Question

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?

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.