Cantilever Beam & Balanced Cantilever

Projecting beam, truss, or slab anchored rigidly at one support end while carrying loads over an unsupported overhang.

Specifications & Metrics

type: Load-Bearing Structural System
load mechanism: Resists vertical loads via internal shear stress and a negative bending moment (tension in top fiber, compression in bottom fiber) at the fixed root
governing relation: M_max = −F·L (root bending moment); δ_max = F·L³ / (3EI) (tip deflection for point load F)
classic configurations: Fixed-root beam, balanced double cantilever bridge, stressed-skin monoplane wing, MEMS microcantilever
exemplars: Forth Bridge (Scotland, 1890), Quebec Bridge, Frank Lloyd Wright's Fallingwater, Junkers J 1 wing (1915)

Anchored with a full moment connection at a single support, a horizontally projecting cantilever carries downward tip loads by placing its upper flange or chord in tension and its lower flange in compression, with maximum bending moment M = −F·L concentrated at the root.
Balanced cantilever truss bridges such as Scotland's 1890 Forth Bridge build symmetrical cantilevers outward from each pier without falsework in the shipping channel below, suspending a shorter central span between the cantilever tips.
The cantilever principle scales across nine orders of magnitude: Hugo Junkers eliminated external wire bracing in aviation with the all-metal cantilever wing of the 1915 Junkers J 1, while micrometer-scale silicon nitride MEMS cantilevers resolve piconewton atomic forces in Atomic Force Microscopes (AFM).