NEW INSIGHTS INTO THE WEB PANEL COMPONENT

The column web panel is a fundamental component of beam‐column joints. This component has been thoroughly studied and codified in the past. In this paper, new insight on its behaviour is obtained using a large amount of high‐quality Finite Element (FE) models, covering a wide range of panel slenderness and aspect ratios. The study shows that the existing models in part 1‐8 of the current and forthcoming Eurocode 3 present a wide scatter in terms of resistance and stiffness, being unconservative in some specific cases.


Introduction
Research about the mechanical behaviour of steel joints has been a major topic over the last decades.The Component Method (CM) from part 1-8 of the Eurocode 3 (EC3-1-8) [1] is a well-established procedure to assess the resistance and stiffness of steel joints.
The application of the CM requires three steps, namely: i) the identification of the joint basic active components; ii) the assessment of their mechanical characteristics; iii) the assemblage of the individual components using rigid links and linear spring models [2].A detailed description of this method is presented in [3].
The main objective of this paper is to evaluate the behaviour of single-sided (1S) welded beam-to-column steel joints located in internal story, transversely unstiffened (U) or stiffened (T), with particular emphasis on the column web panel.Firstly, a sophisticated nonlinear FE model is developed and calibrated with experimental results.Secondly, a parametric study for three different steel grades is carried out.Finally, the observed physical phenomena are critically discussed and compared to the Eurocode 3 predictions.
The columns and beams comprise typically employed hot-rolled open-section profiles.Fig. 1 introduces the geometry of the joints contemplated on this investigation, along with the corresponding section notation.

Eurocode design rules
EC3-1-8 [1] presents CM-based expressions for strong-axis, open-section, welded, beam-column joints.According to the code, the joint resistance is limited by the most restrictive of the following individual components: column web panel in shear (CWS), column web in transverse compression (CWC), column web in transverse tension (CWT), column flange in transverse bending (CFB), beam flange and web in compression (BFC), or beam-column welds (BCW).
The joint stiffness is dependent on the individual stiffnesses of the CWS, CWT and CWC.The CWC and CWT components can be disregarded in the presence of a transverse stiffener, aligned with the beam flange, in the compression or tension zone, respectively.
The updated version of Eurocode 3 part 1-8 that will be subject to formal vote (FprEC3-1-8) [4] is based on a similar approach, but including some adjustments based on recent numerical studies [5,6].The main differences between both codes are: i) the definition of the column shear area ACWS (CWS); ii) the contribution of the column flange and transverse stiffeners (CWS) in strength; iii) the definition of the web panel slenderness and buckling expressions (CWC); iv) the design resistance of the beam-to-column welds (BCW).

Numerical modelling
In this section, the FE model that will be used in the parametric study is succinctly described and validated.

Description of models
Sophisticated numerical models were developed using the commercial FE software Abaqus© [7], and following the requirements given in the forthcoming prEN 1993-1-14 (EC3-1-14) [8].Among the several types of analysis available, the most complex one has been selected, i.e., geometrically and materially nonlinear analysis with initial imperfections included (GMNIA).
The advanced FE model comprises a solid core region connected to shell parts using solidshell couplings.The length of the members within the solid core part was defined as 1.25 times the height of the member on each side, measured from the joint face.Fig. 2a) presents the layout of the model analysed in this study, and Fig. 2b) depicts the solid and shell individual parts.By means of simplification, the beam root radius was not modelled, resulting in a small reduction of the beam moment resistance.Full penetration butt welds were considered in the connection between the beam and the column.Additionally, in the joints with transverse stiffeners, these were assumed of equal width and thickness as the beam flange, but with the same material as the column.
The material was modelled as elastic-perfectly plastic (EPPL) with no strain hardening.The Young's modulus of steel E and Poisson's ratio n were taken as 210 GPa and 0.3, respectively.
Regarding the analysis parameters, the "Static, General" procedure was applied, considering the nonlinear effects of large deformations and displacements (Nlgeom).The initial, minimum, and maximum increment sizes were set as 0.001, 1E-10 and 0.005, respectively.
The nodes at the extremities of the column and beam were constrained to the motion of a reference point through rigid-body constraints.The boundary conditions used in the analysis are shown in Fig. 2a).The load was introduced through a bending moment M1 = M applied at the tip of the beam, and the axial load N, if included, was applied as a concentrated force on the top node of the column.
Considering the computational time and storage required per model and the large size of the parametric study, different element types were tested, and an eight-node linear brick element with reduced integration (C3D8R) was selected to model the solid core.Likewise, the shell parts were modelled using four-node linear shell elements with reduced integration (S4R).
A mesh sensitivity study was performed by reducing the mesh global size until a negligible variation was observed on the moment-rotation curve.At least four elements were placed across the thickness of all plates in the solid core.The region with larger stress gradients (intersection between the beam and the column), presented a finer mesh.This "refined region" extended up to 0.3hb in the beam and 0.6hc in the column, see Fig. 3.The mesh was also optimized at the cross-section level, where regions with stress concentrations were more refined, e.g., close to the root radius.The worst and average aspect ratios of the elements were also controlled and kept below 3 (average) and 6 (worst).Initial geometric imperfections were introduced in the FE models by considering the first buckling mode from a linear buckling analysis (LBA), with an amplitude of dc/200.For the LBA, only the web panel is free to move in the out-of-plane direction and no axial force is applied to the column to avoid spurious modes.Fig. 4 depicts examples of initial imperfections obtained for different web panel aspect ratios hb/dc, and unstiffened (U) and stiffened (T) joints.Residual stresses were not explicitly modelled.The numerical models were generated and run automatically through Python scripts.The analysis is stopped when the maximum equivalent plastic strain epl,eq,max on the solid core reaches 10%, or when instability appears.Joint rotations are derived from displacements and exclude the column flexibility.
As previously mentioned, welds are not modelled and are assumed to be full penetration butt welds, with no oversize.The moment resistance of the joint is limited by the moment resistance of the beam-column contact, calculated using the mechanical properties of the weakest material, either the beam or the column.However, this BCW failure mode would require much more sophisticated FE models in the weld zone to be properly captured.The models for which this phenomenon happens are easily detected, as those for which the Finite Element Method (FEM) moment resistance is larger than the plastic moment resistance calculated multiplying the plastic modulus of the beam Wpl,b by the weakest material strength min{fyc, fyb}.The failure mode for these models is weld failure and is disregarded from the assessment.

Validation of models
The FE model was validated against the experimental results of two welded joints studied by Klein [9].The joints were subjected to hogging bending moment, with no axial load in the column.presents the geometrical properties of the selected joints for validation.Regarding the material properties, only the yield strength fy and ultimate strength fu were made available in [9].Therefore, the quad-linear material model from the EC3-1-14 [8], based on the work of Yun and Gardner [10] was used to build the stress-strain curves for each plate, as given in Fig. 5. Pinned boundary conditions were applied to the column ends, and the out-of-plane displacement was restrained at the beam end.A vertical displacement was introduced on the tip of the beam to simulate the real loading conditions.The initial imperfections were accounted for by considering the first buckling mode from a LBA, with an amplitude of dc/200.Fig. 6 presents a comparison between experimental ("Exp") and numerical ("Num") results.The load-deflection curves correlate the vertical displacement at the tip of the beam (d) and the applied vertical force (F).The comparisons show that there is a very good agreement between experimental and numerical results in terms of initial stiffness, resistance and deformation.Therefore, the FE model was successfully validated using experimental data available in the literature, meaning that the developed model provides a powerful tool for conducting extensive parametric studies.

Parametric study
The objective of the parametric study is to confront the FEM solution with the calculation rules from the EC3-1-8 [1] and the FprEC3-1-8 [4].To reach this aim, a representative sample of beam-column joints has been selected to provide an assessment of the accuracy of the code expressions.

Limitations and case selection
The parametric study presents the following limitations: i) only welded joints are considered; ii) only European hot-rolled, open-sections are assumed; iii) only steel grades S235, S275 and S355 are addressed; iv) only strong-axis joints are considered; v) for stiffened joints, transverse stiffeners are placed in both tension and compression areas; vi) full-penetration butt welds between the beam and the column are assumed, considering perfect continuity between welded parts; and vii) different levels of axial load for the column are considered (0%, 30%, 50% and 70% of the column section plastic resistance).
The response of the joint is expected to depend on the column web panel slenderness dc/twc, the column shear area Avc, and the aspect ratio of the panel zb/dc.The selected combinations of columns and beams on this study is based on these parameters.To select columns based on the current engineering practice, the complete database of rolled sections typically used for columns in Europe (HE and UC, excluding large columns with hc ≥ 600 mm), is placed in the (Avc) -(dc/twc) space, which is then divided in five parts so that each part contains 1/5 of the total number of columns.The process is repeated for the vertical axis.The space is thus divided in 25 quadrants.Five columns are then selected from five different quadrants following the latin hypercube methodology, whereupon each column belongs to a different vertical and horizontal partition than the rest.Additionally, two large columns (hc ≥ 600 mm) are then included in the sample.The points defining the final column selection in the (Avc) -(dc/twc) space are displayed in Fig. 7, as well as the corresponding selected column cross sections.Three European beam profiles have been selected for each column, providing web panel aspect ratios of approximately 1, 1.5 and 2. The aspect ratio of 2 was not possible for column HE800B, therefore a total of 20 cases (3×6 + 2×1) have been defined.The beam profile and beam steel grade were selected in order to: i) avoid beam failure prior to the column failure; and ii) fulfil the requirements of EC3-1-8 (see clause 4.10(3) in the code) for unstiffened joints.
The parametric study is divided into sets.Every set comprises the 20 cases but with differences in i) use ('T') or not ('U') of transverse stiffeners; ii) level of axial force (n = 0%, 30%, 50% or 70%, as a ratio between the applied axial load and the characteristic column axial load resistance Npl,Rk = Ac•fyc, where fyc is the column yield strength).The eight sets defined are listed in Table 2, with 160 models in total.Furthermore, the same sets are defined for three different steel grades of the column (S235, S275 and S355), thus totalling 480 high-quality FE models.The parametric study is focused on the initial stiffness and plastic resistance of the joints.

Post-processing and results output
For this study, the relevant output variables of the FE model are: i) the applied moment M; ii) the displacements dFEM,T1 (top) and dFEM,B1 (bottom), measured as the average of the displacements of the beam top/bottom flange on the column face; iii) the value of epl,eq,max in the solid core.The displacements dFEM,T1 and dFEM,B1 include components due to the column flexibility.
To assess only the joint behaviour, these components must be removed by subtracting the displacement obtained assuming that the column is infinitely rigid in the joint region.Finally, it is possible to determine the total joint rotation fj, which is measured from the column axis.
The joint initial stiffness is calculated as Sj,ini,FEM = M/fj at the first loading step.Following the recommendations from the EC3-1-14, the moment resistance MR,FEM is obtained as the minimum of: i) the maximum value reached during analysis; ii) the moment applied at the loading step where epl,eq,max reaches the largest tolerable plastic strain of 5% in the solid core.For brevity, the subscript 'FEM' is removed from now on.

Results
This sub-section presents the results of the study, focusing on moment resistance MR and initial stiffness Sj,ini.The results are given in ratios using the FE model as reference, where MR,FEM,5% is the moment resistance obtained from the FE analysis at the step where epl,eq,max in the joint is below or equal to 5%; Sj,ini,FEM is the initial stiffness obtained from the FE analysis; MR,EN and Sj,ini,EN are the moment resistance and initial stiffness, respectively, as per EC3-1-8; MR,prEN and Sj,ini,prEN are the moment resistance and initial stiffness, respectively, as per FprEC3-1-8.
Ratios above 1 indicate that the corresponding method (EN, prEN) yields larger results than the corresponding FE model, and in the context of this study are referred to as 'unconservative'.Correspondingly, ratios below 1 indicate that the corresponding method (EN, prEN) renders lower results than the corresponding FE model, and in the context of this study are referred to as 'conservative'.For resistance ratios, those with BCW failure modes are excluded; however, they are considered for the stiffness ratios.
Table 3 presents statistics of resistance and stiffness ratios across all sets.In the table, c represents the number of cases; CoV indicates the coefficient of variation; and (>1) represents the count of unconservative cases.Table 4 gives the mean value across each set, of the CoV of each case across steel grades, which is a measure of the variability of results with steel grade.

Discussion
According to the results presented previously, the following conclusions can be drawn:

Resistance
For cases with large axial force, and for stiffened joints with axial force, the mean resistance ratio is above 1.The mean value systematically increases with the column axial force, particularly for stiffened joints, resulting in larger dispersion, larger maximum and minimum for both codes.Even for low values of n, unconservative results are obtained for stiffened joints with axial load for both EC3-1-8 and FprEC3-1-8, although slightly less for the latter.Since the dominant failure mode in these joints is CWS, it seems that the formulation of this component needs improvement to consider the influence of the axial load.The FprEC3-1-8 procedure improves these results, but only marginally.The low values in Table 4 indicate that the ratios do not vary significantly across the steel grades.

Initial stiffness
The FprEC3-1-8 is much more conservative than the EC3-1-8 in terms of initial stiffness.Moreover, the scatter is high for both codes.This is found for all joints, except unstiffened joints, which feature much better results, i.e., mean below 1 and lower dispersion.Increasing the axial load results in more unconservative results.These trends show that both applied axial load and the stiffness contribution of the stiffeners play an important role on the initial stiffness.

Concluding remarks
This investigation consists of a numerical study conducted at the University of Coimbra to assess the design rules for welded steel beam-to-column joints for open sections.The study comprises 20 cases formed by the combinations of a column and a beam, covering relevant values of column web panel slenderness, aspect ratio and column shear area.
The study is focused on moment resistance, defined using the maximum equivalent plastic strain criterion (as per EC3-1-14), and the initial stiffness.
The resistance ratios for both codes present a high scatter, and are, for a remarkably large proportion of cases, higher than 1.Deviations are particularly large for stiffened joints with axial force, suggesting that the formulation of the column components (particularly CWS) should be revised for cases with column axial force, even for low values of n.
The stiffness ratios present an average larger than 1 for both codes, with a high scatter, very large maxima, and a large proportion of cases with unconservative results.This is more the case when axial load is present in the column, particularly with stiffeners, suggesting that the contribution of stiffeners and the influence of axial load should be considered more carefully when assessing the joint stiffness.
The forthcoming FprEC3-1-8 provides a marginal improvement on these results, except in cases with large axial load.The improvement is slightly larger for stiffness than for resistance.

Fig. 3 :
Fig. 3: FE mesh for the solid core

7 :
a) Situation in the (Avc) -(dc/twc) space b) Column cross sections Fig. Selection of columns

Table 1 :
Geometry of the selected welded joints for validation

Table 2 :
Sets contemplated in the parametric study for every steel grade

Table 3 :
Statistics of resistance and initial stiffness ratios for steel S275

Table 4 :
Mean value of CoV of ratios across steel grades S235, S275 and S355