Q. 4: The column shown in Fig. Q4a is pinned at both ends. The column is 3m long. Using Euler's formula, calculate the critical buckling load with a) the cross section shown in Fig. Q.4b; b) the cross section shown in Fig. Q.4c; Take E=180 GPa.

A column, pinned at top and bottom, is made up of two C 10 x 25 steel shapes (see figure) that act together. Gap- 26 ft. Note that distance d is measured between the centroids of the two C sha ve this problem using the assumptions of ideal, Assume that E = 30,000 ksi and L slender, prismatic, and linearly elastic columns (Euler buckling).) (a) Find the buckling load (in kips) if the gap is zero. 37.3 kips (b) Find required separation distance d (in inches) so that the buckling load is the same in y and z directions. 6.92 in.

(c) An aluminium bar having a cross-sectional area of 0.5 in² carries the axial loads applied at the positions shown in Figure. Compute the total change in length of the bar if E = 10× 106 psi. Assume the bar is suitably braced to prevent lateral buckling. 6000 lb 7000 lb <<5000 lb 4000 lb 3 ft 5 ft 4 ft

5. Determine the allowable axial load PA for a W250 x 67 steel wide-flange column with pinned ends (see figure below) using a Factor of Safety n=1.5 for the following lengths: L-3 m, 5m, 8 m and 10 m. Assume E-200,000 MPa, and G-300 MPa. 7 L A Pl A ISTE Section A-A