1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Virtual work (internal = external)

  1. Oct 27, 2014 #1
    1. The problem statement, all variables and given/known data
    How can one show/prove that for a beam (hinged supports on both ends) subjected to bending due to a uniformly distributed load over its entire length, the virtual work of internal forces is equal to the virtual work of external forces? Given are the length of the beam (L), uniformly distributed load (P = constant), Young's modulus (E), and second moment of area (I).

    2. Relevant equations (I guess)
    [tex]\delta W_{in}={\int_{V}^{}}\delta \tilde{\varepsilon} ^T\tilde{\sigma} dV[/tex] and [tex]\delta W_{ex}={\int_{V}^{}}\delta \tilde{u} ^T\tilde{\textbf{f}} dV+{\int_{S}^{}}\delta \tilde{u} ^T\tilde{\textbf{t}} dS[/tex]
    3. The attempt at a solution
    I think that in this particular case the first equation can be simplified to
    Can the shear stress (τxy) be neglected here? If so, we would get
    I'm not sure what I should do with the other equation. Am I even approaching this correctly? If not, what are the right steps to follow? Any suggestions welcome. Thank you.
    Last edited: Oct 27, 2014
  2. jcsd
  3. Nov 1, 2014 #2
    Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Virtual internal external Date
Virtual Work - Determining Relations Oct 13, 2015
Virtual Work Method on a Truss Mar 18, 2014
Virtualization techniques for Security Mar 14, 2014
Virtual work Jan 21, 2014