Question

The three hinged semicircular arch (as shown below) is subjected to loads on rigidly connected brackets at D and E. Find the normal thrust and radial shear at point 'F' (upto two decimal places, in kN)

• A. 15.14 kN, 15.14 kN
• B. 11.28 kN, 14.76 kN
• C. 24.19 kN, 26.62 kN
• D. 16.97 kN , 16.97 kN

Answer 1

The correct option is D 16.97 kN , 16.97 kN


$V_A\times 10-60\times 8-40\times 3=0$

$\Rightarrow V_A=60kN\Rightarrow V_B=40kN$

$For{H}_A$,

$V_A\times 5-60\times 3-H_A\times 5=0$

$\Rightarrow H_A=\frac{60\times 5-60\times 3}{5}$

$\Rightarrow H_A=24kN$

At F, vertical shear = 0.

Horizontal shear = 24 kN.

$Normalthrust=H_{f}cos\theta =24cos45=16.97kN$

$Radialshear=H_{f}sin\theta =24sin45=16.97kN$