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Wheel and Axle

A three-hinge...

Question

A three-hinged semicircular arch of radius R carries a uniformly distributed load w per unit run over the whole span. The horizontal thrust is

A

w R

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B

\frac{4 w R}{3 π}

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C

\frac{w R}{2}

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D

\frac{2 w R}{3 π}

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Solution

The correct option is C $\frac{w R}{2}$
For three-hinged semicircular arch carrying UDL of 'w' the vertical reaction at hinges.

$V_{A} = V_{B} = w R$

So horizontal thrust

$∴ H \times R = V_{A} \times R - w R \times \frac{R}{2}$

$H = V_{A} - \frac{w R}{2} = \frac{w R}{2}$

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