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Performance of circular CFST column to steel beam frames under lateral cyclic loading
Journal of Constructional Steel Research 67 (2011) 876–890
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Performance of circular CFST column to steel beam frames under lateral cyclic loading Lin-Hai Han a,b,∗ , Wen-Da Wang a,b , Zhong Tao c a
Department of Civil Engineering, Tsinghua University, Beijing, 100084, China
b
Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, China
c
School of Engineering, University of Western Sydney, Penrith South DC, NSW 1797, Australia
article
info
Article history: Received 6 July 2010 Accepted 29 November 2010 Keywords: Concrete filled steel tube (CFST) Frame Seismic behavior Ductility Finite element analysis (FEA) model Mechanical behavior
abstract This paper presents the study on the behavior of composite frames with circular concrete filled steel tubular (CFST) columns to steel beam. Six composite frames were tested under a constant axial load on the CFST columns and a lateral cyclic load on the frame. Each frame specimen consisted of two CFST columns and a steel beam to represent an interior frame in a building. A finite element analysis (FEA) model was developed to investigate the behavior of the composite frame. The results obtained from the FEA model were verified against those experimental results. Detailed analysis was carried out on longitudinal stress in steel beams, axial stress distribution in concrete, concrete stress along the column height and at the connection panel. Parametric studies were conducted to investigate the influence of axial load level, beam to column linear stiffness ratio on the structural behavior of composite frames. A simplified hysteretic lateral load (P ) versus lateral displacement (∆) model was proposed for such composite frames. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Concrete filled steel tubular (CFST) members are well recognized for their excellent performance owing to the combination of the merits of steel and concrete materials. Therefore, concrete filled steel tubes are being increasingly used in high-rise buildings. Fig. 1 shows a composite frame structure with circular CFST columns and steel I-beams connected by external diaphragms in China. Up until now, there have been a large number of research results on the performance of CFST members, which were reviewed by several state-of-the-art reports or papers, such as Shams et al. [1], Shanmugam et al. [2], Gourley et al. [3] and Nishiyama et al. [4]. Little research, however, has been done to investigate the behavior of composite frames consisting of CFST columns [3]. Monotonic or pseudo-dynamic tests were performed by Matsui [5], Kawaguchi et al. [6] and Tsai et al. [7] in the past in this regard. Using the nonlinear dynamic time history analysis method, Muhummud [8] and Herrera [9] presented the seismic behavior of multi-story CFST composite frames. More recently, Tort and Hajjar [10] proposed a mixed finite element modeling of rectangular CFST column to steel beam frames under static and dynamic loads.
∗ Corresponding author at: Department of Civil Engineering, Tsinghua University, Beijing, 100084, China. Tel.: +86 10 62797067; fax: +86 10 62781488. E-mail address: [email protected] (L.-H. Han). 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.11.020
Apart from the above research, a research program has recently been carried out by the authors to investigate the performance of steel beam to CFST column frames under cyclic loading, and part of the research results has already been published. Han et al. [11] presented the behavior of composite frames with concrete filled square hollow section (SHS) columns to steel beam under a constant axial load on columns and a lateral cyclic load on the frame, and developed a finite element model (FEM) to simulate the behavior of composite frames. Wang et al. [12] reported the mechanism of composite frames with square CFST columns based on the experimental research presented by Han et al. [11]. Parametric studies were conducted to investigate the influence of axial load level, beam to column linear stiffness ratio on the structural behavior of composite frames, and a simplified hysteretic lateral load (P) versus lateral displacement (∆) model was proposed for such composite frames. It is well known that, in general, circular CFST columns have more excellent mechanical behavior than square CFST columns, because the confinement effect of circular section members is more effective than that in square sections. But the beam to column connections are more convenient for square CFST columns than for circular columns, and the stiffness of square CFST columns is higher than that of circular columns with a same sectional size as a whole. So it is expected that the behavior of composite frames with circular CFST columns is different from that of frames with square CFST columns, and each type of frames should be investigated accordingly.
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Nomenclature Ac As bf CFST D Ea Ec Ecu Es fc′ fcu ft fy h he ib ic H k K1 Kj L Mub Muc n No Nu P Pua Pue Py P85% tf ts tw
α ∆ ∆y ∆u µ
Concrete cross-sectional area Steel cross-sectional area Overall width of steel I-beam Concrete filled steel tube Sectional diameter of circular CFST Dissipated energy ability Concrete modulus of elasticity Concrete modulus of elasticity under unloading and re-loading stages Steel modulus of elasticity Concrete cylinder compressive strength Concrete cube compressive strength Concrete tensile strength Yield strength of steel Overall height of steel I-beam Equivalent damping coefficient Linear stiffness ratio of beam Linear stiffness ratio of column Height of column of composite frame Beam to column linear stiffness ratio (k = ib /ic ) Lateral rigidity of composite frame when ∆ is equal to ∆y Lateral rigidity of composite frame Length of beam of composite frame Ultimate flexural strength of steel beam Ultimate flexural strength of CFST column Axial load level (n = No /Nu ) Axial load of CFST column Ultimate compressive resistance of CFST column Lateral load of connection Estimated ultimate lateral load capacity of frame by ABAQUS Ultimate lateral load capacity of frame by experiment Yield lateral load capacity of frame 85% of ultimate lateral load capacity (Pue ) of composite frame Flange thickness of I-beam Wall thickness of steel tube Web thickness of I-beam Steel ratio (α = As /Ac ) Lateral displacement of frame Yield displacement of frame Lateral displacement when lateral load of frame falls to 85% of Pue Displacement ductility coefficient.
This paper thus investigates the mechanical behavior of composite frames with circular CFST columns to steel beam. Both theoretical and experimental studies have been carried out, where new test data pertaining to the behavior of CFST circular columns to steel beam frames is presented. Each specimen consisted of two circular CFST columns and a steel I-beam to represent a typical interior frame element in a building frame, and was tested under a constant axial load and a cyclically increasing lateral load. Another objective of this study is to compare the behavior of composite frames with circular and square CFST columns.
External diaphragm Steel beam
CFST columns Fig. 1. A CFST composite frame under construction.
2. Experimental study 2.1. Specimen preparation and loading apparatus Six circular CFST columns to steel beam composite frame specimens were tested. The tested composite frame represents a basic element from the real structures, as shown in Fig. 2(a). Fig. 2(b) shows the sketch of loading and boundary conditions of the tested frame element. Fig. 2 also shows the connection and beam configurations of the test frames in detail, where the column height and the steel beam span were 1450 mm and 2500 mm, respectively. b and t1 in Fig. 2(b) were the width and thickness of the stiffened ring, respectively. The frame specimens were designed in accordance with the concept of strong-column/weak-beam, so beam failure mode was expected to occur in the tests. The ultimate flexural strengths of columns and beams are shown in Table 1, respectively, where the ultimate flexural strength (Muc ) of circular CFST columns was determined according to the specification of Eurocode 4 [13], and the ultimate flexural strength (Mub ) of beams was determined according to the Chinese code for the design of steel structures GB50017-2003 [14]. The test frames with circular CFST columns were designed to investigate the effects of the following parameters on the behavior: the level of axial load n (=0.07 or 0.06, 0.3 and 0.6) in the column, the steel ratio α (=0.06 and 0.103) of the composite column, and the beam to column linear stiffness ratio k (=0.36–0.58). The level of axial load is defined as n = No /Nu , where No is the axial load applied in the column and Nu is the axial compressive capacity of the circular column determined by specification Eurocode 4 [13]. The steel ratio (α ) is defined as α = As /Ac , where As and Ac are the cross-sectional area of steel tube and core concrete, respectively. The beam to column linear stiffness ratio is defined as k = ib /ic , where ib and ic are the linear stiffness of steel beam and CFST column, respectively. ib is defined as Es Ib /L, where Ib is the moment of inertia for steel beam, Es is the modulus of elasticity of steel and L is the length of beam, respectively. ic is defined as (EI )/H, where H is the height of column. The stiffness of circular CFST column (EI) is Es Is + 0.8Ec Ic according to the code DBJ13-51-2003 [15], where Es and Ec are modulus of elasticity of steel and concrete, respectively, and Is and Ic are moments of inertia for hollow steel cross section and core concrete cross section, respectively. Table 1 gives the details of each frame specimen, where h, bf , tw , and tf are the overall height, overall width, web thickness and flange thickness of the I-beam, respectively; D and ts are the
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(a) Frame.
(b) Typical basic frame element (unit:mm). Fig. 2. Schematic view of frame models in a real structure.
Table 1 Summary of frame specimen information. Specimen number
Specimen section (mm)
Muc or Mub (kN m)
k
α
No (kN)
n
Pue (kN)
Pua (kN)
Pua Pue
Ea (kN m)
µ
(mm)
∆y
CF-11
Column Beam
Φ 140 × 2 150 × 70 × 3.44×3.44
15.63 14.54
0.57
0.06
50
0.07
15.25
76.49
67.3
0.88
33.18
3.99
CF-12
Column Beam
Φ 140 × 2 150 × 70 × 3.44×3.44
15.63 14.54
0.57
0.06
205
0.3
13.11
68.43
67.78
0.99
28.99
4.31
CF-13
Column Beam
Φ 140 × 2 140 × 65 × 3.44×3.44
15.63 12.55
0.46
0.06
410
0.6
12.50
55.25
55.49
1.0
25.11
4.78
CF-21
Column Beam
Φ 140 × 3.34 160 × 80 × 3.44×3.44
25.95 17.5
0.58
0.103
50
0.06
15.71
96.38
98.74
1.02
35.79
4.04
CF-22
Column Beam
Φ 140 × 3.34 160 × 80 × 3.44×3.44
25.95 17.5
0.58
0.103
273
0.3
14.78
90.64
91.98
1.02
34.99
4.78
CF-23
Column Beam
Φ 140 × 3.34 140 × 65 × 3.44×3.44
25.95 12.55
0.36
0.103
545
0.6
14.72
75.66
62.17
0.82
30.45
4.71
Note: Beam’s section parameters are in the sequence of h × bf × tw × tf , and column’s section is defined by D × ts . Table 2 Material properties of steel. Steel type
ts or tf /tw (mm)
fy (N/mm2 )
fu (N/mm2 )
Es (N/mm2 )
νs
Tube of CFST
2.00 3.34
327.7 352.0
397.9 430.1
2.063 × 105 2.066 × 105
0.266 0.262
Beam
3.44
303.0
440.9
2.061 × 105
0.262
overall dimension and wall thickness of the circular steel tube, respectively. Table 1 also shows the beam to column linear stiffness ratio k, the steel ratio α , the axial load No and axial load level n for CFST columns. The measured steel mechanical properties given in Table 2 and concrete mechanical properties were used to calculate the Nu . It should be noted that the concrete mechanical properties and the configuration of the composite frames are the same as those presented by Han et al. [11] with square CFST columns. The test setup is the same as that described by Han et al. [11], the axial load (No ) of CFST columns (as shown in Fig. 2(b)) was applied and maintained constant by a hydraulic ram. The measurement arrangement and loading apparatus are the same as those given by Han et al. [11]. The lateral cyclic load (P) was applied at the end of the steel beam (as shown in Fig. 2(b)). The lateral loading history was based on ATC-24 [16] guidelines, and was the same as the described loading history in Han et al. [11] for composite frame with square CFST columns.
2.2. Test results and discussion (1) Failure modes As it was expected, it was found that all the composite frame specimens failed in the strong-column–weak-beam mode, e.g. obvious buckling deformation formed at the beam ends firstly and the bottom of columns sequentially. The plastic hinge in a column located at a distance about 25 mm away from the fastened plate, whilst the plastic hinge at a beam end located at a distance about 25 mm away from the joint ring plate. Typical test frame CF-22 after testing is shown in Fig. 3, and the simulated failure modes were given in this figure too. As can be seen, all frames formed four plastic hinges, where two of them at beam ends, and two of them at the bottom of columns. The first plastic hinge was observed at the beam end near the MTS actuator, and the second hinge occurred at another end of the steel beam. The hinges on the columns
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(a) Comparison of the deformation of specimen CF-22.
(b) Column bottom.
(c) Concrete at the bottom of the column.
(d) The section at left beam end.
(e) The section at right beam end.
(f) Core concrete at joint panel.
Fig. 3. Observed and predicted failure modes of composite frame (CF-22).
occurred after the formation of the beam hinges. Though the steel tube at the hinge location cracked on one side and buckled slightly on the other side, the core concrete showed generally good integrity after test, as shown in Fig. 3(b) and (c), respectively. This phenomenon is a little different from that observed in composite frames with square CFST columns as reported by Han et al. [11]. More severe local buckling of steel tube and concrete crushing were observed for those square CFST columns as shown in Fig. 4(a), and the core concrete near the bottom of the columns was crashed at the end of testing. The local buckling mode of steel tubes of circular CFST columns was also shown in Fig. 4(b) for comparison. Generally, square tubes are more susceptible to local buckling than circular ones, thus circular tubes can provide better confinement to concrete. (2) Lateral load (P) versus lateral displacement (∆) relationship The measured lateral load (P) versus lateral displacement (∆) hysteretic curves of the frame specimens are shown in Fig. 5.
It was observed that there is no obvious strength deterioration and stiffness degradation for the composite frames. The curves of the frames with circular CFST columns are much favorable in general than the curves of the frames with square CFST columns presented by Han et al. [11] since circular tubes can provide better confinement to the core concrete. The ultimate lateral loads (Pue ) obtained in the tests are listed in Table 1. Fig. 6 shows the effect of axial load level (n) on P–∆ envelop curves of the composite frames. It can be seen that the axial load level (n) influences not only the ultimate lateral load (Pue ) but also the ductility of the composite frames. A ductility coefficient (µ) is used as µ = ∆u /∆y (where ∆y is the lateral displacement at material yield and ∆u the lateral displacement when the lateral load falls to 85% of the maximum lateral strength (Pue )) to quantify the ductility on n and the relation of P–∆. From Fig. 6, it can be found that both Pue and µ of the frames decrease with increasing n. The CFST columns of the composite frame are combined axial
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(a) Square CFST column (SF-13).
(b) Circular CFST column (CF-13).
Fig. 4. Typical deformation modes of CFST columns at the bottom.
(a) CF-11 (n = 0.07).
(b) CF-12 (n = 0.3).
(c) CF-13 (n = 0.6).
(d) CF-21 (n = 0.06).
(e) CF-22 (n = 0.3).
(f) CF-23 (n = 0.6). Fig. 5. Lateral load (P) versus lateral displacement (∆) cyclic curves.
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a
881
b
Fig. 6. Lateral load (P) versus lateral displacement (∆) of envelop curves.
a
b
Fig. 7. he –∆/∆y relations.
compression loading and bending, and the incremental axial load will enlarge second-order effect to reduce the lateral ultimate strength and displacement ductility of the CFST columns. (3) Dissipated energy ability (Ea ) and damping coefficient (he ) Dissipated energy ability (Ea ) was used to describe the energy dissipation of the composite frames according to Chinese Standard JGJ101-96 [17], which was also used by Han et al. [11] for square CFST frames. Table 1 shows the ductility coefficient (µ) and energy dissipation (Ea ) of the tested frames, respectively. From Table 1, the following findings can be made: (1) In general, Ea decreased obviously with increasing axial load level for frames. (2) Ea increased with increasing k. (3) Generally, the ultimate lateral load (Pue ) increased slightly with an increasing k for specimens with a same n. The composite frames with square CFST columns in Han et al. [11] have shown similar effects of different parameters on the total dissipated energy ability (Ea ) and ultimate lateral load (Pue ), but the decreasing trend of Ea with increasing axial load level was much more distinct than that for the frames in this paper. It was shown that the axial load level had much more evident influence for the composite frames with square columns, i.e. Ea decreased from 35.79 to 34.99 kN m or 30.45 kN m when the axial load level increased from 0.06 (specimen CF-21) to 0.3 (specimen CF-22) or 0.6 (specimen CF-23) in this paper, but the corresponding values of Ea were 76.44, 68.43 and 47.47 kN m for the frames SF11, SF-12 and SF-13 with square CFST columns in Han et al. [11], respectively. Fig. 7 demonstrates that the accumulative equivalent damping coefficient (he ) of the composite frames increases greatly with increasing relative displacement (∆/∆y ), where he is defined as he = Ea /2π and also used by Han et al. [11]; ∆y is the yielding displacement of the frame. It seems that the axial load level (n) and the beam to column linear stiffness ratio (k) have only slightly effect on the he − ∆/∆y relationship for the current frames.
This is different from that of the composite frames with square CFST columns presented by Han et al. [11]. he of the frames with square CFST columns decreased obviously with increasing n. It is also found that he of the composite frames with circular CFST columns is bigger than those with square CFST columns at a same relative displacement. This demonstrates that the accumulative damping ability of the composite frames in this paper is superior to those frames with square CFST columns. Dissipated energy ability and accumulative damping of composite frames could be greatly affected by the failure of composite columns if their core concrete experience severe damage and strength degradation. But the deterioration of the core concrete can be restricted by the confinement from the steel tubes. Less or even no damage will occur if strong confinement is supplied. Since the confinement effect of circular steel tubes is more effective than that of square steel tubes, the effects of n and k on he are thus different for frames with different column shapes. (4) Rigidity degradation Fig. 8 shows the effect of n on relative rigidity degradation (Kj /K1 ) of specimen as a function of ∆/∆y . The rigidity (Kj ) is ∑m
i=1 expressed as Kj = ∑m
Pji
i i=1 uj
, where Pji and uij are the maximum load
and lateral displacement respectively, under the ith loading cycle when ∆/∆y equals j, and m is the cycle time of loading. K1 is the rigidity when ∆ is equal to ∆y . It can be seen that n has moderate on specimens in series CF-2 since the columns in this series have a higher steel ratio (α ). As the core concrete of a composite column undergoes significant rigidity degradation under cyclic loading, a higher steel ratio (α ) can provide significant confinement to its core concrete and postpones its rigidity degradation. The composite frames with square CFST columns in Han et al. [11] have shown clear effect of rigidity degradation with increasing axial load level (n), and the declining trend was much more distinct than that for
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a
b
Fig. 8. Kj /K1 –∆/∆y relations.
(a) Concrete model.
(b) Steel model.
Fig. 9. Stress versus strain relationships of concrete and steel.
the frames in this paper. The rapid rigidity degradation should be considered for composite frames with square CFST columns if they are designed to sustain cyclic loading or earthquake action. 3. Finite element analysis (FEA) model 3.1. General description The Pacific Earthquake Engineering Research Center (PEER) developed a well-known Open System for Earthquake Engineering Simulation (OpenSees for short) as a software platform for simulation of structural and geotechnical systems [18]. The behavior of frame structures can be simulated commendably by using the nonlinear beam–column element from OpenSees. Tsai et al. [7] simulated the dynamic behavior of CFST column to steel beam composite frames using OpenSees, where the predicted results by OpenSees matched well with the experimental curves. The hysteretic behavior of composite frames in this paper were simulated using OpenSees in the first place. The steel and concrete were simulated by Steel02 model and Concrete02 model in OpenSees, respectively. The stress versus strain relationships of concrete and steel in OpenSees are shown in Fig. 9(a) and (b), respectively, where fc′ and ε0 are the concrete compressive cylinder strength and corresponding strain, respectively; σcu and εcu are the concrete crush compressive strength and corresponding strain, respectively; Ec and Ect are the concrete modulus of elasticity under compression and tension, respectively; ft is the concrete tensile strength; Ecu is the concrete modulus of elasticity under unloading and re-loading stages; σy and εy are the yield stress of steel and corresponding strain, respectively; Es is the steel modulus of elasticity. The loading and unloading rules used in this model were described in the user manual of OpenSees [18]. All the
Fig. 10. Finite element model for composite frame.
circular CFST columns and steel beams of frames were modeled using the flexibility-based nonlinear beam–column elements with discretized fiber section model in OpenSees. This model is also applicable for composite frame consists of square CFST columns and steel beam. The hysteretic relationship of the composite frames can be calculated conveniently by using OpenSees, however, the microcosmic mechanical performance, i.e. stress and deformation at different load stages, cannot be simulated rationally using the solver because it was based on the nonlinear fiber beam–column element theory. To address this discrepancy, an accurate three-dimensional finite element analysis (FEA) is necessary. Han et al. [11] investigated the performance of composite frames with square CFST
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(a) 15-SCP [6].
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(b) 30-SCP [6]. Fig. 11. Comparison of P versus ∆ curves between predicted and measured results.
Fig. 13. P–∆ curves of typical CFST frame CF-22. Fig. 12. Typical P versus ∆ curve of the composite frame.
columns and steel beam under constant axial load on the columns and incremental flexural load on the beam using ABAQUS software [19], and Wang et al. [12] performed a further detailed stress analysis. Similar FEA model as that described by Han et al. [20] and Han et al. [11] is used in this paper to simulate composite frames with circular CFST columns. Details of the finite element types and meshes, boundary conditions, material modeling of steel and core concrete, interface and contact between the concrete and the steel tube can be found in Han et al. [11]. Typical meshes of a composite frame with circular CFST columns are shown in Fig. 10. 3.2. Verification of FEA model To verify the validity of the OpenSees model, P–∆ hysteretic relationships by the above-mentioned OpenSees model were compared with experimental results (composite frames with square CFST columns) presented by Kawaguchi et al. [6] and the tested results in this paper, as shown in Figs. 11 and 5, respectively. The calculated curves using OpenSees are denoted as Model I in Figs. 11 and 5. The comparison indicates that reasonable accuracy has been achieved for OpenSees in predicting the cyclic behavior of the composite frames. Fig. 12 shows a typical lateral load versus lateral displacement hysteretic curve of the composite frame with strongcolumn–weak-beam (specimen CF-12) calculated by OpenSees. Clearly, the curve can be divided into several stages. The different stages of the curve are analyzed below.
(1) Elastic stage (from point O to point A): The flanges of steel beam reach yielding at point A. (2) Elastic–plastic stage (from point A to point B): The web of steel beam starts to yield. The stiffness of columns reduces gradually because the area of the compression zone of circular CFST columns gradually reduces. The curve starts to descend slowly. (3) Unloading stage (from point B to point C ): The lateral load (P) versus displacement (∆) curve shows a linear behavior in general. The unloading stiffness is close to the initial stiffness (OA) of the curve. (4) Elastic–plastic stage of reverse loading (from point C to point D): The curve shows nonlinear behavior. The stiffness of the columns decreases with incremental yielding zones of steel beam. (5) Strengthening stage (from point D to point E or from B to F ): The sectional stiffness of the steel beam or CFST column become very small, and the load increases slowly but the deformation increases quickly. (6) Re-loading stage (from point E to point F ): The curve shows similar behavior as the stage from point B to point C , D and then E. (7) Descending stage (from point F to point G): The curve starts to go down. As can be seen, the characteristics of this curve at every stage are quite similar to those of the relationships of the composite frames with square CFST columns presented by Wang et al. [12], but demonstrate some minor differences at every stage as well, i.e. the strength deterioration and stiffness degradation of the hysteresis curves after peak load of the composite frames with square CFST
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(a) Section B1 (Stage 1).
(b) Section B2 (Stage 1).
(c) Section B1 (Stage 3).
(d) Section B2 (Stage 3).
(e) Section B1 (Stage 5).
(f) Section B2 (Stage 5). Fig. 14. Longitudinal stress of steel beam at the end of sections B1 and B2.
columns became more distinct than those frames with circular columns. It is shown that the damage of the core concrete of the square CFST columns became serious during the load descending stage because the confinement effect of square tube would start to weaken. It should be noted that the strengthening stage will appear from point F to G′ if the value of n is small, i.e. n less than 0.3, the curve FG′ will go up strengthening stage stability, and similar to the curve BF . All the calculated monotonic P–∆ curves of composite frames by ABAQUS are given and denoted as Model II in Figs. 5 and 11, respectively. The predicted curves match generally well with the envelop curves of the measured P–∆ relationships. There is little difference between the envelop curves of the cyclic P–∆ curves by Model I (OpenSees) and the monotonic P–∆ curves predicted by Model II. But the ultimate strengths predicted by Model II are generally a little higher than the values obtained from the OpenSees predictions (Model I), since the strength degradation, accumulative damage, cracking and crushing of core concrete under cyclic loading were ignored in the simulation using Model II under monotonic loading. The ultimate lateral loads (Pue ) of composite frames obtained from the tests and finite element analysis by Model II (Pua ) are given in Table 1. Reasonable agreement has been achieved between the two sets of results for most of the composite frames except for
those tested under an axial load level (n) of 0.6. It is expected that, higher n means higher axial compressive load applied on a column. Therefore, the possible influence of unexpected imperfections of the test setup and unintended load eccentricities may be magnified in this case. It should be noted that, experimental results on beam to CFST column frames remain very scarce. Subsequently, finite element analysis is essential to be carried out to expand the experimental data. The FEA model introduced in this paper can be used conveniently to analyze the performance of composite frames. 4. Analytical behavior Model II is used in the following to conduct a behavior analysis for the composite frames. Frame specimen CF-22 (shown in Table 1) is selected as an example. Fig. 13 shows the whole fullrange P–∆ envelop curve. It can be divided into five stages, as marked in the figure. It should be noted that the points 1 and 3 correspond to the points A and B in Fig. 12, respectively. Four typical sections of the circular CFST columns and steel beam are selected to demonstrate stress distributions of the composite frame CF-22, as shown in Fig. 13. The four sections are so selected that they are at the locations of plastic hinges, i.e. sections B1 and B2 on the steel beam near the ring plates and sections C1 and C2 on the bottom of the CFST columns, respectively. Fig. 3(a)
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(a) Stage 1.
(b) Stage 2.
(d) Stage 4.
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(c) Stage 3.
(e) Stage 5. Fig. 15. Concrete axial stress distribution at section C1 of CFST (CF-22).
Stage 1.
Stage 3.
Fig. 16. Stress distribution of concrete along the column height.
gives the buckling modes and deformations of frame CF-22 after test. The simulated mode of the frame CF-22 at point 5 is also shown in this figure for comparison. The predicted buckling modes of the beam and the deformations at the bottom of the columns match well with those of the test. The observed deformation of the four sections at stage 5 defined in Fig. 13 (from point 4 to point 5) are shown in Fig. 3(b)–(e), respectively. The steel tubes of the circular CFST columns at sections C1 and C2 show evident outward buckling, while obvious local buckling of beam flanges and web occurs at sections B1 and B2. The failure mode of the core concrete at the bottom of the circular CFST column is shown in Fig. 3(c),
and the calculated axial stresses S33 are also shown in the figure. The core concrete at tension zone near the stiffened ribs cracks, and the axial tension stress exceeds the concrete ultimate tension strength. Moreover, obvious local buckling occurs in the flanges and web of beam at sections B1 and B2. The experimental result and FEA result by Model II are consistent, as shown in Fig. 3(d) and (e), respectively. Fig. 3(f) shows the mode of the core concrete at the connection panel. The concrete at the panel demonstrates favorable integrity, and no obvious crack is observed. The axial tension and compression stresses of the concrete of the panel are lower than their ultimate strength. The prediction by Model II
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(a) The left column (Stage 3).
(b) The right column (Stage 3). Fig. 17. Core concrete stress distribution at connection panel (CF-22).
precisely catches the trend of the observed deformation, as shown in Fig. 3. 4.1. Longitudinal stress in steel beams Fig. 14 shows the longitudinal stress distributions of the beam during the various load stages, e.g. stages 1, 3 and 5 as defined in Fig. 13. The longitudinal compression and tension stresses of sections B1 and B2 are shown in Fig. 14(a)–(f). The stress distribution pattern of the left beam end (B1) is different from that of the right beam end (B2). The beam is separated into two parts by a bending inflexion located at the approximate middle of the beam, and the two parts deform in different ways. The steel top flange of the left part of the beam (B1) is in compression and the bottom flange in tension, while the trend of the right part of the beam (B2) is opposite. The values of tension and compression stresses of the steel beam increase with increasing lateral load. The compression stress of the flange at section B2 reaches firstly the yield stress of steel. The yield area then extends from the flange to the web. When the composite frame reaches its ultimate load (point 3), about half of the compression web of section B2 has yielded. The tension area of the web at section B2 does not yield at this stage although the peak load has been reached. The lateral load begins to decrease from stage 3, and local buckling appears on the compressive web near section B2. The stress and deformation distributions at section B1 are quite similar to those at section B2, but the stresses and deformation at section B1 are smaller than those at section B2. 4.2. Concrete axial stress distribution Fig. 15 shows the concrete axial stress distribution of section C1 at the typical five loading stages. In the figures, fc′ is the cylinder compression strength of concrete. In Fig. 15, the axial stresses of concrete are different at various loading stages. The whole section of CFST column is under compression before the lateral load (P) is applied. Part of the circular section undergoes tension with increasing lateral load, and the compression area reduces progressively owing to the bending moment effect. The compression stresses of the steel tubes reach yield stress at stage two but the tension stresses are under the yield strength. This is owing to the combination of the axial compression stress and bending stress. After the lateral load exceeds the ultimate load, local buckling appears at the compression zone of the steel tubes and the stresses begin to decrease. It is believed that the core concrete offers effective support to the outer steel tube and thus delays its local buckling compared with a hollow one. The stress states of section C2 are similar to those of section C1. The concrete stress distributions at sections C1 and C2 are much more homogeneous when compared with those in the corresponding frame with square CFST columns presented by
Wang et al. [12], and no obvious stress concentration is observed in a circular section. In contrast, the concrete stress at the corners of a square CFST column is much higher than that near the flat zones [12], i.e. the maximum stress at the corners of a tube of the frame SF-22 in Wang et al. [12] is 1.7fc′ and the average stress is 0.91fc′ at the flat zones, where fc′ is the concrete cylinder compression strength. Since the CFST columns of the composite frame are subjected to combined axial compression and bending moment, their deformation curves are anti-symmetric with a bending inflexion, where sections C5 and C6 are inverted moment points and the stresses at these two sections are expected to be very low. Sections C3 and C4 of the CFST columns are just below the connections. The concrete stresses of sections C3 and C4 are similar to those of sections C1 and C2, respectively, though the stress direction is reversed. In general, all the sections, from C1 to C6, the stress distribution patterns in the current analyzed frame are similar to those presented by Wang et al. [12] for composite frames with square CFST columns. 4.3. Concrete stress along the column height The concrete stresses of the CFST columns along the vertical symmetry planes are shown in Fig. 16. Only stresses at point 1 and point 3 are shown in Fig. 16. The left and lower parts of the columns are in tension, while the right and upper parts of the columns are under compression. The concrete axial stresses and tension areas increases with increasing lateral load gradually. The stress distributions of the left and right columns are similar in general, but the location of zero moment section on the right column away from the bottom of the column is higher than that of the left column. The stress distribution trends are also similar to those of the square columns described by Wang et al. [12] although the stress values are different, i.e. the maximum axial compressive stress at stage three are 97.6 and 82.4 N/mm2 for the composite frame with square CFST columns in Wang et al. [12] and the frame in this paper, respectively. The value of the frame with square columns is bigger than those frames in this paper because of the stress concentration by the corner steel tube for the square CFST columns. 4.4. Concrete stress at connection panels The core concrete stress distributions at connection panels are shown in Fig. 17. Once again, it is found that the concrete stress distributional patterns at connection panels are similar to those presented by Wang et al. [12] although the stress values are different, and the value of the frame with square columns at every load stage is bigger than those frames in this paper because the square CFST columns tube causes clear stress concentration at
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(a) Typical failure process and sequences of the plastic hinges.
(b) Stress distribution (Stage 1).
(c) Stress distribution (Stage 3).
(d) Stress distribution (Stage 5).
Fig. 18. Failure process and stress distribution (CF-22).
the corner zone. Therefore, only the stress distributions at point 3 are given in Fig. 17. In general, the stress values at the panel of the left column are slightly larger than those of the right column under the same loading. The core concrete at the left-bottom and right-top of the panel is under compression and that at the lefttop and right-bottom is in tension. It can be seen that all the axial
compressive stresses of the core concrete are smaller than the concrete cylinder compressive strength (fc′ ) except at a very small area with local stress concentration. The stress concentration of the frames with square CFST columns is severer than those frames with circular columns because of the corner effect. This explains why the connection strength exceeds those of the columns and beam in
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a
b
Fig. 19. Influence of axial load level (n) on P–∆/H curves.
Fig. 20. A schematic view of simplified P versus ∆ relationship [12].
a composite frame. Therefore, the connections remain intact after plastic hinges form in the frame beam and columns.
5. Parametric analysis and simplified P–∆ hysteretic model 5.1. Effects of parameters on the P–∆ envelope curves
4.5. Stress distributions of the whole frame Fig. 18(a) shows the typical failure process and sequences of plastic hinges of the composite frame. The numbers 1–4 shown in the figure represent the four different plastic hinges of the frame under loading. The first two plastic hinges occurred at the beam ends near the exterior stiffened ring, and the first one appeared on the side near the load actuator. The third and fourth plastic hinges were formed at the bottom of the columns near the stiffened ribs, respectively. The hinges appeared gradually and can be located from the Mises stresses distribution of the whole frame model, which are shown in Fig. 18(b)–(d) for the stages of one, three and five, respectively. The local stresses and deformations at the locations of the plastic hinges are shown in this figure too. It is shown that the maximum stresses are located at the bottom of the columns and beam ends, respectively, where plastic hinges are formed at these locations. The stresses at the hinge locations increase gradually with the incremental lateral displacement. Significant local deformations occur in the four hinge zones. The locations and sequence of plastic hinge of the frame with square CFST columns are similar [12], but the local buckling at the bottom of the square CFST columns is clear and severe.
It was shown that the axial load level n, steel ratio α , yielding strength of steel (fy ) and cube strength of concrete (fcu ), column slenderness ratio (λ), and the beam to column linear stiffness ratio k are the main influential factors on the P-∆ envelope curves. Further parameter analysis carried out in this paper shows that the effects of these parameters on composite frames with circular CFST columns are generally similar to those on frames with square CFST columns presented by Wang et al. [12]. Only the effect of axial load level (n) on P–∆ curves of composite frames with circular CFST columns is shown in Fig. 19. It can be found that the ultimate lateral load and displacement ductility decrease with increasing axial load level (n). The constraint of beam to the columns can be enhanced for a frame with a larger beam to column linear stiffness ratio, thus an increase in the ultimate load of the frame is expected. 5.2. Simplified P–∆ hysteretic model Based on numerical analysis by OpenSees, it was found that the simplified P–∆ hysteretic model proposed for composite frames with square CFST columns by Wang et al. [12] is also applicable for the composite frame with circular CFST columns, as shown in
L.-H. Han et al. / Journal of Constructional Steel Research 67 (2011) 876–890
(a) CF-12 (n = 0.3).
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(b) CF-22 (n = 0.3).
Fig. 21. Comparison of P versus ∆ relationships between simplified model and test results.
Fig. 20. The lateral load (P) versus lateral displacement (∆) relationships of composite frames as shown in Fig. 20 can be divided into seven stages as following: elastic stage, elastic–plastic stage, unloading stage, elastic–plastic stage of reverse loading, strengthening stage, re-loading stage, descending stage or strengthening stage. The simplified P–∆ envelop curves model can be expressed by a tri-linear model as shown in Fig. 20. Where Ka is the stiffness of the elastic stage, Py and ∆p are the ultimate strength of the frame and corresponding displacement, and KT is the stiffness of the descending stage. The line OA represents the elastic stage, and the lines AB and BC are the elastic–plastic stage and descend stage, respectively. The curve can be simulated by the second-order elastic analysis, second-order plastic hinge analysis and rigid-plastic analysis, respectively. The detailed analysis procedures were described in Chen et al. [21]. The equations for the four key parameters used in the model for composite frame with square CFST columns, i.e. Ka , Py , ∆p and KT , were presented by Wang et al. [12], however, the following parameters for composite frame with circular CFST columns should be used. (1) The servicing stiffness of composite columns (EI) should be replaced by Es Is + 0.6Ec Ic for circular CFST column according to Eurocode 4 [13] to calculate Ka . (2) For the calculations of Py and ∆p , formulae available in Eurocode 4 [13] in predicting the ultimate strength (Pyc ) for circular CFST columns should be applied. (3) The expression for the stiffness of the descending stage (KT ) is the same as that given by Wang et al. [12], but the value of the parameter p in the formula is different, where p is the hardening stage coefficient of moment versus curvature model for circular CFST columns and was given by Han and Yang [22]. The unloading stage and re-loading stage of the simplified P–∆ model is same to the model in Wang et al. [12]. The validity ranges of this modified model are: n = 0–0.8, α = 0.03–0.2, λ = 10–80, fy = 200–500 MPa, fcu = 30–80 MPa and ξ = 0.2–4. In which ξ is the confinement effect coefficient of CFST columns, and is defined as ξ = α · fy /fck , where fy and fck are the steel yield strength and the concrete compressive strength (fck = 0.67fcu for normal strength concrete), respectively. To verify the simplified model, the predicted P–∆ hysteretic relationships using the simplified model are compared with experimental curves in this paper. Fig. 21 shows two set typical comparisons. It can be found from the comparison that, generally, a reasonable agreement is achieved. 6. Conclusions The following conclusions may be drawn within the limitations of the research in this paper:
(1) The experiment shows that the composite frame with circular CFST column had excellent seismic resistance. Beam failure was observed first in all the frames. The lateral load-carrying capacity, ductility coefficient and energy dissipation of composite frame decreased as the axial load level in the column increased. The ultimate lateral load of composite frame increased with an increase in beam–column linear stiffness ratio if other conditions were kept the same. (2) The cyclic behavior of the composite frames is similar to that of the frames with square CFST columns in general, but the influences of axial load level and beam–column linear stiffness ratio on the composite frames in this paper are relatively much slighter than on those frames with square CFST columns in terms of rigidity degradation and dissipated energy ability. The load versus displacement curves of the frames with circular CFST columns are more favorable than those of frames with square CFST columns. (3) The introduced FEA model was able to reasonably predict the lateral load versus lateral displacement relationship of the composite frame. Detailed stress analysis was carried out and conducted to realize the microcosmic mechanics performance of the composite frames. (4) A simplified hysteretic lateral load (P) versus lateral displacement (∆) model of the composite frame was proposed. The model should be useful in dynamic analysis for composite frames with circular CFST columns. Acknowledgements The research reported in this paper is the Project supported by Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (20070003087), and part of the Program for Changjiang Scholars and Innovative Research Team in University (IRT00736). This financial support is highly appreciated. References [1] Shams M, Saadeghvaziri MA. State of the art of concrete-filled steel tubular columns. ACI Structural Journal 1997;94(5):558–71. [2] Shanmugam NE, Lakshmi B. State of the art report on steel–concrete composite columns. Journal of Constructional Steel Research 2001;57(10):1041–80. [3] Gourley BC, Tort C, Denavit MD, Schille PH, Hajjar JF. A synopsis of studies of the monotonic and cyclic behavior of concrete-filled steel tube members, connections, and frames. NSEL report series. Report no. NSEL-008. Department of Civil and Environmental Engineering, Univ. of Illinois at Urbana-Champaign; 2008. [4] Nishiyama I, Morino S, Sakino K. et al. Summary of research on concretefilled structural steel tube column system carried out under the US–Japan cooperative research program on composite and hybrid structures. BRI research paper no.147. Japan: Building Research Institute; 2002.
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[5] Matsui C. Strength and behaviour of frames with concrete filled square steel tubular columns under earthquake loading. In: Proceeding of 1st international speciality conference on concrete filled steel tubular structures. 1985. p. 104–11. [6] Kawaguchi J, Morino S, Sugimoto T. Elasto-plastic behaviour of concrete-filled steel tubular frames. In: Composite construction in steel and concrete III. Proceedings of an engineering foundation conference. 1997. p. 272–81. [7] Tsai KC, Weng YT, Lin ML. Pseudo dynamic tests of a full-scale CFT/BRB composite frame: displacement based seismic design and response evaluations. In: Proceeding of the international workshop on steel and concrete composite constructions. 2003. [8] Muhummud T. Seismic design and behaviour of composite moment resisting frame constructed of CFT columns and WF beams. Ph.D. dissertation. Bethlehem (PA, USA): Department of Civil and Environmental Engineering, Lehigh University; 2003. [9] Herrera R. Seismic behaviour of concrete filled tube column-wide flange beam frames. Ph.D. dissertation. Bethlehem (PA, USA): Department of Civil and Environmental Engineering, Lehigh University; 2005. [10] Tort C, Hajjar JF. Mixed finite-element modeling of rectangular concrete-filled steel tube members and frames under static and dynamic loads. Journal of Structural Engineering, ASCE 2010;136(6):654–64. [11] Han LH, Wang WD, Zhao XL. Behaviour of steel beam to concrete-filled steel tubular column frames: finite element model and verifications. Engineering Structures 2008;30(6):1647–58. [12] Wang WD, Han LH, Zhao XL. Analytical behavior of frames with steel beam to
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concrete-filled steel tubular column. Journal of Constructional Steel Research 2009;65(3):497–508. Eurocode 4. Design of composite steel and concrete structures-part 1.1 general rules and rules for buildings. Brussels (Belgium): European Committee for Standardization, BS EN 1994-1-1:2004. GB50017-2003. Code for design of steel structures. Peking: Chinese Planning Press China; 2003 [in Chinese]. DBJ13-51-2003. Technical specification for concrete-filled steel tubular structures. Fuzhou. 2003 [in Chinese]. ATC-24. Guidelines for cyclic seismic testing of components of steel structures. Redwood City (CA): Applied Technology Council; 1992. JGJ101-96. Specification for test methods of seismic buildings. Peking: China Architecture Industrial Press; 1997 [in Chinese]. Mazzoni S, McKenna F, Fenves GL. et al. Open system for earthquake engineering simulation user manual (ver. 1.7.0). Berkeley: Pacific Earthquake Engineering Research Center. PEER, Univ. of California; 2006. Hibbitt, Karlson & Sorensen Inc. ABAQUS/standard user’s manual, version 6.5. Providence (RI): Hibbitt, Karlsson, & Sorensen, Inc.; 2005. Han LH, Yao GH, Tao Z. Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-Walled Structures 2007;45(1):24–36. Chen WF, Toma S. Advanced analysis for steel frames: theory, software and applications. Boca Raton (FL): CRC Press; 1994. Han LH, Yang YF. Cyclic performance of concrete-filled steel CHS columns under flexural loading. Journal of Constructional Steel Research 2005;61(4): 423–52.
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Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Performance of circular CFST column to steel beam frames under lateral cyclic loading Lin-Hai Han a,b,∗ , Wen-Da Wang a,b , Zhong Tao c a
Department of Civil Engineering, Tsinghua University, Beijing, 100084, China
b
Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, China
c
School of Engineering, University of Western Sydney, Penrith South DC, NSW 1797, Australia
article
info
Article history: Received 6 July 2010 Accepted 29 November 2010 Keywords: Concrete filled steel tube (CFST) Frame Seismic behavior Ductility Finite element analysis (FEA) model Mechanical behavior
abstract This paper presents the study on the behavior of composite frames with circular concrete filled steel tubular (CFST) columns to steel beam. Six composite frames were tested under a constant axial load on the CFST columns and a lateral cyclic load on the frame. Each frame specimen consisted of two CFST columns and a steel beam to represent an interior frame in a building. A finite element analysis (FEA) model was developed to investigate the behavior of the composite frame. The results obtained from the FEA model were verified against those experimental results. Detailed analysis was carried out on longitudinal stress in steel beams, axial stress distribution in concrete, concrete stress along the column height and at the connection panel. Parametric studies were conducted to investigate the influence of axial load level, beam to column linear stiffness ratio on the structural behavior of composite frames. A simplified hysteretic lateral load (P ) versus lateral displacement (∆) model was proposed for such composite frames. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Concrete filled steel tubular (CFST) members are well recognized for their excellent performance owing to the combination of the merits of steel and concrete materials. Therefore, concrete filled steel tubes are being increasingly used in high-rise buildings. Fig. 1 shows a composite frame structure with circular CFST columns and steel I-beams connected by external diaphragms in China. Up until now, there have been a large number of research results on the performance of CFST members, which were reviewed by several state-of-the-art reports or papers, such as Shams et al. [1], Shanmugam et al. [2], Gourley et al. [3] and Nishiyama et al. [4]. Little research, however, has been done to investigate the behavior of composite frames consisting of CFST columns [3]. Monotonic or pseudo-dynamic tests were performed by Matsui [5], Kawaguchi et al. [6] and Tsai et al. [7] in the past in this regard. Using the nonlinear dynamic time history analysis method, Muhummud [8] and Herrera [9] presented the seismic behavior of multi-story CFST composite frames. More recently, Tort and Hajjar [10] proposed a mixed finite element modeling of rectangular CFST column to steel beam frames under static and dynamic loads.
∗ Corresponding author at: Department of Civil Engineering, Tsinghua University, Beijing, 100084, China. Tel.: +86 10 62797067; fax: +86 10 62781488. E-mail address: [email protected] (L.-H. Han). 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.11.020
Apart from the above research, a research program has recently been carried out by the authors to investigate the performance of steel beam to CFST column frames under cyclic loading, and part of the research results has already been published. Han et al. [11] presented the behavior of composite frames with concrete filled square hollow section (SHS) columns to steel beam under a constant axial load on columns and a lateral cyclic load on the frame, and developed a finite element model (FEM) to simulate the behavior of composite frames. Wang et al. [12] reported the mechanism of composite frames with square CFST columns based on the experimental research presented by Han et al. [11]. Parametric studies were conducted to investigate the influence of axial load level, beam to column linear stiffness ratio on the structural behavior of composite frames, and a simplified hysteretic lateral load (P) versus lateral displacement (∆) model was proposed for such composite frames. It is well known that, in general, circular CFST columns have more excellent mechanical behavior than square CFST columns, because the confinement effect of circular section members is more effective than that in square sections. But the beam to column connections are more convenient for square CFST columns than for circular columns, and the stiffness of square CFST columns is higher than that of circular columns with a same sectional size as a whole. So it is expected that the behavior of composite frames with circular CFST columns is different from that of frames with square CFST columns, and each type of frames should be investigated accordingly.
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Nomenclature Ac As bf CFST D Ea Ec Ecu Es fc′ fcu ft fy h he ib ic H k K1 Kj L Mub Muc n No Nu P Pua Pue Py P85% tf ts tw
α ∆ ∆y ∆u µ
Concrete cross-sectional area Steel cross-sectional area Overall width of steel I-beam Concrete filled steel tube Sectional diameter of circular CFST Dissipated energy ability Concrete modulus of elasticity Concrete modulus of elasticity under unloading and re-loading stages Steel modulus of elasticity Concrete cylinder compressive strength Concrete cube compressive strength Concrete tensile strength Yield strength of steel Overall height of steel I-beam Equivalent damping coefficient Linear stiffness ratio of beam Linear stiffness ratio of column Height of column of composite frame Beam to column linear stiffness ratio (k = ib /ic ) Lateral rigidity of composite frame when ∆ is equal to ∆y Lateral rigidity of composite frame Length of beam of composite frame Ultimate flexural strength of steel beam Ultimate flexural strength of CFST column Axial load level (n = No /Nu ) Axial load of CFST column Ultimate compressive resistance of CFST column Lateral load of connection Estimated ultimate lateral load capacity of frame by ABAQUS Ultimate lateral load capacity of frame by experiment Yield lateral load capacity of frame 85% of ultimate lateral load capacity (Pue ) of composite frame Flange thickness of I-beam Wall thickness of steel tube Web thickness of I-beam Steel ratio (α = As /Ac ) Lateral displacement of frame Yield displacement of frame Lateral displacement when lateral load of frame falls to 85% of Pue Displacement ductility coefficient.
This paper thus investigates the mechanical behavior of composite frames with circular CFST columns to steel beam. Both theoretical and experimental studies have been carried out, where new test data pertaining to the behavior of CFST circular columns to steel beam frames is presented. Each specimen consisted of two circular CFST columns and a steel I-beam to represent a typical interior frame element in a building frame, and was tested under a constant axial load and a cyclically increasing lateral load. Another objective of this study is to compare the behavior of composite frames with circular and square CFST columns.
External diaphragm Steel beam
CFST columns Fig. 1. A CFST composite frame under construction.
2. Experimental study 2.1. Specimen preparation and loading apparatus Six circular CFST columns to steel beam composite frame specimens were tested. The tested composite frame represents a basic element from the real structures, as shown in Fig. 2(a). Fig. 2(b) shows the sketch of loading and boundary conditions of the tested frame element. Fig. 2 also shows the connection and beam configurations of the test frames in detail, where the column height and the steel beam span were 1450 mm and 2500 mm, respectively. b and t1 in Fig. 2(b) were the width and thickness of the stiffened ring, respectively. The frame specimens were designed in accordance with the concept of strong-column/weak-beam, so beam failure mode was expected to occur in the tests. The ultimate flexural strengths of columns and beams are shown in Table 1, respectively, where the ultimate flexural strength (Muc ) of circular CFST columns was determined according to the specification of Eurocode 4 [13], and the ultimate flexural strength (Mub ) of beams was determined according to the Chinese code for the design of steel structures GB50017-2003 [14]. The test frames with circular CFST columns were designed to investigate the effects of the following parameters on the behavior: the level of axial load n (=0.07 or 0.06, 0.3 and 0.6) in the column, the steel ratio α (=0.06 and 0.103) of the composite column, and the beam to column linear stiffness ratio k (=0.36–0.58). The level of axial load is defined as n = No /Nu , where No is the axial load applied in the column and Nu is the axial compressive capacity of the circular column determined by specification Eurocode 4 [13]. The steel ratio (α ) is defined as α = As /Ac , where As and Ac are the cross-sectional area of steel tube and core concrete, respectively. The beam to column linear stiffness ratio is defined as k = ib /ic , where ib and ic are the linear stiffness of steel beam and CFST column, respectively. ib is defined as Es Ib /L, where Ib is the moment of inertia for steel beam, Es is the modulus of elasticity of steel and L is the length of beam, respectively. ic is defined as (EI )/H, where H is the height of column. The stiffness of circular CFST column (EI) is Es Is + 0.8Ec Ic according to the code DBJ13-51-2003 [15], where Es and Ec are modulus of elasticity of steel and concrete, respectively, and Is and Ic are moments of inertia for hollow steel cross section and core concrete cross section, respectively. Table 1 gives the details of each frame specimen, where h, bf , tw , and tf are the overall height, overall width, web thickness and flange thickness of the I-beam, respectively; D and ts are the
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(a) Frame.
(b) Typical basic frame element (unit:mm). Fig. 2. Schematic view of frame models in a real structure.
Table 1 Summary of frame specimen information. Specimen number
Specimen section (mm)
Muc or Mub (kN m)
k
α
No (kN)
n
Pue (kN)
Pua (kN)
Pua Pue
Ea (kN m)
µ
(mm)
∆y
CF-11
Column Beam
Φ 140 × 2 150 × 70 × 3.44×3.44
15.63 14.54
0.57
0.06
50
0.07
15.25
76.49
67.3
0.88
33.18
3.99
CF-12
Column Beam
Φ 140 × 2 150 × 70 × 3.44×3.44
15.63 14.54
0.57
0.06
205
0.3
13.11
68.43
67.78
0.99
28.99
4.31
CF-13
Column Beam
Φ 140 × 2 140 × 65 × 3.44×3.44
15.63 12.55
0.46
0.06
410
0.6
12.50
55.25
55.49
1.0
25.11
4.78
CF-21
Column Beam
Φ 140 × 3.34 160 × 80 × 3.44×3.44
25.95 17.5
0.58
0.103
50
0.06
15.71
96.38
98.74
1.02
35.79
4.04
CF-22
Column Beam
Φ 140 × 3.34 160 × 80 × 3.44×3.44
25.95 17.5
0.58
0.103
273
0.3
14.78
90.64
91.98
1.02
34.99
4.78
CF-23
Column Beam
Φ 140 × 3.34 140 × 65 × 3.44×3.44
25.95 12.55
0.36
0.103
545
0.6
14.72
75.66
62.17
0.82
30.45
4.71
Note: Beam’s section parameters are in the sequence of h × bf × tw × tf , and column’s section is defined by D × ts . Table 2 Material properties of steel. Steel type
ts or tf /tw (mm)
fy (N/mm2 )
fu (N/mm2 )
Es (N/mm2 )
νs
Tube of CFST
2.00 3.34
327.7 352.0
397.9 430.1
2.063 × 105 2.066 × 105
0.266 0.262
Beam
3.44
303.0
440.9
2.061 × 105
0.262
overall dimension and wall thickness of the circular steel tube, respectively. Table 1 also shows the beam to column linear stiffness ratio k, the steel ratio α , the axial load No and axial load level n for CFST columns. The measured steel mechanical properties given in Table 2 and concrete mechanical properties were used to calculate the Nu . It should be noted that the concrete mechanical properties and the configuration of the composite frames are the same as those presented by Han et al. [11] with square CFST columns. The test setup is the same as that described by Han et al. [11], the axial load (No ) of CFST columns (as shown in Fig. 2(b)) was applied and maintained constant by a hydraulic ram. The measurement arrangement and loading apparatus are the same as those given by Han et al. [11]. The lateral cyclic load (P) was applied at the end of the steel beam (as shown in Fig. 2(b)). The lateral loading history was based on ATC-24 [16] guidelines, and was the same as the described loading history in Han et al. [11] for composite frame with square CFST columns.
2.2. Test results and discussion (1) Failure modes As it was expected, it was found that all the composite frame specimens failed in the strong-column–weak-beam mode, e.g. obvious buckling deformation formed at the beam ends firstly and the bottom of columns sequentially. The plastic hinge in a column located at a distance about 25 mm away from the fastened plate, whilst the plastic hinge at a beam end located at a distance about 25 mm away from the joint ring plate. Typical test frame CF-22 after testing is shown in Fig. 3, and the simulated failure modes were given in this figure too. As can be seen, all frames formed four plastic hinges, where two of them at beam ends, and two of them at the bottom of columns. The first plastic hinge was observed at the beam end near the MTS actuator, and the second hinge occurred at another end of the steel beam. The hinges on the columns
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(a) Comparison of the deformation of specimen CF-22.
(b) Column bottom.
(c) Concrete at the bottom of the column.
(d) The section at left beam end.
(e) The section at right beam end.
(f) Core concrete at joint panel.
Fig. 3. Observed and predicted failure modes of composite frame (CF-22).
occurred after the formation of the beam hinges. Though the steel tube at the hinge location cracked on one side and buckled slightly on the other side, the core concrete showed generally good integrity after test, as shown in Fig. 3(b) and (c), respectively. This phenomenon is a little different from that observed in composite frames with square CFST columns as reported by Han et al. [11]. More severe local buckling of steel tube and concrete crushing were observed for those square CFST columns as shown in Fig. 4(a), and the core concrete near the bottom of the columns was crashed at the end of testing. The local buckling mode of steel tubes of circular CFST columns was also shown in Fig. 4(b) for comparison. Generally, square tubes are more susceptible to local buckling than circular ones, thus circular tubes can provide better confinement to concrete. (2) Lateral load (P) versus lateral displacement (∆) relationship The measured lateral load (P) versus lateral displacement (∆) hysteretic curves of the frame specimens are shown in Fig. 5.
It was observed that there is no obvious strength deterioration and stiffness degradation for the composite frames. The curves of the frames with circular CFST columns are much favorable in general than the curves of the frames with square CFST columns presented by Han et al. [11] since circular tubes can provide better confinement to the core concrete. The ultimate lateral loads (Pue ) obtained in the tests are listed in Table 1. Fig. 6 shows the effect of axial load level (n) on P–∆ envelop curves of the composite frames. It can be seen that the axial load level (n) influences not only the ultimate lateral load (Pue ) but also the ductility of the composite frames. A ductility coefficient (µ) is used as µ = ∆u /∆y (where ∆y is the lateral displacement at material yield and ∆u the lateral displacement when the lateral load falls to 85% of the maximum lateral strength (Pue )) to quantify the ductility on n and the relation of P–∆. From Fig. 6, it can be found that both Pue and µ of the frames decrease with increasing n. The CFST columns of the composite frame are combined axial
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(a) Square CFST column (SF-13).
(b) Circular CFST column (CF-13).
Fig. 4. Typical deformation modes of CFST columns at the bottom.
(a) CF-11 (n = 0.07).
(b) CF-12 (n = 0.3).
(c) CF-13 (n = 0.6).
(d) CF-21 (n = 0.06).
(e) CF-22 (n = 0.3).
(f) CF-23 (n = 0.6). Fig. 5. Lateral load (P) versus lateral displacement (∆) cyclic curves.
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a
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b
Fig. 6. Lateral load (P) versus lateral displacement (∆) of envelop curves.
a
b
Fig. 7. he –∆/∆y relations.
compression loading and bending, and the incremental axial load will enlarge second-order effect to reduce the lateral ultimate strength and displacement ductility of the CFST columns. (3) Dissipated energy ability (Ea ) and damping coefficient (he ) Dissipated energy ability (Ea ) was used to describe the energy dissipation of the composite frames according to Chinese Standard JGJ101-96 [17], which was also used by Han et al. [11] for square CFST frames. Table 1 shows the ductility coefficient (µ) and energy dissipation (Ea ) of the tested frames, respectively. From Table 1, the following findings can be made: (1) In general, Ea decreased obviously with increasing axial load level for frames. (2) Ea increased with increasing k. (3) Generally, the ultimate lateral load (Pue ) increased slightly with an increasing k for specimens with a same n. The composite frames with square CFST columns in Han et al. [11] have shown similar effects of different parameters on the total dissipated energy ability (Ea ) and ultimate lateral load (Pue ), but the decreasing trend of Ea with increasing axial load level was much more distinct than that for the frames in this paper. It was shown that the axial load level had much more evident influence for the composite frames with square columns, i.e. Ea decreased from 35.79 to 34.99 kN m or 30.45 kN m when the axial load level increased from 0.06 (specimen CF-21) to 0.3 (specimen CF-22) or 0.6 (specimen CF-23) in this paper, but the corresponding values of Ea were 76.44, 68.43 and 47.47 kN m for the frames SF11, SF-12 and SF-13 with square CFST columns in Han et al. [11], respectively. Fig. 7 demonstrates that the accumulative equivalent damping coefficient (he ) of the composite frames increases greatly with increasing relative displacement (∆/∆y ), where he is defined as he = Ea /2π and also used by Han et al. [11]; ∆y is the yielding displacement of the frame. It seems that the axial load level (n) and the beam to column linear stiffness ratio (k) have only slightly effect on the he − ∆/∆y relationship for the current frames.
This is different from that of the composite frames with square CFST columns presented by Han et al. [11]. he of the frames with square CFST columns decreased obviously with increasing n. It is also found that he of the composite frames with circular CFST columns is bigger than those with square CFST columns at a same relative displacement. This demonstrates that the accumulative damping ability of the composite frames in this paper is superior to those frames with square CFST columns. Dissipated energy ability and accumulative damping of composite frames could be greatly affected by the failure of composite columns if their core concrete experience severe damage and strength degradation. But the deterioration of the core concrete can be restricted by the confinement from the steel tubes. Less or even no damage will occur if strong confinement is supplied. Since the confinement effect of circular steel tubes is more effective than that of square steel tubes, the effects of n and k on he are thus different for frames with different column shapes. (4) Rigidity degradation Fig. 8 shows the effect of n on relative rigidity degradation (Kj /K1 ) of specimen as a function of ∆/∆y . The rigidity (Kj ) is ∑m
i=1 expressed as Kj = ∑m
Pji
i i=1 uj
, where Pji and uij are the maximum load
and lateral displacement respectively, under the ith loading cycle when ∆/∆y equals j, and m is the cycle time of loading. K1 is the rigidity when ∆ is equal to ∆y . It can be seen that n has moderate on specimens in series CF-2 since the columns in this series have a higher steel ratio (α ). As the core concrete of a composite column undergoes significant rigidity degradation under cyclic loading, a higher steel ratio (α ) can provide significant confinement to its core concrete and postpones its rigidity degradation. The composite frames with square CFST columns in Han et al. [11] have shown clear effect of rigidity degradation with increasing axial load level (n), and the declining trend was much more distinct than that for
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a
b
Fig. 8. Kj /K1 –∆/∆y relations.
(a) Concrete model.
(b) Steel model.
Fig. 9. Stress versus strain relationships of concrete and steel.
the frames in this paper. The rapid rigidity degradation should be considered for composite frames with square CFST columns if they are designed to sustain cyclic loading or earthquake action. 3. Finite element analysis (FEA) model 3.1. General description The Pacific Earthquake Engineering Research Center (PEER) developed a well-known Open System for Earthquake Engineering Simulation (OpenSees for short) as a software platform for simulation of structural and geotechnical systems [18]. The behavior of frame structures can be simulated commendably by using the nonlinear beam–column element from OpenSees. Tsai et al. [7] simulated the dynamic behavior of CFST column to steel beam composite frames using OpenSees, where the predicted results by OpenSees matched well with the experimental curves. The hysteretic behavior of composite frames in this paper were simulated using OpenSees in the first place. The steel and concrete were simulated by Steel02 model and Concrete02 model in OpenSees, respectively. The stress versus strain relationships of concrete and steel in OpenSees are shown in Fig. 9(a) and (b), respectively, where fc′ and ε0 are the concrete compressive cylinder strength and corresponding strain, respectively; σcu and εcu are the concrete crush compressive strength and corresponding strain, respectively; Ec and Ect are the concrete modulus of elasticity under compression and tension, respectively; ft is the concrete tensile strength; Ecu is the concrete modulus of elasticity under unloading and re-loading stages; σy and εy are the yield stress of steel and corresponding strain, respectively; Es is the steel modulus of elasticity. The loading and unloading rules used in this model were described in the user manual of OpenSees [18]. All the
Fig. 10. Finite element model for composite frame.
circular CFST columns and steel beams of frames were modeled using the flexibility-based nonlinear beam–column elements with discretized fiber section model in OpenSees. This model is also applicable for composite frame consists of square CFST columns and steel beam. The hysteretic relationship of the composite frames can be calculated conveniently by using OpenSees, however, the microcosmic mechanical performance, i.e. stress and deformation at different load stages, cannot be simulated rationally using the solver because it was based on the nonlinear fiber beam–column element theory. To address this discrepancy, an accurate three-dimensional finite element analysis (FEA) is necessary. Han et al. [11] investigated the performance of composite frames with square CFST
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(a) 15-SCP [6].
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(b) 30-SCP [6]. Fig. 11. Comparison of P versus ∆ curves between predicted and measured results.
Fig. 13. P–∆ curves of typical CFST frame CF-22. Fig. 12. Typical P versus ∆ curve of the composite frame.
columns and steel beam under constant axial load on the columns and incremental flexural load on the beam using ABAQUS software [19], and Wang et al. [12] performed a further detailed stress analysis. Similar FEA model as that described by Han et al. [20] and Han et al. [11] is used in this paper to simulate composite frames with circular CFST columns. Details of the finite element types and meshes, boundary conditions, material modeling of steel and core concrete, interface and contact between the concrete and the steel tube can be found in Han et al. [11]. Typical meshes of a composite frame with circular CFST columns are shown in Fig. 10. 3.2. Verification of FEA model To verify the validity of the OpenSees model, P–∆ hysteretic relationships by the above-mentioned OpenSees model were compared with experimental results (composite frames with square CFST columns) presented by Kawaguchi et al. [6] and the tested results in this paper, as shown in Figs. 11 and 5, respectively. The calculated curves using OpenSees are denoted as Model I in Figs. 11 and 5. The comparison indicates that reasonable accuracy has been achieved for OpenSees in predicting the cyclic behavior of the composite frames. Fig. 12 shows a typical lateral load versus lateral displacement hysteretic curve of the composite frame with strongcolumn–weak-beam (specimen CF-12) calculated by OpenSees. Clearly, the curve can be divided into several stages. The different stages of the curve are analyzed below.
(1) Elastic stage (from point O to point A): The flanges of steel beam reach yielding at point A. (2) Elastic–plastic stage (from point A to point B): The web of steel beam starts to yield. The stiffness of columns reduces gradually because the area of the compression zone of circular CFST columns gradually reduces. The curve starts to descend slowly. (3) Unloading stage (from point B to point C ): The lateral load (P) versus displacement (∆) curve shows a linear behavior in general. The unloading stiffness is close to the initial stiffness (OA) of the curve. (4) Elastic–plastic stage of reverse loading (from point C to point D): The curve shows nonlinear behavior. The stiffness of the columns decreases with incremental yielding zones of steel beam. (5) Strengthening stage (from point D to point E or from B to F ): The sectional stiffness of the steel beam or CFST column become very small, and the load increases slowly but the deformation increases quickly. (6) Re-loading stage (from point E to point F ): The curve shows similar behavior as the stage from point B to point C , D and then E. (7) Descending stage (from point F to point G): The curve starts to go down. As can be seen, the characteristics of this curve at every stage are quite similar to those of the relationships of the composite frames with square CFST columns presented by Wang et al. [12], but demonstrate some minor differences at every stage as well, i.e. the strength deterioration and stiffness degradation of the hysteresis curves after peak load of the composite frames with square CFST
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(a) Section B1 (Stage 1).
(b) Section B2 (Stage 1).
(c) Section B1 (Stage 3).
(d) Section B2 (Stage 3).
(e) Section B1 (Stage 5).
(f) Section B2 (Stage 5). Fig. 14. Longitudinal stress of steel beam at the end of sections B1 and B2.
columns became more distinct than those frames with circular columns. It is shown that the damage of the core concrete of the square CFST columns became serious during the load descending stage because the confinement effect of square tube would start to weaken. It should be noted that the strengthening stage will appear from point F to G′ if the value of n is small, i.e. n less than 0.3, the curve FG′ will go up strengthening stage stability, and similar to the curve BF . All the calculated monotonic P–∆ curves of composite frames by ABAQUS are given and denoted as Model II in Figs. 5 and 11, respectively. The predicted curves match generally well with the envelop curves of the measured P–∆ relationships. There is little difference between the envelop curves of the cyclic P–∆ curves by Model I (OpenSees) and the monotonic P–∆ curves predicted by Model II. But the ultimate strengths predicted by Model II are generally a little higher than the values obtained from the OpenSees predictions (Model I), since the strength degradation, accumulative damage, cracking and crushing of core concrete under cyclic loading were ignored in the simulation using Model II under monotonic loading. The ultimate lateral loads (Pue ) of composite frames obtained from the tests and finite element analysis by Model II (Pua ) are given in Table 1. Reasonable agreement has been achieved between the two sets of results for most of the composite frames except for
those tested under an axial load level (n) of 0.6. It is expected that, higher n means higher axial compressive load applied on a column. Therefore, the possible influence of unexpected imperfections of the test setup and unintended load eccentricities may be magnified in this case. It should be noted that, experimental results on beam to CFST column frames remain very scarce. Subsequently, finite element analysis is essential to be carried out to expand the experimental data. The FEA model introduced in this paper can be used conveniently to analyze the performance of composite frames. 4. Analytical behavior Model II is used in the following to conduct a behavior analysis for the composite frames. Frame specimen CF-22 (shown in Table 1) is selected as an example. Fig. 13 shows the whole fullrange P–∆ envelop curve. It can be divided into five stages, as marked in the figure. It should be noted that the points 1 and 3 correspond to the points A and B in Fig. 12, respectively. Four typical sections of the circular CFST columns and steel beam are selected to demonstrate stress distributions of the composite frame CF-22, as shown in Fig. 13. The four sections are so selected that they are at the locations of plastic hinges, i.e. sections B1 and B2 on the steel beam near the ring plates and sections C1 and C2 on the bottom of the CFST columns, respectively. Fig. 3(a)
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(a) Stage 1.
(b) Stage 2.
(d) Stage 4.
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(c) Stage 3.
(e) Stage 5. Fig. 15. Concrete axial stress distribution at section C1 of CFST (CF-22).
Stage 1.
Stage 3.
Fig. 16. Stress distribution of concrete along the column height.
gives the buckling modes and deformations of frame CF-22 after test. The simulated mode of the frame CF-22 at point 5 is also shown in this figure for comparison. The predicted buckling modes of the beam and the deformations at the bottom of the columns match well with those of the test. The observed deformation of the four sections at stage 5 defined in Fig. 13 (from point 4 to point 5) are shown in Fig. 3(b)–(e), respectively. The steel tubes of the circular CFST columns at sections C1 and C2 show evident outward buckling, while obvious local buckling of beam flanges and web occurs at sections B1 and B2. The failure mode of the core concrete at the bottom of the circular CFST column is shown in Fig. 3(c),
and the calculated axial stresses S33 are also shown in the figure. The core concrete at tension zone near the stiffened ribs cracks, and the axial tension stress exceeds the concrete ultimate tension strength. Moreover, obvious local buckling occurs in the flanges and web of beam at sections B1 and B2. The experimental result and FEA result by Model II are consistent, as shown in Fig. 3(d) and (e), respectively. Fig. 3(f) shows the mode of the core concrete at the connection panel. The concrete at the panel demonstrates favorable integrity, and no obvious crack is observed. The axial tension and compression stresses of the concrete of the panel are lower than their ultimate strength. The prediction by Model II
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(a) The left column (Stage 3).
(b) The right column (Stage 3). Fig. 17. Core concrete stress distribution at connection panel (CF-22).
precisely catches the trend of the observed deformation, as shown in Fig. 3. 4.1. Longitudinal stress in steel beams Fig. 14 shows the longitudinal stress distributions of the beam during the various load stages, e.g. stages 1, 3 and 5 as defined in Fig. 13. The longitudinal compression and tension stresses of sections B1 and B2 are shown in Fig. 14(a)–(f). The stress distribution pattern of the left beam end (B1) is different from that of the right beam end (B2). The beam is separated into two parts by a bending inflexion located at the approximate middle of the beam, and the two parts deform in different ways. The steel top flange of the left part of the beam (B1) is in compression and the bottom flange in tension, while the trend of the right part of the beam (B2) is opposite. The values of tension and compression stresses of the steel beam increase with increasing lateral load. The compression stress of the flange at section B2 reaches firstly the yield stress of steel. The yield area then extends from the flange to the web. When the composite frame reaches its ultimate load (point 3), about half of the compression web of section B2 has yielded. The tension area of the web at section B2 does not yield at this stage although the peak load has been reached. The lateral load begins to decrease from stage 3, and local buckling appears on the compressive web near section B2. The stress and deformation distributions at section B1 are quite similar to those at section B2, but the stresses and deformation at section B1 are smaller than those at section B2. 4.2. Concrete axial stress distribution Fig. 15 shows the concrete axial stress distribution of section C1 at the typical five loading stages. In the figures, fc′ is the cylinder compression strength of concrete. In Fig. 15, the axial stresses of concrete are different at various loading stages. The whole section of CFST column is under compression before the lateral load (P) is applied. Part of the circular section undergoes tension with increasing lateral load, and the compression area reduces progressively owing to the bending moment effect. The compression stresses of the steel tubes reach yield stress at stage two but the tension stresses are under the yield strength. This is owing to the combination of the axial compression stress and bending stress. After the lateral load exceeds the ultimate load, local buckling appears at the compression zone of the steel tubes and the stresses begin to decrease. It is believed that the core concrete offers effective support to the outer steel tube and thus delays its local buckling compared with a hollow one. The stress states of section C2 are similar to those of section C1. The concrete stress distributions at sections C1 and C2 are much more homogeneous when compared with those in the corresponding frame with square CFST columns presented by
Wang et al. [12], and no obvious stress concentration is observed in a circular section. In contrast, the concrete stress at the corners of a square CFST column is much higher than that near the flat zones [12], i.e. the maximum stress at the corners of a tube of the frame SF-22 in Wang et al. [12] is 1.7fc′ and the average stress is 0.91fc′ at the flat zones, where fc′ is the concrete cylinder compression strength. Since the CFST columns of the composite frame are subjected to combined axial compression and bending moment, their deformation curves are anti-symmetric with a bending inflexion, where sections C5 and C6 are inverted moment points and the stresses at these two sections are expected to be very low. Sections C3 and C4 of the CFST columns are just below the connections. The concrete stresses of sections C3 and C4 are similar to those of sections C1 and C2, respectively, though the stress direction is reversed. In general, all the sections, from C1 to C6, the stress distribution patterns in the current analyzed frame are similar to those presented by Wang et al. [12] for composite frames with square CFST columns. 4.3. Concrete stress along the column height The concrete stresses of the CFST columns along the vertical symmetry planes are shown in Fig. 16. Only stresses at point 1 and point 3 are shown in Fig. 16. The left and lower parts of the columns are in tension, while the right and upper parts of the columns are under compression. The concrete axial stresses and tension areas increases with increasing lateral load gradually. The stress distributions of the left and right columns are similar in general, but the location of zero moment section on the right column away from the bottom of the column is higher than that of the left column. The stress distribution trends are also similar to those of the square columns described by Wang et al. [12] although the stress values are different, i.e. the maximum axial compressive stress at stage three are 97.6 and 82.4 N/mm2 for the composite frame with square CFST columns in Wang et al. [12] and the frame in this paper, respectively. The value of the frame with square columns is bigger than those frames in this paper because of the stress concentration by the corner steel tube for the square CFST columns. 4.4. Concrete stress at connection panels The core concrete stress distributions at connection panels are shown in Fig. 17. Once again, it is found that the concrete stress distributional patterns at connection panels are similar to those presented by Wang et al. [12] although the stress values are different, and the value of the frame with square columns at every load stage is bigger than those frames in this paper because the square CFST columns tube causes clear stress concentration at
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(a) Typical failure process and sequences of the plastic hinges.
(b) Stress distribution (Stage 1).
(c) Stress distribution (Stage 3).
(d) Stress distribution (Stage 5).
Fig. 18. Failure process and stress distribution (CF-22).
the corner zone. Therefore, only the stress distributions at point 3 are given in Fig. 17. In general, the stress values at the panel of the left column are slightly larger than those of the right column under the same loading. The core concrete at the left-bottom and right-top of the panel is under compression and that at the lefttop and right-bottom is in tension. It can be seen that all the axial
compressive stresses of the core concrete are smaller than the concrete cylinder compressive strength (fc′ ) except at a very small area with local stress concentration. The stress concentration of the frames with square CFST columns is severer than those frames with circular columns because of the corner effect. This explains why the connection strength exceeds those of the columns and beam in
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a
b
Fig. 19. Influence of axial load level (n) on P–∆/H curves.
Fig. 20. A schematic view of simplified P versus ∆ relationship [12].
a composite frame. Therefore, the connections remain intact after plastic hinges form in the frame beam and columns.
5. Parametric analysis and simplified P–∆ hysteretic model 5.1. Effects of parameters on the P–∆ envelope curves
4.5. Stress distributions of the whole frame Fig. 18(a) shows the typical failure process and sequences of plastic hinges of the composite frame. The numbers 1–4 shown in the figure represent the four different plastic hinges of the frame under loading. The first two plastic hinges occurred at the beam ends near the exterior stiffened ring, and the first one appeared on the side near the load actuator. The third and fourth plastic hinges were formed at the bottom of the columns near the stiffened ribs, respectively. The hinges appeared gradually and can be located from the Mises stresses distribution of the whole frame model, which are shown in Fig. 18(b)–(d) for the stages of one, three and five, respectively. The local stresses and deformations at the locations of the plastic hinges are shown in this figure too. It is shown that the maximum stresses are located at the bottom of the columns and beam ends, respectively, where plastic hinges are formed at these locations. The stresses at the hinge locations increase gradually with the incremental lateral displacement. Significant local deformations occur in the four hinge zones. The locations and sequence of plastic hinge of the frame with square CFST columns are similar [12], but the local buckling at the bottom of the square CFST columns is clear and severe.
It was shown that the axial load level n, steel ratio α , yielding strength of steel (fy ) and cube strength of concrete (fcu ), column slenderness ratio (λ), and the beam to column linear stiffness ratio k are the main influential factors on the P-∆ envelope curves. Further parameter analysis carried out in this paper shows that the effects of these parameters on composite frames with circular CFST columns are generally similar to those on frames with square CFST columns presented by Wang et al. [12]. Only the effect of axial load level (n) on P–∆ curves of composite frames with circular CFST columns is shown in Fig. 19. It can be found that the ultimate lateral load and displacement ductility decrease with increasing axial load level (n). The constraint of beam to the columns can be enhanced for a frame with a larger beam to column linear stiffness ratio, thus an increase in the ultimate load of the frame is expected. 5.2. Simplified P–∆ hysteretic model Based on numerical analysis by OpenSees, it was found that the simplified P–∆ hysteretic model proposed for composite frames with square CFST columns by Wang et al. [12] is also applicable for the composite frame with circular CFST columns, as shown in
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(a) CF-12 (n = 0.3).
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(b) CF-22 (n = 0.3).
Fig. 21. Comparison of P versus ∆ relationships between simplified model and test results.
Fig. 20. The lateral load (P) versus lateral displacement (∆) relationships of composite frames as shown in Fig. 20 can be divided into seven stages as following: elastic stage, elastic–plastic stage, unloading stage, elastic–plastic stage of reverse loading, strengthening stage, re-loading stage, descending stage or strengthening stage. The simplified P–∆ envelop curves model can be expressed by a tri-linear model as shown in Fig. 20. Where Ka is the stiffness of the elastic stage, Py and ∆p are the ultimate strength of the frame and corresponding displacement, and KT is the stiffness of the descending stage. The line OA represents the elastic stage, and the lines AB and BC are the elastic–plastic stage and descend stage, respectively. The curve can be simulated by the second-order elastic analysis, second-order plastic hinge analysis and rigid-plastic analysis, respectively. The detailed analysis procedures were described in Chen et al. [21]. The equations for the four key parameters used in the model for composite frame with square CFST columns, i.e. Ka , Py , ∆p and KT , were presented by Wang et al. [12], however, the following parameters for composite frame with circular CFST columns should be used. (1) The servicing stiffness of composite columns (EI) should be replaced by Es Is + 0.6Ec Ic for circular CFST column according to Eurocode 4 [13] to calculate Ka . (2) For the calculations of Py and ∆p , formulae available in Eurocode 4 [13] in predicting the ultimate strength (Pyc ) for circular CFST columns should be applied. (3) The expression for the stiffness of the descending stage (KT ) is the same as that given by Wang et al. [12], but the value of the parameter p in the formula is different, where p is the hardening stage coefficient of moment versus curvature model for circular CFST columns and was given by Han and Yang [22]. The unloading stage and re-loading stage of the simplified P–∆ model is same to the model in Wang et al. [12]. The validity ranges of this modified model are: n = 0–0.8, α = 0.03–0.2, λ = 10–80, fy = 200–500 MPa, fcu = 30–80 MPa and ξ = 0.2–4. In which ξ is the confinement effect coefficient of CFST columns, and is defined as ξ = α · fy /fck , where fy and fck are the steel yield strength and the concrete compressive strength (fck = 0.67fcu for normal strength concrete), respectively. To verify the simplified model, the predicted P–∆ hysteretic relationships using the simplified model are compared with experimental curves in this paper. Fig. 21 shows two set typical comparisons. It can be found from the comparison that, generally, a reasonable agreement is achieved. 6. Conclusions The following conclusions may be drawn within the limitations of the research in this paper:
(1) The experiment shows that the composite frame with circular CFST column had excellent seismic resistance. Beam failure was observed first in all the frames. The lateral load-carrying capacity, ductility coefficient and energy dissipation of composite frame decreased as the axial load level in the column increased. The ultimate lateral load of composite frame increased with an increase in beam–column linear stiffness ratio if other conditions were kept the same. (2) The cyclic behavior of the composite frames is similar to that of the frames with square CFST columns in general, but the influences of axial load level and beam–column linear stiffness ratio on the composite frames in this paper are relatively much slighter than on those frames with square CFST columns in terms of rigidity degradation and dissipated energy ability. The load versus displacement curves of the frames with circular CFST columns are more favorable than those of frames with square CFST columns. (3) The introduced FEA model was able to reasonably predict the lateral load versus lateral displacement relationship of the composite frame. Detailed stress analysis was carried out and conducted to realize the microcosmic mechanics performance of the composite frames. (4) A simplified hysteretic lateral load (P) versus lateral displacement (∆) model of the composite frame was proposed. The model should be useful in dynamic analysis for composite frames with circular CFST columns. Acknowledgements The research reported in this paper is the Project supported by Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (20070003087), and part of the Program for Changjiang Scholars and Innovative Research Team in University (IRT00736). This financial support is highly appreciated. References [1] Shams M, Saadeghvaziri MA. State of the art of concrete-filled steel tubular columns. ACI Structural Journal 1997;94(5):558–71. [2] Shanmugam NE, Lakshmi B. State of the art report on steel–concrete composite columns. Journal of Constructional Steel Research 2001;57(10):1041–80. [3] Gourley BC, Tort C, Denavit MD, Schille PH, Hajjar JF. A synopsis of studies of the monotonic and cyclic behavior of concrete-filled steel tube members, connections, and frames. NSEL report series. Report no. NSEL-008. Department of Civil and Environmental Engineering, Univ. of Illinois at Urbana-Champaign; 2008. [4] Nishiyama I, Morino S, Sakino K. et al. Summary of research on concretefilled structural steel tube column system carried out under the US–Japan cooperative research program on composite and hybrid structures. BRI research paper no.147. Japan: Building Research Institute; 2002.
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