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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)

Ay=0.5*P/L^{3}*[2L^{3}-3Lx^{2}+x^{3}]

MA=0.5*P/L^{2}*x*[2L^{2}-3Lx+x^{2}]

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??

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# Homework Help: Finding the collapse load P

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