Probabilistic Analysis and Reliability of Engineering Structures

This thesis, consisting of six papers, concerns methods for probabilistic analysis of engineering structures. The work comprises evaluations of available methods, developments of new and improved methods, and applications of probabilistic analysis to engineering structures.

Comparative calculations using methods representing different strategies for stochastic finite element analysis were carried out, aiming at an evaluation with respect to computational efficiency, general applicability, and availability for practising engineers. Among the evaluated methods, the Monte Carlo simulation technique using Latin hypercube sampling was found to be attractive with respect to general applicability, since the handling of the stochastic variables is separate from mechanical modelling and numerical analysis. A method utilizing principal component analysis was suggested in order to bring Latin hypercube sampling in line with finite element analysis.

Methods for utilizing Latin hypercubes in importance sampling for structural reliability analysis were suggested. It was shown that simple importance sampling, as well as axis orthogonal importance sampling, can be considerably improved, with respect to computational efficiency, using Latin hypercube sampling instead of true random sampling. The improvement of the first method is dependent on a transformation of the stochastic variables in standard Gaussian space, resulting in a sample plan with one direction orthogonal to the tangent hyperplane of the failure surface at the design point.

The effects of damage caused by truck impacts to slender columns of racking systems were investigated by means of numerical simulations and laboratory tests. Three different thin-walled steel profiles were considered and it was found that even moderate geometrical imperfections result in considerable reduction of the load carrying capacity of individual columns. A study of the effects on entire racking systems was also performed in which damage magnitudes were regarded as probabilistic parameters.

Wooden roof trusses with nail-plate joints were analysed focusing on the influence of gaps between wooden members and misplaced nail-plates. Both issues arise as a consequence of lack of precision in the manufacturing process and the magnitudes of the imperfections were regarded as probabilistic parameters. Especially gaps between wooden members were shown to be of considerable importance for the deflection of roof trusses. In addition to the probabilistic analysis, a procedure was employed to optimize the nail-plate locations with respect to the deflection of a roof truss.