Tài liệu Structures congress 2017 buildings and special structures

Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Structures Congress 2017 Buildings and Special Structures Selected Papers from the Structures Congress 2017 Denver, Colorado April 6–8, 2017 Edited by J. G. (Greg) Soules, P.E., S.E., P.Eng Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Structures Congress 2017 Buildings and Special Structures SELECTED PAPERS FROM THE STRUCTURES CONGRESS 2017 April 6–8, 2017 Denver, Colorado SPONSORED BY The Structural Engineering Institute (SEI) of the American Society of Civil Engineers EDITED BY J. G. (Greg) Soules, P.E., S.E., P.Eng Published by the American Society of Civil Engineers Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. 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Structures Congress 2017 iii Preface Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. The Structures Congress has a robust technical program focusing on topics important to Structural Engineers. The papers in the proceeding are organized in 4 volumes Volume 1 includes papers on Blast and Impact Loading and Response of Structures Volume 2 includes papers on Bridges and Transportation Structures Volume 3 includes papers on Buildings and Nonbuilding and Special Structures Volume 4 includes papers on Other Structural Engineering Topics including; Business and Professional Practice, Natural Disasters, Nonstructural Systems and Components, Education, Research, and Forensics Acknowledgments Preparation for the Structures Congress required significant time and effort from the members of the National Technical Program Committee, the Local Planning Committee. Much of the success of the conference reflects the dedication and hard work by these volunteers. We would like to thank GEICO and Pearl for Sponsoring the Congress proceedings and supporting the Structures Congress in such a generous way. The Joint Program Committee would like to acknowledge the critical support of the sponsors, exhibitors, presenters, and moderators who contributed to the success of the conference through their participation. On behalf of our dedicated volunteers and staff, we would like to thank you for spending your valuable time attending the Structures Congress. It is our hope that you and your colleagues will benefit greatly from the information provided, learn things you can implement and make professional connections that last for years. Sincerely, J. Greg Soules, P.E., S.E., P.Eng, SECB, F.SEI, F.ASCE © ASCE Structures Congress 2017 iv Contents Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Buildings Nonlinear Dynamic Analysis of Multi-Sloshing Mode Tuned Liquid Sloshing Dampers Installed in Tall Buildings .......................................................... 1 U. Y. Jeong Eliminating the Exposure Category from Wind Design Pressure ....................... 13 Nicole Ellison and Frederick R. Rutz Wind Load Prediction on Tall Buildings in a Stochastic Framework ................. 24 M. Gibbons, J. Galsworthy, M. Chatten, and S. Kala Experimental Investigation of Deconstructable Steel-Concrete Shear Connections in Sustainable Composite Beams....................................................... 34 Lizhong Wang, Mark D. Webster, and Jerome F. Hajjar Influence of Fastener Spacing on the Slip Modulus between Cold Formed Steel and Wood Sheathing ....................................................................................... 48 Weston Loehr, Bill Zhang, Hani Melhem, and Kimberly Krammer BRBM Frames: An Improved Approach to Seismic-Resistant Design Using Buckling-Restrained Braces .................................................................................... 60 Leo Panian, Nick Bucci, and Steven Tipping Implications of Modeling Assumptions on the Loss Estimation for Shear Wall Buildings ........................................................................................................... 72 Kristijan Kolozvari, Vesna Terzic, and Daniel Saldana Numerical Investigation of the Shear Buckling and Post-Buckling of Thin Steel Plates with FRP Strengthening ............................................................. 87 Mohamad Alipour, Alireza Rahai, and Devin K. Harris Seismic Evaluation of Incremental Seismic Retrofitting Techniques for Typical Peruvian Schools ....................................................................................... 101 Gustavo Loa, Alejandro Muñoz, and Sandra Santa-Cruz Advanced Technical Issues Related to Wind Loading on Tall Building Structures in Consideration of Performance-Based Design ............................... 111 U. Y. Jeong and K. Tarrant © ASCE Structures Congress 2017 ASCE 41-17 Steel Column Modeling and Acceptance Criteria ......................... 121 Daniel Bech, Jonas Houston, and Bill Tremayne Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Leveraging Cloud and Parametric Workflows to Accelerate Performance Based Seismic Design ................................................... 136 Kermin Chok, Pavel Tomek, Trent Clifton, and Branden Dong Stability of Steel Columns in Steel Concentrically Braced Frames Subjected to Seismic Loading ................................................................................ 143 Guillaume Toutant, Yasaman Balazadeh Minouei, Ali Imanpour, Sanda Koboevic, and Robert Tremblay Classifying Cyclic Buckling Modes of Steel Wide-Flange Columns under Cyclic Loading ........................................................................................................ 155 Gulen Ozkula, John Harris, and Chia-Ming Uang Structural Behaviour of Demountable HSS Semi-Rigid Composite Joints with Precast Concrete Slabs ....................................................................... 168 Abdolreza Ataei, Mark A. Bradford, and Hamid R. Valipour Topology and Sizing Optimization of Nonlinear Viscous Dampers for the Minimum-Cost Seismic Retrofitting of 3-D Frame Structures .......................... 179 Nicolò Pollini, Oren Lavan, and Oded Amir Structural Topology Optimization Considering Complexity ............................. 192 Saranthip Koh, May Thu Nwe Nwe, Payam Bahrami, Fodil Fadli, Cristopher D. Moen, and James K. Guest Cast Steel Replaceable Modular Links for Eccentrically Braced Frames ........ 202 J. Binder, M. Gray, C. Christopoulos, and C. de Oliveira New Methods in Efficient Post-Tensioned Slab Design Using Topology Optimization ............................................................................................................ 213 M. Sarkisian, E. Long, A. Beghini, R. Garai, D. Shook, A. Diaz, and R. Henoch Design and Parametric Finite Element Analysis—A Thin Lightweight Two-Way Steel Flooring System ........................................................................... 225 Eugene Boadi-Danquah, Brian Robertson, and Matthew Fadden Structural Form Finding of a Rope Sculpture ..................................................... 237 M. Sarkisian, E. Long, A. Beghini, and N. Wang Discussion of Tubular Steel Monopole Base Connections: The Base Weld Toe Crack Phenomenon; Crack Identification and a Proposed Severity Classification System ................ 248 Brian R. Reese and David W. Hawkins © ASCE v Structures Congress 2017 Design and Theory of Passive Eddy Current Dampers in Building Structures ................................................................................................. 262 Mandy Chen and Lance Manuel Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Effect of Damaged Fireproofing on the Behavior of Structural Steel Members .................................................................................................................. 275 Ataollah Taghipour Anvari, Mustafa Mahamid, and Michael J. McNallan A Re-Evaluation of f’m—Unit Strength Method, Face Shell, and Fully Bedded Mortar Joints............................................................................................. 287 N. Westin and M. Mahamid Parametric Study and Design Procedure for Skewed Extended Shear Tab Connections ............................................................................................................. 301 Mutaz Al Hijaj and Mustafa Mahamid Scaffolding a Landmark: The Restoration of the Dome of the United States Capitol Building ...................................................................................................... 319 Christopher P. Pinto and Joelle K. Nelson Achieving Column-Free Platforms—Design and Construction of Large Span Station Mezzanines on the Second Avenue Subway Project ..................... 329 Renée Grigson and Michael Voorwinde Evaluation of Full-Scale Adobe Brick Walls under Uniform Pressure ............. 343 S. Robert, H. El-Emam, A. Saucier, H. Salim, and Scott Bade Experimental Study of Externally Flange Bonded CFRP for Retrofitting Beam-Column Joints with High Concrete Compressive Strength ..................... 354 Olaniyi Arowojolu, Muhammad Kalimur Rahman, Baluch Muhammad Hussain, and Ali-Al Gadhib Considerations in the Use of Side Load Pier Brackets ........................................ 365 James Robert Harris and Kenneth Cobb Retrofitting of Flange Notched Wood I-Joists with Glass Fiber Reinforced Polymer (GFRP) Plates .......................................................................................... 375 M. Shahidul Islam and M. Shahria Alam Multiple Hazards and Social Vulnerability for the Denver Region ................... 386 A. Rein Starrett and R. B. Corotis A Top Down Approach to Achieve Full System Modeling in Seismic Analysis and Design .................................................................................. 406 F. A. Charney © ASCE vi Structures Congress 2017 Experimental and Numerical Investigation of Flexural Concrete Wall Design Details .......................................................................................................... 418 A. Behrouzi, T. Welt, D. Lehman, L. Lowes, J. LaFave, and D. Kuchma Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Seismic Response Study of Degraded Viscous Damping Systems for Tall Buildings in China .......................................................................................... 434 H. Ataei, M. Mamaghani, and K. Kalbasi Anaraki Topology Optimization and Performance-Based Design of Tall Buildings: A Spatial Framework ............................................................................................. 447 Xihaier Luo, Arthriya Suksuwan, Seymour M. J. Spence, and Ahsan Kareem Effects of Foundation Uplift on the Dynamic Response of Steel Frames .......... 459 Mohammad Salehi, Amir Hossein Jafarieh, and Mohammad Ali Ghannad Performance-Based Wind and Seismic Engineering: Benefits of Considering Multiple Hazards ........................................................... 473 Kevin Aswegan, Russell Larsen, Ron Klemencic, John Hooper, and Jeremy Hasselbauer Effect of Drift Loading History on the Collapse Capacity of Deep Steel Columns ................................................................................................................... 485 T.-Y. Wu, S. El-Tawil, and J. McCormick Properties of and Applications with Full Locked Coil Rope Assemblies .......... 495 K.-J. Thiem and M. Bechtold U.S. Bank Stadium: Transparent Roof Steel Collaboration............................... 503 R. John Aniol, Rick Torborg, and Eric Fielder Advanced Analysis of Steel-Frame Buildings for Full Story Fires .................... 515 Erica C. Fischer and Amit H. Varma Integrated Fire-Structure Simulation Methodology for Predicting the Behavior of Structures in Realistic Fires .............................................................. 527 Chao Zhang Structural Design, Approval, and Monitoring of a UBC Tall Wood Building .................................................................................................................... 541 T. Tannert and M. Moudgil Adaptive Reuse of the Historical Ferdinand Building, Boston, MA .................. 548 John Looney Fire Safety and Tall Timber Buildings—What’s Next? ...................................... 556 David Barber © ASCE vii Structures Congress 2017 viii The New Tocumen International Airport South Terminal in Panama City, Panama .................................................................................................................... 570 Andrea Soligon, Jeng Neo, and Xiaonian Duan Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Multi-Hazard Design of a New Emergency Communications Facility in St. Louis, Missouri .................................................................................................. 582 Nathan C. Gould, Richard Hoehne, and Michael Shea Prison Design in Haiti: Structural Challenges ..................................................... 592 David Dunkman, Christopher Hewitt, and Scott Hollingsworth Underpinning Historic Structures at Grand Central Station, New York ......... 604 Yazdan Majdi and Richard Giffen Design of an Underground Viaduct for the Expansion of the Moscone Center....................................................................................................................... 614 A. Trgovcich, L. Panian, and S. Tipping Nonbuilding and Special Structures Extreme Wave Monitoring and In Situ Wave Pressure Measurement for the Cofferdam Construction of the Pingtan Strait Bridge.................................. 629 Zilong Ti, Shunquan Qin, Yongle Li, Dapeng Mei, and Kai Wei What We Learned from the Cooling Tower Foundation Design Challenges from a Revamp Project .......................................................................................... 643 Silky Wong and Abhijeet Yesare Design of Industrial Pipe Racks Using Modules, Pre-Assembled Units, and Stick-Built Construction ...................................................................... 653 Xiapin Hua, Ron Mase, Khoi Ly, and Jkumar Gopalarathnam Ship Impact and Nonlinear Dynamic Collapse Analysis of a Single Well Observation Platform ............................................................................................. 668 Ahmed Khalil, Huda Helmy, Hatem Tageldin, and Hamed Salem Pile Cap Seismic Load Transfer to Soil ................................................................ 681 Eric Wey, Rollins Brown, Candice Kou, and C. B. Crouse Constructability Solutions for Temporarily Supporting 200’ Flare Stacks during Construction Modifications ........................................................... 693 Mateusz Prusak, Nicholas Triandafilou, Mustafa Mahamid, and Tom Brindley Custom Helical Pile Use for a Refinery Revamp: A Case Study ........................ 706 Eric Wey, Patrick Murray, Howard Perko, Malone Mondoy, and Paul Volpe © ASCE Structures Congress 2017 Structural Fatigue of Process Plant Modules during Ocean Transport ............ 721 Alan Shive and Marco Camacho Innovative Use of FRP in Large-Diameter Piles for Vessel Impact ................... 735 M. A. McCarty, V. Zanjani, E. Grimnes, and J. Marquis Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Seismic Analysis and Design for Wine Barrel Storage Racks ............................ 745 Tauras Stockus and Tzong-Ying Hao Seismic Analysis and Design of a 21,000-Gallon Frac Tank Considering the Fluid-Structure Interaction Effects for a FLEX Response at a Nuclear Power Station ............................................................................................ 758 Christine H. Roy and Michael Mudlock Seismic Behavior of Cylindrical Fluid-Filled Steel Tanks .................................. 772 Erica C. Fischer and Judy Liu A Comparison of Approximate Methods for Period Determination in Rack Structures ...................................................................................................... 782 Andrew Hardyniec, Charles DeVore, and Jeffrey Travis © ASCE ix Structures Congress 2017 1 Nonlinear Dynamic Analysis of Multi-Sloshing Mode Tuned Liquid Sloshing Dampers Installed in Tall Buildings Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. U. Y. Jeong1 1 Gradient Wind Engineering Inc., 127 Walgreen Rd., Ottawa, ON, Canada K0A 1L0. E-mail: [email protected] Abstract This paper presents nonlinear time domain analysis and its iterative formula for a tuned-liquid sloshing damper installed on a tall slender building under strong vortex shedding excitation. A new iterative formula is derived for a nonlinear time domain analysis of a tuned liquid sloshing damper represented in the mathematical model introduced by Warnitchai, P. in 1998. For the accurate modeling of liquid (typically water) sloshing motion, the nonlinear quadratic damping force which is generated by the liquid flow through a screen is directly implemented without linearizing the term applied in previous studies (P. Warnitchai, 1998; M. J. Tait, 2008). Multi-sloshing modes of the liquid are also considered for more accurate modeling. The nonlinear sloshing damper model has been analyzed coupled with tall buildings with heights of 300m and slenderness ratios exceeding 10. The effects of nonlinearity and multiple sloshing mode effects of the liquid and efficiency of the sloshing dampers for different building frequencies and surrounding conditions are investigated. Examples include (i) time and frequency domain analysis of, (ii) linear and nonlinear, (iii) single- and multi- sloshing mode liquid dampers, (iv) coupled with tall slender building with a range of building frequencies, (v) under strong vortex shedding and generated from a target wind load spectra based on a Japanese Building Code (AIJ). The present formula can be used to analyze and design liquid sloshing dampers without physical damper test. INTRODUCTION Tall buildings often experience excessive building motions, which makes the serviceability of buildings in terms of accelerations and torsional velocities exceed the acceptable range according to the industrial guidelines (ISO, 1984; Isyumov, 1993, 1995). To mitigate the excessive motions, Tuned Liquid Sloshing Dampers (TLSDs) have been frequently used due to their low cost, simple frequency tuning, and low maintenance (Kareem, 1987, 1990; Fujino, 1995; Warnitchai, 1997; Tait, 2004, 2008; Tait et al., 2004a, 2004b). The sloshing motion of the liquid in a tank can be expressed as a combination of infinite sloshing modes based on potential flow theory in consideration of wall and free surface boundary conditions (Baucer, 1984; Warnitchai, 1997; Tait, 2004, 2008). In order to dissipate building’s vibration energy, © ASCE Structures Congress 2017 2 TLSDs are usually equipped with porous screens (Fediw et al., 1995; Warnitchai, 1997) immersed in the liquid. The damping force created by the porous screens are a nonlinear function of water velocity flowing through the screens, which makes it difficult to calculate the accurate damping force. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Previous studies consider the nonlinear screen damping force as approximate linear form based on the assumption of the probabilistic distribution of the excitation as sinusoidal or random signals (Caughey, 1963). However, since the wind-induced excitation of the motion is not the same as the sinusoidal or random signals, for more accurate modeling of the sloshing tank, nonlinear effects should be considered. Kaneko and Ishikawa (1999) considered the nonlinear screen damping force in their iterative solution of potential flow over the liquid domain based on Finite Difference Method. Their method produces implicit solution of liquid sloshing motion requiring discretization of liquid domain which makes the solution process a bit complicated and time consuming. In this paper, nonlinear formulas are derived to solve dynamic sloshing motion of multi-sloshing mode a TLSD installed on a tall building in consideration of the nonlinear screen damping force. To implement present method to the windinduced tall building vibration problem, the nonlinear TLSD model is coupled with tall slender building immersed in strong winds. Here, for more accurate analysis of wind-induced vibration of tall slender structure, aerodynamic damping and its timedomain formulas are also derived based on Rational Function Approximation (RFA) (Fujino et al., 1995). ACROSS-WIND BUILDING MOTION WITH AERODYNAMIC DAMPING The dynamic equation of motion for a tall building under wind excitation can be expressed as follows in modal domain in consideration of aerodynamic damping ~ force, f ae : ~ ~ −1 ( ~ ~ x + 2ξ s ωs ~ x + ω2s ~ x =m f + f ae ) (1) x , ~ x and ~ x represent the acceleration, velocity and displacement of the where ~ generalized coordinate; and ξ s and ω s represent modal damping and natural angular ~ = modal mass; ~ f = modal wind load. velocity respectively of the mode; m Aerodynamic damping of tall buildings for across-wind excitation can be measured from forced- or free-vibration response of a pivoting model in the wind tunnel (Steckley, 1989; Watanabe et al, 1997; Katagiri et al., 2000). The aerodynamic damping depends on building geometries, exposures, aspect ratios, side ratios and amplitudes of vibration. The self-excited force in terms of aerodynamic damping and © ASCE Structures Congress 2017 3 stiffness can be expressed as follows in generalized coordinate by aerodynamic force measurements obtained from forced vibration tests (Steckley, 1989): ~ ~ηω2 (α + iβ) ~ f ae = −2m x; (2) ~) ; ω is angular velocity; α and β represent frequencywhere η = ρB H /(3m dependent aerodynamic stiffness and damping respectively measured from the tests; i = − 1 ; B= building width; H = building height. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. 2 BUILDING COUPLED WITH MULTI-SLOSHING MODE TLSD Figures 1(a) to 1(d) show schematic diagrams of a building coupled with simplified linear single-sloshing mode TLSD (Figure 1(a)) versus nonlinear multisloshing mode TLSD (Figure 1(c)), and their corresponding equivalent TMD (Tuned Mass Damper) modeling in Figures 1(b) and 1(d) respectively. Here, it is noted that ~ the Figure 1(d) illustrates the aerodynamic forces, f ae , and the non-conservative damping force, Qn . For a damper with dimensions of b, h, and L corresponding to width, water height and length, the equation of motion of the building-TLSD coupled system under wind loading can be represented as follows based on equilibrium conditions of the equivalent MTMD model in Figure 1(d): ~ ρwbhL ~ nd meq,n ~ ~ −1 ( ~ x + 2ξ ω ~  + ω2 ~ ) x x = m f + f − s s s ae ~ x − m ~ xr ,n m n=1 x x + Χ x x + ω2 x = − ~ r ,n eq , n r,n r ,n eq , n r , n (3) (4) In the above, ρw = liquid density; the second term in (4) corresponds to the nonconservative damping force, Qn , of sloshing mode n, illustrated in Figure 1(d); meq, n is the effective mass of the nth sloshing mode defined below; xr , n , xr , n and xr , n represent relative displacement between the motion of the equivalent mass and the building (see Figure 1), and its first and second-order time derivatives respectively for the nth liquid sloshing mode. Furthermore, the noted parameters are defined as follows based on explicit solution of Laplace equation defining the liquid in rectangular tank based on potential flow theory (Warnitchai, 1997; Tait, 2008): meq , n © ASCE nπh 2ρbL2 (1 − cos( nπ)) 2 tanh( ); = 3 L ( nπ ) (5) Structures Congress 2017 4 Χeq,n = 2(1 − cos(nπ)) nπh tanh2 ( )Cl Δ nΞn ; nπL L (6) 1 nπh + sinh − 2 ( ); 3 L ns nπx j ); Ξ n =  sin3 ( L j =1 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Δn = ωeq , n = (7) (8) nπg nπh tanh( ). L L (9) In the above, x j indicate the location of the screen in the x-coordinate; ns denotes the number of screen in the tank. The amplitude of sloshing height of nth sloshing mode, qn , can be represented as follows using the modal participation ratio, Γn , and relative displacement, xr , n : qn = Γn xr , n . Γn = (10) 2(1 − cos(nπ)) nπh tanh( ). nπ L (11) As shown in (4), the equation of the motion of the TLSD is a nonlinear equation due to the velocity-dependent nonlinear liquid damping term, which is the second term in the left side of the equation. TIME DOMAIN FORMULA OF AERODYNAMIC DAMPING Formulas for the tall building-TLSD coupled problem are derived in timedomain to directly calculate the peak factors and to take advantage of the other benefits described before. Among the governing equations for the time-domain analysis, the frequency-dependent aerodynamic damping and stiffness terms have to be converted to terms solvable in the time-domain. The Rational Function Approximation (RFA) method used originally in aeronautical engineering can be used to represent the frequency-dependent aerodynamic damping and stiffness terms in equation (2) and convert them to the following equations with constant coefficients which can be solved in time-domain (Jeong, 2014): U U U2 ~ −1 ~ m f ae = −2ηa3 ~ x − 2η H a2 ~ x − 2η H a1 ~ x − 2η H2 B B B yj = © ASCE iωa j +3 ~ , for j=1 to m. x UH iω+ dj B m y j (12) j =1 (13) Structures Congress 2017 5 where a j for j=1 to m+3 represent rational function coefficients; d j are damping terms for j=1 to m; m denotes number of rational function terms. The coefficients d j should be selected to best fit the function. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. TIME DOMAIN BUILDING – NONLINEAR MULTI-SLOSHING MODE DAMPER COUPLED SYSTEM ANALYSIS The governing equations for the nonlinear time-domain analysis building motion coupled with TLSD under wind-excitation can be represented as follows by combining the dynamic equation of motion for the building coupled with multisloshing mode TLSD in equations (3) and (4) as well as the auxiliary equations from RFA in (12) and (13): 2 ρωbhL ~ x + (2ξ ω + 2η U H a ) ~  + (ω2 + 2η U H a ) ~ + 2 η a ) x 3 2 1 x s s s ~ m B B2 nd meq,n ~ U2 m +  ~ xr ,n + 2η H2  y j = m −1 f ; m B (1 + n=1 j =1 2 ~ , for n=1 to ns; x + xr ,n + Χ eq,n xr ,n x r ,n + ωeq , n xr , n = 0 y j − a j +3 ~ x + (14) d jU H B y j = 0 , for j=1 to m. (15) (16) In order to solve the coupled nonlinear dynamic equations in (14) to (16), Newmark Beta step-by-step integration method is used after deriving incremental formula including the nonlinear term in (15) for the iterative calculation. The solutions are calculated until converged by the iterations for each time step. EXAMPLE - ACROSS-WIND RESPONSE OF COUPLED TALL BUILDINGNONLINEAR MULTI-MODE TLSD A tall building with building height, H, equals to 300 m, with plan dimension B and D of 20 m by 20 m respectively is analyzed under mean hourly wind speed of 33.55 m/s defined at the top of the building height above the grade in open exposure which corresponds to 10-year wind speed in Seattle, Washington. The exposure is assumed to be open exposure with mean wind speed exponent, γ , of 0.14; turbulence intensity at the building height corresponds to approximately 11 % and 10 % based on 3 ASCE (2010), ESDU respectively. The mass density of the building is 225 kg / m and the mass is assumed to be distributed uniformly along the height of the building. Structural damping ratio, ξ1 , equals to 0.15. The mode shape exponent μ is 1.5 which is a typical value for tall buildings. © ASCE Structures Congress 2017 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Across-wind load spectrum in AIJ (2006) has been used in this example due to its simplicity and versatility covering different side ratios, although the applicable aspect ratios of the building in AIJ are limited below 6. Figure 2 illustrates acrosswind spectrum used in the example. The peak value of the spectra due to the vortex shedding occurs around 0.15 Hz which corresponds to the reduced frequency (= f vs B / U H ) of 0.1, which is typical for the buildings with square plan ( Gu and Quan, 2004; Chen, 2014 ) where f vs = vortex shedding frequency. For time domain analysis, a time history of the modal wind load has been generated from the target spectrum based on Spectral Representation Method (Shinozuka and Jan, 1972; Deodatis, 1996). According to Deodatis (1996), sample functions of multi-variate stochastic process can be generated based on Cholesky decomposition of spectra matrix in combination with random phasing. Figure 2 also illustrates a time series generated by the Spectral Representation Method using the base moment spectrum. The figure shows an excellent match between the spectrum of the generated time series versus the original spectrum, which demonstrates the accuracy of the method. Steckley’s (1989) motion-induced aerodynamic damping and stiffness under pivoting excitation are used in the analysis. Since the amplitude-dependent nonlinear characteristic of the aerodynamic damping (Chen, 2013, 2014) is not considered in this study, the aerodynamic damping measured under small-amplitude is used. Figure 3 illustrates the coefficients of aerodynamic impedance ( α + iβ ) which represents aerodynamic damping and stiffness of a building with a square-shaped building plan with aspect ratio of 13.3 measured under nominal turbulence intensities of 17 %. As shown in the figure, the aerodynamic damping in terms of β reduces as frequency reduce and falls below zero which means negative aerodynamic damping where the reduced frequency, K, is lower than 0.7. The figure also illustrates the fitted curves for α and β using rational functions for the time-domain analysis. Equations in (14) to (16) are analyzed both in frequency-domain and timedomain for the verification with building frequencies varying from 0.08 Hz to 0.3 Hz. Since excessive building motions are expected due to the slenderness of the building, TLSDs are optimally designed with various dimensions to be tuned to different building frequencies, to provide 3% additional damping to the building. The effective ~ m /m mass ratio of the damper (= meq / m I ) is approximately 1.4 %; and the TLSD 1 is optimally tuned to the structural frequencies. The porous screens are also designed to provide optimal damping to the damper based on random sloshing motion. The TLSD-building system has been analysis using the equations (14) to (16) in consideration of aerodynamic damping for 17% Turbulence Intensity. Frequency-domain analysis and time domain analysis of the building-TLSD coupled system is performed for the structural frequencies varying 0.08 to 0.3 Hz using the generated wind load time series and the results are plotted in Figure 4. As © ASCE 6 Structures Congress 2017 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. shown in the figure; around the region where the building frequency matches with the vortex-shedding frequency of 0.15 Hz, the amplitude of vibration reaches its maximum. The aerodynamic damping effects are favorable for the frequencies higher than the vortex shedding frequency, therefore, the response reduced with AD, whereas the amplitude has increased for the frequencies lower than the vortex shedding frequency due to the unfavorable negative aerodynamic damping. With optimally designed dampers installed on the building, the response drastically reduces and the system becomes more stable even under the negative AD at low building frequency. Linear Time-domain analysis results show excellent agreements with those from the Frequency-domain analysis. However, due to the system instability introduced by RFA, the result for 0.8Hz is deviated from that of the Frequency-domain analysis. Nonlinear time-domain analysis results compared to those from the linear analysis have increased for high frequency region, due to the nonlinear damping force effect. However, the nonlinear analysis results fall very close to the linear analysis results for low building frequencies. Figure 5 shows a time history of the average liquid pressure on screens which represents the non-conservatory damping force during the nonlinear time domain analysis. The blue line represents the non-conservatory damping force per unit area (=  Qn / bh ), whereas the red line indicates directly calculated liquid pressure using the liquid velocity and loss coefficient, Cl , of the screen. As shown in the figure, the non-conservatory damping force is accurately calculated based on the present method. Figure 6(a) and 6(b) illustrate liquid sloshing motions at two instantaneous times during the nonlinear time-domain analysis of building with building frequency of 1.0Hz. Whereas Figure 6(a) represents when the water sloshing height reaches its maximum on the left wall in the figure and the motion is governed by the first antisymmetric sloshing mode, Figure 6(b) represents the moment when the water sloshing motion is contributed by multiple modes which is considered in this study. CONCLUSIONS New formulas are derived for a nonlinear dynamic analysis of multi-sloshing TLSD. In order to apply the method to wind design of tall buildings, required formulas for motion-induced aerodynamic damping and stiffness are also derived both in time- and frequency-domain. The TLSD is modeled as multiple equivalent TMDs equipped with nonlinear damping force representing the non-conservatory damping force created by the screen immersed in sloshing liquid. Explicit solution for the sloshing motion of liquid in a rectangular tank is derived in generalized coordinates representing liquid sloshing motion based on potential flow theory. The non-conservatory nonlinear damping force are derived for each mode for the time-domain analysis. A verification of present method is © ASCE 7 Structures Congress 2017 attempted through an example of a typical tall slender building. From the analysis, the nonlinear screen damping force effects are investigated which have increased responses for the building with relatively high frequency. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. The proposed time domain approach will enable more accurate evaluation of wind response of tall buildings, more accurate design of TLSD reducing the expensive dynamic damper testing, evaluating non-Gaussian processes such as real peak factors, which will be very useful in tall building design. REFERENCES American Society of Civil Engineers (ASCE). (2010), Minimum design loads for buildings and other structures, ASCE Standard ASCE/SEI 7-10. Architectural Institute of Japan (AIJ). (2006), Recommendations for loads on Buildings. Baucer, H.F. (1984) “Oscillations of immiscible liquids in a rectangular container: a new damper for excited structures,” J. Sound and Vibration, 93, 117-133. Caughey, T.K. (1963) “Equivalent linearization techniques,” J. of Acoustical Society of America, 35(11) 1706-1711. Chen, X. (2013) “Estimation of stochastic crosswind response of wind-excited tall buildings with nonlinear aerodynamic damping,” Engineering Structures, 56, 766-778. Chen, X. (2014) “Extreme value distribution and peak factor of crosswind response of flexible structures with nonlinear aeroelastic effect,”, J. Struct. Eng., ASCE, online 0401491, 1-18. Deodatis, G. (1996) “Simulation of ergodic multivariate stochastic processes,” J. of Eng. Mech., ASCE, 122(8) 778-787. Engineering Standard Data Unit (ESDU) Wind Engineering Sub-Series, ESDU International Inc. Fediw, A.A., Isyumov, N. and Vickery, B.J. (1995) “Performance of a tuned sloshing water damper,” Journal of Wind Engineering and Industrial Aerodynamics, 57, 237-247. Fujino, Y., Wilde, K., Masukawa, J. and Bhartia, B. (1995) “Rational function approximation of aerodynamic forces on bridge deck and its application to active control of flutter,” Proceedings of the 9th International Conference on Wind Engineering, New Delhi, India. Gu, M. and Quan, Y. (2004) “Across-wind loads on typical tall buildings,” J. of Wind Eng. and Ind. Aerodyn. 92, 1147-1165. International Standards Organization (ISO) 6897-1984: “Guidelines for the evaluation of the response of occupants of fixed structures, especially buildings and offshore structures, to low frequency horizontal motion (0.063 to 1 Hertz).” Isyumov, N. (1993) “Criteria for acceptable wind-induced motions of tall buildings,” Proceedings of the International Conference on Tall Buildings, Council on Tall Buildings and Urban Habitat, Rio de Janerio, Brazil. © ASCE 8 Structures Congress 2017 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. Kaneko, S., Ishikawa, M. (1999) “Modeling of Tuned Liquid Damper with Submerged Nets,” Transactions of ASME, 121, 334-343. Kareem, A. and Sun, W.J. (1987) “Stochastic response of structures with fluidcontaining appendages,” J. of Sound and Vibration, 119(3). Kareem, A. (1990) “Reduction of wind induced motion utilizing a tuned sloshing damper,” J. of Wind Engineering and Industrial Aerodynamics, 36, 725-737. Katagiri, J., Ohkuma, T., Marukawa, H. and Shimomura, S. (2000) “Motion-induced wind forces acting on rectangular high-rise buildings with side ratio of 2,” J. Struct. Constr. Eng., AIJ 534, 25-32. Shinozuka, M. and Jan, C.-M. (1972) “Digital simulation of random processes and its application,” J. of Sound and Vibration, 25(1), 111-128. Steckly, A. (1989) Ph.D. Thesis, University of Western Ontario. Tait, M.J., El Damatty A.A. and Isyumov, N. (2004) “Testing of tuned liquid damper with screens and development of equivalent TMD model,” Wind and Structures, An International Journal, 7, 215-234. Tait, M.J., Isyumov, N. and El Damatty A.A., (2004) “The efficiency and robustness of a uni-directional tuned liquid damper ad modeling with an equivalent TMD,” Wind and Structures, An International Journal, 7, 235-250. Tait, M.J. (2004) The performance of 1-D and 2-D tuned liquid dampers, Ph.D. Thesis, University of Western Ontario. Tait, M.J. (2008) “Modeling and preliminary design of a structure-TLD system,” Engi. Struct., 30, 2644-2655. Warnitchai, P. and Pinkaew, T. (1998) “Modeling of liquid sloshing in rectangular tanks with flow-dampening devices,” Eng. Struct., 20(7), 593-600. Watanabe, Y., Isyumov, N. and Davenport, A.G. (1997) “Empirical aerodynamic damping function for tall buildings,” J. of Wind Eng. and Ind. Aerodynamics, 72, 313-321. © ASCE 9 Structures Congress 2017 10 Porous Screen k1 TLSD ~ ~ x q k1 ~ f fae k eq ~ ~ f ~ m ~ m ~ fae c1 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/05/19. Copyright ASCE. For personal use only; all rights reserved. x c1 (a) Single Sloshing Mode TLSD ~ x+x r m eq ceq (b) Equivalnet Linear TMD Model ~ ~ x f fae(ω) keq,ns ~ Qns TLSD k1 k1 Q2 ~ f ~ m x+x r,ns m eq,ns ~ keq,2 ~ x q ~ ~ m ~ fae c1 ~ x+x r,1 k eq,1 c1 (c) Multi-Sloshing Mode TLSD x+x r,2 m eq,2 Q1 m eq,1 (d) Equivalent N.L.-MTMD model Figure 1. Schematic Diagram of Tuned Liquid Sloshing Damper (TLSD) Installed on top of the Building -1 10 -2 10 -3 fSM/(0.5 ρ UH2)2 10 -4 10 -5 10 -6 10 AIJ, 2006 Generated Wind Time History -7 10 -8 10 -4 10 -3 10 -2 -1 10 10 0 10 1 10 f (Hz) Figure 2. Comparison of Normalized Base Moment Spectra of Target Value based on AIJ and Generated Time History © ASCE