13-44. Consider an ideal column as in Fig 13-10 c , having both ends fixed. Show that the critical load on the column is given by Pcr = 4p2EI/L2. Hint : Due to the vertical deflection of the top of the column, a constant moment M! will be developed at the supports. Show that d2v/dx2 + (P/EI)v = M"/EI. The solution is of the form v = C1 sin(sqrt(P/EIx)) + C2 cos(sqrt(P/EIx)) + M"/P. | |
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