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Failure mode method

Uniplanar welded plate to circular hollow sections T-joints predicted by CBFEM are verified to FMM in this chapter. In CBFEM, the design resistance is limited by reaching 5 % of strain or a force corresponding to 3 % d₀ joint deformation, where d₀ is chord diameter. The FMM is based on the peak load limit or 3 % d₀deformation limit; see Lu et al. (1994). The welds, designed according to EN 1993‑1‑8:2006, are not the weakest components in the joint.

Chord plastification

The design resistance of a CHS chord face is determined using the method given by FMM model in Ch. 9 of prEN 1993-1-8:2020 and in ISO/FDIS 14346; see Fig. 7.3.1. The design resistance of the axially loaded welded plate to CHS joint is:

T joint

Transverse

\[ N_{1,Rd} = 2.5 \cdot C_f f_{y0} t_0^2 (1+3 \beta^2) \gamma^{0.35} Q_f / \gamma_{M5} \]

Longitudinal

\[ N_{1,Rd} = 7.1 \cdot C_f f_{y0} t_0^2 (1+0.4 \eta) Q_f / \gamma_{M5} \]

X joint

Transverse

\[ N_{1,Rd} = 2.1 \cdotC_f f_{y0} t_0^2 (1+3 \beta^2) \gamma^{0.25} Q_f / \gamma_{M5} \]

Longitudinal

\[ N_{1,Rd} = 3.5 \cdotC_f f_{y0} t_0^2 (1+0.4 \eta^2) \gamma^{0.1} Q_f / \gamma_{M5} \]

where:

f_y,i – yield strength of member i (i = 0,1,2 or 3)
t_i – thickness of the wall of CHS member i (i = 0,1,2 or 3)
\(\beta\) – ratio of the mean diameter or width of brace members, to that of the chord
\(\eta\) – ratio of the brace member depth to the chord diameter or width
\(\gamma\) – ratio of a chord width or diameter to twice its wall thickness
Q_f – chord stress factor
C_f – material factor
\(\gamma_{M5}\) – partial factor for resistance of joints in hollow section lattice girders
N_i,Rd – design resistance of a joint expressed in terms of the internal axial force in member i (i = 0,1,2 or 3)

\[ \textsf{\textit{\footnotesize{Fig. 7.3.1 Examined failure mode - chord plastification}}}\]

Range of validity

CBFEM was verified for typical joints of the welded circular hollow sections. The range of validity for these joints is defined in Table 7.8 of prEN 1993-1-8:2020; see Tab 7.3.1. The same range of validity is applied to CBFEM model. Outside the range of validity of FMM, an experiment should be prepared for validation or verification performed for verification according to a validated research model.

Tab. 7.3.1 Range of validity for method of failure modes

General	\(0.2 \le \frac{d_i}{d_0} \le 1.0 \)	\( \theta_i \ge 30^{\circ} \)	\(-0.55 \le \frac{e}{d_0} \le 0.25 \)
	\(g \ge t_1+t_2 \)	\(f_{yi} \le f_{y0} \)	\( t_i \le t_0 \)

Chord	Compression	Class 1 or 2 and \(10 \le d_0 / t_0 \le 50 \) (but for X joints: \( d_0/t_0 \le 40 \))
	Tension	\(10 \le d_0 / t_0 \le 50 \) (but for X joints: \( d_0/t_0 \le 40 \))
Transverse plate		\(0.25\le\beta=b_1/d_0\le1\)
Longitudinal plate		\(0.6\le\eta=h_1/d_0\le4 \)

Validation

In this chapter, the CBFEM is validated to the FMM models of plate to CHS T-joints described in prEN 1993-1-8:2020. The models are compared against the data from mechanical tests in Tabs 7.3.2–7.3.3 with resistance based on deformation limit. Material and geometric properties of numerical tests are described in (Voth A.P. and Packer A.J., 2010). The experiments out of range of validity are marked in tables by star * and in graph indicated to show the quality of the boundary conditions.

Tab. 7.3.2 Geometric properties, material properties, and resistances of connections from experiments and FMM models for transverse T-joint

ID	Reference	d0 [mm]	t0 [mm]	h1 [mm]	h1/d0 [-]	d0/t0 [-]	fy0 [MPa]
TPT 1	Washio et al. (1970)	165,2	5,2	115,6	0,7	31,8	308,0
TPT 2	Washio et al. (1970)	165,2	5,2	148,7	0,9	31,8	308,0
TPT 3	Washio et al. (1970)	139,8	3,5	125,8	0,9	39,9	343,0
TPT 4	Voth et al. (2012)	219,2	4,5	100,3	0,5	48,8	388,8

ID	Nu,exp [kN]	Branch type	Nu,exp/(t02·fy0)	N1,prEN/(t02·fy0)	Nu,exp/N1,prEN
TPT 1	169,4	Compression	20,34	16,25	1,25
TPT 2	250,5	Compression	30,08	22,58	1,33
TPT 3	184,8	Compression	43,98	24,45	1,80
TPT 4	282,5	Tension	36,04	12,45	2,89

Tab. 7.3.3 Geometric properties, material properties, and resistances of connections from experiments and FMM models for longitudinal T-joint

ID	Reference	d0 [mm]	t0 [mm]	h1 [mm]	h1/d0 [-]	d0/t0 [-]	fy0 [MPa]
TPL 1	Washio et al. (1970)	165,2	5,2	165,2	1,0	31,8	308,0
TPL 2	Washio et al. (1970)	165,2	5,2	330,4	2,0	31,8	308,0
*TPL 3	Voth et al. (2012)	219,2	4,5	99,9	0,5	48,8	388,8

ID	Nu,exp [kN]	Branch type	Nu,exp/(t02·fy0)	N1,prEN/(t02·fy0)	Nu,exp/N1,prEN
TPL 1	107,6	Compression	12,92	10,36	1,25
TPL 2	127,4	Compression	15,30	13,32	1,15
*TPL 3	160,6	Tension	20,49	8,75	2,34

\[ \textsf{\textit{\footnotesize{ Fig. 7.3.2 Validation of FMM to mechanical experiments for transverse T-type plate-to-CHS connections (left) and to longitudinal T-type plate-to-CHS connections (right)}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 7.3.3 Validation of FMM to mechanical experiments for transverse T-type plate-to-CHS connections (left) and longitudinal T-type plate-to-CHS connections (right)}}}\]

The validation shown in Figs 7.3.2 and 7.3.3 demonstrates that differences to experiments are at least 15 % generally to the safe side. The experiments out of the range of validity are included and marked. The results indicate the good quality of the chosen boundary conditions.

Uniplanar plate T-joint

An overview of the considered examples in the study is given in the Tab. 7.3.4. Selected cases cover a wide range of joint geometric ratios. Geometry of the joints with dimensions is shown in Fig. 7.3.4. Plate thickness is 15 mm in all cases covered in this study.

Tab. 7.3.4 Examples overview

\[ \textsf{\textit{\footnotesize{Fig. 7.3.4 Dimensions of plate to CHS T joint, transverse (left) and longitudinal (right)}}}\]

Verification

The results of resistance and design failure mode of the FMM are compared with the results of CBFEM in Tab. 7.3.5 and in Fig. 7.3.5.

Tab. 7.3.5 Verification of prediction of resistances by CBFEM on FMM a) transverse orientation b) longitudinal orientation

The study shows good agreement for the applied load cases. The results are summarized in diagrams comparing CBFEM’s and FMM’s design resistances; see Fig. 7.3.5. The results show that the difference between the two calculation methods is in all cases less than 7 %.