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When a beam is subjected to a loading system or by a force couple acting on a plane passing through the axis, then the beam deforms. In simple terms, this axial deformation is called asÂ bending of a beam. Due to the shear force and bending moment, the beam undergoes deformation.Â These normal stress due to bending are called flexure stresses.Contents:

**Assumptions to calculate bending stress**

These stresses formed in theÂ material due to bending can be calculated using certian assumption, they are
- Beam is initiallyÂ straightÂ , and has aÂ constant cross-section.
- Beam is made ofÂ homogeneous materialÂ and the beam has aÂ longitudinal plane of symmetry.
- Resultant of the applied loads lies in the plane of symmetry.
- The geometry of the overall member is such that bending not buckling is the primary cause of failure.
- Elastic limit is nowhere exceeded andÂ âE'Â is same in tension and compression.
- Plane cross - sections remains plane before and after bending.

**Types of Bending Stress**

**1. Pure Bending Stress**

Bending will be called as pure bending when it occurs solely because of coupling on its end. In that case there is no chance of shear stress in the beam. But, the stress that will propagate in the beam as a result will be known as normal stress. Normal stress because it not causing any damages to beam. As shown below in the picture.
**2. Simple Bending Stress**

Bending will be called as simple bending when it occurs because of beam self-load and external load. This type of bending is also known as ordinary bending and in this type of bending results both shear stress and normal stress in the beam. As shown below in the figure.
**Formula for Flexural Stress**

Where,
M= bending moment
I = moment of inertia of the section about the bending axis.
=fibre stress at a distance âyâ from the centroidal/neutral axis.
E = Youngâs Modulus of the material of the beam.
R = radius of curvature of the bent beam.
If y is replaced by c, the distance to remotest element, then
Where, Z= section modulus and is given by, **Z = I/c**