## 2 Design and Operational Principles of Clamp-Based Connections for Structural Systems  
Clamp-based connections rely on a mechanical leverage principle to securely fasten structural components without invasive techniques such as welding or drilling. The operational mechanism begins with applying a preload force (\(T\)) to the clamp's bolt. This preload generates tension in the bolt, which is redistributed through the lever system to produce the clamping force (\(F_{a}\)) that secures the connection (Figure 1). The clamping force is calculated using Equation (1):  
\[F_{a}=T\cdot\frac{b}{a+b} \tag{1}\]  
where the following are defined:  
* \(T\) is the preload force applied to the bolt (N);
* \(a\) is the arm lever length on the bolt side (mm);
* \(b\) is the arm lever length on the clamping side (mm).  
This equation describes how the preload force is redistributed through the clamp's geometry, with the proportions of the lever arms (\(a\) and \(b\)) determining the final clamping force. The redistribution depends on the relative lengths of the lever arms, ensuring that the force is effectively applied to the contact surface without exceeding design tolerances. This formulation has been adopted in prior studies on clamp-based systems [3; 14; 28] and aligns with modeling approaches presented in [29].  
The preload force must be calculated to ensure the connection is reliable and avoids slippage. The required preload is determined by Equation (2).  
\[T=\frac{0.7\cdot f_{ub}\cdot A_{s}}{1.1} \tag{2}\]  
Figure 1: Side view illustrating the clamp’s lever mechanism, where the applied force generates clamping pressure.  
where the following is defined:  
* \(f_{ub}\) is the ultimate tensile strength of the bolt material (MPa);
* \(A_{s}\) is the effective cross-sectional area of the bolt (mm\({}^{2}\)).  
The calculated preload force (Equation (2)) also aligns with the principles of AISC 360-22 [30; 31], ensuring sufficient clamping pressure for connection stability. While AISC 360-22 permits inelastic deformation under extreme conditions, this study emphasizes maintaining the integrity of components intended for reuse and operates strictly within the elastic range. The expression is consistent with the pre-tensioning method established in Eurocode 3 [29]. To account for tightening variability and installation tolerances, a factor of 1.1 was applied, as recommended by [32] and further supported by experimental studies [1; 2; 4; 14].  
Once the clamping force (\(F_{a}\)) is applied, the resulting pressure on the contact surface is distributed as in Equation (3):  
\[P=\frac{F_{a}}{k\cdot w} \tag{3}\]  
where the following are defined:  
* \(P\) is the pressure exerted on the surface (MPa);
* \(k\) is the width of the contact area (mm), and (Figure 2);
* \(w\) is the depth of the contact area (mm) (Figure 2).  
This uniform distribution of pressure across the clamp contact surface reduces localized stress and minimizes the risk of material deformation or damage to coatings. The lever mechanism and precise clamp geometry ensure that the applied force is efficiently transmitted to the structural element. The mechanism redistributes preload during tightening to maintain stability and resistance against dynamic forces. This stress relationship reflects standard contact mechanics and is also compatible with bearing stress approaches discussed in [29] and recent applications in clamp-based structural analyses [1; 2; 3; 14].  
The equations governing clamp-based connections demonstrate their ability to redistribute forces efficiently and safely. These mechanisms make them reliable for applications that require adaptability, non-invasiveness, and structural integrity, unlike traditional methods such as welding or drilling. These systems achieve robust and efficient performance in a variety of structural applications.  
Figure 2: Isometric view highlighting the clamp’s support surface on the profile flange, showing dimensions (\(k\)) and (\(w\)).