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A cylindrical hollow shaft shown is subjected to a compressive load acting though its longitudinal axis. The outer diameter of the tube is 30 mm and the inner diameter
is 25 mm. The tube is made of brass, and it has Young's Modulus E = 105 GPa and yield
strength oys = 135 MPa.
(a)Using Euler's formula, determine the critical buckling load (or maximum allowable compressive load) when the length of the tube is L = 2 m and it is pin-jointed at both ends.
(b)Using Euler's formula, determine the critical buckling load (or maximum allowable compressive load) when the length of the tube is L = 2m and it is fixed at one end and pinned at another.
(c)Verify the validity of Euler's formula in case (a).
Assuming the tube is pin-jointed at both ends, calculate the minimum length of the tube below which Euler's formula is no longer valid.
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