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I have a square hollow sectioned pillar that is 100mmx100mm by 8mm thick, and want to...

I have a square hollow sectioned pillar that is 100mmx100mm by 8mm thick, and want to replace it with a circular solid secioned pillar. The material is carbon steel. What would be the smallest diameter you are able to use?

Engineering   Mechanical-Engineering   
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Answer #1

We have square hollow section pillar of dimensions 100 mm*100 mm*8 mm.

Material = Carbon.

The strength of the component is proportional to section modulus "Z" , which is "I/y".

Let us equate section modulus of a hollow rectangle and circular rod.

Section modulus of hollow square rod = Z = 1/6d(bd3 - b1d31).

Section modulus of square rod = Z = 1/6*100 (100*1003 - 84*843) = 83688 mm3.

Section modules of circular solid rod = 3.14*d3/32.

Let us equate both section modulus,

83688 = 3.14*d3/32

Diameter of solid circular rod = d = 94 mm.

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