Sketch the appropriate graphs, and check each on a calculator. A cantilever column of length L will buckle if too large a downward force P is applied d units off center. The horizontal deflection x (see Fig. 10.32) is x = d [sec(kL) − 1], where k is a constant depending on P, and 0 < kL < π/2. For a constant d, sketch the graph of x as a function of kL.

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Fig. 10.32 L P