A column is axially loaded in compression. The ends were specified to be fixed, but because of a manufacturing error they had (a) One end fixed and the other pinned (b) Both ends pinned Find how much the critical elastic buckling load is decreased because of the errors. Also, calculate the buckling loads for the 4-m-long column made of annealed AISI 1040 steel having a solid, square cross section with 30-mm sides for the three end conditions. Assume theoretical effective column length.

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Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.