Geometrically and physically nonlinear stress calculation of spatial steel beam structures considering real connection and stiffening conditions

Author: Steffen Leihkauf

Abstract
The thesis describes investigations on the geometrical and physical non-linear stress calculation of steel beam structures. Based on the solution of the decoupled differential equations for bending, camber torsion and bar strain, a finite element formulation for the treatment of the bending torsion problem of spatial bar structures as a stress problem according to 2nd order theory (small twists) and as a linearised branching problem is given. Here, the displacement influences from bending and camber shear conduction are taken into account as well as non-linear material behaviour. Formulations for discretely nonlinear connection behaviour and continuously nonlinear material (flow zones) are given, taking into account phenomena such as slip, plasticisation, kinematic and isotropic hardening, as well as unloading and reloading. One focus is the numerical modelling of the kinematics of connection areas in the spatial structure. Starting from a suitable formulation of the compatibility conditions, the linear coupling matrix for the involved degrees of freedom is derived. Two methods are proposed with the help of which the coupling of kinematically underdetermined, determined and undetermined connections can be calculated. Here, the influence of the cross-sectional curvature is particularly taken into account for connections that are not curvature-compatible. Applications of the described methods are demonstrated on the basis of selected, practice-relevant examples and the effects of different connection and stiffening ratios as well as material non-linearities on the load-bearing behaviour are shown.