Building Vibration

Higher Colleges of Technology, Abu Dhabi

June 5
Building Vibration
2011

Project of Building
Vibration for MECH
N349 , Prepared For
Dr. Molham Al Souk
By

Waleed Alyafee
Humood AlShehhi

Mechanical Engineering students

for contact: ggc@windowslive.com

Building Vibration 2011

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

2

MECH N349 | HCT, Abu Dhabi


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.

3



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.
4
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


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 5

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,

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.

6
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.


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)
7
(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

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 8


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) 9

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


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
10
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.

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- 11

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


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
12
Vibration Control of Tall Building Using Mega SubConfiguration:

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

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 13
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


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: 14

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


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. 15

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


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 16
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.



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. 17



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)

18


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).

19


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.

20
Viscous damper


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.

21



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.

22



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:

 x  a a a  f 1
 1   11 12 13    
 x2   a21 a22 a23  f 2 
    
 x3  a31 a33 a34  f 3 
 
 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)

1 
x   k1 0 0   1
 1  1  f 1 
 x 2    0 0  0 
   k1 0 0  
 x3   1  0 
 k1 
 
 For the second column when f2=1 (f1=f3=0)

 1 
 
 x  0
 1  1
k1 0  0 
1   
 x2   0    0 1 
    k1 k 2    
 x3  0 1 1  0  0 
    

  k1 k 2   

 For the third column when f3=1 (f1=f2=0)
 1 
x  0 0 k1  
 1  1 1  
0
 x 2   0 0   0  23
  0 0 k1 k 2   
 x3   1  1  1  1 
 k1 k 2 k 3 
 



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

1 1 1 
  
 x   k1 k1 k1  f1
 1  1  1 1  1 1   
 x2       
  f 2
   k1  k1 k 2  k1 k 2   
 x3  1 1 1  1  1  1  f 3
    

 k1  k1 k 2  k1 k 2 k 3 

 

For example:
The flexibility matrix for a system shown below:
1)

Given information:
K1=2k
K2=k
K3=k

0.5 0.5 0.5
Answer: 0.5 1.5 1.5 
 
0.5 1.5 2.5
 

24


2)

Given information:

K1=3k

K2=k

K3=k

0.3 0.3 0.3
Answer: 0.31.3 1.3 
 
0.31.3 2.3
 

3)

Given information:
K1=5k
K2=3k
K3=7k
25
0.2 0.2 0.2
Answer: 0.2 0.5 0.5
 
0.2 0.5 0.7
 

4)

Given information:
K1=4k
K2=2k
K3=6k

0.25 0.25 0.25
Answer: 0.25 0.75 0.75
 
0.25 0.75 0.92
 

5)

Given information:
K1=9k
K2=3k
K3=5k

0.1 0.1 0.1
Answer: 0.10.4 0.4
 
0.10.4 0.6
  26



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 27
F3= 0 = k31
Repeat with x2=1, x1=x3=0, the forces are now:


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:

28


Example 2.

Solution:

Example 3.

29


Example 4.

Solution:

Example 5.

Solution:

30



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.

31



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

32




x0=[1 0]' %Initial conditions

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

33



%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

34


A=[0.3 0.3;0.3 0.3]; %2 masses

35



A=[0.3 1.3;1.3 0.3]; %2 masses

36



A=[0.3 1.3;1.3 2.3]; %2 masses

37



A=[0.2 1.2;1.2 0.2]; %2 masses

38



A=[0.2 0.5;0.5 0.2]; %2 masses

39



A=[0.2 0.5;0.7 0.2]; %2 masses

40



41




42



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.

43



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

44


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