PSI - Issue 70

Arijit Banik et al. / Procedia Structural Integrity 70 (2025) 604–610

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This approach solves the eigenvalue problem, providing a precise estimation of the structure’s dynamic response characteristics under free vibration conditions. K−ω 2 M=0 (1) Where ω is the circular frequency. The fundamental period is then computed as: T= 2π / ω (2) 4. Results & Discussion In this study, the variation of the fundamental period with respect to the Floor Area Ratio (FAR) was examined for reinforced concrete buildings on both flat and sloped terrains. FAR, which quantifies the level of vertical irregularity due to setbacks, significantly influences the dynamic behavior of structures. As shown in the figure, a clear trend is observed where the fundamental period increases with an increase in FAR. This is because higher FAR values correspond to fully intact buildings with minimal setbacks, resulting in reduced stiffness and consequently higher natural periods. In contrast, lower FAR values represent buildings with greater setbacks, leading to increased stiffness and shorter fundamental periods. To capture the effects of slope and FAR, a typical angle of inclination of 35 degrees was selected for comparison with flat terrain models (0° slope). The results indicate that although both flat and sloped terrain models exhibit a positive correlation between FAR and the fundamental period, buildings on sloped terrain consistently display lower periods for the same FAR values (Fig. 1). This is attributed to the added stiffness provided by the terrain inclination, which enhances the overall rigidity of the structure. The comparative trends, as depicted in the figure, highlight the critical role of both vertical irregularities (FAR) and terrain slope in shaping the seismic response of buildings.

Fig.1 Effect of FAR Reduction on Fundamental Period for Buildings on Flat vs. 35° Sloped Ground