1. Chapter 9.5 Method of Virtual Work: Beams and Frames

2. Virtual Work: Bending
Bending is primary cause of beam and frame deflections.
Deflections due to shear, axial and torsional loadings, and temperature will be ignored in this class.

3. Virtual Work: Bending Deflection - Add virtual unit load Slope
- Add virtual unit moment

4. Virtual Work: Notes
If concentrated loads or couple moments act on the beam or the distributed load is discontinuous, a single integration cannot be used over the entire length of the member.
Separate x-coordinates will have to be chosen within the regions with no discontinuity of loading.
Each x-coordinate does not need to have the same origin; however, the x-coordinate used to solve for M must be the same when solving for m.
Figure 9-12.

5. Virtual Work: Procedure
See Procedure on page 361 of your textbook.
Remember:
Use the same x-coordinate when solving for m and M.
Whatever direction m is assumed to act in, assume M acts in the same direction.
Retain the algebraic sign of each integral.
If the solution is positive, then the deflection/slope is in the assumed direction of the applied load. If the solution is negative, the deflection/slope is in the opposite direction.
Can use Integration tables

6. Example 1: Beam Virtual Work

7. Example 2: Beam Virtual Work

8. Example 3: Beam Virtual Work
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