Contribution to the calculation of steel composite girders in service condition considering scattering input variables

Author: Holger Flederer

Abstract
The thesis deals with a method for the calculation and assessment of the service behaviour of composite girders, which are composed of slackly reinforced concrete chords and full-walled steel girders, based on reliability theory.
As an introduction, the load-bearing behaviour of the steel-concrete composite girders in the service condition is characterised, whereby the interactions between several, partly non-linear effects and influencing variables with a stochastic character are highlighted.
As a basic mechanical solution, a complex deterministic calculation model is developed, which represents the load-bearing behaviour in the form of a time process and takes into account, among other things, the cracking processes, the weakening of the reinforcement bond in the reinforced concrete chord under long-term loading and the effects of the creep and shrinkage phenomena of concrete. The main subject of the calculations are the force magnitudes at the partial cross-sections of one-dimensional beam elements; the explicit response parameters of the load-bearing structure in the service condition - such as crack widths, deflections, stresses - are derived from the force magnitudes. For selected, published test results, comparative calculations are made with the proposed deterministic model.
On the basis of the deterministic model, the probabilistic solution is obtained by Monte Carlo simulation, whereby the use of quasi-random numbers for sample reduction is theoretically investigated, tested on examples and compared for the developed solution algorithm with results of Monte Carlo simulation when using pseudo-random numbers. Parameters for the statistical description are provided for important stochastic material, model, environment and stress variables. Application examples demonstrate the calculation and evaluation possibilities of the probabilistic solution algorithm.