Beam theory

Summary

A beam theory is a one-dimensional model of a slender elastic body that carries loads mainly by bending. Examples of such bodies are girders, shafts and rulers. It replaces the three-dimensional equations of linear elasticity by functions of the position along the axis. These are the deflection, the rotation of the cross-sections, the bending moment and the shear force. An assumption on how cross-sections deform turns the three-dimensional problem into ordinary differential equations. The main examples are the Euler–Bernoulli beam equation and Timoshenko–Ehrenfest beam theory.