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Question
A long rod of uniform rectangular section with thickness t, originally straight, is bent into the form of a circular arch with displacement d at the mid-point of span l. The displacement d may be regarded as small as compared to the length l. The longitudinal surface strain is
A.
B.
C.
D.
Answer ( Option B)

Solution

Its a case of pure shear. Hence Mohr's circle is as shown
Diameter of Mohr's circle = 2q
Centre is at origin
Principal stress are q and –q. Hence they are equal in magnitude but unlike in direction.
 Angle b/w normal to principal plane and normal to maximum shear is 90° in Mohr's circle. so it would be 45°.

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