Cantilever Beam Moment, Shear, and Deflection

Max moment (P L + w L^2/2), max shear (P + w L), and tip deflection (P L^3/3EI + w L^4/8EI) of a cantilever from a tip point load, a uniform load, or both. Elastic small-deflection prismatic member. A design aid, not the engineer of record.

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Formula and source

M = P L + w L^2/2 (max moment at support); V = P + w L (max shear); delta = P L^3/(3 E I) + w L^4/(8 E I) (tip deflection, L in inches).

The standard cantilever beam moment/shear/deflection formulas (Roark's Formulas for Stress and Strain; AISC Manual beam diagrams), by name.

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