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Problem_12_19

# Problem_12_19 - Problem 12.19 Given An aluminum alloy(E=72...

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Problem 12.19 Given: An aluminum alloy (E=72 GPa) column has the cross section shown, a length of 9 m, and is clamped at each end. A support at the midlength of the column prevents deflection in the x direction but does not prevent rotation of the section nor deflection in the y direction. Find: a) the buckling load b) minimum value for the proportional limit. Solution: a) E 72 GPa := L9 m := I y 100 mm 25 mm () 3 12 2 25 mm 150 mm 3 12 + := I y 1.419 10 7 × mm 4 = I x 25 mm 100 mm 3 12 2 150 mm 25 mm 3 12 150 mm 25 mm 62.5 mm 2 + + 3.177 10 7 × mm 4 = := From Table 12.1 for a clamped-clamped column k 1 2 := Look at buckling in the Y direction (1st mode) Pcr Y π 2 E I x kL 2 1114.9 kN = := There are two apporaches for buckling in the x direction.

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Problem_12_19 - Problem 12.19 Given An aluminum alloy(E=72...

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