Chapter 2- Performance Requirements And Compliance Criteria

CHAPTER 2

Performance requirements and compliance criteria

2.1. Performance requirements for new designs in Eurocode 8 and associated seismic hazard levels As a European standard (EN), Part 1 of Eurocode 8 provides for a two-level seismic design with the following explicit performance objectives: •

•

No-(local-)collapse: protection of life under a rare seismic action, through prevention of collapse of the structure or its parts and retention of structural integrity and residual load capacity after the event. This implies that the structure is significantly damaged, and may have moderate permanent drifts, but retains its full vertical load-bearing capacity and sufficient residual lateral strength and stiffness to protect life even during strong aftershocks. However, its repair may be uneconomic. Damage limitation: reduction of property loss, through limitation of structural and non-structural damage in frequent earthquakes. The structure itself has no permanent drifts; its elements have no permanent deformations, retain fully their strength and stiffness, and do not need repair. Non-structural elements may suffer some damage, which can be easily and economically repaired at a later stage.

The no-(local-)collapse performance level is achieved by dimensioning and detailing structural elements for a combination of strength and ductility that provides a safety factor between 1.5 and 2 against substantial loss of lateral load resistance. The damage limitation performance level is achieved by limiting the overall deformations (lateral displacements) of the system to levels acceptable for the integrity of all its parts (including non-structural ones). The two explicit performance levels - (local) collapse prevention and damage limitation are pursued under two different seismic actions. The seismic action under which (local) collapse should be prevented is termed the design seismic action, whilst the one under which damage limitation is pursued is often termed the serviceability seismic action. Within the philosophy of national competence on issues of safety and economy, the hazard levels for these two seismic actions are left for national determination. For structures of ordinary importance the recommendation in EN 1998-1 is for: • •

a design seismic action (for local collapse prevention) with 10% exceedance probability in 50 years (mean return period: 475 years) a serviceability seismic action (for damage limitation) with 10% exceedance probability in 10 years (mean return period: 95 years).

Clause 2.1(1)

DESIGNERS’ GUIDE TO EN 1998-1 AND EN 1998-5

Clauses 2.1(2), 2.1(3), 2.1(4), 4.2.5(1), 4.2.5(2), 4.2.5(3), 4.2.5(4), 4.2.5(5)

Clauses 4.4.3.2(2), 2.2.3(2)

Clause 2.1(4)

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The design seismic action for structures of ordinary importance is the reference seismic action; its mean return period is termed the reference return period, and denoted by TNCR. The ratio, n, of the serviceability seismic action (for damage limitation) to the design seismic action (for local collapse prevention) reflects the difference in hazard levels, and is a nationally determined parameter (NDP). Enhanced performance of essential- or high-occupancy facilities is achieved not by upgrading the performance level, as often specified in US codes, but by modifying the hazard level (the mean return period) for which local-collapse prevention or damage limitation is pursued. For essential- or high-occupancy structures the seismic action should be increased, by multiplying the reference seismic action by an importance factor, gI. By definition, gI = 1.0 for structures of ordinary importance (i.e. for the reference return period of the seismic action). For buildings, the recommended value of the NDP importance factor gI is 1.2, if collapse of the building may have unusually severe social or economic consequences (high-occupancy buildings, such as schools, or public assembly halls, facilities housing institutions of cultural importance, such as museums, etc.). These are termed buildings of Importance Class III. Buildings which are essential for civil protection in the immediate post-earthquake period, such as hospitals, fire or police stations and power plants, belong in Importance Class IV; the recommended value of the NDP importance factor for them is gI = 1.4. A value of gI equal to 0.8 is recommended for buildings of minor importance for public safety (Importance Class I: agricultural buildings, etc.). All other buildings are considered to be of ordinary importance, and are classified as Importance Class II. For buildings of ordinary or lower importance (Importance Classes I and II) a value of 0.5 is recommended for the ratio n of the serviceability seismic action (for damage limitation) to the design seismic action (for local collapse prevention). For buildings of importance above ordinary (Importance Classes III and IV) a value of 0.4 is recommended for n. This gives about the same level of property protection for ordinary and high-occupancy buildings (Importance Classes II and III), 15-20% less property protection for buildings of low importance and 15% higher protection for essential facilities. This additional margin may allow help facilities important for civil protection to maintain a minimum level of operation of vital services during or immediately after a frequent event. Despite the fact that EN 1998-1 recommends specific values for the NDPs - the importance factor of structures of other than ordinary importance, gI, and the ratio of the serviceability seismic action to the design seismic action, n - the nationally or regionally used values should reflect, in addition to national choice regarding the levels of safety and protection of property, also the regional seismo-tectonic environment. Eurocode 8 gives in a note the approach that may be used to determine the ratio of the seismic action at two different hazard levels. More specifically, the usual approximation of the annual rate of exceedance, H(ag), of the peak ground acceleration ag as H(ag) ~ koag-k is mentioned, with the value of the exponent k depending on seismicity, but being generally of the order of 3. Then, the Poisson assumption for earthquake occurrence gives a value of ~(TL /TLR)1/k for the value by which the reference seismic action needs to be multiplied to achieve the same probability of exceedance in TL years as in the TLR years for which the reference seismic action is defined (here, the index L denotes ‘lifetime’). This value is the importance factor gI, or the conversion factor to the serviceability seismic action, n. Alternatively, the value of the multiplicative factor, gI or n, to be applied on the reference seismic action in order to achieve a value of the probability of exceedance of the seismic action, PL, in TL years other than the reference probability PLR, over the same TL years, may be estimated as ~(PLR /PL)1/k. For Importance Classes III and IV, TLR < TL and PLR > PL; then gI > 1. For Importance Class I and for the serviceability seismic action, TLR > TL and PLR < PL; then the importance factor gI of low-importance facilities and the factor n result in values of less than 1. It is noted that the combination of 0.4 and 0.5 for the values recommended for the ratio n of a serviceability seismic action with a recommended mean return period of 95 years to the design seismic action with a recommended mean return period of 475 years is consistent with a value of the

CHAPTER 2. PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA

exponent k for the decay of the annual rate of exceedance of the peak ground acceleration, H(ag), with a value of k around 2. Although not explicitly stated, an additional performance objective in buildings designed for energy dissipation is prevention of global collapse during a very strong and rare earthquake (with a mean return period in the order of 2000 years). Although structural elements can still carry their tributary gravity loads after such an event, the structure may be heavily damaged, have large permanent drifts, retain little residual lateral strength or stiffness and may collapse after a strong aftershock. Moreover, its repair may be unfeasible or economically prohibitive. This implicit performance objective is pursued through systematic and acrossthe-board application of the capacity design concept, which allows full control of the inelastic response mechanism.

Clauses 2.2.1(2), 2.2.4.1(2), 4.4.2.3(2), 4.4.2.6(2)

2.2. Compliance criteria for the performance requirements and their implementation 2.2.1. Compliance criteria for damage limitation An earthquake represents for the structure a demand to accommodate a given energy input or given imposed dynamic displacements. Seismic damage to structural elements, or even to non-structural ones that follow the deformations of the structure, is due to deformations induced by the seismic response. Consistent with this reality, Eurocode 8 states that compliance criteria for the damage limitation limit state (i.e. performance level) should be expressed in terms of deformation limits. For equipment mounted or supported on the structure, limits relevant to damage may be expressed in terms of response accelerations at the positions of the equipment supports.

Clauses 2.2.1(1), 2.2.3(1)

2.2.2. Compliance criteria for the no-(local-)collapse requirement The no-(local-)collapse performance level is considered as the ultimate limit state against which the structure should be designed according to the EN 1990 on the basis of structural design.3 Unlike the damage limitation limit state, which is verified on the basis of deformationbased criteria, design for the no-(local-)collapse ultimate limit state is force-based. This is against the physical reality showing that it is the deformation that causes a structural member to lose its lateral load resistance and it is lateral displacements (and not lateral forces) that cause structures to collapse under their own weight. Force-based seismic design is well established, because structural engineers are familiar with force-based design for other types of action (such as gravity and wind loads), because static equilibrium for a set of prescribed external loads represents a robust basis of analysis methods and, last but not least, because tools for verification of structures for seismic deformations are not yet fully developed for practical application. This last statement refers both to non-linear analysis methods for the calculation of deformation demands and to the methods for the estimation of deformation capacities of structural members.

Clauses 2.2.1(1), 2.2.2(1), 2.2.2(2)

2.2.2.1. Design for energy dissipation and ductility Fulfilment of the no-(local-)collapse requirement under the design seismic action does not mean that the structure has to remain elastic under this action: this would require it to be designed for lateral forces of the order of 50% or more of its weight. Although technically feasible, designing a structure to respond elastically to its design seismic action is economically prohibitive. It is also unnecessary, as an earthquake is a dynamic action, representing for a structure a certain total energy input and a demand to tolerate certain displacements and deformations, but not a demand to withstand specific forces. So, Eurocode 8 allows a structure to develop significant inelastic deformations under its design seismic action, provided that the integrity of individual members and of the structure as a whole is not endangered. This is termed seismic design for energy dissipation and ductility.

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DESIGNERS’ GUIDE TO EN 1998-1 AND EN 1998-5

3.0

2.5

Sa(T1)/q(md)PGA

2.0 m=1 1.5 1.5 1.0 2 4 0.5

6 8

0.0 0

1

2

3

4

5

T1 (s)

Fig. 2.1. Inelastic spectra for TC = 0.6 s, normalized to peak ground acceleration (PGA), according to Vidic et al.4 and equations (D2.1) and (D2.2)

The foundation of force-based seismic design for ductility is the inelastic response spectrum of a single-degree-of-freedom (SDOF) system which has an elastic-perfectly plastic forcedisplacement curve, F-d, in monotonic loading. For a given period, T, of the elastic SDOF system, the inelastic spectrum relates to: • •

the ratio q = Fel /Fy of the peak force, Fel, that would develop if the SDOF system were linear-elastic to the yield force of the system, Fy the maximum displacement demand of the inelastic SDOF system, dmax, expressed as a ratio to the yield displacement, dy (i.e. as the displacement ductility factor, md = dmax /dy). For example, Eurocode 8 has adopted the inelastic spectra proposed in Vidic et al.:4 md = q

if T ≥ TC

m d = 1 + ( q - 1)

TC T

(D2.1) if T < TC

(D2.2)

where TC is the transition period of the elastic spectrum, between its constant spectral pseudo-acceleration and constant spectral pseudovelocity ranges (Fig. 2.1). Equation (D2.1) expresses the well-known Newmark ‘equal displacement rule’, i.e. the empirical observation that in the constant spectral pseudovelocity range the peak displacement response of the inelastic and of the elastic SDOF systems are about the same. With F being the total lateral force on the structure (the base shear, if the seismic action is in the horizontal direction), the ratio q = Fel /Fy is termed in Eurocode 8 the behaviour factor. In North America the same quantity is termed the force reduction factor or the response modification factor, and denoted by R. It is used in Eurocode 8 as a universal reduction factor on the internal forces that would develop in the elastic structure for 5% damping, or, equivalently, on the seismic inertia forces that would develop in this elastic structure, causing in turn the seismic internal forces. With this ‘stratagem’, the seismic internal forces for which the members of the structure should be dimensioned can be calculated through linear elastic analysis. As a price to pay, the structure has to be provided with the capacity to sustain a peak global displacement at least equal to its global yield displacement multiplied by the displacement

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CHAPTER 2. PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA

ductility factor, md, that corresponds to the value of q used for the reduction of elastic force demands (e.g. according to equations (D2.1) and (D2.2)). This is termed ductility capacity or energy dissipation capacity - as it has to develop through cyclic response in which the members and the structure as a whole dissipate part of the seismic energy input through hysteresis. Not all locations or parts of a structure are capable of ductile behaviour and hysteretic energy dissipation. A special instrument, termed capacity design, is used in Eurocode 8 to provide the necessary hierarchy of strengths between adjacent structural members or regions and between different mechanisms of load transfer within the same member, and ensures that inelastic deformations will take place only in those members, regions and mechanisms capable of ductile behaviour and hysteretic energy dissipation, while the rest stay in the elastic range of response. The regions of members entrusted for hysteretic energy dissipation are termed dissipative zones. They are designed and detailed to provide the required ductility and energy dissipation capacity. Before being designed and detailed for the necessary ductility and energy dissipation capacity, dissipative zones should first be dimensioned to provide a design value of force resistance, Rd, at least equal to the design value of the action effect due to the seismic design situation, Ed, from the analysis (see Section 4.4.1): Ed £ Rd

Clauses 2.2.4.1(2), 2.2.4.1(3)

Clauses 2.2.2(1), 2.2.2(5), 4.4.2.2(1)

(D2.3)

The value to be used for Ed in equation (D2.3) is obtained from the application of the seismic action together with the quasi-permanent value of the other actions included in the seismic design situation (i.e. the nominal value of the permanent loads and the quasi-permanent value of imposed and snow loads, see Section 4.4.1). Normally, linear analysis is used, and the value of Ed may then be found by superposition of the seismic action effects from an analysis for the seismic action alone to the action effects from the analysis for the other actions in the seismic design situation. Second-order effects should be taken into account in the calculation of Ed. The value of Rd in equation (D2.3) should be calculated according to the relevant rules of the corresponding material Eurocode (unless these rules do not apply under inelastic cyclic loading and Eurocode 8 specifies alternative rules). It should be based on the design values of material strengths, i.e. the characteristic values, fk, divided by the partial factor gM of the material. Being key safety elements, the partial factors, gM, are NDPs with values defined in the National Annexes of Eurocode 8. Eurocode 8 itself does not recommend the values of gM to be used in the seismic design situation - it just notes the options of choosing the value gM = 1 appropriate for the accidental design situations, or the same values as for the persistent and transient design situation. This latter option is very convenient for the designer, as he or she may then dimension the dissipative zone to provide a design value of force resistance, Rd, at least equal to the largest design value of the action effect due to the persistent and transient or the seismic design situation. With the former choice, the dissipative zone will have to be dimensioned once for the action effect due to the persistent and transient design situation and then for that due to the seismic design situation, each time using different values of gM for the resistance side of equation (D2.3). All regions and mechanisms not designated as dissipative zones are designed to provide a Clause 2.2.4.1(2) design value of force resistance, Rd, at least equal to an action effect, Ed, which is not obtained through analysis but through capacity design. The foundation is of paramount importance for the whole structure. Moreover, the Clause 2.2.2(4) foundation is difficult to inspect for seismic damage and even more difficult to repair or retrofit. Therefore, it is ranked at the top of the hierarchy of strengths in the entire structural system, and should be designed to remain elastic, while inelastic deformations and hysteretic energy dissipation takes place in the superstructure it supports.

2.2.2.2. Seismic design for strength instead of ductility For buildings, Eurocode 8 gives the option of seismic design for strength alone, without Clauses 2.2.1(3), observing any provisions for ductility and energy dissipation capacity. In this option the 3.2.1(4)

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DESIGNERS’ GUIDE TO EN 1998-1 AND EN 1998-5

Clause 4.4.1(2)

Clause 10.10(5)

Clause 2.2.2(2)

building is designed in accordance with Eurocodes 2 to 7, simply considering the seismic action as a lateral loading like wind. The seismic lateral forces are derived from the design response spectrum using a behaviour factor, q, of 1.5, at most (or possibly 2 for steel or composite buildings). Moreover, certain minimum requirements for ductility of the materials (or of steel sections) should be observed as well. As design seismic forces are derived with a value of the behaviour factor, q, greater than 1.0, structures designed for strength alone, without engineered ductility and energy dissipation capacity, are termed low-dissipative instead of non-dissipative. Eurocode 8 states that the option of low-dissipative seismic design for strength alone is not recommended except in cases of low seismicity. Although it leaves it to the National Annex to decide which combination of categories of structures, ground types and seismic zones in a country correspond to the characterization as cases of low seismicity, it recommends (in a note) as a criterion either the value of the design ground acceleration on type A ground (i.e. on rock), ag, or the corresponding value, agS, over the ground type of the site (the soil factor, S, is discussed in Section 3.2.2.2). Moreover, it recommends a value of 0.08g for ag, or of 0.10g for agS, as the threshold for the low-seismicity cases. It should be recalled that the value of ag includes the importance factor gI. For buildings, low-dissipative seismic design according to the first paragraph of this subsection - for strength alone without engineered ductility - is allowed in a specific case that may not necessarily fall within the category of low seismicity: when in the horizontal direction considered, the total base shear over the entire structure at the base level (the foundation or top of a rigid basement) due to the seismic design situation calculated with a behaviour factor equal to the value applicable to low-dissipative structures (see the first paragraph of this subsection) is less than that due to the design wind action, or any other relevant action combination for which the building is designed on the basis of a linear elastic analysis. In buildings designed with seismic isolation, and irrespective of the classification of the building as a low-seismicity case or not, design of the superstructure above the level of the isolation (the ‘isolation interface’) as low-dissipative with a value of the behaviour factor, q, not greater than 1.5 is the rule imposed by EN 1998-1 rather than the exception.

2.2.2.3. The balance between strength and ductility - ductility classification The option described in the previous subsection, namely design for strength alone, without engineered ductility and energy dissipation capacity, is an extreme, recommended by Eurocode 8 only for special cases. However, within the fundamental case of seismic design, namely that of design for ductility and energy dissipation capacity, the designer is normally given the option to design for more strength and less ductility, or vice versa. For buildings of concrete, steel, composite (steel-concrete) or timber construction, this option is exercised through the ductility classification introduced by Eurocode 8 in the corresponding material- specific chapters.

2.3. Exemption from the application of Eurocode 8 Clauses 2.2.1(4), Eurocode 8 itself states that its provisions need not be applied in cases of very low seismicity. 3.2.1(5) As for cases of low seismicity, which combination of categories of structures, ground types and seismic zones in a country will qualify as cases of very low seismicity is left to the National Annex. However, it recommends (in a note) the same criterion as for the cases of low seismicity: either the value of the design ground acceleration on type A ground (i.e. on rock), ag, or the corresponding value, agS, over the ground type of the site. It goes on to recommend a value of 0.04g for ag, or of 0.05g for agS, as the threshold for the very low-seismicity cases. As the value of ag includes the importance factor gI, certain structures in a region may be exempted from the application of Eurocode 8, while others (those housing essential or high-occupancy facilities) may not be. This is consistent with the notion that exemption from

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CHAPTER 2. PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA

the application of Eurocode 8 is due to the inherent lateral force resistance of any structure designed for non-seismic loadings, neglecting any contribution from ductility and energy dissipation capacity. Given that Eurocode 8 considers that, due to overstrength, any structure is entitled to a behaviour factor, q, at least equal to 1.5, implicit in the value of 0.05g for agS recommended for the threshold for very low-seismicity cases is an assumed inherent lateral force capacity of 0.05 × 2.5/1.5 = 0.083g (where 2.5 is the spectral amplification factor in the constant-spectral acceleration region and 1.5 is the value of the behaviour factor). This is indeed a reasonable assumption. If a National Annex states that the entire national territory is considered to be a case of very low seismicity, then Eurocode 8 (all six parts) will not apply at all in that country.

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