CFT Connections: State-of-the-art Report and Numerical Validation by 3D FEM

Composite construction has been used since the late 1800s in the construction of bridges and buildings (Griffis, 1994; Viest et al., 1997), and its use increased substantially in the USA during the early 1900s as a result of the excellent performance of buildings with encased riveted connections in the 1906 San Francisco Earthquake and Fire (Forcier et al., 2002). While research on composite members started in the 1910’s (Pelke & Kurrer, 2015) the first formal comprehensive research on composite connections only took place in the late 1930s (Batho et al., 1939). Composite construction is used in buildings (Faschan, 1992), bridges (Roeder & Lehman, 2012), and industrial facilities (American Petroleum Institute, 2010), as well as for strengthening of existing structures (Kim & Shinozuka, 2004). It is important to mention that composite construction has also been widely used in seismic regions, especially for high-rise structures (Liu & Goel, 1988). The great advantage of composite construction is the synergetic action of both materials. Structural steel has high strength, ductility, lightness, and ease of construction. Concrete provides high rigidity, mass, and fire resistance. Additionally, with concrete filled tubes (CFT) composite elements the costs and construction times are reduced because the tubes act as formwork. There are many analytical (Denavit, 2012; Gourley et al., 2008; Hajjar & Gourley, 1996; Han et al., 2014) and experimental (Perea, 2010) studies on the behavior of the beam-column CFT under static and dynamic loads; however, relatively little work has been done on the beam-column connections with steel tubes filled with concrete in the USA, Europe, and Australia as compared to Japan and China (Zhao et al., 2013).

Predicting composite connection behavior is exceptionally challenging due to the coupled behavior of the steel and concrete, the residual stresses in the steel, local buckling of the connection, and the sensitivity of the stress–strain response to the steel–concrete contact and confinement performance. To address these issues, this article is divided into a two-step process. The first step is the development of a database with important joint experimental/analytical and numerical research on composite connections. The result of this first step is a data set summarized in Appendix A, which describes the range of variables and significant observations from one hundred and thirty-five tests found in the open literature. This data set (a) provides the starting point for a future robust calibration and verification database for composite connection studies, and (b) served as the basis for a number of the modeling decisions made in the second part of the research. The second step is a numerical evaluation of CFTs-connections by 3D finite element modeling (FEM) subjected primarily to axial loads. Initially, a well described test in the literature is selected (Voth & Packer, 2012) and a preliminary but complex model of that test specimen is developed. This model is then compared against the test results, including unfilled and filled specimens. The modeling techniques developed, including material constitutive relations, are then refined and used to model three of the best-described tests in the literature (Chen et al., 2015; Huang et al., 2015; Sakai et al., 2004). This constitutes, essentially, a blind test of the modelling procedure and was applied to three very different connection geometries to assess the generality of the approach. Although the work did not address more complex loading situations, i.e., fatigue, fire and time-dependent effects such as creep or shrinkage, the authors believe that the modeling techniques developed will apply equally well in those cases with appropriate adjustments of the constitutive relations.

Each of the investigations documented the database defined the connection type according to its own criteria. For clarity, the authors have consolidated those into a few types and used the nomenclature shown in Table 1.

Table 2 shows the range of the variables for the 135 tests in the database. Many of the tests are at a small scale (1/5 scale and/or 200 mm or smaller) due to the difficulties of testing full-scale CFT specimens given their great strength and stiffness.

The behavior of CFT connections has been investigated through both analytical and experimental studies, initially focused on offshore structures for the North Sea and the Gulf of Mexico in the 1980s and later applied to buildings and bridges. Appendix A includes more variables and more detailed information on the studies. Additional details can be found in Wilches (2022), and for work in China up to 2012, in Zhao et al. (2013).

The investigations described in Appendix A considered joint experimental/analytical efforts, i.e., a validation of the experimental models is carried out using numerical models, considering different aspect ratios, different types of loads (axial compression and tension, plane flexure, out-of-plane flexure) and other parameters.

This research developed four numerical models for CFT connections, with the final goal of performing calibrations and verifications to suggest improvements to current design provisions. This paper limits itself to the description of the model of the experimental tests carried out by Voth and Packer (2012), which was calibrated and further verified by comparatives studies with the result from tests by Sakai et al. (2004), Chen et al. (2015), and Huang et al. (2015) (see Fig. 1).

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Voth and Packer (2012) conducted experimental and numerical investigations to analyze the performance of rigid branch plate-to-CHS (circular hollow section) connections with and without concrete infill, utilizing branch plates. The study also explored the behavior of non-orthogonal or skewed plate-to-CHS connections, including T-type and X-type configurations, subjected to static tension or compression loads directly applied to the branch plate during testing. In contrast, Sakai et al. (2004) focused solely on an experimental program to determine the ultimate strength and fatigue life of tubular K-connections, both with and without concrete filling. Their testing involved cyclic loads inducing tension and compression simultaneously in the diagonals of the samples. Chen et al. (2015) conducted an experimental investigation evaluating the resistance and behavior of CHS T-connections under axial compression, considering both unfilled and concrete-filled configurations, with concave and straight chords. Finally, Huang et al. (2015) conducted experimental research examining the strength and failure modes of concrete-filled K-type tubular connections. They also investigated the impact of welded bolts on the inner surface of the chord member under pure compression. These studies collectively address various parameters, including structural configurations, types of loads, and material characteristics, as summarized in Table 3. The numerical models by Voth and Packer (2012), Sakai et al. (2004), Chen et al. (2015), and Huang et al. (2015) will hereafter be referred to as Models I, II, III, and IV, respectively.

The selection of these specimens was based on the fact that (1) they represent common types of tubular concrete-filled connections, (2) they vary greatly in their configutations, and (30 they represent four of the best-described tests in the literature.

The pre-processing and computations are performed on the ANSYS LS DYNA platform (ANSYS, 2020), using an explicit integration scheme with the double-precision LS DYNA smp solver (Hallquist, 2006). An explicit approach was selected because both the difference in material properties between steel and concrete and phenomena associated with contact, cracking, crushing, and slip required robust numerical stability. The analyses were run until failure was reached so that behavioral aspects in the highly non-linear and descending range could be captured.

Three-dimensional models were constructed to reproduce all the geometric properties and materials of the experimental test specimens, including details related both to weld type and geometry and the application of the loads. Figure 2 shows the models including boundary conditions. Symmetry was considered in one plane, and therefore Model II, Model III, and Model IV included half of the original geometry (Fig. 2b–d), while the Model I included a quarter of the original geometry (Fig. 2a). Model IV included shear studs, which considerably increased the number of DOFs (Fig. 2d).

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The geometric discretization of the different components is carried out using block structural meshes with reduced integration hexahedral elements with a high aspect ratio. Because hexahedron meshes are difficult to join, numerous discretization schemes were attempted to obtain the highest reliability in the results.

In the region of the weld bead, it is not possible to use hexahedral meshing, so tetrahedral meshing is used. Mesh size was established in all models using numerical convergence tests that indicated that model sizes woill range from 3 × 10⁵ nodes for Model I to 1 × 10⁶ nodes for Model IV. A close-up view of Model I near the plate including the weld is shown in Fig. 3a and a close-up view of Model IV near the diagonals, including the presence of shear studs, is shown in Fig. 3b to give an idea of the discretization level. The largest model, Model IV, had almost 6 × 10⁶ DOFs, with a mesh size of 4 mm for the concrete and 1.5 mm for the steel elements, respectively.

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In general, the numerical models are able to trace well the reported behavior of the selected specimens, including the transition points in the load-deformation curves, ultimate strength and maximum deformation. Figure 4 shows the comparisons of the load-deformation curves for the unfilled and filled connections modeled, while Fig. 5 shows the load-deformation curves for the filled connections with and without studs.

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Figures 4 and 5 indicate very good agreement considering that the shape of the curves for the four specimens varied substantially. Reiterating, the numerical model is only calibrated to the Model I specimen and the response of the Models II, III, and IV specimens are basically blind tests of the model’s capabilities. The initial stiffness and the entire curve for the numerical models show larger stiffness and slightly larger strengths than the experiments.

These differences can be attributed to the overstiffness common in most FE models, but also to (a) the non-linear adherence behavior of the concrete-structural steel interface, (b) the presence of residual stresses, and (c) initial imperfections in the test specimen. As no data are available for these conditions in the tests, they are not considered in the numerical model. Several previous studies have shown satisfactory resuls when ignoring residual stresses [among others (Bursi & Ballerini, 1996; Salari et al., 1998)]. Therefore, the results obtained in this investigation are deemed as reliable. Another observation from Fig. 4 is that the filled connections seem to show a better match. This is probably due to the lesser influence of local buckling in those specimens.

Figure 5 shows the effect of shear studs on the structural behavior of Model IV. The shear studs increased the resistance, stiffness and ultimate deformation of the connections significantly. The model is capable of tracking these changes well.

Figure 4 also illustrate important behavioral milestones for each model, such as initial steel yielding in section, high stress concentrations around the weld perimeter, strain in strain concentration areas reaching 10- and 20-times yield strain, steel–concrete rupture, concrete cracking in tension, steel reaching strain hardening, formation of local buckles, steel crack formation and controlling mechanism at maximum strength. There is a very good match both in terms of strength and deformation as to when these milestones are reached.

A very detailed discussion of the behavior of all specimens is not possible given space limitations, but two examples will be given to demonstrate the model’s capabilities. The first example is shown in Fig. 6, which illustrates the variation of the stresses and strains for the unfilled and filled Voth specimens. For the unfilled specimen, the plot at 1 mm (Point 1, Fig. 6a) shows that most of the specimen was in the elastic range but substantial stress concentrations are already presented. For the specimen filled at 0.1 mm (Point 1, Fig. 6b) the sample is in the elastic range and no stress concentrations are present. The unfilled specimen begins to yield at 4 mm (as indicated by Point 2 in Fig. 6a), displaying slight buckling in the tube and the emergence of stress concentrations in the weld. Conversely, the specimen filled at 0.5 mm (Point 2, Fig. 6b) remains within the elastic range but exhibits the initial signs of stress concentrations. In Fig. 6a, point 3 (located at 14 mm), a pronounced buckling of the tube becomes apparent, particularly in the lower section where the load is applied. The filled specimen at 1 mm (Fig. 6b, Point 3; note the large difference in the horizontal scale) shows that rupture has begun at the steel–concrete interface in the weld between the plate and round section. Beyond Point 3, the unfilled specimen continues to exhibit increased resistance, reaching deformations of approximately 40 mm and 65 mm at Points 4 and 5, respectively. In the case of the filled sample, there is a notable rupture in the steel–concrete interface, and significant stress concentrations around the tube can be observed (as seen in Points 4 and 5, Fig. 6b). It's crucial to highlight that at Point 5, the filled specimen achieves its peak level of resistance. In the end, the unfilled specimen experiences failure at Point 6, reaching a strain of 75 mm (as shown in Fig. 6a), whereas the filled.

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specimen (Point 6, Fig. 9b) fails at a strain of 6 mm.

The second example is shown in Fig. 7, which illustrates the sequence of the variation of the stresses and strains for the unfilled Sakai specimen at 1, 2, 8, 18, 27 and 30 mm of deflections (Fig. 7a). Like the Voth specimen at 1 mm, most of the specimen is shown to be in the elastic range; however, at 8 mm, buckling at the diagonal joint of the chord begins. In the filled specimen (Fig. 7b), the concrete does not suffer any damage, and this agrees with what was observed in the experimental tests (Sakai et al., 2004). Only after point 1 does the concrete begin to crack in the diagonal-chord interface; at this point the steel has already undergone large deformations to the point that it has already detached from the concrete. At point 2, the detachment of the steel and the concrete can be clearly seen.

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It is important to note that the design philosophy of composite connections is that they reach the ultimate strength specified in the codes, regardless of the type of failure or the behavior that occurs. This means that both the steel and concrete reach very large strains such that slip does not prevent the achievement of almost the full plastic capacity of the sections. Taking the above into account, Tables 4 and 5 show the comparisons of the ultimate strengths for the specimens examined. The finite element models were able to adequately predict the ultimate strengths of the connections unfilled and filled with concrete.

Figures 8, 9, 10 and 11 show excellent visual correlation when comparing the deformation responses. The Model I with the connection without concrete (Fig. 8a,b) shows that the deformation of the specimen could be reproduced numerically to very large deformations and agree with the results of Voth and Packer (2012). The contours of the von Mises stress plots (Fig. 8c,d) indicate that the greatest stresses occur in the upper part of the specimen. Figure 8e shows that the cross-section is deformed into a heart shape by the way the load is applied and the boundary conditions imposed. In the Model I with the concrete-filled chord (Fig. 8f,g), the experimental tests do not explicitly show the detachment of the steel tube from the concrete; however, this can be inferred by the way the specimen is deformed (Fig. 8f-h). The stresses are concentrated in the perimeter part of the weld (Fig. 8h,i), while the concrete does not suffer damage. Figure 8j shows that the steel tube is detached from the concrete just below the load plate and the weld.

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In the unfilled Model II, one diagonal member is in compression and the other diagonal member is in tension, resulting in plastic deformation near the weld joint in the diagonal member being compressed (Fig. 9a,b). Figure 9c,d shows the von Mises stresses, with maximum values at the vertex of the diagonals and the weld as expected. Figure 9e shows that the cross-section is only moderately damaged. In the model of Sakai et al., the concrete is not damaged in the concrete-filled chord and diagonals (Fig. 9f,g). However, it is observed that the steel detaches from the concrete at the vertex of the compression member (Fig. 9h,i). The cross-section of the concrete at the ends of the chord does not suffer deformations (Fig. 9j). In this type of connection, the compression member is the most vulnerable element.

In the unfilled Model III, a plasticization of the chord occurs around the vertical member (Fig. 10a,b). The von Mises stresses are about equal along the chord and the vertical member, and they are almost zero at the ends (Fig. 10c,d). The cross-section does not suffer any significant distortion (Fig. 10e). For the specimen with the concrete-filled chord, the numerical model does not accurately show the yielding that occurs in the vertical member. This is probably due to the lack of modeling of residual stresses and initial imperfections in the test (Fig. 10f,g). Figure 10 h,i show that the concrete does not suffer damage, as well as deformations of the cross-section of the chord (Fig. 10j).

Finally, in the Model IV for the connection without studs, bulges were observed at the end of the compression brace (Fig. 11a,b). Figure 11c,d show the von Mises stresses, with maximum values at the end on the compression brace and the weld as expected. Figure 11e shows that the chord cross-section that did not suffer any distortion. For the connection with studs on the interior surface, the model shows a similar failure mode as that without concrete (Fig. 11f,g). However, it is observed that the steel detaches from the concrete at the vertex of the tension brace member (Fig. 11h, i). The cross-section of the concrete at the ends of the chord does not suffer deformations (Fig. 11j).

Since the concrete was not seriously damaged in the specimens tested, the authors considered it convenient to demonstrate that the models were able to capture the failure in the concrete. Therefore, the model of Sakai et al. (2004) was subjected to twice the original displacement of the experimental test, that is, 60 mm. Figure 12 shows the damage suffered by the model through the plot of the plastic volumetric strain, which is contained within the output data of the concrete material MAT_072REL3 (historical variable 5). Figure 12 indicates that the concrete in both diagonals (tension and compression) as well as that in the central part of the chord suffered extensive damage.

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A database on experimental, analytical and numerical models for composite connections is described in the paper and shown in Appendix A. An overview reveals that the previous studies mainly focused both on the influence of concrete filling on the structural behavior and the numerical simulation of composite connections. An important contribution from the data Appendix A is what the authors believe is the first comprehensive database on experimental tests for this kind of connection. The authors intend to keep developing this database by adding more tests as they become available as well as contacting the researchers that have conducted the tests described therein in order to obtain more information relevant to numerical modeling (primarily more detailed material stress–strain information).

The initial results from the proposed numerical model indicate that it can reproduce the most important behavioral aspects observed in the tests, such as the buckling of the thin unfilled specimens, the effect of partial infilling, and the evolution of deformation and strength. The ability of the models to trace the transition points in load-deformation curves will also lead to the inference that the model can track well the steel–concrete interaction. The results also highlight the great advantages that infilling the connection provides in terms of both delaying buckling and more fully utilizing the strength and stiffness of the steel.

It should be noted that the nature and extent of the damage suffered may vary due to the geometric characteristics and load application in each particular connection. Thus, it is difficult to generalize the response and the damage evolution from a particular connection to those of all the specimens shown in the database. Detailed numerical or experimental studies are needed to realistically simulate the response and damage of any given connection.

Currently, the authors are using the model in numerical simulations using optimization processes to determine the most important parameters that influence structural behavior of the CFTs-connections. The intent is to identify the governing structural parameters and find experimental data that will highlight their importance. In particular, current efforts are focused on determining the best numerical ranges for the parameters that affect significantly the contact between the steel and the concrete; those values appear to be in a range of 1–5% of the value of the resistance to compression of the concrete.

In the future, the models will be used to realistically model the performance of composite connections under static and cyclic loads, to evaluate parametrically variables that are difficult or costly to determine experimentally, to assess behavior under multi-states of stress, to assess damage evolution between the contact surface between the steel and concrete, to determine the effect of embedded steel sections and mechanical shear connector, and to understand the role of stress concentration factors and residual stresses from welding.