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Consider an ideal column as in Fig.13-10 c, having both ends fixed. Show that the critical load on the column is Pcr = 4π2EI/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
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