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Procedia Engineering 199 (2017) 2979–2984
X International Conference on Structural Dynamics, EURODYN 2017 X International Conference on Structural Dynamics, EURODYN 2017
Performance of steel-laminated rubber bearings subjected to Performance of steel-laminated rubber bearings subjected to combinations of axial loads and shear strains combinations of axial loads and shear strains COSTAIN Engineering and Construction Limited, London Bridge Station Redevelopment, London, SE1 3QU, UK of Surrey, Faculty of Limited, Engineering andBridge Physical Sciences, Guildford, GU2 7XH,SE1 UK3QU, UK COSTAINbUniversity Engineering and Construction London Station Redevelopment, London, b University of Surrey, Faculty of Engineering and Physical Sciences, Guildford, GU2 7XH, UK
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Konstantinos N. Kalfasaa, Stergios A. Mitoulisbb* Konstantinos N. Kalfas , Stergios A. Mitoulis *
Abstract Abstract Bridge isolation is a common means for mitigating the actions of structures subjected to earthquake excitations, thermal effects, Bridge isolation is a common means for mitigating the are actions of structures to earthquake excitations, thermal isolated effects, creep and shrinkage. Steel-laminated rubber bearings common devicessubjected that are being used widely in seismically structures. Current code requirements for steel-laminated bearings differ significantly with regard relevant creep and shrinkage. Steel-laminated rubber bearings arerubber common devices that are being used widelytoinrequirements seismically isolated structures. Currentthat code for steel-laminated bearingsthere differ significantly with gap regard to requirements relevant to tensile stresses arerequirements developed within the elastomer.rubber Additionally, is an acknowledged regarding the understanding to stressesof that are developed within thetoelastomer. there isaxial an acknowledged gap regarding the understanding of tensile the response bearings when subjected combinedAdditionally, and/or fluctuating loads (compressive or tensile) shearing and rotations due to imposed earthquake excitations, causing local fluctuating and/or global tension buckling. or Thetensile) latter are influenced of the response of bearings when subjected to both combined and/or axial loadsand/or (compressive shearing and rotations due by to imposed both and/or global tension and/or buckling. The latter are influenced significantly the shapeearthquake factor andexcitations, the behaviour ofcausing the steellocal reinforcements. significantly by the an shape factor and the behaviour of the steel reinforcements. In this framework, extensive numerical study was conducted to examine the development of stresses within the elastomer of bearings and the response of the numerical steel reinforcements. In particular, of variable axial displacements from 4% In this framework, an extensive study was conducted to combination examine the development of stresses within ranging the elastomer of bearings and the of the steel In particular, combination of to variable from 4% compression up response to 90% tension, shearreinforcements. strains up to 210 percent and rotations up 0.0205axial rad,displacements were imposedranging on the bearings, compression upstresses to 90% within tension, strainsand up yielding to 210 percent and rotations up to 0.0205 rad,These were loads imposed the bearings, causing tensile theshear elastomer of the steel plating (reinforcements). wereonimposed in the form of tensile displacement histories corresponding to the response of plating bearings(reinforcements). on a seismicallyThese excitedloads bridge thatimposed was analysed causing stressestime within the elastomer and yielding of the steel were in the form of displacement histories corresponding to the response bearings a seismically excited bridge that was was analysed previously, as well as time the bridge bearings which were used for this of research [1].onThe finite element software ABAQUS used previously, as wellanalyses. as the bridge bearings which were used for this research [1]. The finite element software ABAQUS was used for the numerical for the numerical analyses. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility ofElsevier the organizing © 2017 The Authors. Published by Ltd. committee of EURODYN 2017. Peer-review under responsibility of the organizing committee of EURODYN 2017. Peer-review under responsibility of the organizing committee of EURODYN 2017. Keywords: isolation; rubber bearings; time history; tensile stresses; rotation; yielding; Keywords: isolation; rubber bearings; time history; tensile stresses; rotation; yielding;
* Corresponding author E-mail address:author
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[email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review©under ofthe organizing committee 1877-7058 2017 responsibility The Authors. Published by Elsevier Ltd. of EURODYN 2017. Peer-review under responsibility ofthe organizing committee of EURODYN 2017.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of EURODYN 2017. 10.1016/j.proeng.2017.09.533
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1. Introduction Steel-laminated elastomeric bearings are one of the most common base isolation systems, which mitigate the impact of the dynamic loads on structures [2]. The seismic excitations are responsible for the movements - horizontal, vertical and rotations - which are developed in structures and are accommodated by the bearings [3,4]. The design of isolated structures is based on the assumption that the structure will respond essentially elastic when subjected to earthquake excitations. The damage due to dynamic loads is expected to be concentrated in the bearings, which are designed to be easily replaceable. Thus, isolated structures are resilient as their design is aligned to the principles of resilience, i.e. low-damage and quick restoration. The use of steel shims, alternating with rubber layers, provide enhanced vertical stiffness to sustain the self-weight of the structure and horizontal flexibility to the bearing [5]. Regarding the international literature, the shear and compressive response of the isolators has been evaluated with numerical models and experiments under dynamic loads [5,6,7], whilst the tensile response of the isolators has not been assessed thoroughly [8,9]. Gent and Lindley [10] were the first to investigate the development of tensile stresses within the rubber and its severe degradation when 2.75 MPa of global tensile stress was applied to it. The available code provisions seem to have different approaches and requirements regarding the ability of rubber bearings to undertake tensile stresses. The British codes [11,12] take into consideration the possibility of the development of tensile stresses, within the rubber body, up to 2G, where G is the shear modulus of rubber, which values range from 0.55 to 1.2 MPa. AASHTO [13], allows the development of tensile stresses, with the range of them being 2 to 3 G. On the contrary, Eurocode 8-Part 2 [14] prohibits any uplift of the isolators under seismic actions. Figure 1 depicts a typical difference between the codes, regarding the boundary conditions assumed for the bearings during design. Eurocode 8 - Part 2 [14] and AASHTO [13], do not take into consideration an uplift mechanism of the bearing-pier model. Additionally, the nonlinear response of elastomeric bearings under tensile loading is not considered. Also, there is limited research on the influence of the tensile deformation of bearings to their mechanical properties.
Fig. 1. Current design codes showing isolated piers: (a) AASHTO [13], (b) EN 1998-2 [14] and (c) side view of the benchmark bearing
This paper aims to better understand the distribution of stresses within the elastomer layers and the steel shims and to assess whether these stresses cause any issues on them, such as cavitation of the elastomer or yielding of the steel shims. These phenomena are evidence that the bearing does not respond elastically throughout the earthquake excitation, which is against the code prescriptions [14]. The bridge bearings were subjected to combination of displacement time histories (axial, horizontal, rotational), through extensive numerical analyses of the isolators. 2. Steel-laminated rubber bearings 2.1. Geometrical and mechanical characteristics Figure 2 gives the geometry of the benchmark bearing. The circular steel-laminated rubber bearing comprises of six layers of rubber with 11 mm thickness each, alternating with five layers of steel shims with thickness of 4 mm each. At the top and bottom of the isolator there are two anchor plates with 25 mm thickness each. The benchmark bearing has a total thickness of 136 mm. The diameter of the rubber layers, the steel shims and the anchor plates is 400mm (Ø400 x 136 (66)). The discretisation of the rubber layers and steel shims was with linear hexahedral elements of type C3D8 and with linear wedge elements of type C3D6. Geometric non-linearities are incorporated in the analysis.
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Fig. 2. Side view and meshing of the benchmark steel-laminated rubber bearing
The energy dissipation, as well as the stresses that are developed within the rubber are described accurately by the Ogden hyperelastic material [15]. Kalfas et al. [8] calculated the value of the shear modulus equals to 0.66344 MPa and the value of the Poisson ratio equals to 0.49994. The Bulk Modulus was 2000 MPa. 2.2. Seismic actions In this numerical study, variable axial displacements, shear strains and rotations were imposed in the form of time histories corresponding to bridge responses published before [1]. The peak ground acceleration (PGA) of 0.25 g, 0.50 g and the soil Type B was selected [16]. Shear strains up to 210%, were imposed to the isolators, for PGA of 0.50g. The bottom anchor plate was fixed, as can be seen in Fig. 2, whilst the time histories where imposed on the top anchor plate. Figure 3 shows the time histories that were chosen, as well as the time instances when the extreme vertical and rotational time histories were imposed.
Fig. 3. Horizontal, vertical displacement and rotation time histories for (a) 0.25g and (b) 0.50g
3. Development of tensile stresses in steel-laminated rubber bearings – Yielding of the steel shims 3.1. Development of tensile stresses within steel-laminated rubber bearings The fluctuation of the vertical load is a phenomenon which causes development of tensile stresses in the body of the isolators and influences their performance [8]. Figure 4 depicts the values of axial stresses, that are developed in the body of steel-laminated rubber bearings, under combination of variable axial strains of 42% and 90%, shear strains of 195% and rotations of 0.02026 rad. As shown in Fig. 3, the time instances, where the response of the isolator was captured, is when the largest value of tensile displacement had been imposed to the isolator. It can be observed in Figs. 4a and 4b that there is development of tensile stresses in the body of the rubber layers and the steel shims. Additionally, it can be seen, that the compressive stresses are concentrated in the whole length of the steel shims, but not at the rubber layers. In Figs. 5a and 5b, the values of the tensile stresses which are developed in the top, middle and bottom rubber layers can be seen. It is observed that there is development of compressive stresses at the perimeter of the layers and not at the centre of them, where tensile stresses are developed. The value of tensile stresses that are developed in the body of the rubber layers is larger than 2 MPa (grey areas in Figs. 4 and 5). This is in contradiction with the codes [14], which require that the bearings remain elastic and undamaged during the design earthquake.
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Fig. 4. Development of tensile stresses in the isolator for (a) time histories of 0.25g and (b) time histories of 0.50g
Fig. 5. Development of tensile stresses in the top, middle and bottom rubber layers, for time histories of (a) 0.25g and (b) 0.50g
3.2. Yielding of the steel shims due to the flexural deflection and rotation of the isolator The steel-laminated rubber bearings, which are subjected to combination of axial displacements and shear strains, exhibit rotations and flexural deflections of the steel shims. This fact has an impact on the behaviour of the isolators and could cause yielding thus permanent deformations of the steel shims and permanent deformations of the entire isolator. Figure 6 depicts the vertical section of the isolator at the time, when the largest rotation was imposed, as shown in Fig. 3. It is observed that the largest rotations of the steel shims are created at the upper right and bottom left part of the isolator. In Fig. 6 can be seen that the top and bottom steel shims are subjected to larger rotations than the middle steel shims. However, the steel shims do not yield when the isolator is subjected to the combination of the aforementioned time histories. According to Faridmehr et al [17], the S235 steel, which is the one used for this study, yields at values of axial stresses greater than 235.3MPa. The values of the stresses that were developed in the body of the steel shims did not exceed the proposed yielding point [17]. It can be observed that, in the case where time histories of 0.25g had been imposed, there is development of tensile stresses, which exceed the codes, almost in the whole body of the isolator, whilst when time histories of 0.50g had been imposed, there are almost no areas in the isolator body where tensile stresses, which exceed the codes, are developed. This difference in the values of tensile stresses, which
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are developed in the body of the isolator, occurs due to the fact that a combination of time histories had been imposed to the isolator and residual compressive stresses remain in its body. It is observed that when time histories of 0.25g are imposed to the isolator, then the steel shims exhibit rotation up to 13.80, which is shown in Fig. 6a, whilst in the case where time histories of 0.50g are imposed to the isolator, the steel shims exhibit rotation of 50.
Fig. 6. Rotation of the steel shims for time histories of (a) 0.25g and (b) 0.50g
4. Conclusions This paper assessed the response of steel-laminated rubber bearings under combined horizontal and vertical displacements and rotations, which were imposed in the form of time histories. Detailed modelling and analyses of the isolators was carried out to better understand the development of tensile stresses in the body of the rubber layers, as well as the yielding and the deflection of the steel shims of steel-laminated rubber bearings. The mechanical properties of the elastomer were modelled using the hyperelastic Ogden model [15]. This computer-aided research showed that when combination of fluctuating axial and shear loads is imposed to the isolators, then there is development of tensile stresses and rotation of the steel shims. The following conclusions can be drawn based on the numerical analyses: • When a combination of variable axial displacements, shear strains and rotations are imposed in the form of time histories, there is development of tensile stresses in the body of the isolator, with values which are larger than 2MPa. These values were obtained for combination of 210% shear strain, 59mm of axial displacement and rotation of 0.0206rad. When the isolator is subjected to tensile displacements, there is development of tensile stresses with values larger than 2 MPa. Values of tensile stresses larger than 2 MPa are not allowed by the current codes of practice. It is also noted that the aforementioned time histories of displacements and rotations were based on analyses of a I-beam precast bridge [1]. • The rotation of steel shims of the isolators, when they are subjected to combination of axial displacements, shear strains and rotations, is a phenomenon which causes fluctuations to the behaviour of steel-laminated rubber bearings, in terms of the rubber response. Based on the numerical analyses, there is rotation of the top and bottom steel shims of the isolator. The steel shims of the isolators are subjected to rotations of 13.80 and 50, when time histories of 0.25 g and 0.50 g correspondingly are imposed to the realistic isolated bridge model. Nevertheless, such rotations can be found only at the top and bottom steel shims. The rotation of the steel shims may cause degradation of the elastomer behaviour under dynamic loads, because the rubber layers are subjected to additional tensile displacement. The rotation of the steel shims could cause plasticity of them, and subsequently influence of the steel-laminated rubber bearing behaviour. However, for the combination of the time histories that were imposed to the benchmark isolator, there was no exceeding of the steel shims yielding point. References [1] S.A. Mitoulis, Uplift of elastomeric bearings in isolated bridges subjected to longitudinal seismic excitations, Structure and Infrastructure Engineering, (2015) 11:12, 1600-1615, DOI: 10.1080/15732479.2014.983527. [2] M. Kumar, A.S. Whittaker, M.C. Constantinou, Response of base-isolated nuclear structures to extreme earthquake shaking, Nuclear Engineering and Design, 295 (2015) 860–874. [3] J.F. Stanton, C. W. Roeder, P. Mackenzie-Helnwein, C. White, C. Kuester, B. Craig, Rotation limits for elastomeric bearings Washington DC, National Cooperative Highway Research Program (NCHRP), Transportation Research Board, 2007.
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[4] J.M. Kelly, D. Konstantinidis, Mechanics of rubber bearings for seismic and vibration isolation, John Wiley & Sons, New York, USA, 2011. [5] G.C. Manos, S. Mitoulis, V. Kourtidis, V. Sextos, I. Tegos, Study of the behaviour of steel laminated rubber bearings under prescribed loads, 10th World Conference on Seismic Isolation, Energy Dissipation and Active Vibrations, Control of Structures, Istanbul, Turkey, 2007. [6] K.N. Kalfas, S.A. Mitoulis, K. Katakalos, Numerical study on bridge elastomeric bearings subjected to large shear strains with emphasis on local tension, 16th World Conference on Earthquake Engineering, Santiago, Chile, 2017. [7] S. Mitoulis, A. Muhr, H. Ahmadi, Uplift of elastomeric bearings in isolated bridges- A possible mechanism: Effects and remediation, 2nd European Conference on Earthquake Engineering and Seismology, Istanbul, Turkey, 2014. [8] K.N. Kalfas, S.A. Mitoulis, K. Katakalos, Numerical study on the response of steel-laminated elastomeric bearings subjected to variable axial loads and development of local tensile stresses, Engineering Structures, 134 (2017) 346-357. [9] E. Tubaldi, SA Mitoulis, H. Ahmadi, A. Muhr, A parametric study on the axial behaviour of elastomeric isolators in multi-span bridges subjected to horizontal excitations, Bulletin of Earthquake Engineering, 14 (2016), 1285-1310. [10] A.N. Gent, P.B. Lindley, Internal rupture of bonded rubber cylinders in tension. Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences, 249 (1958), 195–205. [11] BS EN 15129: 2009, Anti-seismic devices, BSI British Standards, 2010. [12] EN 1337-3: 2005, Structural bearings – Part 3: Elastomeric bearings, Brussels: European Committee for Standardization, 2005. [13] American Association of State Highway and Transportation Officials, AASHTO, Guide specifications for seismic isolation design, fourth ed., Washington, DC, 2014. [14] EN 1998-2, Eurocode 8: Design of structures for earthquake resistance, Part 2: Bridges, Brussels, Belgium: European Committee for Standardization, 2005. [15] W.R. Ogden, Large Deformation isotropic elasticity–On the correlation of theory and experiment for incompressible rubber like solids, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 326 (1972) 565–584. [16] EN 1998-1, Eurocode 8: Design of structures for earthquake resistance, Part 1: General rules, seismic actions and rules for buildings, Brussels, Belgium: European Committee for Standardization, 2004. [17] I. Faridmehr, M.H. Osman, A.B. Adnan, A.F. Nejad, R. Hodjati, M. Azimi, Correlation between engineering stress-strain and true stress-strain curve, American Journal of Civil Engineering and Architecture, 2 (1) (2014) 53-59.
