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Tall Structures / Vortex Shedding

This research project was carried out by Joanne Saad, working with John Graham and David Crookes.

In recent years Fluid have become increasingly interested in tall structures which are subject to the dynamic effect of wind.

The forces due to wind gusts can be of great concern when the tall structures are habitable. They result in displacements which are judged to be acceptable (or not) based on a service criteria that considers human perception of vibration and motion.

Our research has led us to establish why wind flow may be critical, the effect of Karman vortex shedding and how this can be taken into account in the design of tall structures.

 

Image showing examples of a Karman vortex street at NASA.

Wind Phenomena

Several phenomena give rise to the dynamic response of structures under wind loading. These include buffeting, vortex shedding, galloping and flutter.

Buffeting is a high-frequency forced vibration that is caused by airflow separation from one object striking another as a result of a sudden impulse of increased load.

Vortex shedding occurs when wind flows past a bluff (unstreamlined) body, such as a building, which causes the flow to separate from the surface of the structure rather than follow the body contour (see below). The shed vortices produce a force that acts on the body in the crosswind direction. At relatively low wind speeds the spiral vortices are created periodically and symmetrically from both sides of the body. Since these vortices are symmetrical, the loads tend to cancel each other out and the effect of vortex shedding can be ignored. However, at higher wind speeds, the vortices are shed alternatively, i.e. on one side first then the other. As a result, alternating low pressure zones are formed on the downstream side of the building and a fluctuating transverse load is created. This causes the building to move towards the low pressure zone. If the natural frequency of the structure coincides with the frequency of the vortex shedding, then large amplitude displacement response may occur. This is often called the critical velocity effect.

 

Galloping is the self-induced cross-wind oscillations of flexible structures due to aerodynamic forces that are in-phase with the motion of the structure. It is characterised by the progressively increasing amplitude of transverse vibrations with increased wind speed. Galloping is generally not an issue for buildings.

Flutter is a ‘self-feeding’ oscillatory motion that results from the coupling of aerodynamic forces with the elastic deformation of a structure. It is often the result of combined bending and torsion and affects plate-like structures, such as signboards and suspension bridge decks. The instability is caused when there is a ‘positive feedback’ between the structure’s natural vibration and the aerodynamic forces. In other words, the movement of the object increases the aerodynamic load, which in turn drives the object to move further. The vibration levels can thus build up and are only limited when the mechanical damping of the object match the energy input, which often results in large amplitudes and can lead to rapid failure.

 

One famous example of the flutter phenomenon is the collapse of the original Tacoma Narrows Bridge, a suspension bridge in the U.S. state of Washington. Flutter is generally not an issue for buildings:

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Wind Action

What is wind flow?

Wind flow is a dynamic and random phenomenon that is complex to model. It is composed of eddies of varying size and rotational characteristics that are carried along in a stream of air that moves relative to the earth’s surface. These eddies give wind its gusty or turbulent character, with speeds and forces that vary considerably in both time and space. In order to model wind flow the wind vector at a point may be regarded as the sum of the mean wind vector (static component) and the dynamic, or turbulent, component due to wind speed variations from the mean.

In the lower levels of the atmosphere the turbulence of strong winds largely arises from contact with surface features shown in Figure 1. Therefore wind flow is particularly gusty in urban areas. This is because as wind impacts a building, further chaos is added to the already unstable nature of wind by the separation of flow, the distortion of the mean flow, the formation of vortices, and the development of a wake. These effects generate large, fluctuating wind pressures on the surface of the building that depend on the interactions of the flow characteristics (such as wind speed, wind height, ground surface features, air properties) with the building configuration (i.e. its shape, location, and dynamic and physical structural properties). As a result of these pressures, large aerodynamic loads get imposed on the building that may cause significant structural excitation and vibration provided that the natural frequency is low enough (less than 1 Hz. Above this value the structure is considered to be dynamically ‘rigid’). Therefore understanding the action of wind around dynamically sensitive buildings is of prime concern.

Wind forces on structures

Under the action of wind flow structures can experience two different responses, namely a static response and an aerodynamic (or dynamic) response. Aerodynamic forces on the structure include the drag (along-wind) force, which acts in the direction of the mean wind, and the lift (cross-wind or transverse) force, which acts perpendicular to the direction, as illustrated in Figure 2. These forces arise from different wind effects, described in more detail below. It has been shown that the along-wind response of slender structures is mostly due to the action of turbulence buffeting and that these along-wind accelerations are larger for structures with lower fundamental frequencies. The cross-wind response is more likely to arise from vortex shedding or galloping. This response is likely to exceed along-wind accelerations if the building is slender about both axes.

In general, the force due to wind-induced vibrations can be considered to consist of three components, as shown in Figure 3: a static part due to the 10-minute averaged extreme wind velocity; a static part due to fluctuating wind (turbulence); and a dynamic, or resonance, response caused by the inertial forces of a structure as it vibrates.

The overall response of a structure to wind can therefore be expressed in terms of a mean component, a broadband response, and a narrow-band response. The broad-band term is the component at the background frequencies of the wind and is largely quasi-static, while the narrow-band relates to the vibration at the natural frequency of the structure.

Risk Factors

Why modern tall buildings are at greater risk

As previously stated, the overall response of a structure to wind loading depends on the structure’s natural fundamental frequency. The new generation of high-rise buildings are taller and more slender than those constructed in the past. Additionally, these modern structures are built with high-strength materials that have similar stiffness properties to conventional materials. They also contain fewer non-structural components (such as separation walls), which are often applied in such a way that they stand free with respect to small building motions. As a result there is less damping in the building. This combination of less weight, more flexibility, and lower damping, leads to buildings that are more susceptible to wind action and dynamic behaviour. These buildings tend to have lower natural frequencies of vibration, which are more likely to coincide with the average frequencies of occurrence of wind gusts, hence large resonant motions are more likely to occur. As a result, the design of tall buildings against dynamic movement has gained importance. In the design of these buildings, two important factors must be taken into account: the design has to ensure both the safety of the building and the comfort in the building.

Parameters to consider in the design of tall buildings for wind

In the design of tall buildings for wind it is essential to ensure that the structure has sufficient strength to resist the wind-induced forces, and that it has adequate stiffness to satisfy serviceability criteria in terms of lateral displacement. Furthermore, wind-induced motion should be limited to satisfy the comfort of the occupants. Vibrating buildings can cause unsafe feelings and induce concern regarding the structural quality and integrity. Thus it is generally considered that humans are surprisingly sensitive to vibration, to the extent that even motions that correspond to relatively low levels of stress and strain may feel uncomfortable. Therefore fulfilling the vibration criteria for human comfort is decisive in the structural design of most tall buildings.

What is Too Much Movement?

Excessive lateral building displacements can cause damage to fa̤ade elements, partitions, and interior finishes (such as cracking in paintwork or wall surfaces). To prevent damage to these non-structural elements, inter-storey drifts have to be limited. Although no universally accepted criterion exists with regards to maximum lateral displacements in the serviceability limit state, inter-storey drifts of up to h/400 (h being the storey height), on a maximum of 10mm per floor, are generally considered to be acceptable. To avoid the calculation of all inter-storey displacements, a global drift of H/500 (where H refers to the total height of the building) can be adopted. This overall drift criterion may be over Рor under Рconservative depending on the shape of the displacement diagram, which is the sum of the displacement due to bending, shear, and rotation of the foundations. It is important to note that the criteria of H/500 may be required by the lift manufacturer to ensure satisfactory operation of their carriages, thus it is important to check with them first what limiting serviceability criteria they require.

As mentioned above, the perception of oscillatory motion in tall buildings can cause serious comfort issues to occupants, such as concerns about the structural integrity of the building, and in severe circumstances, may trigger responses analogous to those associated with motion sickness. People do not expect the buildings in which they live or work to vibrate. Therefore if they find the movement of a building to be unacceptable or intolerable they may refuse to stay. Thus from both a safety and an economical standpoint, it is important to design tall buildings with deflection limits that ensure the occupants’ comfort.

The Vortex Flow Measuring Principle

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Human beings are not directly sensitive to displacement or velocity, but rather to forces acting on them; hence they are sensitive to acceleration and its change. Acceleration is therefore used as the decisive factor to evaluate motion perception. Although acceptability criteria for accelerations are not currently codified, general guidelines do exist that are accepted by the wind engineering community. One such guideline that gives the threshold of human perception to vibration is shown in Figure 5 and is the guideline used in this report. This figure was taken from the CIRIA Report 102: Design of shear wall buildings. The x-axis represents the natural frequency (fn) of a building, and the y-axis is the root mean square (r.m.s.) acceleration. Generally, r.m.s. acceleration is defined as the average of a sinusoidal wave form (i.e. peak/?2). Therefore the graph considers the building’s vibration at its natural frequency, i.e. its narrow band response. In wind analysis, the rms value of the narrow-band response at the natural frequency is, in fact, the rms of the response record in time. Over the storm period (which is typically taken as 10 minutes, since a storm is assumed to be fully developed after 10 minutes) the peak acceleration experienced is approximately 3.5 to 4 times the rms acceleration. Hence, for compatibility, the rms ordinate obtained from the graph in Figure 5 should be multiplied by 3.5 or 4 to determine the design peak acceleration throughout the storm period.

Both axes have a logarithmic scale to accommodate the necessary range of accelerations and frequency. The threshold levels are represented by the six curves that pass through the graph. It can be noted that the limiting accelerations are extremely small.

The permissible r.m.s. deflection attributed to the resonant motion of the building may be evaluated by dividing the r.m.s. acceleration by the square of the angular frequency (2?f). The value of the peak allowable deflection is usually 4 times the r.m.s. value, i.e.

The level of adverse comment from occupants of a building to vibration is dependent on the return period and the time over which motion of a particular intensity is sustained for each occurrence. The level of tolerance to vibration is a function of the activities being performed and of the readiness of the occupants to accept the significance of the vibration. For example, in a hospital, the need to carry out delicate operations requires that vibration levels should be minimal.

A certain proportion of people (roughly 2%) is generally receptive to, and complains about, even very small vibrations. According to the CIRIA report, a reasonable serviceability criterion for many building uses may be that a further 10% (i.e. 12% total) comment adversely. These limit curves are displayed in Figure 5 and are for a 1-in-5-year storm.

Options to Reduce Movement

Traditionally structural engineers and designers reduced wind motion of structures by modifying their stiffness and mass properties in order to directly influence their natural frequency. The mass of the building was varied by altering the total amount of concrete, i.e. by making concrete walls and floors thicker or thinner as appropriate. The balancing of the stiffness and mass properties usually produced an efficient design, capable of allowing the architect the freedom to achieve a desired aesthetic and the structural engineer could limit deflections and stresses for a safe structure. However given the desire to build higher buildings, longer bridges, and more daring structures, the envelope of what is possible within conventional structural design imposes limitations, thus new methods have been developed.

Research for the next generation of tall buildings has been devoted, in part, to the mitigation of wind-induced motions and a host of techniques have been developed, ranging from global design modifications to the structural system or building aerodynamics to the incorporation of auxiliary damping systems. These techniques are listed in the table and summary (see right).

In the case of structural system modifications, the appropriate selection of an efficient system can provide the most effective means of controlling structural response to wind in the lateral and torsional directions. This may be accomplished through any number of systems including space frames, mega frame systems, the addition of vierendeel frames, belt trusses, super columns, vierendeel-type bandages and outrigger trusses.

As well as the addition of an appropriate structural system, several aerodynamic modifications to a building can reduce its motion, such as changes to its cross-sectional shape, the variation of its cross-section with height, or changes to its size. Techniques to achieve improved aerodynamics include: slotted and chamfered corners, fins, setbacks, buttresses, sculptured building tops, tapering, drop-off corners, and the addition of horizontal and vertical through-building openings.

Another method commonly implemented to reduce the dynamic motion of buildings is by adding damping to the structure. Damping can be added within a structure, by increasing its inherent damping, or externally, through the use of auxiliary damping. A structure’s inherent damping comes from the combination of its structural damping (the damping inherently available in the materials used), its aerodynamic damping (the damping associated with its shape), and the soil damping (obtained from the soil-foundation interaction). Changing these three forms of damping make only limited contributions to the overall effective damping of a structure. Damping is also difficult to engineer since, unlike the mass and stiffness characteristics, it does not relate to a unique physical phenomenon. Moreover the amount of inherent damping cannot be accurately estimated until the structure is completed, resulting in a certain level of uncertainty. Therefore in the case where inherent damping is not sufficient, an external damping device should be introduced which offers a somewhat more predictable, adaptable, and reliable method of imparting additional damping to a system.

Auxiliary damping sources come in the form of both active and passive systems. Passive systems consist of a secondary system, such as a secondary mass, that is attached to the structure by a spring and damping element which counteracts the building’s motion through passive energy dissipation. The most common passive damper system is the tuned mass damper (TMD). Typically a TMD consists of a secondary inertial mass that is attached to a location in a building that experiences maximum motion (generally near the top) through a spring and damping mechanism (usually viscous or viscoelsatic damping). The mass is given dynamic characteristics that relate closely to that of the primary structure. By varying the mass ratio of the damper mass to the effective mass of the building, the frequency ratio between the two masses, and the damping ratio of the secondary mass, a certain amount of damping can be produced. Essentially, the TMD can be viewed as an energy sink, where excess energy that is built up in the building is transferred to a secondary mass. The energy is then dissipated by some form of viscous damping device that is connected between the building and the TMD mass itself.

Active damping systems are designed to try and counter the force that causes the vibration in order to provide more efficient and swifter control of the vibrating structure. This is accomplished through the use of control mechanisms that are programmed to respond to any changes in the parameters of the vibrating system. The most common type is the Active Mass Damper (AMD). The motion of a structure is sensed by instruments, such as an accelerometer. These measured response signals are analyzed by a computer controlled actuator system which causes a large mass to move. In this way a control force is created based on the feedback of the velocities/accelerations of the structure to counteract the building motion. A benefit of an AMD is that for a given amount of mass, a larger amount of “damping€ can be provided than with a passive TMD. However, a typical AMD is generally more expensive than a passive TMD and has higher maintenance requirements. AMDs are therefore more appropriate for reducing the impact of a seismic event.

Tuned Mass Damper

A tuned mass damper (TMD) is a device consisting of a mass, a spring, and a damping device that is attached to a structure in order to reduce the dynamic response of the structure. The frequency of the damper is tuned to a particular structural frequency so that when that frequency is excited the damper will resonate out of phase with the structural motion. Energy is dissipated by the damper inertia force acting on the structure. In this way the application of TMDs can prevent discomfort, damage or structural failure.

Simple Explanation of How TMDs Work

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, an acceleration is generated. Consequently, the occupants of the skyscraper would feel this acceleration. Therefore in order to make the occupants of the building feel more comfortable, TMDs are placed in structures where the horizontal deflections from the wind’s force are the greatest, to reduce the motion of the building and effectively make it stand still.

Figure 6 is a simple schematic of a TMD attached to a building. The secondary mass is represented as m, the spring as k, the damping device as c, the building as M and the building’s stiffness as K.

As the building begins to oscillate, it sets the TMD into motion by means of the spring. 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 are out of sync with the ‘pushes’ from the wind, thus the building’s motion would still be uncomfortable for the occupants. If their amplitudes were significantly different, the TMD would 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).

 

The Bellagio Bridge in Las Vegas, Nevada

Consists of two bridges spanning 46 and 38 metres. Architectural and engineering design constraints created a need for a damping system to be installed so as to avoid the possibility of exciting the bridges to resonance, which would create an amplitude large enough for pedestrians to feel.

The bridge uses six TMDs, three on each bridge as illustrated in Figure 7, weighing 1360 kg apiece. The TMDs have springs and a viscous damper which absorb the energy from pedestrian movements on the bridges, thereby dissipating the vibration energy of the bridge.

Figure 7. Three tuned mass dampers installed within
the girders on each side of each span

Taipei Financial Centre

The Taipei Financial Centre (Taipei 101) is about 509 metres tall. It is designed to withstand typhoon winds and earthquake tremors common in its area of the Asia-Pacific. Thus, as well as being a prominent architectural feature, a large sphere suspended by flexible steel cables acts as a TMD for the building and prevents large lateral drift (sideways motions), ensuring the comfort of the occupants.

The steel pendulum (shown in Figures 8 and 9) weighs approximately 660 metric tons and consists of 41 circular steel plates, each with a height of 125 mm welded together to form a 5.5 m diameter sphere. It is the largest damper in the world. Suspended from the 92nd to the 88th floor, the pendulum sways to offset movements in the building caused by strong gusts. Another two tuned mass dampers, each weighing six metric ton sit at the tip of the spire. These also help to prevent damage to the structure due to strong wind loads.

Figure 9: The main tuned mass damper atop Taipei 101

Trump World Tower, New York

Trump World Tower is a rectangular building 262 metres tall, and is nearly twice as long as it is wide. This causes it to act like a cantilevered beam in the presence of wind or other lateral forces. Therefore to prevent it from saying back and forth, a tuned mass damper weighing approximately 544 metric tons was installed.

The TMD in this building is similar to a “stacked€ pendulum (shown in Figure 10), with the pendulum supported by massive hydraulic cylinders (similar to the hydraulic shocks on cars), which act as the damping device and through which energy is dissipated.

The actual TMD for the Tower is contained in a reinforced concrete room at the top of the building.

One Wall Centre, Vancouver, British Columbia

One Wall Centre is 150 metres tall. To counteract possible harmonic swaying during high winds, One Wall Centre contains a tuned liquid column damper (TLCD), which is another form of passive damping system that replaces the role of the mass, spring, and damping device of the TMD.

In order to counteract the building’s motion and keep it at rest, a TLCD uses large tanks of water or other liquid and a sluice gate. The geometry of the tanks is designed so that the harmonic frequency of the sloshing of the water in the tanks counteracts the harmonic frequency of the swaying of the building. The sluice gate is used to dissipate the energy created by the water’s motion. The benefits of using a TLCD to reduce motions of a building can be threefold. Firstly, the building acceleration responses due to wind can be reduced. Secondary, the water in the tank can be used for fire fighting or chilled water storage. Thirdly, the construction costs and maintenance costs are much lower compared to conventional damping systems .

One Wall Centre has two TLCDs, each containing 230 tons of water tuned to the proper frequencies. These tanks are illustrated below.