An asymptotically correct, nonlinear, analytical cross-sectional analysis is developed for pretwisted, isotropic beams under axial load and torsion. A comprehensive model is presented that for the first time simultaneously counts for both trapeze and Poynting effects (either positive or negative). Several material models are used and differences are discussed in detail. The limitations of the uniaxial stress assumption and Saint-Venant/Kirchhoff materials are illustrated. Compared to the widely accepted results in the literature, the present theory demonstrates improved results without introducing assumptions commonly used in other works. It is concluded that the trapeze and Poynting phenomena are governed by the material models and warping functions, and nonlinearly coupled extension and torsion can be eliminated by properly selecting the thickness-to-width ratio.