## 4 Case Studies on Tensile Specimens with a Single Bolt
### Parameter Study  
A parameter study has been worked out to get a better insight into the behaviour of the DLO procedure concerning different edge distances. The parameter range was chosen with \(\mathrm{e_{1}}=1.2\mathrm{d_{0}}\ldots 4.0\mathrm{d_{0}}\) and \(\mathrm{e_{2}}=1.2\mathrm{d_{0}}\ldots 4.0\mathrm{d_{0}}\). A steel grade S355 was used. The bearing resistance and the proof of the net section must both be checked. These proofs are automatically included in the resistances from the DLO procedure. For an objective comparison, the resistances from the code EN 1993-1-8, from literature (Equations (18) and (19)), and also the ultimate loads from the DLO procedure were normalized, as shown in Figure 19.  
Figure 18: Failure mechanisms (blue: Slip displacements, red: Normal displacements) from DLO with \(\mathrm{k_{fy}}=2.50\) (top row: Tresca; bottom row: Mises): (**a**) Case 1; (**b**) Case 2; (**c**) Case 3; (**d**) Case 4.  
The normalized forces depend still on the ratio of bolt-hole diameter and bolt. Therefore, two representative cases have been worked out. The first case considers a value of \(\mathrm{d}_{0}/\mathrm{d}=1.1\), which represents a typical bolt-hole tolerance, e.g., M20 bolts. For comparison, the second case considers no bolt-hole tolerance with \(\mathrm{d}_{0}/\mathrm{d}=1.0\). The geometry in the DLO procedure was always modelled with \(\mathrm{d}_{0}\). The calculated and normalized loads are shown in Figures 20 and 21.  
Figure 19: Normalization of the loads from codes, literature, and DLO.  
Figure 20: Comparison of normalized loads for \(\mathrm{d}_{0}/\mathrm{d}=1.1\).  
The loads according to Equations (18) and (19) are significantly higher than the loads from EN 1993-1-8. Especially for small edge distances with \(\mathrm{e_{1}/d_{0}<2.5}\) and \(\mathrm{e_{2}/d_{0}<1.5}\), but also for large edge distances with \(\mathrm{e_{1}/d_{0}>3.0}\) and \(\mathrm{e_{2}/d_{0}>1.75}\). In [26], it is explained that the \(\mathrm{k_{1}}\) value in Equation (16) was only included due to lack of experimental evidence and that for small edge distances the values in EN 1993-1-8 are very conservative. Furthermore, for larger edge distances the question for the need of an upper limit (actually \(\mathrm{k_{1}}=2.5\)) arose. It was stated that if no limit is defined, then the shear resistance of the bolt is automatically an upper limit. Still, if a limit should be set, then a bearing stress of \(3\mathrm{f_{u}}\) would be an appropriate value for the ultimate resistance. Further information was given to prevent a too large hole elongation for service loads, but this is not part of the presented research.  
A similar behaviour was obtained for \(\mathrm{d_{0}/d=1.1}\) and \(\mathrm{d_{0}/d=1.0}\). As expected, the DLO procedure with the Mises criterion delivers in all cases higher loads than the Tresca criterion. Especially for \(\mathrm{d_{0}/d=1.1}\) combined with smaller edge distances \(\mathrm{e_{1}}\) and \(\mathrm{e_{2}}\), the loads obtained with the Mises criterion are slightly unsafe compared to Equations (18) and (19). For larger edge distances \(\mathrm{e_{1}/d_{0}>3.0}\) and \(\mathrm{e_{2}/d_{0}>1.75}\), the DLO resistances are (in some cases significant) lower than the resistances from Equations (18) and (19). The loads from the DLO procedure are similar to the loads from EN 1993-1-8 for very large edge distances. This happened because an upper limit with 2.5 is considered in the code. As explained in Section 4.3, the full bearing resistance can only be reached, if there is no other failure mechanism with a lower resistance, e.g., as shown in Figure 18.  
Figure 21: Comparison of normalized loads for \(\mathrm{d_{0}/d=1.0}\).