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Question
If a constant section beam is subjected to uniform bending moment throughout, it bends as -
A.
zig zag
B.
a catenary
C.
a circular arc
D.
a parabolic arc
Answer ( Option C)

a circular arc

Solution

Bending equation,
Here, R = Radius of curvature, E = Elastic modulus of the beam, I = Area Moment of Inertia, M = Bending moment at the cross-section of the beam 
From (2), it is clear that 
• If M is variable, then the radius of curvature of the beam is variable and the shape of the elastic curve is parabolic
• If M is constant, then the radius of curvature of the beam is constant and the shape of the elastic curve is a circular arc 
• If M is zero, then the radius of curvature of the beam is infinite and the shape of the elastic curve is a straight line

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