Cantilever Beam Deflection
Deflection (in)
0.014
How it works
A cantilever beam is fixed at one end and free at the other — overhangs, diving boards, balcony slabs, and wall brackets are examples. Because one end is unrestrained, cantilevers deflect significantly more than simply supported beams of equivalent span and load. The Cantilever Beam Deflection Calculator handles point load at the free end, UDL, and point load at any position.
**Deflection comparison: cantilever vs. simply supported** For the same span, load, and beam section, a cantilever deflects approximately 5 times more than a simply supported beam under midpoint load. This is why cantilever spans are typically 1/3 to 1/2 of equivalent simply supported spans in floor systems.
**Fixed-end moment** Unlike simply supported beams, cantilevers develop a large bending moment at the fixed end. The maximum moment occurs at the wall for a UDL: M = w × L² / 2. This is where the beam must be strongest — why wide-flange beams oriented with the flange in the horizontal plane (minor axis bending) are inappropriate for cantilever applications.
**Tip deflection for point load at free end** δ = P × L³ / (3 × E × I). The cubic relationship to span means a 50% increase in cantilever length nearly doubles tip deflection. Limiting cantilever spans is almost always more effective than increasing beam size.
**Back-span consideration** A cantilever must be balanced by a back-span or anchor to prevent rotation at the support. The back-span should typically be at least twice the cantilever length. Neglecting back-span stability is a common error in preliminary structural analysis.
For design purposes, verify all results with a qualified structural engineer.
Frequently Asked Questions
- For a point load at the free end vs. midpoint of a simply supported beam of the same span: cantilever deflects PL³/3EI, simply supported deflects PL³/48EI. The ratio is 16:1 — the cantilever deflects 16 times more. For a uniform distributed load: cantilever deflects wL⁴/8EI, simply supported deflects 5wL⁴/384EI. The ratio is ~48:1. This is why cantilever spans in structures are kept much shorter than simply supported spans.
- Building codes limit cantilever spans relative to the backspan — typically the cantilever cannot exceed 1/4 of the backspan for wood floor joists, and must be balanced by sufficient back-span anchorage. Common rules of thumb: floor joists may cantilever up to 24 inches (600 mm) for typical loads without special engineering. Longer cantilevers require engineering calculations and often require deeper or stronger beams, uplift connections at the anchor end, and deflection checks.
- Excessive deflection under live load (people walking) creates a springy feel that's alarming even when structurally safe. This is a stiffness (serviceability) problem, not a strength problem. Solutions: increase beam depth (most effective), reduce cantilever length, add a prop column below (if architecture allows), use post-tensioning in concrete cantilevers, or add a stiffening beam at the free end. The L/300–L/360 deflection limits in codes specifically address this perception of inadequate stiffness.
- The fixed end develops a bending moment that must be transferred into the supporting structure. For a cantilever floor joist, the moment is resisted by the joist connection to the rim board and the backspan. For a concrete cantilever slab, top reinforcement carries the tension from the hogging moment. In steel, the column-beam connection must resist the moment — a simple shear connection is insufficient for cantilever applications. Always check that the support can resist both the vertical reaction and the moment.