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Consider an ideal column as in Fig. 13-10d, having one end fixed and the other pinned. Show that the critical load on the column is Pcr = 20.19 EI/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/EL)v =(R'/EI)(L − x). The solution is of the form v = C1 sin
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