## 3 Results and Discussion
### Optimization of Connector Geometry and Determination of Ultimate Bearing Capacity
#### 3.3.2 Simplified Formula for Computing the Connector Ultimate Bearing Capacity  
A new formula was developed in this study to predict the ultimate shear strength of bolt connectors for sandwich structures. For that purpose, the hole diameter and sandwich wall thickness were modified in the finite element analysis. Figure 10 shows the variation of the connector's ultimate load (\(P\)) with respect to bolt diameter (\(d\)) and sandwich wall thickness [38] (\(t\)). Shear load capacity is insensitive to diameter if the bolt diameter remains relatively small. In this case, bolt shear failure is the dominant mechanism and the overall performance of the connector basically depends on the bolt diameter. When bolt diameter increases beyond 10 mm, strength becomes sensitive to the thickness of the sandwich structure. In particular, larger thickness results in a higher connection strength but also in more significant bolt hole deformation. The failure mode changes from bolt cut-off damage to hole wall bearing failure. In summary, connector strength varies with bolt diameter and sandwich wall thickness based on the hole diameter. In view of this, two simple formulae were derived by fitting results of FE simulations.  
(1) For high-strength bolt shear failure, the ultimate bearing capacity of the connector is determined as  
\[N_{v}^{b}=0.85786^{0.074}d^{1.926}f_{v}^{b}\]  
(The corresponding formula available in the current Chinese Steel Structure Design Specification is \(N_{v}^{b}=\frac{\pi d^{2}}{4}f_{v}^{b}\))  
(2) For bolt hole wall bearing failure, the ultimate bearing capacity of the connector is determined as  
\[N_{c}^{b}=0.854386^{0.554}d^{1.446}f_{c}^{b}\]  
(The corresponding formula available in the current Chinese Steel Structure Design Specification is \(N_{c}^{b}=d\sum t\cdot f_{c}^{b}\)) where \(f_{v}^{b}\) and \(f_{c}^{b}\) are the shear ultimate strength and compression ultimate strength of the high-strength bolt or connection plate material, respectively; \(t\) is the thickness of the honeycomb sandwich structure; \(d\) is the bolt diameter.  
The new derivation from this work yields similar results as the existing Chinese [22], American, and European Steel Structure Design Specifications [38] when bolt shear failure occurs. Under such scenarios, the ultimate strength of the connector is proportional to the bolt shear bearing area. Since all the specifications are mainly applied for steel plates and do not consider the effect of sandwich wall thickness on the load bearing capacity, they are more conservative than the present approach. When bolt hole wall bearing failure occurs, the present formula significantly differs from the previous standards. ANSYS results indicate that bolt opening deforms and significant displacement occurs at the bolt shear surface; hence, the connector does not develop hole wall bearing failure. It indicates  
Figure 10: Variation of connector’s shear load capability with respect to (**a**) bolt diameter and (**b**) sandwich wall thicknesses. (Int = log(\(t\)), InP = log(\(P\))).  
that steel structure design specifications cannot be applied to the honeycomb sandwich structures. Therefore, the fitting formula from the finite-element analysis and test results are more suitable for the connection of honeycomb sandwich structures than the existing standards.