# A Story-Based Random Structure Modeling Method for Regional Buildings Earthquake Loss Estimation
## 2 Basic Framework of the Methodology  
### The Definition of the SBRS Model  
Regional buildings have significant differences in the seismic performances between individual buildings due to building height, structural type, defenses, structural layout, component size, and material strength. These factors can lead to significant variations in the extent and progression of building damage under seismic activity. For example, masonry and RC frame structures belong to low-rise or mid-rise buildings, mainly resulting in shear deformation under seismic action. In contrast, RC wall-frame structures, mainly used in high-rise buildings, display significant flexural-shear coupling damage characteristics under seismic action. The earthquake loss estimation of regional buildings needs to consider both computational accuracy and efficiency. Using a detailed model will require more computational work when analyzing earthquake responses. Currently, the most appropriate method for analyzing damage and calculating losses is to use an MDOF structural analysis model with each story as the basic unit [5; 17; 19; 20]. In the MDOF shear (Figure 1a) and flexural-shear models (Figure 1b) proposed by [PERSON] et al. [29; 30], the backbone curve adopts the trilinear backbone curves model recommended by the HAZUS report (Figure 1c) and the single-parameter pinching model proposed by [PERSON] et al. [31] (Figure 1d) for the inter-story hysteresis model, which can better grasp the balance between the simulation accuracy and the difficulty of parameter calibration. The parameters that need to be calibrated for the MDOF model are elastic parameters, backbone curve parameters, and hysteresis parameters, among which, the elastic parameters of the shear model are the story mass m and shear stiffness \(k_{0}\), where m is obtained by multiplying the floor area with the empirical mass per unit area and \(k_{0}\) is obtained by the empirical relationship between the story mass and stiffness and the structural self-resonance period; the elastic parameter of the flexural-shear model is the ratio of the flexural stiffness \(EI\) to the shear stiffness \(GA\), \(\alpha_{0}\), which is determined by the empirical formula of one and two cycles of the structure. The specific method for parameter calibration is detailed in the literature. The structural arrangement of regional buildings is unknown and uncertain to the researcher at this point due to the frequent lack of structural information on buildings, and these structural design parameters determine the structure's response under seismic excitation, as well as the resulting structural damage and economic losses. So, the design parameters that can express the characteristics of the structural arrangement of the building can be regarded as random variables, such as the type and strength of the material, the proportion, and the size of the components, etc., and simulate the actual structural design through the combination of a random sampling of multiple variables. Thus, the story mass \(m\), the shear stiffness \(GA\) between stories, and the equivalent flexural stiffness \(EI\) of the shear walls are obtained from the component information to establish a simplified MDOF shear or flexural-shear structural analysis model. Multiple MDOF models are established for each building to consider the impacts of the uncertainty in the number of components and the design parameters on the seismic capacity of the structure and the seismic losses. Benefiting from the development of remote sensing mapping technology, it is easy to obtain the appearance of the geometric parameters of a building, such as the building height and plane projection size, etc., through a geographic information system [13; 25]. Therefore, it is possible to quickly obtain the basic information of each building through the GIS and take the rational design layout of the structure as the basic premise, based on the relevant norms and combined with the engineering experience of the typical architectural design.