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

Transcription

1 Dynamic optimization for the wind-induced response of a tall building Workamaw Warsido 1, Ryan Merrick 2 Girma Bitsuamalk 3, 1 Research Assistant, Civil and Environmental Engineering department (CEE), International Hurricane Research Center (IHRC), Florida International University (FIU), Miami, Florida, USA, wwars001@fiu.edu 2 Technical Coordinator, RWDI Inc., Guelph, ON, Canada, Ryan.Merrick@rwdi.com 3 Assistant Professor of Wind/Structural Engineering, CEE, IHRC, FIU, Miami, Florida, USA, bitsuamg@fiu.edu 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. 1

2 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 m x c x k x Where F,m,C and k, are the generalized force, generalized mass, generalized damping constant and generalized stiffness respectively which are defined as follows: F j Φ j T F m j Φ j T M Φ j c j Φ j T c Φ j k j Φ j T k Φ j where F, M, C and K are the force, mass, damping and stiffness matrices of the building respectively. Φ is the j th 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, S M, can be related to the generalized wind force spectrum, S m, using the mechanical admittance function, H, as (Boggs and Peterka 1989, Xie and Irwin 1998, Zhou et al. 2003): S M HωS 6 2

3 Hω 1 1 ω ω 4ζ ω ω 7 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: σ M S M ωdω Hω S ωdω 8 This variance of the base moment has two components, the background componentσ MB and resonant component (σ MR (Davenport, 1995) σ M σ MB σ MR 9 The background component σ MB can be determined by integrating the area under the wind load spectra S as: S ωdω 10 σ MB while the resonant component can be determined from S ω Hω dω σ MR 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: 11 M M g B σ MB g R σ MR 12 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): g R 2lnω T lnω T where T is the total observation time. 13 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. 3

4 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 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. 100 ft 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. 4

5 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 M y and M x b) 50-year return period base torsional moment M z ; 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 Base line First revision Second revision Mode Mode Mode

6 Baseline mass and stiffness Figure 3 Parametric maps for wind-induced responses corresponding to 1% damping ratio 6

7 Baseline mass and stiffness Figure 4 Parametric maps for wind-induced responses corresponding to 2% damping ratio 7

8 1 year Total Acceleration(milli g) Inherent damping additional 2% external damping Damping (%) 50 year My (lb ft) 7.0E E E E E E E E+00 Inherent damping additional 2% external damping Damping (%) 50 year Mx (lb ft) 1.4E E E E E E+09 Inherent damping additional 2% external damping 50 year Mz (lb ft) 4.0E E E E E E E+08 Inherent damping additional 2% external damping 2.0E E E Damping (%) 0.0E 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 8

9 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 M 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), 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, Chan C.M. and Chui J.K.L. (2006), Wind-induced response and serviceability design steel buildings, Journal of Engineering Structures, 28: optimization of tall 9

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