A parabolic 3 hinged arch (AB) carries a u.d.l. of 30 kN/m on the left half of the span. It has a span of 16 m and a central rise of 3 m. What is the resultant thrust at 'A' (left hand end)?

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This question was previously asked in

UPSC ESE (Prelims) Civil Engineering 19 Feb 2023 Official Paper

Answer 1

F1 Engineering Arbaz 16-10-23 D16

Calculation:

Taking moment about A,

RB × 16 – 30 × 8 × 4 = 0

∴ RB = 60 kN.

Now, RA + RB = 30 × 8 = 240

RA = 240 - 60 = 180 kN

Taking moment about C, Mc = 0

180 × 8 – 30 × 8 × 4 - HA × 3 = 0

HA = 160 kN

Now, Resultant force at A will be F

\( F = \sqrt{R^{2}+H^{2}}\)

\( F = \sqrt{180^{2}+160^{2}}\)

F = 241 kN