### Bolts

The initial stiffness and design resistance of bolts in shear are in CBFEM modeled according to Cl. 3.6 and 6.3.2 in EN 1993-1-8. The spring representing bearing and tension has a bi-linear force-deformation behavior with an initial stiffness and design resistance according to Cl. 3.6 and 6.3.2 in EN 1993-1-8.

Design tension resistance of bolt (EN 1993-1-8 – Table 3.4):

\[ F_{t,Rd}=0.9 f_{ub} A_s / \gamma_{M2} \]

Design punching shear resistance of bolt head or nut (EN 1993-1-8 – Table 3.4):

\[ B_{p,Rd} = 0.6 \pi d_m t_p f_u / \gamma_{M2} \]

Design shear resistance per one shear plane (EN 1993-1-8 – Table 3.4):

\[ F_{v,Rd} = \alpha_v f_{ub} A_s / \gamma_{M2} \]

Design shear resistance can be multiplied by reduction factor *β*_{p} if packing is present (EN 1993-1-8 – Cl. 3.6.1. (12)) and this option is selected in Code setup.

Design bearing resistance of plate (EN 1993-1-8 – Table 3.4):

\( F_{b,Rd} = k_1 a_b f_u d t / \gamma_{M2} \) for standard holes

\( F_{b,Rd} = 0.6 k_1 a_b f_u d t / \gamma_{M2} \) for slotted holes

Utilization in tension [%]:

\[ Ut_t = \frac{F_{t,Ed}}{\min (F_{t,Rd},\, B_{p,Rd})} \]

Utilization in shear [%]:

\[ Ut_t = \frac{V}{\min (F_{v,Rd},\, F_{b,Rd})} \]

Interaction in shear and tension [%]:

\[ Ut_{ts}=\frac{V}{F_{v,Rd}}+\frac{F_{t,Ed}}{1.4 F_{t,Rd}} \]

where:

*A*_{s}– tensile stress area of the bolt*f*_{ub}– ultimate tensile strength of the bolt*d*_{m}– mean of the across points and across flats dimensions of the bolt head or the nut, whichever is smaller*d*– bolt diameter*t*_{p}– plate thickness under the bolt head/nut*f*_{u}– ultimate steel strength*α*_{v}= 0.6 for grades 4.6, 5.6, 8.8 and 0.5 for grades 4.8, 5.8, 6.8, 10.9- \( k_1 = \min \left (2.8 \frac{e_2}{d_0}-1.7, \, 1.4 \frac{p_2}{d_0}-1.7, \, 2.5 \right ) \) – factor from Table 3.4
*α*_{b}= 1.0 if the bearing check with ab is deactivated in Code setup; if the check is activated, the value of*α*_{b}is determined according to EN 1993-1-8 – Table 3.4: \( \alpha_d = \min \left ( \frac{e_1}{3 d_0}, \, \frac{p_1}{3 d_0}-\frac{1}{4}, \, \frac{f_{ub}}{f_u} \right ) \)*e*_{1},*e*_{2}– edge distances in the direction of the load and perpendicular to the load*p*_{1},*p*_{2}– bolt pitches in the direction of the load and perpendicular to the load*F*_{t,Ed}– design tensile force in bolt*V*– design shear force in bolt*γ*_{M2}– safety factor (EN 1993-1-8 – Table 2.1; editable in Code setup)

Edge distances used for bolt bearing resistance must be relevant for general plate geometries, plates with openings, cutouts, etc.

The algorithm reads the real direction of the resulting shear force vector in a given bolt and then calculates the distances needed for the bearing check.

The end (*e*_{1}) and edge (*e*_{2}) distances are determined by dividing the plate contour into three segments. The end segment is indicated by a 60° range in the direction of the force vector. The edge segments are defined by two 65° ranges perpendicular to the force vector. The shortest distance from a bolt to a relevant segment is then taken as an end, or an edge distance.

The spacing distances between bolt holes (*p*_{1}; *p*_{2}) are determined by virtually enlarging the surrounding bolt holes by a half of their diameter, then drawing two lines in direction and perpendicular to the shear force vector. The distances to the enlarged bolt holes that are intersected by these lines are then considered as *p*_{1} and *p*_{2} in the calculation.

### Preloaded bolts

Design slip resistance per bolt grade 8.8 or 10.9 (EN 1993-1-8, Cl. 3.9 – Equation 3.8):

\[ F_{s,Rd} =\frac{k_s n \mu (F_{p,C} - 0.8 F_{t,Ed})}{\gamma_{M3}} \]

The preload (EN 1993-1-8 – Equation 3.7)

*F*_{p,C} = 0.7 *f*_{ub} *A*_{s}

The preloading force factor 0.7 can be modified in Code setup.

Utilization [%]:

\[ Ut_s = \frac{V}{F_{s,Rd}} \]

where:

*A*_{s}– tensile stress area of the bolt*f*_{ub}– ultimate tensile strength*k*_{s}– a coefficient (EN 1993-1-8 – Table 3.6;*k*_{s}= 1 for normal round holes,*k*_{s}= 0.63 for slotted holes)*μ*– slip factor editable in Code setup (EN 1993-1-8 – Table 3.7)*n*– number of the friction surfaces. Check is calculated for each friction surface separately*γ*_{M3}– safety factor (EN 1993-1-8 – Table 2.1; editable in Code setup – recommended values are 1.25 for ultimate limit state and 1.1 for serviceability limit state design)*V*– design shear force in bolt*F*_{t,Ed}– design tensile force in bolt

If slip of preloaded bolts is checked for serviceability limit state, they should be afterward switched to "bearing – tension/shear interaction" and checked for the ultimate limit state.

### Detailing

Detailing checks of bolts is performed if the option is selected in Code setup. Dimensions from bolt center to plate edges and between bolts is checked. Edge distance *e* = 1.2 and spacing between bolts *p* = 2.2 are recommended in Table 3.3 in EN 1993-1-8. User can modify both values in Code setup.