Sensitivity Analysis of the Effect of Initial Imperfections on the (i) Ultimate Load and (ii) Fatigue Behaviour of Steel Plate Girders

The study is divided into two parts: (i) in the first one, the plate girder (Fig 1) is considered to be exposed to quasi‐constant loading (ie to loads which are either constant or repeated in a very small number of cycles), while (ii) in the other one, the girder is assumed to be subjected to repeated loading. Then it is understandable that the objective of the first part should be to look into the influence of initial imperfections on the static ultimate load of the girder related to the formation of a plastic failure mechanism in it, while that of the second part was to study the effect of imperfections on the stress state under considerably lesser loads, viz under such as to correspond to the development of fatigue cracks in the girder and, consequently, to its fatigue limit state. In this case the state of stress was measured by bending stresses developing in the crack‐prone areas (Fig 4) of the web “breathing” under the repeated loads, which ‐as demonstrated by the Prague experiments ‐ occur at the toes of the fillet welds connecting the “breathing” web with the girder flanges and stiffeners. In both parts, the results of the theoretical investigation were compared with the conclusions of numerous tests carried out at the Institute of Theoretical and Applied Mechanics in Prague. The correlation was found to be very good; for example, the experimental load‐carrying capacity of the girders tested in Prague was close to the mean value of the corresponding theoretical solutions performed for the same girders. Thereby the analytical model applied in the theoretical investigation can be regarded as verified. The theoretical analysis was based on a non‐linear variant of the finite element method, the girder being modelled by means of shell elements and the ANSYS program being applied. All input imperfections were considered to be random quantities. The statistical distributions were introduced according to both experimentally obtained results and data given in literature. Random realisations of input random quantities were simulated by the LHS (Latin Hypercube Sampling) method. By way of sensitivity analysis it was studied to what extend the variability of initial imperfections was reflected in the variability of stresses in the crack‐prone areas of the girder. The main conclusion can be formulated as follows: While the effect of (and sensitivity to) the initial out‐of‐flatness of the girder web, in the case studied of a plate girder whose web is subjected to predominant shear, on the static load‐carrying capacity is (see the results of the first part of the study) very small (only a few p.c), the same effect on the stress state occurring in the crack‐prone areas of the “breathing” web under service loads can be (see the other part of the study) very important. This is also one of the main explanations of the large scatter of the results of the fatigue tests conducted in Prague.