Techniczna Teoria Zginania Prętów dla Pewnego Przypadku Materiału Fizykalnie Nieliniowego - Jakubowski, A. (Engineering Transactions, 1962)
The non-linear stress-strain relation is assumed, in the uniaxial state of stress, in the form ε = sgn σ * a | σ |n. Pure bending of a bar is considered in the general case (any direction of the vector of the bending moment). The quantities S, I*, D* are introduced, describing the geometric properties of the profile. To determine them, a graphical method is proposed. Fundamental relations are derived enabling us to determine the direction of the neutral axis and the stresses and displacements of the bar axis. Treating Hooke’s law as a particular case the general law assumed, new relations are derived for oblique elastic bending. The theory proposed is applied to determine the limit load (assuming perfect plasticity of the material) and to the creep problem of a bent bar, which is illustrated by a numerical example.