A) 2 points , at L/4 and 3L/4 from left support
B) 1 point , at L/2 from left support
C) 3 points , at L/3, L/2 and 2L/3 from left support
D) No point of contra flexure

As per theory of structural analysis, in a fixed beam with a central point load, there are two points of contraflexure located at a distance of L/4 and 3L/4 from the left support, where L is the span.

fixed beam BMD
Image Source: testbook.com

This is because a fixed beam undergoes double curvature bending under a central point load. The bending moment diagram is symmetric about the centre and changes slope at L/4 and 3L/4 distances. These points of slope change are known as contraflexure points.

Therefore, option A is the correct answer.

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