# Seismic Behavior of Elliptical Concrete-Filled Steel Tubular Columns under Combined Axial Compression and Cyclic Lateral Loading

Authors: YouWu Xu; Jian Yao; Feng Hu; Ying Zhou; Shuai Jiang
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

Elliptical concrete-filled steel tubular (CFST) column is a new form of CFST columns, consisting of an outer elliptical tube filled with concrete. Although the study on mechanical performance of the elliptical CFST members is receiving more and more attention, they have been limited to static behavior. Against this background, an experimental study on elliptical CFST columns was carried out under combined axial compression and cyclic lateral loading. The failure modes, hysteretic curves, skeleton curves, load carrying capacity, deformability, stiffness degradation, and energy dissipation ability was obtained and discussed. The test results indicated that the elliptical CFST columns possess excellent seismic performance and ductility. Valuable experimental data were provided for the formulation of the theoretical hysteresis model of the elliptical CFST columns.


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## Body

## 1. Introduction

Concrete-filled steel tubular (CFST) columns have been widely used in modern construction due to their high strength, high ductility, and ease of construction [1]. In the past few decades, a lot of research on the performance and design of CFST members under various loading condition [2] have been published. As a new section form of CFST, elliptical CFST (Figure 1) has attracted the attention of many scholars from home and abroad. In recent years, research has been carried out on the mechanical behavior and design method of elliptical CFST.Figure 1
Cross-section of elliptical CFST.Experimental study on elliptical CFST stub columns with different thickness and concrete strength subjected to axial loading have been conducted by Yang et al. [3], Zhao and Packer [4], Jamaluddin et al. [5], Chan et al. [6], and Cai et al. [7]. They proved the merits of elliptical CFST stub columns, but all the specimens they tested have the same aspect ratio (a/b = 2.0). With the development of manufacturing technology, the elliptical steel tube with various aspect ratios is available in construction practice. Thus, elliptical CFST stub columns with an aspect ratio from 1.0 to 2.5 were tested by Zha et al. [8], Uenaka [9], Yi and Young [10], Liu et al. [11], and Xu et al. [12]. All the test results confirmed that the confinement effect decreases significantly with the increasing aspect ratio. Simultaneously, the eccentrically compressed columns were also investigated by Sheehan et al. [13], Zha et al. [14], Ren et al. [15], Qiu [16], and Yang et al. [17]. On the other side, systematic finite element analysis [18–22] was performed to simulate elliptical CFST columns subjected to concentric and eccentric axial compression. However, these studies mainly focused on static behavior, and research on their seismic behavior is very limited, which may hamper the application of elliptical CFST members in the seismic region. To the best of the authors’ knowledge, the pseudostatic tests on 5 specimens with an aspect ratio of 2.0 conducted by Ma [23] proved the influence of concrete cube strength and axial compression ratio on the seismic behavior of elliptical CFST columns. Fang et al. [24] further considered the thickness of the elliptical steel tube, axial compression ratio, and the loading direction of horizontal loading; nevertheless, the aspect ratio of the specimens was also limited to 2.0. Consequently, the studies on the seismic behavior of elliptical CFST columns with an aspect ratio of a wider range is urgently needed.In this study, 13 elliptical CFST columns tested under combined axial compression and cyclic lateral loading, the failure mode, carrying capacity, deformation capacity, hysteretic curve, and energy dissipation capacity of the specimens are discussed in detail. The experiment results may provide the reference to the analysis and application of elliptical CFST columns in the seismic area.


## 2. Experimental Program

### 2.1. Test Specimens

A total of 13 specimens were tested under combined constant axial compression and cyclic lateral loading through either the long or short axis. The key parameters were aspect ratioa/b, concrete cube strength fcu, axial compression ratio n, and slenderness ratio λsc, which is expressed as column height h. As shown in Figure 2, each specimen consists of an elliptical CFST column, a top end-plate with a thickness of 20 mm, a series of stiffeners with a thickness of 10 mm welded to the top end-plate and the column, and a 30 mm thick bottom end-plate. The height of welding is hf = 6 mm. According to the insite condition, rolling support on the vertical jack was not so smooth for sliding. So, the stiffeners were not used at the column base to achieve an equivalent calculation length to the cantilever component.Figure 2
Details of the specimens.Table1 provides the details of the 13 specimens, in which a is the length of semimajor axis, b is the length of semiminor axis, t is the thickness of the steel tube, and h is the height of the specimen. The specimen was named by the key parameters as follows: the aspect ratio-concrete cube strength-axial ratio. The letters m and l added at the end denote the medium (2050 mm) and the longest columns (2550 mm), and b for bending around the major axis. If there are no letters at the end, it means 1300 mm height and bending around the minor axis. The axial ratio was determined by equation (1), where Nd is the constant axial compression subjected by the specimen, Ac and As are the measured cross-sectional areas of the steel and concrete, respectively, and fco and fy are the cylinder strength, converted from the measured concrete cube strength [25] of concrete and yield strength of steel.(1)n=NdfcoAc+fyAs.Table 1
Measured information of the specimens.
Specimen2a (mm)2b (mm)t (mm)h (mm)fy (MPa)Es (MPa)fcu (MPa)E1.0-C45-0.2244.81244.815.881300.0033419065045.31E1.3-C45-0.2243.99187.255.891300.0037021450045.31E1.8-C45-0.2243.61132.866.061300.0038921460045.31E2.3-C45-0.2244.45103.925.861300.8740920378045.31E1.8-C60-0.2243.55133.856.071300.5738921460069.97E1.8-C75-0.2243.68133.836.121300.6338921460076.01E1.8-C100-0.2243.20132.416.091302.6738921460092.45E1.8-C45-0.1243.60132.516.091305.5038921460045.31E1.8-C45-0.3243.45132.996.071300.2738921460045.31E1.8-C45-0.2m243.52133.046.042050.4638921460045.31E1.8-C45-0.2l243.51132.866.072552.3138921460045.31E1.8-C45-0.2b243.73132.376.081300.0038921460045.31E1.8-C45-0.3b243.77132.856.031300.3338921460045.31The elliptical steel tubes were cold-formed from the welded circular tubes (Figure3). The material test of the steel tube was conducted according to [26], and the yield stress fy and elastic modulus Es of the steel tubes were obtained from the tensile coupon tests (Figure 4), as given in Table 1. Concrete grade C45, C60, C75, and C100 was used, and the mix proportions and tested cube strength are given in Table 2 and Table 1, respectively.Figure 3
Cold-forming process (Chan et al. [6]).Figure 4
Stress-strain relationships of elliptical steel tubes.Table 2
Mix proportions of the concrete (kg/m3).
Concrete gradeCementWaterFinesCoarseFly ashWater reducerExpansion mixtureC45363191790851176055C603551777409351091054C7537515072010251151258C10039013270010501021660


### 2.2. Instrument and Loading Procedure

As shown in Figure5, the specimens were placed and tested within a reaction testing frame. The axial load was applied by a vertical hydraulic jack which is movable in the horizontal direction. The horizontal electrohydraulic servoactuator with a load capacity of 1000 kN and a stroke of 200 mm was used to apply the horizontal load. The push direction is defined as positive direction.Figure 5
Test setup and instrumentation.Eight LVDTs were used to measure the critical displacements. LVDT 1-2 were used to measure the translational movement of the foundation beam, LVDT 3-4 were used to measure the rotation of bottom end-plate. LVDT 5-6 were used to measure the columns end shortening within the 200 mm range. LVDT 7-8 were used to measure the translational displacement of the top of the column.The loading procedure included three steps. A 30% of the designed vertical load was first preloaded to check the testing system. Then, the designed vertical load was applied and kept constant. Finally, the horizontal load was applied quasistatically following the JGJ/T standard loading protocol (JGJ/T 101-2015) [27], which is shown in Figure 6. Each of the first three levels of amplitude (0.25 Δy, 0.5 Δy, and 0.75 Δy) was repeated only for one cycle, followed by three cycles at the rest levels of amplitude (1 Δy,2 Δy,4 Δy, 6 Δy, 8 Δy…). The loading procedure was stopped when the horizontal load degraded to 85% of the peak load.Figure 6
Horizontal loading procedure.


## 2.1. Test Specimens

A total of 13 specimens were tested under combined constant axial compression and cyclic lateral loading through either the long or short axis. The key parameters were aspect ratioa/b, concrete cube strength fcu, axial compression ratio n, and slenderness ratio λsc, which is expressed as column height h. As shown in Figure 2, each specimen consists of an elliptical CFST column, a top end-plate with a thickness of 20 mm, a series of stiffeners with a thickness of 10 mm welded to the top end-plate and the column, and a 30 mm thick bottom end-plate. The height of welding is hf = 6 mm. According to the insite condition, rolling support on the vertical jack was not so smooth for sliding. So, the stiffeners were not used at the column base to achieve an equivalent calculation length to the cantilever component.Figure 2
Details of the specimens.Table1 provides the details of the 13 specimens, in which a is the length of semimajor axis, b is the length of semiminor axis, t is the thickness of the steel tube, and h is the height of the specimen. The specimen was named by the key parameters as follows: the aspect ratio-concrete cube strength-axial ratio. The letters m and l added at the end denote the medium (2050 mm) and the longest columns (2550 mm), and b for bending around the major axis. If there are no letters at the end, it means 1300 mm height and bending around the minor axis. The axial ratio was determined by equation (1), where Nd is the constant axial compression subjected by the specimen, Ac and As are the measured cross-sectional areas of the steel and concrete, respectively, and fco and fy are the cylinder strength, converted from the measured concrete cube strength [25] of concrete and yield strength of steel.(1)n=NdfcoAc+fyAs.Table 1
Measured information of the specimens.
Specimen2a (mm)2b (mm)t (mm)h (mm)fy (MPa)Es (MPa)fcu (MPa)E1.0-C45-0.2244.81244.815.881300.0033419065045.31E1.3-C45-0.2243.99187.255.891300.0037021450045.31E1.8-C45-0.2243.61132.866.061300.0038921460045.31E2.3-C45-0.2244.45103.925.861300.8740920378045.31E1.8-C60-0.2243.55133.856.071300.5738921460069.97E1.8-C75-0.2243.68133.836.121300.6338921460076.01E1.8-C100-0.2243.20132.416.091302.6738921460092.45E1.8-C45-0.1243.60132.516.091305.5038921460045.31E1.8-C45-0.3243.45132.996.071300.2738921460045.31E1.8-C45-0.2m243.52133.046.042050.4638921460045.31E1.8-C45-0.2l243.51132.866.072552.3138921460045.31E1.8-C45-0.2b243.73132.376.081300.0038921460045.31E1.8-C45-0.3b243.77132.856.031300.3338921460045.31The elliptical steel tubes were cold-formed from the welded circular tubes (Figure3). The material test of the steel tube was conducted according to [26], and the yield stress fy and elastic modulus Es of the steel tubes were obtained from the tensile coupon tests (Figure 4), as given in Table 1. Concrete grade C45, C60, C75, and C100 was used, and the mix proportions and tested cube strength are given in Table 2 and Table 1, respectively.Figure 3
Cold-forming process (Chan et al. [6]).Figure 4
Stress-strain relationships of elliptical steel tubes.Table 2
Mix proportions of the concrete (kg/m3).
Concrete gradeCementWaterFinesCoarseFly ashWater reducerExpansion mixtureC45363191790851176055C603551777409351091054C7537515072010251151258C10039013270010501021660


## 2.2. Instrument and Loading Procedure

As shown in Figure5, the specimens were placed and tested within a reaction testing frame. The axial load was applied by a vertical hydraulic jack which is movable in the horizontal direction. The horizontal electrohydraulic servoactuator with a load capacity of 1000 kN and a stroke of 200 mm was used to apply the horizontal load. The push direction is defined as positive direction.Figure 5
Test setup and instrumentation.Eight LVDTs were used to measure the critical displacements. LVDT 1-2 were used to measure the translational movement of the foundation beam, LVDT 3-4 were used to measure the rotation of bottom end-plate. LVDT 5-6 were used to measure the columns end shortening within the 200 mm range. LVDT 7-8 were used to measure the translational displacement of the top of the column.The loading procedure included three steps. A 30% of the designed vertical load was first preloaded to check the testing system. Then, the designed vertical load was applied and kept constant. Finally, the horizontal load was applied quasistatically following the JGJ/T standard loading protocol (JGJ/T 101-2015) [27], which is shown in Figure 6. Each of the first three levels of amplitude (0.25 Δy, 0.5 Δy, and 0.75 Δy) was repeated only for one cycle, followed by three cycles at the rest levels of amplitude (1 Δy,2 Δy,4 Δy, 6 Δy, 8 Δy…). The loading procedure was stopped when the horizontal load degraded to 85% of the peak load.Figure 6
Horizontal loading procedure.


## 3. Test Results and Discussion

### 3.1. Failure Mode

Two typical failure modes were observed from the experimental results, namely, local buckling near the bottom end-plate and the fracture of the steel tube (Table3 and Figure 7). For the local buckling failure mode, the outward bulges were observed at about 45 mm distance from the bottom end-plate. The bulges became more and more evident with the increase in the horizontal loading amplitude. Finally, the “elephant foot” failure mechanism was formed. For the fracture failure mode, the fracture occurred in the steel tube but not in the weld. It is mainly caused by stress concentration related to the heat-affected zone of the weld. The lack of stiffeners causes massive tension in the bottom of the steel tube, and it may be another reason for the fracture. More experiments or finite element analyses are needed to reveal the convinced reason.Table 3
Failure modes of the specimens.
Failure modesSpecimensLocal bucklingE1.3-C45-0.2, E1.8-C45-0.2, E1.8-C75-0.2, E1.8-C100-0.2,E1.8-C45-0.1, E1.8-C45-0.3, E1.8-C45-0.2m, E1.8-C45-0.2l, E1.8-C45-0.2b, E1.8-C45-0.3bFracture of the steel tubeE2.3-C45-0.2, E1.8-C60-0.2∗The loading procedure of E1.0-C45-0.2 was not completed due to the abrupt failure of the instrument.Figure 7
Typical failure modes of the specimens. (a) Local buckling. (b) Fracture of the steel tube.
(a)(b)In order to further investigate the damage condition of the concrete, end part of the steel tube was cut after the experiments, as shown in Figure8. The concrete was crushed on both sides of the loading direction, and several minor cracks were observed.Figure 8
Typical damage mode of the concrete.


### 3.2. Hysteretic and Skeleton Curves

The horizontal force-displacement responses of the ECFST beam-column specimens are shown in Figure9. The test results showed that the hysteretic curves were chubbiness without pinching, which reveals the high-energy dissipation capacity. The hysteresis remains stable as the amplitude increase, and the three hysteresis loops at the same amplitude is almost the same at the earlier stage. When the applied load reaches the ultimate horizontal force Pu, degradation of the hysteresis begins to be seen, in which case the loops became smaller as the cycle number increases.Figure 9
Horizontal force-displacement responses of the test specimens. (a) E1.0-c45-0.2. (b) E1.3-c45-0.2. (c) E1.8-c45-0.2. (d) E2.3-c45-0.2. (e) E1.8-c45-0.1. (f) E1.8-c45-0.3. (g) E1.8-c45-0.2b. (h) E1.8-c45-0.3b. (i) E1.8-c45-0.2m. (j) E1.8-c45-0.2l. (k) E1.8-c60-0.2. (l) E1.8-c75-0.2. (m) E1.8-c100-0.2.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)Skeleton curves are shown in Figure10 which were constructed by tracing the maximum loads at varying amplitudes. The skeleton curves consist of three stages, namely, the initial elastic ascending stage, nonlinear elastic-plastic ascending stage, and postpeak descending stage. As expected, concrete strength and axial compression ratio has a little effect on the initial stiffness, increasing the concrete strength tends to increase the ultimate load and speed up the degradation progress, and increasing the axial compression ratio is likely to decrease the ultimate load and speed up the degradation progress. The initial stiffness and ultimate load decreases with the increase of aspect ratio and slenderness ratio, and the load drops faster as the aspect ratio increases and slenderness decreases. Major axis bending leads to the larger initial stiffness and ultimate load than minor axis bending, but it results in the more abrupt degradation.Figure 10
Skeleton cures of test specimens. (a) Variation of aspect ratio. (b) Variation of axial compression ratio. (c) Variation of bending axis. (d) Variation of slenderness ratio. (e) Variation of concrete strength.
(a)(b)(c)(d)(e)


### 3.3. Bearing Capacity and Ductility

The ductility of a beam-column is generally regarded as the deformation capacity which is defined as the ability to sustain plastic deformations before its failure. The most commonly used parameter is the ductility indexμ and can be expressed as(2)μ=ΔuΔy,where Δul and Δy are the ultimate displacement and yield displacement, respectively, Δul is taken as the displacement at a 15% reduction in the ultimate load [28], and Δy is calculated from the skeleton curves using the average calculation of the geometric graphic method, equivalent elastoplastic energy method, and R. Park method [29], which are three common methods used to define the yield strength/load and yield displacement/drift. The ultimate load Pu, ultimate displacement Δul obtained from the skeleton curves, and the calculated yield load Py, yield displacement Δy are given in Table 4.Table 4
Load bearing capacity and ductility of test specimens.
SpecimensPu (kN)Δul (mm)Py (kN)Δy (mm)μE1.0-C45-0.2Positive direction119.35a>48.05103.0214.78>3.27Negative direction126.49a>48.06107.0218.88>2.55Average122.92a>48.06105.0216.83>2.91E1.3-C45-0.2Positive direction108.4380.3094.1717.47>4.60Negative direction115.0569.0099.6518.153.81Average111.7474.6596.9117.814.21E1.8-C45-0.2Positive direction89.0375.7275.9512.376.14Negative direction98.4870.7081.7414.165.05Average93.7573.2178.8413.265.59E2.3-C45-0.2Positive direction84.5340.0671.0713.143.05Negative direction77.3540.0867.7311.593.46Average80.9440.0769.4012.373.26E1.8-C60-0.2Positive direction94.2253.6680.4412.354.38Negative direction108.0853.6693.5813.963.85Average101.1553.6687.0113.164.12E1.8-C75-0.2Positive direction97.0961.5181.4214.004.41Negative direction89.7876.7272.2213.875.61Average93.4469.1176.8213.935.01E1.8-C100-0.2Positive direction99.3245.8884.1413.183.48Negative direction107.7035.7194.1013.002.75Average103.5140.7989.1213.093.12E1.8-C45-0.1Positive direction100.1090.0585.0114.756.12Negative direction102.1090.0186.9414.776.11Average101.1090.0385.9714.766.11E1.8-C45-0.3Positive direction86.7048.0174.2212.273.92Negative direction94.5045.5479.9313.363.41Average90.6046.7777.0812.823.66E1.8-C45-0.2mPositive direction47.5878.1445.9725.003.13Negative direction54.6449.8351.9330.001.66Average51.1163.9948.9527.502.39E1.8-C45-0.2lPositive direction32.0099.7828.8240.192.48Negative direction31.2095.1929.1335.502.68Average31.6097.4928.9737.852.58E1.8-C45-0.2bPositive direction54.7056.6848.0022.572.51Negative direction52.0066.2645.9421.393.10Average53.3561.4746.9721.982.81E1.8-C45-0.3bPositive direction48.5044.3547.0821.002.11Negative direction45.6046.7039.6322.062.12Average47.0545.5243.3621.532.12aThe loading procedure of E1.0-C45-0.2 was not completed due to the abrupt failure of the instrument.As given in Table4, the ductility index of most specimens is greater than 3.0, indicating a highly ductile performance. The ductility index decreases with the increase of aspect ratio, axial compression ratio, slenderness ratio, and concrete strength. Major axis bending specimen has a greater ductility than that of minor axis bending specimen. The aspect ratio seems to have moderate influence on the ductility index.


### 3.4. Stiffness Degradation

As guided in the JGJ/T code (JGJ/T 101-2015, 2015), the average stiffness can be obtained from the horizontal load-displacement hysteretic curves, which can be expressed as(3)Ki=∑j=1m|+Pi,j|+−Pi,j∑j=1m|+Δi,j|+−Δi,j,where Ki is the average stiffness of the specimen at the ith amplitude, Pi,j is the maximum load of the jth cycle at the ith amplitude, Δi,j is the maximum displacement of the jth cycle at the ith amplitude, and (+) and (−) mean the positive and negative position, respectively.Figure11 shows the relationship of the average stiffness with horizontal displacement; it illustrates the stiffness degradation with increasing lateral displacement, which is highly correlated with the development concrete cracks. In all test specimens, the stiffness degradation is significant before the displacement reaches to 2Δy; as the displacement continues to increase, the stiffness degradation continues at a lower and continually decreasing rate. The aspect ratio, axial compression ratio, and concrete strength have a little effect on the stiffness degradation. The stiffness reduces faster when the specimen is less slender, and the stiffness degradation rate of minor axis bending specimen is lower than that of major axis bending specimen.Figure 11
Stiffness of test specimens. (a) Variation of aspect ratio. (b) Variation of axial compression ratio. (c) Variation of bending axis. (d) Variation of slenderness ratio. (e) Variation of concrete strength.
(a)(b)(c)(d)(e)


### 3.5. Energy Dissipation Capacity

The energy dissipation per cycle,Ei, is the area enveloped by each hysteretic loop [24, 30, 31]. Figure 12 shows the accumulated energy dissipation ∑Ei of the 13 test specimens. As seen from the table, negligible energy dissipation is observed before the specimen reached the yield point, before which the specimens sustain limited plastic deformation. The energy dissipation starts to accumulate with the accumulated plastic deformation. The ultimate accumulated energy dissipation reflects the energy dissipation performance of the test specimens. As shown in Figure 12, specimens with a smaller aspect ratio, lower concrete strength, smaller axial compression ratio, and smaller slenderness ratio possess better energy dissipation capacity, and major axis bending specimens have a better performance on the energy dissipation quality than that of minor axis bending specimens.Figure 12
Accumulated energy dissipation of test specimens. (a) Variation of aspect ratio. (b) Variation of axial compression ratio. (c) Variation of bending axis. (d) Variation of slenderness ratio. (e) Variation of concrete strength.
(a)(b)(c)(d)(e)


## 3.1. Failure Mode

Two typical failure modes were observed from the experimental results, namely, local buckling near the bottom end-plate and the fracture of the steel tube (Table3 and Figure 7). For the local buckling failure mode, the outward bulges were observed at about 45 mm distance from the bottom end-plate. The bulges became more and more evident with the increase in the horizontal loading amplitude. Finally, the “elephant foot” failure mechanism was formed. For the fracture failure mode, the fracture occurred in the steel tube but not in the weld. It is mainly caused by stress concentration related to the heat-affected zone of the weld. The lack of stiffeners causes massive tension in the bottom of the steel tube, and it may be another reason for the fracture. More experiments or finite element analyses are needed to reveal the convinced reason.Table 3
Failure modes of the specimens.
Failure modesSpecimensLocal bucklingE1.3-C45-0.2, E1.8-C45-0.2, E1.8-C75-0.2, E1.8-C100-0.2,E1.8-C45-0.1, E1.8-C45-0.3, E1.8-C45-0.2m, E1.8-C45-0.2l, E1.8-C45-0.2b, E1.8-C45-0.3bFracture of the steel tubeE2.3-C45-0.2, E1.8-C60-0.2∗The loading procedure of E1.0-C45-0.2 was not completed due to the abrupt failure of the instrument.Figure 7
Typical failure modes of the specimens. (a) Local buckling. (b) Fracture of the steel tube.
(a)(b)In order to further investigate the damage condition of the concrete, end part of the steel tube was cut after the experiments, as shown in Figure8. The concrete was crushed on both sides of the loading direction, and several minor cracks were observed.Figure 8
Typical damage mode of the concrete.


## 3.2. Hysteretic and Skeleton Curves

The horizontal force-displacement responses of the ECFST beam-column specimens are shown in Figure9. The test results showed that the hysteretic curves were chubbiness without pinching, which reveals the high-energy dissipation capacity. The hysteresis remains stable as the amplitude increase, and the three hysteresis loops at the same amplitude is almost the same at the earlier stage. When the applied load reaches the ultimate horizontal force Pu, degradation of the hysteresis begins to be seen, in which case the loops became smaller as the cycle number increases.Figure 9
Horizontal force-displacement responses of the test specimens. (a) E1.0-c45-0.2. (b) E1.3-c45-0.2. (c) E1.8-c45-0.2. (d) E2.3-c45-0.2. (e) E1.8-c45-0.1. (f) E1.8-c45-0.3. (g) E1.8-c45-0.2b. (h) E1.8-c45-0.3b. (i) E1.8-c45-0.2m. (j) E1.8-c45-0.2l. (k) E1.8-c60-0.2. (l) E1.8-c75-0.2. (m) E1.8-c100-0.2.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)Skeleton curves are shown in Figure10 which were constructed by tracing the maximum loads at varying amplitudes. The skeleton curves consist of three stages, namely, the initial elastic ascending stage, nonlinear elastic-plastic ascending stage, and postpeak descending stage. As expected, concrete strength and axial compression ratio has a little effect on the initial stiffness, increasing the concrete strength tends to increase the ultimate load and speed up the degradation progress, and increasing the axial compression ratio is likely to decrease the ultimate load and speed up the degradation progress. The initial stiffness and ultimate load decreases with the increase of aspect ratio and slenderness ratio, and the load drops faster as the aspect ratio increases and slenderness decreases. Major axis bending leads to the larger initial stiffness and ultimate load than minor axis bending, but it results in the more abrupt degradation.Figure 10
Skeleton cures of test specimens. (a) Variation of aspect ratio. (b) Variation of axial compression ratio. (c) Variation of bending axis. (d) Variation of slenderness ratio. (e) Variation of concrete strength.
(a)(b)(c)(d)(e)


## 3.3. Bearing Capacity and Ductility

The ductility of a beam-column is generally regarded as the deformation capacity which is defined as the ability to sustain plastic deformations before its failure. The most commonly used parameter is the ductility indexμ and can be expressed as(2)μ=ΔuΔy,where Δul and Δy are the ultimate displacement and yield displacement, respectively, Δul is taken as the displacement at a 15% reduction in the ultimate load [28], and Δy is calculated from the skeleton curves using the average calculation of the geometric graphic method, equivalent elastoplastic energy method, and R. Park method [29], which are three common methods used to define the yield strength/load and yield displacement/drift. The ultimate load Pu, ultimate displacement Δul obtained from the skeleton curves, and the calculated yield load Py, yield displacement Δy are given in Table 4.Table 4
Load bearing capacity and ductility of test specimens.
SpecimensPu (kN)Δul (mm)Py (kN)Δy (mm)μE1.0-C45-0.2Positive direction119.35a>48.05103.0214.78>3.27Negative direction126.49a>48.06107.0218.88>2.55Average122.92a>48.06105.0216.83>2.91E1.3-C45-0.2Positive direction108.4380.3094.1717.47>4.60Negative direction115.0569.0099.6518.153.81Average111.7474.6596.9117.814.21E1.8-C45-0.2Positive direction89.0375.7275.9512.376.14Negative direction98.4870.7081.7414.165.05Average93.7573.2178.8413.265.59E2.3-C45-0.2Positive direction84.5340.0671.0713.143.05Negative direction77.3540.0867.7311.593.46Average80.9440.0769.4012.373.26E1.8-C60-0.2Positive direction94.2253.6680.4412.354.38Negative direction108.0853.6693.5813.963.85Average101.1553.6687.0113.164.12E1.8-C75-0.2Positive direction97.0961.5181.4214.004.41Negative direction89.7876.7272.2213.875.61Average93.4469.1176.8213.935.01E1.8-C100-0.2Positive direction99.3245.8884.1413.183.48Negative direction107.7035.7194.1013.002.75Average103.5140.7989.1213.093.12E1.8-C45-0.1Positive direction100.1090.0585.0114.756.12Negative direction102.1090.0186.9414.776.11Average101.1090.0385.9714.766.11E1.8-C45-0.3Positive direction86.7048.0174.2212.273.92Negative direction94.5045.5479.9313.363.41Average90.6046.7777.0812.823.66E1.8-C45-0.2mPositive direction47.5878.1445.9725.003.13Negative direction54.6449.8351.9330.001.66Average51.1163.9948.9527.502.39E1.8-C45-0.2lPositive direction32.0099.7828.8240.192.48Negative direction31.2095.1929.1335.502.68Average31.6097.4928.9737.852.58E1.8-C45-0.2bPositive direction54.7056.6848.0022.572.51Negative direction52.0066.2645.9421.393.10Average53.3561.4746.9721.982.81E1.8-C45-0.3bPositive direction48.5044.3547.0821.002.11Negative direction45.6046.7039.6322.062.12Average47.0545.5243.3621.532.12aThe loading procedure of E1.0-C45-0.2 was not completed due to the abrupt failure of the instrument.As given in Table4, the ductility index of most specimens is greater than 3.0, indicating a highly ductile performance. The ductility index decreases with the increase of aspect ratio, axial compression ratio, slenderness ratio, and concrete strength. Major axis bending specimen has a greater ductility than that of minor axis bending specimen. The aspect ratio seems to have moderate influence on the ductility index.


## 3.4. Stiffness Degradation

As guided in the JGJ/T code (JGJ/T 101-2015, 2015), the average stiffness can be obtained from the horizontal load-displacement hysteretic curves, which can be expressed as(3)Ki=∑j=1m|+Pi,j|+−Pi,j∑j=1m|+Δi,j|+−Δi,j,where Ki is the average stiffness of the specimen at the ith amplitude, Pi,j is the maximum load of the jth cycle at the ith amplitude, Δi,j is the maximum displacement of the jth cycle at the ith amplitude, and (+) and (−) mean the positive and negative position, respectively.Figure11 shows the relationship of the average stiffness with horizontal displacement; it illustrates the stiffness degradation with increasing lateral displacement, which is highly correlated with the development concrete cracks. In all test specimens, the stiffness degradation is significant before the displacement reaches to 2Δy; as the displacement continues to increase, the stiffness degradation continues at a lower and continually decreasing rate. The aspect ratio, axial compression ratio, and concrete strength have a little effect on the stiffness degradation. The stiffness reduces faster when the specimen is less slender, and the stiffness degradation rate of minor axis bending specimen is lower than that of major axis bending specimen.Figure 11
Stiffness of test specimens. (a) Variation of aspect ratio. (b) Variation of axial compression ratio. (c) Variation of bending axis. (d) Variation of slenderness ratio. (e) Variation of concrete strength.
(a)(b)(c)(d)(e)


## 3.5. Energy Dissipation Capacity

The energy dissipation per cycle,Ei, is the area enveloped by each hysteretic loop [24, 30, 31]. Figure 12 shows the accumulated energy dissipation ∑Ei of the 13 test specimens. As seen from the table, negligible energy dissipation is observed before the specimen reached the yield point, before which the specimens sustain limited plastic deformation. The energy dissipation starts to accumulate with the accumulated plastic deformation. The ultimate accumulated energy dissipation reflects the energy dissipation performance of the test specimens. As shown in Figure 12, specimens with a smaller aspect ratio, lower concrete strength, smaller axial compression ratio, and smaller slenderness ratio possess better energy dissipation capacity, and major axis bending specimens have a better performance on the energy dissipation quality than that of minor axis bending specimens.Figure 12
Accumulated energy dissipation of test specimens. (a) Variation of aspect ratio. (b) Variation of axial compression ratio. (c) Variation of bending axis. (d) Variation of slenderness ratio. (e) Variation of concrete strength.
(a)(b)(c)(d)(e)


## 4. Simplified Model of Force-Displacement Hysteretic Curve

### 4.1. Introduction of the Simplified Model

A kind of trilinear model is suggested by Han and Yang [32] and Han [2] to simplify the horizontal load P versus horizontal displacement Δ hysteretic relationship. A schematic view of the simplified force-displacement hysteretic relationship is shown in Figure 13. The key parameters of the model are listed as follows.(1)
Elastic stiffnessKe is given by(4)Ke=3EIl03,EI=EsIs+0.6EcIc.Here,l0 is the effective length, Ec is the elastic modulus of concrete, which is expressed as Ec=4730fco [33], and Is and Ic are the moment of inertia for the outer steel cross-section and inner concrete cross-section.(2)
The ultimate strengthPu and corresponding displacement Δu can be given by(5)Pu=1.05a1Myh1<ξc≤4a10.2ξc+0.85Myh0.2<ξc≤1,a1=0.96−0.002ξc0≤n≤0.31.4−0.34ξcn+0.1ξc+0.540.3<n<1,Δu=6.74lnr2−1.08lnr+3.33f1n8.7−s⋅PuKe,f1n=1.336n2−0.044n+0.80400≤n≤0.51.126−0.02n0.5<n<1.Here,ξc=Asfy/Acfck=α⋅fy/fck is the steel confinement factor, in which fck is the prism compressive strength of concrete [25], α=As/Ac is the steel ratio, r = λsc/40, and s = fy/345.(3)
Stiffness of the descending stageKT is given by(6)KT=0.03⋅f2n⋅fr,α⋅Kec2−3.39c+5.41,f2n=3.043n−0.210≤n≤0.7,1.57+0.5n0.7<n<1,fr,α=8α−8.6r+6α+0.9r≤1,15α−13.8r+6.1−αr>1,where c = fcu/60.Figure 13
Simplified force-displacement relationship.


### 4.2. Comparison of the Simplified Model with Tested Curve

To verify the validity of the above formulas, the force-displacement hysteretic relationships calculated with the simplified model were compared with those obtained from the experiment, as shown in Figure14. It is proved that the simplified model predicts the force-displacement hysteretic relationship with reasonable accuracy. But discrepancies also exist; the main difference may be caused by residual stress and the lack of stiffeners; thus, more experimental and finite element research studies are needed to establish the more accurate formulas of the force-displacement hysteretic relationships.Figure 14
Comparison of simplifiedP-Δ relationship with tested P-Δ relationship. (a) E1.0-c45-0.2. (b) E1.3-c45-0.2. (c) E1.8-c45-0.2. (d) E2.3-c45-0.2. (e) E1.8-c45-0.1. (f) E1.8-c45-0.3. (g) E1.8-c45-0.2b. (h) E1.8-c45-0.3b. (i) E1.8-c45-0.2m. (j) E1.8-c45-0.2l. (k) E1.8-c60-0.2. (l) E1.8-c75-0.2. (m) E1.8-c100-0.2.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)


## 4.1. Introduction of the Simplified Model

A kind of trilinear model is suggested by Han and Yang [32] and Han [2] to simplify the horizontal load P versus horizontal displacement Δ hysteretic relationship. A schematic view of the simplified force-displacement hysteretic relationship is shown in Figure 13. The key parameters of the model are listed as follows.(1)
Elastic stiffnessKe is given by(4)Ke=3EIl03,EI=EsIs+0.6EcIc.Here,l0 is the effective length, Ec is the elastic modulus of concrete, which is expressed as Ec=4730fco [33], and Is and Ic are the moment of inertia for the outer steel cross-section and inner concrete cross-section.(2)
The ultimate strengthPu and corresponding displacement Δu can be given by(5)Pu=1.05a1Myh1<ξc≤4a10.2ξc+0.85Myh0.2<ξc≤1,a1=0.96−0.002ξc0≤n≤0.31.4−0.34ξcn+0.1ξc+0.540.3<n<1,Δu=6.74lnr2−1.08lnr+3.33f1n8.7−s⋅PuKe,f1n=1.336n2−0.044n+0.80400≤n≤0.51.126−0.02n0.5<n<1.Here,ξc=Asfy/Acfck=α⋅fy/fck is the steel confinement factor, in which fck is the prism compressive strength of concrete [25], α=As/Ac is the steel ratio, r = λsc/40, and s = fy/345.(3)
Stiffness of the descending stageKT is given by(6)KT=0.03⋅f2n⋅fr,α⋅Kec2−3.39c+5.41,f2n=3.043n−0.210≤n≤0.7,1.57+0.5n0.7<n<1,fr,α=8α−8.6r+6α+0.9r≤1,15α−13.8r+6.1−αr>1,where c = fcu/60.Figure 13
Simplified force-displacement relationship.


## 4.2. Comparison of the Simplified Model with Tested Curve

To verify the validity of the above formulas, the force-displacement hysteretic relationships calculated with the simplified model were compared with those obtained from the experiment, as shown in Figure14. It is proved that the simplified model predicts the force-displacement hysteretic relationship with reasonable accuracy. But discrepancies also exist; the main difference may be caused by residual stress and the lack of stiffeners; thus, more experimental and finite element research studies are needed to establish the more accurate formulas of the force-displacement hysteretic relationships.Figure 14
Comparison of simplifiedP-Δ relationship with tested P-Δ relationship. (a) E1.0-c45-0.2. (b) E1.3-c45-0.2. (c) E1.8-c45-0.2. (d) E2.3-c45-0.2. (e) E1.8-c45-0.1. (f) E1.8-c45-0.3. (g) E1.8-c45-0.2b. (h) E1.8-c45-0.3b. (i) E1.8-c45-0.2m. (j) E1.8-c45-0.2l. (k) E1.8-c60-0.2. (l) E1.8-c75-0.2. (m) E1.8-c100-0.2.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)


## 5. Conclusions

This study has focused on the seismic performance of elliptical CFST beam-columns under combined axial compression and cyclic lateral load. The main conclusions are summarized as follows:(1)
Most of the specimens fail in local buckling, but there are individual specimens that failed in abrupt fracture of the steel tube, which reveals the stiffeners must be used at the column base.(2)
The horizontal load and displacement hysteretic curves of all specimens are chubbiness without obvious pinching. Almost all specimens show good plastic deformation capacity and energy dissipation performance, which indicate that the elliptical CFST beam-column has good seismic performance, and it can be applied in the seismic area.(3)
The ultimate loads increase with the increasing concrete strength, but decrease with the increasing aspect ratio, axial compression ratio, and slenderness ratio. The ultimate load of major axis bending specimens is notably larger than that of minor axis bending specimens.(4)
The ductility index decreases with the increasing concrete strength, axial compression ratio, and slenderness ratio. The ductility index of major axis bending specimens is notably larger than that of minor axis bending specimens. The aspect ratio seems to have no markable influence on ductility index.(5)
The energy dissipation capacity increases with the decreasing aspect ratio, concrete strength, axial compression ratio and slenderness ratio. The energy dissipation capacity of major axis bending specimens is significantly larger than that of minor axis bending specimens.(6)
The simplified trilinear force-displacement model proposed by Han [2, 32] for rectangular and circular CFST beam-columns is also suitable for predicting the force-displacement hysteretic relationship of elliptical CFST beam-columns.(7)
Further studies on the seismic performance of elliptical CFST should conduct for design and engineering practice, including the influence of residual stress, the modified force-displacement model, and detailed parametric analysis.



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*Source: 5892788-2021-12-31.xml*