1.6.2 Further symbols used in Sections 2 and 3 of EN 1998-1 AEd design value of seismic action = γI.AEk AEk characteristic value of the seismic action for the reference return period
S COPE
Scope of EN 1998
(1)P EN 1998 applies to the design and construction of buildings and civil engineering works in seismic regions Its purpose is to ensure that in the event of earthquakes:
− structures important for civil protection remain operational
The unpredictable nature of seismic events, combined with limited resources to mitigate their impacts, means that achieving protection goals is only partially feasible and can only be assessed probabilistically The level of protection available for various building types is determined by the optimal allocation of resources, which is expected to differ across countries based on the significance of seismic risks compared to other risks and the overall economic resources available.
(2)P Special structures, such as nuclear power plants, offshore structures and large dams, are beyond the scope of EN 1998
Eurocode 8 (EN 1998) outlines essential guidelines for designing structures in seismic areas, supplementing the existing provisions of other relevant Eurocodes It serves to enhance the overall framework for earthquake-resistant design.
(4) EN 1998 is subdivided into various separate Parts (see 1.1.2 and 1.1.3).
Scope of EN 1998-1
EN 1998-1 governs the design of buildings and civil engineering structures in seismic zones, consisting of 10 sections, with several sections specifically focused on building design.
(2) Section 2 of EN 1998-1 contains the basic performance requirements and compliance criteria applicable to buildings and civil engineering works in seismic regions
(3) Section 3 of EN 1998-1 gives the rules for the representation of seismic actions and for their combination with other actions Certain types of structures, dealt with in
EN 1998-2 to EN 1998-6, need complementing rules which are given in those Parts
(4) Section 4 of EN 1998-1 contains general design rules relevant specifically to buildings
(5) Sections 5 to 9 of EN 1998-1 contain specific rules for various structural materials and elements, relevant specifically to buildings as follows:
− Section 5: Specific rules for concrete buildings;
− Section 6: Specific rules for steel buildings;
− Section 7: Specific rules for composite steel-concrete buildings;
− Section 8: Specific rules for timber buildings;
− Section 9: Specific rules for masonry buildings
(6) Section 10 contains the fundamental requirements and other relevant aspects of design and safety related to base isolation of structures and specifically to base isolation of buildings
NOTE Specific rules for isolation of bridges are developed in EN 1998-2
(7) Annex C contains additional elements related to the design of slab reinforcement in steel-concrete composite beams at beam-column joints of moment frames
NOTE Informative Annex A and informative Annex B contain additional elements related to the elastic displacement response spectrum and to target displacement for pushover analysis.
Further Parts of EN 1998
(1)P Further Parts of EN 1998 include, in addition to EN 1998-1, the following:
− EN 1998-2 contains specific provisions relevant to bridges;
− EN 1998-3 contains provisions for the seismic assessment and retrofitting of existing buildings;
− EN 1998-4 contains specific provisions relevant to silos, tanks and pipelines;
− EN 1998-5 contains specific provisions relevant to foundations, retaining structures and geotechnical aspects;
− EN 1998-6 contains specific provisions relevant to towers, masts and chimneys.
N ORMATIVE R EFERENCES
General reference standards
EN 1990 Eurocode - Basis of structural design
EN 1992-1-1 Eurocode 2 – Design of concrete structures – Part 1-1: General –
Common rules for building and civil engineering structures
EN 1993-1-1 Eurocode 3 – Design of steel structures – Part 1-1: General – General rules
EN 1994-1-1 Eurocode 4 – Design of composite steel and concrete structures – Part 1-
1: General – Common rules and rules for buildings
EN 1995-1-1 Eurocode 5 – Design of timber structures – Part 1-1: General – Common rules and rules for buildings
EN 1996-1-1 Eurocode 6 – Design of masonry structures – Part 1-1: General –Rules for reinforced and unreinforced masonry
EN 1997-1 Eurocode 7 - Geotechnical design – Part 1: General rules
Reference Codes and Standards
(1)P For the application of EN 1998, reference shall be made to EN 1990 to
(2) EN 1998 incorporates other normative references cited at the appropriate places in the text They are listed below:
ISO 1000 The international system of units (SI) and its application; prEN 12512 Timber structures – Test methods – Cyclic testing of joints made with mechanical fasteners.
A SSUMPTIONS
(1) In addition to the general assumptions of EN 1990:2002, 1.3, the following assumption applies
It is assumed that the structure will remain unchanged throughout the construction phase and its lifespan, unless adequate justification and verification are provided This principle holds true even for modifications that may enhance the structural resistance, given the unique nature of seismic response.
D ISTINCTION BETWEEN PRINCIPLES AND APPLICATION RULES
(1) The rules of EN 1990:2002, 1.4 apply.
T ERMS AND DEFINITIONS
Terms common to all Eurocodes
(1) The terms and definitions given in EN 1990:2002, 1.5 apply
EN 1090-2 Execution of steel structures and aluminium structures – Part 2:
Technical requirements for steel structures;
EN 1993-1-8 Eurocode 3: Design of steel structures – Part 1-8: Design of joints;
EN 1993-1-10 Eurocode 3 focuses on the design of steel structures, specifically addressing material toughness and through-thickness properties It introduces the behaviour factor, which is essential for adjusting forces derived from linear analysis to reflect the non-linear response of structures, influenced by material characteristics, structural systems, and design methods The capacity design approach involves selecting and designing structural elements to effectively dissipate energy during severe deformations, while ensuring that other elements possess adequate strength to support these energy dissipation mechanisms Dissipative structures are characterized by their ability to dissipate energy through ductile hysteretic behavior and other methods, with predetermined dissipative zones where these capabilities are concentrated.
NOTE 1 These are also called critical regions dynamically independent unit structure or part of a structure which is directly subjected to the ground motion and whose response is not affected by the response of adjacent units or structures importance factor factor which relates to the consequences of a structural failure non-dissipative structure structure designed for a particular seismic design situation without taking into account the non-linear material behaviour non-structural element architectural, mechanical or electrical element, system and component which, whether due to lack of strength or to the way it is connected to the structure, is not considered in the seismic design as load carrying element primary seismic members members considered as part of the structural system that resists the seismic action, modelled in the analysis for the seismic design situation and fully designed and detailed for earthquake resistance in accordance with the rules of EN 1998 secondary seismic members members which are not considered as part of the seismic action resisting system and whose strength and stiffness against seismic actions is neglected
NOTE 2 They are not required to comply with all the rules of EN 1998, but are designed and detailed to maintain support of gravity loads when subjected to the displacements caused by the
Further terms used in EN 1998
(1) The following terms are used in EN 1998-1 with the following meanings:
S YMBOLS
General
(1) The symbols indicated in EN 1990:2002, 1.6 apply For the material-dependent symbols, as well as for symbols not specifically related to earthquakes, the provisions of the relevant Eurocodes apply
Further symbols related to seismic actions are defined within the text for convenience Additionally, the most commonly used symbols in EN 1998-1 are listed and explained in sections 1.6.2 and 1.6.3.
Further symbols used in Sections 2 and 3 of EN 1998-1
A Ed design value of seismic action ( = γ I A Ek )
A Ek characteristic value of the seismic action for the reference return period
E d design value of action effects
N SPT Standard Penetration Test blow-count
P NCR reference probability of exceedance in 50 years of the reference seismic action for the no-collapse requirement
The elastic horizontal ground acceleration response spectrum, known as the "elastic response spectrum," indicates that at T=0, the spectral acceleration corresponds to the design ground acceleration on type A ground, multiplied by the soil factor S.
S ve(T) elastic vertical ground acceleration response spectrum
S De(T) elastic displacement response spectrum
S d(T) design spectrum (for elastic analysis)
T vibration period of a linear single degree of freedom system
T s duration of the stationary part of the seismic motion
The NCR reference return period defines the duration for the reference seismic action necessary to meet the no-collapse requirement The reference peak ground acceleration (\$a_{gR}\$) and the design ground acceleration (\$a_{g}\$) are both measured on type A ground, while the design ground acceleration in the vertical direction is represented as \$a_{vg}\$ Additionally, the undrained shear strength of the soil is denoted as \$c_{u}\$, and the design ground displacement is indicated by \$d_{g}\$ The acceleration of gravity is represented by \$g\$, and the behavior factor is denoted as \$q\$.
The average propagation velocity of S waves in the upper 30 meters of the soil profile is denoted as \$v_s,30\$ and is measured at a shear strain of \$10^{-5}\$ or less The importance factor is represented by \$\gamma I\$, while the damping correction factor is indicated by \$\eta\$ The viscous damping ratio, expressed in percent, is denoted as \$\xi\$ Additionally, the combination coefficient for the quasi-permanent value of a variable action \$i\$ is represented by \$\psi_{2,i}\$, and the combination coefficient for a variable action \$i\$ used in determining the effects of the design seismic action is denoted as \$\psi_{E,i}\$.
Further symbols used in Section 4 of EN 1998-1
E E effect of the seismic action
E Edx, E Edy design values of the action effects due to the horizontal components (x and y) of the seismic action
E Edz design value of the action effects due to the vertical component of the seismic action
F i horizontal seismic force at storey i
F a horizontal seismic force acting on a non-structural element (appendage)
H building height from the foundation or from the top of a rigid basement
L max, L min larger and smaller in plan dimension of the building measured in orthogonal directions
S a seismic coefficient for non-structural elements
T 1 fundamental period of vibration of a building
T a fundamental period of vibration of a non-structural element (appendage)
In seismic design, key parameters include the weight of non-structural elements (appendages), displacement, and design interstorey drift Accidental eccentricity refers to the mass of a storey being offset from its nominal location, while interstorey height and the mass of each storey are crucial for understanding building dynamics The number of storeys above the foundation impacts overall stability, and the behaviour factor of non-structural elements, along with the displacement behaviour factor, plays a significant role in performance assessment Additionally, the displacement of mass in the fundamental mode shape and the height of mass above the seismic action application level are critical for accurate modeling The ratio of design ground acceleration to gravity, along with the importance factor and overstrength factor for diaphragms, further influences the design process Lastly, the interstorey drift sensitivity coefficient is essential for evaluating the response of structures during seismic events.
Further symbols used in Section 5 of EN 1998-1
A c Area of section of concrete member
A sh total area of horizontal hoops in a beam-column joint
A si total area of steel bars in each diagonal direction of a coupling beam
A st area of one leg of the transverse reinforcement
A sv total area of the vertical reinforcement in the web of the wall
A sv,i total area of column vertical bars between corner bars in one direction through a joint
In a wall reinforced with inclined bars to resist sliding shear, the total horizontal cross-sectional area is denoted as \$w\$, while \$\Sigma A_{si}\$ represents the sum of the areas of all inclined bars in both directions Additionally, \$\Sigma A_{sj}\$ indicates the sum of the areas of vertical bars within the wall or extra bars placed in the boundary elements for enhanced sliding shear resistance The design values of moments of resistance for beams framing into a joint in the direction of interest are summed as \$\Sigma M_{Rb}\$, and for columns framing into the same joint, the sum is represented as \$\Sigma M_{Rc}\$.
D o diameter of confined core in a circular column
M i,d end moment of a beam or column for the calculation of its capacity design shear
M Rb,i design value of beam moment of resistance at end i
M Rc,i design value of column moment of resistance at end i
N Ed axial force from the analysis for the seismic design situation
T 1 fundamental period of the building in the horizontal direction of interest
T C corner period at the upper limit of the constant acceleration region of the elastic spectrum
V’Ed shear force in a wall from the analysis for the seismic design situation
V dd dowel resistance of vertical bars in a wall
V Ed design shear force in a wall
V Ed,max maximum acting shear force at end section of a beam from capacity design calculation
V Ed,min minimum acting shear force at end section of a beam from capacity design calculation
V fd contribution of friction to resistance of a wall against sliding shear
V id contribution of inclined bars to resistance of a wall against sliding shear
V Rd,c design value of shear resistance for members without shear reinforcement in accordance with EN1992-1-1:2004
The design value of shear resistance against sliding, denoted as \( V_{Rd,S} \), is influenced by various parameters including the width of the bottom flange of the beam (\( b \)), the cross-sectional dimensions of the column (\( b_c \)), and the effective flange width of the beam in tension at the face of a supporting column (\( b_{eff} \)) Additionally, the effective depth of the section (\( d \)), longitudinal bar diameter (\( d_{bL} \)), and design values of concrete compressive strength (\( f_{cd} \)) and yield strength of steel (\( f_{yd} \)) are critical in structural design The spacing of transverse reinforcement (\( s \)), neutral axis depth (\( x_u \)), and internal lever arm (\( z \)) also play significant roles in ensuring structural integrity Factors such as the confinement effectiveness factor (\( \alpha \)), partial factors for concrete (\( \gamma_c \)) and steel (\( \gamma_s \)), and the tension reinforcement ratio (\( \rho \)) are essential for evaluating the performance of structural elements under seismic conditions Understanding these parameters is vital for achieving optimal design and safety in construction.
Further symbols used in Section 6 of EN 1998-1
M Ed design bending moment from the analysis for the seismic design situation
M pl,RdA design value of plastic moment resistance at end A of a member
M pl,RdB design value of plastic moment resistance at end B of a member
N Ed design axial force from the analysis for the seismic design situation
N Ed,E axial force from the analysis due to the design seismic action alone
N Ed,G axial force due to the non-seismic actions included in the combination of actions for the seismic design situation
N pl,Rd design value of yield resistance in tension of the gross cross-section of a member in accordance with EN 1993-1-1:2005
N Rd(M Ed,V Ed) design value of axial resistance of column or diagonal in accordance with
EN 1993-1-1:2005 , taking into account the interaction with the bending moment M Ed and the shear V Ed in the seismic situation
R d resistance of connection in accordance with EN 1993-1-1:2005
R fy plastic resistance of connected dissipative member based on the design yield stress of material as defined in EN 1993-1-1:2005
V Ed design shear force from the analysis for the seismic design situation
V Ed,G shear force due to the non seismic actions included in the combination of actions for the seismic design situation
V Ed,M shear force due to the application of the plastic moments of resistance at the two ends of a beam
V pl,Rd design value of shear resistance of a member in accordance with EN 1993-
V wp,Ed design shear force in web panel due to the design seismic action effects
V wp,Rd design shear resistance of the web panel in accordance with EN 1993- 1-1: e length of seismic link f y nominal yield strength of steel
q behaviour factor t w web thickness of a seismic link t f flange thickness of a seismic link
The multiplicative factor on axial force \( N_{Ed,E} \) is derived from the analysis of design seismic action for non-dissipative members in concentric or eccentric braced frames, as specified in Clauses 6.7.4 and 6.8.3 The ratio \( \alpha \) represents the smaller design bending moment \( M_{Ed,A} \) at one end of a seismic link compared to the greater bending moment \( M_{Ed,B} \) at the end where the plastic hinge forms, with both moments considered in absolute value The multiplier \( \alpha_1 \) indicates the horizontal design seismic action at the formation of the first plastic hinge in the system, while \( \alpha_u \) denotes the multiplier of horizontal seismic design action at the formation of a global plastic mechanism Additionally, \( \gamma_M \) is the partial factor for material properties, \( \gamma_{ov} \) is the material overstrength factor, and \( \delta \) represents the beam deflection at midspan relative to the tangent to the beam axis at the beam end.
The multiplicative factor \( \gamma_{pb} \) influences the design value \( N_{pl,Rd} \) of yield resistance in tension for compression braces in V bracing, which is essential for estimating the unbalanced seismic action effects on the connected beam Additionally, the partial factor for steel \( \gamma_s \), the rotation capacity \( \theta_p \) of the plastic hinge region, and the non-dimensional slenderness \( \lambda \) of a member, as defined in EN 1993-1-1:2005, are critical parameters in this analysis.
Further symbols used in Section 7 of EN 1998-1
A pl horizontal area of the plate
E a Modulus of Elasticity of steel
E cm mean value of Modulus of Elasticity of concrete in accordance with EN 1992-1-1:
I a second moment of area of the steel section part of a composite section, with respect to the centroid of the composite section
I c second moment of area of the concrete part of a composite section, with respect to the centroid of the composite section
I eq equivalent second moment of area of the composite section
I s second moment of area of the rebars in a composite section, with respect to the centroid of the composite section
The design value of plastic moment resistance for a column, denoted as \( M_{pl,Rd,c} \), is established as a lower bound This value is calculated by considering the concrete component of the section along with only the ductile steel components.
The upper bound plastic resistance of a beam, denoted as \( M_{U,Rd,b} \), is calculated by considering both the concrete and all steel components within the section, including those that are not classified as ductile.
V wp,Ed design shear force in web panel, computed on the basis of the plastic resistance of the adjacent dissipative zones in beams or connections
The design shear resistance of the composite steel-concrete web panel is determined according to EN 1994-1-1:2004 Key dimensions include the flange width (\$b\$), the width of the composite beam, and the bearing width of the concrete slab on the column The partial effective width of the flange on each side of the steel web is denoted as \$b_e\$, while the total effective width of the concrete flange is represented by \$b_{eff}\$ Additionally, the minimum dimension of the confined concrete core is indicated as \$b_o\$, and the diameters of the longitudinal rebars and hoops are denoted as \$d_{bL}\$ and \$d_{bw}\$, respectively The design yield strength of steel is represented by \$f_{yd}\$, with specific values for the flange (\$f_{ydf}\$) and web reinforcement (\$f_{ydw}\$) The depths of the composite beam and column section are indicated as \$h_b\$ and \$h_c\$, while the rib shape efficiency factor of profiled steel sheeting is denoted as \$k_r\$ Finally, the reduction factor for the design shear resistance of connectors is represented by \$k_t\$.
The Eurocode 1994-1-1:2004 outlines key parameters for composite columns, including the clear length of the column (l cl) and the length of the critical region (l cr) It defines the steel-to-concrete modular ratio (n) for short-term actions and introduces the behavior factor (q) and reduction factor (r) for concrete rigidity in stiffness calculations Additionally, it specifies the thickness of the flange (t f) and various partial factors such as γ c for concrete, γ M for material properties, γ ov for material overstrength, and γ s for steel The document also addresses the total strain of steel at the Ultimate Limit State (ε a) and the ultimate compressive strain of unconfined concrete (ε cu2), along with the minimum degree of connection (η) as per section 6.6.1.2.
Further symbols used in Section 8 of EN 1998-1
The Modulus of Elasticity of timber under instantaneous loading is influenced by several factors, including the width of the timber section (b), the diameter of the fastener (d), and the depth of the timber beams (h) Additionally, the modification factor for instantaneous loading on the strength of timber, as specified in EN 1995-1-1:2004, is represented by (k) The behavior factor (q) and the partial factor for material properties (γ M) also play crucial roles in determining the overall performance of timber structures.
Further symbols used in Section 9 of EN 1998-1
a g,urm upper value of the design ground acceleration at the site for use of unreinforced masonry satisfying the provisions of Eurocode 8
To ensure compliance with the rules for "simple masonry buildings," a minimum total cross-section area of masonry walls is required in each horizontal direction This includes the normalized compressive strength of masonry units, both normal (\$f_{b,min}\$) and parallel (\$f_{bh,min}\$) to the bed face, as well as the minimum strength for mortar (\$f_{m,min}\$) Additionally, factors such as the greater clear height of openings adjacent to the wall (\$h\$), the effective height of the wall (\$h_{ef}\$), and the length of the wall (\$l\$) must be considered The number of storeys above ground (\$n\$) and the minimum sum of horizontal cross-sectional areas of shear walls in each direction (\$p_{A,min}\$) are also critical, expressed as a percentage of the total floor area per storey Furthermore, the maximum percentage of the total floor area above the level (\$p_{max}\$), the behavior factor (\$q\$), and the effective thickness of the wall (\$t_{ef}\$) play significant roles in structural integrity.
∆ A,max maximum difference in horizontal shear wall cross-sectional area between adjacent storeys of “simple masonry buildings”
The maximum mass difference between adjacent storeys in simple masonry buildings is denoted as ∆m,max The partial factors for masonry properties are represented by γm, while γs indicates the partial factor for reinforcing steel Additionally, λmin refers to the ratio of the length of the shorter side to the length of the longer side in the building's plan.
Further symbols used in Section 10 of EN 1998-1
K eff effective stiffness of the isolation system in the principal horizontal direction under consideration, at a displacement equal to the design displacement d dc
K V total stiffness of the isolation system in the vertical direction
K xi effective stiffness of a given unit i in the x direction
K yi effective stiffness of a given unit i in the y direction
T eff effective fundamental period of the superstructure corresponding to horizontal translation, the superstructure assumed as a rigid body
T f fundamental period of the superstructure assumed fixed at the base
T V fundamental period of the superstructure in the vertical direction, the superstructure assumed as a rigid body
The M s magnitude represents the effective stiffness center's design displacement in the specified direction, while d db indicates the total design displacement of an isolator unit Additionally, e tot,y refers to the total eccentricity in the y direction, and f j denotes the horizontal forces acting at each level j Lastly, r y signifies the torsional radius of the isolation system.
(x i,y i) co-ordinates of the isolator unit i relative to the effective stiffness centre δ i amplification factor ξ eff “effective damping”
S.I U NITS
(1)P S.I Units in accordance with ISO 1000 shall be used
(2) For calculations, the following units are recommended:
− forces and loads: kN, kN/m, kN/m 2
− stresses and strengths: N/mm 2 (= MN/m 2 or MPa), kN/m 2 (=kPa)
2 PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA
F UNDAMENTAL REQUIREMENTS
(1)P Structures in seismic regions shall be designed and constructed in such a way that the following requirements are met, each with an adequate degree of reliability
The structure must be designed to endure the specified seismic action outlined in Section 3, ensuring it does not experience local or global collapse, thereby maintaining its structural integrity and residual load-bearing capacity post-seismic events The design seismic action is defined by the reference seismic action linked to a probability of exceedance, P NCR, over 50 years or a reference return period, T NCR, along with the importance factor γ I, as detailed in EN 1990:2002 and clauses (2)P and (3)P, to account for variations in reliability.
The recommended values for P NCR and T NCR applicable in a specific country can be found in its National Annex of this document, with P NCR expressed as a percentage and T NCR set at 475 years.
The probability of exceedance, \( P_R \), over \( T_L \) years for a specific level of seismic action is connected to the mean return period, \( T_R \), through the formula \( T_R = -\frac{T_L}{\ln(1 - P_R)} \) Therefore, for a specified \( T_L \), the seismic action can be defined in terms of either its mean return period, \( T_R \), or its probability of exceedance.
The structure must be engineered to endure seismic actions with a higher probability of occurrence than the design seismic action, ensuring no damage occurs and avoiding excessive limitations on use that would incur disproportionately high costs compared to the structure's overall expenses For the "damage limitation requirement," the seismic action considered should have a probability of exceedance, P DLR, within a 10-year timeframe and a corresponding return period.
In the absence of detailed information, the reduction factor specified in section 4.4.3.2(2) can be utilized to determine the seismic action necessary for verifying compliance with the damage limitation requirement.
The recommended values for P DLR and T DLR can be found in the National Annex of this document, with P DLR expressed as a percentage and T DLR set at 95 years.
National Authorities set target reliabilities for the no-collapse and damage limitation requirements based on the potential consequences of failure for various types of buildings and civil engineering works.
Reliability differentiation in structural design involves categorizing structures into various importance classes, each assigned an importance factor \( \gamma_I \) This factor should ideally reflect the corresponding return period of seismic events, adjusted according to the reference return period, to ensure appropriate design for each structure category.
The various levels of reliability are determined by multiplying the reference seismic action or, in the case of linear analysis, the relevant action effects by an importance factor Comprehensive guidance on the importance classes and their associated factors can be found in the applicable sections of EN 1998.
The annual rate of exceedance of the reference peak ground acceleration, denoted as \( H(a_{gR}) \), typically varies with \( a_{gR} \) according to the relationship \( H(a_{gR}) \sim k_0 a_{gR}^{-k} \), where the exponent \( k \) is influenced by seismicity and generally approximates to 3 To determine the importance factor \( \gamma_I \) that adjusts the reference seismic action for a specific probability of exceedance over a given time period \( T_L \), it can be calculated using the formula \( \gamma_I \sim (T_{LR}/T_L)^{-1/k} \) Alternatively, if the goal is to achieve a different probability of exceeding the seismic action \( P_L \) over the same duration \( T_L \), the importance factor can be estimated as \( \gamma_I \sim (P_L/P_{LR})^{-1/k} \).
C OMPLIANCE C RITERIA
General
(1)P In order to satisfy the fundamental requirements in 2.1 the following limit states shall be checked (see 2.2.2 and 2.2.3):
Ultimate limit states are those associated with collapse or with other forms of structural failure which might endanger the safety of people
Damage limitation states are those associated with damage beyond which specified service requirements are no longer met
To mitigate uncertainties and ensure the structural integrity during seismic events that exceed design expectations, it is essential to implement specific measures.
(3) For well defined categories of structures in cases of low seismicity (see
3.2.1(4)), the fundamental requirements may be satisfied through the application of rules simpler than those given in the relevant Parts of EN 1998
(4) In cases of very low seismicity, the provisions of EN 1998 need not be observed (see 3.2.1(5) and the notes therein for the definition of cases of very low seismicity)
Section 9 outlines specific rules for "simple masonry buildings," which, when followed, ensure compliance with the fundamental requirements of EN 1998-1, eliminating the need for analytical safety verifications.
Ultimate limit state
(1)P It shall be verified that the structural system has the resistance and energy- dissipation capacity specified in the relevant Parts of EN 1998
The resistance and energy-dissipation capacity of a structure are linked to the extent of its non-linear response This balance is defined by the behavior factor \( q \) and ductility classification outlined in EN 1998 For low-dissipative structures, hysteretic energy dissipation is not considered, and the behavior factor is typically capped at 1.5 In contrast, for steel or composite steel-concrete buildings, the \( q \) factor ranges from 1.5 to 2 Dissipative structures, however, have a behavior factor exceeding these limits, reflecting the hysteretic energy dissipation occurring in specially designed zones known as dissipative zones or critical regions.
The behavior factor \( q \) must be constrained by the dynamic stability limit state of the structure and the potential damage from low-cycle fatigue, particularly in connections It is essential to apply the most unfavorable limiting conditions when determining the \( q \) factor values The \( q \) factor values specified in various Parts of EN 1998 are considered to meet this requirement.
The overall structure must be assessed for stability against design seismic actions, considering both overturning and sliding stability Detailed guidelines for evaluating the overturning of structures are provided in the applicable sections of EN 1998.
It is essential to ensure that both the foundation elements and the underlying soil can withstand the forces exerted by the superstructure without experiencing significant permanent deformations When assessing these reactions, it is important to consider the actual resistance that the structural elements can provide in transmitting these forces.
(5)P In the analysis the possible influence of second order effects on the values of the action effects shall be taken into account
It is essential to ensure that non-structural elements behave safely under design seismic actions, posing no risks to individuals and not adversely affecting the structural response Specific guidelines for buildings are outlined in sections 4.3.5 and 4.3.6.
Damage limitation state
(1)P An adequate degree of reliability against unacceptable damage shall be ensured by satisfying the deformation limits or other relevant limits defined in the relevant Parts of EN 1998
In civil protection structures, it is essential to verify that the structural system possesses adequate resistance and stiffness to ensure the functionality of vital services during a seismic event, considering an appropriate return period.
Specific measures
Structures should ideally feature simple and regular forms in both plan and elevation If needed, this can be achieved by dividing the structure into dynamically independent units through the use of joints.
To achieve a ductile and dissipative behavior in structures, it is crucial to prevent brittle failure and the early onset of unstable mechanisms This can be accomplished by employing the capacity design procedure outlined in the relevant Parts of EN 1998, which helps establish the hierarchy of resistance among different structural components and failure modes This approach is essential for ensuring an effective plastic mechanism while avoiding brittle failure modes.
The seismic performance of a structure heavily relies on the behavior of its critical regions and elements Therefore, the detailing of the structure, especially in these areas, must ensure the capacity to transmit necessary forces and dissipate energy during cyclic conditions Special attention should be given to the design of connections between structural elements and regions anticipated to exhibit non-linear behavior.
The analysis will utilize a suitable structural model that considers soil deformability, non-structural elements, and factors like nearby structures when necessary.
(1)P The stiffness of the foundations shall be adequate for transmitting the actions received from the superstructure to the ground as uniformly as possible
(2) With the exception of bridges, only one foundation type should in general be used for the same structure, unless the latter consists of dynamically independent units
The design documents must specify the sizes, details, and characteristics of the materials used for structural elements Additionally, they should include information on any special devices and the spacing between structural and non-structural elements, along with necessary quality control measures.
Elements of special structural significance that necessitate thorough verification during construction must be clearly marked on the design drawings, along with the specified methods for checking these elements.
In areas with high seismic activity and for structures of significant importance, it is essential to implement formal quality system plans that encompass design, construction, and usage, in addition to the control procedures outlined in the relevant Eurocodes.
3 GROUND CONDITIONS AND SEISMIC ACTION
G ROUND CONDITIONS
Identification of ground types
Ground types A, B, C, D, and E, detailed in Table 3.1, can be utilized to assess the impact of local ground conditions on seismic activity Additionally, considering the effects of deep geology can further enhance the understanding of seismic actions.
The ground classification scheme that considers deep geology can be detailed in a country's National Annex, which includes the parameters S, T_B, T_C, and T_D that define the horizontal and vertical elastic response spectra as outlined in section 3.2.2.2.
Ground type Description of stratigraphic profile Parameters v s,30 (m/s) N SPT
A Rock or other rock-like geological formation, including at most 5 m of weaker material at the surface
B Deposits of very dense sand, gravel, or very stiff clay, at least several tens of metres in thickness, characterised by a gradual increase of mechanical properties with depth
C Deep deposits of dense or medium- dense sand, gravel or stiff clay with thickness from several tens to many hundreds of metres
D Deposits of loose-to-medium cohesionless soil (with or without some soft cohesive layers), or of predominantly soft-to-firm cohesive soil
E A soil profile consisting of a surface alluvium layer with v s values of type C or D and thickness varying between about 5 m and 20 m, underlain by stiffer material with v s > 800 m/s
S 1 Deposits consisting, or containing a layer at least 10 m thick, of soft clays/silts with a high plasticity index
(PI > 40) and high water content
S 2 Deposits of liquefiable soils, of sensitive clays, or any other soil profile not included in types A – E or S 1
(2) The site should be classified according to the value of the average shear wave velocity, v s,30, if this is available Otherwise the value of N SPT should be used
(3) The average shear wave velocity v s,30 should be computed in accordance with the following expression:
The equation \( i i s,30 30 i v v h (3.1) \) represents the relationship between the thickness \( h_i \) (in meters) and the shear-wave velocity \( v_i \) (measured at a shear strain level of \( 10^{-5} \) or less) for the \( i \)-th formation or layer within the top 30 meters, comprising a total of \( N \) layers.
For sites with ground conditions classified as special ground types S1 or S2, it is essential to conduct specialized studies to define the seismic action This is particularly crucial for type S2, where the potential for soil failure during seismic events must be considered.
When dealing with ground type S 1 deposits, it is crucial to recognize their very low shear wave velocity (\$v_s\$), low internal damping, and unusually extended linear behavior range These characteristics can lead to unusual seismic site amplification and soil-structure interaction effects, as outlined in EN 1998-5:2004, Section 6 Therefore, a specialized study is necessary to determine the seismic action, focusing on how the response spectrum is influenced by the thickness and \$v_s\$ value of the soft clay or silt layer, as well as the stiffness contrast with the underlying materials.
S EISMIC ACTION
Seismic zones
For EN 1998, national authorities are responsible for dividing territories into seismic zones based on local hazards, with the understanding that the hazard level within each zone remains constant.
In EN 1998 applications, the primary hazard is represented by a single parameter: the reference peak ground acceleration on type A ground, denoted as \( a_{gR} \) For particular structural types, additional parameters are specified in the relevant sections of EN 1998.
The reference peak ground acceleration on type A ground, denoted as \$a_{gR}\$, can be obtained from zonation maps available in the National Annex of a country or specific regions within it.
The reference peak ground acceleration for each seismic zone, determined by National Authorities, is linked to the reference return period \( T_{NCR} \) for the no-collapse requirement, which corresponds to a 50-year exceedance probability \( P_{NCR} \) An importance factor \( \gamma_I \) of 1.0 is applied to this reference return period For different return periods, the design ground acceleration on type A ground \( a_g \) is calculated as \( a_g = \gamma_I \cdot a_{gR} \), where \( a_{gR} \) is the reference ground acceleration.
(4) In cases of low seismicity, reduced or simplified seismic design procedures for certain types or categories of structures may be used
The National Annex of a country outlines the categories of structures, ground types, and seismic zones applicable for low seismicity provisions It is advisable to classify as low seismicity cases where the design ground acceleration on type A ground, \$a_g\$, does not exceed 0.08 g (0.78 m/s²) or where the product \$a_g \cdot S\$ is not greater than 0.1 g (0.98 m/s²) The determination of whether to use the value of \$a_g\$ or the product \$a_g \cdot S\$ to define low seismicity thresholds is specified in the National Annex.
(5)P In cases of very low seismicity, the provisions of EN 1998 need not be observed
The categories of structures, ground types, and seismic zones exempt from EN 1998 provisions due to very low seismicity are detailed in the National Annex of each country Very low seismicity is typically defined as cases where the design ground acceleration on type A ground, \$a_g\$, does not exceed 0.04 g (0.39 m/s²) or where the product \$a_g \cdot S\$ is less than 0.05 g (0.49 m/s²) The specific criteria for determining whether to use \$a_g\$ or the product \$a_g \cdot S\$ to establish the threshold for very low seismicity can also be found in the National Annex.
Basic representation of the seismic action
(1)P Within the scope of EN 1998 the earthquake motion at a given point on the surface is represented by an elastic ground acceleration response spectrum, henceforth called an “elastic response spectrum”
The elastic response spectrum maintains a consistent shape for both levels of seismic action, as outlined in sections 2.1(1)P and 2.2.1(1)P, addressing the no-collapse requirement (ultimate limit state – design seismic action) and the damage limitation requirement.
(3)P The horizontal seismic action is described by two orthogonal components assumed as being independent and represented by the same response spectrum
The seismic action can be represented by various response spectra shapes, which may vary based on the seismic sources and the magnitudes of the earthquakes they produce.
NOTE 1 The selection of the shape of the elastic response spectrum to be used in a country or part of the country may be found in its National Annex
NOTE 2 In selecting the appropriate shape of the spectrum, consideration should be given to the magnitude of earthquakes that contribute most to the seismic hazard defined for the purpose of probabilistic hazard assessment, rather than on conservative upper limits (e.g the Maximum Credible Earthquake) defined for that purpose
When earthquakes originate from various sources, it is essential to consider multiple spectral shapes to accurately represent the design seismic action In these cases, distinct values of acceleration due to gravity (a_g) are typically necessary for each spectrum and earthquake type.
(6) For important structures (γ I >1,0) topographic amplification effects should be taken into account
NOTE Informative Annex A of EN 1998-5:2004 provides information for topographic amplification effects
(7) Time-history representations of the earthquake motion may be used (see 3.2.3)
(8) Allowance for the variation of ground motion in space as well as time may be required for specific types of structures (see EN 1998-2, EN 1998-4 and EN 1998-6)
(1)P For the horizontal components of the seismic action, the elastic response spectrum S e (T) is defined by the following expressions (see Figure 3.1):
S e(T) is the elastic response spectrum;
T is the vibration period of a linear single-degree-of-freedom system; a g is the design ground acceleration on type A ground (a g = γ I a gR );
T B is the lower limit of the period of the constant spectral acceleration branch;
TC is the upper limit of the period of the constant spectral acceleration branch;
T D is the value defining the beginning of the constant displacement response range of the spectrum;
S is the soil factor; η is the damping correction factor with a reference value of η = 1 for 5% viscous damping, see (3) of this subclause
Figure 3.1: Shape of the elastic response spectrum
(2)P The values of the periods T B, T C and T D and of the soil factor S describing the shape of the elastic response spectrum depend upon the ground type
NOTE 1 The values to be ascribed to T B , T C , T D and S for each ground type and type (shape) of spectrum to be used in a country may be found in its National Annex If deep geology is not accounted for (see 3.1.2(1) ), the recommended choice is the use of two types of spectra: Type 1 and Type 2 If the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of probabilistic hazard assessment have a surface-wave magnitude, M s , not greater than 5,5, it is recommended that the Type 2 spectrum is adopted For the five ground types A, B,
C, D and E the recommended values of the parameters S, T B , T C and T D are given in Table 3.2 for the Type 1 Spectrum and in Table 3.3 for the Type 2 Spectrum Figure 3.2 and Figure 3.3 show the shapes of the recommended Type 1 and Type 2 spectra, respectively, normalised by a g, for 5% damping Different spectra may be defined in the National Annex, if deep geology is accounted for
Table 3.2: Values of the parameters describing the recommended Type 1 elastic response spectra
Table 3.3: Values of the parameters describing the recommended Type 2 elastic response spectra
Figure 3.2: Recommended Type 1 elastic response spectra for ground types A to E (5% damping)
Figure 3.3: Recommended Type 2 elastic response spectra for ground types A to E (5% damping)
Note 2 For ground types S 1 and S 2, special studies should provide the corresponding values of S,
(3) The value of the damping correction factor η may be determined by the expression:
= ξ η (3.6) whereξ is the viscous damping ratio of the structure, expressed as a percentage
(4) If for special cases a viscous damping ratio different from 5% is to be used, this value is given in the relevant Part of EN 1998
(5)P The elastic displacement response spectrum, S De(T), shall be obtained by direct transformation of the elastic acceleration response spectrum, S e(T), using the following expression:
(6) Expression (3.7) should normally be applied for vibration periods not exceeding
4,0 s For structures with vibration periods longer than 4,0 s, a more complete definition of the elastic displacement spectrum is possible
NOTE For the Type 1 elastic response spectrum referred to in Note 1 to 3.2.2.2(2)P, such a definition is presented in Informative Annex A in terms of the displacement response spectrum
For periods longer than 4,0 s, the elastic acceleration response spectrum may be derived from the elastic displacement response spectrum by inverting expression (3.7)
(1)P The vertical component of the seismic action shall be represented by an elastic response spectrum, S ve(T), derived using expressions (3.8)-(3.11)
The values for T B, T C, T D, and a vg for each type of vertical spectrum used in a country can be found in its National Annex It is recommended to use two types of vertical spectra: Type 1 and Type 2 For horizontal components of seismic action, if the contributing earthquakes have a surface-wave magnitude (M s) of 5.5 or less, Type 2 spectrum is advised Recommended parameter values for vertical spectra for ground types A, B, C, D, and E are provided in Table 3.4, but these values do not apply to special ground types S 1 and S 2.
Table 3.4: Recommended values of parameters describing the vertical elastic response spectra
(1) Unless special studies based on the available information indicate otherwise, the design ground displacement d g, corresponding to the design ground acceleration, may be estimated by means of the following expression:
D C g g 0,025 a S T T d = ⋅ ⋅ ⋅ ⋅ (3.12) with a g, S, T C and T D as defined in 3.2.2.2
3.2.2.5 Design spectrum for elastic analysis
Structural systems designed to withstand seismic actions in the non-linear range can typically be engineered to resist smaller seismic forces than those required for a linear elastic response.
To prevent the need for explicit inelastic structural analysis in design, the energy dissipation capacity of the structure is considered through the ductile behavior of its elements and other mechanisms This is achieved by conducting an elastic analysis using a response spectrum that is reduced from the elastic one, referred to as the "design spectrum." The reduction is facilitated by incorporating the behavior factor \( q \).
The behaviour factor \( q \) approximates the ratio of seismic forces experienced by a structure under completely elastic response with 5% viscous damping to those used in design via a conventional elastic analysis model, ensuring satisfactory structural performance Values of \( q \), which consider variations in viscous damping beyond 5%, are provided for different materials and structural systems based on relevant ductility classes outlined in various Parts of EN 1998 It is important to note that the behaviour factor \( q \) may vary in different horizontal directions of the structure, even though the ductility classification remains consistent across all directions.
(4)P For the horizontal components of the seismic action the design spectrum, S d(T), shall be defined by the following expressions:
(3.16) where a g, S, T C and T D are as defined in 3.2.2.2;
S d (T) is the design spectrum; q is the behaviour factor; β is the lower bound factor for the horizontal design spectrum
NOTE The value to be ascribed to β for use in a country can be found in its National Annex The recommended value for β is 0,2
The design spectrum for the vertical component of seismic action is defined by expressions (3.13) to (3.16), utilizing the design ground acceleration in the vertical direction, denoted as \$a_vg\$ instead of \$g\$ The parameter \$S\$ is set to 1.0, with all other parameters specified in section 3.2.2.3.
(6) For the vertical component of the seismic action a behaviour factor q up to to 1,5 should generally be adopted for all materials and structural systems
(7) The adoption of values for q greater than 1,5 in the vertical direction should be justified through an appropriate analysis
(8)P The design spectrum as defined above is not sufficient for the design of structures with base-isolation or energy-dissipation systems.
Alternative representations of the seismic action
(1)P The seismic motion may also be represented in terms of ground acceleration time-histories and related quantities (velocity and displacement)
When developing a spatial model of a structure, it is essential to utilize three accelerograms that act simultaneously to represent seismic motion It is important to note that the same accelerogram cannot be applied in both horizontal directions at the same time However, simplifications may be permitted as outlined in the relevant sections of EN 1998.
The description of seismic motion can be achieved through the use of artificial accelerograms, as well as recorded or simulated accelerograms, depending on the specific application and the available information.
(1)P Artificial accelerograms shall be generated so as to match the elastic response spectra given in 3.2.2.2 and 3.2.2.3 for 5% viscous damping (ξ = 5%)
(2)P The duration of the accelerograms shall be consistent with the magnitude and the other relevant features of the seismic event underlying the establishment of a g
(3) When site-specific data are not available, the minimum duration T s of the stationary part of the accelerograms should be equal to 10 s
The suite of artificial accelerograms must adhere to specific guidelines: at least three accelerograms should be utilized, the mean zero period spectral response acceleration values derived from individual time histories must not fall below the site-specific value of a g S, and within the period range of \(0.2T_1\) to \(2T_1\) (where \(T_1\) represents the structure's fundamental period in the direction of the applied accelerogram), the mean 5% damping elastic spectrum calculated from all time histories should not be less than 90% of the corresponding 5% damping elastic response spectrum value.
Recorded accelerograms or those produced by numerical simulations can be utilized, given that the samples are properly qualified based on the seismogenetic characteristics of the sources and the relevant soil conditions at the site, with their values scaled to the appropriate g value for the specific zone.
(2)P For soil amplification analyses and for dynamic slope stability verifications see
(3) The suite of recorded or simulated accelerograms to be used should satisfy
3.2.3.2 Spatial model of the seismic action
For structures with unique characteristics where uniform excitation at all support points is not a valid assumption, it is essential to utilize spatial models of seismic action.
(2)P Such spatial models shall be consistent with the elastic response spectra used for the basic definition of the seismic action in accordance with 3.2.2.2 and 3.2.2.3
Combinations of the seismic action with other actions
(1)P The design value E d of the effects of actions in the seismic design situation shall be determined in accordance with EN 1990:2002, 6.4.3.4
The inertial effects of the design seismic action must be assessed by considering the masses linked to all gravity loads in the specified combination of actions: \(i k\), \(i E\), and \(j k\), \(Q\).
G + Σψ ⋅ Σ (3.17) where ψ E,i is the combination coefficient for variable action i (see 4.2.4)
(3) The combination coefficients ψ E,i take into account the likelihood of the loads
During an earthquake, the coefficients \( Q_{k,i} \) may not be uniformly distributed across the entire structure, indicating a reduced mass participation in the structural motion This phenomenon can be attributed to the non-rigid connections between the masses, which affect their overall contribution to the dynamic response of the structure.
(4) Values of ψ 2,i are given in EN 1990:2002 and values of ψ E,i for buildings or other types of structures are given in the relevant parts of EN 1998
Scope
(1)P Section 4 contains general rules for the earthquake-resistant design of buildings and shall be used in conjunction with Sections 2, 3 and 5 to 9
(2) Sections 5 to 9 are concerned with specific rules for various materials and elements used in buildings
(3) Guidance on base-isolated buildings is given in Section 10.
C HARACTERISTICS OF EARTHQUAKE RESISTANT BUILDINGS
Basic principles of conceptual design
In seismic areas, it is crucial to consider seismic hazards during the initial phases of a building's conceptual design This approach facilitates the development of a structural system that meets essential requirements while remaining within acceptable cost limits.
(2) The guiding principles governing this conceptual design are:
− bi-directional resistance and stiffness;
− diaphragmatic behaviour at storey level;
These principles are further elaborated in the following subclauses
Structural simplicity is crucial for effective seismic force transmission, as it leads to clearer paths within the structure This simplicity reduces uncertainty in the modeling, analysis, dimensioning, detailing, and construction processes, resulting in more reliable predictions of seismic behavior.
Uniformity in building design is essential for effective transmission of inertia forces from distributed masses This can be achieved by using seismic joints to create dynamically independent units, ensuring that these joints are properly designed to prevent pounding between units.
Uniform development of a building's structure along its height is crucial, as it helps prevent the formation of weak areas that could experience high stress concentrations or excessive ductility demands, potentially leading to premature collapse.
(3) A close relationship between the distribution of masses and the distribution of resistance and stiffness eliminates large eccentricities between mass and stiffness
(4) If the building configuration is symmetrical or quasi-symmetrical, a symmetrical layout of structural elements, which should be well-distributed in-plan, is appropriate for the achievement of uniformity
(5) The use of evenly distributed structural elements increases redundancy and allows a more favourable redistribution of action effects and widespread energy dissipation across the entire structure
4.2.1.3 Bi-directional resistance and stiffness
(1)P Horizontal seismic motion is a bi-directional phenomenon and thus the building structure shall be able to resist horizontal actions in any direction
(2) To satisfy (1)P, the structural elements should be arranged in an orthogonal in- plan structural pattern, ensuring similar resistance and stiffness characteristics in both main directions
Selecting the appropriate stiffness characteristics of a structure is crucial for minimizing seismic impacts, considering the site's unique features This choice should also prevent excessive displacements that could result in instabilities from second-order effects or significant damage.
In addition to lateral resistance and stiffness, it is crucial for building structures to have sufficient torsional resistance and stiffness to minimize torsional motions that can unevenly stress various structural elements Structures designed with primary elements that resist seismic forces positioned near the building's periphery offer significant advantages in this regard.
4.2.1.5 Diaphragmatic behaviour at storey level
Floors, including roofs, are crucial for the seismic performance of buildings, functioning as horizontal diaphragms that gather and transfer inertia forces to vertical structural systems This ensures that these systems work cohesively to withstand horizontal seismic forces, particularly in structures with complex or non-uniform vertical layouts, or when combining systems with varying horizontal deformability, such as in dual or mixed systems.
Floor systems and roofs must possess adequate in-plane stiffness, particularly in scenarios involving non-compact or elongated shapes and large floor openings Special attention is required when these openings are near primary vertical structural elements, as they can disrupt the effective connection between the vertical and horizontal structures.
Diaphragms must possess adequate in-plane stiffness to effectively distribute horizontal inertia forces to the vertical structural systems, as per the analysis assumptions This is especially crucial when there are notable variations in stiffness or offsets of vertical elements situated above and below the diaphragm.
The design and construction of foundations and their connection to the superstructure must guarantee that the entire building experiences uniform seismic excitation.
For structures with a limited number of structural walls that may vary in width and stiffness, it is advisable to select a rigid, box-type or cellular foundation, which includes both a foundation slab and a cover slab.
For structures featuring separate foundation elements such as footings or piles, it is advisable to implement a foundation slab or tie-beams connecting these elements in both principal directions, in accordance with the guidelines outlined in EN 1998-5:2004, section 5.4.1.2.
Primary and secondary seismic members
Certain structural members, such as beams and columns, may be classified as "secondary" seismic members, which do not contribute to the seismic action resisting system of a building The strength and stiffness of these secondary elements against seismic forces can be disregarded, and they are not required to meet the standards outlined in Sections 5 to 9 However, it is essential to design and detail these members and their connections to support gravity loads while accommodating displacements from the most unfavorable seismic design conditions Additionally, the design must consider second-order effects (P-∆ effects).
(2) Sections 5 to 9 give rules, in addition to those of EN 1992, EN 1993, EN 1994,
EN 1995 and EN 1996, for the design and detailing of secondary seismic elements
All structural members that are not classified as secondary seismic members are considered primary seismic members These members are integral to the lateral force resisting system and must be included in the structural analysis accordingly.
4.3.1 and designed and detailed for earthquake resistance in accordance with the rules of
(4) The total contribution to lateral stiffness of all secondary seismic members should not exceed 15% of that of all primary seismic members
(5) The designation of some structural elements as secondary seismic members is not allowed to change the classification of the structure from non-regular to regular as described in 4.2.3.
Criteria for structural regularity
(1)P For the purpose of seismic design, building structures are categorised into being regular or non-regular
In structures with multiple dynamically independent units, the categorization and criteria outlined in section 4.2.3 apply to each individual unit Here, the term "individual dynamically independent unit" refers specifically to a "building."
(2) This distinction has implications for the following aspects of the seismic design:
− the structural model, which can be either a simplified planar model or a spatial model ;
− the method of analysis, which can be either a simplified response spectrum analysis (lateral force procedure) or a modal one;
− the value of the behaviour factor q, which shall be decreased for buildings non-regular in elevation (see 4.2.3.3)
(3)P With regard to the implications of structural regularity on analysis and design, separate consideration is given to the regularity characteristics of the building in plan and in elevation (Table 4.1)
Table 4.1: Consequences of structural regularity on seismic analysis and design
Regularity Allowed Simplification Behaviour factor
Plan Elevation Model Linear-elastic Analysis (for linear analysis) Yes
Lateral force a Modal Lateral force a Modal
The reference value may decrease if the condition specified in 4.3.3.2.1(2)a) is satisfied Additionally, a separate planar model can be utilized in each horizontal direction under the specific conditions outlined in 4.3.3.1(8).
(4) Criteria describing regularity in plan and in elevation are given in 4.2.3.2 and
4.2.3.3 Rules concerning modelling and analysis are given in 4.3
The regularity criteria outlined in sections 4.2.3.2 and 4.2.3.3 are essential conditions that must be met It is important to ensure that the assumed regularity of the building structure remains intact and is not affected by additional characteristics that are not addressed in these criteria.
(6) The reference values of the behaviour factors are given in Sections 5 to 9
(7) For non-regular in elevation buildings the decreased values of the behaviour factor are given by the reference values multiplied by 0,8
4.2.3.2 Criteria for regularity in plan
(1)P For a building to be categorised as being regular in plan, it shall satisfy all the conditions listed in the following paragraphs
(2) With respect to the lateral stiffness and mass distribution, the building structure shall be approximately symmetrical in plan with respect to two orthogonal axes
The plan configuration must be compact, defined by a polygonal convex line for each floor Set-backs, such as re-entrant corners or edge recesses, can still meet regularity requirements as long as they do not compromise the floor's in-plan stiffness Additionally, the area between the floor's outline and a surrounding convex polygonal line must not exceed 5% of the total floor area.
The in-plan stiffness of floors must be significantly greater than the lateral stiffness of vertical structural elements to minimize the impact of floor deformation on force distribution It is essential to analyze plan shapes such as L, C, H, I, and X, particularly focusing on the stiffness of lateral branches, which should be comparable to that of the central section to meet the rigid diaphragm requirement.
The application of this paragraph should be considered for the global behaviour of the building
The slenderness ratio \( \lambda \) of a building in plan must not exceed 4, where \( L_{\text{max}} \) and \( L_{\text{min}} \) represent the maximum and minimum dimensions of the building measured in orthogonal directions.
At each level and for both analysis directions x and y, the structural eccentricity \( e_{ox} \) and the torsional radius \( r_x \) must satisfy two key conditions The first condition states that \( e_{ox} \) should not exceed 0.30 times \( r_x \) (Equation 4.1a) The second condition requires that the torsional radius \( r_x \) must be greater than or equal to the radius of gyration \( l_s \) (Equation 4.1b) Here, \( e_{ox} \) represents the distance between the center of stiffness and the center of mass along the x direction, while \( r_x \) is derived from the ratio of torsional stiffness to lateral stiffness in the y direction Additionally, \( l_s \) is defined as the square root of the ratio of the polar moment of inertia of the floor mass in plan to the floor mass itself.
The definitions of centre of stiffness and torsional radius rare provided in (7) to (9) of this subclause
In single-storey buildings, the center of stiffness is determined by the lateral stiffness of all primary seismic members The torsional radius \( r \) is calculated as the square root of the ratio of global torsional stiffness to the center of lateral stiffness, relative to the global lateral stiffness in one direction, considering all primary seismic members in that direction.
In multi-storey buildings, defining the center of stiffness and torsional radius can only be approximate A simplified approach for assessing structural regularity and analyzing torsional effects is feasible if two conditions are met: first, all lateral load-resisting systems, such as cores, structural walls, or frames, must extend uninterrupted from the foundations to the building's top; second, the deflected shapes of these systems under horizontal loads should not vary significantly This second condition is typically satisfied in frame and wall systems, but is often not met in dual systems.
The National Annex may reference documents that define the center of stiffness and torsional radius in multi-storey buildings, applicable to both those meeting conditions (a) and (b) of paragraph (8) and those that do not.
In structures with slender walls experiencing flexural deformations, the centers of stiffness and torsional radius for each storey can be determined using the moments of inertia of the vertical elements' cross-sections When shear deformations are also considerable, they can be incorporated by applying an equivalent moment of inertia for the cross-section.
4.2.3.3 Criteria for regularity in elevation
(1)P For a building to be categorised as being regular in elevation, it shall satisfy all the conditions listed in the following paragraphs
All lateral load resisting systems, including cores, structural walls, and frames, must extend continuously from their foundations to the building's top or, in cases of setbacks at varying heights, to the upper limit of the applicable zone.
(3) Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually, without abrupt changes, from the base to the top of a particular building
In framed buildings, it is essential that the ratio of actual storey resistance to the resistance required by analysis remains consistent between adjacent storeys This principle is particularly relevant when considering the unique characteristics of masonry infilled frames.
When setbacks are implemented, specific conditions must be met: a) for gradual setbacks that maintain axial symmetry, the setback on any floor cannot exceed 20% of the previous plan dimension in the setback direction; b) for a single setback within the lower 15% of the total height of the main structural system, it must not exceed 50% of the previous plan dimension, and the base zone structure should be designed to withstand at least 75% of the horizontal shear forces typical of a similar building without base enlargement; c) if the setbacks disrupt symmetry, the total setbacks on each face across all storeys must not exceed 30% of the ground floor plan dimension, with individual setbacks limited to 10% of the previous plan dimension.
Figure 4.1: Criteria for regularity of buildings with setbacks
Combination coefficients for variable actions
(1)P The combination coefficients ψ 2i (for the quasi-permanent value of variable action q i) for the design of buildings (see 3.2.4) shall be those given in EN 1990:2002,
(2)P The combination coefficients ψ Ei introduced in 3.2.4(2)P for the calculation of the effects of the seismic actions shall be computed from the following expression:
NOTE The values to be ascribed to ϕ for use in a country may be found in its National Annex
The recommended values for ϕ are listed in Table 4.2
Table 4.2: Values of ϕ for calculating ψ Ei
Storeys with correlated occupancies Independently occupied storeys
* Categories as defined in EN 1991-1-1:2002.
Importance classes and importance factors
Buildings are categorized into four importance classes based on the potential impact of their collapse on human life, their significance for public safety and civil protection during the immediate aftermath of an earthquake, and the resulting social and economic repercussions.
(2)P The importance classes are characterised by different importance factors γ I as described in 2.1(3)
(3) The importance factor γ I = 1,0 is associated with a seismic event having the reference return period indicated in 3.2.1(3)
(4) The definitions of the importance classes are given in Table 4.3
Table 4.3 Importance classes for buildings
I Buildings of minor importance for public safety, e.g agricultural buildings, etc
II Ordinary buildings, not belonging in the other categories
III Buildings whose seismic resistance is of importance in view of the consequences associated with a collapse, e.g schools, assembly halls, cultural institutions etc
IV Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g hospitals, fire stations, power plants, etc
NOTE Importance classes I, II and III or IV correspond roughly to consequences classes CC1, CC2 and CC3, respectively, defined in EN 1990:2002, Annex B
(5)P The value of γ I for importance class II shall be, by definition, equal to 1,0
The values of γ I, which are essential for seismic design, can be found in a country's National Annex and may vary across different seismic zones based on local hazard conditions and public safety considerations For importance classes I, III, and IV, the recommended values of γ I are 0.8, 1.2, and 1.4, respectively.
(6) For buildings which house dangerous installations or materials the importance factor should be established in accordance with the criteria set forth in EN 1998-4.