Wind Resistant Structural Design Of Tall Buildings In Lateral Stiffness Optimization Under Equivalent Static Wind Load

With the fast development in economy in our country, more and more tallbuildings have been built in recent years. As its long natural periods and low damping,these tall buildings are more sensitive to wind action. The main challenges of windresistant optimal design of high-rise buildings have been focused on how to select areasonable balance between safety and economy in structural design. Under thesituation that land resources in China are limited and the increasing requirements onhigh quality of building performance are proposed, the wind resistance optimal designof high-rise buildings is urgent to implement the optimal adaptation and sustainabledevelopment between structural design of high-rise buildings and social prosperity,economic benefits and ecological balance. Structural optimization theory has beenproposed since1950s, it has obtained wide attention in academic and engineeringdesign field and has been successfully applied in automobile manufacturing,aerospace and many other engineering fields. However, its application in the windresistant design of tall buildings structures is still relatively few. In general the windload on tall buildings is quite complex and the number of loading cases, optimaldesign variables and optimal constraints of wind resistant optimal design are huge.Moreover, there are some limitations in numerical optimization algorithm and fewgeneral-purpose integrated optimization design softwares for structural design of tallbuildings have been developed. These difficulties make it challenging especially forwind resistant optimization design of high-rise buildings.The Optimal Criterion (OC) method and equivalent static wind load theory wasproposed in this thesis for developing the wind resistant optimization design for thesection sizes of high-rise buildings. By the application of the general-purpose finiteelement analysis software SAP2000Application Programming Interface (API)environment, some key theories and methodologies were studied in this paper for thewind resistant optimization design of high-rise buildings.First the empirical formula of power spectral density of fluctuating wind loadwere introduced from extensive wind tunnel test results for rectangular sectionhigh-rise buildings in Tokyo Polytechnic University, the matrix of power spectraldensities of fluctuating wind load was subjected to eigenvalue decompositionoperation to calculate and simplfy the integral term of covariance matrix ofwind-induced modal response, thus improved the numerical calculation efficiency for obtaining the equivalent static wind load of high-rise buildings by Extended Load-Response Correlation(ELRC) method.The wind resistant structural optimization design in the section sizes of a41-story frame-tubed reinforced concrete high-rise buildings was proposed in thisthesis subjected to equivalent static wind load. The corresponding mathematicalmodel of wind resistant optimal design was established, the minimization of totalweight of the optimized building was selected as the objective function, the width anddepth of beams and columns, the thickness of shear walls were selected as optimaldesign variables, the wind-induced displacement at the top level, the inter-story driftsat each level and the first order natural frequency of the building in Y-direction wereselected as the optimal constrain conditions. The recursive and iteration formula werededuced in the proposed optimum criterion method. Three commonly adoptedmethods of obtaining the optimized values of the Lagrange multipliers, which weretermed as Gauss-Seidel iteration method, sequential reduced linear equations methodand quadratic programming method, were proposed, analyzed and compared. AsGauss-Seidel iteration method and sequential reduced linear equations methodbasically failed to meet the inequality properties of the Lagrange multiplier linearequations, and their treatment methods for negative values in the Lagrange multiplierhave some disadvantages, the solutions based on these two methods tended to begreater instability. However these disadvantages could be overcome by theapplication of quadratic programming method as its solution could be obtained withgood accuracy in theory.In addition, when the inactive optimization variables were introduced in theoptimal iteration process, the iterative method for dealing with Lagrange multiplierscan affect the accuracy of the original optimization iteration formula. In order toovercome these shortcomings, this paper introduces a modification method for thecorrelation coefficient in Lagrange multiplier equations.Finally, by the integration of Matlab program with SAP2000API interfaceenviorment, a wind resistance optimized structural design was proposed in this paperfor a selected rectangular tall building. By adopting the wind-induced displacement atthe top level, the inter-story drifts at each level as the main constrain conditions andthe first order natural frequency of the building in Y direction as a additional constraincondition, the optimized results for these two optimized structural design cases wereanalysed and discussed. Optimized results showed that the good convergence could be obtained from the Optimal Criterion methods, the updating of the equivalent staticwind load before and after structural optimization cycles were also utilized. Moreanalyzed results also showed that the normalization of constrain condition was notapplied in the Gauss-Seidel iteration method. Therefore the convergence rate forobtaining the optimized results is relatively slow or accurate. Compared with theprevious conventional wind resistant optimization algorithms, the modifications inoptimization design variables would produce corresponding changes in the equivalentstatic wind load. As a result, the integration of recursive solution in the optimizeddesign variables, iteration of Lagrange multipliers and the synchronization updating ofthe equivalent static wind load was proposed in the wind resistant structural optimizeddesign procedure for tall buildings. Through the research in this thesis, the seamlessconnection between the generalized optimization program and general-purposed finiteelement analysis software has been implemented efficiently, and a integrated systemfor wind resistant optimization design of high-rise buildings is proposed in this thesiswhich contained the algorithms for structural optimization design, the solution andupdating of wind-induced vibration responses and equivalent static wind load ofhigh-rise buildings and the finite element analysis for the high-rise buildings.