An aluminum column with a length of L and a rectangular cross-section has a fixed end B and supports a centric load at A. Two smooth and rounded fixed plates restrain end a from moving in one of the vertical planes of symmetry of the column but allow it to move in the other plane. (a) Determine the ratio a/b of the two sides of the cross section corresponding to the most efficient design against buckling. (b) Design the most efficient cross section for the column, knowing that L = 20in., E=10.1 x 10^6 psi, P = 5kips, and a factor of safety of 2.5 is required. Consider Sample Problem 10.1. Solve the same problem, but this time replace the pinned boundary condition on top with a fixed boundary condition. You otherwise leave all other aspects of the problem unchanged. Be sure to answer both Part a and Part b. As careful observation, please do keep in mind that two things happen: First, on top, the pinned boundary condition in one place is replaced by the fixed boundary condition in that plane. But second, on top again, the free boundary condition in the other plane does remain unchanged.
An aluminum column with a length of L and a rectangular cross-section has a fixed end B and supports a centric load at A. Two smooth and rounded fixed plates restrain end a from moving in one of the vertical planes of symmetry of the column but allow it to move in the other plane. (a) Determine the ratio a/b of the two sides of the cross section corresponding to the most efficient design against buckling. (b) Design the most efficient cross section for the column, knowing that L = 20in., E=10.1 x 10^6 psi, P = 5kips, and a factor of safety of 2.5 is required.
Consider Sample Problem 10.1. Solve the same problem, but this time replace the pinned boundary condition on top with a fixed boundary condition. You otherwise leave all other aspects of the problem unchanged. Be sure to answer both Part a and Part b. As careful observation, please do keep in mind that two things happen: First, on top, the pinned boundary condition in one place is replaced by the fixed boundary condition in that plane. But second, on top again, the free boundary condition in the other plane does remain unchanged.
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