Aluminum tubes of diameter d = 1.5" and length L = 20" will be used as simply supported columns subject to an axial load. The load on each column has a mean value of 1000 lb and a standard deviation of 50 lb. What should the thickness of the tube be so that the probability of the column buckling is less than 0.0001? The tolerance on the wall thickness is ±0.001"; the tube diameter and length can be treated as deterministic variables. Treat the column as a thin-walled tube.
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