Economical design of a building is one of the main aims that should be followed because of its importance in constructional projects. In order to have an economical design, longitudinal reinforcing bars in the reinforced concrete members are among those parts of the structure that can be designed economically. The application of fuzzy inference systems provides an effective tools to handle the uncertainties and subjectivities arising in the designing process of buildings. Therefore, the main purpose of this paper is to propose a fuzzy inference system to evaluate the building design codes from an economical point of view. For this purpose, after designing the mentioned fuzzy inference system, three examples of three-dimensional concrete buildings are analyzed and designed using different codes. For all these codes, the structural properties of concrete buildings, the gravity and the seismic loads are considered to be the same. Finally, it finds that the fuzzy logic theory is an effective and practical tool to compute a value that shows the distance between the designed building and the economically designed building. Also, it concludes that between the studied codes, (EUROCODE 2-1992, Hong Kong CP-04, CSA A23.3-04 and ACI 318-05), the ACI 318-05 and Hong Kong CP04 codes lead to a more economical design for taller buildings. For low-rise buildings, the CSA A23.3-04 and ACI 318-05 codes lead to an economical design. Also, the EUROCODE 2-1992 has a minimum value for the economical design of all the considered buildings.

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The nonlinear dynamic analysis provides a more accurate simulation of the structural behavior against earthquakes. On the other hand, this analysis method is time-consuming since the time-step integration schemes are used to calculate the responses of the structure. Wavelet transform is also considered as one of the strong computing tools in studying the properties of the waves. The continuous wavelet transform is a time-frequency study and examines the frequency content of the waves while, the discrete wavelet transform is used to reduce sampling data and also to eliminate the noise of the waves. In this paper, the discrete and continuous wavelet transforms are used to reduce the wave sampling and therefore to reduce the required time for analysis. In this regard, eight near- and far- field earthquakes are studied. The frequency content of the earthquake is investigated by the Fourier spectrum and the continuous wavelet transform. The results show that the first five frequencies for the main earthquakes are similar to those values of earthquakes obtained by wavelet transform. Besides, it is shown that using wavelet transform for the main and decomposed earthquakes indicates that the duration of strong ground motion and the time of dominant frequency occur approximately in the same domain. Finally, it is concluded that the required calculation time reduces to about 80 % with an error less than 6 % when the main earthquake is decomposed by wavelet transform and the approximation waves are used in the nonlinear dynamic analysis.

Wavelet transform is one of the mathematical concepts for studying the frequency content of waves. It is divided into two groups of continuous and discrete. Generally, continuous wavelet transform is used to check the time-frequency and the discrete wavelet transform for filtering and noise reduction in waves. In this paper, for the first time, the combination of these two concepts is used for the earthquake acceleration wave. For this purpose, eight earthquakes from four different locations in the world have been selected. Initially, each earthquake is filtered up to 5 stages using a discrete wavelet transform. At each stage of the filter, two waves of approximations and details are obtained. Due to the close approximation of the frequency content of the wave to the original earthquake, the approximate wave is used for subsequent calculations. In the next stage, the spectrum of Fourier and the diagram of five of the frequency of dominant of the earthquake are plotted. Also, using the continuous wavelet transform, the time-frequency curves of the main earthquakes and the time-frequency curves of the wave obtained from the discrete wavelet transform are investigated. The goal is to find the best stage of a discrete wavelet filter based on frequency content to reduce computations to over 80%. In the next step, the study examines the time of the strong ground motion, the structure response of a single degree of freedom, and the dynamical response of the timing of the structure of a degree of freedom. By examining the above parameters, the best-performing wavelet transformation step is inferred.

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