Problem 1. The steel rod has a radius of 1.25 in. If it is subjected to a shear of V = 5 kip, determine the maximum shear stress from the shear formula T=VQ/(It) and identify where these maximum shear stresses occur. Identify the section area and section area centroid used to calculate the maximum first area moment Qmax where τ = τ By what factor is the maximum shear stress max. -1.25 in. H V = 5 kip greater than the average shear stress acting over the cross- section. From a side view, sketch the shear stress distribution function with perpendicular distance from the Neutral axis. Clearly show the Neutral Axis of the cross-sectional area. Indicate the shear stress components in both transverse and axial directions on a volume element located where shear stress is maximum. Clearly identify the Neutral Plane. Show the longitudinal shear stress on the Neutral Plane of a free-body-diagram (FBD) of the lower half of the rod. If the upper and lower halves are bonded by glue across the Neutral Plane, and if the maximum allowable shear stress in the glue is 2.0 ksi, determine the maximum shear force V which can be applied without failure of the glue bond. If the shear force V were increased to a value higher than the maximum allowable, the glue would fail and the bond between the upper and lower half would be broken: in this condition, which direction would the top have moved relative to the bottom half (forward or backward); indicate the direction by arrow and/or shifted cut FBD's.

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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.