Design Optimization On High-rise Buildings Under Wind Load Based On Reliability And Joint Probability Distribution Of Wind Speed And Direction

In this dissertation, focusing on the problems of high-rise buildings’ high sensitivity to wind loads, the complexity nature of wind loads, and the common conservation in determining wind load, reliability analysis based on probability theory was applied to give full consideration to the effects of wind directions during the wind resistant optimization design of the high-rise buildings. In present work, the algorithm of OC(Optimality Criteria) was adopted for wind resistant optimization, with the total weight of the structural members as the objective function, and with the displacement on the top of structures, the displacement between layers and the natural frequencies as the constraint functions. By adjusting the dimensions of the member sections, the structure could be optimized to have the minimum weight and to satisfy the requirements of structural safety under wind loads. The main contents and conclusions of current project are summarized as follows:(1) The existing frequency domain analysis methods of wind vibration response have been derivated carefully and compared in details. Then a more concise method was proposed, which is more suitable to the high-rise infrastructures. Besides, the precision and efficiency of different frequency domain methods were compared and their pros and cons as well as the application scope were summarized, by setting the high-rise buildings as the engineering example for current study.(2) Focusing on the challenge in calculation and selection of equivalent static wind loads(ESWLs) in wind-resistant design optimization, a multi-objective ESWLs was developed, with setting the wind vibration response, such as the maximum displacement and inter-story drifts, as the equivalent targets, so as to obtain a series of ESWLs which can produce the same maximum response as those targets. In this way, it could avoid to calculate multiple sets of equivalent loads corresponding to different equivalent target responses by the theory of single objective equivalent wind loads.(3) According to the random vibration theory, structural acceleration responses are explicitly expressed by structural natural frequencies and wind loads, where the fundamental natural frequency and damping ratio as well as wind speed were taken into account as random variables. Thus the expression of acceleration includes three kinds of random variables(frequency, damping ratio and wind speed) that obey a certain distribution. According to the specification limits for the acceleration within 10-year return period, from the perspective of probability, the reliability theory could be adopted to obtain natural frequencies of structures corresponding to the acceleration limit. Therefore, the acceleration limit could be converted to structural natural frequency limits, so that to control the first few order of natural frequencies conveniently in high-rise buildings during the wind-resistance design optimization by Rayleigh quotient principle, and thus to control the atop acceleration limits ultimately. Optimization results show the necessity of considering the random variables such as wind speed, and the practical value of establishing the limit of frequency constraints using reliability theory.(4) In order to consider the influence of wind direction and to determine reasonable wind load for design, making the structural wind-resistance design more sensible, on the basis of wind speed measurement data collected by meteorological observatory, a probability model of the distribution of wind speed and wind direction was established. Meanwhile, from the viewpoint of reliability, the acceleration constraints were converted to frequency constraints taking in to account of joint distribution of the wind speed and wind direction, and then substitute the acceleration limit constraints into the reliability and failure probability in the form of conditional probability to obtain reliability equation for each wind direction. And then the failure probability considering multiple wind directions was calculated according to the occurrence frequency of the wind directions, and the upper limit value of structural natural frequencies with acceleration minimum threshold was obtained as well as the reliability index in all directions was satisfied, and it was later applied into design optimization. Optimization results show that considering the joint distribution could broaden the optimization space, and at the same time, by satisfying all constraints the objective function is lower than that under the single wind direction, which indicates the necessity and significance of considering joint distribution.(5) Displacement and the inter-story drifts in structure design are the main objectives to control. To avoid calculating the average, background and resonant response for determining the displacement response which could often give rise to difficulty in determination of the calculation expression, we derived the expressions of story displacement and inter-story drifts by combining wind pressure coefficient from the original wind tunnel tests with the dimensionless fitting method of acceleration response, and realized substitution of displacement constraints by the frequency constraints during optimization. Then like acceleration response, by considering the joint distribution of wind speed and direction, through the control of the failure probability, the frequency constraints limit conditions could be obtained for optimization design. Compared with other tested cases, optimization in current project which considered the joint distribution of all the response shows remarkably better results and the greater application values.