Cantilever

A cantilever is a structural element that is anchored at one end and extends horizontally or outward beyond its support without a counterbalancing support at the free end. Cantilevers are used in many engineering disciplines, including civil, mechanical, and aerospace engineering, as well as in micro-scale devices. They transfer loads to the fixed support primarily through bending, with shear and moment concentrated near the support.

In a typical beam cantilever, the load distribution creates bending moments and deflections that are highest at the fixed support. For a cantilever of length L carrying a concentrated load P at the free end, the bending moment is P L along the length and the end deflection is approximately δ = P L^3 /(3 E I), where E is the modulus of elasticity and I is the second moment of area. If the load is distributed uniformly along the length with intensity w, the maximum moment is w L^2 / 2 and the end deflection is δ = w L^4 /(8 E I).

Variants of cantilevers include overhanging cantilevers, where the structure extends beyond a support with loads, and continuous cantilevers in frames where several members act as cantilevers. Long-span cantilever bridges and architectural features such as cantilevered balconies and canopies exploit this principle to project space without intermediate supports.

Materials commonly used for cantilevers include steel, reinforced concrete, timber, and composite materials. Design considerations focus on ensuring adequate stiffness to limit deflection, sufficient strength to withstand bending moments, and stability under service and dynamic loads. In micro-electromechanical systems, cantilevers function as sensing elements, where deflection relates to force, mass, or other physical quantities.