In this study, the computation of the traction-torsion-bending behavior of single-walled carbon nanotubes (SWCNTs) is investigated. A structural mechanics model is used to describe the response of the nanotube; the atomic interactions are represented with 3D beams. Nanotubes are slender structures, taking benefit from their axial periodicity or helical symmetry. Homogenization theory is used to obtain their overall beam behavior from the solution of basic cell problems. These problems are solved through a finite element approach and involve concise models, whatever the SWCNT type. The computed results show that the bending behavior appears to be decoupled from the axial one and independent of the moment direction. Young's and shear moduli are derived, and it is shown that the Young's moduli are very close in traction and bending. Comparisons with the data in the literature reveal good agreements. Finally, scale effects are studied, and the moduli of the SWCNTs are compared to those of the graphene, thus demonstrating mechanical sensitivity to curvature.