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Chapter 9.5 Method of Virtual Work: Beams and Frames

Chapter 9.5 Method of Virtual Work: Beams and Frames. 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. Virtual Work: Bending. Deflection

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Chapter 9.5 Method of Virtual Work: Beams and Frames

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  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 9.54 page 396

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