Building Vibration

Higher Colleges of Technology, Abu Dhabi

Building Vibration June 5

2011

Project of Building

Vibration for MECH

N349 , Prepared For

Dr. Molham Al Souk

By

Waleed Alyafee Humood AlShehhi

Mechanical Engineering students

for contact: [email protected]

Building Vibration 2011

MECH N349 | HCT, Abu Dhabi

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Contents Abstract ......................................................................................................................................................... 3

Introduction .................................................................................................................................................. 4

Literature Review .......................................................................................................................................... 6

Earthquake Proof Buildings and Structures: http://www.whatprice.co.uk/building/earthquake-proof-

buildings.html............................................................................................................................................ 6

How to Make Buildings & Structures Earthquake Proof:

http://www.reidsteel.com/information/earthquake_resistant_building.htm ................................................. 7

Control of vibration in civil structures: http://journals.pepublishing.com/content/w61g17254m84506j/9

Active/passive vibration control systems for tall buildings: http://iopscience.iop.org/0964-

1726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2 ............................................. 10

Control Algorithms ...................................................................................................................................... 17

Passive control methods: ............................................................................................................................ 17

Lateral Load Resisting Systems: .............................................................................................................. 17

Tuned Mass Damper (TMD) .................................................................................................................... 18

Principle of operation ......................................................................................................................... 19

Viscous damper ................................................................................................................................... 20

FLUID VISCOUS DAMPER DESCRIPTION .............................................................................................. 20

Principle of operation: ........................................................................................................................ 21

Active Control Systems ............................................................................................................................... 21

SEMI-ACTIVE CONTROL: .............................................................................................................................. 22

Flexibility influence coefficients:................................................................................................................. 23

Mass and Stiffness Matrices ....................................................................................................................... 27

MATLAB ....................................................................................................................................................... 31

Applying MATLAB in the results .............................................................................................................. 32

Conclusion ................................................................................................................................................... 43

References: ................................................................................................................................................. 44



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Abstract

This project is to cover the graduation requirements for high Diploma of Higher College Of

Technology. The research was on the earthquakes and it effects on the building. After that ,

designing system that help us to control the effect of earthquakes. This system has structure

components that should be under consideration. Also, installing the Tuned Mass Dumper TMD

in the structure and superstructure of building. This consisting of mass, spring and viscous

dumper. The viscous dumper will absorb the energy of the vibration due to earthquakes. Part of

calculations, it’s important to study the Flexibility influence coefficient. It focuses on the

behavior in terms of stiffness and flexibility. Another important subject is mass stiffness and

matrices. This provides the simplest representation of a building for the purposes of investigating

lateral dynamic responses.



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Introduction

One of the most frightening of natural disasters - an earthquake, leaves behind immediate

destruction, loss of life and despair on a scale that is mind boggling. And all of it due to collapsing

structures and dwellings unable to withstand the tremors of the earthquake. People lucky enough to be

outdoors manage to escape while people caught indoors get trapped or perish. Hence the importance of

constructing earthquake resistant houses and buildings is known in earthquake experienced areas where

architects and engineers plan accordingly. Engineers would like to make every building earthquake-proof,

but can't because it's too expensive. Instead, they recommend making dams and public buildings

earthquake-proof. All other buildings should be earthquake resistant to avoid deaths. The cost of repair is

a fraction of the cost of earthquake-proofing these buildings.

In areas where earthquakes are likely, knowing where to build and how to build can help reduce injury,

loss of life, and property damage during a quake. Knowing what to do when a quake strikes can also help

prevent injuries and deaths. Earth scientists try to identify areas that would likely suffer great damage

during an earthquake. They develop maps that show fault zones, flood plains (areas that get flooded),

areas subject to landslides or to soil liquefaction, and the sites of past earthquakes. From these maps, land-

use planners develop zoning restrictions that can help prevent construction of unsafe structures in

earthquake-prone areas.

Engineers have developed a number of ways to build earthquake-resistant structures. Their

techniques range from extremely simple to fairly complex. Field inspection and analyses of the

performance of structures during earthquake shaking of their foundations have clearly shown that

building design which blindly follows seismic code regulations does not guarantee safety against

collapse or serious damage. First, there are large uncertainties in many of the aspects involved in

the numerical design of structures, particularly in establishing the design earthquake shaking and

in estimating the demands and predicting the supplies of the real three-dimensional soil-

foundation-building (superstructure) system; second, the performance of the system depends on

its state when the earthquake strikes - thus construction and maintenance, which includes repair,

retrofitting and/or modifications, must also be considered in addition to the design aspects.

Design and construction of a structure are intimately related and the achievement of good

workmanship depends, to a large degree, on the simplicity of detailing of the members and of



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their connections and supports. For example, in the case of a reinforced concrete structure,

although it is possible to detail complex reinforcement on paper and even to realize it in

laboratory specimens so that seismic behavior is improved, in the field such design details may

not be economically feasible. A design is only effective if it can be constructed and maintained.

In a comprehensive approach to the design of a structure it is first necessary to establish the

design criteria, that is, behavior of the structure - serviceability, damageability, and safety against

collapse. Once the design criteria are established, depending on the limit state controlling the

design, the selection of the design earthquake(s) should be done according to the comprehensive

approaches. In this comprehensive attempt to overcome the uncertainties involved in modeling

the real three-dimensional soil-foundation-superstructure system and in the estimation of the

demands and supplies, usually derived from numerical analysis, the design cannot be based on a

single deterministic analysis of a single selected model. The designer should consider several

models, based on possible ranges over which the parameters governing the behavior of the real

system can vary. In order to overcome or decrease the uncertainties to which the values of most

of the parameters in the estimation of the demands and supplies are subjected in any current

seismic-resistant design procedure, it is necessary to pay more attention to conceptual design.

Conceptual design is defined as the avoidance or minimization of problems created by the effects

of seismic excitation by applying an understanding of the behavior rather than using numerical

computations. From the analysis of the basic design equations and the general equation for

predicting response, it becomes clear that to overcome detrimental effects of the uncertainties in

many of the factors in these equations the following philosophy can be applied: (1) control or

decrease the demands as much as possible, and (2) be generous in the supply, particularly by

providing large ductility with stable hysteretic behavior (toughness).

Because of the uncertainties regarding the dynamic characteristics of future earthquake ground

motions and their modifications as a result of the interaction of the soil with the foundation-

superstructure system response, the conceptual idea would be to control the input to the structure

foundation. One promising method is through the use of base isolation techniques including

energy absorbing devices in the system. In the case of buildings, a decrease in demand can be

achieved by a proper selection of the configuration of the building and its structural layout and

by the proper proportioning and detailing of the structural and non-structural components, that is,



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by following the basic principles or guideline for achieving efficient seismic-resistant

construction.

Literature Review

Earthquake Proofing Techniques: http://www.bookrags.com/research/earthquake-proofing-

techniques-woi/

This article talks about the ways on how to earthquake proof structures. The major thrust of earthquake-

proofing by architects is to prevent the collapse of buildings. The ability of a building to withstand the

stress of an earthquake depends upon its type of construction, shape, mass distribution, and rigidity.

Various combinations of techniques are used. Square, rectangular, or shell-shaped buildings, and

buildings with few stories, can better resist vibrations than L-shaped structures or skyscrapers. To reduce

stress, a building's ground floor can be supported by very rigid, hollow columns, while the rest of the

building is supported by flexible columns located inside the hollow columns. Another method is to use

rollers or rubber pads to separate the foundation columns from the ground, allowing the columns to shake

horizontally during an earthquake. It also talks on help to prevent collapse, roofs should be made of light-

weight materials. Exterior walls can be made more durable by fortifying them with steel or wooden

beams, or with reinforced concrete. Interior walls can bolster exterior walls, and a continuous collar can

cap a rectangular shaped structure, aiding its stability. If nonstructural walls (not used for support) are

attached only to the floor or only to the ceiling, they can move sideways as the building sways. Flexible

window frames can hold windows in place without breaking during tremors.

Earthquake Proof Buildings and Structures:

http://www.whatprice.co.uk/building/earthquake-proof-buildings.html

This article says that nothing is guaranteed when it comes to earthquakes or other calamities. But luckily,

there are certain building methods and materials to make structures more resistant to earthquakes. Being

aware about this information can potentially save you and your family.

Generally, all buildings can withstand weak earthquakes. They do not fall apart and collapse

instantly. The reason for this is most buildings can support their own weight plus a few more.

http://www.bookrags.com/research/earthquake-proofing-techniques-woi/





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Even poorly built buildings and structures can defy the up-and-down movement caused by

earthquakes. But it is the side-to-side movement that makes buildings collapse. Most buildings

are not designed to endure this. Structures and buildings should be supported to resist the

sideways effect of an earthquake. There are other methods that we can use but the most common

rule is; the lighter the building, the less the loads are and the better for all.

How to Make Buildings & Structures Earthquake Proof:

http://www.reidsteel.com/information/earthquake_resistant_building.htm

This site discusses these issues mentioned.

What is an earthquake?

What makes a building or structure fail in earthquakes?

So, how can we make buildings resistant to earthquakes?

So, when looking at design and construction how do we earthquake proof buildings?

There are a wide variety of earthquake effects - these might include a chasm opening up or a

drop of many metres across a fault line. Therefore, it is not possible to design an earthquake

proof building which is guaranteed to resist all possible earthquakes. However, it is possible

during your design and construction process to build in a number of earthquake resistant

features, which would increase enormously the chances of survival of both buildings and their

occupants. Then it goes on to saying, nothing can be guaranteed to be fully resistant to any

possible earthquake, but buildings and structures like the ones proposed here by ReidSteel would

have the best possible chance of survival; and would save many lives and livelihoods, providing

greater safety from an earthquake.

Earthquake, world book: http://www.nasa.gov/worldbook/earthquake_worldbook.html

This article discusses Earthquake (How an earthquake begins) (How an earthquake spreads)

(Damage by earthquakes) (Where and why earthquakes occur) (Studying earthquakes). Most

earthquakes occur along a fault -- a fracture in Earth's rocky outer shell where sections of rock

repeatedly slide past each other. Faults occur in weak areas of Earth's rock. Most faults lie


http://www.reidsteel.com/information/earthquake_resistant_building.htm#1




http://www.nasa.gov/worldbook/earthquake_worldbook.html



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beneath the surface of Earth, but some, like the San Andreas Fault in California, are visible on

the surface. Stresses in Earth cause large blocks of rock along a fault to strain, or bend. When the

stress on the rock becomes great enough, the rock breaks and snaps into a new position, causing

the shaking of an earthquake. Most earthquakes occur along a fault -- a fracture in Earth's rocky

outer shell where sections of rock repeatedly slide past each other. Faults occur in weak areas of

Earth's rock. Most faults lie beneath the surface of Earth, but some, like the San Andreas Fault in

California, are visible on the surface. Stresses in Earth cause large blocks of rock along a fault to

strain, or bend. When the stress on the rock becomes great enough, the rock breaks and snaps

into a new position, causing the shaking of an earthquake. Earthquakes can damage buildings,

bridges, dams, and other structures, as well as many natural features. Near a fault, both the

shifting of large blocks of Earth's crust, called fault slippage, and the shaking of the ground due

to seismic waves cause destruction. Away from the fault, shaking produces most of the damage.

Undersea earthquakes may cause huge tsunamis that swamp coastal areas. Other hazards during

earthquakes include rockfalls, ground settling, and falling trees or tree branches. Earth scientists

try to identify areas that would likely suffer great damage during an earthquake. They develop

maps that show fault zones, flood plains (areas that get flooded), areas subject to landslides or to

soil liquefaction, and the sites of past earthquakes. From these maps, land-use planners develop

zoning restrictions that can help prevent construction of unsafe structures in earthquake-prone

areas. Engineers have developed a number of ways to build earthquake-resistant structures. Their

techniques range from extremely simple to fairly complex. For small- to medium-sized

buildings, the simpler reinforcement techniques include bolting buildings to their foundations

and providing support walls called shear walls. Shear walls, made of reinforced concrete

(concrete with steel rods or bars embedded in it), help strengthen the structure and help resist

rocking forces. Shear walls in the center of a building, often around an elevator shaft or stairwell,

form what is called a shear core. Walls may also be reinforced with diagonal steel beams in a

technique called cross-bracing.

How We Make Structures Earthquake Resistant: http://www.buildingssteel.com/earthquake-

how.htm

http://www.buildingssteel.com/earthquake-how.htm




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This website talks about making structures to withstand earthquakes. It says that there are

several 'killers' in earthquakes to which non earthquake resistant buildings are more susceptible.

The first is horizontal or vertical acceleration of the ground, which moves suddenly sideways or

up. If the frame has insufficient sway strength, it falls down there and then at the first big jerk.

It's easy to design sway resistance in steel. The second is vibration from shock waves; like a

tuning fork, a building will oscillate at its own frequency if relatively small shock waves come at

the resonant frequency (often leaving taller or shorter structures nearby much less affected).

Oscillation can build up and produce greater and greater sway loads until the building fails in

sway or total overturning. This is where the ductility of the steel frame is so perfect; it deforms,

absorbing energy and simultaneously changing the resonant frequency of the structure; both

effects reduce oscillation. Thus steel framed earthquake resistant buildings with their better

structural performance help to solve these problems.

Control of vibration in civil structures:

http://journals.pepublishing.com/content/w61g17254m84506j/

This paper reports recent trends in active vibration control mainly as developed in Japan for civil

structures. Firstly, it classifies vibration control methods and controllers, especially active dynamic

absorbers that are widely used in mechanical and civil engineering. Secondly, it addresses basic problems

in the control of vibration of flexible structures such as formulating the reduced-order model required for

designing vibration controllers, the correct arranging of sensors and actuators, and how to prevent

spillover instability. Finally, the practical use of control theories such as linear-quadratic control theory,

H∞ control theory, neural network theory and other topics are discussed.

Experimental Active Vibration Control in Truss Structures Considering Uncertainties in System

Parameters: http://www.hindawi.com/journals/mpe/2008/754951.html

This paper deals with the study of algorithms for robust active vibration control in flexible structures

considering uncertainties in system parameters. It became an area of enormous interest, mainly due to the

countless demands of optimal performance in mechanical systems as aircraft, aerospace, and automotive

structures. An important and difficult problem for designing active vibration control is to get a

representative dynamic model. Generally, this model can be obtained using finite element method (FEM)

or an identification method using experimental data. Actuators and sensors may affect the dynamics

properties of the structure, for instance, electromechanical coupling of piezoelectric material must be


http://www.hindawi.com/journals/mpe/2008/754951.html



10

considered in FEM formulation for flexible and lightly damping structure. The nonlinearities and

uncertainties involved in these structures make it a difficult task, mainly for complex structures as spatial

truss structures. On the other hand, by using an identification method, it is possible to obtain the dynamic

model represented through a state space realization considering this coupling. This paper proposes an

experimental methodology for vibration control in a 3D truss structure using PZT wafer stacks and a

robust control algorithm solved by linear matrix inequalities.

Active/passive vibration control systems for tall buildings:

http://iopscience.iop.org/0964-

1726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2

This article talks about the three examples of vibration control systems are described. The first is a hybrid

mass damper system, which is one type of active vibration control system, as installed on the top floor of

a complex triangular building of forty-three stories in order to reduce the response of the building to

strong winds and moderate earthquakes. The second is an unbonded brace damper, which is a kind of

elasto-plastic damper using low-yield-point steel. It has been installed in a fifteen-story building as an

energy absorption member to control severe earthquake motion. The last is a rotational variable damper

using an electrorheological fluid. The feasibility of applying this type of damper to a real scale structure

as a semi-active control device has been investigated.

www.ias.ac.in/resonance/Dec2004/pdf/Dec2004Classroom4.pdf

Earthquake-Resistant Design of Buildings:

Buildings should be designed like the ductile chain. For example, consider the common urban residential

apartment construction – the multi-storey building made of reinforced concrete. It consists of horizontal

and vertical members, namely beams and columns. The seismic inertia forces generated at its floor levels

are transferred through the various beams and columns to the ground. The correct building components

need to be made ductile. The failure of a column can affect the stability of the whole building, but the

failure of a beam causes localized effect. Therefore, it is better to make beams to be the ductile weak links

than columns. This method of designing RC buildings is called the strong-column weak-beam design

method. By using the routine design codes (meant for design against nonearthquake effects), designers

may not be able to achieve a ductile structure. Special design provisions are required to help designers

improve the ductility of the structure. Such provisions are usually put together in the form of a special

seismic design code, e.g., IS: 13920-1993 for RC structures. These codes also ensure that adequate

ductility is provided in the members where damage is expected.

http://iopscience.iop.org/0964-1726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2

http://iopscience.iop.org/0964-1726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2

http://www.ias.ac.in/resonance/Dec2004/pdf/Dec2004Classroom4.pdf



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Quality Control in Construction:

The capacity design concept in earthquake-resistant design of buildings will fail if the strengths of the

brittle links fall below their minimum assured values. The strength of brittle construction materials, like

masonry and concrete, is highly sensitive to the quality of construction materials, workmanship,

supervision, and construction methods. Similarly, special care is needed in construction to ensure that the

elements meant to be ductile are indeed provided with features that give adequate ductility. Thus, strict

adherence to prescribed standards of construction materials and construction processes is essential in

assuring an earthquake-resistant building. Regular testing of construction materials at qualified

laboratories (at site or away), periodic training of workmen at professional training houses, and on-site

evaluation of the technical work are elements of good quality control.

Oscillations of Flexible Buildings:

When the ground shakes, the base of building moves with the ground, and the building swings back and-

forth. If the building were rigid, then every point in it would move by the same amount as the ground.

But, most buildings are flexible, and different parts move back-and-forth by different amounts.

Importance of Flexibility:

The ground shaking during an earthquake contains a mixture of many sinusoidal waves of different

frequencies, ranging from short to long periods. The time taken by the wave to complete one cycle of

motion is called period of the earthquake wave. In general, earthquake shaking of the ground has waves

whose periods vary in the range 0.03-33sec. Even within this range, some earthquake waves are stronger

than the others. Intensity of earthquake waves at a particular building location depends on a number of

factors, including the magnitude of the earthquake, the epicentral distance, and the type of ground that the

earthquake waves travelled through before reaching the location of interest.

www.ikb.poznan.pl/jacek.wdowicki/Pliki/materialy/.../Li03.pdf

wind effects on Di Wang Tower:

In this site the objective of the study is to investigate wind effects on Di Wang Tower under typhoon

condition. Wind speeds, wind directions and acceleration responses presented in this paper were

measured on top of the tall building during the passage of Typhoon Sally. Characteristics of the typhoon-

generated wind, structural dynamic properties and wind-induced responses of this super tall building were

presented and discussed. Furthermore, the full-scale measurements are compared with the wind tunnel

http://www.ikb.poznan.pl/jacek.wdowicki/Pliki/materialy/.../Li03.pdf



12

test results.

ncdr.nat.gov.tw/2icudr/2icudr_cd/PDF/P19.pdf

Earthquake and Typhoon Effects on a 51-story Tall Building:

This site investigates the vibratory characteristics of a 51-story steel high-rise building in response to a

major typhoon, earthquake and ambient vibrations.

www.taylordevices.eu/pdfs/tall-building.pdf

Fluid Viscous Dampers to reduce Wind-induced Vibrations in Tall Buildings:

The fluid viscous damping system proved to be a very cost effective method to effectively reduce wind-

induced vibrations. For large force output at very low displacement, a motion amplification device has

been included in the design in order to reduce the quantity and cost of the dampers.

e-book.lib.sjtu.edu.cn/nascc2004/data/.../WindResDsTallBldgsJapan.pdf

Importance of Design Value of Damping:

Structural damping is the most important, but most uncertain, parameter affecting dynamic responses of

buildings. This uncertainty significantly reduces the reliability of structural design for dynamic effects.

Accurate determination of structural damping is very important, not only for evaluating structural

responses, but also for designing active and passive auxiliary damping devices to be installed in buildings

and structures. However, there is no theoretical method for estimating damping in buildings. Thus, it has

been estimated on the basis of actual measurements of widely dispersed damping ratios.

www.mita.sd.keio.ac.jp/publications/data/c199501.pdf

Vibration Control of Tall Building Using Mega SubConfiguration:

An innovative vibration control system, which takes advantage of mega substructure configuration, was

http://www.taylordevices.eu/pdfs/tall-building.pdf

http://www.mita.sd.keio.ac.jp/publications/data/c199501.pdf



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proposed for tall and super tall building. This mega subcontrol system was designed in such a way that

the vibration energy of the megastructure due to wind or earthquake loads can be transferred in to

substructures and then dissipated in substructures by conventional damping devices.

A LITERARY REVIEW OF STRUCTURAL CONTROL: EARTHQUAKE FORCES

http://www.pbworld.com/news_events/publications/technical_papers/pdf/50_ALiteraryReview.pdf

Damping is the corruption of energy from an oscillating system, primarily through friction. The kinetic

energy is transformed into heat. Dampers can be installed to increase the damping rate. Attention has been

devoted to active control of engineering structures for earthquake hazard mitigation. This type of control

systems are often referred to as protective systems and have the advantage of being able to dynamically

modify the response of a structure in order to increase the safety and reliability.

One of the most promising classes of semi-active control devices is the Magnetorheological (MR)

damper. It overcomes the expenses and technical difficulties associated with other types of semi-active

devices. The fluids are materials that respond to an applied magnetic field with a dramatic change in

rheological behavior. The outstanding characteristic of these fluids is their ability to reversibly change

from free- flowing, linear viscous liquids to semi-solids having controllable yield strength in milliseconds

when exposed to a magnetic field.

Another type of semi-active control device is a controllable tuned liquid damper. It utilizes a sloshing

fluid or a column of fluid to reduce the responses of a structure. In a tuned mass damper, the liquid in a

sloshing tank is used to add damping to the structural system. It is not very effective for a wide variety of

loading conditions.

The hybrid mass damper (HMD) is a common device used in full-scale civil engineering buildings. The

HMD is actually a combination of the tuned mass damper and an active control actuator. The efficiency

of the HMD relies on the forces from the control actuator. A typical HMD requires less energy to operate

than a fully active mass damper system.

An active mass damper (AMD) is a small-auxiliary mass that is installed on one of the upper floors of a

building. An actuator is connected between the auxiliary mass and the structure. Response and loads are

measured at key locations on the building and sent to a control computer. The computer then processed

the information according to an algorithm and sends the appropriate signal to the AMD actuator. The




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actuator then reacts by applying inertial control forces to the structure to reduce the structural responses in

a desired manner.

Passive control systems relate to uncontrolled dampers, which require no input power to operate. They are

simple and generally low in cost, but are unable to adapt to changing needs. Passive control systems are

most commonly used in new and existing buildings that are in low seismic areas. Passive systems include

base isolation systems, friction dampers, viscoelastic dampers, and bracing systems.

Base Isolation systems are used to isolate the dynamic force transfer from the structure to the base.

Friction dampers consist of a steel plate and two plates holding the 9 steel plate from both sides. All

plates work together to absorb energy by friction as the building deforms due to seismic activity.

Viscoelastic dampers attenuate the force due to external and seismic loads. Bracing systems are used to

permanently stabilize buildings from external forces such as wind loads and earthquakes.

Variable semi-active devices have been used to utilize forces generated by surface friction to dissipate

vibratory energy in a structural system. The ability of semi-active devices to reduce drifts within a high

story building that is seismically excited has been investigated. With much success, the friction

controllable system has been employed in conjunction with a seismic isolation system.

Effect of Wind on Structure. http://www.sefindia.org/forum/files/Effect_of_wind_on_structure_141.pdf

Wind produces three different types of effects on structure which is static, dynamic and aerodynamic. The

response of load depends on type of structure. When the structure deflects in response to wind load then

the dynamic and aerodynamic effects should be analyzed in addition to static effect. Sound knowledge of

fluid and structural mechanics helps in understanding of details of interaction between wind flow and

civil engineering structures or buildings Flexible slender structures and structural elements are subjected

to wind induced along and across the direction of wind. When considering the response of a tall building

to wind gusts, both along-wind and across-wind responses must be considered. These arise from different

the former being primarily due to buffeting effects caused by turbulence; the latter being primarily due to

alternate-side vortex shedding. The cross-wind response may be of particular importance because it is

likely to exceed along-wind accelerations if the building is slender about both axes.

Any building or structure which does not satisfy either of the above two criteria shall be examined for

dynamic effects of wind:

a) Buildings and closed structures with a height to minimum lateral dimension ratio of more than about

http://www.sefindia.org/forum/files/Effect_of_wind_on_structure_141.pdf



15

5.0.

b) Buildings and closed structures whose natural frequency in the first mode is less than 1 Hz.

Wind induced oscillation

There are three forms of wind induced motion as follows:-

a) Galloping - is transverse oscillations of some structures due to the development of aerodynamic forces

which are in phase with the motion. It is characterized by the progressively increasing amplitude of

transverse vibration with increase of wind speed. Non circular cross sections are more susceptible to this

type of oscillation

b) Flutter is unstable oscillatory motion of a structure due to coupling between aerodynamic force and

elastic deformation of the structure. Perhaps the’ most common form is oscillatory motion due to

combined bending and torsion. Long span suspension bridge decks or any member of a structure with

large values of d/t ( where d is the depth of a structure or structural member parallel to wind stream and t

is the least lateral dimension of a member ) are prone to low speed flutter.

c) Ovalling - This walled structures with open ends at one or both ends such as oil storage tanks, and

natural draught cooling towers in which the ratio of the diameter of minimum lateral dimension to the

wall thickness is of the order of 100 or more, are prone to ovalling oscillations. These oscillations are

characterized by periodic radial deformation of the hollow structure.

The dynamic component which essentially causes the oscillation of structure is generated due to three

reasons:-

1) Gust The wind velocity at any location varies considerably with time. In addition to a steady wind

there are effects of gusts which last for few seconds, and yield a more realistic assessment of wind load.

In practice the peak gust are likely to be observed over an average time of 3.5 to 15 sec depending on

location and size

of structure..The intensity of gusts is also related to the duration of gusts that affects structures. Larger

structure will be affected more by gust of larger duration and thus subjected to smaller pressure compared

to smaller structure.

The gust effect factor accounts for additional dynamic amplification of loading in the along-wind

direction due to wind turbulence and structure interaction. It does not include allowances for across-wind



16

loading effects, vortex shedding, instability due to galloping or flutter, or dynamic torsional effects.

Buildings susceptible to these effects should be designed using wind tunnel results.

This factor accounts for the increase in the mean wind loads due to the following factors:

• Random wind gusts acting for short durations over entire or part of structure.

• Fluctuating pressures induced in the wake of a structure, including vortex shedding forces.

• Fluctuating forces induced by the motion of a structure.

2) Vortex Shedding

When wind acts on a bluff body forces and moments in three mutually perpendicular directions are

generated- out of which three are translation and three rotation. For civil and structures the force and

moment corresponding to the vertical axis (lift and yawing moment) are of little significance. Therefore

the flow of wind is considered two-dimensional consisting of along wind response and transverse wind

response.

Along wind response refer to drag forces, and transverse wind is the term used to describe crosswind. The

crosswind response causing motion in a plane perpendicular to the direction of wind typically dominates

over the along-wind response for tall buildings.

Consider a prismatic building subjected to a smooth wind flow. The originally parallel upwind

streamlines are displaced on either side of the building due to boundary layer separation. This results in

spiral vortices being shed periodically from the sides into the downstream flow of wind creating a low

pressure zone due to shedding of eddies called the wake. When the vortices are shed across wind

component are generated in the transverse direction. At low wind speeds, since the shedding occurs at the

same instant on either side of the building, there is no tendency for the building to vibrate in the

transverse direction. It is therefore subject to long-wind oscillations parallel to the wind direction. At

higher speeds, the vortices are shed alternately, first from one and then from the other side. When this

occurs, there is a force in the along-wind direction as before, but in addition, there is a force in the

transverse direction.

This type of shedding, which gives rise to structural vibrations in the flow direction as well as in the

transverse direction, is called vortex shedding. The frequency of shedding depends mainly on shape and

size of the structure, velocity of flow and to a lesser degree on surface roughness, turbulence of flow.



17

Control Algorithms There are three types of control methods structural that based in study:

1. Passive control methods

2. Active Control Systems

3. Semi-active control algorithms

Passive control methods: In this case, the passive device does not need an external power. This kind of method has

some features such as :

1. No need for external energy

2. Stable

3. Simple process and operation

Lateral Load Resisting Systems: It’s the system that combines structure components to face and overcome the effects of

earthquakes. This system must be studied when designing a building that can withstand

earthquakes.

The structure components are:

1. Shear walls

2. Braced frames

3. Moment resisting frames

4. Horizontal trusses

This type of system also involved in architect’s structural. When engineers design this system for

any particular building, they should review the concept of architectural of the building.



18

Tuned Mass Damper (TMD) It’s a passive control device that is connected to the structure of building to absorb its responses.

TMD should have:

1. Mass that is 2 % of total mass of the Building.

2. Spring (K) that change the systems and modes of TMD of the controlled building.

3. Viscous damper ( C)



19

Principle of operation

From the laws of physics, we know that F = ma and a =

F/m. This means that when an external force is applied to a

system, such as wind pushing on a skyscraper, there has to be an

acceleration. Consequently, the people in the skyscraper would

feel this acceleration. In order to make the occupants of the

building feel more comfortable, tuned mass dampers are placed in

structures where the horizontal deflections from the wind's force

are felt the greatest, effectively making the building stand

relatively still.

When the building begins to oscillate or sway, it sets the TMD

into motion by means of the spring and, when the building is

forced right, the TMD simultaneously forces it to the left.

Ideally, the frequencies and amplitudes of the TMD and the

structure should nearly match so that EVERY time the wind pushes the building, the TMD

creates an equal and opposite push on the building, keeping its horizontal displacement at or near

zero. If their frequencies were significantly different, the TMD would create pushes that were out

of sync with the pushes from the wind, and the building's motion would still be uncomfortable

for the occupants. If their amplitudes were significantly different, the TMD would, for example,

create pushes that were in sync with the pushes from the wind but not quite the same size and the

building would still experience too much motion.

The effectiveness of a TMD is dependent on the mass ratio (of the TMD to the structure itself),

the ratio of the frequency of the TMD to the frequency of the structure (which is ideally equal to

one), and the damping ratio of the TMD (how well the damping device dissipates energy).



20

Viscous damper

Fluid viscous damping is a way to add energy dissipation to the lateral system of a

building structure. A fluid viscous damper dissipates energy by pushing fluid through an orifice,

producing a damping pressure which creates a force.

FLUID VISCOUS DAMPER DESCRIPTION

1. Very strong shock absorber.

2. Dumpers consists of stainless steel.

3. Live for 40 years.

4. The damping fluid is silicone oil

5. Very high technology seals that provide free leakage.

Viscous damper



21

Principle of operation:

The damping action is provided by the flow of fluid across the piston head. The piston transmits

energy entering the system to the fluid in the damper, causing it to move within the damper. The

movement of the fluid within the damper fluid absorbs this kinetic energy by converting it into

heat. In automobiles, this means that a shock received at the wheel is damped before it reaches

the passengers compartment. In buildings this can mean that the building columns protected by

dampers will undergo considerably less horizontal movement and damage during an earthquake.

Active Control Systems Active control systems have been studied extensively and are currently in use in a number of

structures in Japan for protection against wind excitation and minor earthquakes. The term

“active” is used to indicate that the operation of these systems requires a significant amount of

external power. The mechanical properties of these systems are typically adjusted based on

feedback from the structural system to which they are attached. Control forces are generally

developed by electro-hydraulic actuators which require a large power source for operation (on

the order of tens of kilowatts). Active control systems may also be designated as active energy

dissipation systems because the primary effect of these systems is to modify the level of damping

in a structure with only minor modification of stiffness.



22

SEMI-ACTIVE CONTROL: The use of passive control systems and active control systems represents two extremes in the

application of control theory to earthquake hazard mitigation. A compromise between these two

extremes is available in the form of semi-active control systems which have been developed to

take advantage of the best features of both passive and active control systems. The term “semi-

active” is used to indicate that the operation of these systems requires a very small amount of

external power (on the order of tens of watts). As in an active control system, the mechanical

properties are typically adjusted based on feedback from the structural system to which they are

attached. As in a passive control system, semi-active control systems utilize the motion of the

structure to develop control forces. The control forces are developed through appropriate

adjustment of damping or stiffness characteristics of the semi-active control system.

Furthermore, the control forces always oppose the motion of the structure and therefore promote

stability. Semi-Active control systems are typically considered to be fail-safe in the sense that

semi-active devices can be designed to exhibit either prescribed damping or prescribed stiffness

characteristics in the event of a complete loss of power.



23

Flexibility influence coefficients: This is used for expressing the elastic behavior in terms of stiffness and flexibility.

The flexibility matrix written in terms of its coefficients aij is:

aij: The displacement at i due

to a unit force applied at j when all other forces equal to zero.

First column: the displacements corresponding to f1=1 (f2=f3=0)

Second column: the displacements corresponding to f2=1 (f1=f3=0)

Third column: the displacements corresponding to f3=1 (f1=f2=0)

Rule:

For the first column when f1=1 (f2=f3=0)

00

1

0

0

0

0

0

0

1

11

11

1

1

3

2

1 f

xxx

k

k

k

For the second column when f2=1 (f1=f3=0)

010

000

000

2

1

1

1

2

1

1

11

1

3

2

1

kk

kk

k

xxx

For the third column when f3=1 (f1=f2=0)

100

3

1

2

1

1

12

1

1

11

1

0

0

0

0

0

0

3

2

1

kkk

kk

k

xxx

fff

aaa

aaa

aaa

xxx

3

2

1

34

23

13

33

22

12

31

21

11

3

2

1



24

The complete flexibility matrix is now the sum of the three prior matrixes:

fff

xxx

kkk

kk

k

kk

kk

k

k

k

k

3

2

1

3

2

1

3

1

2

1

1

12

1

1

11

1

2

1

1

1

2

1

1

11

1

1

11

11

1

For example:

The flexibility matrix for a system shown below:

1)

Given information:

K1=2k

K2=k

K3=k

Answer:

5.2

5.1

5.0

5.1

5.1

5.0

5.0

5.0

5.0



25

2)

Given information:

K1=3k

K2=k

K3=k

Answer:

3.2

3.1

3.0

3.1

3.1

3.0

3.0

3.0

3.0

3)

Given information:

K1=5k

K2=3k

K3=7k

Answer:

7.0

5.0

2.0

5.0

5.0

2.0

2.0

2.0

2.0



26

4)

Given information:

K1=4k

K2=2k

K3=6k

Answer:

92.0

75.0

25.0

75.0

75.0

25.0

25.0

25.0

25.0

5)

Given information:

K1=9k

K2=3k

K3=5k

Answer:

6.0

4.0

1.0

4.0

4.0

1.0

1.0

1.0

1.0



27

Mass and Stiffness Matrices Consider a building frame modeled by a set of rigid, massive floors supported by flexible,

massless columns. This provides the simplest representation of a building for the purposes of

investigating lateral dynamic responses, as produced by earthquakes or strong winds. The lateral

position of mass i with respect to the ground will be given the variable ri, ki is the lateral stiffness

of the columns in story i, and the mass of mass i is mi.

For a three-story building, this kind of representation is shown in Figure 1.

�_�_�_�_�_�_�_�_�_�_� _�_�_�_�_�_�_�

�_�_�_�_ Figure 1. A simplified model of a building frame with massive rigid floors and

light flexible columns.

Exercise 1: Show that the mass matrix and stiffness matrix for this three story building can be

written:

Solution: let x1=1 and x2=x3=0. The forces required at 1,2 and 3, considering on the right as

positive, are:

F1= k1+k2= k11

F2= - k2= k21

F3= 0 = k31

Repeat with x2=1, x1=x3=0, the forces are now:



28

F1= - k2= k12

F2= k2 + k3 = k22

F3= - k3 = k32

For the last column of k’s, let x3=1 and x1=x2=0. The forces are:

F1= 0 =k13

F2= - k3 = k23

F3= k3 = k33

Therefore the mass matrix and stiffness matrix for a three story building is:

Example 1.

Solution:



29

Example 2.

Solution:

Example 3.



30

Example 4.

Solution:

Example 5.

Solution:



31

MATLAB

Matlab is a program that performs various numerical operations. Like a big

calculator. Computer languages are generally divided into low-level languages, that

interact with the specific hardware directly and need to be both written and compiled for

the specific setting you are using. This is very powerful, because it allows you to use the

resources of your machine in whatever way you choose. High-level languages, on the

other hand, can be transferred from machine to machine (and, in some cases, from

operating system to operating system), but often will need to be compiled for a specific

setting. Matlab functions as a scripting language. Scripting languages are high-level

computer languages. However, above and beyond the portable nature of most high-

level languages, a system specific interpreter interprets them online, as they run.

Therefore, you will not need to compile the programs you write on Matlab. Scripting

languages are relatively easy to learn. However, they do not retain the same level of

flexibility as low-level languages. Moreover, because they need to be interpreted as

they run, they are often slower than the equivalent program written in a compiled high-

level language.



32

Applying MATLAB in the results A=[-2 0.1;0.1 -2]; %Matrix determined by equations of motion. [v,d]=eig(A) %Find Eigenvalues and vectors. The eigenvectors are

the columns of "v," the eigenvectors are %the diagonal elements of "d"

x0=[1 0]' %Initial conditions

gamma=inv(v)*x0 %Find unknown coefficients gamma



33

A=[-2 0.1;0.1 -2]; %Matrix determined by equations of motion. [v,d]=eig(A) %Find Eigenvalues and vectors. The eigenvectors are


x0=[1 0]' %Initial conditions

gamma=inv(v)*x0 %Find unknown coefficients gamma



34

%Define Array from equations of motion. A=[0.5 1.5;1.5 2.5]; %2 masses [v,d]=eig(A); %Find Eigenvalues and vectors. omega=sqrt(diag(-d)); %Get frequencies x0=[1 0]' %Initial condition gam=inv(v)*x0 %Find unknown coefficients



35




36




37




38




39




40




41





42





43

Conclusion

All in all, earthquakes have so many negative results on building. In this case we can

find devices that can protect the building from the effects of vibration. During the earthquakes,

the energy of the huge vibration will be sent to the building. Engineers designed devices that

absorb this energy and kick it out in a form of heat. To translate the movements of earthquake,

we need to study the types of algorithms that help us to reduce the effects of earthquakes. To

design a building that has resistance of earthquakes, we need to design the Lateral Load

Resisting Systems. This system gathers the structure components to absorb the energy and

overcome the effects of the earthquakes. One of the passive control devices called Tuned Mass

Damper. This device consists of mass, spring and dumper device. One example is the viscous

dumper. It’s part of the TMD, and its installed in the structure and superstructures of building

where is the highest effect of the earthquake on the building. Part of calculations, it’s important

to study the Flexibility influence coefficient. It focuses on the behavior in terms of stiffness and

flexibility. Another important subject is mass stiffness and matrices. This provides the simplest

representation of a building for the purposes of investigating lateral dynamic responses. Based on

the calculations, we can know what is the best way to choose the best module.



44

References:

1. http://www.rwdi.com/cms/publications/18/t06.pdf

2. http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Eva_Burk/Eva's%201st%20page.htm

3. http://www.taylordevices.com/fluidviciousdamping.html

4. http://www.expertune.com/artCE87.html

5. http://nms.csail.mit.edu/papers/binomial-infocom01.pdf

6. http://www.benthamscience.com/meng/samples/meng%201-1/Kumar.pdf

7. http://www.bookrags.com/research/earthquake-proofing-techniques-woi/

8. http://www.whatprice.co.uk/building/earthquake-proof-buildings.html

9. http://www.reidsteel.com/information/earthquake_resistant_building.htm

10. http://www.nasa.gov/worldbook/earthquake_worldbook.html

11. http://www.buildingssteel.com/earthquake-how.htm

12. http://journals.pepublishing.com/content/w61g17254m84506j/

13. http://www.hindawi.com/journals/mpe/2008/754951.html

14. http://iopscience.iop.org/09641726/7/5/003;jsessionid=BA6E2E5EC098268D422448

A75FA80E9F.c2

15. http://www.ias.ac.in/resonance/Dec2004/pdf/Dec2004Classroom4.pdf

16. www.ikb.poznan.pl/jacek.wdowicki/Pliki/materialy/.../Li03.pdf

17. ncdr.nat.gov.tw/2icudr/2icudr_cd/PDF/P19.pdf

18. http://www.taylordevices.eu/pdfs/tall-building.pdf

19. e-book.lib.sjtu.edu.cn/nascc2004/data/.../WindResDsTallBldgsJapan.pdf

20. http://www.mita.sd.keio.ac.jp/publications/data/c199501.pdf

21. http://www.pbworld.com/news_events/publications/technical_papers/pdf/50_ALiterar

yReview.pdf

22. http://www.sefindia.org/forum/files/Effect_of_wind_on_structure_141.pdf

http://www.rwdi.com/cms/publications/18/t06.pdf

http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Eva_Burk/Eva's%201st%20page.htm

http://www.taylordevices.com/fluidviciousdamping.html

http://www.expertune.com/artCE87.html

http://nms.csail.mit.edu/papers/binomial-infocom01.pdf

http://www.benthamscience.com/meng/samples/meng%201-1/Kumar.pdf




http://www.nasa.gov/worldbook/earthquake_worldbook.html



http://www.hindawi.com/journals/mpe/2008/754951.html

http://iopscience.iop.org/09641726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2

http://iopscience.iop.org/09641726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2

http://www.ias.ac.in/resonance/Dec2004/pdf/Dec2004Classroom4.pdf

http://www.ikb.poznan.pl/jacek.wdowicki/Pliki/materialy/.../Li03.pdf

http://www.taylordevices.eu/pdfs/tall-building.pdf

http://www.mita.sd.keio.ac.jp/publications/data/c199501.pdf



http://www.sefindia.org/forum/files/Effect_of_wind_on_structure_141.pdf

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