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

Answer 1

The correct option is C All option are correct

Case -1 : UDL throughtout span of arch.



${}^{\prime }{y}^{\prime }atanysection=Rsin\theta$

(A) Reactions at the supports

(i) Vertical support reactions

$v_B=wR,V_A=wR$

(ii) Horizontal thrust

$H=\frac{4}{3}\frac{wR}{\pi }\left(Remember\right)$

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



(A) Reactions at the support

(i) Vertical support reaction

$V_A=\frac{w\times R}{4},V_B=\frac{3wR}{4}$

(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 .

$H=\frac{1}{2}\times \frac{4}{3}\frac{wR}{\pi }=\frac{2}{3}\frac{wR}{\pi }\left(Remember\right)$

Case : B uniformly varied load on entired span.


(A) reactions at the supports

(i) Vertical support reaction

$V_B=\frac{2}{3}wR,V_A=\frac{wR}{3}$

(ii) Horizontal thrust

$H=\frac{2wR}{3\pi }\left(Remember\right)$

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.