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Question

The horizontal thrust on the ends of a two hinged semicircular arch of radius R carrying

A
A uniformly distributed load w per unit run over its entire span is (4/3)×(wR/π).
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B
A uniformly distributed load w per unit run over its right half span is (2/3)×(wR/π)
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C
All option are correct
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D
A distributed load varying from zero at the left end to w per unit horizontal run at the right end is (2/3)×(wR/π)
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Solution

The correct option is C All option are correct
Case -1 : UDL throughtout span of arch.



y at any section = R sin θ

(A) Reactions at the supports

(i) Vertical support reactions


vB=wR, VA=wR

(ii) Horizontal thrust

H=43wRπ (Remember)

Case- 2 UDL at half right of span of arch :



(A) Reactions at the support

(i) Vertical support reaction


VA=w×R4, VB=3wR4

(ii) Horizontal thrust

Since the arch is symmetrically loaded in previous case thus the horizontal thrust obtain at that case is exactly double compared to this case .

H=12×43wRπ=23wRπ (Remember)

Case : B uniformly varied load on entired span.


(A) reactions at the supports

(i) Vertical support reaction


VB=23wR, VA=wR3

(ii) Horizontal thrust

H=2wR3π (Remember)

Note: Two hinged arch:
  • Two hinged arch is statically indeterminate structure of one degree having two hinge support at its end.
  • Two hinged arch is commonly made of metal & timber.
  • It is not as rigid as fixed arch, thus it is some what insensitive to settlement.
  • Usually, horizontal reaction is treated as redundant and is evaluated by the method of least work.



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