrust at the supports is

• A. $\frac{wl}{h}$
• B. $\frac{w{l}^2}{8h}$
• C. $\frac{whl}{8}$
• D. $\frac{wl}{8h^2}$

Answer 1

The correct option is B $\frac{w{l}^2}{8h}$



$R_C=R_A=\frac{wl}{2}$

$\Rightarrow \sum M_B=0$

$R_A\frac{l}{2}-H_{A}h-\frac{wl}{2}\frac{l}{4}=0$

$H_A=\frac{w{L}^2}{4h}-\frac{w{L}^2}{8h}$

$=\frac{w{L}^2}{8h}$