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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 = 20 in., E = 10.1 × 106 psi, P = 5 kips, and a factor of safety of 2.5 is required.

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 = 20 in., E = 10.1 × 106 psi, P = 5 kips, and a factor of safety of 2.5 is required.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Page 701 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
Sample Problem 10.1 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 = 20 in., E = 10.1 × 106 psi, P = 5 kips, and a factor of safety of 2.5 is required. STRATEGY: The most efficient design is that for which the critical stresses corresponding to the two possible buckling modes are equal. This occurs if the two critical stresses obtained from Eq. (10.13b) are the same. Thus for this problem, the two effective slenderness ratios in this equation must be equal to solve part a. Use Fig. 10.18 to determine the effective lengths. The design data can then be used with Eq. (10.13b) to size the cross section for part b.
Transcribed Image Text:Sample Problem 10.1 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 = 20 in., E = 10.1 × 106 psi, P = 5 kips, and a factor of safety of 2.5 is required. STRATEGY: The most efficient design is that for which the critical stresses corresponding to the two possible buckling modes are equal. This occurs if the two critical stresses obtained from Eq. (10.13b) are the same. Thus for this problem, the two effective slenderness ratios in this equation must be equal to solve part a. Use Fig. 10.18 to determine the effective lengths. The design data can then be used with Eq. (10.13b) to size the cross section for part b.
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