Question 8.1: A column with a length of 7.2 m has a tubular cross-section ...
A column with a length of 7.2 m has a tubular cross-section with internal radius 70 mm and external radius of 75 mm. It is to be used as a pin-ended column carrying compressive load along its axis. The material is steel with elastic limit at 250 MPa and Young’s modulus 200 GPa. Find out the maximum allowable axial load so that it does not buckle.
In this case, both ends of the column are pinned. So, the critical load for buckling is
P_{ Cr }=\frac{\pi^2 E I}{L^2}
Putting the numerical values, we get the critical load for the column, which obviously corresponds to the maximum load that can be applied. Therefore,
P_{ Cr }=\frac{\pi^2 \times 200 \times 10^6 \times\left[75^4-70^4\right] \times \frac{\pi}{4}\left(\frac{1 m }{1000 mm }\right)^4}{(7.2)^2}=228.2 kN
The stress developed on the column is
\text { Stress }=\frac{228.2 \times 1000}{\pi\left(75^2-70^2\right)}=100 MPa
This is well within proportional limit or elastic limit and hence Euler’s equation can be safely applied.