Download Dynamic optimization for the wind-induced response of a tall building

Dynamic optimization for the wind-induced response of a tall building
Workamaw Warsido1, Ryan Merrick2 Girma Bitsuamalk3,
1
Research Assistant, Civil and Environmental Engineering department (CEE), International Hurricane Research Center
(IHRC), Florida International University (FIU), Miami, Florida, USA, [email protected]
2
Technical Coordinator, RWDI Inc., Guelph, ON, Canada, [email protected]
3
Assistant Professor of Wind/Structural Engineering, CEE, IHRC, FIU, Miami, Florida, USA, [email protected]
ABSTRACT
Wind induced forces on buildings depend on several parameters, such as the building’s shape and height,
the nature of upwind terrain, the influence of nearby structures and the structural properties of the building
(mass, stiffness and damping). A significant portion of these wind-induced forces are caused by the building’s
own inertia and are dependent upon the dynamic characteristics of the building. Due to the complexity of these
dynamic inertial loads, it is convenient to use an equivalent static wind load distribution for structural design
computations. Traditionally these ‘pseudo-static’ wind loads are treated as any other static load during the
design process. However, this approach ignores the potential reduction of inertial component of the wind
loads that could be achieved by ‘tuning’ the structural properties of the structure. In this work the results of a
parametric analysis that was carried out to provide strategic guidance on the relationship between the windinduced responses and structural properties is presented. The present study uses the Commonwealth Advisory
Aeronautical Research Council (CAARC) Commonwealth Advisory Aeronautical Research Council (CAARC)
building model as a case study, for which the optimal configuration of dynamic building properties was
sought. The results of the study indicate potential of reduction of inertial component of the wind load could be
obtained as a result of tuning the structural properties and provides parametric maps that can be used a
guidance while designers navigate through selection of different combination of structural properties for
optimal performance for wind.
INTRODUCTION
Tall buildings are designed mainly to meet certain occupancy needs. The main design criteria being
architectural, the structural engineer should come up with a structural system that will satisfy the design
criteria as efficiently and economically as possible, while fitting into the architectural layout. The main design
criteria to be satisfied in the design of tall buildings are element strength, serviceability, lateral drift and motion
perception (acceleration). As building height increases and the structure becomes more slender, the lateral drift
and acceleration gain importance and become critical design factors.
Wind induced forces on tall buildings depend on several factors, such as shape and height of the building,
nature of upwind terrain, influence of nearby structures and structural properties of the building (mass,
stiffness & damping). In an effort to reduce these forces the structural engineer can control only the structural
properties, which affect inertial component of the wind-induced forces. For wind sensitive structures such as
tall buildings, these inertial loads constitute significant portion of the wind-induced forces. Due to the
complexity of these dynamic inertial loads, it is convenient to use equivalent static wind load distribution for
structural design computations. Traditionally these ‘pseudo-static’ wind loads are treated as any other static
load during the design process. This approach does not take in to account the change in the wind-induced
forces resulting from modification of the structural properties during the design process. By doing so, potential
reduction of inertial component of the wind loads that could be achieved by ‘tuning’ the structural properties of
the building has been ignored.
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Some of the previous studies to develop dynamic optimization techniques, which combine
aerodynamic wind tunnel test results with structural design include. Chan and Chui (2006) presented an
integrated wind tunnel load analysis and optimum member sizing procedure that can predict wind-induced
responses from HFFB wind tunnel results and acceleration criteria of ISO Standard 6897 for tall steel buildings
having symmetrical shapes and simple mode shapes. Chan et al. (2009) introduced a technique which
combines aerodynamic wind tunnel load analysis with an element resizing algorithm to minimize the cost of
tall steel buildings subject to lateral design criteria. The method is applicable for tall buildings with noncoupled mode shapes.
Most of the dynamic optimization work focuses on modifying stiffness to get an optimal design.
However, finding the ultimate building configuration involves the precise combination of mass, stiffness &
damping. This research demonstrates the parametric "dynamic optimization" technique developed by RWDI
(Alkhatib et. al 2005) for high-rise buildings to provide strategic guidance on the ‘optimal combination’ of the
structural properties, with the intent of maximizing the structural performance (ensuring adequate safety and
occupant comfort), minimizing the number of design iterations, and hence the overall cost of the building. The
method is illustrated by carrying out parametric analysis on CAARC (Commonwealth Advisory Aeronautical
Research Council) building to relate ranges of structural properties to different wind induced responses.
CAARC building, 100 ft by 150 ft (floor plan) by 600 ft (height), is selected for this study since it has been
used by many researchers to study different wind-induced phenomena. A high frequency force balance (HFFB)
wind tunnel testing technique has been used to determine the wind induced wind loads and responses.
FUNDMENTALS OF HFFB TECHNIQUE
In the HFFB wind tunnel test, a lightweight rigid model of the building is instrumented on a base balance
system, which is capable of simultaneously measuring the base shear, moment and torsion. The mean and
background fluctuating components of the responses are measured directly in the wind tunnel, while the
inertial component is determined analytically by solving the equation of motion. Using classical modal
analysis, equation of motion can be expressed as:
F
mx
cx
kx
1
Where F , m , C and k , are the generalized force, generalized mass, generalized damping constant and
generalized stiffness respectively which are defined as follows:
Fj Φj T F
2
mj Φj T M Φj
3
cj Φ j T c Φj
4
k j Φj T k Φj
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where F, M, C and K are the force, mass, damping and stiffness matrices of the building respectively. Φ is the
jth mode shape and x represents the generalized displacement coordinates.
Time history of the generalized force F can be determined from HFFB test and the corresponding
power spectrum, S , can be calculated by applying a Fourier transform to the time history data. Equation (1)
can be solved using either time domain analysis or frequency domain analysis. Applying frequency domain
analysis, the base moment spectrum, SM, can be related to the generalized wind force spectrum, Sm, using the
mechanical admittance function, H, as (Boggs and Peterka 1989, Xie and Irwin 1998, Zhou et al. 2003):
SM
H ω S
6
2
1
|H ω |
ω
ω
1
4ζ
7
ω
ω
where ω is the natural frequency of the building and is the damping ratio. The fluctuating component of the
base moment can be determined by integrating the area under the base moment spectrum from Eq. (6) as:
σM
|H ω | S
SM ω dω
ω dω
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This variance of the base moment has two components, the background component σMB and resonant
component (σMR (Davenport, 1995)
σM
σMB
σMR
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The background component σMB can be determined by integrating the area under the wind load spectra S as:
σMB
S
ω dω
10
while the resonant component can be determined from
σMR
S
ω
|H ω | dω
11
From Eq. (10) & (11) it is apparent that the background component can be determined directly from the wind
tunnel test, while the resonant component requires evaluation of the natural frequency (ω using dynamic
analysis.These two fluctuating components can be combined with the mean component using the square-rootof-sum-of-squares (SRSS) rule to determine the peak value of the base moment as:
M
M
g B σMB
g R σMR
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where g B is the background peak factor of the wind velocity, usually taken to be 3.5, while g R is the resonant
peak factor, given by (Tschanz and Davenport, 1983):
gR
2lnω T
0.5772
2lnω T
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where T is the total observation time.
This peak base moment can then be distributed to each floor throughout the building height. Detail discussion
on the distribution techniques can be obtained in Boggs and Peterka (1989), Xie and Irwin (1998), Holmes
(2002) and Chen and Kareem, (2004).
PARAMETRIC STUDY
Selecting an appropriate structural system is the first step in the structural design of tall buildings.
Generally, for buildings up to 10 stories, the gravity loading will dominate the lateral loading (Bryan S. & Alex
C., 1991). Hence, the lateral loading can be resisted by sections which are chosen to be sufficient for gravity
loading. As the number of stories increases, however, the lateral loading becomes increasingly important since
additional material may be required to resist the lateral loads. Hence, it is critical to choose an appropriate
structural system, to end up with an economical design.
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100 ft
For the present study, a wall-frame structural system has been opted, where steel frames and concrete
shear walls act together to resist the lateral load (Smith and Coull 1991). The CAARC building is selected for
this study. The CAARC building is 600 ft tall with a rectangular floor plan dimension of 100 ft x 150 ft as
shown in Figure 1. The building is designed for Miami basic wind speed of 146 mph as per recommendation
by ASCE 7-05. Using this basic wind speed, equivalent static wind loads are computed and combined with
dead and live loads to get the initial design of the building. Classical modal analysis is carried out using finite
element model of the building and the resulting dynamic properties are used as the baseline structural
properties. The wind loads for the study building are revised using HFFB wind tunnel test data from RWDI
USA LLC laboratory and using the baseline structural property. Figure 2 shows the model configuration for
the wind tunnel tests.
150 ft
Figure 1 The 50- story CAARC building model
Figure 2 Wind tunnel configuration of the study building (CAARC) at RWDI USA LLC laboratory.
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The natural frequencies, mass distribution and mode shapes of the building, which were obtained from the
classical modal analysis, were combined with the HFFB wind tunnel data. Subsequently, a parametric analysis
was performed to consider the various permutations of the dynamic building properties; namely modifications
to the generalized mass, generalized stiffness and damping of the building’s first three modes of vibration. The
parametric studies were performed for the following ranges of dynamic properties:
a) generalized mass, ranging between 50% and 150% of the baseline structural properties
b) generalized stiffness, ranging between 50% and 150% of the baseline structural properties; and
c) “effective” damping, ranging between 0.5% and 5.0% of critical.
For each possible combination of generalized mass and generalized stiffness change, an analysis was
performed to evaluate the effect on the following responses:
a) 50-year return period base overturning moments My and Mx
b) 50-year return period base torsional moment Mz; and
c) 1-year return period total acceleration at the uppermost occupied floor
The collection of results is presented in the form of parametric maps as shown in Figures 3 and 4 for damping
ratios of 1% and 2% critical respectively. These parametric maps can be used as a guide while a designer
navigates to achieve an optimized structural system.
RESULTS AND DISCUSSION
The dynamic properties of the baseline structure, designed based on the wind load recommendations of
ASCE 7-05 as mentioned earlier, are utilized in the wind tunnel HFFB technique to obtain the revised design
wind loads and total acceleration at the top most occupied floor. In addition for the present study the design
wind loads are computed by applying a fictitious directionality factor of 0.75, which is not specific to any
given location, to the raw wind tunnel data just for illustrative purposes. The design is revised twice utilizing
the wind tunnel loads (i.e. the inertial component of the wind load are recalculated based on the previously
revised structural property and combined with the background and mean components as described in HFFB
section) and the total acceleration at the top most occupied floor is also checked for both cases. The structural
properties obtained with ASCE 7-05 provisions was revised with the wind tunnel load that lead to first revised
structural property based on wind tunnel data which was subsequently used to update the resonant component
of the wind load. The revised wind tunnel load was then used to revise the design for the second time. From
the comparison of the natural frequencies of the first three vibration modes in Table-1 it is apparent that
consistency between the structural property and the wind load has been achieved and there is no need to revise
the design beyond two iterations for the present case. However under circumstances where the serviceability or
strength criteria are not met or the structure needs to be optimized further, the designer can use the parametric
maps to navigate appropriately and fine tune the structure for optimal wind performance. The arrows shown on
the parametric maps indicate the best iteration directions for the respective wind induced loads and responses.
In cases where it is required to decrease both the acceleration and the base loads for example, iterations that
follow a horizontal direction from heading to the right can be opted instead the ones indicated on Fig 3.
Table-1 Natural frequencies of the first three vibration modes (Hz) for the different design iterations
Vibration mode
Mode-1
Mode-2
Mode-3
Base line
0.2279
0.2649
0.4219
First revision
0.2239
0.2600
0.4167
Second revision
0.2240
0.2600
0.4168
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Baseline mass and stiffness
Figure 3 Parametric maps for wind-induced responses corresponding to 1% damping ratio
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
Baseline mass and stiffness
Figure 4 Parametric maps for wind-induced responses corresponding to 2% damping ratio
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7.0E+09
Inherent damping 8
Inherent damping 6.0E+09
7
6
50 year My (lb‐ft)
1 year Total Acceleration(milli‐g)
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additional 2% external damping 5
4
3
5.0E+09
additional 2% external damping 4.0E+09
3.0E+09
2.0E+09
2
1.0E+09
1
0.0E+00
0
0.5
1
1.5
2
2.5
3
3.5
4
0.5
5
1
1.5
2.5
3
3.5
4
5
Damping (%)
Damping (%)
1.4E+10
4.0E+08
1.2E+10
3.0E+08
1.0E+10
additional 2% external damping 8.0E+09
Inherent damping 3.5E+08
Inherent damping 50 year Mz (lb‐ft)
50 year Mx (lb‐ft)
2
6.0E+09
4.0E+09
additional 2% external damping 2.5E+08
2.0E+08
1.5E+08
1.0E+08
2.0E+09
5.0E+07
0.0E+00
0.0E+00
0.5
1
1.5
2
2.5
3
Damping (%)
3.5
4
5
0.5
1
1.5
2
2.5
3
3.5
4
5
Damping (%)
Figure 5. Variation of the wind-induced loads and responses at different damping levels
With regard to damping, the dynamic optimization analysis is carried out and the parametric maps are plotted
for different damping levels. In the present study the inherent damping (1% of the critical) is used in all the
design iterations. Wind induced responses are very much dependent on the damping level. As can be seen in
Figure 4 for an additional 1% critical damping the base loads on average reduces by 26.5% and accelerations
by 29.3%. Although use of additional external damping devices in not part of the present study, the
approximate response obtained for damping level of 3% of critical that assumes additional 2% external
damping indicates that significant reduction of the wind-induced responses could have been obtained by
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implementing external dampers as shown in Figure 5. Note that design revision that accounted the mass of the
damping was not carried out thus Figure 5 only shows the approximate reductions. A recent BLWT study
conducted by the authors for a prismatic tall building with square floor plan and aspect ratio (Height/width) of
approximately 9 with urban terrain exposure condition reveals an acceleration of 28 milli-g in excess of the 18
milli-g usually considered acceptable for office buildings. A parametric map provided by the wind engineer to
the structural engineer was instrumental to fine tune the structural system which resulted in reduction of the
acceleration to 23 milli-g which was then reduced to 18 milli-g through use of an external damper (2.5% of
critical). It is hoped by utilizing the parametric maps the structural engineer can select an optimal combination
of the structural properties mass, stiffness and damping which correspond to minimum wind induced responses
with less number of iterations.
CONCLUSION
The dynamic optimization technique demonstrated in the present study provides strategic guidance to
the structural engineer to select an optimum combination of structural properties (mass, stiffness & damping)
which results in minimum cost of buildings while satisfying all the design requirements with a potential of
minimizing design iterations. The baseline structure is designed based on the recommendations of codes. The
design was then be revised with the wind loads from wind tunnel tests. This results in new structural properties
and depending on the significance of the change in the structural properties the design wind loads as well as
the acceleration may require further revision. This iterative task can be highly facilitated by using the
parametric maps. The parametric maps show the variation of the design wind loads and acceleration with
respect to the variation of the structural properties: stiffness, mass and damping. From the results of the
parametric study it can be seen that the traditional optimization technique which mainly focus on resizing
structural members can be augmented with the use of external dampers. Planned future studies will focus on
the use of additional external damper both for serviceability and strength optimization and integration of wind
tunnel data with local meteorological data.
ACKNOWELGMENT
The authors gratefully acknowledge Rowan Williams Davies and Irwin Inc. (RWDI) for the wind
tunnel data and the multiple high frequency force balance software used to generate the wind induced
responses from the raw wind tunnel data. Also the fruitful discussions on dynamic optimization with Mr. Mark
Chatten from RWDI are greatly acknowledged.
REFERENCES
Alkhatib, R.F., Chatten, M.P., Gamble, S.L (2005), "One Museum Park East, Dynamic Optimization Study"
RWDI Report M05-1222.
American Society of Civil Engineers. “ASCE 7-05 Standard Minimum Design Loads for Buildings and Other
Structures”. Reston, Virginia (2005).
Boggs, D.W. and J.A. Peterka (1989), “Aerodynamic model tests of tall buildings”, Journal of Engineering
Mechanics, 115(3), 618-635.
Xie, J., and Irwin, P.A. (1998), “Application of Force Balance Technique to a Building Complex”, Journal of
Wind Engineering and Industrial Aerodynamics, 77&78, 579-590.
Chan C.M. and Chui J.K.L. (2006), “Wind-induced response and serviceability design
steel buildings”, Journal of Engineering Structures, 28: 503–513.
optimization of tall
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Chan C.M., Chui J.K.L and Huang M.F. (2009), “Integrated aerodynamics load determination and stiffness
design optimization of tall buildings”. Structural Design of Tall and Special Buildings; 18:59–80.
Davenport A.G. (1967), “Gust loading factors”, ASCE Journal of Structural Engineering, 93: 11–34.
Davenport A.G. (1995), “How can we simplify and generalize wind loading?” Journal of Wind Engineering
and Industrial Aerodynamics, 54–55: 657–669.
Holmes, J.D. (2002), “Effective static load distributions in wind engineering”, Journal of Wind Engineering
and Industrial Aerodynamics, 90: 91–109.
Melbourne, W.H. (1980), “Comparison of measurements on the CAARC standard tall building Model in
simulated model wind flows”, Journal of Wind Engineering and Industrial Aerodynamics, 6: 73-88.
Salmon, C.G. and Johnson, J.E. (2009), “Steel Structures – Design and Behavior”, Pearson Education, Inc.
Stafford Smith B. and Coull, A. (1991), “Building structures: Analysis and Design”. John Wiley & Sons, Inc.
Tschanz, T. and Davenport, A.G. (1983), “The base balance technique for the determination of Dynamic wind
loads”, Journal of Wind Engineering and Industrial Aerodynamics; 13:429–39.
Zhou, Y., Kijewski, T., and Kareem, A. (2003), “Aerodynamic loads on tall buildings: an interactive
database”, ASCE Journal of Structural Engineering, 129: 394–404.
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