TSINGHUA SCIENCE AND TECHNOLOGY
ISSN1007-021420/21pp124-130
Volume11,Number1,February2006
Push-Over Analysis of the Seismic Behavior of a Concrete-Filled Rectangular Tubular Frame Structure*
NIE Jianguo (聂建国) **, QIN Kai (秦凯), XIAO Yan (肖岩)
Department of Civil Engineering, Tsinghua University, Beijing 100084, China;
†Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089, USA
Abstract: To investigate the seismic behavior of concrete-filled rectangular steel tube (CFRT) structures, a push-over analysis of a 10-story moment resisting frame (MRF) composed of CFRT columns and steel beams was conducted. The results show that push-over analysis is sensitive to the lateral load patterns, so the use of at least two load patterns that are expected to bound the inertia force distributions is recom-mended. The -
Mφ curves and -
N M interaction surfaces of the CFRT columns calculated either by Han’s formulae or by the USC-RC program (reinforced concrete program put forward by University of Southern Califonia) are suitable for future push-over analyses of CFRT structures. The -P∆effect affects the MRF seismic behavior seriously, and so should be taken into account in MRF seismic analysis. In addition, three kinds of RC structures were analyzed to allow a comparison of the earthquake resistance behavior of CFRT structures and RC structures. The results show that the ductility and seismic performance of CFRT struc-tures are superior to those of RC structures. Consequently, CFRT structures are recommended in seismic regions.
Key words: concrete-filled rectangular steel tube; push-over analysis; capacity curve; reinforced concrete
Introduction
Over the past twenty years the static push-over proce-dure has been presented and developed by several au-thors, including Saiidi and Sozen[1], Fajfar and Gasper-sic[2], Bracci et al.[3], amongst others. This method is also described and recommended as a tool for design and assessment purposes for the seismic rehabilitation of existing buildings[4]. The purpose of push-over analysis is to
evaluate the expected performance of a structural system by estimating its strength and defor-mation demands in design earthquakes by means of a static inelastic analysis, and by comparing these de-mands to available capacities at the performance levels. Push-over analysis is basically a nonlinear static analysis that is performed by imposing an assumed dis-tribution of lateral loads over the height of a structure and increasing the lateral loads monotonically from zero to the ultimate level corresponding to the incipient collapse of the structure. The gravity load remains con-stant during the analysis. Push-over analysis is very useful in estimating the following characteristics of a structure: 1) the capacity of the structure as represented by the base shear versus top displacement graph; 2) the maximum rotation and ductility of critical members; 3) the distribution of plastic hinges at the ultimate load; and 4) the distribution of damage in the structure, as expressed in the form of local damage indices at the ul-timate load. Although push-over analyses of reinforced
﹡Received: 2004-06-30; revised: 2004-11-07
Supported by the Overseas Youth Cooperative Foundation of the National Natural Science Foundation of China (No. 50128807)
﹡﹡To whom correspondence should be addressed.
E-mail: niejg@mail.tsinghua.edu; Tel: 86-10-62772457
NIE Jianguo (聂建国) et al Push-Over Analysis of the Seismic Behavior of …
125 concrete (RC) structures and steel structures have been
carried  out  by  many researchers and designers, at present push-over analyses for the concrete-filled steel tube  (CFT)  structures  are  rarely  reported  in  the literature.
CFT columns have become increasingly popular in structural applications. This is partly due to their ex-cellent earthquake resistant properties such as high strength, high ductility, and large energy absorption capacity [5]. At present, theoretical analysis of these structures focuses mostly on the static behavior of the CFT members, such that the seismic responses of the CFT structures have been rarely studied. Some re-search on the seismic behavior of CFT structures is, however, documented in the literature. The elasto-plastic time-history analysis of CFT structures has been discussed by Li et al.[6] Their results show that no irreparable damage occurs in structures under in-tense earthquake loading, which demonstrates that CFT structures excel in seismic performance. The seismic behaviors of four kinds of 5-story frame structures that are composed of CFT and of RC col-umns have been studied by Huang et al.[7] The SAP2000 program was used in the time-history analyses for calculating the seismi
c responses of the structures. The dynamic behavior and earthquake re-sponse of the CFT and RC structures were analyzed. The authors conclude that the earthquake resistance behavior of CFT structures is excellent compared to that of RC structures. Experimental investigation of a 2-span, 3-story model of a CFT frame has been car-ried out under vertical stable loads and lateral cyclic loads by Li et al.[8] Based on the CFT frame model experiment, a nonlinear finite element analysis was
completed [9]. The calculated results coincided with the test results, providing a practical method for the seismic design of CFT frames. Although the seismic behavior of CFT frame structures has been investi-gated by many researchers in recent years, the differ-ent elasto-plastic analysis methods are confined by their rationality, applicability, and efficiency. These methods need to be modified regarding aspects of their mechanical models, hysteretic characteristics, and calculation efficiency, and more experimental re-search still needs to be carried out to check the accu-racy of these analysis methods.
Although concrete-filled steel rectangular tubular columns are inferior to concrete-filled steel circular tubular columns in terms of bearing capacity, they are superior in many other aspects, such as beam-column connection constructability, stability, and fire resis-tance. Therefore, they are increasingly used for high-rise buildings in many countries all around the world. However, application of concrete-filled rectangular steel tube (CFRT) structures is still restricted because of the lack of engineering informatio
n on the overall seismic behavior of CFRT structures. For the purpose of investigating the seismic responses under severe earthquake conditions, a push-over analysis of a 10-story CFRT structure has been carried out and is re-ported in this paper.
1 Push-Over Analysis
A 10-story moment resisting frame structure that is com-posed of concrete-filled rectangular steel tube columns and steel beams was studied. The plan, elevation, and
typical cross-sections of structural members of the  CFRT
Fig. 1 Plan, elevation, and typical cross-sections of structural members of the CFRT structure (mm)
Tsinghua Science and Technology, February 2006, 11(1): 124-130 126
structure are shown in Fig. 1. The SAP2000 program
is used for the push-over analysis of the CFRT struc-
ture. The floors of the building are 100 mm deep, and
are modeled as shell elements in SAP2000. The di-
documented翻译mensions and material properties of the structural
members are shown in Table 1. In SAP2000 the
CFRT columns and steel beams are modeled as frame
elements.
Table 1 Dimensions and material properties of the
strutural members of the CFRT structure
Story No. Steel beams
(mm)
CFRT columns
(mm)
1,2 7003001324 70020
3 700300132
4 70018
4-6 6923001320 70018
7-10 6923001320 70016 Material property Q345 Q345C40
1.1 Hinge properties
In frame structures plastic hinges usually form at the ends of beams and columns under earthquake action. For beam elements, plastic hinges are mostly caused by uniaxial bending moments, whereas for column elements, plastic hinges are mostly caused by axial loads and biaxial bending moments. Therefore, in push-over analysis different types of plastic hinges should be applied for the beam elements and the col-umn elements separately.
In SAP2000, the M3 hinge is used to simulate the plastic hinge caused by uniaxial moment, so user-defined M3 hinges are applied to the steel beams in this model. To calculate moment-rotation curves of the steel beams, the following assumptions are adopted: 1) a classical bilinear isotropic hardening model is applied to represent the stress-strain behav-ior of the steel beam; and 2) plane sections remain plane. The typical M-φ curve for the steel beams is shown in Fig. 2.
Fig. 2 M-φcurve of steel beams in the 1st-3rd stories
Similarly, the PMM hinge is used by SAP2000 to simulate the plastic hinge caused by axial load and biaxial bending moments. User-defined PMM hinges are therefore applied to the CFRT columns in this model. The M-φ curves and N-M interaction surfaces of the CFRT columns are calculated using both Han’s formulae[10] and the USC-RC program(RC program put forward by University of Southern California), for  the purpose of comparison. The typical N−M interac-tion surface and M-φ curve of the CFRT columns are
shown in Fig. 3.
Fig. 3  -
N M interaction surface and -
Mφ curve of CFRT columns in the 1st and 2nd stories
1.2 Lateral load patterns
The lateral load patterns are intended to represent the distribution of inertia forces in a design earthquake[11]. It is clear that the distribution of inertia forces will vary with the severity of the earthquake (i.e., the extent of inelastic deformations) and with time during an earthquake. Since no single load pattern can capture the variations in the local demands expected in a de-sign earthquake, two lateral load patterns that are ex-pected to bound the inertia force distributions are used in this push-over analysis. One is an inverted triangular lateral load pattern calculated by the base shear method; the other is the design lateral load pattern calculated using SAP2000 including higher mode effects. The
NIE Jianguo (聂建国) et al Push-Over Analysis of the Seismic Behavior of (127)
horizontal loads are applied in the X-direction and Y-direction in turn for the purpose of investigating the seismic behavior of the whole structure.
As Dong et al. mentioned in Ref. [12], the -P∆ effect seriously affects the stability of an unbraced frame. There-fore, push-over analyses with and without accounting for the -P∆ effect are carried out in order to investigate the -P∆effect on the seismic behavior of the CFRT structure.
1.3 Results
The results of the push-over analysis can be used to es-timate the potential ductility of the structure, to evalu-ate its lateral load resistant capacity, and to identify the failure mechanism. It is thus important to analyze the push-over results to obtain the seismic behavior of the CFRT structure.
1.3.1 Load-deformation relationship
The capacity of the structure as represented by the base shear versus top displacement graph is very use-ful in estimating the seismic behavior of a structure in a push-over analysis. The capacity curves obtained in the push-over analyses are shown in Fig. 4, from which we find that for the cases Accel X(Y)-Han-P−, Accel X(Y)-USC-RC-P−, EQ X(Y)-Han-P−, EQ X(Y)-USC-RC-P−, and EQ X(Y)-Han-P+ t
he termination is caused  by  exceeding  the  target  top  displacement (1.6 m), while for the cases Accel X(Y)-Han-P+, Ac-cel X(Y)-USC-RC-P+, and EQ X(Y)-USC, RC-P+ the termination is caused by the formation of a plastic mechanism for the whole structure. The initial stiff-ness values and yield base shears of the cases using Accel X(Y) lateral load patterns are higher than the cases using EQ X(Y) lateral load patterns. Therefore, the conclusion can be drawn that the push-over analy-sis results are sensitive to lateral load patterns. More-over, the trends of the capacity curves in the X-direction and in the Y-direction are similar, as shown in Fig. 4. Consequently, the seismic behavior of the whole structure can be evaluated by one of the direc-tions for this case.
As shown in Fig. 4, the capacity curves are almost the same in the elastic region despite the different -
Mφ curves and -N M interaction surfaces of the CFRT columns. The post-yield stiffness values for cases using -
Mφ and -N M curves calculated by Han’s formulae are higher than those calculated by USC-RC  program,  but  the  differences  are  small compared to other parameters.
Figure 4 also shows that the ultimate base shears de-crease remarkably in the push-over analyses as a result of the -P∆effect. Similarly, the post-yield stiffness de-creases for the same reason. Therefore,
we can draw a con-clusion that the -P∆ effect affects the seismic behavior of the moment resisting frame seriously and consequently, the effect should be taken into account in any future MRF
seismic analyses.
Fig. 4 Capacity curves of different push-over cases of the CFRT structure
Notes: EQ X(Y) represents cases using the inverted trian-gular lateral load pattern calculated by the base shear method, Accel X(Y) represents cases using the design lat-
eral load pattern calculated using SAP2000 including higher mode effects; Han represents cases using the -
Mφ and -N M curves calculated by Han’s formulae, USC-RC represents cases using the -
Mφ and -N M curves calculated using the USC-RC program; P− repre-sents cases without considering the -P∆ effect, P+ represents cases including the -P∆ effect.
1.3.2 Final interstory drifts
The interstory drifts at the moment of termination in the push-over analyses are shown in Fig. 5. These data are useful in predicting the weak stories of the CFRT structure. From Fig. 5, we observe that the interstory drifts of the 1st-3rd stories are remarkably higher than
Tsinghua Science and Technology, February 2006, 11(1): 124-130 128
those of the other stories. Therefore, the weak section of the CFRT structure should be the first 3 stories for this ex-ample,  and  it  is  necessary  to  strengthen  them  in engineering application.
1.3.3 Plastic hinge distributions
It can be found that the plastic hinge distributions are similar in all the push-over analysis cases despite variations  in  the  lateral  load patterns, the -P∆ ef-fect, the -
Mφ and -N M curves of the CFRT col-
umns and the lateral load directions. Figure 6 illus-
trates the progressive occurrence and extent of the
plastic  behavior  of  the  CFRT  frame  at
various Fig. 5
Final interstory drifts of different push-over cases of the CFRT structure
Fig. 6 Progressive occurrence of plastic hinges in EQ X-USC-RC-P− push-over analysis

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