Dynamic analysis can be used to determine dynamic displacements, time history, and the frequency content of loads. One of the analytical techniques for calculating the linear response of structures to dynamic loading is modal analysis. In modal analysis, the structural response is decomposed into several modes of oscillation. A mode is defined by its frequency and shape. Engineers refer to the mode with the lowest frequency (longest period) as the fundamental mode of oscillation. This paper presents Holzer’s approximate method for determining the modes and periods of oscillation for frame structures. The proposed approximation method, based on the relative stiffness of floors and the ground level, is also analyzed. The results obtained using the proposed approximate procedure do not significantly deviate from those obtained through more precise calculations. Therefore, it is emphasized that the method can be used both in practice and for verifying computer analyses of complex systems.

Dynamic analysis can be used to find dynamic displacements, time history, and the frequency content of the load. One analysis technique for calculating the linear response of structures to dynamic loading is a modal analysis. In modal analysis, we decompose the response of the structure into several vibration modes. A mode is defined by its frequency and shape. Structural engineers call the mode with the shortest frequency (the longest period) the fundamental mode. Holzer and Stodola's approximate methods for determining the forms and periods of oscillation for frame structures are presented in the paper. An approximation method, based on approximate relative stiffnesses of the storeys and the ground floor, is analyzed and proposed. The results obtained by the proposed approximate procedure do not greatly deviate from those obtained by more accurate calculations. It is therefore emphasized that the method can be used both in practice and for checking computer-based analysis of complex systems. At the end of the paper was given a comparison of the results obtained by approximate methods and some engineering software.