Homework Help: Solid Mechanics

Posted by rakesh on Wednesday, August 8, 2012 at 6:43pm.

Determine the ratio of strenghts of a solid steel column to that a hollow column of the same material and having the same cross sectional area. The internal diameter of the hollow column is 1/2 of its external diameter. Both the columns are same length and are pinned at their both ends

Solid Mechanics - MathMate, Wednesday, August 8, 2012 at 10:30pm
Hints:
Axial stress is the same because the same load is distributed over the same area.
However, buckling strength is widely different.

Calculate the ratio of the area moments of inertia, and compare buckling their strengths using Euler's buckling formula:
F=π²2EI/(KL)²
where E,I are Young's modulus, I=area moment of inertia, K=end condition constant, equals 1 when pinned, and L=length of columns.

See also for more explanation on buckling:
http://en.wikipedia.org/wiki/Buckling
or other textbooks on strength of materials.

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