# Strength of Materials: Transverse Shear Stress

Before continuing on if you don't have an understand of shear and moment diagrams and how to calculate the area moment of inertia. I strongly recommend that you look at those pages before continuing.

Bending consists of a normal stress and a shear stress. Typically an engineer is more interested in the normal stress, since normally that stress is more prominent. However, there are cases where a beam could be short and stubby which in that case the shear stress becomes more influential.

## Transverse Shear

The shear stress due to bending is often referred to as transverse shear. Like the normal stress there is a stress profile that is based off of the neutral axis of the particular cross-sectional area. Unlike normal stress, the highest stress value occurs at the neutral axis, while there is no stress on the walls. Refer to the figure below to view a typical stress profile.

Notice from the stress profile that the stress distribution is parabolic. Also, since there is a flange and a web on the cross-section there is a jump in the stress distribution at the junction where the web and flange connect. This is due to the cross-sections width changing suddenly.

In order to calculate the shear stress at different location on the stress profile equation 1 would be used.

(1)

Notice in equation 1 that there is term defined by Q. Q is basically a representation of the area above the point of interest in relation to that area's centroid and the main cross-section centroid. Q is defined by equation 2.

(2)

Also, refer to the figure below to get a better idea of what Q is in relation to equation 2.

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