Theory of Structures II Virtual Strain Energy Reference: Structural Analysis 10th Edition in SI Units by R.C.

1. CED 426
Structural Theory II
Lecture 4
Virtual Strain Energy Caused by
Axial Load, Shear, Torsion and Temperature
Mary Joanne C. Aniñon
Instructor

2. Virtual Strain Energy Caused by Axial Load,
Shear, Torsion, and Temperature
• Although deflections of beams and frames are caused primarily by
bending strain energy, in some structures the additional strain energy
of axial load, shear, torsion, and perhaps temperature may become
important. Each of these effects will now be considered.

3. Axial Load
• For members having a constant cross-sectional area, we have

4. Shear
• For the entire beam, the virtual strain energy is determined by
integration.

5. Torsion

6. Temperature

7. Example 3
Problem:
Determine the horizontal
displacement of point C on the frame
shown below. Take E = 200 Gpa and I =
235 (106) mm4 for both members.

8. Example 3
Virtual Moments, m
• For convenience, the x1 and x2 as
shown will be used.
• A horizontal unit load is applied at C,
and the support reactions and
internal virtual moments are shown.
• Solve the axial and shear.
moment

9. Example 3
Real Moments, M
• In similar manner, the support
reactions and real moments are
shown.
shear
shear

10. Example 3
Virtual-Work Equation (BENDING)

11. Example 3
Bending

12. Example 3
Axial

13. Example 3
Shear

14. Example 3
Applying the equation of virtual work: