If the columns cross sectional area were uniform the

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Reference no: EM13344798

Suppose that you want to design a column to support a uniform compressive stress stress naught. If the column's cross sectional area were uniform, the compressive stress at increasing distances x from the top would increase due the column's weight. You can optimize your use of material by varying the column's cross sectional area in such a way that the compressive stress at every position x equals stress naught. Prove that this is accomplished if the column's cross sectional area is A=(Ao)*e^[(gamma/stress naught)*x] where Ao is the cross sectional area at x=0 and gamma is the weight density of the material.

Reference no: EM13344798

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