LOADING
Question

Consider the following statements for a beam based on theory of bending

1. Strain developed in any fibre is directly proportional to the distance of fibre from neutral surface

2. For flexural loading and linearly elastic action the neutral axis passes through the centroid of cross section 

3. The assumption of the plane cross sections remaining plane will not hold good during inelastic action

4. Instances in which the neutral axis does not pass through the centroid of a cross section include a homogenous

    symmetrical beam (with respect to neutral axis) and subjected to inelastic action. 

    Which of the statements given above are correct?

A.
1, 2, 3 and 4
B.
1, 2 and 4
C.
3 and 4 
D.
1 and 2
Answer ( Option D)

1 and 2

Solution

• In theory of bending, strain developed in any fibre is directly proportional to the distance of fibre from 
   NA, also valid during inelastic actions, because linear strain variation is derived from the assumption of 
   plane section before bending remains plane after bending.
• NA coincides with centroid only when hook's law is valid i.e., linear elastic action.
• However if there is symmetry about the axis of bending then even in inelastic conditions N.A will lie at 
   the C.G only. For example in case of rectangular section N.A does not shift even in case of inelastic 
   action and remains at the same location as in case of elastic condition.

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