Structural analysis | EPFL Graph Search

Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures. Structures and loads In the context to structural analy

Berücksichtigung von dynamischen Verkehrslasten beim Tragsicherheitsnachweis von Strassenbrücken

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

Capacité portante de ponts en arc en maçonnerie de pierre naturelle

Alix Grandjean

Historical masonry arch bridges are an integral part of our cultural heritage and deserve the attention and the efforts required to safeguard their patrimonial value. There is currently a diverse range of methods available to engineers for evaluating the load-bearing capacity of masonry arches. The major drawbacks are that these methods are either too conservative or computationally intensive. The study presented here proposes a model based on the theory of plasticity. The result is a transparent model that is both rapid and easy to use. Moreover, its application does not involve heavy computation tools. The model is validated by comparison with available experimental results and with the results of a widely-recognised analysis software. In order to take into account the material and structural behaviour of an arch in an optimal way, the present thesis provides a new integral model divided into three evaluation levels. At the micro-level, the response of masonry under pure compression is used to characterise the material of an arch. At this level, numerical models are used to describe the behaviour of natural-stone masonry. These models distinguish between the constitutive units and mortar as well as the unit – mortar interface. The shape and arrangement of the units have the most influential role in defining the failure mode in comparison to the properties of each constitutive material. At the meso-level, the material behaviour from the preceding level is used to define the limit for the local plastification of an arch section under combined compression and flexure. This phenomenon is described as the formation of a hinge. The resistance of an arch section can be expressed using the bending moment – normal force interaction diagram based on the stress-strain curve of the masonry material. Each point along the interaction diagram refers to a state of stress causing the local plastification of an arch section due to the formation of a hinge. The macro-level focuses on the structural analysis of a masonry arch – a structure with four degrees of indeterminacy. The arch failure corresponds to the successive formation of four hinges defined by the yielding condition determined at the meso-level. The analytical model developed in this study considers an arch at the state of being a statically determinate structure – after three of the four hinges are developed. Using the principle of equilibrium, the model calculates the load-bearing capacity of the arch at the ultimate limit state. A large number of existing natural-stone masonry arches include deficiencies accumulated throughout years of service without any regular maintenance. Three common types of deficiencies on these bridges are considered. The model is extended to take into account their effects on the load-bearing capacity of arches. Finally, the model developed in this study is incorporated into a global methodology for the examination of masonry arch bridges. This methodology implies two complementary approaches, which have to be applied parallel to one another. The first uses the developed model and gives a quantitative evaluation of structural security. The second includes a qualitative appreciation of the risk, based on the condition survey of the structure. This methodology allows an objective examination of the structure and recommendations for intervention measures.

EPFL2010

A Structural Design Methodology for Freeform Timber Plate Structures Using Wood-Wood Connections

Anh Chi Nguyen

Over the past decades, timber has gained popularity as a sustainable building material because of the rising environmental awareness. Furthermore, the resurgence of timber has also been encouraged by the advent of the digital age during the 21st century. The development of computer-aided design programming and digital fabrication tools has stimulated significant advances in both architecture and engineering. Within this context, researchers have shown a growing interest in wood-wood connections, inspired by traditional woodworking joints. Geometrically complex timber structures assembled with joints integrated in their plates have been developed using algorithmic geometry processing. However, although their design and fabrication have been automated, research focused on automated numerical tools for their structural analysis has been very limited. This thesis is providing a design methodology for the structural analysis of timber plate structures composed of a large number of discrete planar elements and wood-wood connections. A finite element model, in which the semi-rigid behaviour of the connections is implemented using springs, is proposed. It is applied to a specific case study, namely the Annen Plus SA head office project in Manternach, Luxembourg, which consists of a series of double-layered double-curved timber plate shells. A design framework is introduced to automate the generation of the model and integrate structural analysis into the existing design and fabrication workflow. The numerical model was built for both small- and large-scale structures through custom scripts and subsequently assessed through experimental investigations: first, laboratory tests were performed on small assemblies with simplified geometry; secondly, a displacement study was carried out onsite on a 24 m span structure. Results obtained with the semi-rigid spring model were found to be in good agreement with experimental tests. The proposed model was therefore validated for the serviceability limit state. Furthermore, the semi-rigidity of the connections in translation as well as in rotation was shown to highly influence the model and is therefore crucial for the accuracy of the model. Based on experimental tests observations, an alternative structural system was proposed and compared to the initial one through numerical investigations within the proposed design framework. A significant influence on the structureâs performance was found, demonstrating the possibilities for structural optimisation. Finally, a three-dimensional finite element model for wood-wood connections was investigated. It aimed to predict their semi-rigid behaviour, generally characterised through experimental tests, necessary for their implementation in global models. The material model was evaluated based on shear load tests performed on different engineered wood products. Stiffness and load-carrying capacity of the connections were approximated with numerical simulations. However, experimental tests remain necessary to precisely predict the behaviour of the joints. This thesis highlights the importance of adopting an integrated design strategy encompassing engineering and fabrication aspects for geometrically complex timber structures, as well as establishing a link between local behaviour of the connections and global behaviour of the structure. The gained knowledge can facilitate the design and realisation of large-scale freeform timber structures with wood-wood connections.

EPFL2020