Equilibrium Equations

These equations define equilibrium and govern statics.

$\Sigma \vec{F}=0$ $\Sigma \vec{M}=0$

Internal Forces

These equations articulate how integrating loading functions gives internal force functions.

Axial force and axial load

$N'_x=-q_x$

Torsional force and torsional load

$T_x'=-t_x$

Internal beam moments, shears, and lateral loads

$M_z''=V_y'=q_y$

$M_y''=V_z'=q_z$