US 0925A Laminated Elastomeric Bearings Aaef
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Technical guide
Laminated elastomeric bearings Use on bridges, viaducts and similar structures
The Technical Department for Transport, Roads and Bridges Engineering and Road Safety (Service d'études techniques des routes et autoroutes  Sétra) is a technical department within the Ministry of Transport and Infrastructure. Its field of activities is the road, the transportation and the engineering structures.
The Sétra supports the public owner The Sétra supplies State agencies and local communities (counties, large cities and urban communities) with information, methodologies and tools suited to the specificities of the networks in order to: • improve the projects quality; • help with the asset management; • define, apply and evaluate the public policies; • guarantee the coherence of the road network and state of the art; • put forward the public interests, in particular within the framework of European standardization; • bring an expertise on complex projects.
The Sétra, producer of the state of the art Within a very large scale, beyond the road and engineering structures, in the field of transport, intermodality, sustainable development, the Sétra: • takes into account the needs of project owners and prime contractors, managers and operators; • fosters the exchanges of experience; • evaluates technical progress and the scientific results; • develops knowledge and good practices through technical guides, software; • contributes to the training and information of the technical community.
The Sétra, a work in partnership • The Sétra associates all the players of the French road community to its action: operational services; research organizations; Scientific and Technical Network (Réseau Scientifique et Technique de l'Equipement – RST), in particular the Public Works Regional Engineering Offices (Centres d'études techniques de l'Equipement – CETE), companies and professional organizations; motorway concessionary operators; other organizations such as French Rail Network Company (Réseau Ferré de France – RFF) and French Waterways Network (Voies Navigables de France  VNF); Departments like the department for Ecology and Sustainable Development… • The Sétra regularly exchanges its experience and projects with its foreign counterparts, through bilateral cooperations, presentations in conferences and congresses, by welcoming delegations, through missions and expertises in other countries. It takes part in the European standardization commissions and many authorities and international working groups. The Sétra is an organization for technical approval, as an EOTA member (European Organisation for Technical Approvals).
Technical guide
Laminated elastomeric bearings Use on bridges, viaducts and similar structures
This document is the translation of the work "Appareils d’appui en élastomère fretté Utilisation sur les ponts, viaducs et structures similaires" published in March 2007 under the reference 0716.
This guide has been written by a working group comprising: – JeanFrançois Derais, Sétra/CTOA – Michel Fragnet, Sétra/CTOA – Gilles Lacoste, Sétra/CTOA – Yvon Meuric, Sétra/CTOA – Ludovic Picard, DREIF – Yves Picard, Consultant – Denis Davi, Sétra/CTOA The following provided advice and observations: – M. Dauvilliers (DREIF/LROP) – H. Guérard (EGISSCETAUROUTE) – P. Kirschner (SECOA) – C. Néant (ETIC) – G. Wattiaux (ETIC) – P. Xercavins (PXDAM Consultants)
The drawings were prepared by JeanPierre Gilcart (Sétra) and the CETE of Lyon.
This guide cancels and replaces the technical guide entitled "Appareils d'appui en caoutchouc fretté – Utilisation sur les ponts viaduc et structures similaires" of September 2000 (reference: F0032)
O=================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Contents Forew ord ............................................................................................................... 5 Chapter 1  Introduction ......................................................................................... 7 1.1 – Why replace the 2000 guide? ......................................................................................................... 7 1.2 – Scope and content .......................................................................................................................... 7 1.3 – Application of the standard NF EN 13373 in the French national context ..................................... 8 1.4 – Scope .............................................................................................................................................. 8 1.5 – Notations and symbols .................................................................................................................... 8 C h a p t e r 2  C o m p o s it i on and description ................................................................ 9 2.1 – General principles of composition ................................................................................................... 9 2.2 – Component parts........................................................................................................................... 10 2.3 – Manufacturing methods................................................................................................................. 14 Chapter 3 – Behaviour and dime nsioning .............................................................. 15 3.1  Introduction .................................................................................................................................... 15 3.2 – The characteristics of bearings ..................................................................................................... 17 3.3 – Dimensioning bearings.................................................................................................................. 19 3.4 – Dimensioning verifications............................................................................................................. 22 C h a p t e r 4 – D e s ig n p r i n c i p le s f or a structure w ith bearings .................................. 31 4.1 – General points – The regulatory context ....................................................................................... 31 4.2  Dimensioning ................................................................................................................................. 33 4.3 – Calculating horizontal force on support heads on a structure with standard bearings ................... 3 4.4  Calculating horizontal force on a structure with sliding bearings ..................................................... 6 Chapter 5  Controls ............................................................................................ 14 5.1 – General principles ......................................................................................................................... 14 5.2 – Production controls prior to CE marking ....................................................................................... 14 5.3 – Controls on reception .................................................................................................................... 17 5.4 – Controls on installation .................................................................................................................. 17 5.5 – Controls of behaviour in service.................................................................................................... 18 Chapter 6 – The predimensioning and ve rification program.................................. 20 A p pe nd i x 1 – C a lc u la t i on s f o r l a m i nat e d e l ast o mer ic be ar in gs f or use i n s e is m ic zones .................................................................................................................. 22 A11 – Regulatory framework................................................................................................................. 22 A12 – Design combinations and direction accumulation ...................................................................... 23 A13  Dynamic calculation model.......................................................................................................... 24 A14 – Using a behaviour factor............................................................................................................. 26 A15  Recommendations....................................................................................................................... 26 A16 – Further construction measures................................................................................................... 27 A p pe nd i x 2 – T he d ur ab i l it y o f l a m i nat e d e l ast o mer ic be ar in gs w it h a slid i ng p la ne3 2 A21 – The characteristic quantity of the functioning of a sliding bearing.............................................. 32 A22 – Measures to be taken at the design stage.................................................................................. 32 A23 – Measures to be taken at the manufacturing stage ..................................................................... 33 A24 – Measures to be taken as part of the monitoring process ........................................................... 33 Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
P
A25  Conclusion................................................................................................................................... 33 A p p e n d i x 3  T a b le of dimensions ........................................................................ 34 A p p e n d i x 4 – A s s i s it a n c e w it h d r a f t in g Pa r t ic u la r T e chnical Clauses (CCTP) ......... 36 A4.1  Examples of clauses to be included in the chapter "quality of materials" ................................... 36 A4.2  Examples of clauses to be included in the chapter "design principle”....................................... 37 A4.3  Examples of clauses to be included in the chapter "implementation" ....................................... 38 Bibliograph y .......................................................................................................... 40 General documents ................................................................................................................................ 40 Standards ............................................................................................................................................... 40 Bibliography specific to Appendix 1 ....................................................................................................... 41
Q================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Foreword Bearings are important elements of a structure for which the notion of wear and durability is not inferior to that of the structure, as, in that case, they would be regarded as consumables. For this reason, particular care needs to be taken over their choice, quality, design and implementation. This is all the more true in that the cost of the product itself is disproportionate in comparison to that involved in interventions to raise the structure and repair the bosses: a ratio of 1 to 50 is considered the minimum. A study carried out by the Sétra as to the causes of interventions on structures to repair bearings (of all types) revealed that that there were three completely equal origins: • Defects arising from poor product quality (such as corrosion or debonding). Concerning this matter, the publication of the standard NF EN 1337 (after the French standards) regarding product specifications and CE marking for laminated elastomeric bearings are giving rise to improvement. • Installation defects. Following the specifications of the guide "Environnement des appareils d'appui en caoutchouc fretté" ("The environment of laminated elastomeric bearings" cf. Bibliography) is a sine qua non condition for improvements in this area. This guide does not cover installation. This is covered in the guide entitled "Environnement des appareils d'appui en caoutchouc fretté ("The environment of laminated elastomeric bearings"). We do however stress the importance of including the specifications described in this document in Particular Technical Clauses (CCTP) and in the QAP (Quality Assurance Plans) and of ensuring their application. • Problems arising from errors in dimensioning (a slide plate that is too short, an insufficient number of elastomeric laminations, insufficient plan dimensions, etc.). It is this third section that this guide intends to examine, as regards laminated elastomeric bearings. We would also like to highlight the importance of designing the deck, bearings and supports as an INDISSOCIABLE whole. It is from this perspective that the present guide has been drafted. Laminated elastomeric bearings (LEB) and pot bearings (PB) represent over 90 % of bearing used on bridges in France. Although at the extremities of the field of use, the reasons for choosing one type of bearing over another are quite obvious, they are less easy to discern in borderline cases. The choice of bearing type depends on a number of factors, including the load path, maximum rotation, horizontal displacement, durability, cost, the type of structure, the environment and structural arrangements. For this reason, it is difficult to determine the respective field of use of one method over another. For reactions of under 12 MN (calculated at ULS) on supports, laminated elastomeric bearings are wholly suitable. This value corresponds to plan dimensions of around 700 x 700 mm. Above 20 MN, pot bearings are preferable as they limit the bulk of the device. Between these two values, LEBs can be used, either by increasing the dimensions to 900 x 900mm for large structures, or by joining two smaller bearings. The latter solution is only easy to implement on box bridges and concrete slab bridges due to the space required for the bearings. They cannot easily be envisaged for girder bridges (composite or of prestressed concrete). However, in the event of large bearing rotations, LEBs may be suitable, but the thickness of the elastomer needs to be greatly increased, thus posing other problems. As regards horizontal displacement, the slide systems of PBs offer better quality and, therefore, higher durability. It is thus the displacement criteria that influence the choice. In any event, manufacturing constraints (mainly the size of presses) mean that the largest size of LEBs is currently limited to around 1000 x 1000 x 300mm as regards French manufacture (abroad, dimensions of 1200 x 1200 x 300mm can be reached). The cost of LEBs is lower than that of PBs. However, it must not be forgotten that the cost of bearings is a small percentage of that of the structure. In seismic areas, even for heavy load paths, LEBs are the preferred choice. In the absence of a fixed point, and taking into account the flexibility offered by LEBs, the overall behaviour of a structure in the event of moderate seismic activity is better. In the event of a strong earthquake, the LEBs would tear and replacing them would be less costly than for PBs.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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`Ü~éíÉê=N=J=Introduction 1.1 – Why replace the 2000 guide? The guide that was published in 2000 was based on projected European standards or on those being drafted, which were, in any event, difficult to obtain directly from AFNOR. This explains the ambiguity of the document that was based on future standards at preparation stage, on structure design documents that had not been finalized either and on French standards regarding the verification of the bearing characteristics. This situation has now been clarified by the publication of all sections of the standard NF EN 1337 (except part 8 – Guide bearings and blocked bearings) and the design standards (the Eurocodes used in this guide, at least). Furthermore, the publication of the sections of NF EN 1337 will, after the coexistence period (i.e. 31.12.2006), lead to the suppression of French standards on the same subject, in particular XP T 47.815. For these reasons, we deemed it necessary to revise the 2000 guide, to provide project designers with advice guidelines that take into account the most recent publications.
1.2 – Scope and content The aim of this guide is to explain the standards in force at the time of writing (cf. Bibliography). It gives additional information regarding these standards, in particular giving details of some important specifications for use on bridges. This guide includes the following: • A brief description of this type of product and any equipment related to it. • The main core regulations and standards. • The dimensioning criteria to be found in the standards drafted by the CEN1. • The principle of controls based on certification by the CE marking. • Design methodology in a bridge project with examples of application. • Information about the Sétra NEOP programme with a preliminary design for this bearing. • A series of appendixes completes the guide, including in particular: • Appendix 1, giving information about the design of this bearing in seismic areas, based on the latest seismic standards. • Appendix 2, focusing on the durability of laminated elastomeric bearings in conjunction with a slide plane. • And appendix 4, giving examples of articles to include in Particular Technical Clauses (CCTP).
1
CEN: European Committee for Standardization
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
T
1.3 – Application of the standard NF EN 13373 in the French national context EN standards do not set all characteristics, leaving it up to each member country to specify them for their use on structures by means of a national application document. This application document is the subject of a technical information note issued by the Sétra 2 (the content of which was partly drafted by the T47A Standardisation Commission). The contents of this document are not detailed here and readers are invited to consult it and read it in parallel with the standard.
1.4 – Scope The rules set out in this technical guide are for the use of Bearings composed of elastomeric plates. These rules are only applicable to Bearings made of at least two elastomeric laminations bonded by vulcanization to metal plates (although the standard authorizes the use of bearings composed of a single lamination between two coated plates) (type B of the NF EN 13373) and if required, completed by sliding elements 3 (type D or E of the NF EN 13373) Antislipping or antilifting elements 4 (type C of the NF EN 13373).
1.5 – Notations and symbols The notations used in this guide are those of the NF EN 13373 as regards the design of laminated elastomeric bearings. We draw the reader’s attention to this document, in particular to chapter 3. We have not copied out these notations and symbols in order to avoid any copy errors and also because we believe the reader cannot use this guide without having the standard to hand. The notations and symbols concerning seismic calculations are given in appendix 1. The notations and symbols pertaining to combinations of actions are those defined in the Eurocodes and can be found in chapter 4.
2
available for download on Sétra sites
3
cf. appendix 2
4
cf. chapter 2
U================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
`Ü~éíÉê=O=J=Composition and description Readers interested in the background of these products, together with the manufacturing technology, design principles, durability and quality control, may like to consult the document entitled "Appareils d'appui en caoutchouc" (Rubber bearings), published in July 1994 by the AFPC in partnership with the Sétra, cf. Bibliography).
2.1 – General principles of composition A laminated elastomeric bearing is a "block of vulcanized elastomer (…) reinforced internally by one or several steel plates, chemically glued (bonded) during vulcanization. (…). Elastomer is a macromolecular material that regains its shape and initial dimensions approximately after being submitted to significant deformation under the influence of a low stress variation" 5.
Figure 2.1: typical composition of a laminated elastomeric bearing The base material is obtained by subjecting the raw material, mixed with various inert or reinforcing fillers, to a series of transformations. After treatment, the product is in the form of sheets a few millimetres thick. These are stacked with metal plates, which have previously been sanded and treated, in moulds, the dimensions of which match those of the product to be obtained. It is then compressed and vulcanized (by heating).
Figure 2.2: release from the mould on the press (photo SNAC) According to the amount of freedom authorized, a laminated elastomeric bearing is, as regards the elementary block, a mobile bearing. As well as the bearing rotations, displacements are accommodated in two directions. It is possible either to increase displacement capacity by adding a slide plane, or to prevent distortions using metal plates, thus making a “fixed” bearing. The scope of the standard (NF EN 13373, § 1) specifies that only bearings of plan dimensions of under (1200 x 1200mm) are concerned.
5
NF EN 13373, § 3.1
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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2.2 – Component parts 2.2.1  Composition The various parts comprising a laminated elastomeric bearing are defined in figure 2.3.
Figure 2.3: typical composition of a type B bearing according to the standard NF EN 13373 (fig. 2)
2.2.2 – The elastomeric material Rubber used in the composition of bearings can be either natural or of vegetal origin, latex, in which case it is an isoprene polymer (polyisoprene or NR for "Natural Rubber" in the standard), or synthetic, in which case the compound is generally a chloroprene polymer (polychloroprene or CR pour "Chloroprene Rubber" in the standard. There are a number of formulas, which have market brand names, such as Neoprene ® (Du Pont of Nemours), Butachlor® (Ugine), etc. Wha t are the criteria for choosing one o r ig in o ver ano ther? Natural rubber (with the appropriate formulation) provides good resistance to traction, excellent failure strain and performs well with dynamic loads and in the cold, although it does tend to crystallize. On the other hand, it is highly gas permeable, its resistance to oils and solvents is quite poor and its susceptibility to aging must be compensated by the use of antioxidant and antiozone6. France, along with many other European countries, has chosen polychloroprene which, among other qualities, provides excellent resistance to aging, a very low loadbearing creep rate and good tear resistance. This makes it perfectly suitable for the requirements of bearings. The scope of the standard (§ 1) specifies that only rubbers described in § 4.4.1 of the standard are covered. Certain shortterm economic considerations may result in a decision to turn to natural rubber. This means taking a longterm risk on the performance of the bearing that is not justified by the difference in price in relation to the cost of change on a structure in service. This explains why the national application document of the standard NF EN 13373, only accepts polychloroprene (or CR) for use in France. As regards ozone resistance, the national application document of the standard NF EN 13373 (§ 4.3.6) only accepted the single level intended for CR, which is suitable for service conditions on a bridge. For our part, we suggest that you do not define the material but, for bearings to be used on bridges and similar structures, we suggest setting a maximum ozone resistance specification (i.e. 50 ppcm). The minimum thickness of a sheet, in accordance with NF EN 13373 (§ 5.3.2), may in no circumstance be under 5 mm, or over 25 mm.
6
cf. "Rubber bearings". § 3.3.1. See Bibliography.
NM================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
2.2.3 – Steel plates These are systematically made of S 2357 steel or of steel with an equivalent minimum failure strain (cf. complement at § 3.2.3). The thickness of the plates may in no circumstance be under 2 mm (NF EN 13373, § 4.4.3.1).
2.2.4 – Sliding elements that may be required 2.2.4.1  Composition The most commonly used configuration in France at the moment is described below, but there are other systems. These sliding elements include a PTFE8 perforated plate fixed on the top of the elastomeric bearing, either on the external elastomer coating (type D bearing according to NF EN 13373), or on an outside steel sheet (type E bearing according to NF EN 13373). A polished stainless steel sheet (the grade of which is defined in NF EN 13372, § 5.4.1), connected to a higher S235 steel plate, slides onto the PTFE plate (NF EN 13373, § 3.1.7). The slide sheet is a single piece of austenitic steel. For a thin austenitic steel plate, two methods are used to fix the stainless steel sheet onto the low carbon steel support plate. The first method involves cold gluing the stainless steel sheet by means of a resin film (epoxydic or other). It is advisable to request a screw or peripheral welding fixation, as shown in the diagram in figure 2.4. In the second method, the stainless steel plate and the support plate are attached by the interposition of a thin sheet of special highhardness elastomer. The bonding of the complex is then obtained by vulcanization.
Figure 2.4: further lateral types of fixation on stainless steel slide plates
The upper part (or slide plate) can be fixed to the part of the structure in contact with the bearing. So as to follow displacements and to allow for checks during civil engineering inspections, these slide plates have a measuring rule. It is essential that the rule be positioned on the side where the inspector will probably take place. Furthermore, it is also highly recommended that the rules are set consistently within a same structure to ease operations. (cf. figure 2.5). To prevent them from being soiled during installation and service, these bearings must be fitted with a device that protects the slide plane (in all normal service circumstances). This device must be easily removable so that the bearing can be inspected and monitored. All these elements are defined in NF EN 13372, standardised through part 3.
7
NF EN 10025. The standard does not specify the part concerned, but it is parts 1 and 2.
8
PolyTetraFluoro Ethylene or Teflon ®.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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Figure 2.5: an example of rule to monitor displacement (vertical bearing in an seismicresistant stop) (photo Sétra)
2.2.4.2 – Horizontal force Bearings fitted with sliding elements are designed to accommodate significant horizontal displacements. Horizontal force ranges from 3 to 8 % (for respective average pressure of 30 to 5 MPa) of vertical force. The bearing can always deform by compression and rotation. This type of bearing is very advantageous for the launch of the structure. The standard (NF EN 13373, § 4.4.4) limits the use of type D sliding bearings (cf. figure 3.1) in cases of irreversible movements (creep, shrinkage, etc.). This limit does not extend to type E. The National Application Document regarding part 3 authorizes a wider use than in the provisional phase, but great care needs to be taken as regards the durability of this type of device and for use in service. Appendix 2 gives information about the durability of these devices and advice for their use.
2.2.4.3 – Slide plate dimensions There should be no hesitation in oversizing the length of the slide plates, even though their dimensions are at ULS. This allows compensation for the many consecutive imprecisions regarding factory presettings, design hypotheses, the actual date of installation and, therefore, the temperature on installation. The text of the standard (cf. NF EN 13371, § 5.4) is remarkably unclear, so the National Application Document needs to be consulted. This specifies that it should be interpreted as follows: "Displacements should be increased in both directions by ± 20mm. Furthermore, the minimum displacement to take into account is ± 50mm in the principle direction of displacement resulting from the structure".
2.2.5 – Antislipping and antilifting devices When there is a risk of slipping in a laminated elastomeric bearing (cf. NF EN 13373, § 5.3.3.6, nonsliding condition), stops can be fitted. These devices must only stop the slipping, without preventing or hampering the deformations: compression, distortion and rotation. In particular, the stops must be in contact with a plate (or external reinforcement) the thickness of which must be at least equal to the height of the stop (type C bearings of NF EN 13373). In no case should the stop be placed on an elastomeric sheet (cf. figure 2.6).
Figure 2.6: the principle of an antislipping device
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Antislipping bearings with lugs (With type C bearings). NB: except in particular cases, lugs are only needed on one side. See also the device of figure 2.6.  gluemounted (not shown) for low tangential forces (with type C bearings).
 with anchors.
 using chequered plates (for low tangential forces).
Limited distortion or blocked bearings
Antilifting system bearings
Figure 2.7: design drawings of "fixed" bearings The drawing of the bearing with the antilifting system, copied from the standard, raises the following points: the drawbars must allow for rotations and it is advisable to position them in the axis of this rotation. The device must not hinder any displacement. It should not therefore be copied as is. It may be necessary to avoid distortion of the bearings. This is the case, in particular, when a line of “fixed” bearings needs to be created. The laminated elastomeric bearings are then fitted with a rigid metal structure that prevents horizontal travel of the deck whilst allowing the compression and rotation of the bearing. Figure 2.7 gives several examples of devices that may be suitable. These are, however, devices that are not often used and should be avoided as a solution with a type C bearing is preferable.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
NP
Figure 2.8: an example of a limited distortion or blocked bearing (photo Sétra)
2.3 – Manufacturing methods In order to manufacture a fully coated laminated bearing, it has to be placed in a mould and only one size can be manufactured per mould. There are, therefore, as many moulds as there are sizes of bearing. So as to limit the number of moulds and to rationalize manufacture, it is therefore preferable to choose a bearing size that falls within a range, an example of which is given in NF EN 13373, table 3 and which offers the advantage for the project designer of typical dimensions that can facilitate the preliminary design. However, this presentation of a range in the form of a table does not comply with the spirit of the standard, the approach of which consists of justifying each bearing in accordance with the loads to which it is subject. This approach therefore clearly disfavours a standardisation of dimensions as has been the practice up to now. However, the absence of a standard range could pose problems for project designers who then have to work "blindly" in their repeated search for a bearing that satisfies the criteria they have defined. Indeed, as we will see in chapter 4, they have to define a bearing that suits and then proceed by iteration until they find the right dimension. They therefore need to know the main dimensions manufactured. This is why for information purposes, a table can be found, in addition to the table of the standard, that gives the most commonly used plan dimensions in France (cf. appendix 3). It is up to the project designer to check that the product conforms to the requirements of the standard. Moreover, large dimensions (over 700 x 700 mm) should be used with precaution as with these bearings, uniform stress distribution calls for particular care when creating bosses. For decks with high rotations, dimensions need to be chosen so that the b/a ratio is of between 1.5 and 2. For decks with high displacements, it is better to use square shapes (a = b). For structures with significant rotations in both directions, diskshaped is best, although the manufacture of this type of bearing is more costly and difficult.
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`Ü~éíÉê=P=Ó=Behaviour and dimensioning 3.1  Introduction This chapter details the geometric and mechanical characteristics of laminated elastomeric bearings, together with the rules for dimensioning and verification. The behaviour of the bearings such as it is described in the following paragraphs is not enough to carry out a complete verification. Indeed, in a structure, the deck, bearings, piers and abutments form a system in which the various parts interact. A balance of the whole structure needs to be found, under the combined effect of horizontal loads and deformations due to temperature, shrinkage, creep, etc. The interactions between the structure and the bearing are dealt with in chapter 4 of this document. This chapter only deals with the performance and the dimensioning of the bearing itself, together with the contact areas with the structure. NF EN 13373 (§ 5.3.2)9 applies to six types of bearing, as defined in the table in figure 3.1:
Figure 3.1: table showing the different types of laminated elastomeric bearings according to NF EN 13373
9
Henceforth in this chapter, the reference of the paragraph concerned from NF EN 13373 will be specified in brackets in bold italics.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
NR
Readers are reminded that this guide only deals with bearings of type B to E. Type A bearings (single reinforcement) or type F (non reinforced or strip bearing) are not used in civil engineering structures.
NF EN 13373 defines the geometric characteristics of the most widely used bearings. On a plan view, bearings are square, rectangular or circular in shape, although elliptic and octagonal shapes are also tolerated. The rules given in this document are for rectangular bearings. Please consult the standard as regards other shapes. Among type B bearings (multiplated and coated on all sides, cf. figure 3.1), the following can be distinguished, in accordance with NF EN 1337: a) type B bearings defined in table 3 NF EN 13373. They include n+1 metal plates and n elastomeric laminations of a constant thickness. Their perimeter is coated with elastomer at least 4 millimetres thick and the upper and lower faces with a nominal 2.5mm thickness of elastomer (with a – 0. + 2 mm tolerance). b) other type B bearings that include "active” external halflaminations (cf. the table in appendix 3 of this guide). These are different in that the upper and lower elastomeric coatings are thicker. These are no longer simple protection coatings, but rather a halflamination, the thickness of which is taken into account in the calculations defined in article 5.3.3.1 of NF EN 13373. It is suggested that they are designated with the number of intermediate laminations, mentioning the two external halflaminations or the external coatings. This gives the following example of a bearing designation: a x b; n(ti + ts); 2 e e.g.
200 x 300; 2 (10 + 3); 2 x 5, 400 x 500; 4 (12 + 4); 2 x 6, ∅ 700; 5 (16 + 5); 2 x 8 for a circular bearing.
Figure 3.2 summarizes the characteristics of these bearings defined in NF EN 13373. Type B With e = a halflamination (examples of plan dimensions in appendix 3)
Type B defined in table 3 of the standard With e = passive coating
e = 2,5 mm e = ti / 2 ts
Tb
ti
ts Tb
Tb = 3 (ti + ts) + ts + 5mm n = 3 intermediate laminations, assuming that the coatings are not part.
ti Tb = 2 (ti+ ts) + ts + 2 ti/2
n = 2, the halflaminations can be taken into account in the calculation.
Figure 3.2: the characteristics of the bearings described in this chapter
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3.2 – The characteristics of bearings 3.2.1 – Geometric definition The geometric definition of a type B bearing of NF EN 13373 (§ 5.3.2) is given in figure 3.3, in which a, b, a', b’ are the dimensions of rectangular shaped bearings and D and D' are the diameters of circular bearings. a and a' always designate the smallest plan dimensions of the bearing if it is rectangular.
e ts Tb
ti
a' , b' ou D'
> 4 mm
a , b ou D Figure 3.3: the geometric definition of a bearing
According to the n number of intermediate laminations, three thicknesses required for dimensioning can be defined: Total nominal thickness of the bearing:
Tb = n (ti + ts) + ts + 2 e
Total nominal thickness of the elastomer:
Te = n ti + 2 e
Average total initial thickness of the shear elastomer, including the upper and lower coatings.
Tq = n ti + 2 e
if e > 2.5 mm
Tq = n ti
if e ≤ 2.5 mm
Indeed, if the nominal thickness of the coating is higher than 2.5mm, it must be taken into account in the design. Below that, it can be disregarded (EN § 5.3.3).* * The advantage of a coating lamination of between 0.5 and 0.7 times the intermediate lamination is to ensure the same functions as the intermediate laminations and to better adapt them to the surface defects on the supports, without deforming the nearby plates. A thin coating lamination cannot absorb translation or almost any rotation and any defect in the flatness of the support can lead to localised slipping.
3.2.2 – The characteristics of elastomer (EN § 4.4.2) The main physical parameter of elastomer that is involved in the dimensioning of a bearing is its conventional shear modulus G. Unless specified otherwise, the nominal value G of the conventional shear modulus is de 0.9 MPa. It is this value that has to be introduced into calculations (cf. § 1.3).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
NT
Under dynamic effects, the standard recommends increasing the calculation value of the elastomer modulus (EN § 5.3.3 – note 2). Under the horizontal effect of operating loads10, we recommend a Gdyn modulus taken to be equal to 1.8 MPa in calculations. For seismic activity, please see appendix 1 of this document. There is a low temperature modulus G. In view of the climatic conditions of metropolitan France, it does not appear necessary to take it into account, as the National Application Document specifies. This would only be valid for ambient temperature of – 25°C and below, at which point the polychloroprene begins to crystallize. Some Nordic countries, Finland in particular, include a low temperature modulus G in their calculations, but only in regions with temperatures of below – 30°C.
3.2.3 – The characteristics of internal plates (EN § 4.4.3.1) The thickness of the plates must equal or be above 2 mm. S235 steel must be used or steel with an equivalent failure strain (in this case, it is advisable to obtain a certificate from the manufacturer, certifying a failure strain at least equal to that of S235 steel). The yield strength to use in calculations is therefore 235 MPa (thickness of less than 16mm in NF EN 10025).
3.2.4 – The characteristics of external plates (EN § 4.4.3.2) For type C bearings, the thickness of the external plates is 15mm for elastomeric laminations with a thickness of 8 mm and under, and 18 mm for thicknesses above. S235 steel or an equivalent is also used.
3.2.5 – The characteristics of slide plates (EN § 4.4.4) The characteristics of sliding planes are given in NF EN 13372. Sliding systems generally consist of a stainless steel plate lying on a side of the bearing on which a polytetrafluoroethylene (PTFE) sheet is bonded (cf. le § 2.2.4 of this guide). These are type D and E bearings. The minimum thickness of the support plate is provided by the formula (EN § 6.9.3): t b = Max ⎛⎜10 mm ; 0,04 a b 2 + b b 2 ⎞⎟ ⎝ ⎠ With a b and b b the width and length of the support plate in mm. The friction coefficient μd of perforated PTFE steel is provided in table 11 of NF EN 13372. This table has been drawn up using the following formula (EN 1337  2  Appendix B): 1,2 k μmax = 10 + σ p with
k = 1 for austenitic steel (stainless steel) σp contact pressure on the PTFE in MPa
These values vary from 3 to 8 % according to usual contact pressure. Furthermore, the average pressure on the block (surface A) is limited to 30 MPa (for a modulus G of 0.9 MPa and k = 1, cf. § 5.6 of NF EN 13373). It is specified that the values given are a function of σp. For a given load path, the friction coefficient is calculated using the ULS stress. We would like to point out the notable variation of the friction coefficient in accordance with the compression stress on the PTFE. To simplify, the 2/3 corrective factor does not need to be taken into account, except in specially justified cases and for application in overseas departments and territories where the effective bearing temperature does not fall below  5°C.
10
For the vertical dynamic effects of operating loads, the modulus G should be used.
NU================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Verification of the deformation of slide plates (NF EN 13372 § 6.9.2) is only justified for difficult or specific applications (e.g. for type E bearings). In other cases, only the orders of magnitude need to be verified.
3.3 – Dimensioning bearings 3.3.1  Principles The dimensioning principle defined in NF EN 13373 consists of justifying each bearing according to its loads. Consequently, the dimension tables (table 3 of the standard or the table in appendix 3 of this guide) are only starting points in the calculation of bearing dimensions and are only given, therefore, for information purposes. The rules for dimensioning and verification of the bearings are intended to restrict their total horizontal distortion at Ultimate Limit State, by the effect of vertical and horizontal loads and horizontal or angular deformations applied to the bearing. For type B bearings, NF EN 13373 differentiates between: • Recommended size bearings, as defined in table 3 of NF EN 13373; • Other types of bearings, in particular those with two external halflaminations. In compliance with NF EN 13373, four types of verification at Ultimate Limit State must be carried out for laminated elastomeric bearings of whatever type: • Maximum total distortion of any point of the bearing must be restricted • The thickness of the plates must be sufficient to resist the traction to which they are subjected • The stability of the bearing must be ensured as regards rotation, buckling and sliding • Actions exerted by the bearing on the rest of the structure must be checked (the direct effect of the bearing on the structure and the indirect effect due to deformation of the support).
3.3.2 – Bearing behaviour N.B: NF EN 13373 takes the external lamination into account in the calculation when its thickness is strictly over 2.5 mm. In practice, for France, the thickness of the external layers is often half of that of the internal laminations. There will therefore be maximum distortion on these internal laminations.
3.3.2.1 – Behaviour under axial force
γ
Fz
Under normal centred force Fz, a linear distribution of the distortion εc is noted, linked to the shear τΝ in a layer of elastomer. Maximum distortion occurs at the middle of the large side b of the bearing.
τN
It is given by the formula (EN § 5.3.3.2): τ N = 1,5 FZ c= G G Ar S
ε
Fz
εc
In this formula: G designates the conventional modulus of elastomer (§ 3.2.2) with G = 0.9 MPa and Ar is the effective plan surface.
a Figure 3.4: distortion of a bearing under axial force. To calculate Ar, the nominal lateral coating needs to be removed to obtain A1 (equal to the surface of plates A' reduced by the holes if there are any) and the horizontal deformations vx and vy need to be taken into account, that are caused by the horizontal force concomitant with the vertical force FZ.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
NV
vx
x
a' Figure 3.5: a surface reduced due to the effect of horizontal deformation.
We thus have
vy ⎞ ⎛ v ⎟⎟ avec A'= a'×b' (if the plates do not have holes) A r = A' ⎜⎜1  x a ' b ' ⎝ ⎠
The calculation of deformations vx and vy is relatively complex. As a first approach, we could often disregard the effect of vy and use the maximum value of vx. •
S is the form coefficient of the layer i in question:
For a rectangular bearing we have:
A' S= lp t e
avec l p = 2 (a '+b') et
pour les feuillets des couches internes ⎧ te = ti ⎨ t = 1,4 t i pour les feuillets des couches externes ⎩e
The standard also gives the means of estimating the total deformation ΣvZ due to a vertical force FZ (EN § 5.3.3.7): vz =∑
Fz t i A'
⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ + 2 5 G S E d b ⎠ 1 ⎝
With Eb = 2000 MPa S1: the form coefficient of the thickest lamination A' = a' x b': surface of the plates
This formula can be simplified as follows: v c = Fz T0 / A’ [1 / (5 G S12) + 1 / E b] This, however, is not logical insofar as, in the presence of external laminations, it is said that Si should be applied instead of S of these external laminations in their settlement calculation. The following formula would be more rational: Fz t i ⎛⎜ 1 1 ⎞⎟ vz = + avec E b = 2000 MPa 2 ⎜ A' ⎝ 5Gd Si Eb ⎟⎠
∑
Let us remember that in this formula, S designates the form coefficient of lamination "i" and that, in the event of a halflamination, the value of S is worth 2/1.4 times that of the intermediate lamination. The values obtained with this formula are slightly lower than those of the standard, thus making for a safer verification of the rotation stability (Cf. § 3.4.1.3 below) and limiting any losses in contact with the support under the effect of rotations. Generally speaking, settlements obtained with these formulas are far too high in relation to the actual behaviour of the bearing, if we disregard the adaptation movements between 0 and 3 MPa. As an example, during tests, variations in pressure of between 5 and 15 MPa gave the following settlements:
OM================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Settlements Dimensions
during tests
following the formula in the standard
following the modified formula above
200 x 300; 2 (8 + 2); 2 x 4
0.5 mm
1.16 mm
0.98 mm
300 x 400; 3 (10 + 3); 2 x 5
0.6 mm
1.49 mm
1.32 mm
400 x 500; 4 (12 + 3); 2 x 6
0.75 mm
1.93 mm
1.76 mm
The standard specifies that the vertical deformation is only more or less proportional to the load after an initial settlement that we can estimate to be 2 mm. This value appears too high, especially when positioned on metal plates. Besides, a close look at a number of settlement tests reveals a very wide dispersion of results and this dispersion is difficult to explain. In fact, the calculated settlement value according to the standard indicates the maximum value obtainable on a compliant bearing. In some tests, settlement values can be observed that are twice as small as those of the normative calculation up to 8 Mpa and above 15 Mpa, they can be 3 times less than the calculated value. Consequently, bearing in mind this incertitude (together with note 2 of § 5.3.3.7 of NF EN 13373), to ensure that the loading on bearings on the same line is uniform, it is highly advisable to plan for a “combined” installation (cf. § 3.4.1.3). In the event of hyperstatic and highly rigid structures, testing is recommended in order to estimate the actual deformations of the bearings.
3.3.2.2 – Behaviour under a horizontal force Under a horizontal force, a uniform distribution of the distortion εq is noted, linked to the shear τΗ in the elastomer.
Fx
γ
Under displacement vx or a horizontal force Fx, distortion is given by the formula (EN § 5.3.3.3):
τH
εq =
Fx
εq
vx F = x Tq G a b
ε q =tgγ
a Figure 3.6: distortion of the bearing under a horizontal force In these formulas, the modulus G shall be taken as equal to 0.9 MPa for static loads and 1.8 MPa under dynamic effects (cf. 3.2.2). For simplification, for nonexceptional structures, displacements caused by wind are only considered at a static state. Furthermore, the project designer must compose the longitudinal and transversal forces vectorially, following the combinations of actions given in chapter 4 of this document (to obtain a force Fxy) when the case occurs.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
ON
3.3.2.3 – Behaviour under a horizontal axis rotation
Mt
The value of the distortion εα, under the effect of the rotations αa et αb of the perpendicular axis on sides a and b of the bearing, is given by (EN § 5.3.3.4):
γ αa
τα
a'2 α a + b'2 α b ) t i ( εα = 2
∑ t3i
The distribution of the distortions is given in figure 3.7.
Mt
εα a Figure 3.7: distortion of the bearing under a horizontal axis moment The restoring moment Mt is obtained according to the rotation α by (EN § 5.3.3.7): Mt=
G α a'5 b' n t 3i K S
In this formula, α is the axis rotation parallel to side b of the bearing and n represents the number of internal laminations. Ks is given in the following table (cf. NF EN 13373, table 4): b/a
0.5
0.75
1
1.2
1.25
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.5
10
∞
Ks
137
100.0
86.2
80.4
79.3
78.4
76.7
75.3
74.1
73.1
72.2
71.5
70.8
68.3
61.9
60
Figure 3.8: values of Ks for a rectangular bearing
The following approximate formula can also be used:
K s = 26,2 e
⎛b⎞ −1, 2785 ln ⎜ ⎟ ⎝a⎠
+60
3.4 – Dimensioning verifications 3.4.1 – Basic verification 3.4.1.1 – Limiting distortion Total distortion at any point of the bearing is limited at Ultimate Limit State (EN § 5.3.3): ε τ = KL ( ε c + ε q + ε α ) < 7 In this formula: • KL is a coefficient equal to 1.00 in general. This coefficient can be extended to 1.5 in the case of railway structures under rolling loads only. •
εc, εq and εα are the distortions calculated respectively under vertical force, horizontal force or displacements and deck rotations.
Moreover, the standard (EN § 5.3.3.3) limits the distortion under horizontal force or displacements to 1: εq < 1.
OO================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
This limitation concerns force and displacements of both short and long duration. Furthermore, the load cases to be considered include concomitant force and displacement in two perpendicular directions that need to be composed vectorially for this verification. It should be noted that there is no limitation for εc alone or Fz (other than that regarding buckling).
3.4.1.2  Traction in the metal plates The plates must be at least 2 mm thick. The standard also requires the minimum thickness of the metal plates at Ultimate Limit State be verified. For bearings without perforations (not drilled), which have laminations of constant thickness ti, the minimum thickness ts of the plates is defined by (EN § 5.3.3.5 simplifying the formula for this hypothetical case):
ts = γ m with: Fz
2,6 Fz ti Ar fy
Maximum applied vertical force,
fy
Yield strength of the steel of which the plates are composed (i.e. 235 MPa for S235 steel);
γm
Partial factor, the value of which is 1 in the National Application Document (cf. § 1.3).
For bearings with varying thicknesses of elastomer layers or with plates that include holes, this formula is no longer valid and the standard should be consulted (EN § 5.3.3.5, general formula). N.B: in cases where the bearings have high rotation requirements or are close to the buckling limit, it is advisable, for b'/a' < 1.24 ratios, to increase the thickness ts by 5 to 10 %.
3.4.1.3 – Rotation limit condition The rotation stability of the bearing is checked at Ultimate Limit State. The following needs to be verified (EN § 5.3.3.6): ( a' α a + b' α b ) ∑ vz ≥ Kr with: αa et αb Kr
∑v
z
Rotations of perpendicular axis on sides a and b of the bearing Coefficient equal to 3 The sum of the vertical deformations calculated as per paragraph 3.3.2.1 of this guide.
Let us not forget that rotations αa and αb must include installation defects. These depend largely on care taken over the installation and the precision of deformation calculations during installation, but also on the extent of homogeneity inside the bearing. Wherever possible, an installation method that combines the surfaces should be used, for example with a mortar bed, caulking or the deck concrete castinplace. NF EN 13373 (§ 7.1.4) is not clear about the values to adopt for installation defects, or about the way to take them into account. The following nominal values are therefore suggested: •
0.003 radian in the case of “combining” methods
•
0.010 radian for structures placed directly onto the bearings.
This installation defect needs to be added to the largest of the rotations, αa or αb.
3.4.1.4 – Buckling stability Buckling stability needs to be checked at Ultimate Limit State in the following conditions (EN § 5.3.3.6): Fz 2 G a' S1 < Ar 3 Te
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
OP
This formula is to be applied with the maximum reaction of the basic combination that has the highest Fz/Ar ratio and with a modulus of 0.9 MPa.
3.4.1.5 – Nonslip condition The nonslip verification is carried out, in the absence of antislipping device, if (EN § 5.3.3.6): Fxy ≤
μ e Fz
et
Fz,Gmin Ar
≥ 3 MPa
with: Fz,Gmin
Minimum reaction under permanent load
Fz and Fxy
μe
The most unfavourable concomitant vertical and horizontal force reaction
Friction coefficient between the bearing and the structure.
N.B: except in cases where the bearing never returns to a position of zero displacement (vxy =0), the surface Ar must be taken equal to A’ to check the condition σm ≥ 3 MPa. For the calculation of Fxy, we vectorially compose the horizontal force coming from all the concomitant actions and combinations of actions presented in chapter 4 of this document. Fxy is therefore composed of permanents or variable force applied directly to the deck (wind and breaking affects) and permanent or variable force from imposed deformations or distortions (temperature, shrinkage, creep, difference in level, etc.). The coefficient μe is imposed by the standard in most cases: 1,5 K f F μe = 0,1 + avec σ m = Z (en MPa) σm Ar K f = 0,60 pour le béton K f = 0,20 pour les autres surfaces y compris mortier en résine
N.B: attention is drawn to the fact that most special mortars are not considered to be resin mortars. This coefficient may however have values below those given above. This is the case, for example, with bearings placed on painted metal sheets or on certain resins.
3.4.1.6 – Pressure on the contact planes Although the standard does include verification of the contact pressure between the bearing and the structure, it only gives the principle, indicating that this pressure may not be uniform (EN § 5.3.3.7), cf. table 4.4 in chapter 4. For a preliminary design, we could take the usual value of average stress on the surface of the plates of around 20 to 25 MPa at ULS (less for small blocks and a little more for large dimensions), it being understood that the final average stress will result from the overall formula of § 5.3.3 of NF EN 13373. If there is a risk of heaving, the final stress should be recalculated. For largesize bearings, higher pressures are possible, as for other types of highpressure bearings (pot bearings, for example). When designing the supports, it is essential to take into account the possibility of the load path spreading on its reduced surface. As regards bearings positioned on concrete bosses, the bosses and the pier crosshead can be checked at Ultimate Limit State, according to the rules in article 6.7 of Eurocode 2 (NF EN 199211). Stress on the concrete can be calculated by taking an evenlyloaded reduced surface and by taking into account not only the translation distortion, but also the rotation and any hardening of the elastomer according to the average pressure. A calculation example is given in § 3.4.2 with the research method into possible heaving at support level.
OQ================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
In conclusion, the verifications to carry out at ULS, under basic combinations, are summarized in the table of figure 3.9. Verification
ULS Basic combinations
Limitation of distorsion ε
ε = KL (εc + εq + εα ) < 7 et εq < 1
Traction in the plates
Limit in rotation
∑ vz ≥
2,6 Fz ti Ar fy
( a'
α a + b' α b ) Kr
Fz 2 G a' S1 < Ar 3 Te
Buckling stability
Nonslip
ts=
Fxy ≤ μ e Fz et
Fz,Gmin A'
≥ 3 MPa
Figure 3.9: synthesis of verifications to be conducted
3.4.2 – Assessment of actual contact surfaces and pressure to be distributed in the supports 3.4.2.1 – Experimental results All limitations given by NF EN 13373 are based on a shear modulus deduced from pure shear tests. However, the behaviour of a bearing in simple compression is more complex. The modulus varies in different points of the elastomer and is not consistent in accordance with the stress applied. Rotation further complicates shear distribution. This could be the cause of a number of heavings that have been noted on bearings in situ, under the effect of rotations applied to the deck. Indeed, even with a correctlysized bearing, extreme rotations may cause decompression higher than the effect of the centred vertical load on the edge of a bearing. This decompression may well cause deterioration in the bearings. Experimental studies11 have enabled limit heaving curves to be established according to the rotation α and the compression σ = Fz / A’. These curves are given in figure 3.10, to illustrate the phenomenon observed in relation to the theoretical calculation. They justify the use of an adjustment coefficient Ka which represents the relation between the distortion due to compression εc and distortion due to rotation εα, when heaving occurs. In theory, this coefficient is 1.00, but experience has shown that it can vary between the two values Ka min and Ka max (the maximum value Ka max varies from 2 to 2.75 respectively for an average pressure Fz/Ar of 0 to 50 MPa). As explained in § 3.3.2.1 (as well as in note 2 of § 5.3.3.7 of NF EN 13373), the wide dispersion of test results only allows for an approximate assessment of the minimum contact surface using calculation.
11
In particular tests carried out at as part of research at the LROP (West Paris Regional Laboratory).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
OR
σ m = Fz / A r
σ = F z / A'
(MPa) 50
K a max en fonction de σ m
K a min
Courbe sécuritaire représentative des essais compressionrotation à la limite du soulèvement
40
30
Limite normative
σ m = 23,84 20
10  Tassement  Possibilité de rotation sans soulèvement
0 K a max =
αn αs
1
αs
2
valeur sécuritaire d'après les essais
K a max = 2,47
3
αn
théorique
Figure 3.10: compressionrotation behaviour prior to heaving. Determination of the adjustment factor Ka max.
3.4.2.2 – The assessment method proposed 3.4 .2.2.1  Introduction The standard stipulates verifying that the average stress on the reduced surface is compatible with the strength of the base materials. This justification is sufficient for materials other than concrete or mortars. Regulations involving concrete (such as Eurocodes and BAEL) consider a more complex verification, comprising the diffusion of a force uniformly distributed over a reduced contact surface. In accordance with these regulations, it is therefore advisable to check the uniform contact pressure and the possibility of this force dispersing into the mass, and to design the thickness and the density of the plate steel. We propose the carrying out of a further, more precise, assessment of contact surfaces between the bearing and its support. This method is a security calculation of the minimum contact surface using a Ka max coefficient given by figure 3.10. It takes into account the interactions between the form coefficient, distortion, settlement and the restoring moment of the standard. As all these relations have been simplified compared to the exact calculation model12, there is not a perfect consistency between all these relations and it cannot therefore be claimed to be a particularly rigorous calculation. The aim was above all to find a simple method (without iterations) to obtain the order of magnitude of the pressure to be distributed on the supports and to determine any contact loss of the elastomeric block in the case of a production with maximum settlement stiffness. The calculation to determine the surfaces submitted to uniform pressure is made in accordance with the informative appendix A of NF EN 13372. The simplified pressure diagrams are shown in table 4.4 of chapter 4.
12
cf. theories of F. Conversy and M. Topaloff and notes of J. Rajade
OS================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
3.4 .2.2.2 – The design p rincip le for determin ing th e unifo rm p ressure and a possib le risk of h ea v ing (N.B: for simplification, only one rotation αa of the axis parallel to side b is envisaged). • Calculation according to the standard of the distortion criteria, • Calculation according to the standard of the pressure σm on the surface Ar, • Determination of Ka max according to σm (cf. figure 3.10), • Calculation of the restoring moment, taking into account the maximum stiffness of the elastomer:
Mt =
G α a'5 b' × K a max n' t 3i K S
– If the 2 coating laminations are active, take n’ = n + 2 (e/ti)3, if not, take n' = n number of internal laminations. – If the installation is combined, take α = αa – 0.003. The value 0.003 rad corresponds to the "internal" precision of combined laying, a feature present in observations made during unsticking tests. Otherwise, take for α the theoretical ULS value of calculations, increased by the installation precision (to be multiplied by 1.35 to obtain a ULS value). • Calculation of the offset of the result of the forces: excmax = Mt/Fz. a)
If the value excmax is below a’/6, they is no risk of heaving. There may however be contact loss without any real unsticking in the event of distortion coming from the displacement vx.
In this event, by simplifying, the value of the uniform pressure on the most stressed support is: σunif = Fz / Aunif That is, on a surface of uniform pressure, Aunif = (a’  2 excmax  vx ) b’ The surface thus defined is that which should be taken into account for the diffusion of force in the supports (cf. table 4.4 of chapter 4). b)
If the value excmax is above a’/6, there is a risk of heaving.
In this case, an approximate calculation needs to be made of a coefficient Krs of reduction in surface contact by rotation using compression and rotation distortion values with the formula:
εc K rs =
3
K a max
εα
(value still < 1)
εα represents the rotation distortion under an angle α. The factor Ka max is given is the following table (as well as in figure 3.10): σm (MPa)
0  10
12.5
15
17.5
20
22.5
25
27.5
30
Ka max
2.00
2.05
2.17
2.29
2.38
2.44
2.50
2.55
2.58
σm (MPa)
32.5
35
37.5
40
42.5
45
47.5
50
Ka max
2.62
2.64
2.67
2.69
2.71
2.72
2.74
2.75
Figure 3.11: table giving the values of adjustment factor Ka max according to the average stress σm = Fz/Ar. The value of the new reduced surface is Krs (a’  vx) b’, from which σm’ = Fz/Krs (a’  vx) b’ and the minimum surface of uniform distribution is worth 2/3 of the preceding, therefore a uniform pressure of: σunif = 3 Fz / 2 Krs (a’  vx) b’ = 1.5 σm The surface 2/3 Krs (a’  vx) b’ is that which should be taken into account for the diffusion of force in the supports (cf. table 4.4 of chapter 4). In fact, we advise against the use of bearings in partial unsticking position under maximum loads. However, a contact loss of around 10% in service under basic combinations can be tolerated for small and mediumsized bearings. Under minimal loads, or in a provisional phase, a slightly higher unsticking can be envisaged. Obviously, the possibility of load diffusion in the supports will be checked.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
OT
It is always preferable to add a lamination, so long as the nonbuckling condition is still observed. N.B: in the case of a rotation in both directions of the bearing, the reduced surface in calculated in 2 steps, using the same method.
3.5 – Layout on supports 3.5.1 – In a single bearing line, bearings must be of the same type (susceptible of having, in particular, the same settlement), although their translation possibilities do not necessarily have to be the same (figure 3.12 & 3.13). 3.5.2 – Lengthwise, it is inadvisable to juxtapose several bearings that are intended to form a single load transfer point (upper part of figure 3.12). This restriction does not apply to split bearings, where the distance between the axis is generally around 2m or above.
Figure 3.12: examples of authorized and highly inadvisable layouts lengthwise.
N.B: in the above example, this layout makes rotations difficult, which should be taken into account in the design.
Figure 3.13: examples of authorized and highly inadvisable layouts transversally.
OU================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
3.5.3 – Crosswise, several bearings that are intended to form a single point of support can be juxtaposed (figure 3.12 upper part). These bearings must be identical in composition and size. It must be remembered that such layouts should be justified, taking into account in particular rotations resulting from installation defects that are likely to exist crosswise. Generally speaking, it is inadvisable to place bearings that do not have the same dimensions perpendicular to the same point of support, due to differences in stiffness (figure 3.12). In the case of a skew bridge, with a number of girders, it is generally preferable to lay in the same line identical bearings, the size of which corresponds to that of the most stressed bearing, but paying attention to the minimum stress of the least stressed bearing in order to avoid slipping. 3.5.4 – When bearings exert high compression stress on the supports, special precautions need to be taken. When the supports are made of reinforced concrete, allow for a minimum clearance of 10 to 15 cms in order to ensure correct stress distribution, the installation of the plates and their anchorages (figure. 3.14). In all cases, the recommendations relating to reinforced concrete constructions should be followed. 3.5.5 – Care should be taken to position, insofar as is possible, the lower face of the bearing above the highest known water level or the hundredyear flood. 3.5.6 – Bearing markings The position on the structure, the size and direction of any presettings, together with the installation direction must be clearly indicated on the bearings. 3.5.7 – Replacing bearings In the case of a change of bearings on a bridge in service, as with any repair, when a replacement bearing is sized, this sizing will be a compromise between the calculation rules of the present document and the possibilities on the existing structure (available height, plan dimensions, etc.). To assess the adjustments to the present rules, contact the design department of the technical network offices.
Figure 3.14: an example of a construction layout, highlighting the necessity of plating perpendicular to the jacking location.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
OV
`Ü~éíÉê=Q=Ó=Design principles for a structure with bearings 4.1 – General points – The regulatory context The design principles for laminated elastomeric bearings have been outlined in the previous chapter. However, a certain number of measurable variables  deformations and longitudinal force in particular – arise from an interaction between the bearings and the structure due to the flexibility of the supports. The exact dimensioning of a bearing therefore requires the dimensions to be predetermined prior to introducing the characteristics of flexibility (vertical, horizontal and rotation) throughout the structure (deck and piers) in order to obtain the force and horizontal displacements that allow for verification that the dimensioning correctly respects the limits set out in the previous chapter. If it is not the case, iteration is neccessary. In NF EN 13373, the calculation of bearings is only made at Ultimate Limit State. Combinations to be used are therefore basic combinations in which, aside from permanent action, actions occur that are due to road loads, the effects of temperature (uniform and thermal gradient) and the wind. These verifications should be completed by accidental combinations if the piers of the structure are likely to suffer from impacts from boats or trucks and combinations under seismic actions if the structure is subject to these. Finally, in some specific cases, other verifications should be carried out, for example, for a beam laid during construction on its definitive bearings. For the calculations given hereafter, we have used the combinations provided by the following texts: • NF EN 199115: this standard specifies the values to be used for uniform temperature actions ΔTN and thermal gradient actions ΔTM. It also specifies the way in which these actions should be combined to account for their simultaneity and obtain the characteristic overall effect Tk • Appendix A2 of NF EN 1990: this appendix defines the combinations to be used in particular for the calculations of supports and bearings. Firstly, we can apply the basic combinations given in table 4.1: N° + 1.35 {UDLk +TSk + q fk,comb} + 1.5 min{FW* ; 0.6 FWk}
1
+ 1.35 {UDLk + TSk + q fk,comb } + 1.5 {0. 6 Tk}
2
+ 1.35 gr1b
3 (1)
+ 1.35 gr2
4
1.35 Gk,sup + Gk,inf + P + S + C + 1.35 {gr3 ou gr4} + 1.5 {0.6 Tk}
5
+ 1.35 gr5
6
+ 1.5 FWk
7
+ 1.5 Tk + 1.35 { 0.4 UDLk + 0.75 TSk + 0.4 q fk,comb}
8
Table 4.1: list of basic combinations
(1) including braking
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
PN
In the calculation example, to simplify, we will only consider the UDL, TSk and qfk loads, together with the braking loads, which give table 4.2. N°
1.35 Gk,sup + Gk,inf + P + S + C
+ 1.35 {UDLk + TSk + q fk,comb } + 1.5 {0. 6 Tk}
2
+ 1.35 gr2
4
+ 1.5 Tk + 1.35 {0.4 UDLk + 0.75 TSk + 0.4 q fk,comb}
8
Table 4.2: the combinations chosen for the example Horizontal force that intervenes in the preceding combinations is to be calculated using the following methods: • For braking: NF EN 19912 defines the breaking force to be applied to the deck as a fraction of the maximum load that can be put on the busiest lane of the load model 1 (NF EN 19912 § 4.4.1). These fractions are 10% for UDL distributed load and 60% for TS concentrated loads. If we take a class 2 structure, the main lane of which is 3 metres wide, the total braking force, in characteristic value, for a deck of length L is given by:
H K = 324 +1,89 × L with L in metres and HK in kN. The breaking force varies from around 340 to 400 kN for smaller structures 10 to 50 metres long and reaches the maximum value of 900kN for structures 350 metres long between expansion joints. This value is far higher than those normally used in former regulations (300kN for the braking of a Bc truck, for example). As regards structures on laminated elastomer, the breaking force is spread over all the deck bearings, which should not cause problems for the pier reinforcements. However, for large structures with fixed bearings that take nearly all the horizontal force, the sizing of the piers can be complicated with such high breaking values. If the structure has high, flexible piers, it is advisable to have several fixed bearings. Otherwise, the fixed bearing should be put on a short pier, or even on an abutment, which may lead to difficulties in sizing the expansion joints (and the slide plates) on the abutment located at the other end of the structure. This maximum breaking force will most probably be reduced in the National Annex as NF EN 19912 allows for this. The maximum breaking force could then be brought down to 500 kN, except if the structure carries military loads that comply with the STANAG (Char Mc 120) standardisation agreements. • For thermal force: The effects of temperature are defined in section 4 of NF EN 199115. Temperature differences Te, max and Te, min in characteristic values are to be calculated according to the material from which the deck is made and the region in which the structure is built. These temperatures are to be determined using maps supplied in the National Annex 13 of NF EN 199115. In the meantime, the following values, found is the National Annex, can be used: Te, min Deck material
Te, max
Concrete
Composite
Steel
Brittany – Provence Côte d'Azur
10 °C
10 °C
20 °C
Centre – North
15 °C
15 °C
25 °C
20 °C
20 °C
30 °C
Concrete
Composite
Steel
40 °C
45 °C
55 °C
SouthWest East  Alps
Temperature variations resulting from these maximum and minimum temperatures can be calculated according to a temperature T0 which is taken as equal to 10 °C in the absence of any specification on the project. To calculate the positioning of bearings or their slide plates, NF EN 199115 recommends that a supplement be added to this temperature variation range. This supplement is ± 20 °C, or ± 10 °C if the installation temperature is specified. The
13
At the time of writing, the National Appendix is being updated in view of future publication.
PO================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
interpretation that we give to this recommendation is that if the bearing is loaded at a temperature close to + 10°C (equilibrium temperature), the supplement will be ± 10°C. The coefficients of expansion provided for in the Eurocode are 1 x 105/°C for concrete decks and 1.2 x 105/°C for steel bridges (NF EN 199115 – Appendix C). For decks of composite structures, NF EN 19942 specifies in paragraph 5.4.2.5 (3) that this coefficient must be taken as equal to 1.2 x 105/°C for the calculation of expansion, and 1 x 105/°C for the calculation of thermal gradients. We should also specify, even though the Eurocodes do not indicate it explicitly, that the calculation of forces distribution in the various bearings, and therefore the forces in the piers, should be carried out using the instantaneous modulus of concrete.
4.2  Dimensioning 4.2.1  Introduction The best way to understand the procedure for calculating the dimensions of bearings is to use an example (which is not a real case and is only used to illustrate the procedure). We shall consider the dimensioning of laminated elastomeric bearings of a structure made of prestressed concrete castinplace (PSIDP). The structure in question has 3 spans and an overall length of 62 m. The width of the slab is 12.30 m for a thickness of 0.90 m.
Figure 4.1: lengthwise section of the structure Each bearing line has two bearings. The forces and deformations imposed are summarized in table 4.3 (forces for a single bearing to basic ULS for the abutment C0. These forces are the result of a general dimensioning calculation of the structure (a computer calculation completed by manual notes that supposes a uniform distribution of forces on each bearing in a same line).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
PP
V (MN)
α (10 rad) 3
Vx* (m)
Hx (MN)
Comb N°
Maxi
4.50
5.7
0.070

2
Mini
0.71
3.3
0.068

2 bis
Maxi
3.75
4.9
0.061
0.055
4
Mini
0.79
1.8
0.059
0.055
4 bis
Maxi
3.82
6.7
0.080

8
Mini
0.75
3.3
0.078

8 bis
1.35 Gsup + Gmin + S + C + 1.35 LMcara + 1.5 (0.6T)
1.35 Gsup + Gmin + S + C + 1.35 gr2 + 1.5 (0.0T)
1.35 Gsup + Gmin + S + C + 1.5 T + 1.35 LMfreq
Gmin (at service start date of the bearings)
N.B:
0.89
S refers to shrinkage, C to creep, P to prestressing. breaking force (Hx).
9
Vx* refers to displacement without the effect of
Table 4.3: calculated force and deformations The following calculations correspond to the recommended procedure for dimensioning a bearing.
4.2.2 – The area of the bearing Except in the case of particular recommendations (for example, provisional bearings of a launched bridge) and subject to added justifications, the average compressive stress must be between 20 and 25 Mpa on the surface A' following the dimension of the bearing. In our example, we are taking a value from the upper end of the range: 25 MPa. For the maximum vertical reaction (combination n° 2 of table 4.3), we therefore obtain: A' >
4,50 25
= 0.1800 m2, that is, 1800 cm2
4.2.3 – The net height of the elastomer The generally predominant condition is that of εq linked to maximum horizontal displacement. This is essentially due to the displacement imposed by the uniform temperature on the structure, as well as, in some cases, displacement due to the breaking force. We therefore have combinations n° 4 and 8 of table 3 to check: εq = •
vx
≤ 1
with
Tq
vx = v1 + v2
Combination n° 4 of table 4.3:
v1 = maximum horizontal displacement due to temperature and shrinkage. v2 = maximum horizontal displacement due to breaking. vx = v 1 + v2 = v + 1
H x x Tq 2G a b
= 0,061 +
0,055× Tq 2 x 0,9× 0,1800
from which Tq ≥ 0.073 m
PQ================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
= 0.061 + 0.170 Tq
•
Combination n° 8 of table 4.3:
v1 = maximum horizontal displacement due to temperature and shrinkage. v2 = 0 vx = v1 = 0.080 m from which Tq ≥ 0.080 m For information, combination n° 2 of table 4.3 gives us:
Tq ≥ 0.070 m
We can choose 6 intermediate laminations of 12mm and 2 coatings of 6 mm, i.e. Te = 84 mm.
4.2.4 – Plan dimensions We can thus chose a bearing from the product range available, following the minimum surface given in 4.2.2, but preserving a minimum average pressure of 3 MPa under minimum permanent load (combination n° 9 of table 3). We thus determine a maximum surface: The dimensions are therefore: 350 x 400 400 x 500 400 x 600 450 x 600 500 x 600
A' A' A' A' A'
= = = = =
A' ≤
0,89 3
m2 m2 m² m² m²
0.1326 0.1911 0.2301 0.2596 0.2891
= 0.2967 m2 , that is 2967 cm2
(not chosen because insufficient: A' < 0.18) (not chosen for this example) chosen
N.B: the surface A' is calculated taking into account a total coating of 2 x 5 = 10 mm. A bearing is generally chosen that is rectangular in shape, and with the smallest side a, parallel to the longitudinal axis of the structure, so as to allow maximum rotation (a < b). These leads to the choice of a bearing of 400 x 600. That is, with values a' = 390 mm
b' = 590 mm
and
A’= 2301 cm².
The new total displacement calculation for combination n° 4 (with actual A’) is: v1 = 0,061 m
v2 =
0,055× 0,084 2 x 0,9× 0,2301
= 0,011 m
vx = v1 + v2 = 0.061 + 0.011 = 0.072 m We therefore choose vx = max(0.070; 0.072; 0.080) = 0.080 m (combination n° 8) Ar =
0, 080 ⎞ 2 2 ( 0, 2301) ⎛⎜ 1 − ⎟ = 0.1829 m > 0.1800 m ⎝ 0, 39 ⎠
The bearing is suitable. For information, combinations n° 2, 4 and 8 of table 4.3 give us: Ar (comb 2) = 0.1888 m² Ar (comb 4) = 0.1875 m² Ar (comb 8) = 0.1829 m2 (see the example above)
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
PR
4.2.5 – Buckling stability Once the plan dimensions and the height of the elastomer have been determined, it is important to check the stability of the bearing as regards buckling. The form coefficient, for the thickest lamination, is: S1 = S =
0,39 x 0,59 a' b' = = 9.783 2 t (a' + b' ) 2 x 0,012 ( 0,39 + 0,59 )
The value of the vertical force is: Vmax = 4.50 MN corresponding to combination n° 2 of table 4.3. (N.B: the combination of the maximum vertical load is not always preponderant). Average pressure of σm =
Vmax
=
4, 50
Ar
= 23.835 MPa
with Ar = 0.1888 m²
Ar
The total thickness of the elastomer is Te = 7 x 0.012 = 0.084 m (Te was given in chapter 3). limit pressure σlim = from which
2 x 0,39 x 0,9 x 9,783 2 a' G S1 = = 27.253 MPa 3 Te 3 x 0,084
σlim = 27.253 MPa > σm = 23.835 MPa
condition checked
If this condition has not been checked, in particular due to the significant height of the elastomer needed to take the longitudinal displacement, sliding bearings or larger surface bearings should be used. For information, combinations n° 4 and 8 of table 4.3 give us respectively: Ar = 0.1875 m² σm = 19.997 MPa Ar = 0.1829 m² σm = 20.886 MPa
σlim = 27.253 MPa σlim = 27.253 MPa
The preceding condition has been checked for these two combinations.
4.2.6 – Respecting the deformation limit We then need to check the total elastomer deformation limit for the various load cases: Case n° 1
Maximum vertical force with displacement due to thermal effects (combination n° 2 of table 4.3). εcd + εqd + εαd < 7
εcd =
1, 5 × 4, 50 1,5 Fz = = 4.061 G Ar S 0, 9 × 0,1888 × 9, 783
With S = S1 as the verification is made on the thickest internal lamination. 0, 070
εqd =
vx = 0.070
0, 084
= 0.833
2
εαd
=
0,39 x 0,0087 x 0,012
(
3
2 x 6 x 0,012 + 2 x 0,006
3
)
= 0.735 (α = 0.0087 = 0.0057 + 0.0030 installation defect)
from which εcd + εqd + εαd = 4.061 + 0.833 + 0.735 = 5.629 < 7
Case n° 2
condition checked
Vertical force with displacement due to thermal effects and breaking (combination n° 4 of table 4.3).
PS================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
1, 5 Fz
εcd =
1, 5 × 3, 75
=
= 3.407
0, 9 × 0,1875 × 9, 783
G Ar S
0, 072
εqd =
vx = 0.072
= 0.857
0, 084
0, 39 × 0, 0079 × 0, 012 2
εαd =
(
2 × 6 × 0, 012 + 2 × 0, 006 3
= 0.668 (α = 0.0079 = 0.0049 + 0.0030 installation defect)
)
εcd + εqd + εαd = 3.407 + 0.857 + 0.668 = 4.932 < 7
from which Case n° 3
3
condition checked
Vertical force with max. rotation (combination n° 8 of table 4.3).
εcd =
1, 5 Fz
1, 5 × 3, 82
=
= 3.558
0, 9 × 0,1829 × 9, 783
G Ar S
0, 080
εqd =
vx = 0.080
0, 084
0, 39 × 0, 0097 × 0, 012
= 0.952
2
εαd =
(
2 × 6 × 0, 012 + 2 × 0, 006 3
3
)
= 0.820 (α = 0.0097 = 0.0067 + 0.0030 installation defect)
εcd + εqd + εαd = 3.558 + 0.952 + 0.820 = 5.330 < 7 condition checked
from which
4.2.7 – Rotation stability We then ensure that the rotation stability is checked on the bearing. The determining load assumption is generally that which gives the maximum rotation. In our case this is combination n° 8 of table 4.3. αmax = 6.7 x 103 that is, with the initial rotation defect of 3 x 103, a value of αa = 9.7 x 103 for Vmax = 3.82 MN, we calculate the settlement of 7 laminations of 12 mm. Theoretical settlement: (with the form coefficient for a 12 mm lamination, S1 = 9.783) vz =
∑
1 1 ⎞ Fz ti ⎛⎜ 1 1 ⎞⎟ 3,82 x 7 x 0,012 ⎛ + = + ⎜ ⎟ = 0.00393 m, that is, 3.93 mm 2 ⎜ ⎟ A' ⎝ 5GS1 Eb ⎠ 0,2301 ⎝ 5 x 0,9 x 9,783 2000 ⎠ 2
Rotation stability value: a 'αa + b 'αb
=
0,390 x 0,0097 + 0,590 x 0,0 3
Kr vc =
∑
Fz t i A'
⎛ 1 ⎜ 5G S ⎝
2 1
+
1
Eb
⎞ ⎟ ⎠
≥
= 0.00126 m, that is, 1.26 mm
a 'αa + b 'αb
condition checked
Kr
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
PT
For information, combinations n° 2 and 4 of table 4.3 give us respectively: a 'αa + b 'αb
Vz = 4.63 mm
= 1.13 mm
Kr a 'αa + b 'αb
Vz = 3.86 mm
= 1.03 mm
Kr
The preceding condition has been checked.
4.2.8  Verifying the nonslip condition We also need to check the nonslip condition, which, generally speaking, presents no difficulties. It is therefore the braking load assumption, combined with the uniform temperature that is in principle determinant under Vmin. In our case it is combination n° 4 bis of table 4.3. 0,059 ⎞ ⎛ Ar = (0,2301) ⎜⎜1 − ⎟ = 0.19529 m2 ⎟ 0,39 ⎠ ⎝
NB: the value 0.07 is obtained by adding V1 (0.059 of table 4.3) and V2 (0.011) calculated for combination 4 of § 4.2.4. Vmin Ar
σmin =
μe = 0.1 +
Fx = (
=
0,79 = 4.187 MPa 0,1887
1, 5 K f
= 0.1 +
σm
0, 059 0, 084
1,5 × 0,6 = 0.315 4,187
(Kf = 0.6 for concrete)
x 0.9 x 0.39 x 0.59) + 0.055 = 0.200 <
μe Fd = 0.315 x 0.79 = 0.249 MN
Condition checked For information, combinations n° 2 bis and 8 bis of table 4.3 give us respectively: Ar = 0.1900 m²
σmin = 3.737 Mpa
μe = 0.341
Fx = 0.168 MN μe Fd = 0.242 MN
Ar = 0.1841 m²
σmin = 4.074 Mpa
μe = 0.321
Fx = 0.192 MN μe Fd = 0.241 MN
The preceding condition has been checked.
4.2.9 – Plate dimensioning The condition to be checked for the plates is ts ≥
2, 6 Fz t i
where 2.6 ti = Kp (t1+t2) (Cf. NF EN 13373 for S235 steel
Ar f y
plates, with an yield strength of fy = 235 MPa). We then arrive at the value of minimum thickness, generally speaking, under maximum vertical force: ts =
2, 6 × 4, 50 × 0, 012 0,1888 × 235
= 0.00316 m
For a bearing of 400 x 600, we will choose 4 mm thick plates.
PU================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
4.2.10 – Determining pressure on supports Important: in order to highlight the various pressures, the rotation has been artificially increased.
4.2.10.1 – A fully compressed bearing Verification of an elastomer block: 400 x 600; 6 (12 + 4); 2 x 6 Combination to be checked: Fz = 4.500 MN vx = 0.070 m
⇒ S = 9.783
αa = 0 .015 rad
vy = 0
αb = 0
2
Results of bearing verifications:
Ar = 0.1888 m σm = 23.84 MPa
Distorsions:
εc = 4.061 εq = 0.833 < 1 εα = 1.268 εt = 6.162 < 7
Plating
Hxy = 0
⇒ A’= 0.2301 m2
ts
= 3.16 < 4 mm
Rotation stability
vz = 4.64 > 1.95 mm
Buckling stability
σm = 23.84 < 27.25 MPa
⇒ Ka max = 2.47
α = αa – 0.003 as the faces are presumed to be combined n' = n + 2 (6/2)3 = 6 + 0.25 = 6.25 Mt = 2.47 [0.9 × (0.015 – 0.003) x 3905 x 590)] / (6.25 × 123 × 75.3) = 174.6 MN.mm excmax = Mt / Fz = 174.6 / 4.500 = 38.8 mm
⇒ ⇒
6 excmax = 232.8 < a’ = 390 mm OK. No risk of heaving
The uniform pressure surface is a rectangle:
a’’ = 390 – ( 38.8 × 2) – 70 = 242 mm b’ = 590 mm, d’où Aunif = 143013 mm2
The intensity of the pressure σunif is 4500000/143013 = 31.47 Mpa The new average pressure is distributed according to a triangular diagram on a width a’’: a’’ = 242 x 1.5 = 363 mm, that is, a surface of 363 x 590 and an average pressure of 4500000/363 x 590 = 20.98 MPa < 27.253 MPa (nonbuckling condition).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
PV
4.2.10.2 – The case of a partial unsticking Taking the same assumptions, but with a rotation αa = 0 .024 rad (that is, α = 0.021): Results of bearing verifications:
Distorsions
Plating
Ar = 188800 mm2 σm = 23.84 MPa
εc = 4.061 εq = 0.833 < 1 εα = 2.028 ⇒ εα = 1.775 for α = 0.021 εt = 6.922 < 7 ts = 3.16 < 4 mm
Rotation stability
vz = 4.64 > 3.12 mm
Buckling stability
σm = 23.84 < 27.253 MPa
⇒ Ka max = 2.47
Mt = 2.47 [0.9 × (0.024 – 0.003) × 3905 × 590] / (6.25 × 123 × 75.3) = 305.6 MN.mm excmax = Mt / Fz = 305.6 / 4.500 = 67.9 mm Krs = ( εc / Ka max:
εα )1/3 =
⇒
6 excmax = 407.4 < a’ = 390 mm NO
( 4.0601 / 2.47: 1.775)1/3 = 0.975
(A heaving risk on around 2.5 % of the surface, without taking into account the horizontal displacement) The uniform pressure surface is a rectangle:
a’’ = 2/3 × Krs ( a’  vx ) = 2/3 × 0.975 (390 –70) = 208 mm b’ = 590 mm, d’où Aunif = 122705 mm2
The intensity of the pressure σunif is 4500000/122705 = 36.67 MPa The new average pressure is distributed according to a triangular diagram on a width a’: a’’ = 208 × 1.5 = 312 mm, that is, a surface of 312 × 590 and a pressure of 4500000/312 x 590 = 24.45 MPa < 27.25 MPa The buckling stability is thus verified for the most critical face of the bearing. If this was not the case, we would need to recheck this condition, making the average of the average stresses on the 2 interfaces. One of the interfaces is not subjected to any decompression, the other can be subject to heaving on the width a’, de (390 – 312) = 78 mm, that is 23.6 % of the interface surface. By adding a lamination, there remains only a loss of contact that is mainly due to horizontal movements as shown by the study of the previous case. If 2 laminations are added, the buckling stability is not respected. A bearing 450 × 600; 5 (16 + 4); 2 × 8 meets the requirements of loads in this case without any risk of heaving and with the least pressure on the interfaces.
QM================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Table 4.4: the breakdown of pressure diagrams according to the type of load
42 ===============Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
4.3 – Calculating horizontal force on support heads on a structure with typical bearings 4.3.1 – General points As was mentioned above, the horizontal force exerted on the deck (such as breaking and wind) depends on the characteristics of the supports themselves. In particular, if there is dissymmetry, this force is not distributed identically, which can be a reason for dimensioning different bearings. The same applies to force developed by the deck in accordance with the displacement imposed by deformations of the structure (such as shrinkage, creep and temperature). The forces are distributed according to the rigidity of each support. The rigidity R of a support is, by definition: 1 R = , Δ being the displacement of the support head under the effect of a horizontal force unit. Δ This displacement Δ = Δ1 + Δ2 + Δ3 comes from the distortion of the bearing, the deformation of the body of the support and, finally, from the deformation of the foundation (figure 4.2). It should be noted that the stiffnesses R1 and R2 of a bearing are to be calculated for both cases indicated above: slow deformations and dynamic force. The Eurocode recommends using the instantaneous modulus of the concrete for the pier. However, as regards elastomer, its instantaneous modulus is to be used for dynamic force (cf. § 3.3.2.2, Gdyn = 2 x 0.9 = 1.8 MPa) and its reference modulus (0.9 MPa) for slow deformations (such as shrinkage, creep and temperature).
4.3.2 – Determining force on support heads We shall consider that it is a rectilinear, and not a skew, bridge.
4.3.2.1  Deformation The data represent variations of lengths Δl i of each span of a continuous deck. We thus know the relative displacement of bearing "i" in relation to bearing "1" situated on the far left: Δi  Δ1 =
i −1
∑ Δ li
= di
1
Figure 4.2: deformation of the bearings n
From the relations H1,i = k1,i Δi and
n
∑ H1,i
∑R
1,i
= 0 we can deduce
Δ1 = −
1
di
1
n
∑R
1,i
1
Knowing Δ1 , we can determine Δi = Δ1 + di and Hi = R1,i (Δ1 + di)
43 ================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
4.3.2.2 Breaking force (dynamic) When a force H2 is applied to the deck, the displacements Δi of the support heads are the same and we can deduce that with: H2,i = Δi R2,i and
∑H
2, i
= Δi
∑R
2, i
= H2
H2,i = H2
R2, i
∑R
2, i
Note that these formulas also apply to centrifugal force.
4.3.2.3 – Digital application 4.3 .2.3.1 – D ig ita l da ta We presume that the structure has been built symmetrically. The abutments are identical and are fitted with two bearings of: 350 x 450; 3 (12 + 3); 2 x 6 The piers have different mechanical characteristics and are fitted with two bearings of: 600 x 600; 2 (16 + 4); 2 x 8 The calculations have given the following shortenings per span: End spans (1) and (3) mm
Central span (2) mm
Shrinkage/creep
7.6
10.6
Uniform temperature
7.6
10.6
Total
15.2
21.2
Figure 4.3: elevation of the structure used as an example The support head displacement is as follows: Abutments: the abutments are presumed to be infinitely rigid, only the bearings distort. Taking into account two bearings per line, we therefore have:  under static force  under dynamic force:
:
Δu1 =
1
Te
2 Gab
=
1 2
x
0,048 0,9 x 0,35 x 0,45
= 0.1693 m/MN
Δu2 = 0.0847 m/MN
We presume that the abutments lie on very highquality soil and that the foundation deformation is therefore negligible. Piers: all displacement caused by rotations and displacement of the foundation is shown in the table below. The displacement caused by the bearings is calculated as for that of the abutments. 4Q================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Abutment (1) and (4)
Pier (2)
Pier (3)
Δstat
Δdyn
Δstat
Δdyn
Δstat
Δdyn
Bearing
0.1693
0.0847
0.0741
0.0370
0.0741
0.0370
Foundation + shaft


0.0091
0.003
0.0431
0.0143
Total
0.1693
0.0847
0.0832
0.040
0.1172
0.0513
Ri = 1
5.91
11.81
12.02
25.0
8.53
19.48
Δi
N.B: for illustration purposes, we have taken highly dissymmetrical values for the flexibility of the supports. It must be remembered that the flexibility of the piers must be taken in consideration of the instantaneous modulus of the concrete for dynamic loads and daily effects of temperature. The attention of the project designer is drawn to the fact that the bearing calculation must take into account the maximum instantaneous stiffness of the soil, whilst it is the minimum time dependent stiffness that is taken for the calculation of the foundations. 4.3 .2.3.2 – Ho r izo n ta l fo rc e d ue to linea r var ia tion s of the d eck The relative displacements di of the supports in relation to the lefthand support are: Displacement support 2 =  0.0152 =  0.015 m Displacement support 3 =  0.0152  0.0212 =  0.036 m Displacement support 4 =  0.0364  0.0152 =  0.052 m n
∑R
1, i
di =  (0.015 x 12.02 + 0.036 x 8.53 + 0.052 x 5.91) =  0.798
1
n
∑R
1, i
= 5.91 x 2 + 12.02 + 8.53
= 32.37
1
n
∑R
1, i
and so Δi= 
di
1
n
∑R
0,798 = 0.0247 m 32,37
=
1, i
1
Δ2 =  0.015 + 0.0247 = 0.0065 m Δ3 =  0.036 + 0.0247 =  0.0117 m Δ4 =  0.052 + 0.0247 =  0.0269 m 4.3 .2.3.3 – Ca lc ula ting the d istributio n of a break ing force The preponderant case is that of breaking force. The force is 0.60 MN14. The forces on the support heads will thus be: 11,81 = 0.60 x = 0.104 MN for the abutments H2,1 = H2,4 68,10 H2,2
= 0.60 x
25,0 = 0.220 MN for pier 2 68,10
H2,3
= 0.60 x
19,48 = 0.172 MN for pier 3 68,10
We can check that: 2 x 0.104 + 0.220 + 0.172 = 0.60 MN
14
Readers are reminded that the value suggested by the national annex to NF EN 19912 is 0.5 MN (cf. § 4.1).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
45
4.3 .2.3.4  Summa ry The following table represents the deformations and forces calculated for a single bearing. It can be noted that differences in displacement are quite low, but the same does not apply to breaking force. These values are summarized in the table below (forces for one bearing). c In this column, the calculation presumes a fixed point in the middle of the structure and uniform distribution of breaking on the 4 bearings. d With the flexibility of the supports and the chosen bearings: Abutment 1
Pier 2
c
d
c
d
Δ1 deformation (m)
0.026
0.027
0.011
0.012
breaking (MN)
0.045
0.031
0.045
0.066
In this case, to simplify, as this is a common engineering structure, we will put the initialsize bearings on the abutments and piers. When all the calculations are completes, force on the abutments is slightly reduced in the event of breaking, but in an insufficient proportion to modify the bearings. Consequently, it is often of little use, in common cases, to make complex calculations taking into account this flexibility. Instead, more care should be taken over the initial dimensioning, not forgetting a combination load that may affect the size. These thus remain 350 x 450; 3 (12 + 3); 2 x 6 on abutments.
4.4  Calculating horizontal force on a structure with sliding bearings 4.4.1 – General points As mentioned above, in cases where there is significant horizontal displacement, in particular on the abutments, the number of laminations required for these deformations risks being incompatible with the buckling stability of the bearing. In this case, sliding bearings may be required instead of ordinary bearings. Combining these two types of bearings is quite complex to design, as the flexibility needs to be taken into account of the supports themselves, as well as of the ordinary bearings and the friction coefficient of the slide bearings. However, the presence of a certain number of ordinary elastomeric bearings gives flexibility to the whole structure. This is a highly positive point, especially if seismic calculations need to be carried out for the structure. A slide bearing can function in various ways: • For a flexible support, under the effect of a variation in length, the horizontal force is gradually mobilized up to the slippage threshold. Once this value H is reached, slippage occurs. A new state of balance is established, bringing the horizontal force back to a value lower than H. • For a very stiff support, such as an abutment, displacement of the deck instantaneously mobilizes the horizontal force at its threshold value H. • Finally, in the case of a very flexible support, the slippage threshold may not be reached and the bearing functions the same as an ordinary bearing.
4S================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
For the verification of an isolated bearing, the relation between the mobilizable force H and the concomitant vertical force is expressed: H = (μ + PP + PL) × V in which – μ is the friction coefficient of the bearing for the vertical load V. – PP is the installation precision of the bearing, corresponding to any defect in horizontality (PP is positive in the formula above). – PL is any gradient voluntarily given to the sliding plane. PP and PL are positive in the preceding formula. In the calculation of the distribution of horizontal force, the installation precision PP is ignored, as it has already been accounted for by the weighting of the friction coefficient (μa and μr) from which H = (μ + PL) V. It should be noted that any force due to breaking on the deck must be wholly assumed by the nonslide bearings. (cf. § 4.4.1.4).
4.4.1.1 – Numerical design values The values of the friction coefficient μ are given in chapter 3: μd =
1,2 ⋅ k with k = 1 for stainless steel and σp contact 10 + σ p
pressure on the PTFE, that we will take equal to Fz/A for type D bearings. We will take into account the actual surface of PTFE for E type bearings. Furthermore, pressure must be limited to 30 MPa.
4.4.1.2 – Operating loads to be applied for the calculation of horizontal force As with sliding pot bearings, we will consider a simplified calculation in which the extreme horizontal force (at ULS) will be determined from extreme vertical loads of corresponding combinations. This has a positive impact on safety without significantly increasing the actions. Readers are invited to consult the document on pot bearings15 for more detailed explanations regarding this simplification.
4.4.1.3  Friction coefficient for sliding bearings We refer here to NF EN 13371 "General design rules" for bearings. In our case, the friction coefficients that apply to sliding bearings are the following: μa = 0.5 μmax (1 + α) μr = 0.5 μmax (1  α) μmax the maximum friction coefficient for a sliding bearing taken individually. μa the friction coefficient to be applied if the friction is unfavourable in relation to the effect studied. μr the friction coefficient to be applied if the friction is favourable in relation to the effect studied. α the degression coefficient depending on "n", the number of sliding bearings intervening in the balance of the structure. n α ≤4
1
4 < n < 10
(16n)/12
≥ 10
0.5
E.g. a 4span structure with two ordinary bearings on central piers and two sliding bearings on each of the abutments: n= 4 from which α = 1 μa = 0.5 μmax (1 + 1) = μmax = 5.3 % (taking into account the pressure σp = 12.65 MPa) μr = 0.5 μmax (1  1) = 0
15
cf. Bibliography
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
4T
4.4.1.4  Horizontal force due to breaking According to paragraph 6.7 of NF EN 13372, sliding bearings should not play a part in assuming horizontal breaking force. In theory, these forces are therefore assumed entirely by the nonsliding bearings. This hypothesis is pessimistic as sliding bears do actually play a part in assuming these forces, but in a nonquantifiable proportion.
4.4.2 – Example of a calculation 4.4.2.1 – Characteristics of the structure. This is a fourspan prestressed structure, built as balanced cantilever method, with the main dimensions as shown on figure 4.4.
Figure 4.4: the main dimensions of the studied structure The load paths are summarized in the following table: For a pier (2 bearings) Permanent loads
Traffic loads
C0 and C4
P1 and P3
P2
V max (MN)
2.98
17.88
18.34
V min (MN)
2.87
17.76
18.32
max rot (103 rad)
1.1
0.5
0.2
min rot
0.8
0.8
0.2
V max (MN)
1.57
3.74
3.78
0.56
0.66
0.54
rad)
2.0
0.5
0
rad)
1.3
0.2
0
0.29
0.40
0.22
0.6
0.3
0
V min (MN) concom rot Vmax concom rot Vmin Thermal gradient
(103
(103
V (MN) Rot
(103
rad)
We show here the linear compressions taken into account for each span, as with the preceding case: End spans (1) and (4)
Central spans (2 and 3)
Shrinkage/creep
10.4 mm
15.6 mm
Uniform temperature
20.8 mm
31.2 mm
Total
31.2 mm
46.8 mm
The displacements are calculated as in paragraph 4.3. If there are sliding bearings, the difficulty lies in the fact that these bearings work up to a certain threshold. Below the sliding force, their flexibility is the same as if they were not sliding. Above, their flexibility is "infinite". An initial calculation thus needs to be made, taking them as nonsliding bearings and then, if the force corresponding to the displacement goes beyond the threshold, their flexibility needs to be replaced by a corresponding limit force and the balance of horizontal force needs to be recalculated.
4U================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
4.4.2.2 – Predimensioning bearings To do this, an initial dimensioning of the bearing needs to be carried out, mainly from vertical force and rotations (that are not dependent on horizontal force). The following force is obtained for a bearing: C0 and C4
P1 and P3
P2
V max (MN)
2.35
10.71
11.12
V min (MN)
1.16
8.39
8.87
 max rot  (103 rd)
2.4
1.2
2.1
1.0
0.6
1.5
 min rot 
(103
rd)
We choose (thereby verifying the maximum stress of 30 MPa on the concrete): C0 and C4
P1  P2  P3
1 bearing of 400 x 500
2 bearings of 700 x 600*
* the values calculated for maximum and minimum reactions on piers takes into account a difference in stiffness of ± 15 % for each twinned bearing (cf. note of § 5.3.3.7 of NF EN 13373).
Figure 4.5: the layout of pier bearings. For horizontal displacements, calculations are greatly simplified if we consider a point 0 in the geometric centre of the structure. In this case, the maximum displacements to take into account will be: C0 and C4 P1 and P3 P2 unit vi max
78
47
0
mm
This calculation immediately shows that abutment bearings –of small size – must be sliding as it would be impossible to stack enough layers of elastomer to absorb the displacement. With the principles of paragraph 4.2, we arrive at: C0 and C4
P1  P2 P3
1 bearing of 400 x 500; 3 (12 + 3); 2 x 6
2 bearings of 700 x 600; 6 (16 + 4); 2 x 8
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
4V
4.4.2.3 – Horizontal force for sliding bearings We calculate the flexibility of these bearings, all considered as nonsliding. • Static On an abutment: a line of 2 bearings of 400 x 500; 3 (12 + 3); 2 x 6 1 0,048 flexibility = = 0.1333 m/MN 2 0,9 x 0,4 x 0,5 On a pier: a line of two times 2 bearings of 700 x 600; 6 (16 + 4); 2 x 8 1 0,112 = 0.0741 m/MN flexibility = 4 0,9 x 0,6 x 0,7 •
(static)
(static)
For dynamic (breaking), flexibility is divided by 2.
Sliding bearings on abutments have a friction coefficient of around 5.3 % on maximum load. Taking into account a maximum vertical force of 2.33 MN (for one bearing), the maximum limit sliding force – per abutment – is: Hlim = 0.053 x 2 x 2.33 = 0.25 MN
4.4.2.4  Horizontal force for nonsliding bearings 4.4 .2.4.1 – Force due to linea r varia tions of th e d e ck 1 s t itera tio n An initial calculation is carried out in a similar way to that of paragraph 4.3. Abutments 0 and 4
Pier 1
Piers 2 and 3
Δstat
Δstat
Δstat
Bearing
0.1333
0.0741
0.0741
Foundation + shaft

0.0091
0.0431
Total
0.1333
0.0832
0.1172
Ri = 1/Δ
7.502
12.019
8.532
For maximum deformation, taken as equal to 6 x 104 (CP and uniform temperature), the relative displacements di of the bearings in relation to the lefthand support are: Displacement of support 1 =  0.031
=  0.031 m
Displacement of support 2 =  0.031  0.047 =  0.078 m Displacement of support 3 =  0.078  0.047 =  0.125 m Displacement of support 4 =  0.125  0.031 =  0.156 m n
∑
n
R1,i di = 3.276
1
∑R
1, i
= 44.09
1
n
∑R
1, i
and therefore
Δ0 = 
di
1
n
∑R
=
3,276 = 0.074 m 44,09
1, i
1
Δ1 =  0.031 + 0.074 = 0.043 m Δ2 =  0.078 + 0.074 =  0.004 m Δ3 =  0.125 + 0.074 =  0.051 m Δ4 =  0.156 + 0.074 =  0.082 m
5M================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Point 0 is therefore located at the distance x0 =
0,074 × 260,00 = 123.83 m 0,156
The corresponding horizontal force can be deduced: C0
P1
P2
P3
C4
displacement
M
0.074
0.043
0.004
0.051
0.082
H
MN
0.56
0.52
0.03
0.43
0.61
0.25



0.25
Hlim
We can confirm that the bearings C0 and C4 slide. 2 n d itera tion Sliding bearings have zero stiffness. We replace the values of Ri for C0 and C4 by 0. The calculations gets more complicated, however, as we have to successively study three case scenarios, namely: • The sliding bearings all have the same friction. • Those of the supports situated on the left of the point 0 have a value equal to the minimum value (§ 4.4.1.3), and maximum for thus situated on the right. • And the opposite, namely the maximum values for the supports on the left and the minimum for those on the right. There are 4 sliding bearings on the full number of bearings. The friction coefficients are therefore (§ 4.4.1.3): • minimum μa = μmax = 5.3 % • maximum μr =0
Case 1 – the same friction coefficient value on the left and the right In this case, we replace the value of the product Ri x di by the limit value of H for the supports C0 and C4. The calculation becomes: C0
P1
P2
P3
C4
0
12.019
8.532
8.532
0
0.235
0.375
0.666
1.065
0.235
displacement
0.072
0.041
0.006
0.052
0.084
H
0.25
0.50
0.05
0.45
0.25
Hlim
0.25



0.25
Ri Sum Ri
29.084
Ri x di or Hlim Sum Hi
2.105
point 0
120.65
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
5N
Case 2  friction coefficient on the left 0 % and on the right 5.3 % We obtain the following table:
Ri Sum Ri
C0
P1
P2
P3
C4
0
12.019
8.532
8.532
0
0
0.375
0.666
1.065
0.235
0.064
0.033
0.014
0.060
0.092
0
0.40
0.12
0.52
0.25
0.25



0.25
29.084
Ri x di or Hlim Sum Hi
1.870
point 0
107.18
displacement H Hlim
Case 3  friction coefficient on the left 5.3 % and on the right 0 % We obtain the following table: C0
P1
P2
P3
C4
0
12.019
8.532
8.532
0
0.235
0.375
0.666
1.065
0
displacement
0.080
0.049
0.002
0.044
0.076
H
0.24
0.59
0.02
0.38
0
Hlim
0.24



0.24
Ri Sum Ri
29.084
Ri x di or Hlim Sum Hi
2.340
point 0
134.11
We conclude that the maximum displacement in P 1 can be in P 2 in P 3 Under only permanent loads, the displacements are:
0.049 m 0.014 m 0.060 m in P 1 in P 2 in P 3
0.014 m 0.001 m 0.017 m
N.B: it must be understood that the presence of sliding bearings transforms the structure into a nonlinear system. Strictly speaking, it is not therefore possible to superimpose the forces and displacements of each of these actions to combine them. However, that would lead to complicated calculations that are quite useless in relation to the differences in the values to be calculated. We could therefore simply consider that the displacement value due to the uniform temperature is the difference between the calculation with the maximum linear compression (here 6.104) and the linear compression due to permanent loads (2.104).
5O================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
4.4 .2.4.2 – Ca lc ula ting the d istributio n of a braking fo rce As regards breaking, it is presumed to be distributed only on nonsliding bearings. The value of the force assumed by the support is directly proportional to the stiffness of the bearing. We obtain: Pier 1
Piers 2 and 3
v1
v1
Bearing
0.0370
0.0370
Foundation + shaft
0.003
0.0143
Total
0.040
0.0514
24.969
19.474
Ri = 1 v
The sum of the stiffnesses is equal to 63.92. For a breaking force of 0.36 MN, the distribution is thus: 24,97  pier 1 H1 = = 0.391 HT = 0.14 MN 64,92  piers 2 and 3
H2 =
19,47 = 0.305 HT = 0.11 MN 64,92
4.4 .2.4.3 – The in cidence on b earing ca lcula tions When verifying bearings, the preceding calculations give rise to a slight oversizing of bearings on the piers, with those on the abutments having been correctly dimensioned from the start. When all the calculations have been completes, so as to adapt as precisely as possible to the forces and deformations applied to bearings, we could reduce the number of laminations. C0 and C4
P1
1 bearing of 400 x 500 3 x (12 + 3); 2 x 6 (unchanged)
P2
P3
2 bearings of 700 x 600 4 x (16 + 4); 2 x 8
3 x (16 + 4); 2 x 8
6 x (16 + 4); 2 x 8 (unchanged)
As the bearings on the piers have been modified, we need to recalculate the distribution of forces. This calculation proves that the bearings on the piers are suitable.
4.4.3  Conclusion as regards calculations on structures with sliding bearings As with the conclusion of paragraph 4.3.2.3.4, we draw attention to the balance between the calculations and material economies that can be made on bearings. The preceding example was deliberately chosen with a significant difference between the flexibility of the piers, so as to exaggerate the variations that can result from the dimensioning of bearings. Even in this case, it shows a very modest saving on the total volume of these bearings (4 and 5 laminations instead of 7 on predimensioning) – an economy that becomes marginal in relation to the overall cost of the structure. Moreover, the cost of the studies needed to optimize these bearings needs to be taken into account. If we add to that the (not insignificant) risk of an error in installation between very similar bearings (e.g. with 5 laminations instead of 4, etc.) – an error far more harmful for the functioning of the supports than the conceivable savings – we strongly recommend simplicity in the determination of bearings. It is far preferable to pay the utmost attention to the –careful – installation of these bearings, as this is the price to pay for durability.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
5P
`Ü~éíÉê=R=Ó=Controls 5.1 – General principles Bearings are important elements of structures, such as bridges and viaducts, ensuring that they operate correctly. The durability of the structure depends on their quality, as does it remaining in a state of service. We can appreciate the need for quality bearings by the financial consequences of any failure on their part. Indeed, the costs incurred by having to change a failed bearing are out of all proportion in relation to the supply cost. The ratio is around 50 to 1 and is sometimes much higher. The life expectancy of bearings is the result both of their intrinsic qualities and of the care taken over this implementation. Together with the rational choice of the different types of bearings, the quality and the consistency of their manufacture also needs to be assured. The quality of these products depends on expertise in the manufacturing process. Quality Assurance provisions should enable you to: • convey the quality required in terms of manufacturing methods • obtain the quality required • check that it has been reached • justify subsequently that it has been reached and checked. As well as the general quality aspect, laminated elastomeric bearings have certain particularities: • their manufacture and marketing requires equipment and investments that are prerogative of specialized companies • their technology necessitates long and costly analyses and laboratory tests that can only be conducted on each construction site. The full range of these considerations has lead to the implementation of a certification procedure to assess compliance with the essential requirements defined by the Directive on products of construction (known as the DPC of 21/12/88) and which is validated by a level 1 CE marking (there is level 3 CE marking on bearings, which is not used on bridges). This CE marking depends on the standardised part of NF EN 13373.
5.2 – Production controls prior to CE marking 5.2.1 – The content of the CE certification In order to obtain level 1 CE marking, the corresponding task distribution between the manufacturer and the notified body is as follows: a) the manufacturer • must have production control implemented in the factory • must perform supplementary tests on samples taken in the factory in accordance with a prescribed test programme b) the thirdparty organisation (or notified body) • performs the initial standard tests • carries out an initial inspection of the factory and the factory production controls • conducts continuous monitoring, an assessment and acceptation of factory production controls. It should be noted that, contrary to the voluntary NF quality certification label, there are no annual control tests performed by a thirdparty organisation. This constitutes a lowering in the level of quality, particularly when we know the production monitoring defects that these tests bring to light.
5Q================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
This question remains open and negotiations are underway to try to implement a quality label that brings back this aspect of a regular annual control, in addition to the CE marking.
5.2.2 – Test methods These define the methods for measuring the fitness for use of the finished product. They allow the product to be judged according to the following four aspects (§ 5.2.2.1 à 5.2.2.4):
5.2.2.1 – Behaviour to shortterm effects These are the fundamental tests that assess aptitude to fulfil three degrees of freedom: a) Shear behaviour • Determination of the shear modulus G in accordance with appendix F of NF EN 13373 The modulus G is determined using two bearings that are inserted between three plates. The sides of the upper and lower plates are fixed solidly to the press platens, while a horizontal force is applied on the middle plate (figure 5.1). To prevent the bearings from slipping, a constant load is also applied during the test.
Figure 5.1: a distortion test to determine the modulus G and the shear strength. (photo Sétra)
Figure 5.2: an example of a shear modulus determination curve
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
NR
•
Determination of shear bond in accordance with appendix G of NF EN 13373
Following the preceding test, the horizontal force is increased, at the same time as the vertical load is increased until a deformation is obtained corresponding to γ = 2.0. b) Compression behaviour in accordance with appendix H of NF EN 13373 The deformation of a test specimen is continually measured up to a predetermined compressive stress. c) Rotation behaviour under an eccentric load in accordance with appendix J of NF EN 13373 The test consists: • Either of measuring the rotation angle and any contact surface loss of the test specimen under an increasing and eccentric compressive force of a predetermined value • Or of finding the eccentricity limit corresponding to a predetermined contact surface, under a fixed compressive force.
5.2.2.2  Behaviour to longterm effects a) Determination of creep in compression in accordance with standard T 47.806 Under the following conditions: at an ambient temperature – 23°C ± 2°C – during a minimum test period of one month, under a compressive stress of 25 MPa, the following results should be obtained: • The creep index ΔΣ/Σ1 must be lower than 0.2 •
No defects accepted: bond, small cracks, larger cracks, breakdown, breakage, etc.
b) Determination of stress relaxation in shear with standard XP T 47.807 Under the following conditions: at an ambient temperature – 23°C ± 2°C – during a minimum test period of three months, under a compressive stress of 6 MPa and a distortion of tg γ = 0.7, the following results should be obtained: • Rcst ≤ 20 %. DRC à 23 °C, C ≤ 25 % • No defects accepted: bond, small cracks, larger cracks, breakdown, breakage, etc. These evaluations have not been chosen for the assessment for CE marking. However, French standards are maintained and it is possible to perform evaluation tests for specific situations.
5.2.2.3 – Behaviour to environmental influences a) Determination of ozone resistance in accordance with appendix L of NF EN 13373 Cf. § 1.3 on the choice of ozone concentration. b) Accelerated ageing or heat resistance The change in mechanical characteristics after artificial ageing or heat resistance involves the appendixes F, G and H of NF EN 13373. c) Determination of salt fog resistance in accordance with XP T 47.813 d) Determination of the nonslip condition in accordance with XP T 47.811 Under test conditions, at an ambient temperature of 23°C ± 2°C with a modulus G = 0.9 MPa ± 0.1 MPa, the following results should be obtained: Vertical stress, in MPa
5
10
15
Elastomer/concrete
≥ 0.3
≥ 0.25
≥ 0.20
Elastomer/painted steel
≥ 0.12
≥ 0.06
≥ 0.04
NS================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
e) Other standards, applicable to vulcanized elastomer and not to the finished product, enable any physical variations to be assessed and the results to be measured. It is the case, for example, with the standard NF ISO 1817: "determination of the effect of liquids (form oils)".
5.2.2.4 –Behaviour to dynamic effects This involves the behaviour to accidental dynamic effects, such as impacts, cyclonic winds and earthquakes. As regards behaviour to seismic effects, readers may refer to the specific tests defined in the prEN 15129 on antiseismic devices, or, failing that, to appendix K of NF EN 19982 (EC82).
5.2.3 – Compliance to the standard The situation for construction managers is very simple: there must not be any products without CE marking on the market. They must therefore check that the CE marking is clearly visible on the product and that the accompanying documents give all necessary information about this marking and the correct adaptation of the product to the field of use, in particular that the product has a level 1 compliance certificate (there is indeed a level 3 for bearings that only gives a declaration of compliance: cf. le § 5.1 above).
0123CPD0001 10
Company X Ltd
Figure 5.3: example of a CE marking.
There is, however, nothing to stop you checking compliance by the performing of controls on reception. If the CE marking and the specifications of the standard have not been respected, the antifraud service should be informed. However, for a specific application, constructions managers are completely free to define a product that will be specific to the structure and will be manufactured solely for it. In this case, they should ensure, based on the standards NF EN and/or simply on national standard (cf. § 5.2.2.2 and 5.2.2.3 of the test standards not taken up at European level in the EN standard) that the product is marketcompliant. As regards the National Application Document of NF EN 13373, we recommend that construction managers use the examples of Particular Technical Clauses (CCTP) that are to be found in appendix 4.
5.3 – Controls on reception These shall be restricted to the following actions: • verification of the presence of the marking (CE) and the compliance of the accompanying documents • visual verification to ensure there are no defects or damage • control of the compliance of the actual dimensions with the dimensions featuring on the construction plans of the structure • if necessary, the performance of compliance control tests.
5.4 – Controls on installation For details regarding the controls on installation, it is useful to refer to the corresponding sheet in the Memoar guide (see bibliography). The construction manager must ensure the existence of the following documents:
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
5T
5.4.1 – The drafting of prior documents 5.4.1.1 – The existence of specific procedures • • •
the construction method of the bosses the installation of the bearings any rebalancing of deformations by distortion of the bearing, taking into account, in particular, the thermal conditions at the time of year of construction16.
5.4.1.2 – The provisional operating state of bearings A summary of the forces (vertical and horizontal) and provisional deformations (distortion, rotation) for permanent loads, operating loads and thermal effects: • when the bearings are loaded • for the finished structure • after creep and shrinkage deformation.
5.4.2 – Controls during construction Prior to installing the bearings, the construction tolerances of the bosses needs to be controlled (cf. the guide "the environment of laminated rubber bearings", § 1.3.2.3, cf. Bibliography). This control is a HOLD POINT. Once in place, the correct positioning of the bearing will be controlled by checking the compliance of the bearing type in relation to its location provided for on the plans. Check that there are no wedging defects, especially at the level of the higher boss, and that the sliding bearings are perfectly adjusted. These controls are to be performed: • if possible, at the earliest moment after loading • before and after operations to liberate, by jacking, deformation that has occurred during construction • before the structure is put into service (the point 0 defined below) • periodically, according to general or specific instructions. It must be remembered to determine the point 0 of all the bearing on reception of the bridge (distortion, rotation, boss defects, etc.).
5.5 – Controls of behaviour in service This aspect is dealt with in specific section 13 "bearings"17 of the second part of "Instruction Technique sur la Surveillance, l'Entretien et la Réparation des Ouvrages d'Art" (Technical Instructions for the Monitoring, Maintenance and Repair of Engineering Structures), a circular of 19 October 1979, revised on 26.12.95.
16
This operation is performed by jacking and can avoid the use of sliding bearings on the abutments.
17
A Sétra publication  reference F0230 and LCPC FASC13.
5U================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
`Ü~éíÉê=S=Ó=The predimensioning and verification program There is program for predimensioning laminated bearings, called the NEOP program, which is part of the Sétra software catalogue (available on order from the sales office). This program sizes bearings according to the rules defined in NF EN 13373 and in this document. The application enables users to process the complete structure by entering the definitions of the lines of supports and the bearings of each line, together with the definition of the spans. It has several independent modules, depending on if the user is interested in the whole structure or just in a particular bearing. As regards the structure, two tools are available: • The quick predimensioning of the bearings of each line of support, based on the minimum and maximum load paths and the horizontal force and displacement. • The calculation of horizontal force and displacement under the effect of horizontal force applied to the deck (breaking force, for example) or a rapid or slow expansion of the deck. This module requires the value of the overall bearing flexibility and of its foundation in which it automatically integrates the bearing flexibility that has been predimensioned or imposed by the user. The results are then entered into the predimensioning module to refine it. By choosing a specific bearing, the user can: • Choose the geometry in a typical range of rectangular or circular bearings, or else define it manually • Define the various combinations and calculation options • Create a precise predimensioning of the bearing and choose one from the list of propositions made by the application • Perform a complete verification of the bearing as per NF EN 13373 • Modify certain design parameters (installation defects, shear modulus, etc.). In all cases, the results can be printed or integrated into a Word calculation sheet. The NEOP program works on a Pentiumtype PC or the equivalent, using the interface Windows 98, 2000 or XP. It comes in a pack with an installation CD, a protection disc and documentation. The PRD network (regional distribution centres) can provide information regarding the distribution and use of this program. The PRD network has one correspondent per CETE (Technical research centre).
6M================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
^ééÉåÇáñ=N=Ó=Calculations for laminated elastomeric bearings for use in seismic zones
A11 – Regulatory framework In France, it is now obligatory to take seismic risk into account when building a bridge, as defined in the following laws: • Law n°87565 of 22 July 1987 as regards (...) the prevention of major risks • Decree n°91461 of 14 May 1991 as regards the prevention of seismic risk • Decree of 15 September 1995 as regards the classification and regulations of seismicresistant construction applicable to bridges in the category “normal risk”. This last decree specifies that these verifications must be performed in compliance with one of the following documents: • The guide AFPS 92 for the seismicresistant construction of bridges • The National Application document of the ENV, 1998  Part 2: Eurocode 8 – The design and dimensioning of structures for their resistance to seismic activity  Part 2: Bridges. As the NF EN 19982 standard is due for publication soon, this guide refers to it. Each of these documents contains specifications for laminated elastomer bearings. Indeed, the high flexibility of elastomer enables the natural mode periods of the structure to be increased and to thus avoid the most critical frequency bands. For this reason, the use of laminated elastomeric bearings is a simple and effective way of obtaining seismic resistance. Of the two authorized regulations, (AFPS 92 and Eurocode 8), the Eurocode is that which has calculation methods closest to those of NF EN 13373. It is therefore logical that we refer to them here. In order to facilitate the joint application of Eurocode 8 and NF EN 13373, table A.1 specifies the notations of the two documents: Shear modulus under seismic activity Axial stress Vertical force Plate width Plate length Thickness of a current layer: Form coefficient Form coefficient of the thickest layer Reduced area Total elastomer thickness Distortion due to horizontal force Total nominal distortion
Gdyn Rated Gb = 1.1 Gg in l'EC82 § 7.5.2.3.3 (2) σm Fz,d a' b' ti S S1 Ar (at 1° order) Te Rated te in l'EC82 § 7.5.2.3.3 (2) εq,d εt,d
Table A.1: notations of Eurocode 8 and NF EN 13373
6O================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
The EC8 puts elastomeric bearings into two classes: special elastomeric bearings and simple elastomeric bearings. The socalled special elastomeric bearings have to be tested according to a detailed procedure (EC82 appendix K and prEN 15129) that is relatively extensive and is applicable to all seismicresistant insulation devices. Elastomeric bearings that have not undergone these tests on prototypes are called simple. The vast majority of laminated elastomeric bearings used in France today fall into the simple category. For this reason, this appendix deals with simple laminated elastomeric bearings.
A12 – Design combinations and direction accumulation A12.1 – Seismic action The seismic effect on a structure is normally calculated separately according to three directions in space X, Y and Z. For a straight bridge, these directions are the longitudinal, transversal and vertical axis of the deck. This last component of seismic movement has to be taken into account for the verification on the bearings (NF EN 19982, article 4.1.7 (3) P). We thus have three seismic forces acting on the bearing: • Fx: horizontal force that creates longitudinal distortion • Fy: horizontal force that creates transversal distortion • Fz: vertical force that causes the load path to become heavier or lighter The concomitance of these three forces has to be taken into account. Among the two options proposed by NF EN 19982 to combine the effects calculated in each direction, the most practical one to apply to laminated elastomeric bearings consists of three weighted linear combinations, as shown in the diagram of figure A.1 (NF EN 19982, article 4.2.1.4(2)).
Fy
0,3 Fy
0,3 Fy 0,3 Fx
0,3 Fx
Fx
0,3 Fz
0,3 Fz
0 3 Fx Fz
Figure A.1: combinations of seismic directions.
A12.2  Combinations with other load cases Seismic action must be cumulated with (NF EN 19982, articles 6.6.2.3(2) and 7.6.2(2)): • Permanent loads, in characteristic values • The effects of shrinkage and creep for concrete decks • 50 % of displacements due to temperature variations (more specifically, the values to take into account are equal to 50 % of those used for the design of bearings excluding seismic combinations). For urban bridges carrying heavy traffic, i.e. those of class 1 of NF EN 19912, 20 % (30 % for railway bridges) also needs to be added to normal operating loads (to be specified in the Particular Technical Clauses (CCTP) on the basis of the National Annex of NF EN 19982).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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A13  Dynamic calculation model A13.1  Shear modulus G The flexibility of elastomeric bearings is inversely proportional to the shear modulus. This modulus, however, depends on the speed or frequency of the excitation. For example, the effects of breaking are normally calculated with a modulus twice as high as the value corresponding to quasistatic loads (cf. § 3.2.2). Under seismic activity, the Eurocode proposes the use of a shear modulus Gb = 1.1 Gg for common bearings (NF EN 19982, § 7.5.2.3(5)). According to the regulations of the AFPS (French Seismic Engineering Association), the value of G used for seismic calculation should be between 0.8 and 1.2 MPa. This is based on tests carried out during the construction of nuclear power stations in regions subject to seismic risk. In view of incertitude over the estimation of the value of G, particularly in connection with the ageing of elastomer and the ambient temperature, it is not desirable to unrealistically complicate calculation methods. For this reason, we recommend estimating seismic effects with a shear modulus of 1.2 MPa. Moreover, this proposition has been included in the AFPS 92 guide. It is difficult to define a more precise law of behaviour without knowing the formulation of the elastomer that varies depending on the supplier. Obviously, a different value of shear modulus could be adopted if the manufacturer provided the necessary justifications (NF EN 19982, appendix J).
A13.2  Modelling of bearings
Figure A2: mass beam design model When a deck lies on laminated elastomeric bearings, it is the bearings that provide the most flexibility to the structure. It is therefore essential that they are taken into account in the dynamic model that enables the natural periods to be calculated. In theory, the bearing should be modelled by a multidirectional spring that functions both in tractioncompression and rotation, that is, by six stiffnesses (figures A2 and A3).
6Q================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Figure A.3: modelling using springs The stiffnesses should be calculated as shown in table A.2 (NF EN 13373, § 5.3.3.7). In the vast majority of cases, the bearing can be considered as infinitely rigid in a vertical direction and infinitely flexible in rotation, resulting in the simplified formulation of the third column. Stiffness
Complete formulae according to the notations of NF EN 13373
Simplified formulae
Kx and Ky
A.Gb / Te
A.Gb / Te
Kz
Kθ rectangular
Kθ circular
Kθz
⎡ ti ⎛ 1 1 ⎞⎤ ⎟⎥ + ⎢∑ ⋅ ⎜⎜ 2 E b ⎟⎠⎥⎦ ⎢⎣ A′ ⎝ 5 ⋅ G b ⋅ S1
Gb ⋅ Gb ⋅
−1
∞ 0
a ′5 ⋅ b′ 3
n ⋅ ti ⋅ Ks 0
π ⋅ D' 6 512 n ⋅ t i
3

0
Table A.2: calculation of stiffnesses Ks is a tabulated parameter according to the relation b/a (NF EN 13373, article 5.3.3.7, table 4).
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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A14 – Using a behaviour factor A14.1 – The two seismic design methods When the seismic design of a structure is such that the main part of the energy transmitted by the ground to the structure can de dispelled by damage to the piers, it is routine practice to reduce the forces obtained by an elastic calculation. The reduction works by dividing the effects of the action by a behaviour factor that depends on the construction material and the shape of the piers. This is then referred to as a ductile design or the plastic hinge method. On the other hand, choosing ductile seismic behaviour (q > 1.5) leads to significant complexity of design that we are unable to detail here (reinforcement of the plastic hinges confinement, coherence criteria, capacity design, etc.). Interested readers may refer to Seismic design of reinforced concrete and masonry buildings by Paulay and Priestley (Wiley & Sons 1992). The other method consists of designing the structure so that damage is greatly reduced under the seismic calculation, as is generally done under normal loads: the essentially elastic or restricted ductility design. This does not mean that necessary measures should not be taken to ensure a minimum of ductility in the structure. It is, moreover, permissible to take cracking in the supports into account, preferably by an iterative calculation method that ensures coherence between the forces calculated and the inertia used. These two design methods apply whenever elastomeric bearings are used, either on all or part of the supports.
A14.2 – Elastomeric bearings on all the supports Structures with decks that lie solely on laminated elastomeric bearings are flexible and their natural vibration periods are beyond the range that is the most prone to seismic activity. In general, this flexibility is sufficient for the seismic resistance of the structure and consequently a behaviour factor limited to 1.5 may be used (NF EN 19982, article 7.3.2(2)P). This is then an essentially elastic (or restricted ductility) design.
A14.3  Elastomeric bearings on part of the supports For certain structures, it may be beneficial to have elastomeric bearings on just some of the supports. In that case, the overall verification of the bridge can be carries out according to one of the following methods: • By dividing the elastic forces by a behaviour factor appropriate to each pier (cases of irregular bridges, NF EN 19982, article 4.1.8). In this case, laminated elastomeric bearings must be calculated “in capacity”, that is, for the level of force that ensures the formation of the plastic hinges provided for in the fixed piers by the project designer. • Without using a behaviour factor. If there is a risk of load transfers to the elastomeric bearings, care should be taken to get as close as possible to the actual flexibility of the piers not supporting elastomeric bearings (cracking, plastification of steel and significant displacements). For this, an iterative calculation may be performed using a buckling programme (such as PYLOSTAB from the Sétra), or, if not, cracked inertia may be used as defined in appendix C of NF EN 19982.
A15  Recommendations Generally speaking, verifications to be performed are the same as for other loads. No heaving is permitted perpendicular to elastomeric bearings. Recommendations under seismic load combinations are detailed below (NF EN 19982, article 7.6).
A15.1 – Maximum distortion These verifications involve total distortion and distortion coming solely from horizontal force.
A15.1.1 – Total distortion Typical elastomeric bearings need to be checked in accordance with the regulations of 5.3.3 of NF EN13373, using the value KL=1 in the expression (5.1) of NF EN 13373 (NF EN 19982, § 7.6.2(5)).
6S================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
The value given to γm in the expression (5.2) of NF EN 13373 will be set by the national application document. The value currently recommended in NF EN 19982, is γm = 1.15. Furthermore, the seismic calculation displacement must be allocated a reliability coefficient γIS=1, 50 (recommended value, to be set in the National Annex of NF EN 19982).
A15.1.2  Distortion due to horizontal force Distortion resulting solely from authorized seismic horizontal force is twice as high as the value permitted for other loads (1.0):
ε q ,d ≤ 2,0 The distortion calculation takes into account the deformations imposed as specified above (cf. A.1.2).
A15.2  Buckling As for other loads, seismic combinations are used for verification:
Fz ,d Ar
≤
2 ⋅ a ′ ⋅ Gb ⋅ S ′ 3 ⋅ Te
A15.3  Slippage Here also, the same verifications are to be performed as for normal loads, but taking into account the seismic effect. However, the friction coefficient to use is that of the Service Limit State. ⎛ K ⎞ Fxy,d ≤ ⎜ 0,1 + f ⎟ ⋅ Fz,d σm ⎠ ⎝
and
where
σm =
Fz,d Ar
σ m ≥ 3,0 MPa
Contrary to the specifications of NF EN 13373, this last clause is not to be checked under permanent loads, but rather under the most unfavourable seismic combination (probably when there is an upward vertical seism). In most cases, it will not be possible to check nonslip conditions in a seismic zone and antislipping devices will have to be implemented.
A16 – Further construction measures The environment of laminated elastomeric bearings (visibility, jacking potential, etc.) must be supplemented by measures for seismic action. These measures mainly involve extreme displacements between a deck and its supports, as highlighted during recent earthquakes, such as those in Kobe (Japan 1996) and Loma Prieta (California 1989). These displacements are of a very different amplitude to that foreseeable by means of calculations. Further measures therefore need to be taken to ensure the integrity of the structure. The following cases can be distinguished: • Elastomeric bearings that take up seismic force • Elastomeric bearings that are supplemented by a blocking device that takes up the seismic force • Elastomeric bearings in conjunction with a sliding device. Moreover, in certain cases, it needs to be checked that the cover between the element supported and the support is sufficient (minimum support rest).
A16.1 – Elastomeric bearing that take up seismic forces When the laminated elastomeric bearing transmits forces due to excitation of the deck mass to the supports, the project designer can choose between the two following options (NF EN 19982, article 6.6.2.3): • Design bearings that take up the entire calculation seismic force, plus 50 % (NF EN 19982, § 7.6.2) • Supplement the bearing with a stop (also known as seismic coupling). Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
6T
A16.1.1 – Seismic couplings as safety stops In some cases, it can be beneficial to supplement elastomeric bearings with seismic couplings that act as safety stops. This is particularly the case lengthwise for the upgrading of existing bridges perpendicular to the mobile end supports between the deck and the abutment or the pier, when the requirements for minimum support rest have not been fulfilled (NF EN 19982, § 6.6.3.1(2)c). These couplings need to be designed with appropriate clearance or margins so as they remain inactive during the calculation seismic action, and only intervene at the limit of the bearing. In the AFPS rules, this measure is proposed in accordance with both horizontal directions: longitudinal and transversal. It is then recommended that a part of the thermal effects and all the time dependent effects be taken into account in the clearance calculation: d S = d G + 0,40 d T + d + dE diff  dG: displacement due to the longterm effects of permanent and quasipermanent actions  dT: calculation displacement due to thermal movements  ddiff: displacements due to time dependenteffects  dE: calculation seismic displacement
The clearance must not be greater so as to limit the impact effects resulting from the movement of the deck, and the stop is designed to take up a force H equal to 40 % of the seismic design force. Figure A.4 shows one possible arrangement. This involves a reinforced concrete stop integral with the pier shaft. This stop penetrates into a recess made in the underside of the deck at a height of around 10 cm, sufficient for the transmission of force H. Seismic coupling thus constituted works equally well transversally and longitudinally.
Figure A.4: example of a stop Seismic couplings should be calculated according to the regulations adapted to their material. Verifications are to be performed at Ultimate Limit State with the nominal value of the weight taken up by the support concerned (in other words, Q will not be weighted by 1.35). The safety coefficients applicable to the materials are those corresponding to the basic combinations (EC82 DAN article 5.2). For reinforced concrete stops, the part of NF EN 19922 (EC2) that deals with short corbels can be applied. Care must be taken so as the stops do not bring about modifications that could adversely affect the life on the bearings (water discharge, jacking potential, hindering thermal expansion, etc.).
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A16.1.2 – Elastomeric bearings supplemented by a blocking device taking up seismic forces In some cases, it is useful to block the functioning of bearings in one of the two horizontal directions, for example, to preserve the integrity of the equipment (such as expansion joints or restraint systems) or else because we do not wish to design bearings for seismic design force. Obviously, the dynamic calculation model must take account of this block. The device can be the same as the seismic coupling described above, the difference being that the clearance is reduced to a value not exceeding 15 mm. This measurement is a compromise between: • The onsite construction tolerances • A clearance required to leave deformations free in the direction perpendicular to the blockage • A clearance not to be exceeded so as to avoid the effects of impacts. In this case, seismic coupling must be designed to resist the calculation effects arising from the principle of capacity design (forces resulting from the plastification level being exceeded in the underlying pier). For uncommon or specific structures, specialized devices can also be designed. For example, a laminated elastomeric bearing placed vertically in conjunction with a sliding device. However, the project designer and the manager must bear in mind that the more sophisticated the system, the more likely it is cease functioning due to ageing and the more it will cost to maintain.
A16.1.3 – Elastomeric bearings in conjunction with a sliding device It is obvious that such bearings do not take up seismic forces. However, it must be designed to support, without damage, the calculation seismic displacement (NF EN 19982, article 7.6.2): dEd = γIS dE + dG ± 0,50 . dT
A16.2 – Minimum support rest As well as the construction measures outlined above, it is essential to check that the cover between the deck and its support is sufficiently long. The value of the minimum support rest defined in the Eurocode is calculated using the following formula (NF EN 19982, article 6.6.4):
lov = lm + d eg + d es The first term, lm, represents the minimum length of the support cover allowing the transmission of loads. A value lower than 40 cm should not be used. The last two terms represent the relative displacement between the deck and its support under seismic activity. It has two parts: • des is the displacement calculated under seismic excitation (NF EN 19982, article 6.6.4 (3) A); • deg is the actual displacement between two parts resulting from differential ground displacement (cf. figure A.6). It enables the relative difference between the foundations of the two supports to be taken into account, a factor that is not considered in the dynamic calculation of the structure (giving des). It must be assessed in accordance with the specifications of laws defining seismic action (NF EN 19982, § 6.6.4 (3) and appendix D or guide AFPS 92). Verification should be carried out, for example, of the support rest when the longitudinal stops are unilateral devices placed on the crossheads of the abutments. It needs to be ascertained that the overhang of the bearing shelf is sufficient for the deck not to fall in the event of a relative variance between the two abutments. Similarly, for decks that are relatively rigid in design and for short structure, it can be sufficient to put transversal seismic couplings on the abutments. It then needs to be ascertained that the support rest is sufficient for the various piers.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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Figure A.5: determination of support rests
Figure A.6: differential ground displacement
7M================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
^ééÉåÇáñ=O=Ó=The durability of laminated elastomeric bearings with a sliding plane
Although the durability of laminated elastomeric bearings is satisfactory, thanks mainly to the certification process that relies on a series of tests, some of which are to examine resistance to environmental conditions, the same does not apply to the combination comprising a couple of laminated elastomeric bearings featuring a sliding plane (sliding bearings). In this case, the qualities of one and the other cannot be accumulated – in fact, the disadvantages need to be added together. The result is that the durability of sliding bearings is far more random. This appendix is a reminder of the main measures that need to be taken to attain devices with a more satisfactory durability. These measures are to be applied throughout from manufacture through to the design and installation phases, as well as to monitoring and maintenance.
A21 – The characteristic quantity of the functioning of a sliding bearing The friction coefficient is the characteristic quantity generally chosen for the functioning of a sliding bearing. Statistical knowledge of the probability of obtaining the defined value of this coefficient would be the most accurate way of characterizing the functioning of a sliding bearing. In the current state of technical knowledge, noone is able to affirm, with known probability, that the value of this coefficient will be reached or exceeded during a given length of service. For this reason, we resort to empirical methods, which are to be implemented at the following stages: • the design of the structure • construction • maintenance
A22 – Measures to be taken at the design stage As a general rule, preference should be given to elements with a robust design that are not sensitive to installation and environmental conditions. From this viewpoint, sliding bearings are doubtless one of the construction products that are particularly sensitive to installation conditions, bad weather and ageing. Sliding bearings should therefore only be resorted to when other possibilities have been excluded. Loads, together with displacements affecting the structure, are to be taken at maximum value, in the following decreasing order of priority: • the flexibility of the supports. If some supports are too rigid, pendulum supports or roller bearings can be used, which are relatively high in relation to the expected displacement • the distortion capacity of the laminated elastomeric bearings • when the two previous solutions are deemed insufficient, sliding bearings of a mechanical design, with parts machined from thick sheet metal. This type of sliding bearing is commonly incorporated into pot bearings. The installation for these products is stricter than for sliding laminated elastomeric bearings. Similarly, quality controls during production are more rigorous and precise. Laminated elastomeric bearings with a sliding plane are to be used in the following conditions:  the taking up of differed deformations (shrinkagecreep) solely by the sliding plane  the taking up of other actions (temperature, breaking, etc.) by distortion of the laminated elastomeric part. N.B: jacking after construction and before acceptance, can avoid having to bring in sliding planes and restrict their use to standardised laminated elastomeric bearings.
7O================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
A23 – Measures to be taken at the manufacturing stage Only type D or E bearings of NF EN 13373 are suitable for the addition of a sliding plate. Lubrication pockets for oiling the sliding plane, along with an appropriate protection against dirt on the structure, need to be designed. The combination of the sliding plane and the elastomeric block needs to be delivered as a monolithic part, for handling and installation reasons. Once installed, it should be easy to separate the sliding plan from the elastomer block.
A24 – Measures to be taken as part of the monitoring process In order to prevent disorders that are specific to sliding bearings, regular monitoring is required. Risks specific to mechanical bearings need to be distinguished from those made of laminated elastomer. Laminated elastomeric bearings with a sliding plane are highly deformable products. They frequently have noticeable distortions from the first year of service. By recording the distortion onsite, and with knowledge of the dimensions together with an estimation of the bearing load, a friction coefficient can be deduced. This assessment of the nonslip coefficient is a default value of the sliding coefficient, as the bearing is yet to slide. A value can be found of around 10 %, which justifies the restriction of the duration of use of the products previously mentioned.
A25  Conclusion Whatever measures have already been taken, or will be taken at European Standardisation level, as far as the manufacture of sliding bearings is concerned, the risk and the gravity of disorders have to be assessed, along with the cost of replacing the bearings throughout the entire service life of the structure, as from the project stage.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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^ééÉåÇáñ=P=J=Table of dimensions Type B bearing with e = halfsheet Coating by 2 halfsheets, Tq < a'/3 and Tb max < 300 mm
Dimensions
Sheet thickness in mm
a
b
6
8
100
150
x
100
200
150
10
12
16
Dimensions 20
Sheet thickness in mm
350
500
x
x
350
550
x
x
x
x
350
600
x
x
200
x
x
400
400
x
x
150
250
x
x
400
450
x
x
150
300
x
400
500
x
x
200
200
x
400
550
x
200
250
x
x
400
600
x
200
300
x
x
450
500
200
350
x
x
450
550
x
200
400
x
x
450
600
x
250
250
x
500
500
250
300
x
x
500
550
x
250
350
x
x
500
600
x
x
250
400
x
x
500
650
x
x
300
300
x
500
700
x
x
300
350
x
x
600
600
x
x
300
400
x
x
600
650
x
x
300
450
x
x
600
700
x
x
300
500
x
x
700
700
x
x
300
550
x
x
700
800
x
x
300
600
x
x
700
900
x
x
350
350
x
800
800
x
x
350
400
x
800
900
x
350
450
x
900
900
x
7Q================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
x
x
x
^ééÉåÇáñ=Q=Ó=Assistance with drafting Particular Technical Clauses (CCTP)
The appendix offers examples of clauses to be integrated into Particular Technical Clauses (CCTP), both for reasons of consistency and so that they include the advice given in this guide. For applications in seismic zones, engineers are requested to supplement these clauses based on appendix 1. The propositions of articles contained in this appendix concern technical aspects. Their application must, however, take account of the rules defined in the Procurement Contract Code
A4.1  Examples of clauses to be included in the chapter "quality of materials" Relevant article of the guide
Example of clause
Comments
The laminated elastomeric bearings shall comply with the standard NF EN 1337, parts 1 and 3 (and part 2*) and with the National Application Document.
*To be added in the case of bearings with a sliding plane. See in particular the precision given by the National Application Document relating to the standard NF EN 13373, § 4.4.4, for the use of this type of bearing.
This compliance shall be certified by level 1 CE marking. § 2.2.2
In compliance with § 4.4.1 of the standard NF EN 13373, the bearings are to be made of polychloroprene (CR).
§ 2.2.2
In compliance with § 4.3.6 of the standard NF EN 13373, the concentration of ozone for the bearing ozone resistance test is 50 ppcm.
Article in the event of using laminated elastomer bearings with sliding planes § A2.3
Bearing with sliding planes are to include perforations in the PTFE with lubrication and an appropriate protection of the sliding plane (cf. § 7.3 and 7.4 of NF EN 13372).
Note that the 5th paragraph of § 4.4.4.3 of NF EN 13373 does not exclude the use of nonperforated PTFE sheets for type D bearings, if the structure designer has so specified.
7S================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
A4.2  Examples of clauses to be included in the chapter "design principle” Relevant article of the guide
Example of clause
Comments
§ 3.3 et 3.4 The bearings shall be justified as indicated in § 5.3.3 of the standard NF EN 13373, supplemented by the indications of § 3.3 et 3.4 of the Sétra guide, taking the following into account:  the external halfsheets that can be taken into account in the calculation  sheets of See Appendix 3 of the guide 10 mm are possible  The thickness of the plates, which can be taken as equal to at least 2 mm (cf. formula 12 of § 5.3.3.5 of the standard NF EN 13373). § 3.2.2
Under the application of § 4.3.1.1 "Shear modulus at nominal temperature" of the standard NF EN 13373, the value of modulus G = 0.9 is applicable.
Except for a detailed, specific requirement that will then be included in this article.
The requirements under clause 4.3.1.3 of the standard NF EN 13373 "Shear modulus at very low temperature" are not applicable. Under the application of clause § 4.3.3 "Compression stiffness" of the standard NF EN 13373, test 3 level is not a requirement*.
* Because these are manufactured parts containing polychloroprene (cf. § 2.2.2 of this guide and the National Application Document).
Under the application of clause § 4.3.5 "Static rotation capacity (and table 7)" of the standard NF EN 13373, only the test described in clause 4.3.5.2: "Eccentric loading test" is required. In the present Particular Technical Clauses (CCTP), the 3rd paragraph of the requirements is required “Under eccentricity equal to 1/6 of the smallest plan dimension of the test sample, no defect shall be accepted ( defects, cracks, etc.) for a rotation angle of 0.025 rad". In the event of the angle not being reached, pressure shall be limited to 3.5 Gd * A' * S/1.5. In compliance with § 4.3.7 of the standard NF EN 13373, the PTFE/elastomer shear bond test (and table 7) is required.
If using bearings with sliding planes.
Friction coefficient: § 4.4.4 of the standard NF EN 13373
In normal cases, to simplify, the correcting factor of 2/3 shall not be taken into account. Otherwise, take it into account in cases of specific justification and for applications in overseas departments and territories (DOMTOM) where the effective bearing temperature does not drop below – 5 °C.
§ 3.4.1.4
Under the application of § 5.3.3.6 of the standard NF EN 13373 regarding the limit conditions for buckling stability, it is stipulated that, for simplification purposes, we shall, in formula (15) apply the maximum reaction under a basic combination and with a modulus G = 0.9. In compliance with § 5.3.3.a of the standard NF EN 13373, the value of γm = 1 is applicable to the present Particular Technical Clauses (CCTP). For applications corresponding to the scope of the present Particular Technical Clauses (CCTP), only the value of KL = 1.0* is to be taken into consideration.
*cf. Appendix C of the standard NF EN 13373
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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Relevant article of the guide
Example of clause
Comments
In compliance with § 5.3.3.4 of the standard NF EN 13373 "Design strain due to angular rotation", verification under rotation angles is to be performed at ULS. In compliance with § 5.3.3.5 of the standard NF EN 13373 "Reinforcing plate thickness", the value of γm = 1 is applicable to the present Particular Technical Clauses (CCTP). § 3.4.1.3
The rotations αa and αb must include installation defects of a value equal to: To be completed following the instructions opposite This installation defect shall be added to the larger of the rotations αa or αb.
§ 5.2.3
§ 2.2.4.1 and § 2.2.4.3
This depends greatly on care taken during installation. The standard NF EN 13373 (§ 7.1.3) is not clear on the values to be adopted for installation defects, or on how they should be taken into account. The following standard values are therefore 0.003 radian in the case of “combining” proposed: • 0.010 radian for structures placed directly on methods • the bearings. For a specific application, constructions managers are completely free to define a product that will be specific to the structure and will be manufactured solely for it. In this case, they should ensure, based on the standards NF EN and/or simply on national standard (cf. § 5.2.2.2 and 5.2.2.3 of the test standards not taken up at European level in the EN standard) that the product is marketcompliant.
The fixing method used for the stainless steel sliding plates on the supports steel shall be submitted to the construction manager for approval. The position of the measuring devices, together with the dirt protection method shall be submitted to the construction manager for approval. As regards the dimensioning of the sliding plates, displacements shall be increased in both directions by ± 20 mm. Furthermore, the minimum displacement to be taken into account is ± 50 mm in the principal direction of the displacements resulting from the structure.
A4.3  Examples of clauses to be included in the chapter "implementation" Relevant article of the guide § 5.4.2
Example of clause Hold points:  acceptance of bearing bosses  acceptance on delivery of the bearings  acceptance of the installation of the bearings (adjustments and installation).
7U================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
Comments
_áÄäáçÖê~éÜó General documents •
•
• •
• •
Environnement des appareils d'appui en élastomère fretté. Recueil des règles de l'art. Sétra /LCPC 10/1978. Réf. F 7810. The environment of laminated elastomeric bearings. A best practice guide. Sétra /LCPC 10/1978. Ref. F 7810. Les appareils d'appui à pot. Utilisation sur les ponts, viaducs et structures similaires. Guide technique. Sétra. Août 2007  Réf. 0734 – Annule et remplace le guide "Les appareils d'appui à pot de caoutchouc édité en septembre 1999". Pot bearings. Use on bridges, viaducts and similar structures. Technical guide. Sétra. August 2007 – ref. 0734 – Cancels and replaces the guide “Rubber pot bearings”, published in September 1999. Appareils d'appui en caoutchouc. Documents scientifiques et techniques. AFPC. 07/1994. Rubber bearings. Scientific and technical documents. AFPC. 07/1994. Instruction technique pour la surveillance et l'entretien des ouvrages d'art. Seconde partie: Fascicule 13 "appareils d'appui". Sétra / LCPC. 2002. Réf. 0230 Technical instruction for the monitoring and maintenance of civil engineering structures. Part two: section 13 “bearings”. Sétra / LCPC. 2002. Ref. 0230 MÉMOAR (Mémento pour la mise en œuvre sur ouvrages d'art). MEMOAR (Implementation guide for civil engineering structures) See in particular the following: 
VIII1: Appareils d'appui en élastomère fretté Laminated elastomeric bearings

VIII3: Bossages des appareils d'appui Bearing bosses
•
VIII4: Vérinage/Calage
Jacking/Wedging Note d'information technique n° 27 sur l'application nationale de la norme NF EN 1337 (appareils d'appui structuraux). Sétra. Décembre 2006. The technical information note no. 27 on the National Application of the standard NF EN 1337 (structural bearings). Sétra. December 2006.
Standards • • • • • • • •
NF EN 13371 – Structural bearings. Part 1: General design rules NF EN 13372  Structural bearings. Part 2: Sliding elements NF EN 13373  Structural bearings. Part 3: Elastomeric bearings NF EN 19912  Eurocode 1: Actions on structures  Part 2: Traffic loads on bridges and its National Annex (to be published) NF EN 199211: Eurocode 2 – Design of concrete structures  Part 11: Common rules and rules for buildings NF EN 19932: Eurocode 3 – Design of steel structures  Part 2: Steel bridges (to be published) NF EN 199115: Eurocode 1 – Actions on structures  Part 15: General actions – Thermal actions NF EN 1990: Structural Eurocodes: Basis of structural design and NF EN 1990/A1: Appendix A2 (application to bridges)
8M================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
•
Rubber bearing series: – T 47.806  Détermination du fluage en compression –
Determination of creep in compression
– XP T 47.807  Détermination de la relaxation de contrainte en cisaillement. –
Determination of shear stress relaxation
– XP T 47.811  Détermination de la condition de nonglissement –
Determination of the nonslipping condition
– XP T 47.813  Détermination de la résistance au brouillard salin –
Determination of salt fog resistance
– XP T 47.814  Détermination de la dureté apparente Shore A au moyen d'un duromètre de poche –
Determination of apparent Shore A hardness using a pocket durometer
Bibliography specific to Appendix 1 • • •
• • •
Loi n° 87565 du 22 Juillet 1987 relative à (...) la prévention des risques majeurs. Law no. 87565 of 22 July 1987 regarding (…) the prevention of major risks. Décret n° 91461 du 14 Mai 1991 relatif à la prévention du risque sismique. Decree no. 91461 of 14 May 1991 regarding the prevention of seismic risk. Arrêté du 15 septembre 1995 relatif à la classification et aux règles de construction parasismique applicables aux ponts de la catégorie dite "à risque normal". Decree of 15 September 1995 regarding the classification and regulations for seismicresistant construction applicable to bridges of the category labelled “at normal risk”. Guide AFPS 92 pour la protection parasismique des Ponts. The AFPS 92 guide for the seismic protection of bridges. NF EN 19982: Eurocode 8 – Design of structures for earthquake resistance  Part 2: Bridges (to be published) and its National Annex (to be published). PrEN 15129 – Seismic devices
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures
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8O================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
This technical guide is mainly intended for bridge designers. The contents should enable them to design laminated elastomeric bearings with a view to using them on bridges, viaducts and similar structures. The documents principally includes the following: • A brief description of the various types of laminated elastomeric bearings and any specific related equipment • The main regulations and standards • The design criteria based on draft regulations drawn up by the CEN (European Committee for Standardization) • The principle of controls for the CE marking • A design methodology for a bridge project with application examples Lastly, it is supplemented by a series of appendixes on the design of this type of bearing in seismic zones, on the durability of laminated elastomeric bearings with sliding planes and examples of clauses to be included in performance specifications.
Service d'études sur les transports, les routes et leurs aménagements 46 avenue Aristide Briand – BP 100 – 92225 Bagneux Cedex – France Phone: 33 (0)1 46 31 53 – Fax: 33 (0)1 46 11 33 55 This document is awailable and can be downloaded on Sétra website: http://www.setra.developpementdurable.gouv.fr/
Reference : 0925A This document may not be reproduced – even partially – without Sétra's prior consent. © 2009 Sétra – ISRN No. : EQSETRA09ED09FR+ANG
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