Question

A 3 hinged arch consists of straight segment is subjected to loading system as shown in figure. The difference of horizontal reactions at support A and B is:

• A. 12.50 kN
• B. 25 kN
• C. 18.75 kN
• D. 20 kN

Answer 1

The correct option is A 12.50 kN


$\sum M_c=0\text{(Left)}$

$(5\times 5\times 2.5)+5H_A=5V_A$

$V_A=H_A+12.5...\left(1\right)$

$\sum M_c=0\left(Right\right)$

$3H_B=7V_B$

$V_B=\frac{3}{7}{H}_B...\left(2\right)$

$\sum F_x=0H_A+25=H_B....\left(3\right)$

$\sum F_y=0V_A+V_B=50....\left(4\right)$

$\text{Substituting}{V}_A\&V_B\text{in equation 4}$

$H_A+12.5+\frac{3}{7}{H}_B=50$

$H_A+\frac{3}{7}{H}_B=37.5kN$

$H_A+\frac{3}{7}(H_A+25)=37.5\Rightarrow H_B=18.75kN$

$\therefore H_A=(18.75-25)$

$H_A=-6.25kN=6.25kN(\leftarrow )$

Difference of horizontal reactions,
$=(18.75-6.25)=12.50kN$