Compliance criteria for the nolocalcollapse requirement

The no-(local-)collapse performance level is considered as the ultimate limit state against Clauses 2.2.1(1), which the structure should be designed according to the EN 1990 on the basis of structural 2.2.2(I), design.3 Unlike the damage limitation limit state, which is verified on the basis of deformation- 2.2.2(2)

based 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.

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.

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

Norway Seismic Spectrum

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

Fig. 2.1. Inelastic spectra for Tc = 0.6 s, normalized to peak ground acceleration (PGA), according to Vidic et a/.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 force-displacement curve, F-S, in monotonic loading. For a given period, T, of the elastic SDOF system, the inelastic spectrum relates to:

• the ratio q = Fd/Fy of the peak force, Fel, that would develop if the SDOF system were linear-elastic to the yield force of the system, F ' the maximum displacement demand of the inelastic SDOF system, ¿imix, expressed as a ratio to the yield displacement, 6y (i.e. as the displacement ductility factor, /./,,, = 6max/Sy).

For example, Eurocode 8 has adopted the inelastic spectra proposed in Vidic et al.:4

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=Fcl/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 ductility factor, ¡i6, 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:

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,/k, divided by the partial factor 7M of the material. Being key safety elements, the partial factors, 7M, are NDPs with values defined in the National Annexes of Eurocode 8. Eurocode 8 itself does not recommend the values of 7M to be used in the seismic design situation - it just notes the options of choosing the value 7M = 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 7M 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)

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^ value of 0.08g for ag, or of 0.1 Og for agS, as the threshold for the low-seismicity cases. It should be recalled that the value of ag includes the importance factor

Clause 4.4.1 (2) 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.

Clause 10.10(5) 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

Clause 2.2.2(2) 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.

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