Hannes Ludescher
It has been known for more than 150 years that action effects in bridges due to traffic action are higher than it has to be expected for purely static loads. In the design of road bridges, this difference is considered by multiplying static traffic loads with a "dynamic amplification factor". The amplification factors defined in codes are based on dynamic load tests on existing bridges. Despite of hundreds of tests in several countries, experimental investigation has not given satisfactory explanation of the observed phenomena, which has resulted in marked differences between amplification factors defined in different codes. This is due to the fact that the core of the matter – the dynamic interaction between vehicles and bridges– is a complex mechanical problem. Based on a detailed analysis it is shown in the introduction, that it can also be attributed to the fact, that the experimental investigation is more part of the problem than its solution. This thesis aims at getting a solid and systematic grounding in the problem using theoretical analysis. The centre of attention is the question, which importance dynamic phenomena have in those scenarios which are effectively relevant for the structural safety of a bridge. All scenarios are considered that justify an amplification factor, and not only dynamic vehicle – bridge interaction. The structural safety evaluation of a bridge includes the verification of the ultimate and the fatigue limit state. Accordingly, this thesis distinguishes between the interaction at ultimate limit state, for which inelastic bridge behaviour is assumed, and the interaction at service limit state with linear elastic bridge behaviour. The structural analysis of a bridge shows in addition, that the elements of the bridge deck differ considerably from the main girders: For the elements of the deck – i.e. primarily for the deck slab – dynamic interaction is of little importance, and amplification of action effects is essentially due to amplification of traffic action. In the case of the main girders, action effects are additionally amplified due to the oscillations of the structure. In order to analyse interaction at service limit state in detail, very sophisticated models are required, which do not only cover all relevant eigenmodes of the bridge but also the non-linear, dynamic behaviour of heavy vehicles and the precise road surface profile. Design and analysis of such models are mostly conferred to specialists in numeric analysis and structural dynamics. In the contrary, this thesis aims at capturing the fundamental connections by simple models, which facilitates the identification of the key parameters and the interpretation of their influence. The most important result of the analysis of vehicle – bridge interaction at service limit state is that the amplification factor is most influenced by the weight and the number of vehicles on a bridge. Whereas the amplification is negligible for high vehicle loads, tests with relatively lightweight vehicles on long bridges lead to a significant over-estimation of amplification factors. Furthermore it is shown that neither the span nor the natural frequency of a bridge is appropriate for fixing the amplification factor for a particular bridge and safety verification, respectively. It has been observed in dynamic load tests that deflection measurements consistently result in higher amplification factors than strain measurements. This phenomenon has been known for more than fifty years, but no explanation has been given so far. In this thesis an explanation is proposed and it is shown that deflection measurements result in an over-estimation of amplification factors. Similar considerations lead to a proposal for a more suitable application of amplification factors in the verification of shear force. A completely new approach is chosen for the analysis of vehicle – bridge interaction at ultimate limit state. The effective behaviour at rupture is taken into account, which necessitates first to deal with the influence of loading velocity on material strength. It is shown that only for impact loading of deck slabs due to dynamic tyre forces a minor increase in concrete strength can be expected. An important prerequisite for the understanding of dynamic behaviour at ultimate limit state is the "gravity effect", which is shown to cause massive reduction in the dissipation capacity of a structure. The determinant criterion with inelastic behaviour is deformability and not stiffness. Simple models are used to study the influence of deformability and gravity effect in the most important cases of dynamically amplified traffic action. The results show, under which conditions the dynamic amplification of action effects can be compensated by plastic deformation of the structure without causing its failure. If the steel yield stress is already attained due to the static part of traffic action, compensation of the dynamic part is only assured if the rupture behaviour is characterised by strain hardening. A simple condition of equilibrium shows that dynamic amplification due to centrifugal forces cannot be absorbed by deformations of the structure. However, rupture behaviour characterised by significant deformation causes a delay in the failure of the structure, which can be sufficient to prevent the definitive rupture anyway, depending on the scenario. In addition to these reflections, it is attempted to determine the importance of shear failures with respect to flexural failures, in order to estimate the probability of this comparatively brittle failure mechanism. In view of the application of the findings, the relevant results are synthesized and a concept for the safety verification accounting for dynamic traffic action is developed. The concept is based on the distinction between verifications at ultimate and service limit state on the one hand, and the separate treatment of elements of the deck and main girders on the other hand. This differentiation allows integrating risk based considerations using explicit hazard scenarios. An important point in the application of the findings is the recommendation to emphasize the benefit of good road surface evenness in the maintenance of structures. A necessary complement in establishing the recommended amplification factors is the detailed analysis of the reaction of vehicles to road surface irregularities. The dynamic tyre forces for different vehicle and axle types, respectively, are analysed, since the findings indicate that the amplification of tyre forces is much more important in fixing amplification factors than the dynamic behaviour of bridges. The investigations clearly show that higher axle loads imply lower amplification factors, and that the maximum amplification of axle forces in axle groups never occurs simultaneously for all axles. The thesis is finished by an annexe including introductions to the dynamic behaviour of vehicles and bridges as well as to the modelling of traffic loads and road surface irregularities. In addition to an extensive review of the state of the art, these introductions constitute an important basis of the work and facilitate understanding of the calculations in the main part.
EPFL2003
