Figure Q2(b) shows the cross-section of a cantilever beam ABC. The beam is subjected to uniformly distributed loading and a concentrated force as shown in Figure Q2(c). Determine: (i) the second moment of area or moment of inertia for the cross-section about its neutral axis (NA) (ii) the internal bending moment and bending stress at section x-x as shown in Figure Q2(c) and at points P and Q of the cross section as shown in Figure Q2(b) of the beam and state whether the bending stress is in tension or compression.

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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.