Question

A three-hinged parabolic arch rib of span 'L' and crown rise 'h' carries a uniformly distributed superimposed load of intensity 'w' per unit length. The hinges are located on two abutments at the same level and the third hinge at a quarter span location from left hand abutment. The horizontal thrust on the abutment is

• A. $\frac{w{L}^2}{12h}$
• B. $\frac{w{L}^2}{8h}$
• C. $\frac{w{L}^2}{4h}$
• D. $\frac{w{L}^2}{6h}$

Answer 1

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

$V_A=V_B=\frac{wL}{2}$



$\because \frac{h}{(L/2{)}^2}=\frac{h-h_1}{(L/4{)}^2}$
$\Rightarrow 4(h-h_1)=h$
$3h=4h_1$

$h_1=\frac{3h}{4}$

Taking moment about hinge at D = 0

$\Rightarrow V_A\times \frac{L}{4}-H\times h_1-\frac{wL}{4}\times \frac{L}{8}=0$

$\Rightarrow \frac{wL}{2}\times \frac{L}{4}-H\times \frac{3h}{4}-\frac{w{L}^2}{32}=0$

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