Elastic beam

An elastic beam is a slender body that supports bending moments and transverse loads. In the small-slope Euler-Bernoulli approximation its bending moment is $M=EI{y}_{xx}$, and transverse momentum balance gives $\rho A{y}_{tt}+EI{y}_{xxxx}=q$ for a uniform beam under distributed force per length $q$. Here $I$ is the second moment of area; boundary conditions specify the end constraints and applied moments and forces.