# ScienceDirect. The Numerical Analysis of the Joint of the Steel Beam to the Timber Girder

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2 Ján Kortiš et al. / Procedia Engineering 91 ( 2014 ) Description of the numerical model The numerical simulation in this work considers a test specimen based on a real bolted joint used for a timber bridge. The selected joint connects a cross-beam and main timber girder. Dimensions of the test specimen were defined in proportion to the real structural components. Only a small part of the main timber girder was modelled just like the tested specimen had been made [1], [2]. Boundary conditions were applied to define the modeled part of main girder as a fixed body by applying zero displacement for upper lower and both side faces. The cross-beam is I-beam made of structural steel as well as the end-plate which is welded to the I-beam. The stiffness of the connection is increased by the shaped plate put between both parts perpendicular to the end-plate. Hence, this part is modelled as a shell structure beside the end-plate which has to be in contact with bolts. The isoparametric material is used for both parts made of steel and also for timber materials. The timber material should be defined as orthotropic material but the material characteristics for this type of material were not applied to obtain results for the simple model. The Young Modulus of the steel part is 210 GPa and Poisson s ratio is 0.3 and the Young Modulus of the timber is 11 GPa and Poisson s ratio is 0.3. Fig. 1. The geometry of the cross-beam and bolted joints. The care of generation of the appropriate shape of the mesh has to be pursued due to avoid having poor results. The mesh was made denser in the local area close to the bolts. It was important to do because of the cylindrical shape of the hole and the bolts. Having mesh with lower dimensions of the elements would have been created a hole with a shape closer to a rectangle than a circle. It is also desirable to apply fixity on the parts of the model which are not supported as a result of an inactive contact at the beginning of the solution. In this case it is possible to use axisymmetric conditions in the middle of the cross-beam to define zero displacement for horizontal directions. These boundary conditions did not influence the results of the solution. Consequently the convergence criterion was reached sooner for the time steps when the contacts are being activated.

3 162 Ján Kortiš et al. / Procedia Engineering 91 ( 2014 ) Fig. 2. Mesh generated on the cross-beam and on the timber close to the contacts domain. The issues linked to the satisfaction of the convergence criterion were cut down by creating a rigid connection between the end-plate and bolts. Knowing the stress state in the timber material will be the main aim so this limitation did not affect the domain of the interest. Fig. 3 shows the cross-beam and the bolts which were defined as one body having different material characteristics for each part. 3. The results of the numerical model Fig. 3. The mesh of the cross-beam and the bolts. The first step to obtain valuable results was to check if the mesh generated on the parts of the cross-beam is generated properly. Doing a solution for the whole model is not an effective way to find out the quality of the mesh on one part. The recommendations are mostly aimed on doing solution for each part separately and then follow the solution by defining contacts between parts. The same way was used to check the model of the cross-beam where the shell elements are connected with 3D elements. Fig. 3. The final solution is done at the end of the process. The loading was defined in the middle of the cross-beam as a force with value of 100 kn. The same loading was used for tested specimen. Fig. 4 shows the results of effective stress on the cross-beam.

4 Ján Kortiš et al. / Procedia Engineering 91 ( 2014 ) Fig. 4. Effective stress on the cross-beam. The most interesting result is the response of the bolts on the prescribed vertical loading. Fig. 5 shows that the maximum values are at upper and lower edge of the bolts close to the heads. It means that there are bended that parts of bolts as a result of a low stiffness of timber. The loading of upper and lower bolts is higher to compare with bolts located in the middle of the joint. This is the result of the bending of the cross-beam. The different loading of the bolts is also influenced by the applied boundary conditions which define the timber structure as a fixed body for horizontal direction. There can be expected that results for real joints will be slightly different. Hence, the boundary conditions for the timber part of the model as a main girder are different, thus it does not act as a fixed body. Fig. 5 The effective stress on the bolts.

5 164 Ján Kortiš et al. / Procedia Engineering 91 ( 2014 ) Conclusion The main objective was to study the local behavior of the structural components especially how to produce the appropriate FE model to obtain valuable results. For that purpose commercial software ADINA was used that offers necessary techniques for creating bodies and contact among them. The functionality of the software which is used to customize the density of the mesh is very useful. It helps to create a model that has lower demand for high power hardware. The stress analysis on the bolts confirms expectations which are usually used for simpler models that are recommended for practical design. In this case it is very important to cover the effect of the low stiffness of the timber. The following step will be to compare the results of the numerical solution with test results of the test. Acknowledgements This contribution is the result of the research supported by GA MŠVVaŠ SR VEGA, grant No. 1/0259/12. References [1] Odrobi ák, J. - Vi an, J. - Gocál, J.: Behaviour analyses of timber steel footbridge decks. XXI. Russian Slovak Polish Seminar s medzinárodnou ú as ou Theoretical foundation of civil engineering", Moscow-Arkhangelsk, , Druk i Oprawa Oficyna Wydawnicza Politechniki Warszawskiej Warszawa 2012, ISBN , p [2] W. Strunk Jr., E.B. White, The Elements of Style, third ed., Macmillan, New York, [3] Gocál, J. - Vi an, J. - Sýkora, M.: Theoretical and experimental analysis of timber footbridge. IV. International Conference Footbridge 2011, zborník abstraktov, CD-edition, Wroc aw, Poland, July 2011, edited by: Jan Biliszczuk, Jan Bie, Pawe Hawryszków, Tomasz Kami ski, published by: Dolno l skie wydawnictwo edukacyjne, Wroclaw, Poland, ISBN , p abstrakt, p CD-edition. [4] Gizejowski, M. Salah, W. Wioleta, B.: Steel beam-to-column joints with thin end-plates. 5 th European Conference on Steel and Composite Structures, EUROSTEEL 2008, 3-5 September, Graz, Austria, edited by: Robert Ofner, Darko Beg, Josef Fink, Richard Greiner, Harald Unerweger, published by: ECCS European Convention for Constructional Steelwork, Brussels, Belgium, ISBN , p

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