## 1 Introduction  
The structural damage and the resulting casualties and property losses under the action of strong earthquakes are very painful. Therefore, the accurate evaluation of the damage of ground motions to structures (that is, the damage potential of ground motions) is very important to select the input ground motions for seismic design. In recent years, a number of studies [1; 2; 3; 4; 5; 6; 7] on the evaluation of the damage of ground motions to structures have been published. Researchers first believe that ground motion load is the root cause of damage to engineering structures. It was found that there are many intensity measures (_IM_s) that can represent the damage potential of ground motion, and the _IM_s in the early studies are mainly obtained from the ground motion record itself. [PERSON] et al. [8] discussed and analyzed the commonly used damage potential parameters such as peak acceleration (_PGA_), peak velocity (_PGV_), peak displacement (_PGD_), Arias strength (_AI_), and so on. [PERSON] et al. [9] found that the \(PGV\) of ground motion can characterize well the destructive strength of ground motion to medium- and long-period reinforced concrete frame structures. [PERSON] et al. [10] studied the efficiency of cumulative velocity (_CAV_), _AI_, and structural response and obtained a small dispersion between them. However, the study found that a damage potential _IM_ containing seismic and structural characteristic information may better describe the structural damage caused by ground motions [11; 12]. Some experts study the _IM_s obtained from the elastic or inelastic response of the structure as the damage potential _Im_s of ground motions, such as acceleration response (\(S_{a}\)) spectrum, velocity response (\(S_{p}\)) spectrum, displacement response (\(S_{d}\)) spectrum, displacement ductility (\(u\)) and hysteretic energy (\(E_{H}\)), and so on [13; 14; 15]. When the damage potential _Ims_ of ground motions include both seismic and structural information, the changes in seismic or structural parameters will change the damage potential parameter values. Some researchers have studied the effect of seismic factors on the constant-strength response spectrum and the constant-ductility response spectrum [16; 17]. [PERSON] [18] explained the effect of seismic information factors such as magnitude and epicenter distance on the constant-ductility response spectrum in detail. Some experts have also studied the variation law of the response spectrum subjected to different types of ground motions, such as ground motions with different duration [19], main shock-aftershock sequence ground motions, pulse-like ground motions [13; 14; 15], and extracting high-frequency and low-frequency ground motions, respectively [20], etc. Considering structural parameters, [PERSON] and [PERSON] [11] use \(u\) and \(E_{p}\) as damage potential _IMs_ when selecting the most unfavorable design ground motions. At the same time, the effect of structural parameters such as damping ratio and post-yield stiffness on the hysteretic energy spectrum are analyzed. It is important to note that the hysteretic energy is the one associated with the work performed by rate-independent hysteretic forces [21]. It is concluded that the variation of the hysteretic energy spectrum has little variation under different damping ratios and post-yield stiffness. [PERSON] and [PERSON] [22] studied the effect of lateral strength ratio, stiffness degradation, and pinching effect on the relative displacement response spectrum. It is concluded that strength degradation has little effect on the nonlinear response spectrum, stiffness degradation has a certain influence on the nonlinear response spectrum, and the pinching effect cannot be ignored in the study of the nonlinear response spectrum. Other experts have also carried out related studies [15; 23; 24].