Question

An isolated load W is acting at a distance 'a' from the left-hand support of a three-hinged arch of span ${}^{\prime }2l^{\prime }$ and rise ${}^{\prime }{h}^{\prime }$ hinged at the crown. The vertical reaction of the arch is

• A. $Wa/2l$
• B. $Wl/a$
• C. $Wa/l$
• D. $W^2/2l$

Answer 1

The correct option is A $Wa/2l$



Support reactions
$From\sum F_X=0,H_A=H_B=H$

$From\sum F_Y=0,V_A+V_B=W$

$From\sum M_B=0$

$V_A\times 2l-W\times (2l-a)=0$

$V_A=\frac{W(2l-a)}{2l}$

$V_B=W-V_A$

$=W-\frac{W(2l-a)}{2l}$

$V_B=\frac{Wa}{2l}\text{(ANS)}$

$From\sum M_C=0$

$H_B\times h-V_B\times l=0$

$H_B=\frac{V_B\times l}{h}=\frac{Wa}{2l}\times \frac{l}{h}=\frac{Wa}{2h}$