1.4.1 Force-Based/Displacement Checked
Deficiencies inherent in the force-based system of seismic design, some of which have been outlined in the preceding sections, have been recognized for some time, as the importance of deformation, rather than strength, in assessing seismic performance has come to be better appreciated. Consequendy a number of new design methods, or improvements to existing methods, have been recendy developed. Initially the approaches were designed to fit within, and improve, existing force-based design. These can be characterized as force-based/displacement checked, where enhanced emphasis is placed on realistic determination of displacement demand for structures designed to force-based procedures.
Such methods include the adoption of more realistic member stiffnesses for deformation (if not for required strength) determination, and possibly use of inelastic time-history analysis, or pushover analysis, to determine peak deformation and drift demand. In the event that displacements exceed the code specified limits, redesign is required, as suggested in F ig.l.3. Many modern codes [ e.g. XI, X2, X3, X4]require some version of this approach. Several recent design approaches have used this approach [e.g. FI, F2, X8]. In general, no attempt is made to achieve uniform risk of damage, or of collapse for structures designed to this approach.
Chapter 1. Introduction: The N eed for D isplacem ent-B ased Seism ic D esign 31
Paulay1 has suggested that the deficiencies noted in previous sections can be eliminated within a force-based design approach. As explained in detail in section 4.4, yield displacement can be determined from section and structure geometry without a prior knowledge of strength. Displacement demand, A^, at least for frame buildings will normally be governed by code drift limits and the building geometry. The yield strength V is assumed, and hence the initial stiffness K = V/Ay is calculated. The elastic period is calculated from Eq.(1.6), and the elastic displacement demand from Eq. (1.22). This is compared with the code drift limit, and the strength adjusted incrementally until the elastic displacement equals the drift limit. Strength is then distributed between the different lateral-force resisting elements based on experience, rather than on elastic stiffness. This has been termed a displacement focusedforce-based approach.
There are, however, problems associated with this approach. Although the yield displacements of the lateral-force resisting elements may be known at the start of the procedure, the equivalent system yield displacement will not be known until the distribution of strength between elements is decided. The approach relies on assumptions about the equivalence between elastic and ductile displacements (e.g. the equal displacement approximation), which as discussed in relation to Fig. 1.18 may be invalid, and considerable experience is required of the designer. The procedure is suitable for those well versed in seismic design, but ill-suited for codification. As will be shown in subsequent chapters of this text, a design approach based directly on displacements is simpler, better suited to codification (see Chapter 14), and does not require assumptions to be made about elastic/inelastic displacement equivalence.
1.4.2 Deformation-Calculation Based Design
A more refined version of the force-based/displacement-checked approach relates the detailing of critical sections (in particular details of transverse reinforcement for reinforced concrete members) to the local deformation demand, and may hence be termed deformation-calculation based design. Strength is related to a force-based design procedure, with specified force-reduction factors. Local deformation demands, typically in the form of member end rotations or curvatures are determined by state-of-the-art analytical tools, such as inelastic pushover analyses or inelastic time-history analyses. Transverse reinforcement details are then determined from state-or-the-art relationships between transverse reinforcement details and local deformation demand, such as those presented in Chapter 4.
Initial work on this procedure was related to bridge structuresPY'J, and followed by work on reinforced concrete buildingslMl). Many additional variants of the approach have recendy been developed [e.g. B l, K l, P7]. In the variant suggested by Panagiatokos and Fardis^7! the structure is initially designed for strength to requirements of direct combination of gravity load plus a serviceability level of seismic force, using elastic
32 P riestley, Calvi and Kowalsky. D isplacem ent-B ased Seism ic D esign of Structures
analysis methods. The designed structure is then analysed using advanced techniques such as inelastic time-history analysis or inelastic pushover analysis to determine the required transverse reinforcement details. It is not clear that this is an efficient design approach wfcen response to the full design-level earthquake is considered, since inelastic time- history analyses of frame buildings by Pinto et al I P15l have indicated that member inelastic rotations are rather insensitive to whether gravity loads are incorporated in the analysis, or ignored. An alternative procedure for combination of gravity and seismic loads is suggested in Section 3.7. The approaches described in this section have the potential of producing structures with uniform risk of collapse, but not with uniform risk of damage.
1.4.3 Deformation-Specification Based Design
Recently a number of design approaches have been developed where the aim is to design structures so that they achieve a specified deformation state under the design-level earthquake, rather than achieve a displacement that is less than a specified displacement limit. These approaches appear more philosophically satisfying than those of the preceding two sections. This is because damage can be directly related to deformation. Hence designing structures to achieve a specified displacement limit implies designing for a specified risk of damage, which is compatible with the concept of uniform risk applied to determining the design level of seismic excitation. It thus means that different structures designed to this approach will (ideally) have the same risk of damage, rather than the variable risk associated with current design approaches, as discussed in Section 1.3. Using state-of-the-art detailing/deformation relationships, structures with uniform risk of collapse, as well as of damage can theoretically be achieved.
Different procedures have been developed to achieve this aim. The most basic division between them is on the basis of stiffness characterization for design. Some methods [e.g. A l, C2, SI], adopt the initial pre-yield elastic stiffness, as in conventional force-based design. Generally some iteration is required, modifying initial stiffness and strength, to achieve the desired displacement, as discussed in relation to the approach suggested by Paulay in Section 1.4.1. These approaches also rely on existing relationships between elastic and inelastic displacement, such as the equal-displacement, or equal- energy approximations. It is shown in Section 4.9.2(g) that these approximations have been based on invalid elastic damping assumptions.
The second approach utilizes the secant stiffness to maximum displacement, based on the Substitute Structure characterization^1 «S21, and an equivalent elastic representation of hysteretic damping at maximum response [e.g. P8, K2, P9]. Generally these methods require little or no iteration to design a structure to achieve the specified displacement, and are hence known as Direct Displacement-Based Design (DDBD) methods. The different stiffness assumptions of the two approaches are illustrated for a typical maximum hysteretic force-displacement response in Fig. 1.19, where A/and Ks are the initial and secant stiffness to maximum response respectively. It will be recalled that one of the principal problems with force-based seismic design is that reliance on initial stiffness
Chapter 1. Introduction: T he N eed for D isplacem ent-B ased Seism ic D esign 33
results in illogical force distribution between different structural elements. It will be shown in Chapter 3 that this problem disappears when the secant stiffness is used.
Fig.l.19 Initial and Secant Stiffness Characterization of Hysteretic Response
The way in which hysteretic energy dissipation is handled also varies between the methods. Two main classes of procedure can be identified — those that use inelastic spectra, and those that use equivalent viscous damping. Inelastic spectra are generally related to acceleration, though there is no inherent reason why inelastic displacement spectra cannot be generated (see Section 3.4.3(e)). They are generated by single-degree-of- freedom analyses of structures of different initial elastic periods, using a specified hysteresis rule, and a specified maximum ductility. Since the ductility demand cannot generally be predicted prior to the analyses, the analyses are carried out using a range of specified force-reduction factors, and the spectrum for a given ductility factor is found by interpolation within the results of the analyses. Alternatively, simplified relationships between force-reduction factor and ductility that vary between equal-displacement at long periods, and equal energy at short periods are direcdy generated. An example based on this approach, using the basic ECSP^l acceleration spectrum for firm ground and peak ground acceleration of 0.4g is shown in Fig.l.20(a).
As will be apparent from the discussion related to Fig. 1.18, different inelastic spectra would need to be generated for different structural systems and materials that exhibited different hysteretic characteristics. Methods for generation of inelastic spectra are discussed in Section 3.4.3(e).
The second alternative is to represent ductility and energy dissipation capacity as equivalent viscous damping, using relationships based on inelastic time-history analyses. This procedure is only appropriate when the secant stiffness to maximum response is used in the design process. The procedure for design using displacement spectra requires little or no iteration and hence is termed Direct Displacement-based Seismic Design (DDBD).
34 Priestley, Calvi and Kowalsky. D isplacem ent-B ased Seism ic D esign of Structures
The method is discussed in detail in Chapter 3.
An example of a spectral displacement set for different damping levels is shown for the displacement spectrum of EC8, firm ground, 0.4g PGA, in Fig.l.20(b). It will be
evfdent that a single spectral set, covering the expected range of equivalent viscous damping, will apply for all hysteretic characteristics, provided the relationships between equivalent viscous damping, ductility, and hysteretic rule have been pre-calibrated by inelastic time-history analyses. It is also possible, as discussed above, to express the displacement spectra in terms of ductility, rather than equivalent viscous damping, in a form analogous to that used for the acceleration spectra of Fig. 1.20(a). It will be shown in Chapter 3 that inelastic displacement spectra can be generated using precisely the same data and analyses used to generate the rules relating ductility to damping for a given hysteresis rule, and that the approaches are then directly equivalent. The disadvantage of this approach is that inelastic spectra must be generated for each hysteresis rule, and the determination of equivalent system ductility requires careful consideration.
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