Resonance and cancellation phenomena in two-span continuous beams and its application to railway bridges

The objective of this study is to evaluate the vibratory response of two-span continuous beams subjected to moving loads and, in particular, to investigate the maximum resonance and cancellation of resonance phenomena. The main practical interest is the evaluation of the maximum acceleration response in railway bridges, which is one of the most demanding Serviceability Limit States for traffic safety according to current regulations. Two-span continuous bridges, in their simplest version (i.e. uniform identical spans), present antisymmetric and symmetric modes with closely spaced natural frequencies, leading to a more involved dynamic behaviour than that of simply-supported bridges. First, the free vibration response of a Bernoulli-Euler two-span beam after the passage of a single load at constant speed is formulated analytically, and non-dimensional speeds leading to cancellation or maximum response in free vibration are obtained for each mode. Then, these conditions are equated to resonant speeds induced by equidistant load series, and span length-to-characteristic distance ratios causing cancelled out resonances, or remarkably prominent ones, are obtained. Based on the previous derivations, a methodology for detecting which could be the most aggressive trains for a particular structure based on pure geometrical considerations is discussed. Finally, the applicability of the theoretical derivations is shown through the numerical analysis of two real bridges belonging to the Swedish railway network

Free vibration of viscoelastically supported beam bridges under moving loads: Closed-form formula for maximum resonant response

[EN] In this paper, a closed-form approximate formula for estimating the maximum resonant response of beam bridges on viscoelastic supports (VS) under moving loads is proposed. The methodology is based on the discrete approximation of the fundamental vertical mode of a non-proportionally damped Bernoulli-Euler beam, which allows the derivation of closed-form expressions for the fundamental modal characteristics and maximum amplitude of free vibration at the mid-span of VS beams. Finally, an approximate formula to estimate maximum resonant acceleration of VS beams under passage of articulated trains has been proposed. Verification studies prove that the approximate closed-form formula estimates the resonant peaks with good accuracy and is a useful tool for preliminary assessment of railway beam bridges considering the effect of soil-structure interaction at resonance. In combination with the use of full train signatures through the Residual Influence Line (LIR) method, the proposed solution yields good results also in the lower range of speeds, where resonant sub-harmonics are more intensely reduced by damping.This research was partly sponsored by the Swedish Research Council FORMAS and has also received funding from the Shift2Rail Joint Undertaking under the European Union's Horizon 2020 research and innovation program under grant agreement No 826255 which are gratefully acknowledged.Zangeneh, A.; Museros Romero, P.; Pacoste, C.; Karoumi, R. (2021). Free vibration of viscoelastically supported beam bridges under moving loads: Closed-form formula for maximum resonant response. Engineering Structures. 244:1-11. https://doi.org/10.1016/j.engstruct.2021.112759S11124

Experimental and Numerical Dynamic Properties of Two Timber Footbridges Including Seasonal Efects

This paper deals with experimental and numerical dynamic analyses of two timber footbridges. Both bridges have a span of 35 m and consist of a timber deck supported by two timber arches. The main purpose is to investigate if the dynamic properties of the bridges are season dependent. To this end, experimental tests are performed during a cold day in winter and a warm day in spring in Sweden. The frst bending and transverse mode frequencies increase 22% and 44%, respectively, due to temperature efects in the case of Vega Bridge. In the case of Hägernäs bridge, the corresponding values are 5% and 26%. For both bridges, the measured damping coefcients are similar in winter and spring. However, the damping coeffcients for the frst bending and transverse modes are diferent for both footbridges: about 1% for the Hägernäs bridge and 3% for the Vega bridge. Finite-element models are also implemented. Both numerical and experimental results show good correspondence. From the analyses performed, it is concluded that the connections between the diferent components of the bridges have a signifcant infuence on the dynamic properties. In addition, the variation of the stifness for the asphalt layer can explain the diferences found in the natural frequencies between spring and winter. However, due to the uncertainties in the modelling of the asphalt layer, this conclusion must be taken with caution

Recommendations for finite element analysis for the design of concrete slabs

In the bridge design community the usage of 3D finite element analyses has increased  substantially in the last few years. Such analyses provide the possibility for a more accurate study of the structure than what is possible by using more traditional design tools. However, in order to use the full strength of the finite element method in daily design practice a number of critical issues have to be addressed. These issues are related either to the FE-modeling itself (geometry, support conditions, mesh density, etc.) or to the post processing of the obtained results (stress concentrations, choice of critical sections, distribution widths and so on). The purpose of this report is to address these problems and provide recommendations and guidelines for the practicing engineers. The recommendations given here are based on what was found in literature combined with engineering judgement and considerations from engineering practice. The recommendations are believed to be conservative, implicating a potential for improvement based on increased knowledge on the response and distribution of shear in concrete slabs and how this is reflected by linear FE analysis. This also means that, in many cases, there may be other alternatives that are equally correct as the ones suggested in this report.QC 20130812</p

Recommendations for Finite Element Analysis for Design of RC Slabs

The finite element method (FEM) is increasingly used for design of reinforced concrete structures. 3D FE analysis can provide more accurate structural analysis, but to use its full strength in daily design a number of critical issues have been addressed. Practical guidelines are provided for detailed design of reinforced concrete slabs. Recommendations are given on linear FE modelling, e.g. regarding geometry, support conditions and mesh density, as well as on the use of analysis results, e.g. regarding stress concentrations, choice of critical sections and redistribution widths for practical reinforcement design

Recommendations for Finite Element Analysis for Design of RC Slabs

The finite element method (FEM) is increasingly used for design of reinforced concrete structures. 3D FE analysis can provide more accurate structural analysis, but to use its full strength in daily design a number of critical issues have been addressed. Practical guidelines are provided for detailed design of reinforced concrete slabs. Recommendations are given on linear FE modelling, e.g. regarding geometry, support conditions and mesh density, as well as on the use of analysis results, e.g. regarding stress concentrations, choice of critical sections and redistribution widths for practical reinforcement design

Recommendations for finite element analysis for the design of reinforced concrete slabs

In the bridge design community the usage of 3D finite element analyses has increased substantially in the last few years. Such analyses provide the possibility for a more accurate study of the structure than what is possible by using more traditional design tools. However, in order to use the full strength of the finite element method in daily design practice a number of critical issues have to be addressed. These issues are related either to the FE-modeling itself (geometry, support conditions, mesh density, etc.) or to the post processing of the obtained results (stress concentrations, choice of critical sections, distribution widths and so on). The purpose of this report is to address these problems and provide recommendations and guidelines for the practicing engineers. The recommendations given here are based on what was found in literature combined with engineering judgement and considerations from engineering practice. The recommendations are believed to be conservative, implicating a potential for improvement based on increased knowledge on the response and distribution of shear in concrete slabs and how this is reflected by linear FE analysis. This also means that, in many cases, there may be other alternatives that are equally correct as the ones suggested in this report