Answer to Question #148180 in Mechanical Engineering for ABHINAV SETHI

Question #148180
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?
Expert's answer

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"

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