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13.3 Dynamic Effects of Wind Loading on Structures

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13.3.1 Introduction

The turbulent nature of the wind is characterized by sudden gusts superimposed upon a mean wind

velocity. The wind vector at a point may be regarded as the sum of the mean wind vector (static

component) and a dynamic component

Vðz; tÞ ¼ V􀀊 ðzÞ þ vðz; tÞ ð13:12Þ

Wind is a phenomenon of great complexity because of the many flow situations arising from the

interaction of wind with structures. Wind is composed of a multitude of eddies of varying sizes and

rotational characteristics carried along in a general stream of air moving relative to the Earth’s surface.

These eddies give wind its gusty or turbulent character. The gustiness of strong winds in the lower levels

of the atmosphere largely arises from interaction with surface features. The average wind speed over a

time period of the order of 10 min or more tends to increase with height, while the gustiness tends to

decrease with height.

A further consequence of turbulence is that dynamic loading on a structure depends on the size of the

eddies. Large eddies, whose dimensions are comparable with the structure, give rise to well-correlated

pressures as they envelop the structure. On the other hand, small eddies result in pressures at various

parts of the structure being practically uncorrelated. Eddies generated around a typical structure are

shown in Figure 13.12.

(a) Elevation (b) Plan

FIGURE 13.12 Generation of eddies. (a) Elevation; (b) plan.

13-22 Vibration and Shock Handbook

Some structures, particularly those that are tall or slender, respond dynamically to the wind. The bestknown

structural collapse due to wind was the Tacoma Narrows Bridge which occurred in 1940 at a wind

speed of only about 19 m/sec. It failed after it had developed a joint torsional and flexural mode of

oscillation.

There are several different phenomena giving rise to dynamic response of structures in wind. These

include buffeting, vortex shedding, galloping, and flutter. Slender structures are likely to be sensitive to

dynamic response in line with the wind direction as a consequence of turbulence buffeting. Transverse or

crosswind response is more likely to arise from vortex shedding or galloping, but may be excited by

turbulence buffeting also. Flutter is a coupled motion, often a combination of bending and torsion, and

can result in instability.

An important problem associated with the wind-induced motion of buildings is concerned with the

human response to vibration. At this point, it will suffice to note that humans are surprisingly sensitive to

vibration, to the extent that motions may feel uncomfortable even if they correspond to relatively

unimportant stresses. The next few sections give a brief introduction to the dynamic response of

structures in wind. More details can be found in wind engineering texts (e.g., Sachs, 1978; Holmes, 2001).

13.3.2 Wind Speed

At great heights above the surface of the Earth, where frictional effects are negligible, air movements are

driven by pressure gradients in the atmosphere, which in turn are the thermodynamic consequence of

variable solar heating of the Earth. This upper level wind speed is known as the gradient wind velocity.

Different terrains can be categorized according to the roughness length. Table 13.3 shows the different

categories specified in the Australian/New Zealand wind code, AS/NZS 1170.2 (2002). Closer to the

surface, the wind speed is affected by frictional drag of the air over the terrain. There is a boundary layer

within which the wind speed varies from almost zero, at the surface, to the gradient wind speed at a

height known as the gradient height. The thickness of this boundary layer, which may vary from 500 to

3000 m, depends on the type of terrain, as depicted in Figure 13.13. As can be seen, the gradient height

within a large city center is much higher than it is over the sea where the surface roughness is less.

In practice, it has been found useful to start with a reference wind speed based on statistical analysis of

wind speed records obtained at meteorological stations throughout the country. The definition of the

reference wind speed varies from one country to another. For example, in Australia/New Zealand, it is the

3-sec gust wind speed at a height of 10 m above the ground assuming terrain category 2. Maps of

reference wind speeds applying to various countries are usually available.

An engineering wind model for Australia has been developed by Melbourne (1992) from the Deaves

and Harris (1978) model. This model is based on extensive full-scale data and on the classic logarithmic

law in which the mean velocity profile in strong winds applicable in noncyclonic regions (neutral stability

conditions) is given by Equation 13.13

V􀀊 z < up

0:4

loge

􀀏 􀀐

þ 5:75

􀁻 !

2 1:88

􀁻 !2

􀁻 !3

þ 0:25

􀁻 !4 " #

ð13:13Þ

The numerical values are based on a mean gradient wind speed of 50 m/sec.

TABLE 13.3 Terrain Category and Roughness Length ðz0 Þ

Terrain Category Roughness

Length ðz0 Þ

Exposed open terrain with few or no obstructions and water surfaces at serviceability wind speeds 0.002

Water surfaces, open terrain, grassland with few, well-scattered obstructions having heights

generally from 1.5 to 10 m

0.02

Terrain with numerous closely spaced obstructions 3 to 5 m high such as areas of suburban

housing

0.2

Terrain with numerous large, high (10.0 to 30.0 m high) and closely spaced obstructions such as

large city centers and well-developed industrial complexes

Vibration and Shock Problems of Civil Engineering Structures 13-23

For values of z , 30:0 m the z=zg values become insignificant and the above equation simplifies to

V􀀊 z < up

0:4

loge

􀀏 􀀐

ð13:14Þ

where:

V􀀊 z ¼ the design hourly mean wind speed at height z; in m/sec

up ¼ the friction velocity

up ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

surface friction shear stress

atmospheric density

z ¼ the distance or height above ground, in m

zg ¼ the gradient height in meters (the value ranges from 2700 to 4500 m), see Table 13.4 (derived by the

authors)

zg ¼

6 £ 1024

As given in Table 13.3, there is an interaction between roughness length and terrain category, so it is

necessary to define a terrain category to find the design hourly wind speeds and gust wind speeds. The

link between hourly mean and gust wind speeds is as follows:

V ¼ V􀀊 1 þ 3:7

V􀀊 z

􀀒 􀀏 􀀐􀀓

ð13:15Þ

where

sv ¼ 2:63hup 0:538 þ 0:09 loge

􀀒 􀀏 􀀐􀀓h16

ð13:16Þ

Open sea Open level country Woodlands,

suburbs

City centre

Elevation

z0 = 0.002 z0 = 0.02 z0 = 0.2 z0 = 2

FIGURE 13.13 Mean wind profiles for different terrains.

TABLE 13.4 Roughness Length, Friction Velocity, and Gradient Height

Terrain Category z0 (m) up zg (m)

1 0.002 1.662 2769

2 0.02 1.910 3184

3 0.2 2.243 3738

4 2 2.708 4514

13-24 Vibration and Shock Handbook

h ¼ 1:0 2

􀁻 !

ð13:17Þ

For design, the basic wind speed is classified into three different speeds as follows:

Vs ¼ V20 yr ¼ serviceability limit state design speed having an estimated probability of exceedance of

5% in any one year, for the serviceability limit states

Vp ¼ V50 yr ¼ permissible, or working, stress design wind speed and can be obtained directly from Vu

using the relation Vp ¼ Vu=ð1:5Þ0:5

Vu ¼ V1000 yr ¼ ultimate limit state design wind speed having an estimated probability of exceedance

of 5% in a lifetime of 50 years, for the ultimate limit states

Using rigorous analysis incorporating probability distribution of wind speed and direction, basic

design wind speeds for different directions and different return periods can be derived. For example,

AS/NZS 1170.2 provides a wind direction multiplier, which varies from 0.80 for wind from the east to 1.0

for wind from the west, and having wind speeds up to a 2000-year return period.

13.3.3 Design Structures for Wind Loading

The characteristics of wind pressures are a function of the characteristics of the approaching wind, the

geometry of the structure, and the geometry and proximity of the upwind structures. The pressures are

not steady, but highly fluctuating, partly as a result of the gustiness of the wind, but also because of local

vortex shedding at the edges of the structures themselves. The fluctuating pressures result in fatigue

damage to structures, and in dynamic excitation, if the structure happens to be dynamically wind

sensitive. The pressures are also not uniformly distributed over the surface of the structure, but vary

with position.

The complexities of wind loading should be kept in mind when designing a structure. Because of the

many uncertainties involved, the maximum wind loads experienced by a structure during its lifetime may

vary widely from those assumed in the design. Thus, the failure or nonfailure of a structure in a

windstorm cannot necessarily be taken as an indication of the nonconservativeness, or conservativeness,

of the wind-loading standard. The standards do not apply to buildings or structures that are of unusual

shape or location. Wind loading governs the design of some types of structures, such as tall buildings and

slender towers. Experimental wind tunnel data may be used in place of the coefficients given in the code

for these structures.

13.3.3.1 Types of Wind Design

Typically, for wind-sensitive structures, three basic wind effects need to be considered:

* Environmental wind studies — to study the wind effects on the surrounding environment caused

by erecting the structure (e.g., a tall building). This study is particularly important to assess the

impact of wind on pedestrians and motor vehicles and so on, which utilize the public domain

within the vicinity of the proposed structure.

* Wind loads for facade — to assess design wind pressures throughout the surface area of the

structure to design the cladding system. Owing to the significant cost of typical facade systems in

proportion to the overall cost of very tall buildings, engineers cannot afford the luxury of

conservatism in assessing design wind loads. With due consideration to the complex building

shapes and dynamic characteristics of the wind and building structure, even the most advanced

wind codes generally cannot accurately assess design loads. Wind tunnel tests to assess design

loads for cladding are now a normal industry practice, with the aim of minimizing initial capital

costs, and more significantly, to avoid the expensive maintenance costs associated with

malfunctions due to leakage and/or structural failure.

Vibration and Shock Problems of Civil Engineering Structures 13-25

* Wind loads for structure — to determine the design wind load so as to design the lateral loadresisting

structural system of a structure and therefore satisfy the various design criteria.

13.3.3.2 Design Criteria

In terms of designing a structure for lateral wind loads, the following design criteria need to be satisfied:

* Stability against overturning, uplift, and/or sliding of the structure as a whole.

* The strength of the structural components of the building, and stresses that must be withstood

without failure during the life of the structure.

* Serviceability, for example for buildings, where interstory and overall deflections are within

acceptable limits. The control of deflection and drift is imperative for tall buildings in order to

limit damage and cracking to nonstructural members such as the facade, internal partitions,

and ceilings.

As adopted by most international codes, to satisfy stability and strength limit state requirements, ultimate

limit state wind speed is used. In many codes, such a speed has a 5% probability of being exceeded in a

1-year period.

An additional criterion that requires careful consideration in wind-sensitive structures such as tall

buildings is the control of accelerations when subjected to wind loads under serviceability conditions.

Acceptability criteria for vibrations in buildings are frequently expressed in terms of acceleration limits

for a 1- or 5-year return period wind speed, and are based on human tolerance to vibration discomfort in

the upper levels of buildings. Wind response is relatively sensitive to both mass and stiffness, and response

accelerations can be reduced by increasing either or both of these parameters. However, this is in conflict

with earthquake design optimization where loads are minimized in buildings by reducing both the mass

and stiffness. Increasing the damping results in a reduction in both the wind and earthquake responses.

The detailed procedure described in wind codes is subdivided into static analysis and dynamic analysis

methods. The static approach is based on a quasi-steady assumption. It assumes that the building is a

fixed rigid body in the wind. The static method is not appropriate for tall or slender structures or

structures susceptible to vibration in the wind. In practice, static analysis is normally appropriate for

structures up to 50 m in height. The subsequently described dynamic method is for exceptionally tall,

slender, or vibration-prone buildings. The codes not only provide some detailed design guidance with

respect to dynamic response, but also state specifically that a dynamic analysis must be undertaken to

determine overall forces on any structure with both a height (or length) to breadth ratio greater than five,

and a first mode frequency less than one.

Wind-loading codes may give the impression that wind forces are relatively constant with time. In

reality, wind forces vary significantly over short time intervals, with large amplitude fluctuations at highfrequency

intervals. The magnitude and frequency of the fluctuations is dependent on many factors

associated with the turbulence of the wind and local gusting effects caused by the structure and

surrounding environment.

To simplify this complex wind characteristic, most international codes have adopted a simplified

approach by utilizing a quasi-steady assumption. This approach simply uses a single value equivalent,

static wind pressure, to represent the maximum peak pressure the structure would experience.

13.3.3.3 Static Analysis

This method assumes the quasi-steady approximation. It approximates the peak pressures on the

building surfaces by the product of gust dynamic wind pressure and the mean pressure coefficients. The

mean pressure coefficients are measured in a wind-tunnel or full-scale tests and are given by pbar =qzðbarÞ:

The implied assumption is that the pressures on the building surface (external and internal) faithfully

follow the variations in upwind velocity. Thus, it is assumed that a peak value of wind speed is

accompanied by a peak value of pressure or load on the structure. The quasi-steady model has been

found to be fairly good for small structures.

13-26 Vibration and Shock Handbook

In static analysis, gust wind speed, Vz ; is used to calculate the forces, pressures, and moments on the

structure.

The main advantages and disadvantages of the quasi-steady/peak gust format can be summarized as

follows:

* Advantages:

* Simplicity.

* Continuity with previous practice.

* Pressure coefficients should need little adjustment for different upwind terrain types.

* Existing meteorological data on wind gusts are used directly.

* Disadvantages:

* The approach is not suitable for very large structures, or for those with significant dynamic

response.

* The response characteristics of the gust anemometers and the natural variability of the peak

gusts tend to be incorporated into the wind load estimates.

* The quasi-steady assumption does not work well for cases where the mean pressure coefficient is

near zero.

However, the advantages outweigh the disadvantages — certainly for smaller, stiff structures for which

the code is mainly intended.

The philosophy used in specifying the peak loads in AS/NZS 1170.2 has been to approximate the real

values of the extremes. In many cases, this has required the adjustment of the quasi-steady pressures with

factors such as area reduction factors and local pressure factors.

The dynamic wind pressure at height z is given by

q􀀊z ¼ 0:6V􀀊 2z

£ 1023 ð13:18Þ

where

V􀀊 z ¼ the design gust wind speed at height z; in meters per second ¼ VMðz;catÞMz MtMi

V ¼ the basic wind speed

The multiplying factors ðMÞ take into account the type of terrain ðMtÞ; height above ground level ðMz Þ;

topography, and the importance of the structure ðMiÞ: The above derivation essentially forms the basis of

most international codes.

The mean base overturning moment Mbar is determined by summing the moments resulting from the

net effect of the mean pressure and leeward sides of the structure given by

F􀀊z ¼

cp;eq􀀊zAz

or for structures with discrete elements:

F􀀊d ¼

cdq􀀊zAz ð13:19Þ

where

F􀀊z ¼ the hourly mean net horizontal force acting on a structure at height z

Cp;e ¼ the pressure coefficients for both windward and leeward surfaces

Az ¼ the area of a structure or a part of a structure, at height z; in square meters

F􀀊d ¼ the hourly mean drag force acting on discrete elements

Cd ¼ the drag force coefficient for an element of the structure

13.3.4 Along and Across-Wind Loading

Not only is the wind approaching a building a complex phenomenon, but the flow pattern

generated around a building is complicated by the distortion of the mean flow, the flow

Vibration and Shock Problems of Civil Engineering Structures 13-27

separation, the vortex formation, and the wake

development. Large wind pressure fluctuations

due to these effects occur on the surface of a

building. As a result, large aerodynamic loads

are imposed on the structural system and

intense localized fluctuating forces act on the

facade of such structures. Under the collective

influence of these fluctuating forces, a building

vibrates in rectilinear and torsional modes, as

illustrated in Figure 13.14. The amplitude of

such oscillations is dependant on the nature of

aerodynamic forces and the dynamic characteristics

of the building.

13.3.4.1 Along-Wind Loading

The along-wind loading or response of a building

due to the gusting wind can be assumed to consist

of a mean component due to the action of the mean wind speed (e.g., the mean hourly wind speed), and a

fluctuating component due to wind speed variations from the mean. The fluctuating wind is a random

mixture of gusts or eddies of various sizes, with the larger eddies occurring less often (i.e., with a lower

average frequency) than smaller eddies. The natural frequency of vibration of most structures is

sufficiently higher than the component of the fluctuating load effect imposed by the larger eddies. That is,

the average frequency with which large gusts occur is usually much less than any of the structure’s natural

frequencies of vibration and so they do not force the structure to respond dynamically. The loading due

to those larger gusts (which are sometimes referred to as “background turbulence”) can therefore be

treated in similar way to that due to the mean wind speed. The smaller eddies, however, because they

occur more often, may induce the structure to vibrate at or near one of the structure’s natural frequencies

of vibration. This in turn induces a magnified dynamic load effect in the structure which can be

significant.

The separation of wind loading into mean and fluctuating components is the basis of the

so-called “gust factor” approach, which is the basis of many design codes. The mean load

component is evaluated from the mean wind speed using pressure and load coefficients. The

fluctuating loads are determined separately by a method which makes an allowance for the intensity

of turbulence at the site, size reduction effects, and dynamic amplification (Davenport, 1967;

Vickery, 1971).

The dynamic response of buildings in the along-wind direction can be predicted with reasonable

accuracy by the gust factor approach, provided the wind flow is not significantly affected by the presence

of neighboring tall buildings or surrounding terrain.

13.3.4.2 Across-Wind Loading

There are many examples of slender structures that are susceptible to dynamic motion

perpendicular to the direction of the wind. Tall chimneys, street lighting standards, towers, and

cables frequently exhibit this form of oscillation, which can be very significant, especially if the

structural damping is small. Crosswind excitation of modern tall buildings and structures can be

divided into three mechanisms (AS/NZS 1170.2, 2002). These and higher time derivatives are

described as follows:

1. The most common source of crosswind excitation is that associated with “vortex shedding.”

Tall buildings are bluff (as opposed to streamlined) bodies that cause the flow to separate from

the surface of the structure, rather than follow the body contour (Figure 13.15). For a

Wind Direction

Across-wind

Along-wind

Torsion

FIGURE 13.14 Wind response directions.

13-28 Vibration and Shock Handbook

particular structure, the shed vortices have

a dominant periodicity that is defined by

the Strouhal number. Hence, the structure

is subjected to a periodic pressure loading,

which results in an alternating crosswind

force. If the natural frequency of the

structure coincides with the shedding

frequency of the vortices, large amplitude

displacement response may occur, and this

is often referred to as critical velocity effect. The asymmetric pressure distribution created

by the vortices around the cross section results in an alternating transverse force as they are

shed. If the structure is flexible, oscillation will occur transverse to the wind, and the conditions

for resonance would exist if the vortex shedding frequency coincided with the natural

frequency of the structure. This situation could give rise to very large oscillations and

possibly failure.

In practice, vertical structures are exposed to a turbulent wind in which both the wind

speed and the turbulence level vary with height, so that excitation due to vortex shedding is

effectively broadband. Therefore, the term “wake excitation” is used to include all forms of

excitation associated with the wake and not just those associated with the critical wind velocity.

2. The “incident turbulence” mechanism refers to the situation where the turbulence properties of

the natural wind give rise to changing wind speeds and directions that directly induce varying

lift and drag forces and pitching moments on the structure over a wide band of frequencies.

The ability of incident turbulence to produce significant contributions to crosswind response

depends very much on the ability to generate a crosswind (lift) force on the structure as a

function of longitudinal wind speed and angle of attack. In general, this means that sections

with a high lift curve slope or pitching moment curve slope, such as a streamlined bridge deck

section or a flat deck roof, are possible candidates for this effect.

3. Higher derivatives of crosswind displacement: there are three commonly recognized

displacement-dependent excitations (i.e., “galloping,” “flutter,” and “lock-in”), all of which

are also dependent on the effects of turbulence (turbulence affects the wake development, and

hence, the aerodynamic derivatives). Many formulae are available to calculate these effects

(Holmes, 2001). Recently, computational fluid dynamics techniques have also been used

(Tamura, 1999) to evaluate these effects.

13.3.5 Wind Tunnel Tests

There are many situations in which analytical methods cannot be used to estimate certain types of wind

loads and the associated structural response. For example, when the aerodynamic shape of the building is

rather uncommon, or the building is very flexible so that its motion affects the aerodynamic forces acting

on the building. In such situations, more accurate estimates of wind effects on buildings are obtained

through aeroelastic model tests in a boundary-layer wind tunnel.

Wind tunnel tests currently being conducted on buildings and other structures can be divided into two

types. The first is concerned with the determination of wind-loading effects to enable the design of a

wind-resistant structure. The second is concerned with the flow fields induced around the structure, such

as its effects on pedestrian comfort and safety at ground level or air intake concentration levels of exhaust

pollutants.

Wind tunnel studies involve blowing wind on the subject building model and its surrounding at

various angles relative to the building orientation, representing the wind directions. This is typically

achieved by placing the complete model on a rotating platform within the wind tunnel. Once testing is

FIGURE 13.15 Vortex formation in the wake of a bluff

object.

Vibration and Shock Problems of Civil Engineering Structures 13-29

complete for a select direction, the platform is simply rotated by a chosen increment to represent a new

wind direction. A typical wind tunnel model is illustrated in Figure 13.16.

The design wind speed is based on meteorological data for the given city or area, which are analyzed to

produce the required probability distribution of gust wind speeds. By appropriate integration processes

and the application of necessary scaling factors, directional wind speeds for the wind tunnel can be

determined.

Although wind tunnel testing attempts to duplicate a complex problem, the actual models are quite

simple and are based on the premise that the fundamental mode of displacement for a structure such

as a tall building can be approximated by a straight line. In general terms, it is not necessary to achieve

a correct mass density distribution along the building height as long as the mass moment of inertia

about the pivot point is the same as the prototype density distribution. The pivot point is typically

chosen to obtain a mode shape which provides the best agreement with the calculated fundamental

mode shapes of the prototype. Springs are located near the pivot points to achieve the correct

frequencies of vibrations in the two fundamental sway modes corresponding to the orthogonal

building axis. An electromagnet or oil dashpot provides the model with a damping corresponding

to that of the full scale tower. In addition to the stiffness and damping compatibility, it is essential

that structural length scale, timescale, and the inertial force are the same between the model and the

full structure.

Buildings of similar size located in close proximity to the proposed building can cause large increases

in across-wind responses. Fortunately, in wind tunnel studies, surroundings comprising existing and/or

future buildings can easily be incorporated with relatively minor costs.

13.3.6 Comfort Criteria: Human Response to Building Motion

There are no generally accepted international standards for comfort criteria. A considerable amount of

research has been carried out into the important physiological and psychological parameters that affect

human perceptions of motion and vibration in the low-frequency range of 0 to 1 Hz encountered in tall

buildings. These parameters include the occupant’s expectations and experience, activity, body posture,

and orientation; visual and acoustic cues; and the amplitude, frequency, and acceleration of both the

translational and rotational motion to which the occupant is subjected. Table 13.5 gives some guidance

on the general human perception levels.

FIGURE 13.16 Wind tunnel test.

13-30 Vibration and Shock Handbook

Acceleration limits are a function of the frequency of the vibration felt. Upper limits have been

recommended for corresponding frequencies of vibration with the relationship suggested by Irwin

(1978). Peak acceleration limits as suggested by Melbourne (1988) and Chen (1987) have been plotted

along with the Irwin E2 curve in Figure 13.17. To obtain the peak acceleration, the root-mean-square

(rms) value can be multiplied by a peak factor. The peak factor is generally between 3 and 4.

13.3.7 Dampers

The damping in a mechanical or structural system is a measure of the rate at which the energy of motion

of the system is dissipated. All real systems have some damping. An example is friction in a bearing.

Another example is the viscous damping created by the oil within an automotive shock absorber. In many

systems, damping is not helpful and it has to be overcome by the system input. In the case of windsensitive

structures such as tall buildings, however, it is beneficial, as damping reduces motion, making

the building feel more stable to its occupants.

Controlling vibrations by increasing the effective damping can be a cost-effective solution.

Occasionally, it is the only practical and economical solution.

0.01

0.1

0.01 0.1 1 10

Frequency n0 (Hz)

Horizontal acceleration m/s

RETURN

PERIODS

10 YEARS

5 YEARS

1 YEAR

Irwin's E2 Curve and ISO 6897 (1984)

Curve 1, maximum standard deviation

horizontal criteria for 10 minutes in 5

years return period for a building.

STET

Melbourne,s (1988) maximum peak horizontal acceleration criteria

based on Irwin (1978) and Chen and Robertson (1972), for T = 600

seconds, and return period R years

FIGURE 13.17 Horizontal acceleration criteria for occupancy comfort in buildings.

TABLE 13.5 Human Perception Levels

Level Acceleration

(m/sec2)

Effect

1 , 0.05 Humans cannot perceive motion

2 0.05 to 0.1 Sensitive people can perceive motion; hanging objects may move slightly

3 0.1 to 0.25 The majority of people will perceive motion; the level of motion may affect

desk work; long-term exposure may produce motion sickness

4 0.25 to 0.4 Desk work becomes difficult or almost impossible; ambulation still possible

5 0.4 to 0.5 People strongly perceive motion; it is difficult to walk naturally; standing

people may lose their balance

6 0.5 to 0.6 Most people cannot tolerate the motion and are unable to walk naturally

7 0.6 to 0.7 People cannot walk or tolerate the motion

8 . 0.85 Objects begin to fall and people may be injured

Vibration and Shock Problems of Civil Engineering Structures 13-31

The types of damping systems that can be

implemented include:

* Tuned mass damper (TMD; an example is

given in Figure 13.18)

* Distributed viscous dampers

* Tuned liquid column dampers (TLCD),

also known as liquid column vibration

absorbers (LCVA)

* Tuned sloshing water dampers (TSWD)

* Impact-type dampers

* Visco-elastic dampers

* Semiactive dampers

* Active dampers

While general design philosophy tends to favor

passive damping systems due to their lower capital

and maintenance costs, active or semiactive

dampers may be the ideal solution for certain

vibration problems. More details about passive

and active systems to control vibrations are given

by Soong and Costantinou (1994).

13.3.8 Comparison with Earthquake Loading

Extremes of wind loading, which may be as much as three or four times the loading associated with

the mean result, are possible, and a significant contribution to this extreme is often supplied by the

resonant component in the turbulence of the wind. Resonance refers to a condition in which the

periodicity of forcing is identical to that of the structure, with a consequential amplification of

response that is limited only by the level of damping of the structure. A typical wind contains a wide

range of frequency components in its turbulence, so it is always possible that the peak response has a

resonant component.

Earthquake ground motions are characterized by a series of rather random spikes, with the range of

frequencies present (i.e., the range of intervals between zero crossings on the ground acceleration

record) being somewhat narrower than for normal wind turbulence. Structures that are stiff will move

essentially in unison with the ground motion. For more flexible structures, response is analogous to

that from a series of impulses, with the dominant frequency in the response being that of the

structure itself. This frequency, the natural frequency of the structure, is dependent on the mass and

stiffness of the system.

Wind loading depends on exposed area; earthquake loading depends on the (hidden) mass of the

structure. Structures attract wind loadings which increase steadily with the major dimension (height or

span, say). The earthquake loading experienced by such structures increases much less rapidly, with the

result that, for high-rise structures, wind loading is almost always the dominant lateral loading. This

assumes elastic responses for both regimes of loading.

Wind loading depends on topography and, in urban areas, on the proximity of other buildings.

Earthquake loading, on the other hand, depends to a marked degree on the foundation materials. It is

universally observed that buildings founded on soft soils perform much worse than those founded on

rock.

The most important differences between wind and earthquake loading are summarized in

Table 13.6.

FIGURE 13.18 One of the TMDs designed for the

skybridge legs of the Petronas Towers by RWDI Inc.

(12 TMDs were installed, three in each of the four legs).

13-32 Vibration and Shock Handbook

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