# Seismic Design Procedure for Low-Rise Cold-Formed Steel-Special Bolded Moment Frames
## 2 Proposed Bolted Connection for CFS-SBMFs
### Proposed Connection Design Procedure  
The following is a summary of the proposed design procedure based on the design strategy mentioned above.  
1. Flexural strength required for the beam:  
The expected moment, \(M_{e}\), required at the bolted connection will be computed from the seismic design procedure. Following the capacity design principle, the beam strength, \(M_{by}\), must be equal to or greater than this value.  
\[M_{by}\geq M_{e} \tag{1}\]  
where \(M_{e}\) is the expected moment required at the bolted connection, including the effects of bolt slippage and bolt bearing (see Figure 3), and \(M_{by}\) is the effective yield strength of the beam.  
2. Hierarchy criterion:  
The beam-to-column connection must satisfy the strong column-weak beam philosophy.  
\[\sum M_{cy}^{*}\geq\sum M_{e}^{*} \tag{2}\]  
where \(\Sigma M_{cy}^{*}\) is the sum of the projections of the nominal flexural strengths of the columns above and below the connection to the beam centreline with a reduction for the axial force in the column, and \(\Sigma M_{e}^{*}\) is the sum of projections of the expected moments at the bolted beam end joints to the column centreline (see Figure 3).  
Figure 2: Proposed bolted connection: (**a**) 2D drawings; (**b**) 3D configuration; (**c**) closeup of the bolted connection.  
Connecting plate thickness:  
In order to determine the thickness of the connecting plate, \(t_{cp}\), the following requirements must be met.  
\[t_{cp}\geq\max\left\{\frac{12I_{b}}{N\cdot D_{cp}^{3}},\frac{6}{N\cdot D_{cp}^{2 }\cdot F_{ypc}}M_{cp}\right\} \tag{3}\]  
where \(D_{cp}\) is the depth of the connecting plate, \(F_{ypc}\) is the specified minimum yield stress of the connecting plate, \(l_{b}\) is the moment of inertia of the beam (=\(N\cdot l_{b1}\)), \(l_{b1}\) is the moment of inertia of the individual channel section, \(M_{cp}\) is a larger value of the expected moment at the column face or the effective yield strength of the beam, and \(N\) is the number of C-section beams (i.e., 1 for a single beam and 2 for double beams).  
4. Weld strength of the connecting plate:  
The connecting plates are attached to the column by welding. Due to the configuration limitation, fillet and flare welds will be used. The size of the weld must meet the following requirements.  
\[M_{weld}\geq\frac{\sum\left\{M_{e}+Q_{b}\left(e+\frac{D_{c}}{2}\right)\right\}} {N} \tag{4}\]  
where \(M_{weld}\) is the expected moment that needs to be resisted by welding, \(Q_{b}\) is the shear force at the beam, \(e\) is the distance from the column face to the centre of the group of bolts, and \(D_{c}\) is the depth of the column (see Figure 3).  
5. Panel zone strength:  
The column and the attached connecting plates will compose the panel zone of the beam-to-column connections. Following the capacity design principle, the following inequality must be satisfied in the panel zone to avoid yielding.  
\[\frac{0.6F_{ypc}\cdot D_{c}\left(N\cdot t_{cp}+2t_{c}\right)}{\left(\frac{ \sum M_{cc}}{D_{cp}}\right)}\geq 1.0 \tag{5}\]  
where \(t_{c}\) is the column thickness, and \(M_{c,c}\) is the expected moment at the column face.