## Shear Stresses in Beams

**Introduction:**

When a beam is loaded, the shear force at a section always comes into play along with the bending moment. It has been observed that the effect of the shear stress, as compared to the bending stress, is quite negligible and is of not much importance. But, sometimes, the shear stress at a section is of much importance in the design. It may be noted that the shear stress in a beam is not uniformly distributed over the cross-section but varies from zero at the outer fibres to a maximum at the neutral surface.

**Shear Stresses in Beams**

Shear stress in a rectangular beam Shear stress in a circular beam

The shear stress at any section acts in a plane at right angle to the plane of the bending stress and its value is given by

where F = Vertical shear force acting on the section,

I = Moment of inertia of the section about the neutral axis,

b = Width of the section under consideration,

A = Area of the beam above neutral axis, and

= Distance between the C.G. of the area and the neutral axis.

The following values of maximum shear stress for different cross-section of beams may be noted

2. For a beam of circular section as shown in Fig., the shear stress at a distance y from neutral axis is given by

** 3. **For a beam of circular section as shown in Fig., the shear stress at a distance y from neutral axis is given by

Shear stress at the joint of the web and the flange

and shear stress at the junction of the top of the web and bottom of the flange