Free and forced vibration analysis of linear, elastic building and arch type plane frames

Abstract

In this study, behaviour of linear, elastic building and arch type plane frame structures subjected to lateral dynamic loads are investigated. For this purpose, computer programs were developed for the static analysis of plane frame structures, frequency/mode shape computations, time history analysis by the mode superposition and the direct step-by-step integration methods. A static analysis program is designed, which enables the solution of large scale structures with many degrees-of-freedom by employing an out-of-core solution algorithm. For reasonable half-band width values, there is no limit to the number of equations to be solved, as long as the pheripheral memory may be assumed "infinitely large." Effective computer utilaziton in terms of time, memory and precision is considered in developing these computer programs. These three factors gain significance, especially, in the case of using low speed, small memory and low precision microcomputers in the analysis and design of large structural systems. Using the computer programs that were developed during this study, two types of structures were examined high-rise buildings (multi-storey building frames and towers), and arches. The following aspects of the problem are studied. 1. The accuracy of the results of the static analysis. For large number of unknowns, error accummulation due to rounding may be a serious problem. 2. Effect of the slenderness and aspect ratios of arch type structures to the symmetry or antimetry of the modeshapes and to the value of the participation factors. 3.Effect of the choice of solution time step , to the accuracy and stability of the integrations performed in direct step-by-step integration method. 4. Effect of the number and type of the mode shape vectors belonging to each of the modes superposed, to the accuracy of the results. The detected maximum displacement values from the modal analysis were compared to those obtained from the direct step-by-step integration of the coupled equations of motion. Some of the findings from the case studies are summarized below. 1. The algorithm used in the static analysis program is very effective to analysevery high multi-storey structures. The accuracy of the results is significantly affected by the wordsize of the computer and the solution algorithm employed. 2. The choice of the solution time step. affects both the accuracy of the results and the execution time. As t decreases the solution timesincrease and the weighted percent errorsof the results decrease. However, very small llt values may cause error, accumulation due to rounding. 3. For larger llt values, the numerical integration performed in step by step procedures may diverge Appropriate values for llt, which will give a converging result may not be chosen depending on a previously stated emphirical formula. 4. Superposing only a few of the highest modes of vibration gives. satisfactory results. However, when the lower modes of vibration are superposed, the error in the results may increase. This is due to the computation error made in the lower modes of vibration. 5. Free vibration characteristics of arches with symmetric stiffness and mass distribution depends on the slenderness and aspect ratios. Their participation factors for symmetric mode shapes are equal to zero. Therefore, in modal analysis, superposing only those modes with non-zero participation factors will further reduce the computation time.