Beams can be also subjected to combined bending, torsion as well as axial tensile or compressive loads. Finally time-step methods are discussed to show basic features of numerical analysis for non-linear inelasticity problems.īeams are structural members that are designed to support lateral forces and bending moments. Solutions are presented for different loading paths illustrating stress-range dependent creep, creep recovery, relaxation and tensile behaviors. Hardening, softening and damage processes are neglected to make the analysis transparent. Section 1.3 gives an overview of uni-axial constitutive models describing idealized non-linear inelastic behavior. Results are compared with closed form solutions to conclude on numerical accuracy and stability. They include one-step explicit and implicit time integration methods. In addition to analytical solutions, examples for numerical time-step methods are introduced. Various force controlled and displacement-controlled loading profiles are discussed. Closed-form solutions for a two-bar system under assumption of linear viscous material behavior are presented in Sect. Section 1.2 presents elementary solutions for stresses in linear thermo-elastic bars subjected to non-uniform heating. 1.1 governing equations a for two-bar system are introduced and initial value problems for one-dimensional inelastic stress analysis are formulated. Basic features of inelastic structural responses including creep, relaxation, stress redistribution and others are discussed. Chapter 1 presents elementary examples for bars and bar systems and gives an introduction to inelastic stress analysis.

Bars are structural members that support uni-axial tensile or compressive loadings.

Structural analysis examples