## 2 State of the Art  
Different parameters contribute to the (\(M\)-\(\theta\)) behavioral characterization of bolted connections, as shown in Figure 2[15; 16; 17; 18; 19; 20], and it is thus first necessary to use reliable modeling techniques. In the case of modular steel buildings, non-linear link elements are generally incorporated for computational efficiency, where the bending moment, shear, axial force, and corresponding moment-rotation (\(M\)-\(\theta\)) curves are simplified and included as spring elements. Nevertheless, since the knowledge of the structural behavior of modular steel buildings is limited, the simplified models for the force-displacement and moment-rotation curves are not well established. Therefore, the intrinsic uncertainty can lead to excessively conservative design practices, requiring additional investigations on the topic. Extended literature studies are indeed available for TSACs and TSACWs. To simulate the beam-to-column connection behavior, apart from experimental tests, three different modeling options are introduced in the form of analytical or empirical models [21], advanced finite element (FE) models [22; 23; 24], and component mechanical models [25; 26]. Figure 2: Moment–rotation curve of common types of beam-to-column connections (adapted from [5] under the terms and conditions of a Creative Commons Attribution License (CC BY)). Analytical and empirical models naturally extract simple mathematical expressions, and thus typically facilitate their application in practice, with a reasonable level of accuracy. On the other hand, by applying advanced FE methods, it is possible to simulate more precisely the complex non-linear beam-to-column connection response. Some limitations are unavoidably introduced in terms of high computational cost and sophisticated preparation process (assembly, calibration, etc.). Component-based mechanical models, finally, consider an assembly of rigid elements and equivalent springs relay on the two previous modeling approaches, considering computational complexity and reliability. Several research studies have documented the (\(M\)-\(\theta\)) performance of TSCWs, especially through extended experimental investigations. In 1985 and 2000, respectively, [PERSON] and [PERSON] (2015) and [PERSON] et al. (2015) experimentally investigated the (\(M\)-\(\theta\)) behavior of TSCW specimens under monotonic and cyclic loading. The hysteresis behavior of TSCW specimens was investigated in several cited projects. The presented results indicated that the main sources of plastic deformation are typically located in the top and bottom cleats, which represent the governing components. In addition, the same studies proved a limited influence of the column size on the overall hysteretic performance of the examined connections. A considerable number of literature studies has also been published in support of the prediction of the (\(M\)-\(\theta\)) behavior, initial stiffness, and ultimate strength of TSCW systems through various mechanical and analytical models. In 1987, [PERSON] et al. (2018) proposed a set of relevant equations to predict initial stiffness. [PERSON] et al. (2018, 2019) presented an analytical model to estimate both the initial stiffness and ultimate moment capacity of TSCWs through cantilever beam theory. In more detail, a three-parameter power model was discussed in ([PERSON] et al., 2018), in which the elastic stiffness and ultimate moment capacity of connection of TSCWs were estimated by a simple analytical method. [PERSON] (2018) proposed a simplified mechanical model along with relevant initial stiffness and ultimate moment equations. A three-linear (\(M\)-\(\theta\)) constitutive law based on the fiber element formulation was proposed by [PERSON] and [PERSON] (2018). In that study, two possible mechanisms were considered, according to the strength of the angles relative to the bolt.