Calculate instant tip deflection and root bending moment for cantilever beams with formulas. Free structural analysis tool supporting point loads, UDL, and moment loads.
Enter the beam length, the Young's Modulus (E) of the material, and the Moment of Inertia (I). For steel, E is typically 200-210 GPa.
Input the applied load (Point load or Uniformly Distributed Load - UDL). Select the support condition: Simply Supported, Cantilever, or Fixed-Fixed.
The tool outputs the maximum deflection (δ) and rotation (θ). Ensure the deflection is within the limits set by building codes (e.g., L/360 for floor beams).
A tip point load deflects the free end by δ = PL³/3EI, sixteen times the PL³/48EI of the same beam simply supported over the same span. The entire load is resisted by a single fixed end working in cantilever, so cantilevers are far more flexible and almost always governed by deflection rather than stress.
Always at the fixed (root) support, never at the free end. A tip point load gives a root moment M = PL; a uniform load gives M = wL²/2. For instance, a 5 kN load at the tip of a 2 m cantilever develops a 10 kN·m moment at the wall, which is where the section and connection must be sized.
It is the angle the free end rotates from horizontal: θ = PL²/2EI for a tip load, or wL³/6EI for a uniform load. A 5 kN tip load on a 2 m steel cantilever (E = 200 GPa, I = 8.36×10⁷ mm⁴) rotates about 0.0006 rad. Slope matters for cladding, glazing, and anything cantilevered further off the tip.
Yes. With an applied end moment M₀ the reaction force is zero, the moment is constant M₀ along the whole length, the tip deflects by M₀L²/2EI, and the tip rotation is M₀L/EI. This case is useful for checking eccentric loads or balcony rail moments transferred into a cantilever.