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Mechanics of Materials · Stress transformation and combined loading

A prismatic aluminum cantilever is fixed at A and free at B, with AB = 3.20 m

Problem

A prismatic aluminum cantilever is fixed at A and free at B, with AB = 3.20 m. The intensity of a downward distributed load varies linearly from 12.0 kN/m at the wall A to zero at the free end B. Take E = 70.0 GPa and I = 62.5 × 10^6 mm^4. Integrate the load-shear-moment-curvature sequence with the boundary conditions v'(0) = 0 and v(0) = 0 at the fixed end. Determine the rotation and the downward deflection at B, and locate the point of maximum bending stress if the cross section is a rectangle 40 mm wide by 250 mm deep.

Hint

Use the given I in EI; the 40 mm × 250 mm rectangle only names the extreme fibers. Max-stress location does not require matching I = bh³/12.

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