Cantilever Beam Calculator
Calculate reactions, maximum negative bending moment at the fixed root, and tip deflection for cantilever beams subjected to point loads, uniformly distributed loads (UDL), and tip moments.
δ_tip = (w·L⁴) / (8EI) + (P·L³) / (3EI)
Beam Master handles any combination of point loads, uniform distributed loads (UDL), varying loads (UVL), and applied moments with instant SFD, BMD, and deflection curves.
Cantilever Beam Mechanics & Boundary Conditions
A cantilever is anchored rigidly at one end (fixed support) and completely free at the opposite end. Because the fixed support resists vertical displacement and rotation, the boundary conditions are:
// At Fixed Root (x = 0):
Deflection v(0) = 0
Slope θ(0) = dv/dx = 0
// At Free End (x = L):
Shear Force V(L) = 0 (or concentrated tip load P)
Bending Moment M(L) = 0 (or applied tip moment M₀)
Engineering Formulas & Governing Equations
Fixed End Reaction Moment (UDL over full span L)
Equation 01The fixed wall must resist the entire overturning moment caused by the distributed load.
Maximum Tip Deflection (UDL w)
Equation 02Peak downward displacement occurring at the free tip of the cantilever under uniform load.
Maximum Tip Deflection (Point Load P at Tip)
Equation 03Elastic deflection at x = L produced by a concentrated force at the unsupported tip.
Maximum Tip Slope Angle (Point Load P)
Equation 04The rotational slope in radians at the free end of the cantilever.
Calculation Details & Clarifications
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