As was mentioned in 24, the differential equation (7) that governs the defl.cction y(x)

Chapter 3, Problem 25

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As was mentioned in 24, the differential equation (7) that governs the defl.cction y(x) of a thin elastic column subject to a constant compressive axial force P is valid only when the ends of the column are hinged. In general, the differential equation governing the deflection of the column is given by d 2 ( d'y) d'y th2 El th2 + p dx2 = 0. Assume that the column is uniform (EI is a constant) and that the ends of the column are hinged. Show that the solution of this condition fourth-order differential equation subject to the boundary sy(O) = O,y"(O) = O,y(L) = O,y"(L) = O isequivalent to the analysis in Example 4