SteelVerificationsEN (Eurocode)CBFEMBolts

Bolted connection - Interaction of shear and tension

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This is a selected chapter from book Component-based finite element design of steel connections by prof. Wald et al. The chapter is focused on verification of bolts loaded by a combination of tension and shear.

Description

The objective of this chapter is a verification of the component-based finite element method (CBFEM) for the interaction of shear and tension in a bolt to an analytical model (AM). A beam-to-beam joint with end plates and two rows of bolts was selected for verification; see Fig. 5.5.1. The bending stiffness of the joint is high enough to be classified as rigid.

\textsf{\textit{\footnotesize{Fig. 5.5.1 Joint arrangement of bolted beam-to-beam joint}}}

Analytical model

Bolt resistance in interaction of shear and tension is designed according to Tab. 3.4 in chapter 3.6.1 in EN 1993-1-8:2005. A bilinear relation is used. The geometry and the end plate dimensions of the joint are selected to limit the design resistance of the joint by bolt failure. The design resistance of equivalent T-stub in tension is modeled according to Tab. 6.2 in chapter 6.2.4 in EN 1993‑1‑8:2005.

Verification of resistance

Parameters of the model are a bolt diameter and a beam dimension; see Figs 5.5.2 to 5.5.5. Dimensions of the end plate and the bolt distances are modified to limit the joint resistance by the bolt failure. The shear and bending resistance of the joint is compared in loading at the bolt failure. The results are summarised in Tab. 5.5.1 and 5.5.2.

\textsf{\textit{\footnotesize{Fig. 5.5.2 Sensitivity study for resistance in bending with variation of bolt diameter}}}

\textsf{\textit{\footnotesize{Fig. 5.5.3 Sensitivity study for resistance in bending with variation of beam dimension}}}

\textsf{\textit{\footnotesize{Fig. 5.5.4 Sensitivity study for resistance in shear with variation of bolt diameter}}}

\textsf{\textit{\footnotesize{Fig. 5.5.5 Sensitivity study for resistance in shear with variation of beam dimension}}}

Tab. 5.5.1 Sensitivity study for resistance with variation of bolt diameter

Parameter			AM		CBFEM		AM/CBFEM
Beam; end plate	Diameter	Distances	M_Rd[kNm]	V_Rd[kN]	M_Rd[kNm]	V_Rd[kN]	M_Rd	V_Rd
IPE270; t_p = 30mm; 150×310mm	M16/8.8	e₁= 60 mm; p₁= 190 mm; w = 90 mm	41	155	38	146	1,06	1,06
	M20/8.8	e₁= 70 mm; p₁= 170 mm; w = 90 mm	61	242	50	200	1,21	1,21
HEA300; t_p = 40mm; 300×330mm	M24/8.8	e₁= 85 mm; p₁= 160 mm; w = 150 mm	89	349	83	328	1,06	1,06
	M27/8.8	e₁= 95 mm; p₁= 140 mm; w = 150 mm	110	453	89	365	1,24	1,24
HEA500; t_p = 40mm; 330×520mm	M30/8.8	e₁= 160 mm; p₁= 200 mm; w = 150 mm	216	554	198	509	1,09	1,09

Tab. 5.5.2 Sensitivity study for resistance with variation of the beam dimension

Parameter			AM	AM	CBFEM	CBFEM	AM/CBFEM	AM/CBFEM
Beam; fin plate	Diameter	Distances	M_Rd[kNm]	V_Rd[kN]	M_Rd[kNm]	V_Rd[kN]	M_Rd	V_Rd
HEA260; t_p = 25mm; 260×290mm	M20/8.8	e₁= 75 mm; p₁= 140 mm; w = 130 mm	53	242	50	229	1,06	1,06
IPE300; t_p = 30mm; 150×340mm	M20/8.8	e₁= 70 mm; p₁= 200mm; w = 90 mm	69	242	65	228	1,06	1,06
HEB300; t_p = 40mm; 300×340mm	M27/8.8	e₁= 100 mm; p₁= 140 mm; w = 150 mm	111	453	105	427	1,06	1,06
IPE500; t_p = 45mm; 220×560mm	M27/8.8	e₁= 105 mm; p₁= 350 mm; w = 120 mm	220	453	206	423	1,07	1,07

\textsf{\textit{\footnotesize{Drawing 5.5.1 Joint geometry and dimensions}}}

The results of sensitivity studies are summarized in graphs in Fig. 5.5.6 and 5.5.7. The results show that the differences between the two calculation methods are below 10 %. The analytical model gives generally higher resistance.

\textsf{\textit{\footnotesize{Fig. 5.5.6 Verification of CBFEM to AM for the interaction of shear and tension in bolt in case of loading to bending resistance of a joint}}}

\textsf{\textit{\footnotesize{Fig. 5.5.7 Verification of CBFEM to AM for the interaction of shear and tension in bolt in case of loading to shear resistance of a joint}}}

Benchmark example

Inputs

Connected members

$Steel S355$
$Beams HEA300$
$End plate thickness t p = 40 mm$
$End plate dimensions 300 \times 330 mm$

Bolts

$4 \times M24 8.8$
$Distances e 1 = 85 mm; p 1 = 160 mm; w 1 = 75 mm; w = 150 mm$

Outputs

$Design resistance in bending M Rd = 93 kNm$
$Design resistance in shear V Rd = 291 kN$
$Collapse mode is bolt failure in interaction of shear and tension$

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