Research on seismic behavior of special-shaped CFST column to H-section steel beam joint

Abstract

To investigate the seismic behavior of joint between special-shaped concrete-filled steel tubular (CFST) column and H-section steel beam, a pseudo-static test was carried out on five specimens with scale ratio of 1:2. The investigated factors include stiffening types of steel tube (multi-cell and tensile bar) and connection types (exterior diaphragm and vertical rib). The failure modes, hysteresis curves, skeleton curves, stress distribution, and joint shear deformation of specimens were analyzed to investigate the seismic behaviors of joints. The test results showed the connections of exterior diaphragm and vertical rib have good seismic behavior and can be identified as rigid joint in the frames with bracing system according to Eurocode 3. The joint of special-shaped column with tensile bars have better seismic performance by using through vertical rib connection. Furthermore, a finite element model was established and a parametric analysis with the finite element model was conducted to investigate the influences of following parameters on the joint stiffness: width-to-thickness ratio of column steel tube, beam-to-column linear stiffness ratio, vertical rib dimensions, and axial load ratio of column. Lastly, preliminary design suggestions were proposed.

Keywords

beam to column joint finite element model pseudo-static test seismic behavior special-shaped concrete-filled steel tubular column

Introduction

The traditional rectangular column has column corners which protrude toward the inside of the rooms. The special-shaped column refers to a structural column with L-shaped, T-shaped or cross-shaped sections, and the column limbs are as thick as the wall (Figure 1). Concrete-filled steel tubular (CFST) columns have been widely applied in practical engineering owing to the excellent structural performance. The special-shaped column structure of CFST inherits the advantages of high bearing capacity and good ductility of CFST structure (Liu et al., 2018a). Meanwhile, the steel tube can be used as the formwork for concrete pouring and simplified the construction process. Compared with the traditional CFST column with circular, square, or rectangular cross-sections, the special-shaped column has smaller column limb dimension and has smooth connection with adjacent infilled walls. Therefore, it can avoid the column protruding from walls, utilizes the indoor space more efficiently, and have good architectural performance (Liu et al., 2019).

Figure 1.

Rectangular and special-shaped cross-sectional columns in frame structures: (a) rectangular cross-sectional columns and (b) special-shaped cross-sectional columns.

Beam-to-column joints are a weak but important part of the frame structure, especially affecting the performance of the entire structure under earthquake. Peng et al. (2018a, 2018b) proposed the new end-plate and new ring-bar reinforced connections betweenT-shaped CFST columns and RC beams with slab and carried out experimental and numerical studies on the seismic performance. A cyclic loading test on nine joint specimens of CFST columns and steel beams were conducted to investigate the failure modes and seismic behavior by Zhou et al. (2012). Xu et al. (2012) carried out experimental research on the seismic performance of T-shaped and cross-shaped CFST columns frame joints. The forms of special-shaped CFST column frame joint in the previous research mainly include interior diaphragm and exterior diaphragm. The joint with exterior diaphragms shows favorable ductility and high energy dissipation capacity, but it will extend to indoor space and interfere the indoor architectural function. On the contrary, the joint with interior diaphragms will not extend to indoor space, but it is not suitable for the case of small section column, such as special-shaped CFST column, which will reduce the quality of concrete pouring. Zhao (2017) proposed a vertical rib connector and conducted a pseudo-static test of three frame specimens. The specimens showed good seismic performance, but the application of vertical rib connector in non-lattice CFST columns was not studied. The seismic research and finite element analysis on the four CFST column and H-section steel beam frame joints with vertical ribs were conducted by Liu et al. (2017). But the tensile bars in joint panel zone are insufficient to transfer internal force of steel beam since the vertical rib failed to pass through the joint panel zone.

In this paper, the form of vertical ribs was improved and the special-shaped multi-cell CFST column was adapted. The special-shaped CFST column to H-section steel beam joint with vertical ribs we proposed has the advantages of direct load transfer path, simple configuration, convenient fabrication process, and minimum interference in indoor space. The area with low stress at the convex corner of the exterior diaphragm connection adopted in our research was reduced to minimize the interference to indoor space, meanwhile its good mechanical behavior was also guaranteed. To further analyze the seismic performance of special-shaped CFST column frame joints, five types of special-shaped CFST column to H-shaped steel beam frame joints were tested, including two exterior frame joints and three interior frame joints. Through the pseudo-static test, the bearing capacity, stiffness, stress distribution, and shear deformation of joint panel zone were analyzed. A finite element model with software ABAQUS, verified by experimental results was established to study the following parametric influence on joint stiffness: width-to-thickness ratio of column steel tube, beam-to-column linear stiffness ratio of, vertical rib dimensions, and axial load ratio of column. Lastly, preliminary design suggestions were proposed, which provides reference for the practical application and popularization of special-shaped CFST column to H-shaped steel beam frame.

Experimental design

General information of specimens

Five specimens of CFST special-shaped column to H-shaped steel beam frame joint with the scale ratio of 1/2 were designed in the experiment. Two stiffening types of steel tube (multi-cell and tensile bar) and two connection types (exterior diaphragm and vertical rib) were studied. The axial load level (n) of 0.6 was adopted for all specimens. The specific parameters of specimens are shown in Table 1.

Table 1.

The details of specimens.

Specimen	Joint position	Stiffening type of column	Type of connection	n
T-1	Exterior joint	Tensile bar	Exterior diaphragm	0.6
T-2	Exterior joint	Tensile bar	Vertical rib (non through)	0.6
C-1	Interior joint	Multi-cell	Vertical rib	0.6
C-2	Interior joint	Multi-cell	Exterior diaphragm	0.6
C-3	Interior joint	Tensile bar	Vertical rib (through)	0.6

C stands for interior joint and T stands for exterior joint.

The cross-sectional configuration and dimensions of special-shaped CFST column to steel beam joint specimens are shown in Figure 2. The special-shaped multi-cell CFST column was welded at the concave corners with four seamless steel tubes (Figure 2(c)). The internal tensile bars with diameter of 8 mm and vertical spacing of 100 mm were welded at the concave corners and on the steel plate with large width-to-thickness ratio to prevent local buckling of steel tube in the special-shaped CFST column (Figure 2(d) and (e)). Besides, the limb width of each cross section is 100 mm and the sectional depth-to-width ratio is 3:1.

Figure 2.

Dimensions of specimens (dimension unit:mm): (a) muti-cell (cross-shaped), (b) tensile bar (cross-shaped), (c) tensile bar (T-shaped), (d) interior joint with exterior diaphragms, and (e) exterior joint with vertical ribs.

Figure 3 exhibits the connection details of specimens. The vertical rib connected the beam flange and column steel tube by fillet welds. Two types of vertical rib connection details (through joint and non-through joint) were adopted in the tensile bar stiffened columns. Only non-through vertical rib was employed in the multi-cell column for its built-in steel plate can transfer joint shear force effectively. The non-through vertical rib only needs to be welded with side face of the tube, while the through vertical rib needs to pass through the joint panel zone and be welded with the side faces of tube. To effectively transfer internal force of beam, the thicknesses of exterior diaphragm and vertical rib are the same with that of beam flange.

Figure 3.

The details of specimens (dimension unit:mm): (a) specimen T-2, (b) specimen C-1, (c) specimen C-3, (d) specimen T-1, and (e) specimen C-2.

Material properties

According to Code for design of concrete structures (GB 50010-2010, 2010), standard plain concrete cubes were designed and tested. The concrete prismatic compressive strength f_ck for exterior joint specimens and interior joint specimens were calculated as 44.2 and 33.0 MPa respectively. According to Chinese National standard—metallic materials-tensile testing at ambient temperature GB/T 228.1-2010, 2010, mechanical properties of steel tube, steel plate and reinforcement were tested and listed in the Table 2.

Table 2.

Material properties of steel plate and reinforcement.

Component	Thickness/diameter (mm)	f_y (MPa)	f_u (MPa)	E (MPa)
Beam flange	7.6 (7.4)	260 (318)	428	194,804
Beam web	5.7 (4.4)	444 (317)	511	205,100
Column tube	3.7 (1.9)	304 (225)	453	184,855
Reinforcement	8.0 (6.5)	444 (375)	623	206,758
Exterior diaphragm	7.6 (7.4)	260 (318)	428	194,804
Vertical rib	7.6 (7.4)	260 (318)	428	194,804

The values in the brackets are the material properties of the exterior joint specimens.

Loading program and measuring scheme

Figure 4(a) shows loading program of the experiment. The loads applied on the column of specimen include constant vertical compressive load and cyclic horizontal loads (or displacements). All the beam and column ends were pinned to the experimental devices to satisfy the boundary condition of inflection points in frame structures. Lateral supports were provided to prevent the out-of-plane movement of specimens. According to Specification for seismic test of buildings (JGJ/T 101-2015, 2015), the cyclic horizontal loading scheme in Figure 4(b) is determined as force-displacement hybrid loading scheme. When reaching the yield load, the loading scheme is transferred to displacement-controlled loading scheme. The displacement increment is 0.5% of the floor height. The loading direction toward reaction wall was designated as positive direction. When the horizontal load drops below 85% of its peak bearing capacity, the test terminated.

Figure 4.

The loading devices and loading scheme: (a) experimental set-up and (b) horizontal loading scheme.

The configuration of measurements is shown in Figure 5(a). Two LVDT displacement sensors were used to measure the horizontal displacement of the top and bottom hinges of the column respectively, and two cross-arranged YHD displacement meters were placed at the joint panel zone to measure its shear deformation. Four inclinometers were placed closely to the joint panel zone to measure the rotation angles of beam and column’s plastic hinges. Strain gauges were installed on the beam flange, the vertical rib, and the exterior diaphragm to measure the stress development. Strain rosettes were placed in the plastic hinge region of beam web and the joint panel zone to measure the strain distribution and shear deformation. The arrangement of strain gauges is shown in Figure 5(b).

Figure 5.

Measurement program: (a) diagram of measurement and (b) the arrangement of strain gauges.

Discussion on the test results

Test phenomena

Specimen T-1

The loading scheme was switched to displacement loading control when the horizontal load reached yield load of 20 kN. The horizontal load at column top reached peak value at the inter-story drift ratios α of 1.30% (positive direction) and −1.34% (negative direction). When the inter-story drift ratio α reached −1.39%, the fillet weld between the beam upper flange and front surface of the steel tube cracked (Figure 6(a)). When the inter-story drift ratio α reached −2.81%, the butt weld cracked at the sharp corners of the exterior diaphragm (Figure 6(b)). After the test, the steel tube in the joint panel zone did not buckle significantly and the concrete in the joint panel zone was intact when the steel tube was removed (Figure 6(c)). The failure mode of specimen T-1 can be judged as beam plastic hinge failure based on the test phenomenon and the following analysis of beam bearing capacity in Table 4.

Figure 6.

The experimental phenomenon of T-1: (a) inter-story drift ratio = −1.39%, (b) inter-story drift ratio = −2.81%, and (c) concrete in joint panel zone.

Specimen T-2

The loading scheme was switched to displacement loading control when the horizontal load reached yield load of 20 kN. The horizontal load at column top reached peak value at the inter-story drift ratio α of 1.07% (positive direction) and −0.92% (negative direction). When the inter-story drift ratio α reached −1.39%, the steel tube near the upper vertical rib appeared buckling (Figure 7(a)). Eventually, the steel tube in the joint panel zone seriously buckled (Figure 7(b)). It was observed that the crushing area of concrete in the joint panel zone of surface 5 was in an X shape after the steel tube was removed (Figure 7(c)). The ultimate failure mode of the specimen T-2 can be determined as the joint panel zone failure.

Figure 7.

The experimental phenomenon of T-2: (a) inter-story drift ratio = −1.39%, (b) inter-story drift ratio = −2.79%, and (c) concrete in joint panel zone.

Specimen C-1

The loading scheme was switched to displacement loading control when the horizontal load reached yield load of 40 kN. The horizontal load at column top reached peak value at the inter-story drift ratio α of 1.45% (positive direction) and −1.5% (negative direction). When the inter-story drift ratio α reached 3.00%, slight compression buckling occurred at the junction of compression flange and vertical rib (Figure 8(a)). When the inter-story drift ratio α reached 3.78%, the flange at the junction of the lower beam flange and the vertical rib cracked as shown in Figure 8(b). Due to the asymmetric cracking on the flange, the H-shaped steel beam obviously deflected out of plane, so the test terminated. After the test, the steel tube in the joint panel zone was removed, and the concrete in the joint panel zone was intact (Figure 8(c)).

Figure 8.

The experimental phenomenon of C-1: (a) inter-story drift ratio = 3.00%, (b) inter-story drift ratio = 3.78%, and (c) concrete in joint panel zone.

Specimen C-2

The loading scheme was switched to displacement loading control when the horizontal load reached yield load of 30 kN. Meanwhile, the strain at the flange near the junction of the beam flange and the exterior diaphragm reached the yield strain. The horizontal load at column top reached peak value at the inter-story drift ratio α of 1.55% (positive direction) and −1.56% (negative direction). The butt weld between the upper flange of the left beam and the exterior diaphragm suddenly cracked when loading to the inter-story drift ratio α of 3.42% due to the initial imperfection in the weld (Figure 9(a)). Besides, the stress concentration at the junction of the beam flange and the exterior diaphragm and the accumulative plastic deformation under cyclic loadings also intensified the cracking of the butt weld. After the test, the steel tube in the joint panel zone was removed, and the concrete in the joint panel zone was intact (Figure 9(b)).

Figure 9.

The experimental phenomenon of C-2: (a) inter-story drift ratio = 3.42% and (b) concrete in joint panel zone.

Specimen C-3

The loading scheme was switched to displacement loading control when the horizontal load reached yield load of 30 kN. The horizontal load at column top reached peak value at the inter-story drift ratio α of 1.65% (positive direction) and −1.43% (negative direction). When loading to the inter-story drift ratio α of −3.05%, the upper flange of the left beam was slightly buckled under compression (Figure 10(a)). When the inter-story drift ratio α reached −4.44%, the beam flange cracked close to the original weld cracking position on the right beam, and the crack developed along the beam width, as shown in Figure 10(b). After the test, the steel tube in the joint panel zone was removed, and the concrete in the joint panel zone was intact (Figure 10(c)).

Figure 10.

The experimental phenomenon of C-3: (a) inter-story drift ratio = −3.05%, (b) inter-story drift ratio = −4.44%, and (c) concrete in joint panel zone.

In summary, the failure mode of the specimens was mainly the failure of plastic hinge at beam end and the damage of the specimens mainly concentrated on the beam flange. The exterior joint specimen T-2 showed more severe damages in joint panel zone than other specimens since it suffered joint panel zone failure in the later stage of the test.

Load-displacement curves

The horizontal load P-inter story drift ratio α hysteretic curves at the column top and skeleton curves measured in the test are shown in Figure 11. The joint specimens mainly have the plastic hinge at the beam end, and it can be seen that the hysteresis curves of the test specimens are plumper.

Figure 11.

Horizontal load-inter story drift curves of specimens: (a) T-1, (b) T-2, (c) C-1, (d) C-2, (e) C-3, and (f) skeleton curves.

The horizontal loads at the column top of specimens T-1 and T-2 are basically the same. However, the horizontal load at the column top of specimen C-3 is slightly higher than those of specimens C-1 and C-2, due to that the vertical rib pass-through joint panel zone to guarantee transmission of the tension force in the beam flange. Based on the load-displacement skeleton curves, the characteristic loads of each specimen and the corresponding inter-story drift ratios are listed in Table 3. The yield point (P_y, α_y) of the curve is determined by the geometric drawing method (Tang, 1989); (P_p, α_p) is the peak point of the curve; (P_u, α_u) is the ultimate point of the curve. The ultimateinter-story drift ratio α of interior joint specimens is 2.41%–3.19% and the ductility coefficient of interior joint specimens is 2.69–3.07. It can be seen all interior joint specimens show good deformation ability. While, the ultimate inter-story drift ratio α and the ductility coefficient of exterior joint specimens are slightly lower than those of interior joint specimens because the exterior joint specimens suffered the brittle failure in the later stage of the test.

Table 3.

The horizontal load at column top and inter-story drift ratio at feature points.

Specimen	Direction	Yield point		Peak point		Ultimate point		Ductility factor γ_u/γ_y
Specimen	Direction	P_y (kN)	α_y (%)	P_p (kN)	α_p (%)	P_u (kN)	α_u (%)	Ductility factor γ_u/γ_y
T-1	+	17.5	0.88	19.9	1.30	16.9	1.66	1.89
T-1	−	−16.1	−0.81	−18.1	−1.34	−14.9	−1.71	2.11
T-2	+	17.9	0.82	19.7	1.07	16.8	1.55	1.89
T-2	−	−19.3	−0.76	−21.2	−0.92	−18.0	−1.41	1.86
C-1	+	46.9	0.84	53.4	1.45	45.4	2.41	2.87
C-1	−	−42.9	−0.89	−48.4	−1.50	−41.1	−2.48	2.79
C-2	+	46.6	0.97	53.0	1.55	45.1	2.94	3.03
C-2	−	−43.2	−1.04	−51.1	−1.56	−43.4	−2.80	2.69
C-3	+	56.8	1.03	63.5	1.65	54.0	3.16	3.07
C-3	−	−53.4	−1.05	−60.4	−1.43	−51.3	−3.19	3.04

Referred to American code (ANSI/AISC 360-2010, 2010), European code (BS EN 1993-1-1, 2005), and Chinese code for design of steel structures (GB 50017-2017, 2017), the test and design bending capacity of H-shaped steel beam are compared in Table 4. V_y is the vertical yield load and V_p is the vertical peak load of beam obtained from the experiment. The vertical peak load V_p of all specimens exceed the beam full plastic strength V_cp and code-determined strengths (V_AISC, V_BS, and V_GB) due to steel hardening. The beam full plastic strength V_cp was calculated based on the full section plastic criterion. The test bearing capacity of specimens is 1.21–1.65 times of the calculated bearing capacity in relevant standards. It can be seen that all joint specimens in this paper meet the requirements of the specification and have engineering application value.

Table 4.

The comparison between load of specimens at fearture point and load according to codes.

Specimen	Direction	V_y/V_cy	V_p/V_cp	V_p/V_AISC	V_p/V_BS	V_p/V_GB
T-1	+	1.32	1.30	1.42	1.30	1.39
T-1	−	1.28	1.29	1.41	1.29	1.38
T-2	+	1.26	1.28	1.40	1.28	1.37
T-2	−	1.24	1.24	1.36	1.24	1.33
C-1	+	1.26	1.35	1.50	1.35	1.47
C-1	−	1.21	1.30	1.44	1.30	1.41
C-2	+	1.19	1.25	1.39	1.25	1.36
C-2	−	1.15	1.21	1.36	1.21	1.32
C-3	+	1.39	1.49	1.65	1.49	1.62
C-3	−	1.35	1.43	1.59	1.43	1.56

Notes: V_cy = M_y/l, M_y is the moment at yielding of the extreme fiber of beam end and l is the beam span; V_cp = M_p/l, M_p is the plastic bending moment of beam end and l is the beam span; V_AISC is the strength of beam determined from AISC 360-2010 (LRFD); V_BS is the strength of beam determined from BS EN 1993-1-1 (2005); V_GB is the strength of beam determined from GB 50017-2017.

Stress analysis

According to the calculation method in reference (Chen, 2003; Cheng et al., 2019; Hu, 2014), the strain measured by strain gauges were converted into stress. The calculated stress are shown in Figure 12, and the sections A-A and B-B are marked in sure 5(b). The stress on the A-A section of the beam flange reached yield. The stress on the B-B section is significantly lower than those of the A-A section, for the load on the B-B section was mostly transmitted to the connectors. However, the Mises stress of the mid-height web of the beam did not reach the yield stress, indicating that the steel beam was in bending failure. It can be seen that the stresses on the steel tube of the column web (B1, B2, and B3) are greater than those on the steel tube of the column flange (A1, A2, and A3), for the load of the beam is directly transferred to the column web. Meanwhile, the column flange coordinated its deformation with column web, in order to contribute to shear bearing capacity.

Figure 12.

The stress of the specimens: (a) flange of the exterior joint, (b) flange of interior joint, (c) joint panel zone of C-1, (d) web of exterior joint, (e) web of interior joint, and (f) joint panel zone of T-1.

Joint stiffness analysis

Referring to the method for judging the stiffness of a joint in Eurocode 3, the M/M_p—ϕ/ϕ_p curve at the beam end was used to analyze the joint stiffness, which was shown in Figure 13, where M is the bending moment at the beam end; M_p is the plastic bending moment; ϕ is the rotation angle of beam end, which is the difference between the inclinometers I-1 and I-3. I-1 and I-3 are arranged at the beam end and column end close to the joint panel zone respectively (Figure 5); ϕ_p = M_pL_b/(EI_b), in which L_b is the beam span (distance between the axes of two adjacent columns); I_b is the moment of inertia of the beam section. Three types of joints can be identified as rigid joint in the frames with bracing system according to Eurocode 3.

Figure 13.

The M/M_p–ϕ/ϕ_p curves of specimens.

Finite element analysis

Modeling and verification

In order to further study the bearing capacity and stiffness of the joint specimens, a finite element software ABAQUS was used to model the specimens and to conduct parametric analysis.

Material constitutive models

The Concrete Damage Plasticity is employed in the software, and five parameters in this concrete constitution, describing its yield function and plastic flow procedure, are taken as following values: the dilation angle is 35°; the eccentricity is 0.1; the f_b0/f_c0 is 1.16; the K is 0.667; the viscosity parameter is 0.0001 (Liu et al., 2018b, 2020).

The elastic modulus of concrete is calculated as formula (2):

E_{c} = 4730 \sqrt{f_{c}}

(2)

where f_c is the prismatic compressive strength of the concrete. The Poisson’s ratio of the concrete µ is taken as 0.2.

The uniaxial stress-strain curve employs the research results of reference (Liu, 2005). The compressive stress-strain curve of concrete is expressed as formula (3):

y = {\begin{matrix} 2 x - x^{2} & (x \leq 1) \\ \frac{x}{β_{0} {(x - 1)}^{η} + x} & (x > 1) \end{matrix}

(3)

where x = ε/ε₀; y = σ/σ₀; ε₀ = ε_c + 800ξ^0.2/10⁶; σ₀ = f_c; ε_c = (1300 + 12.5f_c)/10⁶; η = 1.6 + 1.5/x; β₀ = f_c^0.1/(1.2 $\sqrt{1 + ξ}$ ); ξ (=f_yA_s/f_cA_c) is the confinement coefficient of the concrete-filled steel tube column; f_y is the yield strength of steel tube; A_s is the cross-sectional area of steel tube and A_c is the cross-sectional area of concrete.

The tensile stress-strain curve of concrete is expressed as formula (4):

y = {\begin{matrix} 1.2 x - 0.2 x^{6} & (x \leq 1) \\ \frac{x}{0.31 \cdot σ_{p}^{2} \cdot {(x - 1)}^{1.7} + x} & (x > 1) \end{matrix}

(4)

where x = ε/ε_p; y = σ/σ_p; ε_p = 43.1σ_p; σ_p = 0.26(1.25f_c)^0.667.

The stress-strain curve of steel, including elastic, elastic-plastic, plastic, hardening, and fracture stages (Wang et al., 2014), is expressed as formula (5):

σ = {\begin{matrix} E_{s} ε & ε \leq ε_{e} \\ - A ε^{2} + B ε + C & ε_{e} < ε \leq ε_{e 1} \\ f_{y} & ε_{e 1} < ε \leq ε_{e 2} \\ f_{y} [1 + (\frac{f_{u}}{f_{y}} - 1) \frac{ε - ε_{e 2}}{ε_{e 3} - ε_{e 2}}] & ε_{e 2} < ε \leq ε_{e 3} \\ f_{u} & ε_{e 3} \leq ε \end{matrix}

(5)

where E_s is the elastic modulus of steel; ε_e1 = 10ε_e; ε_e2=10ε_e1; ε_e3=10ε_e2; A=0.2f_y/(ε_e1–ε_e)²; B = 2Aε_e1; C = 0.8f_y + Aε_e²-Bε_e.

Finite element type, boundary condition, and loading scheme

The finite element model consisted of three element types available in ABAQUS: (1) Shell element with four-node general linear reduced integration (S4R) for the steel tubes, steel beams, exterior diaphragms, and vertical ribs; (2) Two-node linear beam element (B31) for the tensile bars; (3) Three-dimensional solid element with eight-node linear reduced integration (C3D8R) for the concrete. The specific specimen dimensions, boundary conditions, and loading scheme were the same as those in the test.

Steel tube-concrete interface

A “surface to surface contact” in ABAQUS, including normal property and tangential property, was adopted between the steel tube and concrete. A “hard contact” was used to simulate the normal interaction of the interface, in which the pressure can be transferred and the separation was allowed between steel tube and concrete. A coulomb friction model was adopted in the tangential direction, with the friction coefficient being 0.6 and the maximum friction stress being 6 MPa (Schneider and Alostaz, 1998). The beams and columns are connected by “Merge.” The vertical ribs were bound to the beam flange and column steel tube to simulate the welding interaction, and the binding area was selected using the Node region.

Verification of FE model

Figure 14 illustrates the comparison of M/M_p—ϕ/ϕ_p curves and horizontal load P-inter story drift ratio α curves. The joint stiffness M/M_p—ϕ/ϕ_p curves between experiment and FE model are compared in Figure 16(a–c). The test and simulated joint stiffness are generally consistent with each other. The virtual displacement between the experimental setup and specimen resulted in the slight discrepancy in initial stiffness between test results and FE results. The M/M_p—ϕ/ϕ_p curve between test result and FE result do not agree well in later stage. The reason is that the rotation angle of beam end ϕ is calculated by the inclinometer fixed on the beam flange and the buckling of the beam flange will lead to a sharp increase of the inclinometer data. However, the judgment of the joint stiffness is based on the initial slope of the M/M_p—ϕ/ϕ_p curve according to Eurocode 3. Both test results and calculated results show the connections of exterior diaphragm and vertical rib can be identified as rigid joint in the frames with bracing system. The finite element results are in good agreement with the test results, which verifies the reliability of the finite element model.

Figure 14.

Comparison of the experiment and FEM results: (a) M/M_p–ϕ/ϕ_p curve of C-1, (b) M/M_p–ϕ/ϕ_p curve of C-2, (c) M/M_p–ϕ/ϕ_p curve of C-3, (d) P-α curve of C-1, (e) P-α curve of C-2, and (f) P-α curve of C-3.

Figure 15 shows the comparison in specimen failure mode between the test and FE models. Both experiment and FE models show that the severe buckling of the column steel tube occurred in the joint panel zone of specimen T-1 (Figure 15(a)). The butt weld between the upper flange and the exterior diaphragm of the C-2 specimen damaged in the test, which reflects the stress of the upper flange at the left beam end is concentrated in the finite element calculation results (Figure 15(b)). The upper flange of the steel beam of C-3 specimen has local buckling in the FE model, which is consistent with the test phenomenon (Figure 15(c)).

Figure 15.

Comparison of failure modes between experiments and FEM results: (a) T-1, (b) C-2, and (c) C-3.

Parametric analysis and design recommendations of joint stiffness

The finite element model was established to analyze the stiffness of the joints. The analysis parameters include height of vertical rib h₁ and h₂ (Figure 2), length of connection between vertical rib and flanges l₁, thickness of the vertical rib t, width-to-thickness ratio of the column steel tube b_c/t_c, and axial compression ratio of the column n.

The calculated results of the parametric analysis are shown in Figure 16. It can be seen that the width-to-thickness ratio of the column steel tube b_c/t_c has a significant effect on the initial and plastic stage stiffness of the joint; the parameter l₁ have a certain degree of influence on the initial stiffness, and have a more significant effect on the stiffness in the plastic stage; the parameter h₁ and the thickness t of the stiffener have a small effect on the initial stiffness of the joint and have a certain effect on the stiffness in the plastic stage; the column axial compression ratio n and the parameters h₂ have the smallest effect on the stiffness of the joint. There is a positive correlation between the joint stiffness and the vertical rib size (h₁, h₂, l₁, t), while the parameters b_c/t_c is negatively correlated with the joint stiffness, revealing that the joint stiffness mainly depends on vertical rib size and tube thickness.

Figure 16.

The parametric analysis of FE models: (a) parameter h_1, (b) parameter h_2, (c) parameter l_1, (d) parameter t, (e) parameter n, and (f) parameter b_c/t_c.

According to the calculated results of parametric analysis, to satisfy the design requirements of rigid joint in the frames with bracing system, the parameter h₁ should not be less than 0.5 times of beam width; the parameter h₂ should not be less than 0.2 times of beam width; the connection length l₁ between vertical rib and beam flange should not be less than 1.5 times of beam width; the thickness of vertical rib t should not be less than the thickness of beam flange, and the width-to-thickness ratio b_c/t_c of column steel tube should be less than 40.

Conclusions

This article describes and discusses the seismic behavior of special-shaped CFST column to H-shaped steel beam joints based on experimental and numerical study. The following conclusions can be drawn from the study:

All specimens formed plastic hinge at beam end, although exterior specimen T-2 suffered joint panel zone failure in the later stage of the test. The test bearing capacity of the beams in all specimens meet the related code requirements of America, Europe and China. It is suggested to adopt the through vertical ribs for the special-shaped column with tensile bars, to avoid the brittle failure of the joints.

The ductility coefficient of the interior joints is 2.69–3.07, indicating the interior joints have better seismic performance than the conventional RC joints. With reference to the Eurocode 3, vertical rib and exterior diaphragm joints meet the requirements for rigid joints in the frames with bracing system.

Based on the finite element analysis of the multi-cell CFST column with vertical rib connection, it is suggested that the width-thickness ratio b_c/t_c of the column steel tube should be less than 40; the thickness of the vertical rib t should not be less than the thickness of the beam flange; and the connection length l₁ between the vertical rib and the beam flange should not be less than 1.5 times of the beam width.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are very grateful to the support provided by Foundation of Key Laboratory of Structures Dynamic Behavior and Control (Ministry of Education) in Harbin Institute of Technology (Grant No. 30620180333), National Natural Science Foundation of China (Grant No. 51878098), and Research on bridge construction risk and control technology under complicated environment of Sichuan-Tibet Railway (Grant No. 2019YJ036).

ORCID iD

Yuanlong Yang

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