PSI - Issue 70

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

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of 3 meters, representing typical mid-rise structures. The total building height is kept constant at 21 meters across all cases, while the terrain slope is varied to simulate realistic conditions encountered in hilly regions. For the case of a 7-storey building on flat ground (0° slope), the numerical fundamental period closely matches the IS 1893 estimate of 0.736 seconds, demonstrating the validity of the modeling approach under regular geometric conditions. As the terrain becomes inclined, the minimum effective height of the structure is reduced, leading to changes in dynamic response. On a mild slope of 10°, where the minimum height drops to 17.5 meters, the estimated fundamental period from IS 1893 decreases to 0.642 second s. This reduction reflects the standard’s consideration of effective building height in estimating dynamic characteristics. At a steeper slope of 35°, with a minimum height of only 4.25 meters, IS 1893:2016 provides a significantly reduced value of 0.222 seconds, highlighting the sensitivity of the code to vertical irregularities introduced by sloping ground. The numerically computed values follow a consistent trend with the IS 1893:2016 estimates, validating the modeling framework’s ability to capture the effect of terrain slope on structural dynamics. 6. Conclusion This study provides a comprehensive assessment of how the floor area ratio (FAR) and terrain slope influence the fundamental period of reinforced concrete (RC) buildings, with a particular focus on structures located in hilly regions. While building height continues to be the primary parameter in code-based period estimation, the findings clearly demonstrate that both vertical irregularities due to FAR reduction and geometric asymmetry introduced by sloped terrain substantially alter the dynamic behavior of buildings. As the FAR decreases — reflecting increased setbacks and reduction in mass at higher levels — the fundamental period consistently shortens, indicating a rise in overall structural stiffness. This effect is further magnified when buildings are placed on inclined ground, where the terrain slope contributes to a redistribution of mass and stiffness, leading to additional reductions in the fundamental period. Importantly, the study reveals that for the same FAR and building height, RC buildings on sloped terrains exhibit shorter fundamental periods than those on flat ground. This implies that terrain inclination, beyond simply affecting elevation profiles, has a notable impact on modal characteristics, which is not sufficiently accounted for in current empirical models. The combined effect of both parameters (FAR and Slope) must be integrated into any realistic assessment of seismic demand. These insights have practical implications for seismic design, as the underestimation of the fundamental period in hillside buildings could lead to erroneous base shear calculations, compromising structural safety. These insights have direct practical implications for the seismic design of hillside RC buildings. They support the case for revising or augmenting existing code-based formulas to include slope and FAR as additional predictive variables, especially for structures with significant vertical irregularities. The modeling approach employed in this study, based on detailed eigenvalue analysis using SAP2000, proves effective in capturing the nuanced influence of geometry and terrain on seismic response. The scope of the present work is limited to low- to mid-rise RC buildings (up to 7 storeys), which are most commonly encountered in hilly urban contexts. As part of the future scope, this parametric framework can be extended to include high-rise buildings and more complex architectural forms, thereby enhancing the generalizability and applicability of the findings to a wider range of design scenarios. References Moelhe, R., 1984. Seismic behavior of R.C. buildings with vertical irregularities. In: Proc. 8th World Conf. Earthquake Eng., San Francisco. Aranda, G.R., 1984. Ductility demands on R.C. buildings with setbacks. In: Proc. 8th World Conf. Earthquake Eng., San Francisco. Wong, C.M., Tso, W.K., 1994. Modal mass effects in buildings with vertical irregularities. Canadian Journal of Civil Engineering 21(5), 754–764. Duan, X., Chandler, A.M., 1995. Limitations of modal spectral analysis in setback frames. Earthquake Engineering & Structural Dynamics 24(2), 207–224. Kappos, A.J., Scott, R.H., 1998. Static vs dynamic analysis in setback buildings. Earthquake Engineering & Structural Dynamics 27(2), 161–180.