Question

A symmetrical three hinged parabolic arch has 50 m span an 5 m rise. A vertical downward load of 40 kN and a horizontal load of 25 kN (acting in the right hand side direction) act at one quarter span from left hand support what is the resultant reaction at supports B is ________(in kN)

• A. 60.55

Answer 1

The correct option is A 60.55


$Equationofaparabola,y=\frac{4hx}{l^2}(l-x)$
At x = 12.5 m, y =?

$y=\frac{4\times 5\times 12.5}{{50}^2}\times (50-12.5)$
y = 3.75 m

$Apply\sum M_A=0$

$V_B\times 50=40\times 12.5+25\times 3.75$
$V_B=11.87$ kN
$\sum V=0$

$V_A+V_B=40kN$
$V_A=40-11.875$
$V_A=28.125kN$
$Apply\sum M_c=0,$ from right side
$V_B\times 25=H_B\times 5$

$H_B=\frac{11.875\times 25}{5}$

$H_B=59.375kN$
$TheresultantreactionatB=\sqrt{V_B^2+H_B^2}$
$=\sqrt{(11.875{)}^2+(59.375{)}^2}$
= 60.55 kN