Elastic beam
= 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 $M=EIy_{xx}$, and transverse momentum balance gives $\rho Ay_{tt}+EIy_{xxxx}=q$ 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.