EN 1998-2:2025
(Main)Eurocode 8 - Design of structures for earthquake resistance - Part 2: Bridges
Eurocode 8 - Design of structures for earthquake resistance - Part 2: Bridges
EN 1998-2 is intended to be applied to the design of new bridges in seismic regions. It covers the design of reinforced concrete, steel and composite steel-concrete bridges and provides guidance for the design of timber bridges.
EN 1998-2 is applicable to the seismic design of bridges exploiting ductility in structural members or through the use of antiseismic devices. When ductility is exploited, this part primarily covers bridges in which the horizontal seismic actions are mainly resisted through bending of the piers or at the abutments; i.e. of bridges composed of vertical or nearly vertical pier systems supporting the traffic deck superstructure. It is also applicable to the seismic design of arched bridges, although its provisions should not be considered as fully covering these cases.
Suspension bridges and masonry bridges, moveable bridges and floating bridges are not included in the scope of EN 1998-2.
Eurocode 8 - Auslegung von Bauwerken gegen Erdbeben - Teil 2: Brücken
Eurocode 8 - Calcul des structures pour leur résistance aux séismes - Partie 2: Ponts
Le présent document s'applique au dimensionnement et à la vérification des ponts neufs dans les régions sismiques. Il donne des règles générales pour le dimensionnement et la vérification des ponts des classes de conséquences CC1, CC2 et CC3, telles que définies dans l'EN 1990:2023, A.2.
NOTE 1 L'EN 1998 2 couvre le calcul des ponts en béton armé, en acier et des ponts mixtes acier-béton, à l'exception des piles précontraintes. Des recommandations pour le dimensionnement des ponts en bois sont données dans l'Annexe C informative.
NOTE 2 L'évaluation des ponts existants est couverte dans l'EN 1998 3.
(2) Sauf indication contraire, l'EN 1998 1 1 et l'EN 1998 5 s'appliquent.
(3) L'EN 1998 2 est applicable en complément des autres Eurocodes pertinents.
NOTE L'EN 1998 2 ne contient que les dispositions qui sont utilisées pour la conception des ponts neufs en zone sismique, en plus des dispositions contenues dans les autres Eurocodes pertinents. À cet égard, l'EN 1998 2 complète les autres Eurocodes.
(4) L'EN 1998 2 fournit des exigences de performance de base et des critères de conformité applicables aux ponts neufs dans les régions sismiques.
(5) L'EN 1998 2 est applicable au calcul sismique des ponts exploitant la ductilité des éléments structuraux ou par l'utilisation de dispositifs antisismiques.
(6) L'EN 1998 2 donne des règles de dispositions constructives pour la ductilité des éléments structuraux des ponts conçus pour exploiter la ductilité comme moyen de protection sismique. Lorsque la ductilité est exploitée, l'EN 1998 2 couvre en premier lieu les ponts pour lesquels la résistance aux actions sismiques horizontales est principalement assurée par la flexion des piles ou des culées, c'est-à-dire les ponts composés de systèmes de piles verticales ou presque verticales sur lesquelles repose la structure du tablier supportant la circulation.
(7) L'EN 1998 2 donne des règles spécifiques pour les ponts équipés de dispositifs antisismiques, pour les ponts à haubans et extradossés et pour les ponts intégraux.
(8) L'EN 1998 2 est également applicable au dimensionnement sismique des ponts en arc, bien qu'il convienne que ses dispositions ne soient pas considérées comme couvrant entièrement ce cas.
NOTE Les ponts suspendus et les ponts en maçonnerie, les ponts mobiles et les ponts flottants ne sont pas inclus dans le domaine d'application de la présente partie.
Evrokod 8 - Projektiranje potresnoodpornih konstrukcij - 2. del: Mostovi
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
oSIST prEN 1998-2:2023
01-maj-2023
Evrokod 8 - Projektiranje konstrukcij na potresnih območjih - 2. del: Mostovi
Eurocode 8 - Design of structures for earthquake resistance - Part 2: Bridges
Eurocode 8 - Auslegung von Bauwerken gegen Erdbeben - Teil 2: Brücken
Eurocode 8 - Calcul des structures pour leur résistance aux séismes - Partie 2: Ponts
Ta slovenski standard je istoveten z: prEN 1998-2
ICS:
91.120.25 Zaščita pred potresi in Seismic and vibration
vibracijami protection
93.040 Gradnja mostov Bridge construction
oSIST prEN 1998-2:2023 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
oSIST prEN 1998-2:2023
oSIST prEN 1998-2:2023
DRAFT
EUROPEAN STANDARD
prEN 1998-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
March 2023
ICS Will supersede EN 1998-2:2005
English Version
Eurocode 8 - Design of structures for earthquake
resistance - Part 2: Bridges
Eurocode 8 - Calcul des structures pour leur résistance Eurocode 8 - Auslegung von Bauwerken gegen
aux séismes - Partie 2: Ponts Erdbeben - Teil 2: Brücken
This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee
CEN/TC 250.
If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations
which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.
This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC
Management Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are
aware and to provide supporting documentation.
Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2023 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 1998-2:2023 E
worldwide for CEN national Members.
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Contents Page
European foreword . 5
Introduction . 6
1 Scope . 8
1.1 Scope of EN 1998-2 . 8
1.2 Assumptions . 8
2 Normative references . 9
3 Terms, definitions and symbols . 9
3.1 Terms and definitions . 9
3.2 Symbols and abbreviations . 10
3.2.1 General. 10
3.2.2 Symbols . 11
3.2.3 Abbreviations . 18
3.3 S.I. Units . 19
4 Basis of design . 19
4.1 Basic requirements . 19
4.2 Seismic actions . 19
4.2.1 General. 19
4.2.2 Spatial variability of the seismic action . 21
4.3 Characteristics of earthquake resistant bridges . 21
4.3.1 Conceptual design . 21
4.3.2 Primary and secondary seismic members. 22
4.3.3 Resistance and ductility conditions – Capacity design rules . 22
4.3.4 Connections . 23
4.3.5 Control of displacements – Detailing of ancillary elements . 23
4.3.6 Choice of ductility class – Limits of seismic action for design to DC1, DC2 and DC3 . 24
4.3.7 Simplified criteria . 25
5 Modelling and structural analysis . 25
5.1 Modelling . 25
5.1.1 General. 25
5.1.2 Torsional effects about a vertical axis . 27
5.1.3 Second-order effects . 28
5.2 Methods of analysis . 29
5.2.1 General. 29
5.2.2 Force-based approach . 29
5.2.3 Displacement-based approach . 35
5.3 Methods of analysis accounting for spatial variability of ground motion . 36
5.3.1 General. 36
5.3.2 Long bridges on uniform soil . 38
5.3.3 Short to medium length bridges on non-uniform soil . 39
5.3.4 Long bridges on non-uniform soil . 39
5.4 Combination of the seismic action with other actions . 40
6 Verifications of structural members to limit states . 41
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6.1 General . 41
6.2 Material requirements . 41
6.2.1 General . 41
6.2.2 Design for DC2 and DC3 . 41
6.3 Verification of Significant Damage (SD) limit state . 42
6.3.1 General . 42
6.3.2 Capacity design effects . 42
6.3.3 Concrete members . 43
6.3.4 Steel and steel-concrete composite members . 47
6.3.5 Foundations . 48
6.3.6 Connections . 48
6.3.7 Concrete abutments . 49
6.3.8 Verification for the displacement-based approach . 49
6.4 Verification to other limit states . 49
6.4.1 Verification of Near Collapse (NC) limit state . 49
6.4.2 Verification of Damage Limitation (DL) limit state . 50
6.4.3 Verification of Operational (OP) limit state . 50
7 Detailing for ductility . 50
7.1 General . 50
7.2 Concrete piers . 50
7.2.1 General . 50
7.2.2 Longitudinal reinforcement . 50
7.2.3 Critical region . 50
7.2.4 Confinement . 51
7.2.5 Buckling of longitudinal compression reinforcement . 54
7.2.6 Other rules . 54
7.2.7 Hollow piers. 55
7.2.8 Joints adjacent to critical regions . 55
7.3 Steel piers . 57
7.4 Foundations . 57
7.4.1 Spread foundation . 57
7.4.2 Pile foundations . 57
8 Specific rules for bridges equipped with antiseismic devices . 57
8.1 General . 57
8.2 Seismic action, basic requirements and compliance criteria . 57
8.3 General provisions concerning antiseismic devices . 58
8.4 Methods of analysis . 58
8.4.1 General . 58
8.4.2 Equivalent linear lateral force method. 58
8.4.3 Equivalent linear response spectrum method . 60
8.4.4 Response-history analysis . 60
8.5 Minimum overlap length at connections . 60
9 Specific rules for cable-stayed and extradosed bridges . 61
9.1 General . 61
9.2 Basis of design . 61
9.3 Modelling and structural analysis . 62
9.4 Verifications . 62
9.4.1 General . 62
9.4.2 Avoidance of brittle failure of specific non-ductile components . 62
9.5 Detailing . 63
10 Specific rules for integral abutment bridges . 63
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10.1 General. 63
10.2 Basis of design . 64
10.3 Modelling and structural analysis . 65
10.3.1 General. 65
10.3.2 Force-based approach . 65
10.3.3 Displacement-based approach . 68
10.3.4 Culverts . 68
10.4 Verifications . 69
10.4.1 Verification of Significant Damage limit state . 69
10.4.2 Verification to other limit states . 69
Annex A (informative) Characteristics of earthquake resistant bridges . 70
A.1 Use of this annex . 70
A.2 Scope and field of application . 70
A.3 Deck . 70
A.4 Skew bridges . 70
A.5 Choice of supporting members resisting the seismic action . 71
A.6 Choice of ductility class . 72
Annex B (informative) Added mass of entrained water for immersed piers . 73
B.1 Use of this annex . 73
B.2 Scope and field of application . 73
B.3 Effective mass of an immersed pier . 73
Annex C (informative) Additional information on timber bridges . 75
C.1 Use of this annex . 75
C.2 Scope and field of application . 75
C.3 Basis of design . 77
C.4 Modelling . 78
C.5 Force-based approach . 78
Annex D (normative) Displacement-based approach for integral abutment bridges . 80
D.1 Use of this annex . 80
D.2 Scope and field of application . 80
D.3 Modelling for nonlinear analysis . 80
D.4 Nonlinear static analysis . 82
D.5 Nonlinear response-history analysis . 84
Bibliography . 86
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European foreword
This document (prEN 1998-2:2022) has been prepared by Technical Committee CEN/TC 250
“Structural Eurocodes”, the secretariat of which is held by BSI. CEN/TC 250 is responsible for all
Structural Eurocodes and has been assigned responsibility for structural and geotechnical design
matters by CEN.
This document will supersede EN 1998-2:2005.
The first generation of EN Eurocodes was published between 2002 and 2007. This document forms part
of the second generation of the Eurocodes, which have been prepared under Mandate M/515 issued to
CEN by the European Commission and the European Free Trade Association.
The Eurocodes have been drafted to be used in conjunction with relevant execution, material, product
and test standards, and to identify requirements for execution, materials, products and testing that are
relied upon by the Eurocodes.
The Eurocodes recognize the responsibility of each Member State and have safeguarded their right to
determine values related to regulatory safety matters at national level through the use of National
Annexes.
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Introduction
0.1 Introduction to the Eurocodes
The Structural Eurocodes comprise the following standards generally consisting of a number of Parts:
• EN 1990 Eurocode: Basis of structural and geotechnical design
• EN 1991 Eurocode 1: Actions on structures
• EN 1992 Eurocode 2: Design of concrete structures
• EN 1993 Eurocode 3: Design of steel structures
• EN 1994 Eurocode 4: Design of composite steel and concrete structures
• EN 1995 Eurocode 5: Design of timber structures
• EN 1996 Eurocode 6: Design of masonry structures
• EN 1997 Eurocode 7: Geotechnical design
• EN 1998 Eurocode 8: Design of structures for earthquake resistance
• EN 1999 Eurocode 9: Design of aluminium structures
• New parts are under development, e.g. Eurocode for design of structural glass
The Eurocodes are intended for use by designers, clients, manufacturers, constructors, relevant
authorities (in exercising their duties in accordance with national or international regulations),
educators, software developers, and committees drafting standards for related product, testing and
execution standards.
NOTE Some aspects of design are most appropriately specified by relevant authorities or, where not
specified, can be agreed on a project-specific basis between relevant parties such as designers and clients. The
Eurocodes identify such aspects making explicit reference to relevant authorities and relevant parties.
0.2 Introduction to EN 1998 Eurocode 8
EN 1998 defines the rules for the seismic design of new buildings and engineering works and the
assessment and retrofit of existing ones, including geotechnical aspects, as well as temporary
structures.
NOTE This standard also covers the verification of structures in the seismic situation during construction,
when required.
Attention has to be paid to the fact that, for the design of structures in seismic regions, the provisions of
EN 1998 should be applied in addition to the relevant provisions of EN 1990 to EN 1997 and EN 1999.
In particular, EN 1998 should be applied to structures of consequence classes CC1, CC2 and CC3, as
defined in prEN 1990:2021, 4.3. Structures of consequence class CC4 are not fully covered by the
Eurocodes but may be required to follow EN 1998, or parts of it, by the relevant authorities.
By nature, perfect protection (a null seismic risk) against earthquakes is not feasible in practice, in
particular because the knowledge of the hazard itself is characterized by a significant uncertainty.
Therefore, in Eurocode 8, the seismic action is represented in a conventional form, proportional in
amplitude to earthquakes likely to occur at a given location and representative of their frequency
content. This representation is not the prediction of a particular seismic movement, and such a
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movement could give rise to more severe effects than those of the seismic action considered, inflicting
damage greater than the one described by the Limit States contemplated in this Standard.
Not only the seismic action cannot be predicted but, in addition, it should be recognized that
engineering methods are not perfectly predictive when considering the effects of this specific action,
under which structures are assumed to respond in the nonlinear regime. Such uncertainties are taken
into account according to the general framework of EN 1990, with a residual risk of underestimation of
their effects.
0.3 Introduction to EN 1998-2
EN 1998-2 provides general requirements for earthquake resistant design of new bridges. Except
where otherwise specified in this Part, the seismic actions are as defined in prEN 1998-1-1:2022, 5. The
scope of this Part of EN 1998 is defined in 1.1.
Since the seismic action is mainly resisted by the piers and the latter are usually constructed of
reinforced concrete, a greater emphasis has been given to such piers. Additionally, bearings are in many
cases important parts of the seismic resisting system of a bridge and are therefore treated accordingly.
The same holds for seismic isolation devices.
EN 1998-2 is subdivided in ten clauses and includes four annexes, where Annexes A to C are
informative and Annex D is normative.
0.4 Verbal forms used in the Eurocodes
The verb “shall” expresses a requirement strictly to be followed and from which no deviation is
permitted in order to comply with the Eurocodes.
The verb “should” expresses a highly recommended choice or course of action. Subject to national
regulation and/or any relevant contractual provisions, alternative approaches could be used/adopted
where technically justified.
The verb “may” expresses a course of action permissible within the limits of the Eurocodes.
The verb “can” expresses possibility and capability; it is used for statements of fact and clarification of
concepts.
0.5 National annex for EN 1998-2
National choice is allowed in this document where explicitly stated within notes. National choice
includes the selection of values for Nationally Determined Parameters (NDPs).
The national standard implementing EN 1998-2 can have a National Annex containing all national
choices to be used for the design of new bridges to be constructed in the relevant country.
When no national choice is given, the default choice given in this document is to be used.
When no national choice is made and no default is given in this document, the choice can be specified by
a relevant authority or, where not specified, agreed for a specific project by appropriate parties.
National choice is allowed in EN 1998-2 through notes to the following:
4.1(4) 4.2.1(1) 4.3.5(8) 4.3.7(1)
6.3.2(2)
National choice is allowed in EN 1998-2 on the application of the following informative annexes:
Annex A Annex B Annex C
The National Annex can contain, directly or by reference, non-contradictory complementary
information for ease of implementation, provided it does not alter any provisions of the Eurocodes.
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1 Scope
1.1 Scope of EN 1998-2
(1) This document is applicable to the design and verification of new bridges in seismic regions. It
gives general rules for the design and verification relevant to bridges of consequence classes CC1, CC2
and CC3, as defined in prEN 1990:2021, A.2.
NOTE 1 EN 1998-2 covers the design of reinforced concrete, steel and composite steel-concrete bridges, with
the exception of prestressed piers. Guidance for design of timber bridges is given in Informative Annex C.
NOTE 2 The assessment of existing bridges is covered in EN 1998-3.
(2) Unless specifically stated, prEN 1998-1-1:2022 and prEN 1998-5:2022 apply.
(3) EN 1998-2 is applicable in complement to the other relevant Eurocodes.
NOTE EN 1998-2 contains only those provisions that, in addition to the provisions of the other relevant
Eurocodes, are used for the design of new bridges in seismic regions. EN 1998-2 complements in this respect the
other Eurocodes.
(4) EN 1998-2 provides basic performance requirements and compliance criteria applicable to new
bridges in seismic regions.
(5) EN 1998-2 is applicable to the seismic design of bridges exploiting ductility in structural members
or through the use of antiseismic devices.
(6) EN 1998-2 gives detailing rules for ductility of the structural members in bridges designed to
exploit ductility as a means of seismic protection. When ductility is exploited, EN 1998-2 primarily
covers bridges in which the horizontal seismic actions are mainly resisted through bending of the piers
or at the abutments, i.e. of bridges composed of vertical or nearly vertical pier systems supporting the
traffic deck superstructure.
(7) EN 1998-2 gives specific rules for bridges equipped with antiseismic devices, for cable-stayed and
extradosed bridges and for integral abutment bridges.
(8) EN 1998-2 is also applicable to the seismic design of arched bridges, although its provisions should
not be considered as fully covering these cases.
NOTE Suspension bridges and masonry bridges, moveable bridges and floating bridges are not included in
the scope of this Part.
1.2 Assumptions
(1) The assumptions of prEN 1998-1-1:2022, 1.2, are assumed to be applied.
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2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
NOTE See the Bibliography for a list of other documents cited that are not normative references, including
those referenced as recommendations (i.e. in ‘should’ clauses), permissions (‘may’ clauses), possibilities (‘can’
clauses), and in notes.
prEN 1998-1-1:2022 Eurocode 8 – Design of structures for earthquake resistance – Part 1-1: General rules
and seismic action
prEN 1998-5:2022, Eurocode 8 – Design of structures for earthquake resistance – Part 5: Geotechnical
aspects, foundations, retaining and underground structures
ISO 80000 (all parts), Quantities and units
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 1990, prEN 1998-1-1:2022,
3.1 and the following apply.
3.1.1
positive linkage
connection implemented by seismic links
3.1.2
spatial variability (of seismic action)
situation in which the ground motion at different supports of the bridge differs and, hence, the seismic
action cannot be based on the characterisation of the motion at a single point
3.1.3
longitudinal and transverse directions of the bridge
the longitudinal direction x is defined by the line connecting the centres of the two end-sections of the
deck. The transverse direction y is assumed to be orthogonal to the longitudinal direction
Note 1 to entry: In skew bridges, the above defined horizontal directions generally do not coincide with the
bearings’ principal axes of inertia, which can underestimate seismic effects if the two directions are considered
independently. For this reason, it is important that the skew is properly accounted for in the numerical model and
that the two horizontal directions of seismic action are properly combined.
3.1.4
seismic links
restrainers through which part or all of the seismic action may be transmitted. Used in combination
with bearings, they can be provided with appropriate slack, so as to be activated only in the case when
the design seismic displacement is exceeded
3.1.5
minimum overlap length
safety measure in the form of a minimum distance between the inner edge of the supported and the
outer edge of the supporting member. The minimum overlap is intended to ensure that the function of
the support is maintained under extreme seismic displacements
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3.1.6
design seismic displacement
displacement induced by the design seismic actions
3.1.7
total design displacement in the seismic design situation
displacement used to determine adequate clearances for the protection of critical or major structural
members. It includes the design seismic displacement, the displacement due to the long-term effect of
the permanent and quasi-permanent actions and an appropriate fraction of the displacement due to
thermal movements
3.1.8
critical region, critical zone
region/zone of a primary seismic member, where the most adverse combination of action effects (M, N,
V, T) occurs and where plastic hinges can form
Note 1 to entry: In concrete bridge piers, critical regions are potential dissipative zones such as defined in
prEN 1998-1-1:2022, 3.1.10. The length of the critical region is defined in 7.2.1.
3.1.9
skew bridge
bridge whose spans are not perpendicular to the axis of the supports, with an angle of skew (3.2.2.2)
larger than 20°
3.1.10
curved bridge
bridge with an angle between the initial and final tangents to the curved longitudinal axis larger than
25°. All other bridges are considered straight
3.1.11
ductile member
primary seismic member where a plastic hinge can form
3.2 Symbols and abbreviations
3.2.1 General
The symbols and abbreviations listed in prEN 1990:2021, 3.2 and in prEN 1998-1-1:2022, 3.2, apply.
For the symbols related to materials, as well as for symbols not specifically related to the seismic
situation, the provisions of the relevant Eurocodes should be applied.
Further symbols and abbreviations, used in connection with seismic actions, are defined in the present
standard where they occur, for ease of use. However, in addition, the most frequently occurring symbols
used in EN 1998-2 are listed and defined in 3.2.2 and additional abbreviations are given in 3.2.3.
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3.2.2 Symbols
3.2.2.1 Symbols used in 4
3.2.2.1.1 Lower case Latin symbols
d Design seismic displacement (due only to the design seismic action)
E
d Total design displacement in the seismic design situation
Ed
d Long-term relative displacement due to permanent and quasi-permanent actions
G
dT Displacement due to thermal movements
k , k Stiffness of timber fasteners or connectors
u d
3.2.2.1.2 Lower case Greek symbols
η Normalised axial force
k
ψ Combination factor for the quasi-permanent value of the thermal action
3.2.2.2 Symbols used in 5
3.2.2.2.1 Upper case Latin symbols
A Concrete area of the cross-section
c
B Width of the deck
E Seismic action effects
d
E Deformation energy induced in component i by the seismic action
di
S
Quasi-static part of the seismic action effect
E
d
D
Dynamic part of the seismic action effect
E
d
S
Contribution of the k-th static mode under the peak ground displacement at support k.
E
dk
E Seismic action effects due to higher quasi-antisymmetric modes
d,i
E Seismic action effects due to uniform excitation
d,u
D
Contribution of the i-th mode under the design seismic action
E
di
D
i-th mode response to the seismic input (response spectrum) at the k-th support
E
dik
F Horizontal force
F Static force on pier i in the lateral forces method
i
F Static forces due to the contribution of higher quasi-antisymmetric modes
i
F Seismic base shear force
b
L Total length of the continuous deck
Total length of the bridge
Llim
Total bridge mass above the foundations
M
M Equivalent modal mass
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M Maximum value of design moment at the intended plastic hinge location of ductile member i
Ed,i
as derived from the analysis for the seismic design situation
M Design flexural resistance of the same section with its actual reinforcement under the
Rd,i
concurrent action of the non-seismic action effects in the seismic design situation
M Equivalent static moment
t
N Axial force at the plastic hinge seismic design situation
Ed
N , Number of static and dynamic modes used in the analysis of long bridges on non-uniform
S
N soil
D
P Total vertical force acting at the top of the pier
tot
Q Variable gravity loads as appearing in the seismic design situation
k,i
Mode amplification factor
SF
i
T Fundamental period in the considered direction
T Fundamental period of the i-th pier or i-th modal period from modal analysis
i
V Shear force acting on the pier in the seismic design situation
p
3.2.2.2.2 Lower case Latin symbols
a Shear span ratio (=L /h)
s V
d Design pier top displacement under the design seismic action
E,p
d Average of the piers top displacements under a transverse uniformly distributed load on the
m
deck
e Total eccentricity (e + e )
a d
e Theoretical eccentricity between the centre of stiffness of the supporting members and the
o
centre of mass of the deck
e Accidental eccentricity
a
e Additional eccentricity reflecting the dynamic effect of simultaneous translational and
d
torsional vibration
f Characteristic concrete strength
ck
h Depth of basin or pier height
q’ Reduced value of q-factor
q Reduced value of the ductility-related q-factor component due to axial force
D,N
q Reduced value of the ductility-related q-factor component due to soil-structure interaction
D,SSI
m Mass over the i-th support
i
r
i M
Ed,i
Parameter defined as rq=
i
M
Rd,i
Correlation coefficient between dynamic modes
r
ij
r Vector collecting the k-th static mode
k
r Minimum value of r among all ductile members i
min i
r Maximum value of r among all ductile members i
max i
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s Displacement over the i-th support in the horizontal direction when the structure is acted
i
upon by the acceleration of gravity
3.2.2.2.3 Upper case Greek symbols
i-th modal participation factor due to spatially variable excitation
Γ
i
Δd Maximum difference in displacement between any two pier tops under a transverse uniformly
distributed load on the deck
3.2.2.2.4 Lower case Greek symbols
η Damping correction factor for the elastic response spectrum
η Normalised axial force
k
θ Pier top displacement sensitivity coefficient
λ Factor for the calculation of behaviour factor q
ξ Equivalent viscous damping ratio
ξ Equivalent viscous damping ratio of component i
i
ξ Effective viscous damping of the structure
eff
ρ, Parameters for regular seismic behaviour
ρ
o
ρ Correlation coefficient between seismic input motion at different supports
kl
φ Parameter for calculating ψ or skew angle (angle between the longitudinal axis of the bridge
Ei
and a line perpendicular to the alignment of intermediate or end supports)
φ i-th modal shape from modal analysis
i
ψ Combination coefficients
E,i
3.2.2.3 Symbols used in 6
3.2.2.3.1 Upper case Latin symbols
A Design action effects in the seismic design situation
Ed
A Effective area of the joint
j,eff
M Design moment in the seismic design situation
Ed
M Overstrength moment
o
M Design value of the flexural resistance of the section
Rd
N Axial force of the pier under the non-seismic actions in the seismic design situation
cG
N Axial force in the seismic design situation
Ed
N Vertical axial joint force
jz
N Horizontal axial joint force
jx
Njy Horizontal axial joint force in the transverse direction
T Resultant force of the tensile reinforcement of the pier corresponding to the design
Rc
flexural resistance, M , of the plastic hinge
Rd
V Shear force of the horizontal member adjacent to the tensile face of the pier,
b1C
oSIST prEN 1998-2:2023
prEN 1998-2:2022 (E)
corresponding to the capacity design effects of the plastic hinge
V Minimum joint shear resistance
Rdj,min
V Design horizontal shear force of the joint
jx
V Design vertical shear force of the joint
jz
3.2.2.3.2 Lower case Latin symbols
b , Cross-section width of the pier
c
b , Effective width of the joint
j
b Cross-section width of the web of the deck
w
d Diameter of circular pier
c
f Design value of the tensile strength of concrete
ctd
f Design value of the tensile strength of the horizontal reinforcement in the joint
yd,h
h Cross-section depth of the “beam” (e.g. deck)
b
h Cross-section depth of the pier
c
l Critical region length
cr
3.2.2.3.3 Lower case Greek symbols
n , n , n Joint axial stresses
x y z
v , v , v Joint shear stresses
x y z
z , z Internal lever arms of pier and deck, respectively
c b
β Angle between the vertical and the diagonal of the joint
Overstrength factor
γRd
η Normalised axial force
k
θ Chord rotation
σ Stress in the horizontal reinforcement in the joint
sh
ω Material randomness factor
rm
ω Strain hardening factor
sh
3.2.2.4 Further symbols used in 7
3.2.2.4.1 Upper case Latin symbols
A Area of the gross concrete section
c
A Confined (core) concrete area of the section to the hoop centre line
cc
A Area of the spiral or hoop bar
sp
A Area of the horizontal
...
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