Stresses in Beams: Assumptions of Simple Bending

 Assumptions in Simple Bending Theory

There are six assumptions made in Simple Bending Theory. Without these assumptions, other factors come into scenes and this simple theory doesn't work any longer.

Let's see what are the six assumptions are:

1. The beam is initially straight and every layer of the beam expands/contracts freely.

If the beam is not assumed to be initially straight, secondary forces and displacements are considered to be accountable in the calculation and this theory doesn't hold good. Also if the layers are not free to act from each other, the internal relationship between the layers is also to be established and taken into account while calculating.

2. The material is homogeneous and isotropic

Homogeneity and Isotropic behaviors is to be maintained withing the beam as because due to the absence of it  it will be much more complex to capture the variation of physical material properties, which plays a major role in the calculation.

3. Elasticity modulus is same for Tension and Compression

In the stress strain curve, the continuity of stress strain plot is maintained same up to elastic limit  for both Tension side and Compression side for simplistic calculation. Hence Elasticity modulus is also same for both cases..

4. Stresses are within Elastic Limit

As mentioned in the previous point, we consider the stress strain graph up to Elastic limit. Because beyond this point, the plot starts to show non-linear behavior which is a more advanced characteristics which we are going to ignore in Simple Bending theory.

5. Plane section remains plane even after bending

To ignore warping of the section due to bending, we have to assume this criteria.

6. The radius of the curvature is large compared to depth of the beam

If we don't assume this criteria, P-Delta effect comes into picture and the calculations become much complex, which we want to ignore in this level. So we have to assume this one.