PSI - Issue 70

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

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such buildings may respond to earthquakes in more complex ways than those on flat ground, potentially making them more susceptible to damage. One important factor that influences how a building behaves during an earthquake is the Floor Area Ratio (FAR), wh ich is the ratio of a building’s total floor area to the area of the plot it occupies. In many hillside developments, setback buildings — where the floor area decreases with height — are a common architectural choice, often adopted for aesthetic reasons or to improve access to light and ventilation. While these designs have their advantages, the changes in floor area along the height can create discontinuities in the structure, which in turn can affect how the building responds dynamically during an earthquake. Previous research has pointed out that these vertical irregularities, such as setbacks, can alter the way buildings vibrate or sway during seismic events. However, most of the existing studies and commonly used formulas are based on regular buildings located on level ground and may not fully capture the combined effects of terrain slope and FAR variations. As a result, the available design guidelines might not always reflect the actual behavior of hillside buildings with setbacks, leading to possible discrepancies in estimating their seismic performance. This study aims to bridge that gap by taking a closer look at how FAR reduction affects the fundamental period — a key measure of a building’s natural vibration— of RC buildings on both flat and sloped terrains. Through a series of carefully designed numerical models and modal analyses, the study examines how changing the floor area with height, especially in combination with sloped ground conditions, influences the building's dynamic characteristics. 2. Literature Review The seismic behavior of reinforced concrete (RC) buildings with vertical irregularities, particularly setbacks, has been widely studied due to their complex dynamic response during earthquakes. Early investigations by Moelhe (1984) and Aranda (1984) highlighted the concentration of ductility demands and increased vulnerability in regions near the setback. These studies demonstrated that such irregularities lead to higher localized damage, especially under lateral seismic forces. Wong and Tso (1994) further examined the effect of vertical irregularities on modal mass distribution. Their findings suggested that such configurations could significantly alter dynamic characteristics, influencing the allocation of seismic forces. Similarly, Duan and Chandler (1995) reported limitations in the accuracy of modal spectral analysis methods when applied to setback structures, arguing that such methods often underestimate the critical effects caused by abrupt geometric changes. To compare the efficacy of analytical procedures, Kappos and Scott (1998) studied both static and dynamic analyses for setback buildings. They found noticeable differences in predicted responses, with dynamic analysis capturing irregular behavior more effectively. Tremblay and Poncet (2005) expanded on this by evaluating seismic performance in mass-irregular buildings, concluding that codified methods are often inadequate for predicting accurate responses in such cases. In recent decades, emphasis has been placed on the impact of setback geometry. Karavallis et al. (2008) and Athanassiadou (2008) assessed multistorey frames with setbacks and noted increased displacement and interstorey drift demands in setback regions. Kappos and Stefanidou (2010) proposed deformation-based design approaches to better address the nonlinear behavior observed in RC setback frames. Sehgal et al. (2011) studied the role of setback length and found that increased setback results in more adverse seismic effects. A comprehensive review by Varadharajan et al. (2012a, 2012b, 2013) synthesized these findings and emphasized that buildings with vertical irregularities are particularly vulnerable during seismic events, especially short-period and tall structures. More recently, research has extended to include the influence of terrain slope on seismic behavior. Wu et al. (2024) investigated the interaction between adjacent hillside structures, highlighting the importance of considering structure – soil – structure interaction in sloped terrains. Reddy and Badry (2024) examined the dynamic response of RC buildings on inclined ground and emphasized the limitations of conventional design approaches when applied to hillside buildings. Banik and Debbarma (2025) contributed significantly by proposing an empirical formula for estimating the fundamental period of RC buildings situated on slopes, accounting for terrain inclination and associated structural behavior. Their numerical analyses demonstrated that slope inclination