Analytical Model
The numerical model is verified by analytical model proposed by Eurocodes. EN 1993-1-8 provides design equations for calculating the shear resistance of a bolt per shear plane as follows:
\[F_{v,Rd}=\frac{\alpha_v f_{ub} A}{\gamma_{M2}}\]
where fub is the ultimate bolt material strengths, A is the nominal unthreaded or threaded body areas of the bolt and \(\alpha_v\) is a coefficient dependent on bolt class – for classes 4.6, 5.6 and 8.8 it is equal to 0.6, and for classes 4.8, 5.8, 6.8 and 10.9 it is equal to 0.5.
EN 1993-1-8 defines the bearing resistance per bolt as follows:
\[F_{b,Rd}=\frac{k_1 \alpha_b f_u dt}{\gamma_{M2}}\]
where d is the nominal bolt diameter, fu is nominal ultimate tensile strength of the plate, t is the thickness of connected material and \(\gamma_{M2}\) is the partial factor with the recommended value of 1.25. Parameters \(\alpha_b\) and k1 are determined considering mainly geometrical parameters as given below:
- perpendicular to the direction of load transfer for edge and inner bolts, respectively
\[k_1=\min \left ( 2.8\frac{e_2}{d_0} -1.7, \, 1.4 \frac{p_2}{d_0} -1.7, \, 2.5 \right )\]
\[k_1=\min \left ( 1.4 \frac{p_2}{d_0} -1.7, \, 2.5 \right )\]
