jMarch 2007 Translate June 2009
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 co-operations, 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).
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.
Technical guide
Laminated elastomeric bearings
Use on bridges, viaducts and similar structures
O=================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures This guide has been written by a working group comprising:
– Jean-François 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 (EGIS-SCETAUROUTE)
– P. Kirschner (SECOA) – C. Néant (ETIC)
– G. Wattiaux (ETIC)
– P. Xercavins (PX-DAM Consultants)
The drawings were prepared by Jean-Pierre 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)
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Contents
F o r ew o r d . . . 5
C h a p t e r 1 - I n t r o d u c t i o n . . . 7
1.1 – Why replace the 2000 guide? ... 7
1.2 – Scope and content ... 7
1.3 – Application of the standard NF EN 1337-3 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 i t i on a n d d e s c r i p t i o n . . . 9
2.1 – General principles of composition ... 9
2.2 – Component parts... 10
2.3 – Manufacturing methods... 14
C h a p t e r 3 – B e h a vi o u r a n d d i m e n s i o n i n g . . . 1 5 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 i g n p r i n c i p l e s f o r a s t r u c t u r e w i t h b e a r i n g s . . . 3 1 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
C h a p t e r 5 - C o n t r o l s . . . 1 4 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
C h a p t e r 6 – T h e p r e - d i m e n s i o n i n g a n d ve r i f i c a t i o n p r o g r a m . . . 2 0 A p p e n d i x 1 – C a l c u l a t i o n s f o r l a m i n a t e d e l a s t o m e r i c b e a r i n g s f o r u s e i n s e i s m i c z o n e s . . . 2 2 A1-1 – Regulatory framework... 22
A1-2 – Design combinations and direction accumulation ... 23
A1-3 - Dynamic calculation model... 24
A1-4 – Using a behaviour factor... 26
A1-5 - Recommendations... 26
A1-6 – Further construction measures ... 27
A p p e n d i x 2 – T h e d u r a b i l i t y o f l a m i n a t e d e l a s t o m e r i c b e a r i n g s w i t h a s l i d i n g p l a n e 3 2 A2-1 – The characteristic quantity of the functioning of a sliding bearing... 32
A2-2 – Measures to be taken at the design stage... 32
A2-3 – Measures to be taken at the manufacturing stage ... 33
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A2-5 - Conclusion ... 33
A p p e n d i x 3 - T a b l e o f d i m e n s i o n s . . . 3 4 A p p e n d i x 4 – A s s i s i t a n c e w it h d r a f t i n g P a r t i c u l a r T e c h n i c a l C l a u s e s ( C C T P ) . . . 3 6
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
B i b l i o g r a p h y . . . 4 0
General documents ... 40 Standards ... 40 Bibliography specific to Appendix 1 ... 41
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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 de-bonding). 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.
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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).
U================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
1.3 – Application of the standard NF EN 1337-3 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 1337-3) and if required,
completed by sliding elements 3 (type D or E of the NF EN 1337-3) Anti-slipping or anti-lifting elements 4
(type C of the NF EN 1337-3).
1.5 – Notations and symbols
The notations used in this guide are those of the NF EN 1337-3 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
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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 1337-3, § 1) specifies that only bearings of plan dimensions of under (1200 x 1200mm) are concerned.
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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 1337-3 (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.
W h a t a r e t h e c r i t e r i a f o r c h o o s i n g o n e o r i g i n o v e r a n o t h e r ?
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 anti-oxidant and anti-ozone6. France, along with many other European countries, has chosen polychloroprene which, among other qualities, provides excellent resistance to aging, a very low load-bearing 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 short-term economic considerations may result in a decision to turn to natural rubber. This means taking a long-term 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 1337-3, only accepts polychloroprene (or CR) for use in France.
As regards ozone resistance, the national application document of the standard NF EN 1337-3 (§ 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 1337-3 (§ 5.3.2), may in no circumstance be under 5 mm, or over 25 mm.
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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 1337-3, § 4.4.3.1).
2.2.4 – Sliding elements that may be required
2 .2 .4 . 1 - Co m p o si t io nThe 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 1337-3), or on an outside steel sheet (type E bearing according to NF EN 1337-3). A polished stainless steel sheet (the grade of which is defined in NF EN 1337-2, § 5.4.1), connected to a higher S235 steel plate, slides onto the PTFE plate (NF EN 1337-3, § 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 high-hardness 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 1337-2, 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 ®.
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Figure 2.5: an example of rule to monitor displacement (vertical bearing in an seismic-resistant stop) (photo Sétra) 2 . 2 . 4 . 2 – Ho r i zo n t a l f o r c e
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 1337-3, § 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 – S l i d e p l a t e d i m e n s i o n s
There should be no hesitation in over-sizing the length of the slide plates, even though their dimensions are at ULS. This allows compensation for the many consecutive imprecisions regarding factory pre-settings, design hypotheses, the actual date of installation and, therefore, the temperature on installation. The text of the standard (cf. NF EN 1337-1, § 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 – Anti-slipping and anti-lifting devices
When there is a risk of slipping in a laminated elastomeric bearing (cf. NF EN 1337-3, § 5.3.3.6, non-sliding 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 1337-3). In no case should the stop be placed on an elastomeric sheet (cf. figure 2.6).
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Anti-slipping 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.
- glue-mounted (not shown) for low tangential forces (with type C bearings).
- with anchors.
- using chequered plates (for low tangential forces).
Limited distortion or blocked bearings
Anti-lifting system bearings
Figure 2.7: design drawings of "fixed" bearings
The drawing of the bearing with the anti-lifting 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
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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 1337-3, 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, disk-shaped is best, although the manufacture of this type of bearing is more costly and difficult.
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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 1337-3 (§ 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 1337-3
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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 1337-3 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 (multi-plated 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 1337-3. 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 half-laminations (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 half-lamination, the thickness of which is taken into account in the calculations defined in article 5.3.3.1 of NF EN 1337-3. It is suggested that they are designated with the number of intermediate laminations, mentioning the two external half-laminations 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 1337-3. Type B defined in table 3 of the standard
With e = passive coating
Type B
With e = a half-lamination (examples of plan dimensions in appendix 3) e = 2,5 mm t s t i T b e = ti / 2 t s t i T b Tb = 3 (ti + ts) + ts + 5mm Tb = 2 (ti+ ts) + ts + 2 ti/2 n = 3 intermediate laminations, assuming that the
coatings are not part. n = 2, the half-laminations can be taken into account in the calculation.
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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 1337-3 (§ 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
t
t
s ia' , b' ou D'
a , b ou D
> 4 mm
T
bFigure 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).
NU================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
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 1337-2.
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): tb=Max⎝⎜⎛10mm; ,0 04 ab2+bb2⎞⎠⎟
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 1337-2. This table has been drawn up using the following formula (EN 1337 - 2 - Appendix B):
p max 10 k 1,2 σ μ + =
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 1337-3).
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.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures NV Verification of the deformation of slide plates (NF EN 1337-2 § 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 1337-3 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 1337-3 differentiates between:
• Recommended size bearings, as defined in table 3 of NF EN 1337-3;
• Other types of bearings, in particular those with two external half-laminations.
In compliance with NF EN 1337-3, 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 1337-3 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 – B e h a v i o u r u n d e r a x i a l f o r c e
ε
ca
F
F
z
z
τ
Nγ
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.It is given by the formula (EN § 5.3.3.2):
S Ar G F 1,5 = G = N Z c
τ
ε
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.
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.
OM================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
vx
a'
x
Figure 3.5: a surface reduced due to the effect of horizontal deformation.
We thus have avec A'= ' '
' v -' v -1 A' = A x y r a b b a ⎟⎟⎠ × ⎞ ⎜⎜ ⎝ ⎛
(if the plates do not have holes)
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:
e pt l A' = S
(
)
⎩ ⎨ ⎧ + externes couches des feuillets les pour t 1,4 = t internes couches des feuillets les pour t = t ' ' 2 = l i e i e p et b a avecThe standard also gives the means of estimating the total deformation
Σ
v
Z due to a vertical force FZ (EN § 5.3.3.7):⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛
∑
b dS E G 1 + 5 1 A' t F = v 2 1 i z z With Eb = 2000 MPaS1: 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:
MPa 000 2 = E avec 1 + 5 1 A' t F = v z i 2 z b b i dS E G ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛
∑
Let us remember that in this formula, S designates the form coefficient of lamination "i" and that, in the event of a half-lamination, 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.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures ON
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 1337-3), 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 – Be h a v io u r un d e r a h o ri zo n t a l f o rc e
ε
qa
F
F
x
x
τ
Hγ
Under a horizontal force, a uniform distribution of the distortion εq is noted, linked to the shear τΗ in the elastomer. Under displacement vx or a horizontal force Fx, distortion is given by the formula (EN § 5.3.3.3):
b
a
G
F
T
v
x q x q=
=
ε
γ
ε
q=
tg
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 non-exceptional 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.
OO================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures 3 .3 .2 . 3 – Be h a v io u r un d e r a h o r i z o n t a l a x i s r o t a t i o n
a
ε
ατ
αMt
Mt
αγ
aThe 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):
(
)
ε
α α α = a' b' 2 t 2 2 i 3 a+ b ti∑
The distribution of the distortions is given in figure 3.7.
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): K t n b' a' G = M S 3 i 5 t α
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 1337-3, 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:
60 2 , 26 = Ks 1,2785ln + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − a b
e
3.4 – Dimensioning verifications
3.4.1 – Basic verification
3 .4 .1 . 1 – L i m i t i n g d i s t o r t i o nTotal 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.
•
ε
c,ε
q andε
α are the distortions calculated respectively under vertical force, horizontal force or displacements and deck rotations.Laminated elastomeric bearings –Use on bridges, viaducts and similar structures OP 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
ε
c alone or Fz (other than that regarding buckling).3 .4 .1. 2 - Tr a c t io n in t h e m e ta l p l at e s
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):
f
A
F
2,6
=
t
y r z m s it
γ
with:Fz 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 – R o t a t i o n l i m i t c o n d i t i o n
The rotation stability of the bearing is checked at Ultimate Limit State. The following needs to be verified (EN § 5.3.3.6):
(
)
vz a b∑
≥ a' +b' Kr α α with:αa et αb Rotations of perpendicular axis on sides a and b of the bearing
Kr Coefficient equal to 3
vz
∑
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 cast-in-place.
NF EN 1337-3 (§ 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 – Bu c k li ng s ta b il it y
Buckling stability needs to be checked at Ultimate Limit State in the following conditions (EN § 5.3.3.6): T 3 S a' G 2 A F e 1 r z <
OQ================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
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 – N o n - s l i p c o n d i t i o n
The non-slip verification is carried out, in the absence of anti-slipping device, if (EN § 5.3.3.6):
F F et F A 3 MPa xy z z,Gmin r ≤ μe ≥ with:
Fz,Gmin Minimum reaction under permanent load
Fz and Fxy The most unfavourable concomitant vertical and horizontal force reaction μe 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:
résine en mortier compris y surfaces autres les pour 20 , 0 K béton le pour 60 , 0 K MPa) (en F = avec K 1,5 1, 0 f f Z f = = + = r m m e A σ σ μ
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 – P r e s s u r e o n t h e c o n t a c t p l a n e s
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 1337-3. If there is a risk of heaving, the final stress should be recalculated. For large-size bearings, higher pressures are possible, as for other types of high-pressure 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 1992-1-1). Stress on the concrete can be calculated by taking an evenly-loaded 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.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures OR 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 platesf A F 2,6 = t y r z s i t Limit in rotation v
(
)
z a b∑
≥ a' +b' Kr α α Buckling stability T 3 S a' G 2 A F e 1 r z < Non-slip 3MPa A F et F F z,Gmin' z xy≤μe ≥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 – E x p e r i m e n t a l r e s u l t s
All limitations given by NF EN 1337-3 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 correctly-sized 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 1337-3), the wide dispersion of test results only allows for an approximate assessment of the minimum contact surface using calculation.
OS================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures - Tassement - Possibilité de rotation sans soulèvement théorique α n 1 2 3 valeur sécuritaire α s
d'après les essais
Ka max
= 2,47 K a max = α n
α s
Limite normative Courbe sécuritaire représentative des essais compression-rotation à la limite du soulèvement K en fonction de σ m z σ m = F / A r a max (MPa) z σ = F / A' K a min σ m = 23,84 0 50 40 30 20 10
Figure 3.10: compression-rotation behaviour prior to heaving. Determination of the adjustment factor Ka max.
3 . 4 . 2 . 2 – T h e a s s e s s m e n t m e t h o d p ro p o s ed
3 . 4 . 2 . 2 . 1 - I n t r o d u c t i o n
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 1337-2. The simplified pressure diagrams are shown in table 4.4 of chapter 4.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures OT
3 . 4 . 2 . 2 . 2 – T h e d e s i g n p r i n c i p l e f o r d e t e r m i n i n g t h e u n i f o r m p r e s s u r e a n d a p o s s i b l e r i s k o f h e a v i n g
(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: max S 3 i 5 t n't K b' a' G = M
α
×Ka– 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 off-set 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:
3 max α
ε
ε
a c rsK
K
=
(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 medium-sized 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.
OU================Laminated elastomeric bearings – Use on bridges, viaducts and similar structures
It is always preferable to add a lamination, so long as the non-buckling 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.
Laminated elastomeric bearings –Use on bridges, viaducts and similar structures OV
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 hundred-year flood.
3.5.6 – Bearing markings
The position on the structure, the size and direction of any pre-settings, 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.