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UPSC Civil Service Exam Questions

Q1:

A three-hinged circular arch ACB is formed by two quadrants of circles AC and BC of radii 2R and R respectively with C as crown, as shown in the figure at side. Consider the following in respect of the reactive forces developed at support A and B due to concentrated load W at the Crown.
1. Line of action RA at A is inclined as 45° to the horizontal.
2. VA = VB = W/2
3. HB = 2 HA
4. HA = HB = W/2
Which of the above is/are correct ?

A 1 and 3

B 2 and 3

C 1, 2 and 4

D 4 only

ANS:A - 1 and 3

Va = Vb= W/2
by taking moment about crown get;
Vb = Hb = W/2
Va = Ha = W/2.

So, tanx = Va/Ha.
so the line of action is 45 degrees.



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