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Finding the collapse load P

  1. May 1, 2010 #1
    finding the collapse load "P"

    i am taking a course on solid mechanics, and we are learning plastic deformations in transverse loading, in this question i am asked to find an expression for the "collapse load P" as a function of its placement on the beam "x"


    i do not remember learning the term "collapse load" but from what i could assume, i would say that this means the the force P is enough to cause a collapse in the beam no matter where it is placed, - P will be a function of X, at X=0 P will be 0, then it will get larger and then smaller again till X=L, P=0 again,

    first of all is this a correct assumption??

    now to solving the problem:

    using castiglianos 2nd theorem i found
    (A is the leftmost point)



    now as far as i can tell the maximum moment, which will be equal to the plastic moment, will either be felt at point A and will be equal to MA, or will be found at point X and will be equal to Ay*x-MA
    --how do i know which is the correct one???

    P can be minimum when the moment found is maximum.

    i found both of these functions' maximums

    for MA i get maximum when X=0.4040L
    for Ay*x-Ma i get X=0.6364L

    neither of these is correct, what am i doing wrong??
  2. jcsd
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