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Force-Deformation Equations Application

  1. May 2, 2018 #1
    Just found this forum--hope there isn't a max post limit haha.

    I have been a bit stumped on this, but when doing problems about deflection and axial loadings, I am confused when to use which equation.

    I think I know that axial member need to be 2 force members, loaded only at the ends, and this means you can use δ=FL/AE. However, I had a problem with two axial bars connected at two ends and it was made clear that I could not use the above equation, but had to use σ=δL/E.

    I guess my main question is where do I use which, what exactly is axial loading, and what is statically indeterminate mean does this make it unusable??

  2. jcsd
  3. May 3, 2018 #2


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    Your 2nd formula is incorrect , perhaps you copied it down incorrectly, for axial loading it should be [itex] \delta = \sigma L/E[/itex], and since axial stress is F/A, this equation is identical to your first equation. It comes from Hookes Law, where stress is proportional to strain, and the proportionality constant is E, the Elasticity of the material, or that is [itex] \sigma = \epsilon E[/itex], where the strain [itex] \epsilon [/itex] is axial deformation/L. I'm not sure why you have to use the 2nd equation (as I have corrected) rather than the first , which gives the same result, unless the givens make it easier to use, perhaps you can post the problem. Deformations for bending loads are a bit more complex.

    Statically indeterminate problems mean that you have to use more than the equilibrium equations to solve them, like calculating deflections and such, but they certainly are valid beams or trusses with more supports and members.
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