Behavior of large-scale connections between circular concrete-filled steel tubular columns and H-section steel beams

Abstract

Three large-scale connections between circular concrete-filled steel tubular columns and H-section steel beams were tested. The specimens include one connection with T-shaped stiffeners under static load and two connections, respectively, with T-shaped stiffeners and diaphragms (including interior and exterior diaphragms) under cyclic loads. During the test, the experimental phenomena were observed. The static properties of strength and ductility are calculated for static connection based on load–displacement curves, while the seismic properties of strength, ductility, and energy dissipation are analyzed for seismic connections based on hysteretic load–displacement curves. Combining experimental phenomena, mechanical properties, and stress development, the beam-hinge failure mode can be identified for all specimens. The measured beam strengths of specimens are compared with those predicted by the current AISC-360, EC4, and GB 50017-2017 codes. The study results show that all connections are reliable. A finite element model, established and verified with the experimental results, is used to perform parametric analysis. Furthermore, design suggestions of T-shaped stiffeners and diaphragms are proposed based on a parametric analysis.

Keywords

beam–column connection circular concrete-filled steel tubular diaphragm static and seismic behavior T-shaped stiffener

Introduction

Concrete-filled steel tubular (CFST) columns are practical structural components that have been widely used for several decades because of their excellent strength, ductility, and constructional convenience (Du et al., 2017; Sheet et al., 2013; Tang et al., 2017). The most important component of a CFST frame structure is beam–column connection (Fanaie and Moghadam, 2019; Lima et al., 2019; Varma et al., 2002; Wu et al., 2005). The seismic behavior of connection has a significant influence on the reliability of a building.

Because of the popularity of structures with CFST columns in applications, many research works on the behavior of connections between CFST columns and steel beams have been reported in the past three decades. Connection details can be generalized into two broad categories: connections that attach to the face of the steel tube only and connections that use elements embedded into the concrete core. Connections to the face of the steel tube include, for example, connections with stiffening rings (or diaphragms) (Park et al., 2005; Qin et al., 2014a; Wang et al., 2008, 2009) and connections with vertical stiffeners (Kimura et al., 2005; Roudsaria et al., 2018; Shin et al., 2008). Conclusions from these studies showed that these connection details exhibited good seismic performance. However, restricted by column size, these connection details are not applicable to large-section columns (much larger than beam sections) located at the lower floors of high-rise buildings. Connections with embedded elements include, for example, through-bolting with end plates (Li et al., 2009; Wang JF et al., 2009; Wu et al., 2007; Yao et al., 2008) and continuous structural steel components through the column (Nishiyama et al., 2004; Qin et al., 2014b, 2015; Wu et al., 2016). The test data indicated that embedding connection components into the concrete core could alleviate high shear demand on the tube wall, which may improve the seismic performance of the connections.

This article presents an in-depth study on the static and seismic behaviors of large-scale connections between circular CFST columns and H-section steel beams, based on a 468-m high-rise building project. The cross sections of column and beam on lower levels (B3-L4) are Φ2800 × 70 and H1500 × 600 × 40 × 60, respectively. Two types of connections (T-shaped stiffeners and diaphragms) are studied and compared. The strength, ductility, and other mechanical properties of specimens are analyzed in the experiments. A further parametric study is conducted with finite element model (FEM) to investigate the influencing parameters. Based on the parametric analysis, some design suggestions on the T-shaped stiffeners and diaphragms are proposed for actual engineering structures.

Experimental design

Details of specimens

Based on the real connections of T2 tower of Chongqing Shuison project, a total of three circular CFST column to H-section steel beam connection specimens were tested. The specimens include one static connection with T-shaped stiffeners (JS-1) and two seismic connections, respectively, with T-shaped stiffeners and diaphragms (JD-1 and JD-2). More detailed information of the test specimens including the dimensions and locations of strain gauges are, respectively, given in Table 1 and Figures 1 and 2.

Table 1.

Detailed parameters of experimental specimens.

Specimen	Reduced scale	Tube section	α (%)	Beam section	n	N (kN)
JS-1	1:4	700 × 18	11.1	H375 × 150 × 10 × 16	0.48	8000
JD-1	Column section (1:7) Beam section (1:5)	406 × 10	10.6	H300 × 120 × 8 × 12	0.33	1650
JD-2	Column section (1:7) Beam section (1:5)	406 × 10	10.6	H300 × 120 × 8 × 12	0.36	1930

α = steel ratio of concrete-filled steel tubular (CFST) column section; N = axial compressive load; n = N/(A_sf_y + A_cf_ck) = axial compression ratio of columns; A_s = area of steel tube; f_y = yield strength of steel tube; A_c = area of concrete; f_ck = prismatic compressive strength of concrete.

The 1/4 to 1/7 scale models of this article are determined by the limitations of the loading devices.

Figure 1.

Dimensions and arrangement of strain gauges of JS-1: (a) elevation drawing of JS-1 (mm) and (b) sectional view of JS-1 (mm).

Figure 2.

Dimensions and locations of strain gauges of JD-1 and JD-2: (a) elevation drawing of JD-1 and JD-2 (mm), (b) details of JD-1 (mm), and (c) details of JD-2 (mm).

Large reduced scales were adopted for static and seismic connections within the limit of experiment devices (Table 1). For JS-1, the axial compression ratio n of column is 0.48. For JD-1 and JD-2, the axial compression ratio n of columns is 0.33 and 0.36, respectively. Steel ratio α of CFST column is about 10%. The measured steel and concrete material properties of the specimens in material characteristic test are listed in Table 2. The prismatic compressive strength of concrete f_ck was converted from cubic compressive strength f_cu,m according to Chinese concrete code GB 50010-2010 (2010). The concrete cylinder compressive strength $f'_{c}$ is 0.79 f_cu,m in the concrete strength range of this article.

Table 2.

Material properties of steel and concrete.

Specimen	Steel				Concrete
	Components	Thickness (mm)	f _y (MPa)	f _u (MPa)	f _cu,m (MPa)	f _ck (MPa)
JS-1	Tube	17.8	267.7	423.1	27.5	18.4
	Flange	15.6	267.8	443.5
	Web	9.8	267.3	429.1
	Web of T-shaped stiffener	9.8	267.3	429.1
	Flange of T-shaped stiffener	13.6	275.2	450.2
JD-1	Tube	9.8	246.3	401.0	25.0	16.7
	Flange	11.6	240.5	387.1
	Web	7.7	238.3	404.1
	Web of T-shaped stiffener	7.7	238.3	404.1
	Flange of T-shaped stiffener	11.6	240.5	387.1
JD-2	Tube	9.8	246.3	401.0	28.7	19.2
	Flange	11.6	240.5	387.1
	Web	7.7	238.3	404.1
	Diaphragm	11.6	240.5	387.1

f _y = yield strength of steel tube; f_u = ultimate strength of steel tube; f_cu,m = compressive cubic strength of concrete.

The conventional concrete strength and steel strength are adopted due to the limitations of the loading devices.

Experimental device, measuring apparatus, and loading scheme

The experimental device, locations of measuring apparatus, and loading scheme for static loading test (JS-1) and seismic loading test (JD-1 and JD-2) can refer to author’s previous research (Li et al., 2018).

Static behavior of CFST column to H-section connection

Failure mode of specimen JS-1

The failure mode of specimen JS-1 is shown in Figure 3. When loading to 331.7 kN (corresponding vertical displacement was 6.78 mm to beam 1 and 8.31 mm to beam 2), the data of strain gauges showed that beam flanges reached yield strain. The loading process was finally stopped at a maximum beam displacement of 35 mm (beam 1) and 53 mm (beam 2), and the corresponding rotation angle of beams reached about 0.0467 and 0.0676 rad, which was large enough for engineering application. Because lateral supports could not fully prevent the torsion of beams, the final torsional angles of beams reached about 1° (beam 1) and 5° (beam 2). Besides, beam torsion led the ultimate load of beam 2 to be about 15.4% lower than that of beam 1. Meanwhile, there was no obvious phenomenon on steel tube during the whole test. Taking these aspects into consideration, the failure mode of JS-1 can be identified as beam-hinge failure.

Figure 3.

Failure mode of JS-1: (a) flexural deformation of steel beams, (b) torsional angle of beam 1, and (c) torsional angle of beam 2.

Load–deformation curve of specimen JS-1

The load–displacement curves and moment–rotation curves of beams in JS-1 are shown in Figure 4(a) and (b). The vertical shear load of beams kept increasing constantly from yield point to the completion of test, and the rotational angles of steel beams were largely developed (0.0467 rad for beam 1 and 0.0676 rad for beam 2). The shear capacity V_pp (520.08 kN) of beam web is greater than the calculated vertical plastic load V_pf (377.6 kN) of steel beam, which shows the failure mode of JS-1 can be identified as beam-hinge failure.

Figure 4.

Load–deformation curves and stress–load curves of specimen JS-1: (a) load–displacement curves of beams, (b) moment–rotation curves of beams, (c) the stress–load curves of beam 1, and (d) the stress–load curves of beam 2.

The mechanical properties of JS-1 and further comparison of vertical loads of steel beams between experiment and codes (ANSI/AISC 360-10, 2010; BS EN 1993-1-1:2005, 2005; GB 50017-2017, 2017) are given in Table 3. Because of strain hardening, the experimental ultimate vertical loads are approximately 34%, 24%, and 32% higher than those of ANSI/AISC 360-10 (2010), BS EN 1993-1-1:2005 (2005), and GB 50017-2017 (2017), respectively. Analysis above reveals T-shaped stiffener is a kind of practical connection between circular CFST and H-section beam and reliable enough to allow the beam achieve calculated plastic moment.

Table 3.

The mechanical properties of JS-1 and comparison with codes.

Beam number	V _y (kN)	V _u (kN)	M _y (kN m)	M _u (kN m)	Δ _y (mm)	Δ _u (mm)	θ _y (rad)	θ _u (rad)
1	331.7	493.1	270.3	384.3	6.8	35.1	0.0057	0.0467
2	320.1	417.3	238.6	326.9	8.3	53.2	0.0059	0.0676
Beam number	V _AISC (kN)	V _BS (kN)	V _GB (kN)	V _pf (kN)	V _u (kN)	V _u/V_AISC	V _u/V_BS	V _u/V_GB
1	340.0	365.6	345.1	377.6	493.1	1.45	1.35	1.43
2					417.3	1.23	1.14	1.21
Average						1.34	1.24	1.32

V _y = vertical yield load of steel beam; V_u = vertical ultimate load of steel beam; M_y = V_y × L = yield moment at the fixed ends of beam; L = length of beam; M_u = V_u × L = ultimate moment at the fixed ends of beam; Δ_y = displacement at the loading ends of beam corresponding to V_y; Δ_u = displacement at the loading ends of beam corresponding to V_u; θ_y = Δ_y/L = average rotational angle of beam corresponding to Δ_y; θ_u = Δ_u/L = average rotational angle of beam corresponding to Δ_u; V_AISC = vertical design load calculated according to AISC 360-2010 (load and resistance factor design (LRFD)); V_BS = vertical design load calculated according to BS EN 1993-1-1:2005 (2005); V_GB = vertical design load calculated according to GB 50017-2017 (2017).

Stress analysis

The elastic–plastic analysis method is adopted to analyze the stress of the steel component. According to this method, the stress along the thickness is small and can be neglected. Therefore, the steel plate can be treated as a plane-stress problem. Von Mises yield criterion is thus employed to describe the yielding behavior of the steel. Figure 4(c) and (d) illustrates the analysis results of JS-1, in which σ_z is the equivalent stress determined from the following equation

σ_{z} = \frac{\sqrt{2}}{2} \sqrt{{(σ_{v} - σ_{h})}^{2} + σ_{v}^{2} + σ_{h}^{2}}

(1)

where σ_v and σ_h are longitudinal stress and transverse stress of the steel plates, respectively. In Figure 4(c) and (d), the equivalent stress σ_z along the beam length reached the yield stress (the yield stresses of flange and web are 267.8 and 267.3 MPa, respectively). Since then, the growth rate of equivalent stress σ_z at mid-height of web was accelerated and reached yield stress (S23-2 in Figure 1(a)). The stress development shows that the whole sections of beams reached yield stress.

Seismic behavior of CFST column to H-section connection

Failure mode of specimen

Specimen JD-1

The failure mode of JD-1 is shown in Figure 5(a) and (b). When the story drift ratio reached about 0.88% corresponding to the top horizontal force at 171 kN in both positive loading and negative loading, the strain of beam flanges reached yield strain. When the story drift ratio reached about 3.3% corresponding to the top horizontal force at 182 kN in positive loading and at 174 kN in negative loading, the test was terminated due to large deformation of beams. Local bucklings on beam flanges were detected (Figure 5(a)), and fracture of welds was not detected during the test. Meanwhile, the steel tube had no obvious phenomenon during the test and concrete was intact in the joint zone (Figure 5(b)).

Figure 5.

Failure mode of specimens JD-1 and JD-2: (a) beam 1 of JD-1, (b) concrete in joint zone, and (c) beam 1 of JD-2.

The failure mode of JD-2 is shown in Figure 5(b) and (c). When the story drift ratio reached about 0.88% corresponding to the top horizontal force at 200 kN in positive loading and at 203 kN in negative loading, the strain of beam flanges reached yield strain. When the story drift ratio reached about 2.3% corresponding to the top horizontal force at 238 kN in positive loading and at 241 kN in negative loading, the test was terminated because of the serious weld cracking between exterior diaphragms and beam flanges (Figure 5(c)). Similar to JD-1, steel tube and concrete had no obvious phenomenon in the joint zone (Figure 5(b)).

Load–deformation curve

The horizontal load–displacement hysteresis curves of JD-1 and JD-2 are shown in Figure 6(a) and (b). Because there are almost no slips of T-shaped stiffener and interior diaphragm (Schneider and Alostaz, 1998), the hysteresis curves have no pinch effect and show good energy dissipation capacity and seismic performance.

Figure 6.

Load–displacement hysteresis curves and skeleton curves: (a) horizontal load–displacement hysteresis curves of JD-1, (b) horizontal load–displacement hysteresis curves of JD-2, (c) horizontal load–displacement skeleton curves of columns, and (d) moment–rotation skeleton curves of beams.

Strength, ductility, and stiffness classification

Figure 6(c) and (d) shows the skeleton curves of specimens. The mechanical properties of the specimens are listed in Table 5. Figure 6(c) and (d) shows that the stiffness, yield load, and peak load of specimen JD-1 are all smaller than those of specimen JD-2 as well as the yield bending moment and peak bending moment of the beam. However, the plastic deformation capacity of specimen JD-1 is obviously superior to that of specimen JD-2. This is mainly due to the strengthening effect of exterior diaphragms, thus resulting in the appearance of the plastic hinge of beam outside the exterior diaphragm zone. The welding cracks between exterior diaphragm and flange, caused by the stress concentration, lead to the worse ductility of specimen JD-2. Since the load of beam flanges is transmitted by diaphragms to column more effectively than T-shaped stiffeners, the moment capacity of beams of JD-2 is a little higher than that of JD-1 (Figure 6(d)). Because of strain hardening, the vertical peak loads of beams V_p are 64%–83% higher than the design value V_AISC in ANSI/AISC 360-10 (2010), 60%–68% higher than the design value V_BS in BS EN 1993-1-1:2005 (2005), and 75%–83% higher than the design value V_GB in GB 50017-2017 (2017). Besides, the experimental vertical loads of beams are approximately 64% higher than those corresponding to calculated plastic flexural capacity.

For the ductility analysis, there are normally two ways to define the ductility of a structure or member. One way is to use the ductility coefficients μ_p at the peak load, which is given by

μ_{p} = \frac{Δ_{p}}{Δ_{y}}

(2)

where Δ_p and Δ_y are the peak displacement and the yield displacement, respectively.

The other way is to calculate the ductility coefficient μ_u at the ultimate stage

μ_{u} = \frac{Δ_{u}}{Δ_{y}}

(3)

where Δ_u and Δ_y are the ultimate displacement and the yield displacement, respectively.

The tests of JD-1 and JD-2 were terminated before dropping to 85% of peak strength due to the failure of specimens. Therefore, the data Δ_u of JD-1 and JD-2 were not available and μ_p was used to evaluate the ductility of specimens. As shown in Table 4, both specimens show good ductile post-peak load behavior, and specimen JD-1 has better ductility. The elastic inter-story drift ratios of JD-1 and JD-2 are approximately 0.9%, which can fully satisfy the elastic deformation demand of 1/550 (0.18%) in Chinese concrete code (GB 50010-2010). In addition, the inter-story drift ratios of JD-1 and JD-2 are 3.3% and 2.3%, respectively, when specimens are in failure, which can satisfy the plastic deformation demand of 1/50 (2%) in Chinese concrete code (GB 50010-2010).

Table 4.

The mechanical properties of JD-1 and JD-2.

Specimen	JD-1		JD-2
	Positive direction	Negative direction	Positive direction	Negative direction
F _y (kN)	148.3	147.9	195.0	203.1
F _p (kN)	192.2	−191.9	234.0	242.5
Δ _y/H (%)	0.71	0.75	0.89	0.94
Δ _p/H (%)	2.58	1.99	2.65	1.97
Δ _u/H (%)	–	–	–	–
μ _p	3.63	2.65	2.98	2.10
μ _u	–	–	–	–
V _AISC (kN)	91.3		116.7
V _BS (kN)	101.2		116.4
V _GB (kN)	92.5		106.4
V _y (kN)	95.6	123.8	156.7	154.5
V _p (kN)	166.7	162.1	191.0	195.0
V _yf (kN)	88.1		101.4
V _pf (kN)	101.2		116.4
M _yf (kN m)	114.5		114.5
M _pf (kN m)	131.5		131.5
V _p/V_AISC	1.83	1.78	1.64	1.67
V _p/V_BS	1.64	1.60	1.64	1.68
V _p/V_GB	1.80	1.75	1.80	1.83
V _y/V_yf	1.09	1.41	1.55	1.52
V _p/V_pf	1.64	1.60	1.64	1.68

F _y = horizontal yield load of column; F_p = horizontal peak load of column; V_p = vertical peak load of steel beam; Δ_y = displacement of column corresponding to yield load; Δ_p = displacement of column corresponding to peak load; Δ_u = displacement of column corresponding to a 15% degradation from the peak load.

The classification of joint according to Eurocode 3 Part 1-8 (BS EN 1993-1-8:2005, 2005) is shown in Figure 7. Quantitatively, the relationship between M/M_p and Φ/Φ_p is used to classify the stiffness of joint. M_p and Φ_p are the plastic moment and plastic rotation angle of steel beam, respectively. Φ_p can be obtained from

Φ_{p} = \frac{M_{p} L_{p}}{E I_{n}}

(4)

where L_p is the beam span (twice the beam length L of the specimen), I_n is the moment of inertia of beam section, and M is the moment of steel beam which is calculated by shear force V multiplied by beam length L; Φ, the rotation angle within plastic hinge of steel beam, can be calculated with data of inclinometers on two sides of plastic hinge.

Figure 7.

Stiffness classification of joints: (a) JD-1 and (b) JD-2.

As shown in Figure 7, both T-shaped stiffeners and diaphragms can achieve rigid joint.

Finite element analysis

FEM

An FEM with ABAQUS software was established to simulate specimen with T-shaped stiffener and specimen with diaphragm. The input constitution relationships of concrete and steel, element types, interactions, boundary conditions, and loading scheme, simulated completely according to those in the experiment, can refer to author’s previous research (Li et al., 2018).

Verifications

The comparisons of load–displacement curves of FEM and experiments are shown in Figure 8(a). D is the vertical displacement of beam and V is the vertical load of beam. The elastic stiffness of JS-1 based on the FEM is 1.2 times the experimental result, while the bearing capacity is basically the same with the experimental result. This is mainly due to the small space for welding, and the welding quality of specimen is difficult to be guaranteed. The FEM results generally agree well with the experimental results, showing that the FEM is reasonable and reliable.

Figure 8.

Comparison of FEM and experimental results of JS-1: (a) comparisons of V-D curves and (b) comparison of failure mode.

The failure model of JS-1 based on the FEM is shown in Figure 8(b). The stresses of beam flange and web are both up to 325 MPa, indicating the whole section of beam can reach yield strength and steel tube remains in elastic stage. The failure mode of the FEM is consistent with the experimental result.

The comparisons of load–displacement skeleton curves of FEM and experiments for JD-1 and JD-2 are shown in Figure 9. Δ is the horizontal displacement at the top of column, F is the horizontal load at the top of column, and V is the vertical load of beam. Good agreement is achieved in stiffness and bearing capacities.

Figure 9.

Comparison of load–displacement skeleton curves between FEM and experiment: (a) horizontal load of JD-1, (b) shear force of beam of JD-1, (c) horizontal load of JD-2, and (d) shear force of beam of JD-2.

The stress distributions of JD-1 and JD-2 are shown in Figure 10. Plastic hinges are observed in FEM, which coincides with the failure modes in the experiments (in Figure 10(a) and (b)). The T-shaped stiffener in tension reaches yield stress, while that in compression reaches yield stress only in the region near steel tube (in Figure 10(c)). The yield zone of diaphragm in tension is greater than that in compression (in Figure 10(d)), which agrees with the experimental result. According to the stress distributions, the transmission of tension force from beam flange depends partly on T-shaped stiffener and diaphragm, while the transmission of compression force from beam flange depends mainly on the concrete within joint panel zone.

Figure 10.

The stress distributions for JD-1 and JD-2: (a) failure models of JD-1 between experiment and FEM, (b) failure models of JD-2 between experiment and FEM, (c) stress distribution of T-shaped stiffener of JD-1, and (d) stress distribution of interior exterior diaphragm of JD-2.

Based on the experimental and numerical research, the T-shaped stiffener and diaphragm are both effective connection types in the circular CFST column structures. With T-shaped stiffener or diaphragm, the joint core and connection are strong enough so that the beam-hinge failure mode can be achieved. However, these two connections should be further investigated in square CFST column structures. By comparison, the diaphragm has more direct load transmission capacity for beam flanges, but it may disturb the building indoor space; the T-shaped stiffener has less load transmission capacity than diaphragm, but it can facilitate fabrication and cause little disturbance to building indoor space.

Parameter analysis

Further parameter analysis with ABAQUS was carried out to study the influences on strength of connections based on the above FEM. When the parametric studies are taken on a certain parameter, other parameters are identical to those of JD-1 and JD-2. The parameters include (1) thickness of T-shaped stiffener’s web t_w (3, 8, 12, and 16 mm); (2) height of T-shaped stiffener’s web h_w (60, 100, 120, and 150 mm); (3) thickness of T-shaped stiffener’s flange t_f (3, 8 16, and 18 mm); (4) width of T-shaped stiffener’s flange b_f (0, 40, 60, and 80 mm); (5) thickness of diaphragm t_a (3, 9, 16, and 18 mm); and (6) width of diaphragm b_a (0, 45, 90, and 135 mm).

The results of parametric studies are shown in Figure 11. t_b is the thickness of beam flange and w_b is the width of beam flange. The parameters t_w, t_a, and b_a have significant effect on the strength of specimens (in Figure 11(a), (e), and (f)), while h_w, t_f, and b_f have a slight influence on the strength of specimens (in Figure 11(b), (c), and (d)). These critical values are suggested as reference values for preliminary design (Table 5).

Figure 11.

Parametric study: (a) parameter t_w, (b) parameter h_w, (c) parameter t_f, (d) parameter b_f, (e) parameter t_a, and (f) parameter b_a.

Table 5.

The suggested value for parameters.

Type of connection	Parameters	Specimen value	Suggested value
T-shaped stiffener	t _w	2/3 t_b	0.7 t_b to 1.2 t_b
	h _w	5/6 w_b	0.8 w_b to 1.0 w_b
	t _f	1.0 t_b	1.0 t_b
	b _f	1/3 w_b	0.5 w_b
Diaphragm	t _a	1.0 t_b	1.0 t_b to 1.5 t_b
	b _a	0.75 w_b	0.75 w_b to 1.0 w_b

Conclusion

This article investigates both static and seismic behavior of two types of large-scale connections between circular CFST columns and H-section steel beams. According to the experiments and the FEM, the following conclusions can be drawn:

Static failure mode of connection between CFST column and steel beams is plastic hinges of steel beams. The T-shaped stiffener guarantees plastic yielding of steel beam and effectively transfers internal forces of steel beam to joint panel zone under static loading. Meanwhile, the specimen has very good ductility.

Seismic failure mode of connections with T-shaped stiffeners and diaphragms are both plastic hinges of steel beams. These two types of connections can effectively transfer internal forces of steel beam to joint panel zone under seismic loading and have very good seismic performance, such as good ductility and energy dissipation capacity. According to provision of joint stiffness in EC4, these two types of connections can be identified as rigid joint.

An FEM is established and agrees well with the experimental results. Parametric analysis is conducted based on the FEM, and the following design suggestions of T-shaped stiffeners and diaphragms are proposed: (1) thickness of T-shaped stiffener’s web t_w is suggested to be 0.7–1.2 times of t_b; (2) height of T-shaped stiffener’s web h_w is suggested to be 0.8–1.0 times of w_b; (3) thickness of T-shaped stiffener’s flange t_f is suggested to be 1.0 times of t_b; (4) width of T-shaped stiffener’s flange b_f is suggested to be 0.5 times of w_b; (5) thickness of diaphragm t_a is suggested to be 1.0–1.5 times of t_b; and (6) width of diaphragm b_a is suggested to be 0.75–1.0 times of w_b.

Footnotes

Authors’ Note

Xianggang Liu is also affiliated with China Southwest Architectural Design and Research Institute Corp., Ltd., Chengdu, 610042, China.

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: This study was supported by the National Natural Science Foundation of China (Grant No. 51878098) and National Key Research and Development Program of China (Grant Nos 2016YFC0701201, 2017YFC0703805).

ORCID iDs

Yuanlong Yang

Jun Zhang

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