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.

To Section III.3