A three hinged parabolic arch having a span of 20 m and

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A three hinged parabolic arch having a span of 20 m and a rise of 5 m carried a point load of 10 kN at quarter span from the left end as shown in the figure. The resultant reaction at the left support and its inclination with the horizontal are respectively

1. 9.01 kN and 56.31°
2. 9.01 kN and 33.69°
3. 7.50 kN and 56.31°
4. 2.50 kN and 33.69°

Correct Option: A

Take moment about A, ´
V_B × 20 = 10 × 5
∴ V_B = 2.5 kN
V_B × V_B = 10
∴ V_A = 7.5 kN
Take moment about C, to right.
H_B × 5 = V_B × 10
⇒ H_B = 5 kN
Resultant of H_A and H_B

= 9.014 kN
R_A cos θ = H_A

∴ cos θ =	5
	9.014

∴ θ = 56.31°