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Clamped-clamped beam load deflection with residual stress

  1. Mar 1, 2013 #1
    I have a system that consists of a clamped-clamped beam with a residual stress and am trying to find an equation that governs its deflection due to a point force that takes stress into consideration. A formula I have come across:

    d = (F*L^3)/(192*E*I)

    does not accurately model the measured displacement of the beam.

    d : maximum central deflection (m)
    F : magnitude of applied point force (N)
    L : length of the beam (m)
    E : Young's modulus (Pa)
    I : moment = (w*t^3)/12 (m^4)

    Is there a formula that includes residual film stress as well? Or is there a good tutorial available for deriving such a formula?
    As a word of warning, I do not have a strong background in mechanics, so I apologize if I overlooked something simple.
    Thank you in advance for you help!
  2. jcsd
  3. Mar 1, 2013 #2


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    It depends on how you model the residual stress, are you modeling it like a UDL on one side of the beam or like a compressive/tensile force along its axis?
  4. Mar 4, 2013 #3
    Thank you for your response! I have been modeling it as an axial force, but perhaps that is the cause of some of my trouble? Do you recommend modeling it as a UDL?
    In that case, can I just subtract the force due to stress from the applied force and use that net force quantity in the equation in my original post?
  5. Mar 6, 2013 #4
    Does anybody have any ideas about this?
    Thanks again in advance.
  6. Mar 8, 2013 #5


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    mike_oh: What is the pattern of your residual stress? Is it a uniform axial stress, due to an axial force? If so, is it uniform axial tensile stress, or uniform axial compressive stress? What causes it? Is this small deflection theory, or large deflection theory? Is this a school assignment?
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