A stepped cantilever carries P = 3 N at its free end. The free-end segment is 2 m long with second moment I; the segment next to the fixed end is 1 m long with second moment 3I. Material modulus is E. Neglect transverse shear and stress concentrations. Find free-end deflection.
Let x run from the free end, so bending moment magnitude is Px. The unit-load method gives $\delta=P[\int_0^2x^2/(EI)dx+\int_2^3x^2/(3EI)dx]$. These integrals give $P[8/3+19/9]/(EI)=43P/(9EI)$. With P = 3 N, δ = 43/(3EI), C.
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