A column has a pinned ends and is axially loaded in compression. The length is 6

Question

A column has a pinned ends and is axially loaded in compression. The length is 6 m and the weight is 1962 N, but the form of the cross section can be changed. The column is made of steel AISI 1040. Find the Euler buckling load for A solid square section. A square tube with outside dimension of 100 nun. A circular cross section bar with a diameter of 2 in and a length of 40 in is axially loaded. The bar is made of medium carbon steel and both ends are pinned. Determine Whether the Johnson or Euler criteria should be used. The critical load.

Explanation / Answer

For column pinned at both ends, buckling load, P = 2EI/L2

For AISI 1040 steel, E = 200 GPa, Density = 7845 kg/m^3

a) For solid square section, I = b4/12

Weight = 1962 N = 7845*(b^2)*6*9.81

Side of square b = 0.0652 m = 65.2 mm

I = (0.0652^4)/12 = 1.5045*10^-6 m^4

P = 2*(200*10^9)*(1.5045*10^-6)/(6^2) = 82409.5 N

b) Weight = 1962 N = 7845*(0.1^2 - b^2)*6*9.81

Inner side of square tube b = 0.0758 m = 75.8 mm

I = (0.1^4 - 0.0758^4)/12 = 5.577*10^-6 m^4

P = 2*(200*10^9)*(5.577*10^-6)/(6^2) = 305492 N

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