Cantilever Deflection from End Moment
Cantilever Deflection from End Moment
A moment applied at the free end of a cantilever curves it uniformly, producing a tip deflection set by the moment and stiffness.
The tip deflection is δ = M·L²/(2·E·I). where M is the end moment, L the length, E the modulus and I the second moment of area.
Inputs
M := 8 kN·m=8000 Nm
L := 2.5 m=2.5 m
E := 200 GPa=200000 MPa
I := 4.0e7 mm^4=4e-05 m^4
Apply the end-moment cantilever deflection formula.
delta := M·L^2/(2·E·I)=3.12 mm
Results
The deflection grows with the square of length. An end moment bends a cantilever into a circular arc, unlike the cubic curve from an end force.
Assumptions & limitations
- Elastic, prismatic cantilever.
- Pure moment at the tip.
- Small deflections.