Example 6⁶

Problem: A steel bar and an aluminum bar are bonded together to form the composite beam shown. The modulus of elasticity for aluminum is 70 GPa and that for steel is 200 GPa. A couple M = 1500 Nm is applied as shown. Determine the maximum stress in the aluminum and the steel.

Solution: First I compute n:

Now I use this n to create the transformed section...

And now I use the transformed section to compute the position of the overall centroid :

 

section
1	1200	20	24000
2	1714	50	85710
sums	2914		109710

And therefore . This calculation was necessary to compute the moment of inertia I using the centroidal formula modified by the parallel axis theorem:

Now the stresses can be computed...

⁶ This is Problem 4.40 in Beer & Johnston's Mechanics of Materials, 2^nd Edition, McGraw-Hill.