Exam #4 - Review Question #2

Problem 2: This is problem 11.26 on page 689.
Solution: The free body diagram is:

The members are "two-force." The forces in the members are necessary to compute the strain energy, since

From the sum of the forces in the y-direction, By = 200 kN. Moments about B provide Dx = 180 kN. Then, the sum of the forces in the x-direction results in Bx = 420 kN. The angle is the arctangent of 0.75/1.8, or 22.6o. A free body diagram around joint D produces

From right triangle trigonometry, FBD = 75 kN and FCD = 195 kN. I now have three of the four forces acting at joint C and can find (work not shown) using the sum of the forces that FBC = 325 kN.
Now I have the information necessary to find the strain energy:

The factor of 106 converts the square of kN to N2.