loaddeflection

Load deflection, often written as load-deflection, describes the relationship between an externally applied load and the resulting displacement in a structure or component. It is a central concept in structural analysis, mechanical design, and materials science, used to assess serviceability and safety. In the elastic regime, many materials and geometries follow a linear relation: deflection δ is proportional to applied load F, with stiffness k = dF/dδ and, equivalently, δ = F / k. For beams and plates, standard formulas or numerical methods yield deflection under various loading and support conditions; for example, simple beam theory or Castigliano's theorem provides δ expressions as functions of E, I, geometry, and load.

A load-deflection curve plots deflection against load and characterizes the structural response. The slope indicates stiffness; the area under the curve relates to energy absorbed. The initial linear portion represents the elastic region; beyond the proportional limit, deflection increases more rapidly as material yields or nonlinear effects occur. Serviceability criteria impose maximum allowable deflection to ensure function and comfort, such as L/360 for floors or other limits specified by codes.

Design and analysis employ methods from classical mechanics, energy methods, and computational tools, including finite element analysis, to predict deflection under complex loading. Deflection control is achieved by increasing stiffness (larger E or second moment of area), reducing span, using higher-modulus materials, introducing pre-stress, or adding stiffeners and supports. Practical measurements during testing validate predictions and ensure performance under real conditions. The concept also extends to dynamic loading, nonuniform loads, and temperature effects, where creep and thermal expansion influence observed displacement.