Esempio di verifica

Bending stiffness of welded joint of open sections

Steel

Connection

CBFEM

Rotational stiffness

Stiffness

Welds

EN (Eurocode)

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This verification example contains chapter 10.1 of the book "Benchmark cases for advanced design of structural steel connections" written by prof. Wald and his team.

Description

The prediction of rotational stiffness is described on a welded eaves moment joint. A welded joint of open section column HEB and beam IPE is studied, and the joint behavior is described on a moment-rotation diagram. The results of the analytical model by component method (CM) are compared with the numerical results obtained by the component-based finite element method (CBFEM). A benchmark case is available.

Analytical model

The rotational stiffness of a joint should be determined from a deformation of its basic components, which are represented by the stiffness coefficient k_i. The rotational stiffness of the joint S_j is obtained from:

\[ S_j = \frac{E z^2}{\mu \Sigma_i \frac{1}{k_i}} \]

where:

k_i is the stiffness coefficient for the joint component i;
z is the lever arm; see 6.2.7;
μ is the stiffness ratio; see 6.3.1.

The joint components that are taken into account in this example are column web panel in shear k₁, column web in compression k_2, and column web in tension k₃. The stiffness coefficients are defined in Table 6.11 in EN 1993-1-8:2005. The initial stiffness S_j,ini is obtained for a moment M_j,Ed ≤ 2/3 M_j_,Rd.

\[S_j = \frac{E \, z^{2}}{\frac{1}{k_1} + \frac{1}{k_2} + \frac{1}{k_3}}\]

\[S_{j,\text{ini}} = \frac{S_j}{1.5^{\psi}}\]

where

\(S_{j}\) — rotational stiffness of the joint

\(\psi\) = 2.7 — EN 1993-1-8 table 6.8

An open section beam IPE 400 is welded to a column HEB 300 in the example. Beam flanges are connected to the column flange with welds with the throat thickness of 9 mm. The beam web is connected with welds with the throat thickness of 5 mm. Plastic stress distribution is considered in welds. The material of the beam and column is S235. The design resistance is limited by the components column panel in shear and column panel in transverse compression . The calculated stiffness coefficients of the basic components, initial stiffness, stiffness by design resistance, and rotation of the beam are summarised in Tab. 10.1.1.

\[ \textsf{\textit{\footnotesize{Tab. 10.1.1 Results of the analytical model}}}\]

Numerical model

Detailed information about the prediction of stiffness in CBFEM may be found in chapter 3.9. The same eaves moment joint is modeled, and the results are in Tab. 10.1.2. The design resistance is reached by 5% plastic strain in the component column web in tension. The CBFEM analyses allow calculating rotational stiffness at any stage of loading.

Experimental overview

For the purpose of the comparison, a cross-section was set to HEB300 and the beam cross-section was variable. All materials utilised were S235.

\[ \textsf{\textit{\footnotesize{Tab. 10.1.2 Experimental overview}}}\]

\[ \textsf{\textit{\footnotesize{Tab. 10.1.3 Experimental overview}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 1 Verification of CBFEM to CM}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 2Sensitivity study of beam IPE cross-section}}}\]

Verification of stiffness

The rotational stiffness calculated by CBFEM is compared with CM. The comparison shows good agreement in initial stiffness and correspondence of joint behavior. The calculated stiffness from CBFEM and CM are summarised in Tab. 10.1.3.

A comparison of the global behavior of a welded eaves moment joint described by a moment-rotation diagram is prepared. The joint is analyzed, and the stiffness of the connected beam is calculated. The main characteristic is the initial stiffness calculated at 2/3M_j,Rd, where M_j,Rd is the design moment resistance of the joint. The moment-rotation diagram is shown in Fig. 10.1.1.