Finite element modelling of voided slab bridge decks using orthotropic plate theory

Circular voids are often incorporated into concrete bridge decks to reduce their self-weight without greatly reducing the flexural stiffness. Incorporating voids within a slab offers many advantages over a conventional solid concrete slab, for example a lower total cost of construction, reduced material use, and enhanced structural efficiency. The advantages of this topology are obvious, however the voids within the slab complicate the analysis of the structure. The incorporation of the voids within the slab results in different flexural stiffness in the longitudinal and transverse directions, resulting in an orthotropic slab. Another feature which distinguishes voided slabs from other common bridge types is the deformable nature of their cross-sections, which influences the load distribution of the structure. The need for a method of analysis which accounts for the orthotropic behaviour and deformable nature of the cross-section has been suggested by many in the past. The idealisation of voided slabs as an orthotropic plate has been the subject of extensive research. When modelling a voided slab as an orthotropic plate, it is necessary to calculate the reduction in the longitudinal and transverse stiffness due to the presence of the voids. Several equivalent plate parameters, which take on numerous forms, have been suggested by various authors to account for the effect of the voids. No research has been reported in technical literature to compare these different methods employing orthotropic plate parameters. Key shortcomings to these methods include the lack of definition of the suggested equivalent plate parameters, and the geometrical parameters of voided slabs which influence their behaviour. In an attempt to address these limitations, the aim of this study is to verify and validate the effect of the void diameter ratio and void spacing on the structural behaviour of voided slabs, which are the main influences on the orthotropic behaviour and cross-section deformation. The different methods of analysis using orthotropic plate theory suggested by various authors employing equivalent plate parameters are compared and discussed. The objectives of the study were achieved based on the finite element approach using ABAQUS. Finite element models with a void diameter to slab depth ratio range of 0.5 to 0.9, and a void spacing range of 0.9m to 2.7m were considered and analysed. Comparisons were made of the longitudinal and transverse stress distribution results from these models in order to draw conclusions. Results from solid models using both isotropic and orthotropic materials based on the equivalent plate parameters suggested from literature are also presented for comparison in order to verify the methods suggested by the technical literature for the analysis of voided slab bridge decks. Results of the finite element modelling show that the addition of voids causes large variations to the transverse stress distribution from the typical parabolic transverse stress distribution shape, leading to large peak transverse stresses in the flanges above and below the voids. These variations are due to the deformable nature of the cross-section. The voids also lead to a stress raising effect on the longitudinal stresses. It was found that an increase in void diameter to slab thickness ratio results in a rapid increase in both the longitudinal and transverse stresses, which shows that there is an increase in orthotropic behaviour and deformation of the cross-section with an increase in void diameter ratio. From the results, it can be concluded that the optimal void diameter ratio is between 0.6 and 0.8. This range of void diameter ratios allow for greater efficiency due to reduced dead load and material use, without generating excessive stresses due to cellular distortion resulting from excessively thin and flexible flanges above and below the voids. The spacing of the voids was found to have minimal effect on the stress distributions for a logical void spacing. These results show that the orthotropic behaviour and deformation of the cross-section are more sensitive to variations in void diameter ratio than the spacing of the voids. The void diameter ratio should therefore form the basis of the equivalent plate parameters for the use of orthotropic plate theory. The use of a solid orthotropic plate to idealise a voided slab showed reasonable agreement with the results from three-dimensional models, with some discrepancies in the different authors' methods noted. The net effect of using a two-dimensional analysis is the averaging out of the stress transverse distribution, which cannot predict the peak stresses around the voids. The orthotropic models compared more favourably with the 3D model than the isotropic models with increasing void diameter ratio. The results presented have shown that the incorporation of voids begins to affect the structural behaviour of the slab once the void diameter ratio exceeds 0.6, and the orthotropic behaviour becomes considerable. The stress raising effect of the voids should therefore be accounted for in the analysis of a voided slab once the void diameter ratio exceeds 0.6. It is recommended that a solid isotropic slab can be used to idealise a voided slab when the void diameter to slab depth ratio is less than 0.6. When the void diameter ratio is greater than 0.6, the transverse stiffness should be evaluated independently from the longitudinal stiffness, and orthotropic models are more suitable. For higher void diameter ratios, the method employed by Sen et al. (1994), which employs a reduced depth solid orthotropic slab in conjunction with stress multipliers, was found to be the most accurate method for idealising voided slabs. It is evident from this study, that while a three-dimensional finite element model may be too complex for everyday use, it may be extremely valuable for determining the local effects due to the presence of the voids

The structural behaviour of horizontally curved prestressed concrete box girder bridges

Bridges are important and efficient structures which are comprised of a number of elements andsubstructures, namely the deck, abutment and foundation and possibly additional intermediatesupports. Recently the horizontally curved box girder bridge has become more desirable inmodern motorway systems and big cities. Even though numerous amounts of research have beenin progress to analyse and understand the behaviour of all types of box-girder bridges, the resultsfrom these different research projects are unevaluated and dispersed. Therefore, a clear understanding of an accurate study on straight and curved box-girder bridgesis needed. In this study, a three dimensional straight and horizontally curved prestressed boxsection has been analysed with shell elements using the finite element analysis program ANSYSto examine structural behaviour and load carrying capacity. The box girder under static gravity,pre-stressed and gravity + pre-stressed loading has been analysed. The model which has beeninvestigated in this report is taken from a published paper and expanded to study the effects ofcurvature under different loads applied (UDLs). The report concludes that the FEA using shellelements is able to predict the behaviour of box girders with adequate accuracy through thecomparisons made between stress results from analytical hand calculations and published work,both for the straight and curved box girder bridges. Further theoretical and analytical investigations have been carried out to study the effects ofparameters such as horizontal curvature, prestressing, and traffic patterning. For this purpose, anew model was created, modelled with an accurate prestress representation and analysed as athree-dimensional model using the ANSYS. This thesis presents a complete description of the bridge system, addressing the aforementionedparameters and presenting the results through graphs of stress distribution, and displacement.Recommendations for the practical use of FE for bridge design are discussed

COMPRESSIVE MEMBRANE ACTION in BRIDGE DECK SLABS

Merged with duplicate record 10026.1/654 on 27.02.2017 by CS (TIS)An elastic analysis of restrained slab strips shows that membrane action enhances serviceability behaviour. However, the enhancement is not as great as for strength and serviceability is critical when membrane action is considered in design. A relatively simple form of non-linear finite element analysis is developed which is able to model bridge deck behaviour allowing for membrane action. This reduces some of the disadvantages of non-linear analysis which have prevented its use in practice. It uses line elements but, because of novel features of the elements and because it considers all six degrees of freedom at each node, it is still able to model in-plane forces reasonably realistically. It gives acceptable predictions for behaviour. The tension stiffening functions used in non-linear analysis, which are important to the prediction of restraint, are considered. Explanations are proposed for several aspects of the behaviour and a new function is developed. This gives better results than previous expressions, particularly for deflections on unloading and reloading. Tests under full HB load have been performed on two half scale bridges. These, and the analysis, show that conventional design methods for deck slab reinforcement are very conservative. They also show that the restraint required to develop membrane action is not dependent on diaphragms; it comes from under-stressed material surrounding the critical areas. Thus, over much of a bridge's span, there is transverse tension in the slab and membrane action does not significantly enhance the resistance to global moments. Both bridge models failed by a wheel punching through the slab. It is shown that these were primarily brittle bending compression failures which were strongly influenced by global behaviour. This is confirmed both by the analysis and by the higher wheel load at failure in single wheel tests. Recommendations are made for using the results in design and assessment.British Cement Associatio

Preslab - micro-computer analysis and design of prestressed concrete slabs

Bibliography: pages 128-132.A micro-computer based package for the analysis and design of prestressed flat slabs is presented. The constant strain triangle and the discreet Kirchhoff plate bending triangle are combined to provide an efficient "shell" element. These triangles are used for the finite element analysis of prestressed flat slabs. An efficient out-of-core solver for sets of linear simultaneous equations is presented. This solver was developed especially for micro-computers. Subroutines for the design of prestressed flat slabs include the principal stresses in the top and bottom fibres of the plate, Wood/Armer moments and untensioned steel areas calculated according to Clark's recommendations. Extensive pre- and post-processing facilities are presented. Several plotting routines were developed to aid the user in his understanding of the behaviour of the structure under load and prestressing

Bridge Design to Eurocodes – Worked examples

This document is a Technical Report with worked examples for a bridge structure designed following the Eurocodes. It summarizes important points of the Eurocodes for the design of concrete, steel and composite road bridges, including foundations and seismic design, utilizing a common bridge project as a basis. The geometry and materials of the example bridge as well as the main assumptions and the detailed structural calculations are presented in the first chapter of the report. Each of the subsequent chapters presents the main principles and rules of a specific Eurocode and their application on the example bridge, namely: • The key concepts of basis of design, i.e. design situations, limit states, the single source principle and the combinations of actions (EN 19990); • Permanent, wind, thermal, traffic and fatigue actions on the bridge deck and piers and their combinations (EN 1991); • Bridge deck modeling and structural analysis; • The design of the bridge deck and the piers for the ULS and the SLS, including the second-order effects (EN 1992-2); • The classification of the composite cross-sections, the ULS, SLS and fatigue verifications and the detailed design for creep and shrinkage (EN 1994-2); • The settlement and resistance calculations for the pier, three design approaches for the abutment and the verification of the foundation for the seismic design situation (EN 1997); • The conceptual design for earthquake resistance considering the alternative solutions of slender or squat piers; the latter case involves seismic isolation and design for ductile behavior (EN 1998-1, EN 1998-2). The bridge worked example analyzed in this report was prepared and presented at the workshop “Bridge Design to the Eurocodes” that was held on 4-6 October 2010 in Vienna, Austria. The workshop was organized by JRC with the support of DG ENTR and in collaboration with CEN/TC250/Horizontal Group Bridges, the Austrian Federal Ministry for Transport, Innovation and Technology and the Austrian Standards Institute. The document is part of the Report Series “Support to the implementation, harmonization and further development of the Eurocodes”, prepared by JRC in collaboration with DG ENTR and CEN/TC250 “Structural Eurocodes”.JRC.G.5-European laboratory for structural assessmen

Dynamic and static analyses of continuous curved composite multiple-box girder bridges.

Horizontally curved concrete deck on multiple steel box girder bridges is a structurally efficient, economic, and aesthetically pleasing method of supporting curved roadway systems. Modern highway constructions are often in need of bridges with horizontally curved alignments due to the tight geometry restrictions. Continuous curved composite box girder bridges allow for the use of longer spans, thus reducing costs of the substructure. Despite all inherent advantages of continuous curved composite box girder bridges, they do pose challenging problems for engineers in calculating the load distribution due to moving vehicles across the bridges. Curved bridges are subjected to high torsional as well as flexural stresses. The interaction between the box girders is also more complicated in curved bridges than that in straight bridges. North American codes for bridges have recommended expressions for the load distribution factors only for straight bridges and not for curved bridges. Impact factors proposed in these codes are generally restricted also to straight bridges. In addition, simplified formula to predict the fundamental frequency of analyzing the bridges is not available. To assist engineers in dealing with the complexities of continuous curved composite box girder bridges, a reliable, accurate, and simple method is required to calculate the structure\u27s response under self-weight and vehicular loading. The refined three-dimensional finite-element analysis method is employed to investigate the static and dynamic responses of the bridge. Two two-equal-span two-box physical bridge models were constructed in the laboratory. One of the bridge models was straight in plan while the other was horizontally curved. The physical models were tested under several static loading cases to better comprehend their elastic behaviour. Free-vibration tests were also conducted to obtain the natural frequencies and the corresponding mode shapes of the bridge models. Both models were loaded up to failure to examine the collapse mechanism and its correlation with the finite element modeling. Findings obtained from the two physical bridge models were compared to those predicted by the analytical models. The agreement between the finite element model and the experimental model made it possible to use the analytical models to conduct three parametric studies on several bridges.Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .S26. Source: Dissertation Abstracts International, Volume: 65-07, Section: B, page: 3593. Advisers: J. Kennedy; K. Sennah. Thesis (Ph.D.)--University of Windsor (Canada), 2004

Behavior and Design of Spread Prestressed Concrete Slab Beam Bridges

The Texas Department of Transportation (TxDOT) uses precast prestressed concrete slab beam bridges in a side-by-side configuration for short span bridges in low clearance areas. A new bridge type called a spread slab beam bridge was recently developed using the same concept as spread box beam bridges in which the beams are spaced apart with precast panel stay-in-place forms between beams and a cast-in-place concrete deck. This research presents an evaluation of spread slab beam bridges in terms of design, constructability and performance. The main objective of this project is to develop appropriate design guidelines for this alternative spread slab beam bridge system. Forty-four bridge geometries are designed using standard TxDOT slab beam types to determine the feasible design space. One of the most aggressive geometries with widely spaced slab beams is constructed as a full-scale test bridge and tested under static and dynamic vehicular loads to evaluate constructability and structural performance. Load distribution behavior is investigated during field testing and the measured data is utilized to validate modeling techniques including orthotropic plate analysis, grillage analysis and finite element method based on research findings. It is concluded that spread slab beam bridges that utilize precast concrete panels with a cast-in-place concrete deck provide a viable construction method for short-span bridges. For the tested bridge, the desired performance is achieved for in-service loading. Field testing shows that beam live load deflections are within the design limits, with no significant cracking or reduction in the overall stiffness of the bridge observed. Experimental load distribution factors (LDFs) are evaluated using alignments that provided the most adverse loading cases. Bridge responses under dynamic loads are larger compared to the static counterparts. The American Association of State Highway Transportation Officials (AASHTO) Load and Resistance Factor Design (2012) LDF equations for spread box beams are reviewed for applicability to spread slab beams and shown to range from being unconservative to very conservative when applied to spread slab beam bridges. Unique LDF expressions are developed for spread slab beam bridges to provide an appropriate estimate of load sharing for beam design

The finite element analysis of thin-walled box spine-beam bridges

This thesis considers the theoretical and experimental analysis of thin-walled box spine-beam bridges. Existing methods available for the analysis of spine-beam bridges have been reviewed, with special attention being paid to thin-walled box beam theories. A new approach combining the finite element technique and the thin-walled beamtheory, which is appropriate for design purposes, has been proposed. This approach is specially suitable for medium and long spans. It is intended to be a realistic and versatile method to be used during the preliminary analysis and design stage, when a full three-dimensional analysis is likely to be impractical. Special features related tothebending analysis of thin-walled members and the warping torsion theory of open and closed section members are summarized in the thesis. In addition, supplementary formulae for the calculation of the stress distributions and the thin-walled section properties are derived. The distortional effect on single-spined box beams subjected to torsion has been extended to a general form based on the principles of ordinary folded plate theory. A family of special one-dimensional sub-parametric elements has been developed. In addition to the usual truss and beam elements the family includes a general thin-walled box beam element which may be curved in space and may have a variable cross-section. Additional degrees of freedom have been included to account for the warping and distortion effects whichoccur in box beams. An inclined cable element with catenary action is included, and an approximate nonlinear process for the analysis of cablestayed bridges has been correlated with tests on an actual bridge structure. A finite element-grillage approach for the analysis of multibox structures with deformable sections has also been developed. The complete family of elements has been incorporated into a computer program called CUBAS. A supplementary program called PFRAN for calculating the distortional properties and the influence values of the equivalent Vierendeel frame has also been implemented. The accuracy of the results obtained is demonstrated by comparison with results obtained by other published methods. A series of model box beams were tested to •further substantiate the theoretical results. The model dimensions were chosen to highlight both warping and cross-sectional distortion effects. The degree of correlation obtained shows that the theoretical developments proposed in this thesis may be applied successfully to the analysis of box spine-beam bridges