Example 1¹

Problem: In the truss shown, all members are made of the same material and have the uniform cross sectional areas indicated.  Determine the strain energy of the truss when the load P is applied.

Solution:  Here's the free body of the truss:

Since the strain energy is dependent on the length and force, I need to find these:

Drawing free body diagrams for joints C and B...

From the right hand free body, we can see that F_BC = F_CD, and that

Using this with the left hand free body,

Now I compute the strain energy...

¹ This is problem 10.30 in Beer & Johnston's Mechanics of Materials, 2nd Edition.