Cantilever Beams: Moments, Shear and Deflection
2026-10-15 · 2 min read
A cantilever is a beam fixed at one end and free at the other. Everything the loads do — every newton and every newton-metre — is carried by the fixed support as force plus moment.
Why the fixed end matters
A simple support can only push back. A fixed support pushes back and resists rotation, which means it develops a fixing moment. For a cantilever of length L with an end load P:
- Vertical reaction:
R = P - Fixing moment:
M = P·L(hogging — negative under the sagging-positive convention)
The moment diagram is a straight line from −PL at the wall to zero at the
free end. Maximum stress is at the wall, at the top fibre — which is why
cantilever reinforcement goes on top.
Standard cases
| Load | Fixed-end moment | Max deflection (free end) |
|---|---|---|
| End point load P | PL |
PL³ / 3EI |
| Full-span uniform w | wL² / 2 |
wL⁴ / 8EI |
| Load rising to w at wall (triangular) | wL² / 6 |
11·wL⁴ / 120EI |
| End moment M₀ | M₀ (constant) |
M₀L² / 2EI |
Note the uniform-load fixing moment wL²/2 is twice the midspan moment of
a simply supported beam under the same load — cantilevers are efficient in
deflection (8 vs 384 denominator) but punishing at the support.
Balconies and canopies
Real cantilevers rarely carry a single load. A balcony slab is a cantilever strip with:
- self-weight (uniform) over the full embedment,
- finishes (uniform),
- live load (uniform, per code),
- a parapet or wall line near the edge (a line load near the tip — the worst position for the fixing moment).
Check both strength (moment and shear at the root) and serviceability (tip deflection and the rotation at the root that cracks the back-span). A cantilever that rotates 0.5° at the wall feels bouncy underfoot long before it is anywhere near failure.
The overturning check
A cantilever is also a lever. A heavy load near the tip tries to rotate the whole structure about the support — check that the back-span or the foundation is heavy enough to hold it down. Balcony failures are frequently overturning, not bending.
Model your case in the beam calculator — set a single fixed support and watch the diagrams build.