The block shear failure was reported firstly in 1978 for joints with not optimal geometry from an internal forces point of view. The test results proved the potential failure mode of tearing out in the web of the beam. Several studies concerning block shear failure were published in the last twenty years predicting the block shear capacity as a combination of fracture on the tension and shear plane. Block shear rupture is the potential failure mode for gusset plates, fin plates, coped beams, single/double angles and tee connections, where significant tension/shear forces are present.
The block shear failure was first reported in 1978 in 
for joints without optimal geometry from an internal forces point of view. The test results proved the potential failure mode of tearing out in the web of the beam. Several studies concerning the block shear failure were published in the last twenty years 
, predicting the block shear capacity as a combination of fracture on the tension and shear plane (see Figure 1
). Block shear rupture is the potential failure mode for gusset plates, fin plates, coped beams, single/double angles and tee connections, where significant tension/shear forces are present.
The analytical approaches of designing against block shear failure are described in standards. The design approaches are based on a simple assumption that the block shear capacity is the combination of the yielding along shear planes and rupture on the tensile plane. The analytical models used for verification in this study include currently valid Eurocode EN1993-1-8:2006 
, US structural steel design code A360-16 
, 2nd generation of Eurocode prEN1993-1-8 
, which is planned to be issued after 2020, Canadian structural steel design standard CSA S16-09 
and analytical models proposed by Topkaya 
and Driver 
. The major advantage of these models is that they can be used in most cases and they are easy to apply, but no studies have dealt with complex loading, including substantial eccentricities and general block failure. Despite the existence of several design approaches to predict block shear capacity, the prediction of failure mode appears to have the same importance.
With the development of computational technology, it is possible to create advanced finite element models. These can be validated by experiments; therefore, the behaviour of numerical simulation is close to the physical test behaviour. Their main advantage is that once the appropriate finite element model is created, it is possible to carry a parametric study on it with minor modifications without the need for carrying out additional physical tests. However, making an accurate finite element model is laborious and, due to many variables, such as the definition of boundary conditions, meshing, etc., the results are not always representative. The finite element analysis of block shear failure has been developed since 2002, when numerical simulations were presented in 
. The majority of the following numerical models covered the tensile fracture but not the shear rupture and development of a shear crack. The block shear failure, capturing the ductile fracture and combining both shear and tension failure, is presented in 
. The prediction of the shear crack development in the bolted connection is presented by the appropriate failure criteria.
The approach, which combines the component method and finite element method, is called component-based FEM (CBFEM). As the name suggests, it combines aspects of the finite element method and component method to provide a satisfactory way of designing steel joints, while simultaneously complying with valid standards. Contrary to complex finite element simulations, it is commonly used for designing steel joints in practice. The CBFEM model is verified by the analytical and research-oriented FEM models comparing the block shear capacity in three levels of complexity.
3. Sensitivity Study
The CBFEM model T1 was used to study the influence of input parameters on the resistance of the joint. The tested parameters were the pitch distance and plate thickness. The output value subjected to comparison was the ultimate strength of the joint, which was compared to the results obtained by different design standards.
The CBFEM model ultimate resistances were calculated according to AISC 360-16 standard with the LRFD method. The ultimate resistance for the CBFEM model was assumed to appear when the strain reached 5%. The CBFEM results were plotted together with the analytical model results of recent/upcoming codes—EN1993-1-8:2006, AISC 360-16, prEN1993-1-8.
Specimen T1 was used to study the influence of the bolt pitch (Figure 5) and the plate thickness (Figure 6) on the block shear resistance. The bolt pitch was successively set to 56, 66, 76, 86, 96 and 106 mm. The study was carried out on 6 different plate thicknesses: 4.6; 5.6; 6.6; 7.6; 8.6 and 9.6 mm. The models provide expected results and show the increase in block shear resistance with increased parameters in the case of symmetrical loading. The EN1993-1-8:2006 is the most conservative, followed by CBFEM, prEN1993-1-8 and AISC 360-16.
The steel grade S235 and bolts M22 grade 10.9 were used in the sensitivity study of eccentrically loaded bolted connection. Material safety factors were set to one. The geometry of the joint is shown in Figure 7
. The load deflection curves of CBFEM and analytical models are shown in Figure 8
. The analytical models used in codes use a constant reduction factor regardless of the magnitude of the eccentricity. It was claimed in 
that the effect of in-plane eccentricity is not crucial for the total resistance, up to a 10% reduction. The reduction in resistance is significantly higher for analytical models used in the current codes. The results of the CBFEM model lie between the models presented in 
and those used in codes. In contrast to analytical models where a constant reduction in resistance is used, CBFEM models employ finite element analysis for the calculations which may be advantageous in covering the actual size of the eccentricity.
CBFEM models were created and compared to analytical models. If the currently valid EN 1993-1-8:2006 is excluded from the comparison, in the case of concentric connections, the CBFEM models have a good rate of compliance with analytical models and, except for one case, they are on the safe side. Models calculated according to prEN1993-1-8:2020 and AISC 360-16 were used. The study was carried out for four different pitch distances p = 56; 66; 76 and 86 mm, and six different plate thicknesses t = 4.6; 5.6; 6.6; 7.6; 8.6 and 9.6 mm. The bolt grade was A325 and 10.9 according to the relevant design standards. The results of sensitivity studies for concentric and eccentric bolted connections are summarised and shown in Figure 9. The CBFEM method is conservative for concentric connections and predicts up to 13.3% lower resistance. The validated models for eccentric connections predict up to 21% higher resistance.
The CBFEM model uses a bilinear material diagram with negligible strain hardening. On the other hand, the analytical models use a combination of yield and ultimate strengths in their formulas. The CBFEM model provides lower block shear resistances compared to the analytical models if a steel grade with a high ratio of ultimate to yield strength is used. Mesh refinement slightly decreases the block shear resistance; however, the mesh size near bolt holes is fixed.