cantilevers

A cantilever is a structural element that is anchored or fixed at one end and carries loads along its length, with the free end projecting outward. It is designed to resist bending through the fixed support, which provides reaction moments and shear to balance applied loads.

In classical beam theory, cantilevers are analyzed as fixed-end beams. For a cantilever of length L with a concentrated load P at the free end, the deflection at the tip is δ = P L^3 / (3 E I), the slope at the fixed end is θ = P L^2 / (2 E I), and the fixed-end moment is M0 = P L. For a uniformly distributed load w per unit length, the tip deflection is δ = w L^4 / (8 E I), and the fixed-end slope is θ = w L^3 / (6 E I). E is the modulus of elasticity and I is the moment of inertia of the cross-section. These relations illustrate how length, stiffness, and loading shape determine bending and displacement.

Cantilevers are used in a wide range of materials, including steel, concrete, wood, and composites. Design considerations address deflection limits, bending stress σ = M c / I, and reliability concerns such as fatigue, buckling, and environmental effects. The slenderness of a cantilever makes precise control of stiffness and end conditions important in practice.

Applications span architecture (cantilevered balconies and overhangs), civil engineering (bridge segments and booms), and machinery (lattice booms and robotic arms). At micro and nano scales, cantilevers serve as sensors in MEMS and AFM devices, where small deflections and high sensitivity are essential. Variants include tapered, curved, and propped cantilevers, each tailored to specific loading and deployment requirements.