Section III.3 Example 2

Section III.3 Example 2 SECTION III.3 EXAMPLE 2

A beam with the cross section shown is acted upon in its plane of symmetry by a 3 kN force. For points A and B located at section n-n, shown in the figure below, determine the average shear stress. The moment of inertia and centroid location are given in the figure.

Note: Stresses induced by the load do not exceed the elastic limits of the corresponding material.

EQUATION USED

SOLUTION

First the vertical shear 'V' at n-n is determined from the free body diagram shown below

The moment of area Q at point A, for a horizontal cut is given as

Thickness 't' is defined by the width of the 'cut' which in this case is 100 mm. Hence, the average shear stress at point A is

Notice this is the vertical component of shear stress at point A.

The moment of area Q at point B, for a horizontal cut is given as

Point B is at the intersection of the web and the flange. The width of the cut is 20 mm, making the shear stress

The shear stress at a point is mostly dependent on the thickness of the member at that point. Usually, in thinner members more shear stress will be present as demonstrated by this example.

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