**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Principal Stresses in Beams

__ Principal Stresses in Beams:__ It becomes clear that the bending stress in beam s

_{x}is not a principal stress, since at any distance y from the neutral axis; there is a shear stress t ( or t

_{xy}we are assuming a plane stress situation)

In general the state of stress at a distance y from the neutral axis will be as follows.

At some point ‘P' in the beam, the value of bending stresses is given as

After substituting the appropriate values in the above expression we may get the inclination of the principal planes.

**Illustrative examples: **Let us study some illustrative examples,pertaining to determination of principal stresses in a beam

1. Find the principal stress at a point A in a uniform rectangular beam 200 mm deep and 100 mm wide, simply supported at each end over a span of 3 m and carrying a uniformly distributed load of 15,000 N/m.

**Solution: **The reaction can be determined by symmetry