Åu=
Chapter 3 ISOLATOR DEVICES AND SYSTEMS
3.1 ISOLATOR COMPONENTS AND ISOLATOR PARAMETERS
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In the simplest case a linear isolation system is produced by using components with linear flexibility and linear damping. In other cases the isolation system may be nonlinear.
A special case of nonlinearity, the bilinear system, occurs when the shear-force/displacement loop is a parallelogram, as shown in Figure 2.3 and discussed in the associated text. Different seismic responses result from linear, bilinear and other nonlinear isolation systems.
In the simplest case, a system which has both a linear flexibility component and a linear damping component can be modelled in terms of the differential equation (2.1), i.e.
where the flexibility is the inverse of the stiffness constant 'k' and the velocity-damping is described by a constant 'c'. Figure 2.2 and the associated text define this kind of system and show the elliptical velocity-damped shear-force/displacement hysteresis loop which results.
However, the components may not be linear. The most common source of nonlinearity in a component is amplitude-dependence. For example, in the typical bilinear isolation system the stiffness is amplitude-dependent, changing from Kb1 to Kb2 at the yield displacement. The damping in this case is also nonlinear because the hysteretic contribution to the damping, which usually dominates, depends on the area of the hysteresis loop and therefore also depends on the maximum amplitude Xb.
Table 3.1 analyses the flexibility and damping of some common isolator components, examining each to see if it is linear or nonlinear. The analysis is somewhat idealised and over-simplified, since material properties can vary. Also, it is worthwhile checking to see if a particular system is rate- or history-dependent. For example, types of high-damping rubber depend both on the amplitude and on the number of cycles which the sample has undergone.
PROPERTY LINEAR NONLINEAR Restoring Force
(providing spring constant and flexibility)
*Laminated rubber bearing
*Flexible piles or columns
*Springs
*Rollers between curved surfaces (gravity)
*High-damping rubber bearing
*Lead rubber bearing
*Buffers
*Stepping (gravity)
Damping *Laminated rubber bearing
*Viscous damper *High-damping rubber bearing
*Lead rubber bearing
*Lead extrusion damper
*Steel dampers
*Friction (e.g. PTFE) Table 3.1: Flexibility and Damping of Common Isolator Components
u m -
= ku + u c + u
m
gAs seen in Table 3.1, the laminated rubber (elastomeric) bearing is the only single-unit isolation system, among those considered, which has both linear restoring force and linear damping. In the commercially used form, this comprises layers of rubber vulcanised to steel plates.
Considerable experience exists for the design and use of the elastomeric bearing, since its initial major application was to accommodate thermal expansion in bridges and it was only later adopted as a solution to seismic isolation problems. However, for seismic isolation, this system has the disadvantage that the maximum achievable damping is very low, approximately 5% of critical. Attempts to overcome this disadvantage by increasing the inherent damping of the rubber have not yet produced an ideal system with linear stiffness and linear damping.
Flexible piles or columns provide a simple, effective linear restoring force but dampers need to be added to control the displacements during earthquakes and on other occasions. If the dampers are linear, e.g., viscous dampers, then a linear system results. Viscous dampers are excellent candidates for linear dampers, but may be difficult to obtain at the required size, may be strongly temperature-dependent and may require maintenance, given that the required lifetime may be 30 to 80 years.
Springs with the required stiffness are likely to be difficult to produce, but do provide a linear restoring force. The German GERB system achieves this, mainly intended for industrial plant, such as large silos. Rollers or spheres between curved (parabolic) surfaces can provide linear restoring forces. Since they have 'line' or 'point' contact it is difficult to provide for high loads.
Again, damping will usually need to be added in practice and linear damping will produce a linear system.
Gravity in the form of a 'stepping' behaviour (see, for example the Rangitikei viaduct, Chapter 6) can provide an excellent nonlinear restoring force. Such systems need additional damping for effective isolation. The resultant isolation systems are nonlinear.
High-capacity hysteretic dampers may be based on the plastic deformation of solids, usually lead or steel. The damper must ensure adequate plastic deformation of the metal when actuated by large earthquakes. It must be detailed to avoid excessive strain concentrations; for example these may cause premature fatigue failure of a steel damper at a weld. Excessive plastic cycling of steel dampers, for example by wind gusts, must be avoided since this gives progressive fatigue deterioration.
Steel damping devices, often in the form of bending beams of various cross-sections, have a high initial stiffness and are effective dampers but care must be taken in their manufacture to ensure a satisfactory lifetime. They are strongly amplitude-dependent. Combined with components to provide flexibility, they can result in bilinear or nonlinear isolation systems. Elasto- plastic steel dampers have been used in New Zealand and other countries, including the seismic isolation of many bridges in Italy (see Chapter 8).
The lead extrusion damper behaves as a plastic device operating at a constant force with very little rate- or amplitude-dependence at earthquake frequencies. It creeps at low loads (see Figure 3.10), enabling thermal expansion to be accommodated.
When combined with a linear component for flexible support, e.g., flexible piles, then a bilinear system can result, as was used in the Wellington Central Police Station (see Chapter 8).
The lead rubber bearing, which comprises an elastomeric bearing with a central lead plug, gives structural support, horizontal flexibility, damping and a centring force in a single easily installed unit. It has high initial stiffness, followed by a lower stiffness after yielding of the lead, and is for many situations the most appropriate isolation system. The hysteretic damping of this device is via the plastic deformation of the lead. The device is nonlinear but can be well described as bilinear, i.e., it has a parallelogram-shaped hysteresis loop as shown in Figure 2.3 and discussed in the associated text.
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Friction devices behave in a similar way to the extrusion damper, are simple but may require maintenance. Changes may occur in the friction coefficient due to age, environmental attack, temperature or wear during use. A further problem is that of 'stick-slip', where after a long time under a vertical load the device requires a very large force to initiate slipping. A dramatic example of a system isolated by this means is the Buddha at Kamakura; a stainless steel plate was welded to the base of the statue and it was rested on a polished granite base without anchoring.