13-45. Consider an ideal column as in Fig 13-10 d , having one end fixed and the other pinned. Show that the critical load on the column is given by Pcr = 20.19EI>L2. Hint : Due to the vertical deflection at the top of the column, a constant moment M! will be developed at the fixed support and horizontal reactive forces R" will be developed at both supports. Show that d2v>dx2 + (P/EI)v = (R">EI)(L - x). The solution is of the form v = C1sin (sqrt(P/EIx)) + C2 cos (sqrt(P/EIx)) +(R"/P)(L - x). After application of the boundary conditions show that tan (1P/EIL) =sqrt(P/EI) L. Solve by trial and error for the smallest nonzero root. | |
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