The paper presents a nonlinear formulation and a finite-differences ba
sed numerical solution for the structural behavior of generic orthotro
pic beams of solid cross-sections. The analysis includes a detailed de
scription of the three-dimensional out-of-plane warping and the soluti
on is achieved by successive iterations while preserving all geometric
al nonlinearities. The axial body forces are introduced consistently t
hrough the axial differential equilibrium equation. The formulation yi
elds some basic closed-form analytic solutions for homogeneous beams,
and the numerical results provide an insight into the coupling effects
mechanisms in generic laminated composite beams, including the result
ing interlaminar stresses.