The roof beams of a warehouse are supported
by pipe columns (see figure on the next page) having outer
diameter d2 = 100 mm and inner diameter d1 = 90 mm. The columns have length L = 4.0 m, modulus E = 210 GPa, and columns have length L = 4.0 m, modulus E = 210 GPa, and fixed supports at the base.
Calculate the critical load Pcr of one of the columns using the following assumptions:
(1) The upper end is pinned and the beam prevents horizontal displacement;
(2) The upper end is fixed against rotation and the beam prevents horizontal displacement;
(3) The upper end is pinned but the beam is free to move horizontally; and
(4) The upper end is fixed against rotation but the beam is free to move horizontally.

Transcribed Image Text:

Roof beam Pipe column d2