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Three Hinged Arch - Procedure for Analysis

A circular se...

Question

A circular segmental three-hinged arch of span 36 m and a rise of 6 m hinged at the crown and springings. It carries a horizontal load of 1000 N/m covering full height of the arch on left side. The horizontal thrust on the springing will be

A

6000 N

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B

3000 N

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C

4500 N

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D

1500 N

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Solution

The correct option is D 1500 N
The vertical reaction at right support

$V_{R} = \frac{1000 \times 6 \times 3}{36} = 500 N$

Considering right segment and taking moment about crown.

$H_{R} \times 6 = V_{R} \times 18$

$H_{R} = 1500 N$

$H_{L} = 6000 - 1500 = 4500 N$

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