Description
This study is focused on the verification of the component-based finite element method (CBFEM) for the resistance of the end plate connection with four bolts in a row to an analytical model (AM), and a research-oriented finite element model (ROFEM) validated on experiments.
Analytical model
The bolt resistance in shear and tension and the plate resistance in bearing and punching shear are designed according to Tab. 3.4, Chapter 3.6.1 in EN 1993-1-8:2006. The equivalent T-stub in tension, according to Chapter 6.2.4, was modified by Jaspart et al. (2010) , see Fig. 5.7.1 and Tab. 5.7.1.
\[ \textsf{\textit{\footnotesize{Fig. 5.7.1 Failure modes of T-stub with four bolts in a row: mode 1 (left), mode 2 (middle), mode 3 (right)}}}\]
Tab. 5.7.1 Failure modes of T-stub with four bolts in a row (Jaspart et al. 2010)
In Tab 5.7.1 is 𝐹t,Rd the bolt tensile resistance, 𝑒w=𝑑w/4, 𝑑w is the diameter of the washer, or the width across points of the bolt head or nut, as relevant, 𝑚, 𝑛=𝑒1+𝑒2;𝑛≤1.25𝑚, 𝑛1=𝑒1, 𝑛2=𝑒2;𝑛2≤1,25𝑚+𝑛1 see Fig. 5.8.2, 𝑀pl,1,Rd=0.25𝑙eff,1𝑡f2𝑓y/𝛾M0, 𝑀pl,2,Rd=0.25𝑙eff,2𝑡f2𝑓y/𝛾M0, 𝑙eff is effective length, 𝑡f is the flange thickness, and 𝑓y is the yield strength, see Fig. 5.7.2.
\[ \textsf{\textit{\footnotesize{Fig. 5.7.2 T-stub geometry with four bolts in a row}}}\]
Validation and verification of resistance
Design resistances calculated by CBFEM were compared with the results of the analytical model (Zakouřil, 2019) and experiments with research-oriented finite element model (Samaan et al. 2017), see Fig. 5.7.3. The results are summarized in Fig. 5.7.4. Bolt grade 8.8 and steel grade S450 were used. The yield and tensile strengths correspond closely to the experimental values, e.g. bolt yield strength is 600 MPa, bolt tensile strength is 800 MPa.
\[ \textsf{\textit{\footnotesize{Extended unstiffened end plate labeled ENS}}}\]
\[ \textsf{\textit{\footnotesize{Flushed end plate labeled F}}}\]
\[ \textsf{\textit{\footnotesize{Extended stiffened end plate labeled EX}}}\]
\[ \textsf{\textit{\footnotesize{Fig. 5.7.3 Tested specimens}}}\]
The bending moment resistance determined by CBFEM is usually between resistances determined by the component method and experimentally. Table 5.7.2 shows the comparison between the CM, CBFEM, ROFEM, and experimental resistances for the specimens with end plate thicknesses of 20 mm and 32 mm. Both the component method and CBFEM underestimate the resistance of the specimen with a flushed end plate.
Tab. 5.7.2 Comparison between the CM , ROFEM, CBFEM, and Experiment
Table 5.7.3 and Fig. 5.7.4 show verification of CBFEM to CM for models ENS with different end plate thickness, bolt diameter, and beam height
Tab. 5.7.3 Verification CBFEM to CM ENS
\[ \textsf{\textit{\footnotesize{Fig. 5.7.4 Verification of CBFEM to CM}}}\]
The results of sensitivity studies are summarized in plots in Fig. 5.7.5, Fig. 5.7.6, Fig. 5.7.7
\[ \textsf{\textit{\footnotesize{Fig. 5.7.5 Sensitivity study for plate thickness}}}\]
\[ \textsf{\textit{\footnotesize{Fig. 5.7.6 Sensitivity study for bolt diameter}}}\]
\[ \textsf{\textit{\footnotesize{Fig. 5.7.7 Sensitivity study for beam height}}}\]
Table 5.7.4 and Fig. 5.7.8 show verification of CBFEM to CM for models F with different end plate thickness and bolt diameter
Tab. 5.7.4 Verification CBFEM to CM F
\[ \textsf{\textit{\footnotesize{Fig. 5.7.8 Verification of CBFEM to CM}}}\]
The results of sensitivity studies are summarized in plots in Fig. 5.7.9 and 5.7.10
\[ \textsf{\textit{\footnotesize{Fig. 5.7.9 Sensitivity study for plate thickness}}}\]
\[ \textsf{\textit{\footnotesize{Fig. 5.7.10 Sensitivity study for bolt diameter}}}\]
Table 5.7.5 and Fig. 5.7.11 show verification of CBFEM to CM for models F with different end plate thickness and bolt diameter
Tab. 5.7.5 Verification CBFEM to CM EX
\[ \textsf{\textit{\footnotesize{Fig. 5.7.11 Verification of CBFEM to CM}}}\]
The results of sensitivity studies are summarized in plots in Fig. 5.7.12 and 5.7.13.
\[ \textsf{\textit{\footnotesize{Fig. 5.7.12 Sensitivity study for plate thickness}}}\]
\[ \textsf{\textit{\footnotesize{Fig. 5.7.13 Sensitivity study for bolt diameter}}}\]
Benchmark example
Inputs
- Steel S450
Column
- Rolled I
- h = 390mm
- b = 350mm
- tf = 20mm
- tw = 12mm
- r = 27mm
Column stiffeners
- ts = 16mm
Beam
- Rolled I
- hb = 340mm
- bb = 350mm
- tf = 20mm
- tw = 12mm
- r = 27mm
End plate
- tp = 20mm
- bp = 350mm
- hp= 540mm
Bolts
- 4 rows x 4 x M16 8.8
- Distances e1 = 50 mm, p1 = 120 mm, p2 = 100mm, e2= 50mm, w1 = 75mm, w2 = 100mm
Welds
- aw = 7mm
Outputs
- Design resistance FRd = 247 kN
- Critical components are bolts with forces increased by the prying of the end plate
\[ \textsf{\textit{\footnotesize{Fig. 5.7.14 Benchmark example}}}\]