PSI - Issue 70

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

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significantly alters the dynamic response, leading to underestimation of seismic demands when traditional flat-ground assumptions are applied. Despite these advancements, most existing studies focus either on setback irregularities or sloping ground separately. The combined effect of vertical geometric setbacks (often caused by varying floor area ratios) and terrain slope — common in real-world hillside constructions — remains underexplored. This study seeks to fill that gap by analyzing how both these parameters together influence the fundamental time period of RC buildings, contributing to more robust and realistic seismic design.

3. Methodology 3.1. Building Properties

The present study is based on detailed computational modeling of reinforced concrete (RC) buildings to evaluate the influence of building height and terrain slope on their seismic behavior, particularly focusing on the fundamental period. The structural configurations include low- to mid-rise buildings with 3, 5, 6, and 7 storeys, representing a realistic range of common building heights found in urban hilly regions. All models are developed with a regular plan layout comprising four bays in both the longitudinal and transverse directions, with a uniform bay width of 4 meters. To maintain consistency in vertical geometry, the inter-storey height is fixed at 3 meters across all models. The buildings are modeled on varying terrain conditions, including flat ground (0° slope) and sloped terrains with inclinations of 10°, 20°, 30°, and 35°, thereby covering a spectrum from level sites to steep hillside conditions. Uniform material properties are assumed to ensure consistency in the comparative analysis. The compressive strength of concrete is taken as 30 MPa, and the yield strength of reinforcing steel is assumed to be 500 MPa. These values are representative of standard construction materials used in conventional RC buildings in India and similar seismic regions. The structural systems are modeled as bare-frame moment-resisting RC buildings, excluding masonry infill walls. All columns are assumed to be fixed at the base, simulating fully restrained foundation conditions. For modal (eigenvalue) analysis, self-weight and reduced live loads (2.54kN/m2) are considered, and material behavior is assumed to be linear elastic, as the focus is on estimating the fundamental period rather than nonlinear seismic response. The analysis is carried out using a commercial finite element software SAP 2000, employing 3D space frame elements to represent beams and columns. Structural modeling and modal analysis were conducted using SAP2000 version 21 to evaluate the dynamic characteristics of reinforced concrete buildings with varying heights and slope conditions. Each model features a symmetric plan layout to eliminate the influence of plan irregularities, allowing for focused analysis on the effects of vertical irregularities and terrain inclination. Variations in building height and slope angle are systematically introduced to assess their impact on the fundamental time period. All models are idealized as bare frame systems with fixed support conditions at the base, ensuring consistent boundary conditions across the analysis. The structural elements are modeled using standard finite element formulations. Beams and columns are represented as two-noded frame elements, each with six degrees of freedom per node, allowing for both translational and rotational movements. Slabs are modeled using shell elements to effectively capture both in-plane stiffness and out-of-plane flexural behavior, ensuring realistic simulation of diaphragm action and vertical load distribution. Modal analysis is performed to extract the natural frequencies and corresponding mode shapes of the structures. The fundamental time period (T) is computed using R ayleigh’s method, which relies on the system’s global stiffness matrix (K) and mass matrix (M). 3.2. Modelling & Analysis in SAP2000