PSI - Issue 70

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

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Fig.2 Variation of Fundamental Period as a Function of Floor Area Ratio and Terrain Slope

To explore the combined effects of terrain slope and floor area ratio (FAR) on the fundamental period of reinforced concrete (RC) buildings, a contour plot was developed based on interpolated results from a structured set of numerical simulations. The data for this plot were generated using eigenvalue modal analysis of multiple building configurations, varying both the terrain slope (0°, 10°, 20°, 30°, and 35°) and the FAR (ranging from 1.0 to 0.2), while keeping other structural parameters constant (e.g., number of storeys, bay width, material properties). For each unique slope – FAR combination, the corresponding fundamental period was computed. These values were then used to construct a smooth interpolated surface using grid-based interpolation techniques, and the resulting contour lines were plotted to visualize trends (Fig. 2). The resulting contour plot provides a clear visualization of how the fundamental period responds to changes in both slope and FAR. It shows that buildings with higher FAR — representing minimal setbacks and fuller floor plates — exhibit longer fundamental periods, especially when located on flatter terrain. This reflects a more flexible global behavior due to the increased mass and reduced stiffness typically associated with such configurations. In contrast, as FAR decreases — indicative of greater vertical setbacks — the fundamental period is reduced, suggesting increased structural stiffness. This effect is further amplified when combined with steeper slope angles. Buildings with low FAR constructed on steep inclines exhibit the shortest fundamental periods across the dataset, clearly demonstrating the stiffening influence of both vertical irregularities and inclined foundations. The contour gradient reveals a consistent trend: as the slope angle increases, the fundamental period decreases across all FAR values. This indicates that terrain inclination has a stronger and more direct influence on dynamic behavior than FAR alone. 5. Validation of Fundamental Period Estimates To validate the numerical modeling approach adopted in this study, the fundamental periods computed for various RC building configurations were compared with the empirical values recommended by IS 1893:2016. All buildings considered in this comparison feature a regular plan layout with four bays of 4 meters each and an inter-storey height