Section III.5

### Section III.5 Shear Flow Analysis for Unsymmetric Beams

In chapter II, a general equation for the bending stress was introduced. It was further shown that this equation could be used on any cross section, symmetric or unsymmetric, under symmetric or unsymmetric bending moment. There is a similar general equation for shear flow. It too can be used for any cross section, symmetric or unsymmetric, under symmetric or unsymmetric transverse shear force. This equation is derived from Eq. (II.1), and is given as

When the section is symmetric there will be no product of inertia, and if only a vertical shear force is applied, this equation reduces to what we have used previously for determining shear flow distribution at a given section.

The analysis procedure for unsymmetrical cross sections is as follows:

• Determine, as needed, the centroid, moments of inertia, and the shearing load in the problem.
• Consider the two parts of the general shear flow equation separately.
• Determine the shear flow resulting from each part.
• Combine the two parts together to get the final shear flow distribution.
When using this equation, it is important to consider the 'signs' on the transverse shear force components, Vx and Vy. The sign convention used is as follows:

EXAMPLE PROBLEMS

• Example 1 Shear flow distribution, shear center location, and max shear stress calculation of a transversely loaded beam with an L cross section

To Section III.6