Answer to Question #148180 in Mechanical Engineering for ABHINAV SETHI

Question

A steel pipe of outside diameter 20 mm and thickness 3 mm is
deflected by 3 mm when used as a beam supported at its ends, 1
m apart, and subjected to a central load of 170 N. Find the
buckling load when the pipe is used as a column with hinged
ends. What is the maximum lateral deflection of this column
before the material attains the yield stress of 250N/mm2?

Answer 1

a. Steel pipe is used as a simply supported beam.

The deflection formula for simply supported beam is $\sigma = \frac{PL^3}{48EI}$

$I = \frac{\pi}{64}*(D^4-d^4)= \frac{\pi}{64}*(20^4-14^4)=5968.2406 mm^4$

$Therefore 3 = \frac{170*1000^3}{48*E5968.2406}$

$E=197806.293 MPa = 197.806 MPa$

b. If the steel pipe is used as a column with both ends hinged

The buckling load for both ends, $P_b=\frac{\pi^2EI}{Le^2}$

$P_b=\frac{\pi^2*197806.329*5968.2406}{1000^2} = 11651.62 N$