Virtual Work Fall 2009

Virtual Work Fall 2009 - Virtual Work for Beams and Frames...

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Virtual Work for Beams and Frames 1- FBD 2- Equations of static equilibrium 3- Draw the shear and moment (M) diagrams due to the applied loads 4- Remove all the applied loads 5- Apply a unit load corresponding to the displacement in question, at the point into consideration. i. e. apply a unit vertical force to find the vertical displacement, a unit horizontal force to find the horizontal displacement, and a unit moment to find the rotational displacement or slope. 6- Draw the shear and moment (m) diagrams for the virtual system 7- Apply the virtual work equation. 1. = ∫ Mm dx/EI 1. =1/EI ∫ Mm dx if EI = constant 1. θ = ∫ Mm dx/EI 1. θ =1/EI ∫ Mm dx if EI = constant The integration must be carried out all over the beam or the frame. Make use of the integration Mohr's diagrams. May be you need to use integration and Mohr's diagrams. Check for discontinuities in the M and m diagrams. If the answer is positive, then, the displacement is in the direction of the
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Virtual Work Fall 2009 - Virtual Work for Beams and Frames...

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