Investigating the response of multi-story structures under base excitation using Time-weighted residual method Mostafa Sadeghi Googhari ( mostafa.sadeghi96@cv.iut.ac.ir ) Date of Submission: September 15, 2020 Department of Civil Engineering Isfahan University of Technology, Isfahan 84156-83111, Iran Degree: M.Sc Language: Farsi Supervisor’s: Dr. Bijan Boroomand ( boromand@cc.iut.ac.ir ) Dr. Bashir Movahedian ( b.movahedian@cc.iut.ac.ir ) In this study, a new solution method based on the use of exponential functions is used to solve basic excitation problems in structures consisting of one-dimensional members. This method is called the step-by-step time-weighted residual method. The basis of this method is the use of pre-integration method in solving equilibrium equations. In this method, the problem solving time is divided into several subsets and the response of the acceleration field in each time interval is considered as a combination of an unknown function in terms of spatial variable and a series consisting of valid exponential base functions in a strong form of equation with constant coefficients. In the mentioned method, the initial conditions are satisfied accurately and the equilibrium equations are satisfied using the time-weighted residual method. Also, by satisfying the boundary conditions at both ends of each element and at the end of each time step, fixed coefficients are determined. In the time-weighted residual method, at each time step the information is stored on the coefficients of the exponential functions and only at the end of each step, these coefficients are corrected using a suitable recursive relation. In this research, using the mentioned method, the problems of base excitation in rods, bending structures, multi-storey frames and tall structures are solved. In this study, various types of base excitation are expressed and the formulation of the time weighted residual method for the application of each of them is developed. Then, this method has been used to analyze the time history of structures under various base excitation, including changes in earthquake acceleration, and the efficiency of this method in terms of accuracy and cost reduction of calculations compared to the finite element method that is the basis of most commercial software. Also in the final part of this study,various structural modeling methods including discrete modeling and continuous modeling and equivalence relations between these models are presented. Using these modeling methods, the behavior of tall structures under basic excitations has been investigated and the cost of calculations and errors of various models have been estimated. To reduce continuous modeling errors, a correction factor for the stiffness of the continuous model has been used. This coefficient has been obtained by fitting the response curves. Key words: Time-weighted residual method, Scalar wave propagation, Exponential basis function, Basic excitation, Discrete Model, Continuous modeling.