Cantilever Beam Moment, Shear, and Deflection
Max moment (P L + w L^2/2), max shear (P + w L).
Example
You enter
- Cantilever length L (ft) 6
- Tip point load P (lb, optional) 2000
- Modulus E (psi; 29e6 steel, 1.6e6 wood) 29000000
- Moment of inertia I (in⁴) 53
You get
- Max moment (at support) 12000 lb-ft
- Max shear (at support) 2000 lb
- Delta (in) 0.162
Details, formula, and sources
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.
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.
Cantilever beam diagrams are published free in engineering references and the AISC Steel Construction Manual beam-diagram tables. The engineer of record governs the design.
Estimate. AHJ and licensed professional govern.
Field names used by the API: L_ft, P_lb, E_psi, I_in4, M_lbft, V_lb, delta_in
- Support/loads fixed at one end; a tip point load, a uniform load, or both, superposedRoark / AISC beam diagrams
- Deflection form delta = P L^3/(3 E I) + w L^4/(8 E I)elastic beam theory
- Not a capacity check no LTB, shear deformation, or allowable-stress checkscope of this tile