Shear centre

Shear centre

Shear centre of a section can be defined as a point about which the applied force is balanced by the set of shear forces obtained by summing the shear stresses over the section.

In unsymmetrical sections and in particular angle and channel sections, the summation of the Shear Stresses in each leg gives a set of Forces which must be in equilibrium with the applied Shearing Force.

(a) Consider the angle section which is bending about a principle axis and with a Shearing Force F at right angle to this axis. The sum of the Shear Stresses produces a force in the direction of each leg as shown above. It is clear that their resultant passes through the corner of the angle and unless F is applied through this point there will be a twisting of the angle as well as Bending. This point is known as The Shear Centre or Centre of Twist

(b) For a channel section with loading parallel to the Web, the total Shearing Force carried by the web must equal F and that in the flanges produces two equal and opposite horizontal forces. It can be seen that for equilibrium the applied load causing F must lie in a plane outside the channel as indicated. 

Note:
1. In case of a beam having two axes of symmetry, the shear centre coincides with the centroid.
2. In case of sections having one axis of symmetry, the shear centre does not coinside with the centroid but lies on the axis of symmetry.
3. When the load passes through the shear centre then there will be only bending in the cross section and no twisting.