## 1 Introduction  
Reinforced concrete (RC) buildings not designed according to modern seismic design codes can be vulnerable to collapse during earthquakes [1]. Postearthquake researches indicated that columns are one of the most critical structural components in seismically active regions due to their nonductile reinforcement details [2; 3; 4; 5; 6]. Deficiencies such as lack of confinement due to widely spaced transverse reinforcement [1], ineffective anchorage length, and insufficient development length [7; 8; 9; 10; 11] can cause premature shear failure in RC columns [12; 13], thus leading to rapid lateral strength degradation [14] or even collapse [15; 16; 17; 18]. To understand the seismic behavior of such columns under earthquakes and to propose an adequate retrofit scheme, the seismic capacity of RC columns with nonseismic reinforcement details should be estimated.  
To predict the seismic capacity of such RC columns with acceptable accuracy, an accurate backbone curve is required, which defines the lateral load-deformation capacity of a structural component. An extensive amount of research has been carried out on developing backbone curves of RC columns [14; 15; 19; 20; 21; 22]. The nonlinear load-deformation relation proposed by ASCE 41-17 [23] (as noted hereafter as ASCE 41-17) is most widely used in the fields. This standard is provided to conduct seismic evaluation and retrofit of existing building by the American Society of Civil Engineer (ASCE), which includes performance objectives and seismic hazards, Tiers 1-3 seismic performance evaluation procedures, and retrofit.  
Due to the importance of this standard, it has been continuously revised since its first release to provide a better accuracy in estimating nonlinear load-deformation response of structural components.  
[PERSON] and [PERSON] [24] proposed equations for RC columns to calculate modeling parameters to construct a backbone curve, instead of using fixed values used in the previous standard [25]. These equations are shown in ASCE 41-17, which lead to better estimation of modeling parameters compared with those in the previous standard. Accurate estimation of modeling parameters is a key factor in seismic performance evaluation [26] by selecting input seismic ground motions [27].  
However, the deformation parameters suggested in ASCE 41-17 do not consider height-to-depth ratios, which can significantly alter the column behavior [19; 28]. For RC members with a height-to-depth ratio lower than 2 (as noted hereafter as stocky columns), their cyclic behavior is always dominated by shear [5; 29; 30]. Therefore, shear deformation induced by shear cracking expansion can be significant [31; 32]. When the ASCE 41-17 modeling parameter equations are applied to columns with low height-to-depth ratios (stocky columns), the estimation error between measured and estimated values may become significant.  
In order to better estimate the load-deformation response of stocky RC columns, this study proposes a calibration factor for the equations of deformation modeling parameters provided in ASCE 41-17. For this purpose, the values of deformation parameters for 47 rectangular RC columns with low height-to-depth ratios are extracted. To minimize the difference between measured values and those predicted by the ASCE 41-17 equations, the calibration factor was estimated for individual column specimens. Then, the empirical equations including the calibration factor are proposed from regression analyses.