## 2 Shear-Slip Behavior of Headed Studs  
The strength of headed studs has been studied in numerous experimental tests over the past 50 years. One of the earliest studies on the strength of shear connectors was conducted in 1956 by [PERSON] [11], who considered the stud diameter and compressive strength of concrete as the most influential parameters. Experimental studies by [PERSON] et al. (1971) [12] also introduced the effects of the stud diameter and the elastic modulus of concrete on the AISC [13] and AASHTO [14] formulations. Additional studies [15; 16; 17; 18] investigated the impact of reinforcement mesh position, shear stud height, and shear stud spacing on the ultimate slip and shear strength of the connection.  
The behavior of a connection with headed studs remains complex to model because failure can be attributed to either concrete or steel. In the case of concrete failure, it may occur with or without the yielding of the stud, thereby altering the strength and ductility of the connection. Moreover, recent studies have reviewed the reliability of formulations found in codes and the literature [19]. In this work, the evaluation of the strength and ductility of the studs is not addressed; rather, only the effect of these properties on the response of the structure is considered. Therefore, the properties of the studs provided by the European code on composite constructions (Eurocode 4 [10]) are assumed.  
Eurocode 4 introduces an approach with two formulations, as shown in Equation (1), addressing the failure of steel or concrete. In a mixed mechanism, the design shear strength (\(P_{Rd}\)) of the stud is determined by the lower of the two results:  
\[P_{Rd}=0.29\cdot\alpha\cdot d_{s}^{2}\cdot(E_{c}\cdot f_{cd})^{0.5}/\gamma_{v} \text{ or }P_{Rd}=0.8\cdot f_{u}\cdot(\pi d_{s}^{2}/4)/\gamma_{v} \tag{1}\]  
where \(d_{s}\) is the diameter of the stud shank, \(f_{cd}\) is the design compressive cylinder strength of concrete, \(f_{u}\) is the strength of a stud steel, \(\alpha\) is a factor to introduce the effect of the height/diameter ratio, and \(\gamma_{v}\) is the partial safety factor.  
The shear-slip law was developed in only a few studies; the most common shape was suggested by [PERSON] et al. [12], but a simpler approach is a trilinear representation assuming a first point at the elastic limit (\(P_{\text{e}}=P_{\text{max}}/2\), \(S_{\text{e}}\)), a second point at (\(P_{\text{max}}\), \(S_{\text{m}}\)), and the ultimate condition at (\(P_{\text{u}}=95\%\) of \(P_{\text{max}}\), \(S_{\text{u}}\)), as reported in Figure 1.  
In particular, the slip of the main points can be evaluated by the formulations suggested by [PERSON] and [PERSON] [20], which considered normal-density concretes with \(20<f_{\text{c}}<70\) MPa but were reviewed by [PERSON] and [PERSON] [21] for an \(f_{\text{c}}\) varying between 23 and 82 N/mm\({}^{2}\). They suggested the formula reported in Equations (2)-(4) for the main points:  
\[S_{e}=(80\cdot 10^{-3}-86\cdot 10^{-5}\cdot f_{c})\cdot d\ _{s} \tag{2}\]  
\[S_{m}=(0.39-0.0023\cdot f_{c})\cdot d_{s} \tag{3}\]  
\[S_{u}=(0.48-0.0042\cdot f_{c})\cdot d_{s} \tag{4}\]  
In their study, the above formulation was found to be valid for stud diameters ranging between 13 and 22 mm, particularly emphasizing the common use of 19 mm. More recently,Lee et al. [15] confirmed very similar formulations and concluded that Equation (4) could be applicable to larger study with diameters exceeding 25 mm.