J. Cent. South Univ. (2018) 25: 1774-1785

DOI: https://doi.org/10.1007/s11771-018-3868-7

Numerical and experimental study on seismic behavior of concrete-filled T-section steel tubular columns and steel beam planar frames

ZHANG Ji-cheng(张继承)¹, HUANG Yong-shui(黄泳水)¹, CHEN Yu(陈誉)^{1, 2},DU Guo-feng(杜国锋)¹, ZHOU Ling-jiao(周灵姣)¹

1. School of Urban Construction, Yangtze University, Jingzhou 434023, China;

2. College of Civil Engineering, Huaqiao University, Xiamen 361021, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: The seismic behavior of planar frames with concrete-filled T-section columns to steel beam was experimentally and numerically studied. A finite element analysis (FEA) model was developed to investigate the engineering properties of the planar frames. Two 1:2.5 reduced-scale specimens of T-section concrete-filled steel tubular column and steel beam of single-story and single-bay plane frames were designed and fabricated based on the design principles of strong-column, weak-beam and stronger-joint. One three-dimensional entity model of the investigated frame structure was built using a large-scale nonlinear finite-element analysis software ABAQUS. Experimental results show that the axial compression ratio has no effect on the failure mode of the structure, while with the increase of axial compression ratio and the dissipated energy ability increasing, the structural ductility decreased. The results from both experiments and simulations agree with each other, which verifies the validity and accuracy of the developed finite element model. Furthermore, the developed finite element model helps to reflect the detailed stress status of the investigated frame at different time and different positions.

Key words: planar frames; T-section steel tubular columns; seismic behavior; mechanical properties; finite element analysis

Cite this article as: ZHANG Ji-cheng, HUANG Yong-shui, CHEN Yu, DU Guo-feng, ZHOU Ling-jiao. Numerical and experimental study on seismic behavior of concrete-filled T-section steel tubular columns and steel beam planar frames [J]. Journal of Central South University, 2018, 25(7): 1774–1785. DOI: https://doi.org/10.1007/s11771-018-3868-7.

1 Introduction

Concrete-filled steel tubular (CFST) members are well recognized for their excellent advantages such as high bearing capacity, high anti-seismic performance, convenient construction, great fire- resistance, and low cost. They are often used in high buildings and other industrial structures.

Up until now, a large amount of research has been studied on the performance of CFST members [1–7]; however, the behavior of CFST frames has not been investigated much. The current research on seismic behavior of CFST frames is mostly conducted in low-cycle loading tests, while related seismic simulations are investigated.

WANG et al [8] built an innovative frame structure composed of concrete-encased steel beams and concrete-encased CFST columns of two one- bay and one-story specimens under lateral low cyclic loading. Experimental results indicated that the frame performed perfect energy dissipation and ductility. ZHOU et al [9] investigated the behavior of L-shaped columns composed of CFST frames with two stories and a single span subjected to constant axial load and cyclically varying flexural load and conducted a finite element analysis to simulate the behavior of the frame. QI et al [10] designed eight concrete-steel composite frames to investigate the influence of the axial compression ratio of column, slenderness ratio and linear stiffness ratio of beam to column on the frames under low reversed cyclic loading. The test shows that this type of composite frame has favorable seismic behaviors and various effects on composite frames based on different parameters. HAN et al [11] studied the seismic behavior of CFST column frames with a single story and single span under a combination loading protocol of constant axial load on the CFST columns and a lateral cyclic load on the frame. Further, a FEA model of the composite frame was developed. BRACONI et al [12] designed a full-scale 3D prototype frame of ten concrete-filled steel composite beam-to-column sub-assemblages under monotonic and cyclic loading test protocols to identify the suitable structural properties (dissipated energy, ductility, over-strength and equivalent viscous damping) for seismic behavior of concrete-filled steel composite frames. WANG et al [13] studied the stiffness degradation and energy dissipation capacity of square CFST frame under a constant axial load and a lateral cyclic load. It can be concluded that the hysteresis loop of frames has no significant pinch phenomenon. The overall ductility coefficient is more than 4.0 which meets the earthquake-resistant standard.

The authors recently performed a pseudo-static test on two composite frames with concrete-filled T-section steel tubular columns to steel beam with reduced scale 1:2.5. The failure point of loading, the position and order of the plastic hinge were observed in different axial compression ratios. The influence of axial compression ratio on energy dissipation capacity, ductility, and stiffness

degradation was studied in this paper. Further, an accurate finite element model was developed using ABAQUS to simulate the structural behavior under a constant axial load. A constitutive model of concrete with equivalent confinable effect coefficient was used for the T-section CFST column. The numerical results agree with the experimental ones, which verifies the validity and accuracy of the proposed model.

2 Experimental study

2.1 Specimen preparation

In this paper, two composite frames with concrete-filled T-section steel tubular columns to steel beam with reduced scale 1:2.5 were designed on actual size of the housing structure and laboratory conditions. The dimensions and design parameters of the specimens are shown in Figures 1, 2 and Table 1.

Figure 1 Main dimension of specimen KJ1 and KJ2 (Unit: mm)

Figure 2 Section dimension of column specimen

Table 1 Design parameters of models

T-shaped extended inner diaphragm joints were used in the specimen in order to avoid the failure of column web caused by overlarge compressive and tensile stress. Detail drawings of joints are shown in Figure 3.

Figure 3 Detail drawings of joint (Unit: mm):

2.2 Material properties

The Q235 seamless steel tube was used in fabricating the specimen. The mechanical properties of the steel were obtained from standard tensile test specimens, as shown in Figure 4. The tensile tests were completed in the Building Structure Laboratory of Yangtze University, China. The mechanical properties of the steel is given in Table 2.

Figure 4 Steel tensile samples: (Unit: mm)

The mixed concrete used in the specimen consists of well graded aggregates with no mud on the surface, ordinary medium sand, ordinary composite Portland cement and water. Each concrete specimen has the same mixture proportion, i.e. cement: water: sand: stone=1:0.39:1.29:2.88. Layered tamping method was used when pouring concrete to assure the compactness of the concrete. The concrete strength was estimated by using the cubic compression strength tests at the 28th day, which is listed in Table 3.

2.3 Loading apparatus

The pseudo-static test was carried out in Civil Engineering Experiment Center of Yangtze University, China. The frame was fixed on foundation by anchor bolts to avoid overall lateral sway in the loading process. The vertical load on the top of the column transferred through loading plate and stiffening rib. The horizontal load was applied through supporting plate and tension rod after connecting with MTS actuator. The schematic diagram and photos of loading setup are shown in Figures 5 and 6. In order to transfer vertical axial load to the column, the centroid of T-shaped column was marked in advance so that it could coincide with the center of hoisting jack. To ensure better test results and eliminate the non-uniformity of component interior tissue, 15% pre-loading was applied on the top of the column before the designed loading test. During the loading test, hydraulic jack was arranged to apply vertical load with the axial compression ratios of 0.4 and 0.6, respectively, i.e. N=nN_u, N_u=f_ckA_c+f_yA_s, where n is the axial compression ratio. In addition, the vertical load remained at a constant value while MTS actuator was applied low reversed cyclic horizontal load along the beam centerline.

Table 2 Mechanical properties of steel

Table 3 Mechanical properties of concrete

Figure 5 Photo of loading setup

Figure 6 Test set-up of scene photo

With the constant vertical force, the displacement control was also adopted in horizontal loading, gradation loading was applied when the specimen yielded. The loading details are as follows: The displacement increment was controlled at 2 mm when horizontal displacement was less than 10 mm, each displacement step circulating only once; the displacement increment was set at 5 mm after the horizontal displacement was over 10 mm, each displacement step circulating thrice. Loading did not complete until the horizontal bearing capacity of the frame reduced to below 85% of the ultimate bearing capacity. Horizontal displacement control is shown in Figure 7. Horizontal load and displacement were measured by using the MTS system.Five strain gauges were mounted on upper and lower flanges of the beam end, column bottom, and 50 mm away from the top of stiffening rib, as shown in Figure 8.

Figure 7 Horizontal loading system of displacement control

2.4 Test results and discussion

2.4.1 Failure mode

During the loading process, there was similar failure mode in the two composite frames. When the displacement was below 8.5 mm, the longitude or transverse deformation of the steel tube on beam end and column bottom was small. At this stage, the skeleton curve was in a straight line because the specimen was in elastic stage. When displacement was applied over 9 mm in negative direction, slight cracking sounds were audible, and small local buckling on the beam end appeared and around 20 mm in negative direction, the bulge on the upper or lower beam flange was obvious. The plastic hinge of beam end appeared. While around 17 mm in positive direction, there was slight bulge on the column bottom, the bulge disappeared with an increase of displacement. Around 30 mm in negative direction, the plastic hinge of column bottom appeared. Finally around 40 mm in negative direction, the lateral capacity was down to 85% of peak load; at this time, the structure had been destroyed and loading completed. Figure 9 shows the failure mode of the frame.

2.4.2 Horizontal load vs horizontal displacement

The hysteretic curves of horizontal load (P) vs horizontal displacement (Δ) of the frame are shown in Figure 10. It can be seen that the curves are in plump shuttle shape. The hysteretic loop of specimen KJ2 has slight pinch phenomenon due to small slip between column bottom and foundation beam. Overall, the two frames have preferable energy dissipation capacity and earthquake-resistant properties. Furthermore, as horizontal displacement increases, the hysteretic loops become plumper. Under the same displacement, the including areas of hysteretic loops increase with the axial compression ratio which means the energy dissipation of the frame also increases.

Figure 11 shows the horizontal load (P) vs horizontal displacement (Δ) skeleton curves of the both frame specimens. It can be found that the skeleton curves are basically in a straight line during the initial loading period which reflects that the specimen is in elastic stage. With the increase of the horizontal displacement, the frame presents elastic-plastic property. The beam end and column bottom start to yield firstly, presenting flat curves in the figure. This means that the stiffness of the specimens gradually decreases. After the peak load, small displacement load is applied, which leads to the decrease of the bearing capacity. Finally, the tested frames step into ultimate failure stage.

Figure 8 Installation of strain gauges on bottom of column and end of beam:

Figure 9 Failure mode of frames:

Figure 10 P–Δ hysteretic curves of specimens:

Figure 11 P–Δ skeleton curves of specimens

2.4.3 Dissipated energy ability and ductility

In this research, the second equal energy method is used to determine the yield point of the frame. Table 4 lists the yield displacement and ductility of the frame. It can be found that the ultimate bearing capacity of the specimen slightly increases with the increase of the axial compression ratio; however, the structural ductility reduces. When the two frames approach ultimate capacity, the maximal interlaminar displacement angle meets the relative current standards of 1/50. This indicates that the carrying capacity and plastic deformation can be further improved. Generally, the ductility coefficients of two frames are both more than 4.0 which meets the specification of structural ductility requirements.

Energy dissipation coefficient (E) and equivalent damping coefficient (h_e) are adopted in expressing the dissipated energy ability of the structure, which is consistent with the Chinese Standard JGJ 101–96 [14].

Table 4 Top displacement and ductility factor at different stages

The energy dissipation coefficient (E) can be defined as

                          (1)

where S_ABCD is the area under curves ABCD as shown in Figure 12. S_OAE and S_OCF are the areas within the triangles OAE and OCF.

Figure 12 Solving energy dissipation coefficient E

The equivalent damping coefficient (h_e) can be defined as

                              (2)

Energy dissipation values at different stages are shown in Table 5. It can be observed that: 1) The plastic hinges at beam end and column bottom constantly develop with the increase of the displacement load. 2) With the increase of the axial compression ratio, the structural energy dissipation at different stages, energy dissipation coefficient (E) and equivalent damping coefficient (h_e) increase.3) When axial compression ratio changed from 0.4 to 0.6, total energy dissipation increased by 13.9%, and E and h_e increased by 21.6%. This indicates the great influence of axial compression ratio on energy dissipation ratio.

2.4.4 Strength and rigidity degradation

Figure 13 shows the strength degradation curves of frame in the whole loading process. The equivalent stiffness degradation curves under the same level load are presented in Figure 14. It can be noticed from Figure 13 that there is basically no degradation in the overall load strength of all the test frame model structure before the displacement load (Δ/Δ_y) reaches 2.6. While by the end of the experiment, with the development of the damage in core concrete, the overall strength of the structure with larger axial compression is more obvious. From Figure 14, it can be observed that, the stiffness of the frame increases with larger axial compression in the early stage of loading; however, it decreases linearly after the peak load is reached.

3 Finite element modeling

The behavior of frame structures is using the nonlinear beam–column element from ABAQUS. In the simulation process, some key issues have to be addressed in advance, including the material modeling and the finite element type of steel and core concrete, quantity of element division and computational accuracy, concrete-steel tube interface, boundary conditions simulation, convergence criterion and iterative calculation.

3.1 Material modeling of steel

The double lines strengthening elastic-plastic model and two flow plastic models are mainly used in material modeling of steel in finite element program [15]. Numerical evaluation demonstrates that the two material models can reflect the actual situation of steel tube. Two flow plastic models are used in this research as shown in Figure 15, where the dotted line represents stress–stain curve and the solid line represents simplification model. The curve can be divided into five stages, i.e. elastic (oa), elastic-plastic (ab), plastic (bc), strain hardening (cd) and two flow plastic stage. Each formula in each stage is expressed as:

Table 5 Energy dissipation at different stages

Figure 13 Strength degradation curves

Figure 14 Equivalent stiffness degradation curves

(3)

where f_y is the yield strength of the steel; E_s is the modulus of elasticity; ultimate strain of elastic stage ε_e=0.8f_y/E_s; initial strain of plastic stage ε_e1=1.5ε_e; initial strain of hardening stage ε_e2=10ε_e; initial strain of two flow plastic stages ε_e3=100ε_e1; A=0.2f_y(ε_e1–ε_e)²; B=0.2Aε_e1;

The Mises yield criterion is used to define isotropic yielding for steel material and assume associated plastic flow rule for steel. Hence, strain and stress are as follows:

     (4)

       (5)

Figure 15 Stress–strain relationship curves of steel

3.2 Material modeling of core concrete

In the CFST structure, the stress state of core concrete is complex due to the confinement effect of the outer tube. Accordingly, HAN et al [16] proposed the constitutive relationship for core concrete. Based on the study, a material model of core concrete, applicable to T-shaped CFST column nonlinear finite element analysis was given in Refs. [17–19]. This model is adopted in this research to simulate the core concrete of the tested frame. It can be described as:

                    (6)

In the formula, σ_o=f_c;

             (7)

                            (8)

                           (9)

where ε_o is the peak strain of the concrete; σ_o is the peak stress of the concrete; f_c is the compressive strength of the concrete; η and β_o are the effect coefficients; ξ_eq is equivalent restraint effect coefficient,

When CFST member is under axial eccentric load or horizontal load, there will be tensile phenomenon in partial section. So, tensile softening property of concrete needs to be defined in stress–strain relationship of concrete. In this paper, cracking strain-fracture energy relation model of tensile concrete is used in finite element analysis. The model allows inputting fracture energy and peak failure stress. The fracture energy of normal concrete is generally in 70–200 N/m, sometimes more than 300 N/m.

3.3 Boundary conditions and load

The column bottom of frame was applied fixed end constraint, namely, U_R1=U_R2=U_R3=U₁=U₂= U₃=0. The top of CFST columns supported constant axial load; the node domain of beam and column were subjected to horizontal load. The axial loads of top column were concentrated loads which were applied to the reference point coupled to the top surface of the loading plate. It was arranged in analysis step 1. The horizontal loads of beam and column node were controlled by displacement under displacement boundary condition. It was arranged in analysis step 2.

3.4 Finite element type and mesh

Typical finite element model of composite CFST frames was built in ABAQUS\standard module. The model included T-shaped CFST column and beam. For four-node doubly curved general-purpose shell with finite membrane strain, fully integrated linear shell element (S4) is used for steel tube. To meet the requirements of accuracy, 9 integral points of Simpson integral were arranged along the thickness of the shell. A fine mesh of three-dimensional eight-node linear brick and reduced integration with hourglass control solid element (C3D8R) is used for inner concrete, so as the loading plate on the column top, to connecting plate on the column bottom. Considering of the simple geometrical shape of frame, sweep mesh generation technique was used in this paper. Maintaining all other factors constant, the number of meshes increased by multiples. The difference between the two calculated results is less than 1% which means that the number of meshes can meet the accuracy requirements and they are divided by the previous meshes; otherwise, refined meshes are continued.

3.5 Model of contacts and interfaces

In the process of finite element modeling, inner concrete, steel tube, stiffening rib, loading plate on the column top, connecting plate on the column bottom, L-shaped internal diaphragms, connecting plate of beam web and steel beam are independent parts. Thus the interaction among them needs to be defined by a certain contact relation. The definition of the contact between steel tube and concrete is essential to ensure the accuracy of the simulation. The normal direction of the interface of concrete and steel tube is hard contact and the tangent contact is bond-slip. The friction between concrete and steel tube is simulated by the Coulomb friction model. The coefficient of friction is taken as 0.25.

There are many interface problems to be handled in framework model while they are not the main factors affecting the mechanical properties of the frame. Thus in finite element software ABAQUS, the interfacial treatment modes between concrete and loading plate on the column top, connecting plate on the column bottom were hard contact and non-slip, with regard to steel tube, they were connected by shell-to-solid coupling options, so as stiffening rib and connecting plate on the column bottom.

3.6 Simulation results

The finite element model of the test frame is shown in Figure 16. The size of the finite element model is consistent with the actual situation. Firstly, the axial force was applied on the top of the column, then the monotonic lateral displacement load was applied at both ends of the column. The lateral load (P) versus lateral displacement (Δ) envelop curves were obtained by calculation. Table 6 gives the maximal test value and the maximal calculate value of frames. Figures 17 and 18 show the Mises stress nephogram and equivalent plastic strain nephogram of ABAQUS calculated model, respectively. The mechanical characteristics of the column are similar with compression-bending components. The section of the column is under compression when there is only axial load on the top of the column, while the tensile zone appears in a section with increase of the horizontal load. In addition, the natural axis offsets continuously, tensile zone increases and compression zone decreases.

3.7 Verification of FEA model

Figure 19 shows the comparison between the hysteresis curves and envelop curves of lateral load (P) vs lateral displacement (Δ). It can be found from Figure 19 that the numerical envelop curves agree well with the experimental hysteresis curves while the peak value of envelop curves is smaller than that of hysteresis curves. This is obvious for KJ2 whose axial compression is larger. The main reason is the favorable plastic performance of concrete- filled steel tubular members. The good restraining effect of the core concrete makes the cumulative damage in the concrete-filled steel tubular member become less obvious. Overall, the FEA model established in this paper based on ABAQUS can be used to analyze the interaction of steel and concrete in composite frames. The test results match well with the FEA results.

Figure 16 FEA model of specimens:

Table 6 Maximal tested value and maximal calculated value of frames

4 Conclusions

In this work, experiments and finite element analysis are conducted to study the seismic behavior of concrete-filled T-section steel tubular columns and steel beam planar frames. The following conclusions can be drawn within the scope of this study:

Figure 17 Mises stress nephogram of ABAQUS calculated model:

Figure 18 Equivalent plastic strain (PEEQ) nephogram of ABAQUS calculated model:

1) During the loading process of concrete- filled T-section steel tubular columns and steel beam planar frames, the beam end flange yielded first, and then the steel tube followed. There was no obvious deformation on the nodes of the beam and column. This phenomenon agrees with the principle of strong-column, weak-beam and stronger-joint. The CFST frames have excellent earthquake resistance, which is mainly reflected on the plump shuttle shape of the hysteresis curves of lateral load (P) vs lateral displacement (Δ) of the frame, and the ductility coefficient is more than 4.0 which meets the requirement of ductility of the structure in the seismic code.

Figure 19 Comparison of load versus displacement curves between calculated and experimental results:

2) Axial compression ratio is an important factor that affects the seismic behavior of concrete- filled T-section steel tubular columns and steel beam planar frames. With the increase of the axial compression ratio, the ductility of the frame reduces. After the peak load, the degradation rate of strength and stiffness increases while the structural energy dissipation enhances.

3) Equivalent restraint effect coefficient ξ_eq can better reflect the constraint effect of T-shaped steel tube to core concrete. In this paper, good agreement is obtained between numerical envelop curves and experimental hysteresis curves in FEA model. FEA model can well reflect the stress state of the tested frame.

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(Edited by YANG Hua)

中文导读

T形钢管混凝土柱–钢梁平面框架抗震性能试验研究与数值分析

摘要：通过试验和数值模拟研究了T形钢管混凝土柱–钢梁平面框架的抗震性能，并开发了一种有限元分析模型用于研究平面框架的工程特性。基于强柱弱梁和强节点的设计原则，设计并制作了两榀1:2.5缩尺比例的T形钢管混凝土柱–钢梁平面框架，利用大型非线性有限元分析软件ABAQUS建立了所研究框架结构的三维实体模型。试验结果表明，轴压比对结构的破坏模式没有影响，随着轴压比的增大和耗能能力的提高，结构延性下降。试验结果与数值模拟结果一致，验证了开发的有限元模型的有效性与准确性。此外，开发的有限元模型有助于反映该平面框架在不同时间、不同位置的详细应力状态。

关键词：平面框架；T形钢管混凝土柱；抗震性能；力学性能；有限元分析

Foundation item: Projects(51378077, 51478047, 51778066) supported by the National Natural Science Foundation of China; Project(D20151304) supported by Science and Technology Research Project of Education Department of Hubei Province, China; Project(2017CFA070) supported by Hubei Provincial Natural Science Foundation, China

Received date: 2017-03-28; Accepted date: 2017-11-06

Corresponding author: CHEN Yu, PhD, Professor; Tel: +86–18030219629; E-mail: kinkingingin@163.com