Section II.3 example 2 SECTION II.3 EXAMPLE 1
A bending moment of 74,734 N-m is applied to a uniform composite beam shown in the figure below. If the allowable stress for steel is 250 MPa and the allowable stress for aluminum is 100 MPa, what is the minimum width of the 5-mm thick steel plates attached to the aluminum I-beam. Also determine the neutral axis location and bending stress distribution.

EQUATIONS USED:

SOLUTION

Since this is a doubly symmetric cross section, the centroid will be located at the center. This is true for both the original and the modified cross sections. With the applied moment acting about the horizontal axis, the NA will be horizontal in this case. From inspection, it is known that the maximum strain will occur in the steel plates. Also, with steel being the stiffest of the two materials it is very likely that it will carry more stress.

To calculate the modified moment of inertia, the entire section is modified to all aluminum. The modified moment of inertia in terms of w is

Let the steel plates be stressed to their limit. The top plate will have the same stress and strain as the bottom plate because of symmetry.

Check the stress at the farthest point in the aluminum part.

Use the stress equation and solve for the width

The bending stress distribution for this cross section is

ALTERNATE SOLUTION

To Section II.3