The Effect of Vertical Setbacks on Earthquake Response and Fundamental Period of RC Building Frames

Abstract The objective of this study is to investigate the influence of vertical setback on the seismic response and fundamental period of reinforced concrete (RC) building frames. International seismic design codes generally require a dynamic analysis for setback buildings, with base shear scaled according to the fundamental period obtained from code-specified empirical expressions. However, existing provisions provide limited guidance on estimating the fundamental period of both regular and setback RC buildings with up to 40 m height. Although Eurocode EN 1998–1:2004 defines vertical irregularity based on the ratio of lateral dimensions between adjacent stories, it does not explicitly address the estimation of the fundamental period (T 1 ) for buildings with vertical setbacks. Moreover, the Eurocode empirical expression for T 1 depends solely on building height, which may lead to inaccuracies when applied to geometrically irregular configurations. In this study, representative RC setback building frame models were developed and analyzed using eigenvalue analysis in ETABS 2015 in accordance with EN 1998–1:2004 provisions. Key response parameters, including fundamental period, base shear, and story drift, were evaluated across different setback configurations. The results indicate the fundamental period (T1) decreases with increasing setback severity, even for buildings of identical total height, highlighting the sensitivity of RC frames to geometric discontinuities. Base shear demand correspondingly decreases due to reduced effective seismic mass, with reductions more pronounced as setback magnitude and location vary along the building height. Story drift exhibits a non-uniform distribution, with peak concentrations near setback levels, reflecting stiffness irregularities. Across different configurations (SB, SM, SBT, SBTM), base shear is generally lower than in regular buildings (R), except for top-story setbacks (ST), which exhibit comparable values. The study identifies critical geometrical parameters governing the dynamic response of vertically axially symmetric RC setback frames. To quantify the effect of setbacks, two non-dimensional geometrical parameters, $$\frac{{\text{H}}_{\text{ave}}}{\text{H}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mtext>ave</mml:mtext> </mml:msub> <mml:mtext>H</mml:mtext> </mml:mfrac> </mml:math> and $$\frac{{\text{D}}_{\text{ave}}}{\text{D}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:msub> <mml:mtext>D</mml:mtext> <mml:mtext>ave</mml:mtext> </mml:msub> <mml:mtext>D</mml:mtext> </mml:mfrac> </mml:math> , are introduced. These parameters are proposed as correction factors to enhance the empirical fundamental-period formulation of EN 1998–1:2004, thereby improving its applicability to RC buildings with vertical setbacks.