Cantilever Beam Deflection (End Point Load)
Cantilever Beam Deflection Under an End Load
A cantilever is fixed at one end and free at the other. This sheet computes the vertical deflection at the free tip and the bending stress at the fixed root when a single point load acts at the tip — the governing case for balconies, brackets and overhanging members.
From beam theory the tip deflection is δ = FL³/(3EI) and the maximum bending moment occurs at the support, M = FL.
Inputs
F := 5 kN=5000 N
L := 2.5 m=2.5 m
E := 200 GPa=200000 MPa
b := 100 mm=100 mm
h := 200 mm=200 mm
Section properties
I := b·h^3/12=6.67e-05 m^4
Tip deflection and root stress
The deflection grows with the cube of the length, so a cantilever is far more flexible than a simply supported span of the same length.
delta := F·L^3/(3·E·I)=1.95 mm
sigma_max := F·L·(h/2)/I=18.75 MPa
Results
Cantilever tip deflections are typically limited to about L/180 of the projection. Because deflection scales with L³, doubling the overhang increases the tip movement eightfold — keep cantilevers short or deep.
Assumptions & limitations
- Rigid, fully fixed support with no rotation.
- Linear-elastic, small-deflection theory.
- Point load at the very tip; self-weight excluded.