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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.

Tranverse Shear Stress: Stress Diagram

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.

Transverse Shear Stress Equation (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.

How to calculate Q Transverse Shear Stress (2)

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

Tranverse Shear Stress: Q representation: Stress Diagram

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