Cantilever Deflection Under a UDL
Cantilever Deflection Under a UDL
A cantilever under self-weight or a distributed load deflects most at its free tip; this is the governing serviceability case for canopies and balconies.
For a cantilever under a UDL the tip deflection is δ = wL⁴/(8EI). where w is the distributed load, L the length, E the modulus and I the second moment of area.
Inputs
w := 6 kN/m=6000 kg/s^2
L := 2.5 m=2.5 m
E := 200 GPa=200000 MPa
I := 4.5e7 mm^4=4.5e-05 m^4
Apply the cantilever UDL tip-deflection formula.
delta := w·L^4/(8·E·I)=3.26 mm
Results
Tip deflection scales with the fourth power of length, so a modest increase in projection greatly increases movement. Limit it to roughly L/180 of the cantilever length.
Assumptions & limitations
- Rigid fixed support.
- Elastic, prismatic member.
- Small-deflection theory.