Åu=
2.6 GUIDE TO ASSIST THE SELECTION OF ISOLATION SYSTEMS
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Maximum base shears and displacements of isolated structures are dominated by first-mode responses. Maximum first-mode responses of bilinear hysteretic isolation systems can in turn be approximated by the maximum responses of equivalent linear systems, as discussed earlier in this chapter. The final section of Table 2.1 demonstrates the degree of validity of the equivalent linearisation approach. It gives effective dampings and periods calculated for the equivalent linearisation of the bilinear isolators, using equation (2.11b) for TB and equations (2.11c) to (2.13) for B. The response spectrum accelerations and displacements for these values of period and damping are listed. The spectral values for the base displacements give reasonable approximations to the actual values, with correction factors CF of approximately unity, except for case (vii), with the nearly plastic post-yield stiffness, for which the correction factor is 1.6.
However, the spectral accelerations SA(TB,B) provide much poorer estimates of either the first- mode or overall base-mass accelerationX b. Much improved estimates of the base shear Sb can be obtained from KBXb, which has a smaller relative error than the estimate of Xb from SD(TB,B).
This is the procedure we recommend when using the equivalent linearisation approach (Section 2.2).
Table 2.2: Guide to the behaviour of isolation systems, showing seven classes
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Thus, class (vi) has been extended to include rectangular hysteresis loops (Kb1=, Kb2=0), while the example of case (vi) has 'high' and 'low' values of these stiffnesses respectively. The response characteristics of simple sliding friction systems included by this generalisation are similar to those of the example of case (vi). The ways in which the various cases of Table 2.1 have been generalised to the classes of Table 2.2 are discussed below.
Class (i) represents unisolated linear structures with periods up to about 1 second and damping up to about 10%. This class is provided only for purposes of comparison. Most short- to moderate-period unisolated structures will be designed to respond nonlinearly, so their acceleration- and force-related responses may be considerably less than those of the linear elastic cases considered here. Isolation still provides benefits in that nonlinear response in such unisolated structures requires ductile behaviour of the structural members, with the considerable energy dissipation within the structure itself often associated with significant damage.
Class (ii) represents lightly-damped, linear isolation systems, with the isolator damping less than 10%. Only systems providing a high degree of isolation are considered, with an isolation factor Tb/T1(U) of at least 2 and a period Tb of at least 1.5 s for El Centro-type earthquakes.
The response of such systems is almost purely in the first mode, with very little higher-frequency response, so they virtually eliminate high-frequency attack on contents of the structure. This type of isolation can be readily obtained with laminated rubber bearings, with the low isolator damping provided by the inherent damping of the rubber. Higher-damping rubbers may be necessary to achieve the 10% damping end of the range without the provision of additional damping devices. The higher-damping rubbers may not behave as linear isolators since they are often amplitude dependent and history dependent. Various mechanical spring systems with viscous dampers fall into this category.
Class (iii) corresponds to linear isolation with heavier viscous damping, ranging between about 10% and 25% of critical. Increased damping reduces the isolator displacement and base shear, but generally at the expense of increased high-frequency response. The high-frequency response results from increased isolator impedance at higher frequencies. These systems still provide a high degree ofprotection for subsystems and contents vulnerable to motions of a few Hz or greater, but with reduced isolator displacements compared to more lightly damped systems.
We consider class (iv), bilinear hysteretic systems with good elastic-phase isolation (Tb1/T1(U) > 2) and moderate nonlinearity (corresponding to equivalent viscous base damping of 20-30% of critical), as a reference class. For many applications, this represents a reasonable design compromise to achieve low base shears and low isolator displacements together with low to moderate floor response spectra. This type of isolation can often be provided by lead rubber bearings.
Class (v) represents bilinear isolators with poor elastic-phase isolation (Tb1/T1(U) < 1) and relatively short post-yield periods (~ 1.5s). The relatively high stiffnesses of these isolation systems produce very low isolator displacements, but strong high-frequency motions and stronger base shears than the reference bilinear-hysteretic isolator class.
Class (vi) is similar in many respects to class (v), but with a long post-yield period (Tb2 > ~ 3s), which gives nearly elasto-plastic characteristics and thus high hysteretic damping and a high nonlinearity factor. Rigid-plastic systems, such as given by simple sliding friction without any resilience, are extreme examples of this class. Low base shears can be achieved because of the low post-yield stiffness and high hysteretic damping, but at the expense of strong high- frequency response. Even this advantage is lost with high yield levels. This class of bilinear isolator is not appropriate when protection of subsystems or contents vulnerable to attack at frequencies less than 1 Hz is important, but some systems in this class can provide low base shears and moderate isolation-level displacements very cheaply. Displacements can become very large in greater than anticipated earthquake ground motions.
Class (vi) consists of nonlinear hysteretic isolation systems with a high degree of elastic-phase isolation (Tb1/T1(U) > 3) and a long post-yield period (Tb2 > ~ 3s), producing high hysteretic damping. The low post-yield stiffness means that the base shear is largely controlled by the yield force, is insensitive to the strength of the earthquake, and can be very low. The high degree of elastic-phase isolation largely overcomes the problem of strong high-frequency response usually associated with high nonlinearity factors. Systems of this type are particularly useful for obtaining low base shears in very strong earthquakes when provision can be made for large isolator displacements. One application of this class of system was the long flexible pile system used in the Wellington Central Police Station (Chapter 8.2 (f)), with the elastoplastic hysteretic damping characteristics provided by lead-extrusion energy dissipators mounted on resilient supports.
As indicated by the preceding descriptions of the isolator systems and the discussion of the response characteristics of the various examples in the last section, the selection of isolation systems involves 'trade-offs' between a number of factors.
Decreased base shears can often be achieved at the cost of increased base displacements and/or stronger high-frequency accelerations. High-frequency accelerations affect the distribution of forces in the structure and produce stronger floor response spectra. If strong high- frequency responses are unimportant, acceptable base shears and displacements may be achieved by relatively crude but cheap isolation systems, such as those involving simple sliding.
In some cases, limitations on acceptable base displacements and shears and the range of available or economically acceptable isolation systems may mean that strong high-frequency accelerations are unavoidable, but these may be acceptable in some applications. Some systems may be required to provide control over base shears in ground motions more severe than those expected, requiring nearly elasto-plastic isolator characteristics and provision for large base displacements.
The selection of appropriate isolation systems for a particular application depends on which response quantities are most critical to the design. These usually can be specified in terms of one or more of the following factors:
i) base shear
ii) base displacement
iii) high-frequency (i.e., > ~ 2Hz) floor response spectral accelerations
iv) control of base shears or displacements in greater than design-level earthquake ground motions
v) cost
Isolation systems are easily subdivided on the basis of those for which high-frequency (> 2Hz) responses can be ignored and those where they make significant contributions to the acceleration distributions and floor spectra. Floor spectral accelerations are important when an important design criterion is the protection of low-strength high-frequency subsystems or contents.
In well-isolated linear systems, high-frequency components, which correspond to higher-mode contributions, can generally be ignored, although they become more significant as the base damping increases (Figure 2.7, cases (ii) and (iii)). In nonlinear systems, there will generally be moderate to strong high-frequency components when there is a low elastic-phase isolation factor, less than about 1.5. This generally eliminates systems with rigid-sliding type characteristics when strong high-frequency response is to be avoided. For a given elastic-phase isolation factor, high-frequency effects have been found to generally increase with the nonlinearity factor. These considerations suggest that the selection of isolation systems for the protection of high-frequency subsystems is limited to linear systems, or nonlinear systems with high elastic- phase isolation factors and moderate nonlinearity factors (i.e., corresponding to cases (ii), (iii) or (iv) in Figure 2.7). Some systems with high nonlinearity factors but also with high elastic-phase isolation factors may also produce acceptably low high-frequency response.
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For example, case (vii) in Figure 2.7 with a high nonlinearity factor has a similar top-floor response spectrum to case (iv) for which the nonlinearity factor is moderate, and has a spectrum not much stronger than that of the linearly-isolated case (iii) with high viscous damping. The linear systems usually give better performance strictly in terms of high-frequency floor-response spectral accelerations, but the introduction of nonlinearity can reduce the base shear and isolator displacement, which may give a better overall performance when the structure, subsystems and contents are considered together.
For situations where a need for small floor-response spectral accelerations is not a major design criterion, the range of acceptable nonlinear isolation systems is likely to be much greater. The main performance criteria are then usually related to base shear and base displacement. Both these quantities depend primarily on the first-mode response.
Except for nearly elasto-plastic systems, the base shear decreases as Qy/W increases from zero, passes through a minimum value at an optimal yield force, and then increases as Qy/W continues to increase. Thus the base shear of most linear isolation systems can be reduced by selecting a nonlinear isolation system with Tb2=Tb of the linear system and an appropriate yield force ratio and elastic-phase period. For a given yield force, the base shear generally decreases as Tb2 increases, i.e., the system becomes more elasto-plastic in character. This is illustrated by the examples in Figure 2.7. This is generally at the expense of greater base displacement, as for case (vii), or strong high-frequency response when the elastic-phase isolation is poor, as in case (vi). When base shear and base displacements are the controlling design criteria, systems with rigid-plastic type characteristics, such as simple pure friction systems, which are not appropriate when the protection of high-frequency subsystems or contents is a concern, may give cheap, effective solutions provided the coefficient of friction remains less than the maximum acceptable base shear. However, some centring force is usually a desirable isolator characteristic. For protection against greater than design-level excitations, systems with a nearly plastic yielding-phase characteristic have the advantage that the base shear is only weakly dependent on the strength of excitation, but the disadvantage that their isolator displacements may become excessive. A system similar to our reference case with characteristics of moderate nonlinearity and good elastic-phase isolation is often a good design compromise when minimisation of high-frequency floor-response spectral accelerations is not an overriding design criterion.