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# Custom Seismic Isolator Essay

This is an essay covering the study of seismic isolator as a tool used in earthquake engineering for protecting buildings against earth tremors. It is effective enough to help buildings and non-building structures withstand the impact of an earthquake. However, it should be noted, that it does not eliminate them from the negative effects of an earthquake, even though it’s very efficient.

Seismic isolation does not help buildings resist earthquake forces by making them rigid but by making structures slide with the earthquake motion, using bearings placed at the foundations of building columns.

This technology can be applied at the initial design of a building or subsequent amendments can be done to a structure, using well researched concept to come up with an earthquake resistant structure (Komodromos).

This design was developed using reliable experiments and computer models. It involves jacking up a building column and installing one of the many bearing designs, and then the building is allowed to stand on them. (Sons, seismic analysis of structures)

The base isolation system involves the isolation units which basically are elements that are involved in decoupling. They are the whole essence of the technology; they lessen the effect of the shock wave on the superstructure lying on top of a foundation, which is in turn on a shaky ground, susceptible to earthquakes. These isolation units are held together by isolation component which has no decoupling effect.

All isolation units are divided into two: shear units and sliding units.

Introduction

Seismic isolation mechanisms have been developed to reduce the adverse effects of major earthquakes. The mechanism entails weakening the shock of an earthquake on a structure by dissipating the seismic energy. The technology have proved to be most effective in mitigating the misfortunes brought by earthquakes as compared to the making of robust structures, using materials such as steel, to fight the force of earthquake tremors.

In base isolation, a fixed building, which stands directly on the ground and moves with the motion of the earthquake and consequently can get seriously damaged.

A superstructure, one isolated from the ground, resting on flexible bearing, suffers little or no damage caused by the earthquake.

The principle works like a car. Its tires are the one that are in contact with the ground and, therefore, experience all its havoc while the people in the car are sheltered from the adverse effects.

The principle works on stones, bricks or reinforced concrete structures, making them and their residents protected from serious damage. However, this technology does not suit all kinds of structures. It works best on hard soil, not on soft. Base isolated structures are constructed in various ways. Some designs have big bearings with few columns, while others have lots of little bearings. An example of a base isolator is the lead rubber bearing. It came around 1970s. It consists of three components which are the lead plug, rubber and steel. These three are arranged in layers. (Skinner)

The rubber part is used for its flexibility property. It returns a building to its original position after an earthquake. However, it must be noted that this might take months.

Lead, on the other hand, was used for its plastic properties. It deforms after it’s subjected to a straining force but regains its original shape. It also does not lose its strength. The kinetic energy of an earthquake is absorbed as heat energy by the lead during its deformation.

Steel is used with rubber in the bearing, giving it a horizontal movement, but it remains stiff vertically.

Another principle that is very similar to the above mentioned is the seismic damper. Just as the latter, it uses lead to absorb the earthquake motion changing it into heat energy, therefore preventing the kinetic energy from spreading and damaging the building.

Another type of isolation system is the sliding isolation system. This mainly uses Teflon-stainless steel, flat or spherical interface. Sometimes, separate elements are provided for reentering of the isolated system.

For this system to work the soil must be of the right texture, to avoid producing a predominance of a long period of ground motion.

Secondly, the structure must be fairly squat with sufficiently high column load. The site should also allow horizontal displacement at the base of order 200mm or more.

Lateral loads, due to wind, should be approximately 10% of the weight of the structure.

Other techniques have come up replacing the passive dampers. These are the active and semi-active devices. They help limit excessive deformation.

The equation of motion for the superstructure is as follows:

Mü + Cû + Ku =-MR ü_{g }+ ü_{b}

While that of the base isolated system is:

R^{T}M ü +R üg+ü_{b }+ M_{b }ü_{g }+ ü_{b +} C_{b}û_{b }+ K_{b}u_{b }+ f + f _{c }= 0

Where M, C and K = superstructure mass, damping and stiffness matrices respectively, in the fixed condition.

ü_{b }= vector of base acceleration relative to the ground; ü_{g }= vector of absolute ground acceleration; M_{b }= diagonal mass matrix of the rigid base; C_{b }= resultant damping matrix of viscous isolation elements; K_{b }= resultant stiffness matrix of linear elastic isolation elements and f = vector containing the forces mobilized in the isolation bearings and devices, and f_{c }=control forces.

These equations can be used to obtain seismic responses.

How Base Isolation works:

To illustrate how base isolation works, let’s take a skeleton curve of the given relationship:

F = K_{eff}X

Where f is the shear force, X is the shear displacement and K_{eff} is the effective shear stiffness of the bearing.

K_{eff }is obtained from the empirical formula for elastomeric shear modulus as a function of shear strain. That is:

K_{eff }= G A and = _{h}

H_{r} H_{r}

Where G is the elastomer shear modulus as a function of shear strain, is the shear strain, A the bearing shear area, H_{r }the height of rubber in the bearing, and _{h} is the relative displacement between the top and bottom ends of the bearing.

The equations below are derived and they successfully model the behavior of elastomeric bearings into the large strain range.

F= F_{1 }+ F_{2 }

F_{1} = ½ (1- u) F_{m }{ x + sgn (X )I x I^{n }}

F_{2 }= uF_{m }{1– 2e^{-a( 1+x)} +b( 1 + x )e^{a( 1 + x) }}^{ } X>0

F_{2 }= - uF_{m} {1 – 2e^{-u (1-x) }+ b(1-x)e^{-a(1-x)}} X<0

Where F_{m }is the shear peak force on the skeleton curve, x is the normalized shear displacement on the skeleton curve.

In the next equation, n represents the stiffness and the in the last equation u is the ratio of shear force at zero displacement; F_{u }to F_{m }(u = F_{u/}F_{m}) a and b are calculated as follows:

1 – e^{-2a} = 2u – _{eq}

b = c^{2 }[ h_{eq}- {2 + 2/a (e^{-2a} - 1)}]

Where h_{eq }is the equivalent viscous damping ratio and is evaluated from an empirical formula as a function of shear strain. The parameter c is a constant; that gives the shape of the hysteresis loop. The above equations solve all parameters that control the hysteresis loop.

The above formulae apply to hysteresis loop at a steady state. For earthquakes causing unpredictable displacement different equations are obtained. These are:

F_{2 }= F_{2i }+ uF_{m}{2 – 2e^{-a(x-x}_{1}^{)} + b(x- x_{i})e^{-e(x- x}_{i}^{)}}, (X>0)

Or

F_{2i }- uF_{m}{2 – 2 e^{a(x-x}_{i}^{) }- b(x-x_{i})e^{c(x - x}_{i}^{)}} (X< 0)

a. low shear strain level; b. high shear strain level

where

F_{2i }= F_{i – }F_{1}

x_{i }= X_{i}

X_{m}

To greater enlargement of the hysteresis loop at load reversal in the stiffening range from occurring: the prior equation is replaced by one given below:

F_{2 }= F_{2i }+ _{1}uF_{m }{ 2 – 2e^{-a(x - x}_{i}^{)} }, X> 0

Or

F_{2i }- _{2}uF_{m }{ 2 – 2e^{-a(x - x}_{i}^{)} }, X < 0

Where

_{ 1 }= 2 – 2e^{a (x}_{i }^{– x}_{i – 1 }^{)} – b (x_{i} – x_{i - 1}) e^{a ( x}_{i }– ^{x}_{i }_{- 1}^{)}

2 – 2e^{a(x}_{i}^{ - x}_{i-1}^{)}

_{2 }= 2 – 2e ^{-a (x}_{i }^{– x}_{i – 1 }^{)} + b (x_{i} – x_{i - 1}) e ^{-a ( x}_{i }– ^{x}_{i }_{- 1}^{)}

2 – 2e^{-a(x}_{i}^{ - x}_{i-1}^{)}

Bearings deform under high strain. However, the stiffness lessens slowly with repeated cycling at the same displacement amplitude. To represent the phenomena, an additional force given by the equation below is added to the first equation

F = (K_{eff.i }- K_{eff} ) X (X < X_{min }or X> X_{max})

F = 0 (X_{min }< X < X_{max} )

Where X_{min }and X_{max} are the minimum and maximum values of experienced displacement, K_{eff.i} is the effective shear modulus of the elastomer obtained without any load history, unlike K_{eff }in the first equation.

When X_{min }and X_{max }changes F should be increased gradually to obtain a smooth transition for the two equations.

X’_{max }= X_{max + } _{’}T_{r}

X’_{min }= X_{min } _{’}T_{r}

Shear strain for stiffness recovery

About Seismic Designs

Seismic designs used in buildings take advantage of special detail or specific devices to change or harness the dynamic behavior of buildings. The structures that use this principle can be classified as passive, active or hybrid control system.

In passive control system, the earthquake energy is given away in specialized devices, which deforms and yields as a result. This in turn ensures that no other part of the building suffers damage. It’s referred to as passive, since it functions on its own; it does not require any other device to function. It’s also activated by the earthquake movement. Examples of the passive control system include the seismic isolation and passive energy dissipation.

In seismic isolation, the superstructure is prevented from absorbing the earthquake energy and, therefore, it’s mounted on discrete bearings. Movements are concentrated on the isolation devices and the top building remains rigid.

In passive energy dissipation, a lot of concentration is put on damping in order to reduce the effects of an earthquake. Therefore, a building resists most of the earthquake energy by using the energy dissipation devices. (Engineering, 1996)

In active control system, the idea is to produce a force that antagonizes with the earthquakes force and, therefore, nullifies its effects.

It’s said to be active because it is brought into function and controlled by computers, motion sensors, feedback mechanisms and moving parts that may require services or maintenance.

Hybrid control systems are a combination of both the passive and active control systems. It takes the best features of each. As a result, it consumes less power; more reliable and cheaper.

With passive control system, various designs can be obtained, leading to better security and improved lifestyles. However, it does not improve the performance of the building.

The objective of this method is to prevent loss of life. Therefore, in minor earthquakes, no damage occurs to a structure while in major, buildings are affected, but they do not collapse. It’s a life saving strategy.

In order for a building to remain firm when exposed to larger earthquake forces, convectional design is used; whereby the buildings are designed with elasticity to be able to withhold the earthquakes with less reliance on ductility and high levels of damping significant inelastic behavior (Foreword).

Passive control system is another measure, other than alternative design, it utilizes seismic isolation together with dissipation of energy; all this can be utilized to diminish the input of the earthquake concentrating on the inelastic deformations in the isolators or dumping devices. Isolation and dissipation procedures contain a yield threshold, and also display elastic behavior after initial yielding; and when below the threshold, the inelastic behavior. Hence, it is essentially imperative that earthquakes of different magnitudes be investigated, so as to ascertain the effectual range of the behavior of the device in use.

The seismic isolation system design depends on many attributes, which include fixed base structure, the type of soil at the site, the input response spectrum’s shape and the force deformation relationship for that specific isolation device.

The fundamental objective concerning the design is to get a structure such that, that the period the building is isolated is longer than the fixed–based period of that particular building and the main period of the site’s soil; hence, the superstructure can lessen the effect from the maximum earthquake input energy.

There are three main types of system definitions, namely: passive control system, hybrid control systems and active control systems. Active control systems are active and, therefore, require a source of energy and actuators, controlled by computers, to operate dampers that are strategically located throughout the building. The idea behind this system is to impose forces that counterbalance the forces, which are induced by an earthquake, so that they do not upset property on the ground. They need a constant energy source and an emergency energy source so that in the event of a major earthquake they are in a position to operate immediately.

Passive control systems are passive in the sense that they do not require an energy source in order to operate. Their operation is triggered by the earthquake’s motion. This input motion is dissipated into special connection details and specialized devices that deform then yield in the event of an earthquake. The deformation and destruction is therefore concentrated on the device, reducing the damage or deformation of other elements within the affected building. Examples of this control system are passive energy dissipation and seismic isolation.

Hybrid control systems, as the name suggests, exhibit a combination of passive and active control systems. They have an advantage over active control systems, because they use less power, are more reliable and cost less.

Seismic isolation systems, which are an example of passive control systems, are designed to protect the superstructure of the building. This is achieved by placing discrete isolators in the superstructure to absorb the earthquake energy in place of the building’s structure. Deformation, yielding and displacement are concentrated on the isolators, and they bear the pressure of the earthquake energy in the place of the building. In the event of an earthquake, these isolators ensure minimal to no damage to t he building.

An alternative type of passive control systems is the passive energy dissipation system. These systems offer supplementary damping through the use of viscoelastic dampers, lead extrusion systems or hydraulic devices, so that the response of the building structure to earthquake motion is reduced. Therefore, in the event of an earthquake, the building dissipates a lot of the earthquake motion energy through friction or deformation, which will be concentrated in the dissipation devices.

The seismic isolation system design is dependent on a couple of factors, including characteristics of the soil at the given site, the isolated structure’s period, the input response spectrum’s shape and the fixed base structure’s period. An ideal design is one, in which the building’s isolated period is longer than both that of the soil on the site and the superstructure’s period. This enables the superstructure of the building to be decoupled from the maximum earthquake energy.

Seeing earthquakes as natural disasters that cannot be stopped, it is important that the damage, they are capable to produce, is prevented. Seismic isolators are able to prevent damage to just any structure. The installation and operation costs of seismic isolators are initially high, but the damage that is averted, eventually, is worth every penny. They are, therefore, a prevention measures that are worth taking.

Seismic isolators, however, do not guarantee no damage at all. However, they can guarantee little to no damage to major structures, especially the building structure, which is of importance. Non structural components, such as piping, glazing and partitions may suffer damage. Therefore, while installing seismic isolators, it is important to identify exactly what is vulnerable to damage and how it can be protected. There are cases where displacement control is required, while others require acceleration control. Still, others require both variants.

The selection of the system to be used takes a couple of factors into consideration. These factors include non structural components that are considered critical, the soil surrounding, the given building and the building structure characteristics. Another very important consideration is the building’s proximity to an active fault, therefore the likelihood of it suffering damage in the event of an earthquake. The overall costs both present application costs and potential future damage costs must be put into consideration.

There are however sites, where seismic isolators are not recommended. These include deep soil sites and near fault sites. Seismic isolators designed to accommodate spectral displacements as large, as those exhibited in near fault sites, are yet to be developed. Deep soil sites may result in amplified structural response due to the likelihood of the isolators resonating, with the ground motion and this would be disastrous. Apart from these two sites, seismic isolators are good enough for other areas.

Conclusion

Base isolation is the most effective mean of protecting structures against earth tremors. The technique has been adopted by various countries which experience earthquakes. These include India, Japan London, the USA etc.; the design is also used to construct non-building structures like bridges. As the technology improves, it grows more and more popular. Its effectiveness is unquestionable.

The provided derived equations are very effective, because they cater for different magnitudes of shear forces. Using modified models of Bilinear and Ramberg – Osgood, they can be used to predict accurately the seismic response base isolated structures.