Deflection in engineering refers to the degree to which a part of a long structural element changes shape when a load is applied). Deflection can be quantified in terms of an angle or a distance, and it may be caused by externally applied loads or from the weight of the structure itself and the force of gravity. Deflection can occur in beams, trusses, frames, and basically any other structure. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load). Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations. Otherwise, methods such as virtual work, direct integration, Castiglianos method, Macaulays method, or the direct stiffness method are used). The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory).

Different types of loads can cause deflections, including point loads, uniformly distributed loads, wind loads, shear loads, ground pressure, and earthquakes. Deflection is a crucial consideration in the design of a structure, and failure to apply due attention to it can be catastrophic. Building codes usually determine what the maximum allowable deflection should be to ensure the safety of a building’s users and overall structural integrity. For example, building codes determine the maximum deflection of a beam, usually as a fraction of the span, e.g., 1/400 or 1/600).