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) Ay=0.5*P/L3*[2L3-3Lx2+x3] MA=0.5*P/L2*x*[2L2-3Lx+x2] 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??