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Seismic behavior study on RC-beam to CFST-column non-welding joints in field construction
Journal of Constructional Steel Research 116 (2016) 204–217
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Journal of Constructional Steel Research
Seismic behavior study on RC-beam to CFST-column non-welding joints in field construction Xiaoxiong Zha ⁎, Chengyong Wan, Hang Yu, Jean-Baptiste Mawulé Dassekpo Department of Civil and Environmental Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
a r t i c l e
i n f o
Article history: Received 12 October 2013 Received in revised form 10 July 2015 Accepted 14 July 2015 Available online xxxx Keywords: RC beam to CFST column joint Joint without welding Seismic behavior Skeleton curve Theoretical model Finite element analysis
a b s t r a c t A newly developed reinforced concrete (RC) beam to concrete-filled steel tube (CFST) column joint without welding in the construction field is introduced in this paper. The seismic experiment is conducted on the joint, and the hysteretic curve of the specimen under cyclic loading on the top of the column is obtained. By analyzing the mechanical characteristics and the failure mode of the joint, a three-stage skeleton curve model is presented. In the elastic stage, the initial stiffness is evaluated by solving the stiffness matrix. In the perfect plastic stage and strength degradation stage, the ultimate strength and the degradation stiffness of the joint can be obtained with the limit equilibrium method. Moreover, the test is also simulated with FEM, and the results agree well with the skeleton curves obtained from the test. So this joint shows good ductility and the ability to dissipate energy, and it can be used to replace the joints welded with reinforcement on the outer annular plate. And the finite element analysis results are compared with the theoretical results, which verifies the theoretical model presented above. It is suggested that the three-stage skeleton curve model can be used to depict the mechanical behavior and bearing capacity of this new type of joint. In addition, Parametric analysis is conducted on this joint, with the consideration of different designs of beams, columns and steel brackets, and failure mode is discussed. © 2015 Elsevier Ltd. All rights reserved.
1. Preface The concrete-filled steel tube column is considered as a composite structure style, which has many excellent mechanical behaviors and bearing capacity. For RC beam to CFST column joint, the response to disaster loads has a very important impact on such a structure. Generally, due to the form of beam members, CFST beam to column joints can be divided into steel beam-CFST column joint and RC beam-CFST column joint. Among them, the current reinforced concrete beam-CFST column joint types usually include rigid joints with interior and exterior reinforced loop, anchor and cross-core, etc. Based on the needs of this project, the related research and the improvement of the joints are more focused in China. Where, Xu et al. [1] analyzed the working mechanism and seismic behavior of beam-column joints of CFST frames systematically, based on some results from experimental research and engineering application. The formation suited in the frame structure system, calculation methods and several design suggestions are presented and discussed. Nie et al. [2–3] carried out fourteen connection specimens composed of concrete-filled square steel tubular columns (CFSSTCs) and steel-concrete composite beams with interior diaphragms, exterior diaphragms, or anchored studs in order to investigate the seismic behavior were tested, and the strength, deformation, and energy dissipation capacity of these composite connections were analyzed; 3-D ⁎ Corresponding author. E-mail address: [email protected] (X. Zha).
http://dx.doi.org/10.1016/j.jcsr.2015.07.017 0143-974X/© 2015 Elsevier Ltd. All rights reserved.
nonlinear finite element models were established to analyze the mechanical properties of these three types of connection using ANSYS. Finite element analyses were conducted under both monotonic loading and cyclic loading. Han et al. [4] conducted an experiment on eight thin-walled steel tube confined concrete (TWSTCC) columns to reinforced concrete (RC) beam joints subjected to cyclic loading, where the level of axial load in the column and the type of column crosssection were selected as test parameters. In addition, two concretefilled thin-walled steel tubular columns to RC beam joints were also tested for comparison. Qu et al. [5] tested eight reinforced concrete (RC) beams to concrete-filled steel tubular (CFST) column joints enclosed by rebar under reversal horizontal displacement with constant axial load in order to study their seismic behavior. The test parameters are the axial load level and the section type of CFST column. In this study, the failure model, hysteretic characteristic, ductility and energy dissipation were investigated. Wang et al. [6] studied the semi-rigid joint of steel-concrete composite beam to CFST column with stiffening rings. Two specimens were tested by incremental loading and cyclic loading. The finite element package ABAQUS was used to study the nonlinear behavior of such specimens. Li et al. [7–8] researched the seismic behavior of the joint of gangue concrete-filled steel tubular columnbeam with ring stiffeners and steel corbels, and the quasi-static tests on the interior joint of gangue concrete-filled steel tubular columnring beam joints in the low cycle reverse load by which the failure patterns, hysteretic characteristics, ductility and energy dissipation were studied. Liu et al. [9] carried out finite element analysis on the aseismatic
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behavior of the joints of the new type of concrete-filled steel tubes, which is based on fuzzy mathematics. The results of the example analysis have showed that the finite element calculation model based on fuzzy mathematics is suited for the mechanical properties of the analysis of the joints. Wang and Liu [10] presented the test results of six connections under cyclic loading. Each test specimen was properly designed to model the interior joint of a moment resisting frame, and was identically comprised of three parts that include the circular concrete-filled steel tube columns, the reinforced concrete beams, and the short fabricated connection stubs. Chen et al. [11] studied the bearing capacity, crack patterns, deformation, and strain of the reinforcements of the specimens through the compressive tests on this concrete-filled steel tubular (CFST) column-beam joint with the column tube discontinuous in the joint zone after cyclic reversed loading. J et al. [12] conducted an experimental investigation into the behavior of composite column-to-beam connections using ten large-scale connections, four under monotonic loadings and six under cyclic loadings. All connections consisted of a concrete-filled steel tube (CFST) column (circular), a compact universal beam section and a shop fabricated connection stub. Monotonic testing was first carried out and the results were used to conduct the cyclic tests. Wang et al. [13] investigated the seismic performance of the composite joint consisting of square concrete-filled thin-walled steel tubular (CFTST) column and steel beam with end plate and blind bolts. Four exterior joint specimens were tested under axially compressive load on the top of the columns and cyclic loads on the beam tip. The experimental parameters in the study were the thickness of the steel tube and the type of end plate. Zhang et al. [14] presented experimental and analytical studies on the seismic behavior of steel I-beam to circular CFST column assemblies with external diaphragms. In the experimental study, four specimens, i.e. two exterior joints and two interior joints in a frame structure, are tested under constant axial loads on columns and cyclic vertical loads on beam ends. The specimens are designed to be strong column-weak beam for exterior joints and strong beam-weak panel zone for interior joints. The above joint types in the project have a range of applications to some extent, nevertheless, there are imperfections in some types, such as the need for a large number of welding work at the site, the influence of anchoring parts in column to internal concrete pouring, or as a result of the openings, the impact of the strength of joint region and continuity of steel tube, etc. Based on the above problems, this paper conducted experimental study to seismic behavior, theoretical derivation and finite element calculation study on new typical RC beam to CFST column joints (shown in Fig. 1) without welding in the construction field, in which the joint steel components are required to be completed by factory processing.
a) Whole beam-to-column joints
205
2. Experiment research 2.1. Experiment design During a real earthquake, joints tend to be larger in operating cyclic loading due to the ever-changing seismic wave to structure foundation. In order to ensure the safety of structures in the earthquake, the general design requirement is required to meet “strong column, weak beam, and stronger joints”. Ductility is an important seismic performance index, which marks energy consumption of the joints as well as deformation properties after yielding. Based on this, in the cyclic loading experiment, beam-column joint is conducted by constantly changing the positive and negative bending moment. Thus, it is obtained to analyze ductility coefficient, viscous damping coefficient and energy dissipation ratio, and others, which can be used to determine energy consumption and seismic performance of joints, and also give the reference for the engineering design. In order to simulate real hysteretic behavior of joints, a typical part of the beam-column joints derived from the plane frame subjected to seismic loading have been tested with simulating beamend and column-end actual boundary condition, as shown in Fig. 2. In which H is the distance between inflection point of the upper and lower frame column, L is the distance between inflection point of the left and right frame beam, N is axial force, V is the shear at the position of inflection point on beam, P, Δ/2 are the horizontal shear and lateral displacement at the position of inflection point on column, respectively, and the second-order effect can be considered. Based on the above model, the proposed simplified test model is shown in Fig. 3. On account of some constraints such as test environment and load capacity, the reduced scale test model is put forward, as shown in Fig. 1. Firstly in the factory manufactured phase, the steel column joint region is processed into exterior reinforced loop plate form, and connected with steel bracket. In addition, the steel bracket upper and lower flange position are welded with reinforced connection pieces with holes, and as the reinforced limit agencies, all holes of design corresponds to reinforced distribution location. In the installation phase, the processed reinforcement is planed pass through the holes on the reinforced connection pieces after column installation is completed, and connected with the reinforcement sleeve. This installation of the joints in the construction field is shown in Fig. 1. The joint is installed in the construction site without additional large number of welding work, saving funds for welding and inspection and greatly shortening the construction period. Through the above analysis, it shows that the new joint has good mechanical properties and ductility, and it can be served as a CFST beam-column joints in the project to promote the use.
b) Connection of reinforcement
Fig. 1. Joint with no welding in the construction field.
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test. Selecting some column joints in the projects and taking beamcolumn contra-flexure point intermediate part reduced to the scale with a proportion 1:5, the related parameters of the specimens are shown in Table 1. The joint of column concrete strength grade is C60 and the beam concrete strength grade is C30. At the same time, the corresponding material property test of concrete blocks and steel are conducted, and the results are shown in Tables 2 and 3, where the reinforcement yield strength is measured as 451.2 MPa and ultimate strength 592.7 MPa. The specific joints connections part is shown in Fig. 4. 2.3. Experiment result analysis Fig. 5 shows the failure phenomenon of the specimen, from which it can be found that both of the joints have obvious vertical cracks along the bracket external edge position with loads increasing. At the same time, the upper concrete appears spalling, and the reinforcement exposing, thus the specimen appear like a plastic hinge in the bracket's outside edge location. Fig. 6 shows the hysteresis curve of two specimens, where both specimens have the plump hysteresis curve, showing the good energy dissipation capacity. At the same time, the curve assumes inverted s-shaped slightly. It demonstrates that there is certain degree of slip between the reinforcement and concrete. The skeleton curves are given based on the load–displacement hysteresis curve of joints, as shown in Fig. 7. By which, it acquires the ductility coefficient μ of joints and the ductility coefficient μ = Δu/Δy, as shown in Table 4. From which, it can be found that the two specimens with ductility coefficient are greater than 5.0 with good ductility, meeting the needs of the project.
Fig. 2. Joint force model in plane frame structure.
2.2. Experiment introduction In order to further verify the reliability of the joint form in engineering application, this paper conducted the seismic performance 3. Theory analysis The seismic behavior of the newly developed RC beam to CFST column joint without welding in the construction field is analyzed with a theoretical method based on the research of the companion paper. According to the proposed joint form, the simplified three-step skeleton curve model is presented, including the elastic stage, ideal plastic stage and strength degradation stage, respectively. In the elastic stage, the skeleton curve stiffness remain the same, thus the joints can be approximately regarded as being in the elastic state as a whole; in the ideal plastic stage, RC beam gradually enters the plasticity and RC beam cross-section in corbel junctional position and eventually develops into a plastic hinge. At this time, the ideal plastic stage ends; after entering the strength degradation stage, the plastic hinge location and the bearing ultimate bending moment remains unchanged. As the top of the horizontal column displacement increases, the top of the horizontal column load decreases as a result of the second-order effect of axial force. The three-stage skeleton curve simplified model is shown in Fig. 8.
N
P
Fig. 3. Experimental model with loading at the top of column.
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Table 1 Illustration of CFST joint specimens. No.
l (mm)
ts (mm)
Section Size (mm)
L (mm)
Bar arrangement
h (mm)
N (kN)
NJ1
120
50
800
Upper flange:3Φ12 Lower flange:2Φ12
1000
1200
NJ2
600
B:260 × 100 C:219 × 5 B:260 × 100 C:219 × 6
Note: No. is node numbering, l is the length of the bracket, ts is the width of the loop plate, B is beam, C is column, L is beam total length, h is column total height and N is column axial force.
Table 2 Test value of beam concrete block. No.
B1 (MPa)
B2 (MPa)
B3 (MPa)
Mean (MPa)
fc (MPa)
NJ1 NJ2
47.3 41.2
52.4 47.2
44.5 38.5
48.1 42.3
36.7 32.3
Note: B1 is beam 1, fc is conversion prism compressive strength.
Table 3 Test value of column concrete block. No.
C1 (MPa)
C2 (MPa)
C3 (MPa)
Mean (MPa)
fc (MPa)
NJ1 NJ2
46.5(Rejected) 65.2
68.8 70.2
68.8 69.1
68.8 68.2
52.5 52.0
Note: C1 is column 1, fc is conversion prism compressive strength.
3.1. Elastic stage analysis Taking into account the whole joint model being in the elastic stage, we can reference the joint region simplified calculation method from Li et al. [15] while ignoring concrete cracking and yielding failure in the beam, where it can be simplified as a model in Fig. 9. Each beam segment and joint region are conducted to split, as shown in Fig. 10, and each part of the component is numbered. Considering the symmetry of the joint the effect of beams C and D can be replaced with beams A and B. Equilibrium equations are given as follows:
Q g1 Mg1
¼ KA
δg1 θg1
ð1aÞ
8 8 9 9 −Q g1 > δg1 > > > > > > > < < = = −Mg1 θg1 ¼ KB Q δ > > > > g2 g2 > > > > : : ; ; Mg2 θg2
ð1bÞ
a) NJ1
b) NJ2 Fig. 4. Steel part of joint specimens.
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a) NJ1
b) NJ2 Fig. 5. Damage of joint specimens.
9 9 8 8 < P = < Δ = ¼ KE vc1 Q ; : c1 ; : Mc1 θc1
Q c2 Mc2
¼ KF
vc2 θc2
ð1cÞ
ð1dÞ
in which 2
12 6 l 2 6 a 6 6 6 3mEI 1 −lb EI 6 la KB ¼ 6 KA ¼ 2 3 −lb lb la 6 lb 6 − 12 6 2 6 la 4 6 la
6 12 6 − 2 la la la 6 4 − 2 la 6 12 6 − − l a la 2 la 6 2 − 4 la
3 7 7 7 7 7 7 7 7 7 7 5
2 3 2 2 1=h −1=h 1=h 3nEI 6 3nEI 1 h 7 KE ¼ 4 −1=h2 1=h2 −1=h 5 K F ¼ 3 2 h h h h 2 2 1 1=h −1=h
150
Horizontal Force (KN)
Horizontal Force (KN)
where δg1, θg1, δg2, and θg2 is the right-side vertical displacement with the angle from beam-segments A and B, respectively; νc1, and θc1 is the lowerend horizontal displacement with the angle from column-segment E, respectively; νc2, and θc2 is the top-end horizontal displacement with the angle from column-segment F, respectively; Qg1, Mg1, Qg2, and Mg2 is the right-side shear with the bending moment from beam-segments A and B, respectively; Qc1, and Mc1 is the lower-side shear with the bending moment from column-segment E, respectively; Qc2, and Mc2 is top-end shear with the bending moment from column-segment F, respectively; KA, KB, KE, and KF is element stiffness matrix (note that we ignore the influence of shear deformation) from beam-segments A and B, and column-segments E and F, respectively; EI is section bending stiffness from beam-segment B; m, n is
100 50 0 -50 -100 -60
-40
-20 0 20 40 Displacement (mm)
60
100 50 0 -50 -100 -60
-40 -20 0 20 40 Displacement (mm)
a) NJ1
b) NJ2 Fig. 6. Hysteretic curves of joint specimens.
60
209
Horizontal Force (KN)
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Displacement (mm) 1-NJ1 ; 2-NJ2 Fig. 7. Test results of skeleton curves of joint specimens.
Table 4 Ductility coefficient ratio. No.
Δy(mm)
Δu(mm)
μ
NJ1 NJ2
7.42 7.07
44.29 45.27
5.97 6.40
Note: Δy is elastic displacement of joint, Δu is limit displacement of joint, μ is ductility coefficient.
section bending stiffness from beam-segment A and column-segments E and F, respectively, and m = E2I2/(E1I1), n = EscIsc/(E1I1);la,lb. is the length from beam-segments A and B, respectively, and la = λL, lb. = (1-λ)L. Since the joint region has an effect on the stiffness of the joint in the elastic stage, thus the deformation and stiffness matrices of the components need to be transformed; the force equilibrium equation of each component based on joint domain deformation is given as follows:
Q1 M1
¼
3mEI
3
lb
2
1; −lb 2 −lb ; lb
12;
u1 θ1
ð2aÞ
6la ;
−12;
6ðhc þ la Þ;
−3ðhc −la Þ 1 − la ð3hc −2la Þ 2 3EIðhc −la Þ
6 2 8 9 6la ; 4la ; −6la ; la ð3hc þ 2la Þ; 6 ‐Q 1 > 6 > > > > > 6 > −M1 > 6EI 12EI 6EI ðhc þ la Þ < = EI 6 − 12EI ; − 2 ; ; − ; 6 3 3 3 3 Q gv2 ¼ 36 l l l la la a a a > > 6 l > > M a > > 6 gθ2 1 2 > > 2 2 2 : ; 6 6ðhc þ la Þ; la ð3hc þ 2la Þ; −6ðhc þ la Þ; 3hc þ 6hc la þ 4la ; − 3hc −2la Mgγ2 6 2 4 1 1 2 1 2 2 2 − 3hc −2la ; 3hc −6hc la þ 4la −3ðhc −la Þ; − la ð3hc −2la Þ; 3ðhc −la Þ; 2 2 4
P Pu 0.85Pu
Kd Kc
Fig. 8. P-Δ skeleton model for calculation.
3 78 9 7 u 7> > 1> > > 7> < θ1 > = 7> 7 7 u0 7> > θ0 > > > 7> : > ; 7> 7 γ0 5
ð2bÞ
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N P
Esc Isc E1I1
h E2I2
hg
Esc Isc
h
hc Fig. 9. Simplified calculation model for CFST joint.
3 1 1 1; ‐1; 2h−hg ; ‐ 2h þ hg 78 9 6 8 9 2 4 7 Δ 6 P > > > 7> 6 1 1 > > < = 3nEI 6 < > = 7> ; −1; 1; − 2h−h 2h þ h g g Q cv1 7 ν0 6 2 4 ¼ 3 6 7 1 1 1 1 M θ > > > > 2 7 6 h 6 2h−hg ; ‐ 2h−hg ; 2h−hg ; ‐ 4h2 −hg 2 > : cθ1 > ; : 0> ; 7> Mcγ1 γ0 7 62 2 4 8 1 4 1 1 2 5 1 2 2 2h þ hg − 2h þ hg ; 2h þ hg ; − 4h −hg ; 4 4 8 16
ð2cÞ
3 2 1 1 1; 2h−hg ; − 2h þ hg 9 8 7 6 2 4 < Q cν2 = 3nEI 6 7 1 2 1 1 2 7 u1 6 2 Mcθ2 ¼ 3 6 2h−hg ; 7 2h−hg ; 4h −hg ; : 7 θ1 62 4 8 h Mcγ2 1 4 1 1 2 2 5 2 4h −hg ; 2h þ hg − 2h þ hg ; 4 8 16
ð2dÞ
2
where {u1, θ1, u0, θ0, γ0} is the displacement vector from the beam-segment A and the joint domain under the coordinate of the joint region, respectively; {Q1, M1} is shear with bending moment from the right side of beam-segment A under the coordinate of the joint region, respectively; {Qgv2, Mgθ2, Mgγ2, Qcv1, Mcθ1, Mcγ1} is shear with bending moment from the junction of the beam, column and joint region, respectively; hc, hg is the width and height from the joint region. Substituting the internal force boundary condition of the components and the related force equilibrium equation of the joint regions into the above equilibrium equations, we obtain the force equilibrium equation of the joints as a whole, namely f f g ¼ ½K fδg
ð3Þ
N P
Mc1
E
Qc1 Mc1 A
Mg1 Qg1
Mg1 Qg1
B
Qc1
Mg2 Mg3 Qg2
Qg2 C
Qg3
Mg4 Mg4 Qg4
D
Qg3
Mg2
Mg3
Qg4
Mc2
Qc1
Qc1 F
Mc2
a) Diagram of internal force on beam members
b) Diagram of internal force on joint region
Fig. 10. Members of CFST joint for calculation.
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211
N P
Fig. 11. Calculation model for limit equilibrium method.
where T P 2h þ hg P 2h þ hg ;− ; 0; P; P; −kγ0 2L 2L fδg ¼ ½u1 ; θ1 ; v0 ; θ0 ; γ 0 ; ΔT
ff g ¼
2
−
3mEI
3mEI ; lb 4EI ; la
;
3 0;
0;
0;
0
2 6 lb 6 6 6EI EIð3hc þ 2la Þ EIð3hc −2la Þ 6 0; ; − ; 0 − 2 ; 6 2 2 6 l l 2la a a 6 6 2 2 2 2 2 2 2 2EI 3hc þ 6hc la þ 4la EI 3hc −4la 3nEI 4h −hg 6 12EIðhc þ la Þ 2EIð3hc þ 2la Þ 3nEI 2h−hg 3nEI 2h−hg 6 ; ; 0; þ ; − − ; 6 3 2 3 3 3 3 3 6 la la 2h 2h la la 8h ½K ¼ 6 6 3nEI 2h−h 3nEI 2h þ h 3nEI 3nEI g g 6 0; 0; − 3 ; ; − ; 6 3 3 3 6 h h 2h 4h 6 3nEI 2h−h 3nEI 2h þ h 3nEI g g 6 0; 0; ; ; − ; 0 6 3 3 3 6 h 2h 4h 6 2 2 2 2 2 2 2 6 EI 4la −3hc 3nEI 4h −hg EI 3hc −6hc la þ 4la 3nEI 4h þ 4hhg þ hg 4 6EIðla −hc Þ 3EIð2la −3hc Þ ; ; 0; − ; − ; 0 3 2 3 3 3 3 la la la 4h 2la 8h
7 7 7 7 7 7 7 7 7 7 7 7 7: 7 7 7 7 7 7 7 7 7 7 5
Solving the above sixth-order equations, it is easier to get the relationship between value P and Δ; initial stiffness Kc = P/Δ. 3.2. Plastic stage analysis
Horizontal Force (KN)
Horizontal Force (KN)
When the joint test enters into the plastic stage, the simplified model also enters into the second stage of the trilinear model. It's corresponding parameters include ultimate load Pu and displacement Δp of the starting point at the descending stage. Where, Δp is the displacement at the corbel location when RC beam has developed into a plastic hinge. Using the limit equilibrium method [16], it can be approximately viewed that at this time
Displacement (mm) a) NJ1
Displacement (mm) b) NJ2
1-NJ1 Test Value ; 2-FEM Value ; 3-NJ2 Test Value Fig. 12. Comparisons of FEA and test results of skeleton curves of joint specimens.
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a) Stress contour of steel member
b) Equivalent plastic strain contour of concrete (Deformation scale factor = 3)
Fig. 13. Contour of FEA result of specimen NJ1.
the virtual work produced by the column-top horizontal load and the vertical load is completely transformed into a plastic hinge with plastic strain energy, with a simplified calculation model as shown in Fig. 11. From which the virtual work equation is given in Eq. (4), the plastic hinge position relative angles with small deformation hypothesis can be obtained by Eq. (5) as follows 12 δΔ δΔ 2 δW ¼ PδΔ þ Nδ 4h −Δ2 ¼ PδΔ þ N pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ≈PδΔ þ N 2 2 2h 4h −Δ
ð4Þ
π π λ 1 −θ þ − θ ¼− δθ δφ ¼ δ 2 2 1−λ 1−λ
ð5Þ
δU ¼ Mp δφ
ð6Þ
where, Mp is the sum of limit flexural bearing capacity from the left to the right side beam of the bracket junction location. Substituting Eqs. (4) and (5) into Eq. (6), leads to Mp 1 Δ ¼Pþ N: 1−λ 2h 2h
ð7Þ
When the starting point displacement Δp at the descending stage is determined, Pu is the only determining column-top ultimate horizontal load, see Eq. (8) as follow: Pu ¼
Mp 1 Δp − N 1−λ 2h 2h
ð8Þ
where the starting point displacement Δp at the descending stage can be obtained in two ways. When the condition allows, it is suggested that using the finite element method for modeling analysis of RC beam to get the angle and Mp when it reaches the ultimate flexural strength; or it uses the following calculation method Eq. (9) to gain the corresponding joint angle. By the plane section assumption of beam, the relation is as follow: εs 1 dφ ¼ ¼ y r dx
ð9Þ
where εs is the strain of tensile steel when the beam reaches the limit state; y is the distance between tensile steel and neutral axis; r is the gyration radius in the beam section.
Table 5 Parameters of different reinforcement ratio for RC beam. ρ
E1I1 (1012N·mm)
E2I2 (1012N·mm)
EscIsc (1012N·mm)
Other Parameters (mm)
1.0% 1.8% 2.6%
16.9 17.1 17.4
5.00 5.47 5.95
8 8 8
la = 170, lb. = 521 hc = 219, hg = 260 h = 513, L = 800
Note: ρ is reinforcement ratio.
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Table 6 Parameters of different bracket length for RC beam. l (mm)
la (mm)
lb (mm)
Stiffness (1012N·mm)
Other Parameters (mm)
60 100 160
110 150 210
581 541 481
E1I1 = 17.3 E2I2 = 5.75
hc = 219, hg = 260 h = 513, L = 800
Note: l is length of the bracket.
Analyzing the plastic hinge angle while referring to Fig. 11, the relation is shown as follow: δ δ þ 1 φ φ λL ð1−λÞL δ ¼ ¼ ¼ ¼ L r λL þ ð1−λÞL L λð1−λÞL2
ð10Þ
where δ is the vertical displacement at the plastic hinge locations. Since the entire joint deformation concentrates where the plastic hinge occurs, and the flexural deformation of column is small, we can approximately view it as a rigid body movement, thus the vertical displacement and deformation of the column can be simplified in the following formula: δ ¼ λLθ ¼
λL Δ 2h
ð11Þ
Substituting Eqs. (9) and (10) into Eq. (11), leads to the relation between the steel strain and the column-top displacement when the beam reaches the state of ultimate bearing capacity: εs φ Δ ¼ ¼ : y L 2ð1−λÞhL
ð12Þ
Substituting Eqs. (9) and (12) into Eq. (8), leads to the column-top ultimate horizontal load Pu. When it is designed as reinforced beam in the joint position of the RC beam, the deformation characteristics of the joint can be obtained greatly through hand-calculation using the simplified model, but when it is designed as over reinforced beam, concrete is crushed and the constitutive relations at the concrete destruction stage have a great influence on each part of the strain value under the ultimate state circumstances. It is suggested that using the finite element method to analyze RC beam is more accurate. 3.3. Strength degradation stage analysis After the joint enters into the degradation stage, the flexural bearing capacity of the plastic hinge at the junctional position of RC beam and steel corbel remains the same until the shear failure happens as a result of the overlarge deformation. Therefore, it can be approximately assumed that the position is subjected to bending moment value Mp in the process. At this time the column-top horizontal force P and displacement Δ meet the following relation: P¼−
Mp 1 N Δþ 1−r 2h 2h
ð13Þ
where all of r, N and Mp are fixed values; and there is a linear relation between horizontal load P and displacement Δ, slope Kd has the following relation: Kd ¼ −
N 2h
ð14Þ
where, Kd is the stiffness value at the joints degradation stages. 4. Finite element analysis and verification In order to further understand the behaviors of composite columns reported in the previous sections, the finite element analysis using
Table 7 Parameters of different load ratio for RC beam.
4.1. Constitutive models
nf
N (kN)
Stiffness (1012N·mm)
Other Parameters (mm)
0.2 0.5 0.8
554.5 1386 2218
E1I1 = 17.3 E2I2 = 5.75
la = 170, lb. = 521 hc = 219, hg = 260 h = 513, L = 800
Note: nf is axial load ratio, and N is column axial force.
ABAQUS [17] is conducted. This method is often used in static and dynamic analysis and has proven to be efficient for nonlinear analysis. The material nonlinearities of concrete and steel are considered in the analysis. The details of the FE model used for RC beam to CFST column joints are described in the following sections.
The damaged plasticity model defined in ABAQUS [17] was used for the concrete in the analysis. Concrete damage plasticity model assumes that the failure of the concrete material is mainly caused by the destruction of compression and tensile crack, which can be used to simulate the mechanical behavior of the concrete under cyclic and dynamic loading. In the present finite element models
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
Load (KN)
Load (KN)
Load (KN)
214
Displacement (mm)
Displacement (mm)
Displacement (mm)
a) Reinforcement ratio 1.0%
b) Reinforcement ratio 1.8%
c) Reinforcement ratio 2.6%
Theory
FEM
Load (KN)
Load (KN)
Load (KN)
Fig. 14. Comparison of theoretical and FEM model with different reinforcement ratio.
Displacement (mm)
Displacement (mm)
Displacement (mm)
a) Length of steel bracket 60mm
b) Length of steel bracket 100mm
c) Length of steel bracket 160mm
Theory
FEM
Fig. 15. Comparison of theoretical and FEM model with different steel bracket lengths.
Since the property of steel is relatively stable, the developmental process from the elastic to the plastic stage has less effect on structural performance. Thus, steel is assumed to behave as an elastic–plastic material with strain hardening after yield strength. The response of the steel products is modeled by an elastic–plastic theory with the VonMises yield criteria, associated with flow rule and isotropic strain hardening. The bilinear elastic–plastic stress–strain curve with linear strain hardening used to simulate the steel material. When the stress points fall inside the yield surface, the behavior of the steel tube is linearly elastic, where Young's modulus of ES = 206 GPa and Poison's ratio of μS = 0.3 were used. If the stress of the steel tube reaches the yield surface, in the hardening part of the curve, a modulus of 2 GPa was used, and the behavior of the steel tube becomes perfectly plastic.
Displacement (mm)
a) Axial load ratio 0.2
Load (KN)
Load (KN)
Load (KN)
subjected to cyclic loading, when the loading direction is changed, the stiffness of the concrete will partially be restored, especially when the tensile loads change into compressive loads it becomes more significant. Therefore, the model introduces concrete damage factor under tensile and compressive loading. The stiffness will be part of the recovery, especially when the load from stretching to compression in this situation is more significant, therefore, model calculation, introduces the concrete tensile and compression case damage factors. For concrete in tension, the tension softening behavior of concrete was defined and the fracture energy Gf versus cracking displacement relationship is used to describe the tensile behavior of concrete.
Displacement (mm)
Displacement (mm)
b) Axial load ratio 0.5
c) Axial load ratio 0.8
Theory
FEM
Fig. 16. Comparison of theoretical and FEM model with different reinforcement ratio.
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215
Load (KN)
parameter (*NLGEOM) is included to deal with the large displacement analysis. 4.4. Test model verification
Displacement (mm) 1-t=4mm ; 2-t=5mm ; 3-t=6mm ; 4-t=7mm ; 5-t=8mm Fig. 17. The skeleton curves obtained from different steel tube thickness model.
Through analyzing it on the basis of material models constituted in the test, Fig. 12 shows the results of the comparison between the finite element analysis and the experimental skeleton curve, and the result is that the two kinds of curves are parallel. Thus, it can do a series of finite element analysis on different joint parameters based on the above model. Fig. 13 shows the joint NJ1 stress and strain distributions, from which, at the junction of corbel, the steel bars yielded the large plastic strain, the same as concrete. Besides, it forms the plastic hinges at the location of the section, constituting that of the tests.
4.2. Finite element type and mesh
4.5. Theory model verification
In general, due to the simulated result with the hexahedron unit, it is more accurate than the wedge and the tetrahedron unit. In order to save computational cost and guarantee the accuracy of calculation, the parts of components in the model are simulated by an 8-node linear brick element with reduced integration (C3D8R) and with three translation degrees of freedom at each node. A structured mesh technique can be adopted for element partition.
According to the above proposed skeleton curve calculation model, it is verified and researched by FEM, as shown in Fig. 8. From which, it takes into account the variation of reinforcement ratio, the length of the corbel and the axial compression ratio. Related parameters are hc = 219 mm, hg = 260 mm; h = 870 mm, L = 691 mm; la = λL, lb = (1− λ)L, and the other specific parameters are shown in Tables 5–7. Substituting the above parameters into the force equilibrium equations in Eq. (3) at the elastic stage, by which it can be used to obtain initial stiffness Kc of the joint. Besides, the value Mp solved by the handcalculation method and the value φp by a finite element method, which are substituted into Eqs. (8) and (12), so the value Pu and Δp are given, respectively. Moreover, Substituting the axial force N and column height h into Eq. (14) gives the stiffness value Kd. According to the above relevant results, it makes up the three-stage skeleton curve and compares with the result of finite element method, as shown in Figs. 14–16. From these figures, it can be seen that the theoretical analysis of the three-stage simplified model is closer to the finite element analysis results. However, in the location of the descending point from the skeleton curve, it has some error as a result of the ideal plastic hinge simplification whiles neglecting the tensile deformation of the steel bar and also where there is a certain effect on the corner.
4.3. Boundary conditions and load application The cover plate considered herein is employed in the form of an analytical rigid body. The cover plate connects with the column-end and beam-end by “Tie” (an interface model in ABAQUS), which ensures the displacements and rotational angles of the contact elements remain the same in the whole loading process. Based on the above joints test model, the end-constraint satisfies the characteristics and requirements of the inflection point. Both ends of the beam and column can be free to rotate, and it is required to restrain the beam-end of the vertical displacement and also all the column-bottom directions of the translational degrees of freedom. The load application is divided into two analysis steps. In the first step, the vertical point axial loading is applied statistically to the top of the surface of the cover plate for simulating axial force loading process of the column; And in the second step, the load is simulated by applying displacement instead of directly applying load, and the horizontal displacement is imposed on the top of the column in the analysis step. The load is applied incrementally using the well-known Newton– Raphson incremental-iterative solution method, to determine the response of the joints subjected to axial and lateral compressive loads. The response of the RC beam to CFST column joints after each step is calculated from the equilibrium equations. The nonlinear geometry
4.6. Parametric analysis To further analyze the effect of the other related parameters on the skeleton curves, this paper conducts the analysis of the skeleton curve model using different relevant parameters on the basis of joint NJ1, which includes the design parameters of the column, beam and steel component parts. In order to simply analyze the influence of different factors, the design parameters of the column selected are the steel tube thickness and concrete strength. The joint skeleton curves obtained are shown
Load (KN)
Load(KN)
150 120 90 60 1 30 2 0 3 -30 4 5 -60 6 -90 -120 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
Displacement (mm) 1-C35 ; 2-C40 ; 3-C45 ; 4-C50 ; 5-C55 ; 6-C60 Fig. 18. The skeleton curves obtained from different concrete strength model.
1-C45 ; 2-C40 ; 3-C35 ; 4-C30 ; 5-C25 ; 6-C20 Fig. 19. The skeleton curves obtained from different concrete strength.
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Load(KN)
120 90 60 30 0 -30 -60 -90 -120 -50 -40 -30 -20 -10 0 10 20 Displacement(mm)
150 100
7 8 9
Load (KN)
216
50
1 2 3 4 5 6 7 8 9
0 -50 -100
30 40 50
7-S400 ; 8-S335 ; 9-S235
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
1-l=160mm ; 2-l=140mm ; 3-l=120mm ; 4-l=100mm ; 5-l=80mm ; 6-l=60mm ; 7-l=40mm ; 8-l=20mm ;
Fig. 20. The skeleton curves obtained from different rebar strength model.
5. Conclusion The seismic experiment, theoretical derivation and finite element analysis on the RC beam to CFST column joint without welding in the
Load(KN)
150 120 90 10 60 11 30 12 0 13 -30 14 -60 15 -90 -120 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
10-p=3.0% ; 11-p=2.6% ; 12-p=2.2% ; 13-p=1.8% ; 14-p=1.4% ; 15-p=1.0% Fig. 21. The skeleton curves obtained from different reinforcement ratio model.
Fig. 22. The skeleton curves obtained from different steel bracket length model.
field of construction are conducted based on this paper. The hysteretic curve, skeleton curve and ductility coefficient of the joint on the top of the column are obtained under low cyclic loading. The three-stage load–displacement skeleton curve model is put forward on the basis of theoretical research. In order to verify the accuracy of the test and the theory model above, nonlinear finite element analysis method is adopted. According to the diverse parameters of the joints, it discusses the variation of bearing capacity. The follow conclusions can be drawn based on the study about this paper: (1) In this paper, A newly developed RC beam to CFST column joint without welding in the construction field possesses fine energy dissipation capability and ductility request contenting with construction projects, besides the strength and stiffness. (2) The failure of the joints focuses on the steel corbel truncation position, in which the plastic hinge is formed, therefore the failure mode associates with the selection and design of the beam section, regardless of the failure of column. (3) Where the greater design bearing capacity of the beam section is, the longer the length of the corbel and the higher the bearing capacity of the joint. But at the descending stage, it has little effect. (4) The axial compression ratio of the column has a significant impact on the skeleton curves, and the greater the axial compression ratio, the lower the strength and stiffness. When we enter into the descending stage, the decline is faster. (5) In this paper the three-stage skeleton curve theory model was established based on simplifying assumptions, which has proven to be feasible, so it can better describe the bearing capacity and strength degradation process of the joint and such a new joint form is available for design reference.
150 120 90 60 1 2 30 3 0 4 -30 5 6 -60 7 -90 8 9 -120 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
Load (KN)
in Figs. 17 and 18 and is based on the account of changing different parameters, respectively. From Figs. 17 and 18, it can be found that the effect of steel tube thickness and concrete strength on the skeleton curve is small, and it seems to be ignored approximately. The study result shows that the failure mode of the joint has nothing to do with the design of the column. In addition, the design parameters of the beam are considered as concrete strength, steel strength and steel ratio. Figs. 19–21 show us the different simulation results. The study result shows that the change of the corresponding design parameters can significantly affect the joint skeleton curves. It explains that the failure modes of the joints are directly related to beam design. Based on further research, it shows that the stronger the flexural bearing capacity of the concrete crosssection, the higher the maximum bearing load of the joint, but the slope at the descending stage will remain basically unchanged. Because the corbel designs have a certain impact on the bearing capacity of the joint, this paper simulates the different corbel length of the joint model and obtains the corresponding skeleton curve as shown in Fig. 22. From Fig. 22, the longer the length is, the stronger the bearing capacity of joint, but the slope affected at the descending stage is still small and can be ignored. Moreover, in this project, since the axial compressive ratio of the concrete-filled steel tube has no limits, this paper analyzes the bearing capacity of the joint under the axial compressive ratio, and the corresponding skeleton curve is shown in Fig. 23. The result shows that the greater the axial compression ratio, the less the bearing capacity, and the faster the strength degradation, the worse the ductility.
9-l=0mm
1-nf=0.1 ; 2-nf=0.2 ; 3-nf=0.3 ; 4-nf=0.4 ; 5-nf=0.5 ; 6-nf=0.6 ; 7-nf=0.7 ; 8-nf=0.8 ; 9-nf=0.9 Fig. 23. The skeleton curves obtained from different axial load ratio model.
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References [1] X. Chengxiang, M. Jing, D. Wang, Selection and design of beam-column joints of concrete-filled steel tubular frames[C], Proceedings of The Seventh International Symposium on Structural Engineering for Young Experts 2002, pp. 904–908 (Tianjin, China). [2] N. Jianguo, Q. Kai, C.S. Cai, Seismic behavior of connections composed of CFSSTCs and steel-concrete composite beams — finite element analysis[J], J. Constr. Steel Res. 64 (2008) 680–688. [3] N. Jianguo, Q. Kai, C.S. Cai, Seismic behavior of connections composed of CFSSTCs and steel-concrete composite beams — experimental study [J], J. Constr. Steel Res. 64 (2008) 1178–1191. [4] H. Linhai, Q. Hui, T. Zhong, W. Zaifeng, Experimental behaviour of thin-walled steel tube confined concrete column to RC beam joints under cyclic loading[J], ThinWalled Struct. 47 (2009) 847–857. [5] Q. Hui, H. Linhai, T. Zhong, Seismic performance of reinforced concrete beam to concrete-filled steel tubular columns joints[J], Key Eng. Mater. 400–402 (2009) 685–691. [6] W. Zhan, P. Jianrong, Y. Jixiong, The study on semirigid joint of steel-concrete composite beam to CFST column[J], Adv. Steel Constr. 5 (4) (2009) 421–431. [7] L. Guochang, Y. Zhijian, T. Jingyang, Selection and design of beam-column joints of concrete-filled steel tubular frames[C], International Symposium on Innovation and Sustainability of Structures in Civil Engineering, ISISS'09, GuangZhou, China 2009, pp. 745–750. [8] L. Guochang, N. Yao, L. Lin, Dynamic behavior of joint of gangue CFST column-beam with ring stiffeners and steel corbels[C], International Symposium on Innovation
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Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Seismic behavior study on RC-beam to CFST-column non-welding joints in field construction Xiaoxiong Zha ⁎, Chengyong Wan, Hang Yu, Jean-Baptiste Mawulé Dassekpo Department of Civil and Environmental Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
a r t i c l e
i n f o
Article history: Received 12 October 2013 Received in revised form 10 July 2015 Accepted 14 July 2015 Available online xxxx Keywords: RC beam to CFST column joint Joint without welding Seismic behavior Skeleton curve Theoretical model Finite element analysis
a b s t r a c t A newly developed reinforced concrete (RC) beam to concrete-filled steel tube (CFST) column joint without welding in the construction field is introduced in this paper. The seismic experiment is conducted on the joint, and the hysteretic curve of the specimen under cyclic loading on the top of the column is obtained. By analyzing the mechanical characteristics and the failure mode of the joint, a three-stage skeleton curve model is presented. In the elastic stage, the initial stiffness is evaluated by solving the stiffness matrix. In the perfect plastic stage and strength degradation stage, the ultimate strength and the degradation stiffness of the joint can be obtained with the limit equilibrium method. Moreover, the test is also simulated with FEM, and the results agree well with the skeleton curves obtained from the test. So this joint shows good ductility and the ability to dissipate energy, and it can be used to replace the joints welded with reinforcement on the outer annular plate. And the finite element analysis results are compared with the theoretical results, which verifies the theoretical model presented above. It is suggested that the three-stage skeleton curve model can be used to depict the mechanical behavior and bearing capacity of this new type of joint. In addition, Parametric analysis is conducted on this joint, with the consideration of different designs of beams, columns and steel brackets, and failure mode is discussed. © 2015 Elsevier Ltd. All rights reserved.
1. Preface The concrete-filled steel tube column is considered as a composite structure style, which has many excellent mechanical behaviors and bearing capacity. For RC beam to CFST column joint, the response to disaster loads has a very important impact on such a structure. Generally, due to the form of beam members, CFST beam to column joints can be divided into steel beam-CFST column joint and RC beam-CFST column joint. Among them, the current reinforced concrete beam-CFST column joint types usually include rigid joints with interior and exterior reinforced loop, anchor and cross-core, etc. Based on the needs of this project, the related research and the improvement of the joints are more focused in China. Where, Xu et al. [1] analyzed the working mechanism and seismic behavior of beam-column joints of CFST frames systematically, based on some results from experimental research and engineering application. The formation suited in the frame structure system, calculation methods and several design suggestions are presented and discussed. Nie et al. [2–3] carried out fourteen connection specimens composed of concrete-filled square steel tubular columns (CFSSTCs) and steel-concrete composite beams with interior diaphragms, exterior diaphragms, or anchored studs in order to investigate the seismic behavior were tested, and the strength, deformation, and energy dissipation capacity of these composite connections were analyzed; 3-D ⁎ Corresponding author. E-mail address: [email protected] (X. Zha).
http://dx.doi.org/10.1016/j.jcsr.2015.07.017 0143-974X/© 2015 Elsevier Ltd. All rights reserved.
nonlinear finite element models were established to analyze the mechanical properties of these three types of connection using ANSYS. Finite element analyses were conducted under both monotonic loading and cyclic loading. Han et al. [4] conducted an experiment on eight thin-walled steel tube confined concrete (TWSTCC) columns to reinforced concrete (RC) beam joints subjected to cyclic loading, where the level of axial load in the column and the type of column crosssection were selected as test parameters. In addition, two concretefilled thin-walled steel tubular columns to RC beam joints were also tested for comparison. Qu et al. [5] tested eight reinforced concrete (RC) beams to concrete-filled steel tubular (CFST) column joints enclosed by rebar under reversal horizontal displacement with constant axial load in order to study their seismic behavior. The test parameters are the axial load level and the section type of CFST column. In this study, the failure model, hysteretic characteristic, ductility and energy dissipation were investigated. Wang et al. [6] studied the semi-rigid joint of steel-concrete composite beam to CFST column with stiffening rings. Two specimens were tested by incremental loading and cyclic loading. The finite element package ABAQUS was used to study the nonlinear behavior of such specimens. Li et al. [7–8] researched the seismic behavior of the joint of gangue concrete-filled steel tubular columnbeam with ring stiffeners and steel corbels, and the quasi-static tests on the interior joint of gangue concrete-filled steel tubular columnring beam joints in the low cycle reverse load by which the failure patterns, hysteretic characteristics, ductility and energy dissipation were studied. Liu et al. [9] carried out finite element analysis on the aseismatic
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
behavior of the joints of the new type of concrete-filled steel tubes, which is based on fuzzy mathematics. The results of the example analysis have showed that the finite element calculation model based on fuzzy mathematics is suited for the mechanical properties of the analysis of the joints. Wang and Liu [10] presented the test results of six connections under cyclic loading. Each test specimen was properly designed to model the interior joint of a moment resisting frame, and was identically comprised of three parts that include the circular concrete-filled steel tube columns, the reinforced concrete beams, and the short fabricated connection stubs. Chen et al. [11] studied the bearing capacity, crack patterns, deformation, and strain of the reinforcements of the specimens through the compressive tests on this concrete-filled steel tubular (CFST) column-beam joint with the column tube discontinuous in the joint zone after cyclic reversed loading. J et al. [12] conducted an experimental investigation into the behavior of composite column-to-beam connections using ten large-scale connections, four under monotonic loadings and six under cyclic loadings. All connections consisted of a concrete-filled steel tube (CFST) column (circular), a compact universal beam section and a shop fabricated connection stub. Monotonic testing was first carried out and the results were used to conduct the cyclic tests. Wang et al. [13] investigated the seismic performance of the composite joint consisting of square concrete-filled thin-walled steel tubular (CFTST) column and steel beam with end plate and blind bolts. Four exterior joint specimens were tested under axially compressive load on the top of the columns and cyclic loads on the beam tip. The experimental parameters in the study were the thickness of the steel tube and the type of end plate. Zhang et al. [14] presented experimental and analytical studies on the seismic behavior of steel I-beam to circular CFST column assemblies with external diaphragms. In the experimental study, four specimens, i.e. two exterior joints and two interior joints in a frame structure, are tested under constant axial loads on columns and cyclic vertical loads on beam ends. The specimens are designed to be strong column-weak beam for exterior joints and strong beam-weak panel zone for interior joints. The above joint types in the project have a range of applications to some extent, nevertheless, there are imperfections in some types, such as the need for a large number of welding work at the site, the influence of anchoring parts in column to internal concrete pouring, or as a result of the openings, the impact of the strength of joint region and continuity of steel tube, etc. Based on the above problems, this paper conducted experimental study to seismic behavior, theoretical derivation and finite element calculation study on new typical RC beam to CFST column joints (shown in Fig. 1) without welding in the construction field, in which the joint steel components are required to be completed by factory processing.
a) Whole beam-to-column joints
205
2. Experiment research 2.1. Experiment design During a real earthquake, joints tend to be larger in operating cyclic loading due to the ever-changing seismic wave to structure foundation. In order to ensure the safety of structures in the earthquake, the general design requirement is required to meet “strong column, weak beam, and stronger joints”. Ductility is an important seismic performance index, which marks energy consumption of the joints as well as deformation properties after yielding. Based on this, in the cyclic loading experiment, beam-column joint is conducted by constantly changing the positive and negative bending moment. Thus, it is obtained to analyze ductility coefficient, viscous damping coefficient and energy dissipation ratio, and others, which can be used to determine energy consumption and seismic performance of joints, and also give the reference for the engineering design. In order to simulate real hysteretic behavior of joints, a typical part of the beam-column joints derived from the plane frame subjected to seismic loading have been tested with simulating beamend and column-end actual boundary condition, as shown in Fig. 2. In which H is the distance between inflection point of the upper and lower frame column, L is the distance between inflection point of the left and right frame beam, N is axial force, V is the shear at the position of inflection point on beam, P, Δ/2 are the horizontal shear and lateral displacement at the position of inflection point on column, respectively, and the second-order effect can be considered. Based on the above model, the proposed simplified test model is shown in Fig. 3. On account of some constraints such as test environment and load capacity, the reduced scale test model is put forward, as shown in Fig. 1. Firstly in the factory manufactured phase, the steel column joint region is processed into exterior reinforced loop plate form, and connected with steel bracket. In addition, the steel bracket upper and lower flange position are welded with reinforced connection pieces with holes, and as the reinforced limit agencies, all holes of design corresponds to reinforced distribution location. In the installation phase, the processed reinforcement is planed pass through the holes on the reinforced connection pieces after column installation is completed, and connected with the reinforcement sleeve. This installation of the joints in the construction field is shown in Fig. 1. The joint is installed in the construction site without additional large number of welding work, saving funds for welding and inspection and greatly shortening the construction period. Through the above analysis, it shows that the new joint has good mechanical properties and ductility, and it can be served as a CFST beam-column joints in the project to promote the use.
b) Connection of reinforcement
Fig. 1. Joint with no welding in the construction field.
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test. Selecting some column joints in the projects and taking beamcolumn contra-flexure point intermediate part reduced to the scale with a proportion 1:5, the related parameters of the specimens are shown in Table 1. The joint of column concrete strength grade is C60 and the beam concrete strength grade is C30. At the same time, the corresponding material property test of concrete blocks and steel are conducted, and the results are shown in Tables 2 and 3, where the reinforcement yield strength is measured as 451.2 MPa and ultimate strength 592.7 MPa. The specific joints connections part is shown in Fig. 4. 2.3. Experiment result analysis Fig. 5 shows the failure phenomenon of the specimen, from which it can be found that both of the joints have obvious vertical cracks along the bracket external edge position with loads increasing. At the same time, the upper concrete appears spalling, and the reinforcement exposing, thus the specimen appear like a plastic hinge in the bracket's outside edge location. Fig. 6 shows the hysteresis curve of two specimens, where both specimens have the plump hysteresis curve, showing the good energy dissipation capacity. At the same time, the curve assumes inverted s-shaped slightly. It demonstrates that there is certain degree of slip between the reinforcement and concrete. The skeleton curves are given based on the load–displacement hysteresis curve of joints, as shown in Fig. 7. By which, it acquires the ductility coefficient μ of joints and the ductility coefficient μ = Δu/Δy, as shown in Table 4. From which, it can be found that the two specimens with ductility coefficient are greater than 5.0 with good ductility, meeting the needs of the project.
Fig. 2. Joint force model in plane frame structure.
2.2. Experiment introduction In order to further verify the reliability of the joint form in engineering application, this paper conducted the seismic performance 3. Theory analysis The seismic behavior of the newly developed RC beam to CFST column joint without welding in the construction field is analyzed with a theoretical method based on the research of the companion paper. According to the proposed joint form, the simplified three-step skeleton curve model is presented, including the elastic stage, ideal plastic stage and strength degradation stage, respectively. In the elastic stage, the skeleton curve stiffness remain the same, thus the joints can be approximately regarded as being in the elastic state as a whole; in the ideal plastic stage, RC beam gradually enters the plasticity and RC beam cross-section in corbel junctional position and eventually develops into a plastic hinge. At this time, the ideal plastic stage ends; after entering the strength degradation stage, the plastic hinge location and the bearing ultimate bending moment remains unchanged. As the top of the horizontal column displacement increases, the top of the horizontal column load decreases as a result of the second-order effect of axial force. The three-stage skeleton curve simplified model is shown in Fig. 8.
N
P
Fig. 3. Experimental model with loading at the top of column.
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Table 1 Illustration of CFST joint specimens. No.
l (mm)
ts (mm)
Section Size (mm)
L (mm)
Bar arrangement
h (mm)
N (kN)
NJ1
120
50
800
Upper flange:3Φ12 Lower flange:2Φ12
1000
1200
NJ2
600
B:260 × 100 C:219 × 5 B:260 × 100 C:219 × 6
Note: No. is node numbering, l is the length of the bracket, ts is the width of the loop plate, B is beam, C is column, L is beam total length, h is column total height and N is column axial force.
Table 2 Test value of beam concrete block. No.
B1 (MPa)
B2 (MPa)
B3 (MPa)
Mean (MPa)
fc (MPa)
NJ1 NJ2
47.3 41.2
52.4 47.2
44.5 38.5
48.1 42.3
36.7 32.3
Note: B1 is beam 1, fc is conversion prism compressive strength.
Table 3 Test value of column concrete block. No.
C1 (MPa)
C2 (MPa)
C3 (MPa)
Mean (MPa)
fc (MPa)
NJ1 NJ2
46.5(Rejected) 65.2
68.8 70.2
68.8 69.1
68.8 68.2
52.5 52.0
Note: C1 is column 1, fc is conversion prism compressive strength.
3.1. Elastic stage analysis Taking into account the whole joint model being in the elastic stage, we can reference the joint region simplified calculation method from Li et al. [15] while ignoring concrete cracking and yielding failure in the beam, where it can be simplified as a model in Fig. 9. Each beam segment and joint region are conducted to split, as shown in Fig. 10, and each part of the component is numbered. Considering the symmetry of the joint the effect of beams C and D can be replaced with beams A and B. Equilibrium equations are given as follows:
Q g1 Mg1
¼ KA
δg1 θg1
ð1aÞ
8 8 9 9 −Q g1 > δg1 > > > > > > > < < = = −Mg1 θg1 ¼ KB Q δ > > > > g2 g2 > > > > : : ; ; Mg2 θg2
ð1bÞ
a) NJ1
b) NJ2 Fig. 4. Steel part of joint specimens.
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a) NJ1
b) NJ2 Fig. 5. Damage of joint specimens.
9 9 8 8 < P = < Δ = ¼ KE vc1 Q ; : c1 ; : Mc1 θc1
Q c2 Mc2
¼ KF
vc2 θc2
ð1cÞ
ð1dÞ
in which 2
12 6 l 2 6 a 6 6 6 3mEI 1 −lb EI 6 la KB ¼ 6 KA ¼ 2 3 −lb lb la 6 lb 6 − 12 6 2 6 la 4 6 la
6 12 6 − 2 la la la 6 4 − 2 la 6 12 6 − − l a la 2 la 6 2 − 4 la
3 7 7 7 7 7 7 7 7 7 7 5
2 3 2 2 1=h −1=h 1=h 3nEI 6 3nEI 1 h 7 KE ¼ 4 −1=h2 1=h2 −1=h 5 K F ¼ 3 2 h h h h 2 2 1 1=h −1=h
150
Horizontal Force (KN)
Horizontal Force (KN)
where δg1, θg1, δg2, and θg2 is the right-side vertical displacement with the angle from beam-segments A and B, respectively; νc1, and θc1 is the lowerend horizontal displacement with the angle from column-segment E, respectively; νc2, and θc2 is the top-end horizontal displacement with the angle from column-segment F, respectively; Qg1, Mg1, Qg2, and Mg2 is the right-side shear with the bending moment from beam-segments A and B, respectively; Qc1, and Mc1 is the lower-side shear with the bending moment from column-segment E, respectively; Qc2, and Mc2 is top-end shear with the bending moment from column-segment F, respectively; KA, KB, KE, and KF is element stiffness matrix (note that we ignore the influence of shear deformation) from beam-segments A and B, and column-segments E and F, respectively; EI is section bending stiffness from beam-segment B; m, n is
100 50 0 -50 -100 -60
-40
-20 0 20 40 Displacement (mm)
60
100 50 0 -50 -100 -60
-40 -20 0 20 40 Displacement (mm)
a) NJ1
b) NJ2 Fig. 6. Hysteretic curves of joint specimens.
60
209
Horizontal Force (KN)
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
Displacement (mm) 1-NJ1 ; 2-NJ2 Fig. 7. Test results of skeleton curves of joint specimens.
Table 4 Ductility coefficient ratio. No.
Δy(mm)
Δu(mm)
μ
NJ1 NJ2
7.42 7.07
44.29 45.27
5.97 6.40
Note: Δy is elastic displacement of joint, Δu is limit displacement of joint, μ is ductility coefficient.
section bending stiffness from beam-segment A and column-segments E and F, respectively, and m = E2I2/(E1I1), n = EscIsc/(E1I1);la,lb. is the length from beam-segments A and B, respectively, and la = λL, lb. = (1-λ)L. Since the joint region has an effect on the stiffness of the joint in the elastic stage, thus the deformation and stiffness matrices of the components need to be transformed; the force equilibrium equation of each component based on joint domain deformation is given as follows:
Q1 M1
¼
3mEI
3
lb
2
1; −lb 2 −lb ; lb
12;
u1 θ1
ð2aÞ
6la ;
−12;
6ðhc þ la Þ;
−3ðhc −la Þ 1 − la ð3hc −2la Þ 2 3EIðhc −la Þ
6 2 8 9 6la ; 4la ; −6la ; la ð3hc þ 2la Þ; 6 ‐Q 1 > 6 > > > > > 6 > −M1 > 6EI 12EI 6EI ðhc þ la Þ < = EI 6 − 12EI ; − 2 ; ; − ; 6 3 3 3 3 Q gv2 ¼ 36 l l l la la a a a > > 6 l > > M a > > 6 gθ2 1 2 > > 2 2 2 : ; 6 6ðhc þ la Þ; la ð3hc þ 2la Þ; −6ðhc þ la Þ; 3hc þ 6hc la þ 4la ; − 3hc −2la Mgγ2 6 2 4 1 1 2 1 2 2 2 − 3hc −2la ; 3hc −6hc la þ 4la −3ðhc −la Þ; − la ð3hc −2la Þ; 3ðhc −la Þ; 2 2 4
P Pu 0.85Pu
Kd Kc
Fig. 8. P-Δ skeleton model for calculation.
3 78 9 7 u 7> > 1> > > 7> < θ1 > = 7> 7 7 u0 7> > θ0 > > > 7> : > ; 7> 7 γ0 5
ð2bÞ
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N P
Esc Isc E1I1
h E2I2
hg
Esc Isc
h
hc Fig. 9. Simplified calculation model for CFST joint.
3 1 1 1; ‐1; 2h−hg ; ‐ 2h þ hg 78 9 6 8 9 2 4 7 Δ 6 P > > > 7> 6 1 1 > > < = 3nEI 6 < > = 7> ; −1; 1; − 2h−h 2h þ h g g Q cv1 7 ν0 6 2 4 ¼ 3 6 7 1 1 1 1 M θ > > > > 2 7 6 h 6 2h−hg ; ‐ 2h−hg ; 2h−hg ; ‐ 4h2 −hg 2 > : cθ1 > ; : 0> ; 7> Mcγ1 γ0 7 62 2 4 8 1 4 1 1 2 5 1 2 2 2h þ hg − 2h þ hg ; 2h þ hg ; − 4h −hg ; 4 4 8 16
ð2cÞ
3 2 1 1 1; 2h−hg ; − 2h þ hg 9 8 7 6 2 4 < Q cν2 = 3nEI 6 7 1 2 1 1 2 7 u1 6 2 Mcθ2 ¼ 3 6 2h−hg ; 7 2h−hg ; 4h −hg ; : 7 θ1 62 4 8 h Mcγ2 1 4 1 1 2 2 5 2 4h −hg ; 2h þ hg − 2h þ hg ; 4 8 16
ð2dÞ
2
where {u1, θ1, u0, θ0, γ0} is the displacement vector from the beam-segment A and the joint domain under the coordinate of the joint region, respectively; {Q1, M1} is shear with bending moment from the right side of beam-segment A under the coordinate of the joint region, respectively; {Qgv2, Mgθ2, Mgγ2, Qcv1, Mcθ1, Mcγ1} is shear with bending moment from the junction of the beam, column and joint region, respectively; hc, hg is the width and height from the joint region. Substituting the internal force boundary condition of the components and the related force equilibrium equation of the joint regions into the above equilibrium equations, we obtain the force equilibrium equation of the joints as a whole, namely f f g ¼ ½K fδg
ð3Þ
N P
Mc1
E
Qc1 Mc1 A
Mg1 Qg1
Mg1 Qg1
B
Qc1
Mg2 Mg3 Qg2
Qg2 C
Qg3
Mg4 Mg4 Qg4
D
Qg3
Mg2
Mg3
Qg4
Mc2
Qc1
Qc1 F
Mc2
a) Diagram of internal force on beam members
b) Diagram of internal force on joint region
Fig. 10. Members of CFST joint for calculation.
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
211
N P
Fig. 11. Calculation model for limit equilibrium method.
where T P 2h þ hg P 2h þ hg ;− ; 0; P; P; −kγ0 2L 2L fδg ¼ ½u1 ; θ1 ; v0 ; θ0 ; γ 0 ; ΔT
ff g ¼
2
−
3mEI
3mEI ; lb 4EI ; la
;
3 0;
0;
0;
0
2 6 lb 6 6 6EI EIð3hc þ 2la Þ EIð3hc −2la Þ 6 0; ; − ; 0 − 2 ; 6 2 2 6 l l 2la a a 6 6 2 2 2 2 2 2 2 2EI 3hc þ 6hc la þ 4la EI 3hc −4la 3nEI 4h −hg 6 12EIðhc þ la Þ 2EIð3hc þ 2la Þ 3nEI 2h−hg 3nEI 2h−hg 6 ; ; 0; þ ; − − ; 6 3 2 3 3 3 3 3 6 la la 2h 2h la la 8h ½K ¼ 6 6 3nEI 2h−h 3nEI 2h þ h 3nEI 3nEI g g 6 0; 0; − 3 ; ; − ; 6 3 3 3 6 h h 2h 4h 6 3nEI 2h−h 3nEI 2h þ h 3nEI g g 6 0; 0; ; ; − ; 0 6 3 3 3 6 h 2h 4h 6 2 2 2 2 2 2 2 6 EI 4la −3hc 3nEI 4h −hg EI 3hc −6hc la þ 4la 3nEI 4h þ 4hhg þ hg 4 6EIðla −hc Þ 3EIð2la −3hc Þ ; ; 0; − ; − ; 0 3 2 3 3 3 3 la la la 4h 2la 8h
7 7 7 7 7 7 7 7 7 7 7 7 7: 7 7 7 7 7 7 7 7 7 7 5
Solving the above sixth-order equations, it is easier to get the relationship between value P and Δ; initial stiffness Kc = P/Δ. 3.2. Plastic stage analysis
Horizontal Force (KN)
Horizontal Force (KN)
When the joint test enters into the plastic stage, the simplified model also enters into the second stage of the trilinear model. It's corresponding parameters include ultimate load Pu and displacement Δp of the starting point at the descending stage. Where, Δp is the displacement at the corbel location when RC beam has developed into a plastic hinge. Using the limit equilibrium method [16], it can be approximately viewed that at this time
Displacement (mm) a) NJ1
Displacement (mm) b) NJ2
1-NJ1 Test Value ; 2-FEM Value ; 3-NJ2 Test Value Fig. 12. Comparisons of FEA and test results of skeleton curves of joint specimens.
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a) Stress contour of steel member
b) Equivalent plastic strain contour of concrete (Deformation scale factor = 3)
Fig. 13. Contour of FEA result of specimen NJ1.
the virtual work produced by the column-top horizontal load and the vertical load is completely transformed into a plastic hinge with plastic strain energy, with a simplified calculation model as shown in Fig. 11. From which the virtual work equation is given in Eq. (4), the plastic hinge position relative angles with small deformation hypothesis can be obtained by Eq. (5) as follows 12 δΔ δΔ 2 δW ¼ PδΔ þ Nδ 4h −Δ2 ¼ PδΔ þ N pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ≈PδΔ þ N 2 2 2h 4h −Δ
ð4Þ
π π λ 1 −θ þ − θ ¼− δθ δφ ¼ δ 2 2 1−λ 1−λ
ð5Þ
δU ¼ Mp δφ
ð6Þ
where, Mp is the sum of limit flexural bearing capacity from the left to the right side beam of the bracket junction location. Substituting Eqs. (4) and (5) into Eq. (6), leads to Mp 1 Δ ¼Pþ N: 1−λ 2h 2h
ð7Þ
When the starting point displacement Δp at the descending stage is determined, Pu is the only determining column-top ultimate horizontal load, see Eq. (8) as follow: Pu ¼
Mp 1 Δp − N 1−λ 2h 2h
ð8Þ
where the starting point displacement Δp at the descending stage can be obtained in two ways. When the condition allows, it is suggested that using the finite element method for modeling analysis of RC beam to get the angle and Mp when it reaches the ultimate flexural strength; or it uses the following calculation method Eq. (9) to gain the corresponding joint angle. By the plane section assumption of beam, the relation is as follow: εs 1 dφ ¼ ¼ y r dx
ð9Þ
where εs is the strain of tensile steel when the beam reaches the limit state; y is the distance between tensile steel and neutral axis; r is the gyration radius in the beam section.
Table 5 Parameters of different reinforcement ratio for RC beam. ρ
E1I1 (1012N·mm)
E2I2 (1012N·mm)
EscIsc (1012N·mm)
Other Parameters (mm)
1.0% 1.8% 2.6%
16.9 17.1 17.4
5.00 5.47 5.95
8 8 8
la = 170, lb. = 521 hc = 219, hg = 260 h = 513, L = 800
Note: ρ is reinforcement ratio.
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213
Table 6 Parameters of different bracket length for RC beam. l (mm)
la (mm)
lb (mm)
Stiffness (1012N·mm)
Other Parameters (mm)
60 100 160
110 150 210
581 541 481
E1I1 = 17.3 E2I2 = 5.75
hc = 219, hg = 260 h = 513, L = 800
Note: l is length of the bracket.
Analyzing the plastic hinge angle while referring to Fig. 11, the relation is shown as follow: δ δ þ 1 φ φ λL ð1−λÞL δ ¼ ¼ ¼ ¼ L r λL þ ð1−λÞL L λð1−λÞL2
ð10Þ
where δ is the vertical displacement at the plastic hinge locations. Since the entire joint deformation concentrates where the plastic hinge occurs, and the flexural deformation of column is small, we can approximately view it as a rigid body movement, thus the vertical displacement and deformation of the column can be simplified in the following formula: δ ¼ λLθ ¼
λL Δ 2h
ð11Þ
Substituting Eqs. (9) and (10) into Eq. (11), leads to the relation between the steel strain and the column-top displacement when the beam reaches the state of ultimate bearing capacity: εs φ Δ ¼ ¼ : y L 2ð1−λÞhL
ð12Þ
Substituting Eqs. (9) and (12) into Eq. (8), leads to the column-top ultimate horizontal load Pu. When it is designed as reinforced beam in the joint position of the RC beam, the deformation characteristics of the joint can be obtained greatly through hand-calculation using the simplified model, but when it is designed as over reinforced beam, concrete is crushed and the constitutive relations at the concrete destruction stage have a great influence on each part of the strain value under the ultimate state circumstances. It is suggested that using the finite element method to analyze RC beam is more accurate. 3.3. Strength degradation stage analysis After the joint enters into the degradation stage, the flexural bearing capacity of the plastic hinge at the junctional position of RC beam and steel corbel remains the same until the shear failure happens as a result of the overlarge deformation. Therefore, it can be approximately assumed that the position is subjected to bending moment value Mp in the process. At this time the column-top horizontal force P and displacement Δ meet the following relation: P¼−
Mp 1 N Δþ 1−r 2h 2h
ð13Þ
where all of r, N and Mp are fixed values; and there is a linear relation between horizontal load P and displacement Δ, slope Kd has the following relation: Kd ¼ −
N 2h
ð14Þ
where, Kd is the stiffness value at the joints degradation stages. 4. Finite element analysis and verification In order to further understand the behaviors of composite columns reported in the previous sections, the finite element analysis using
Table 7 Parameters of different load ratio for RC beam.
4.1. Constitutive models
nf
N (kN)
Stiffness (1012N·mm)
Other Parameters (mm)
0.2 0.5 0.8
554.5 1386 2218
E1I1 = 17.3 E2I2 = 5.75
la = 170, lb. = 521 hc = 219, hg = 260 h = 513, L = 800
Note: nf is axial load ratio, and N is column axial force.
ABAQUS [17] is conducted. This method is often used in static and dynamic analysis and has proven to be efficient for nonlinear analysis. The material nonlinearities of concrete and steel are considered in the analysis. The details of the FE model used for RC beam to CFST column joints are described in the following sections.
The damaged plasticity model defined in ABAQUS [17] was used for the concrete in the analysis. Concrete damage plasticity model assumes that the failure of the concrete material is mainly caused by the destruction of compression and tensile crack, which can be used to simulate the mechanical behavior of the concrete under cyclic and dynamic loading. In the present finite element models
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
Load (KN)
Load (KN)
Load (KN)
214
Displacement (mm)
Displacement (mm)
Displacement (mm)
a) Reinforcement ratio 1.0%
b) Reinforcement ratio 1.8%
c) Reinforcement ratio 2.6%
Theory
FEM
Load (KN)
Load (KN)
Load (KN)
Fig. 14. Comparison of theoretical and FEM model with different reinforcement ratio.
Displacement (mm)
Displacement (mm)
Displacement (mm)
a) Length of steel bracket 60mm
b) Length of steel bracket 100mm
c) Length of steel bracket 160mm
Theory
FEM
Fig. 15. Comparison of theoretical and FEM model with different steel bracket lengths.
Since the property of steel is relatively stable, the developmental process from the elastic to the plastic stage has less effect on structural performance. Thus, steel is assumed to behave as an elastic–plastic material with strain hardening after yield strength. The response of the steel products is modeled by an elastic–plastic theory with the VonMises yield criteria, associated with flow rule and isotropic strain hardening. The bilinear elastic–plastic stress–strain curve with linear strain hardening used to simulate the steel material. When the stress points fall inside the yield surface, the behavior of the steel tube is linearly elastic, where Young's modulus of ES = 206 GPa and Poison's ratio of μS = 0.3 were used. If the stress of the steel tube reaches the yield surface, in the hardening part of the curve, a modulus of 2 GPa was used, and the behavior of the steel tube becomes perfectly plastic.
Displacement (mm)
a) Axial load ratio 0.2
Load (KN)
Load (KN)
Load (KN)
subjected to cyclic loading, when the loading direction is changed, the stiffness of the concrete will partially be restored, especially when the tensile loads change into compressive loads it becomes more significant. Therefore, the model introduces concrete damage factor under tensile and compressive loading. The stiffness will be part of the recovery, especially when the load from stretching to compression in this situation is more significant, therefore, model calculation, introduces the concrete tensile and compression case damage factors. For concrete in tension, the tension softening behavior of concrete was defined and the fracture energy Gf versus cracking displacement relationship is used to describe the tensile behavior of concrete.
Displacement (mm)
Displacement (mm)
b) Axial load ratio 0.5
c) Axial load ratio 0.8
Theory
FEM
Fig. 16. Comparison of theoretical and FEM model with different reinforcement ratio.
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
215
Load (KN)
parameter (*NLGEOM) is included to deal with the large displacement analysis. 4.4. Test model verification
Displacement (mm) 1-t=4mm ; 2-t=5mm ; 3-t=6mm ; 4-t=7mm ; 5-t=8mm Fig. 17. The skeleton curves obtained from different steel tube thickness model.
Through analyzing it on the basis of material models constituted in the test, Fig. 12 shows the results of the comparison between the finite element analysis and the experimental skeleton curve, and the result is that the two kinds of curves are parallel. Thus, it can do a series of finite element analysis on different joint parameters based on the above model. Fig. 13 shows the joint NJ1 stress and strain distributions, from which, at the junction of corbel, the steel bars yielded the large plastic strain, the same as concrete. Besides, it forms the plastic hinges at the location of the section, constituting that of the tests.
4.2. Finite element type and mesh
4.5. Theory model verification
In general, due to the simulated result with the hexahedron unit, it is more accurate than the wedge and the tetrahedron unit. In order to save computational cost and guarantee the accuracy of calculation, the parts of components in the model are simulated by an 8-node linear brick element with reduced integration (C3D8R) and with three translation degrees of freedom at each node. A structured mesh technique can be adopted for element partition.
According to the above proposed skeleton curve calculation model, it is verified and researched by FEM, as shown in Fig. 8. From which, it takes into account the variation of reinforcement ratio, the length of the corbel and the axial compression ratio. Related parameters are hc = 219 mm, hg = 260 mm; h = 870 mm, L = 691 mm; la = λL, lb = (1− λ)L, and the other specific parameters are shown in Tables 5–7. Substituting the above parameters into the force equilibrium equations in Eq. (3) at the elastic stage, by which it can be used to obtain initial stiffness Kc of the joint. Besides, the value Mp solved by the handcalculation method and the value φp by a finite element method, which are substituted into Eqs. (8) and (12), so the value Pu and Δp are given, respectively. Moreover, Substituting the axial force N and column height h into Eq. (14) gives the stiffness value Kd. According to the above relevant results, it makes up the three-stage skeleton curve and compares with the result of finite element method, as shown in Figs. 14–16. From these figures, it can be seen that the theoretical analysis of the three-stage simplified model is closer to the finite element analysis results. However, in the location of the descending point from the skeleton curve, it has some error as a result of the ideal plastic hinge simplification whiles neglecting the tensile deformation of the steel bar and also where there is a certain effect on the corner.
4.3. Boundary conditions and load application The cover plate considered herein is employed in the form of an analytical rigid body. The cover plate connects with the column-end and beam-end by “Tie” (an interface model in ABAQUS), which ensures the displacements and rotational angles of the contact elements remain the same in the whole loading process. Based on the above joints test model, the end-constraint satisfies the characteristics and requirements of the inflection point. Both ends of the beam and column can be free to rotate, and it is required to restrain the beam-end of the vertical displacement and also all the column-bottom directions of the translational degrees of freedom. The load application is divided into two analysis steps. In the first step, the vertical point axial loading is applied statistically to the top of the surface of the cover plate for simulating axial force loading process of the column; And in the second step, the load is simulated by applying displacement instead of directly applying load, and the horizontal displacement is imposed on the top of the column in the analysis step. The load is applied incrementally using the well-known Newton– Raphson incremental-iterative solution method, to determine the response of the joints subjected to axial and lateral compressive loads. The response of the RC beam to CFST column joints after each step is calculated from the equilibrium equations. The nonlinear geometry
4.6. Parametric analysis To further analyze the effect of the other related parameters on the skeleton curves, this paper conducts the analysis of the skeleton curve model using different relevant parameters on the basis of joint NJ1, which includes the design parameters of the column, beam and steel component parts. In order to simply analyze the influence of different factors, the design parameters of the column selected are the steel tube thickness and concrete strength. The joint skeleton curves obtained are shown
Load (KN)
Load(KN)
150 120 90 60 1 30 2 0 3 -30 4 5 -60 6 -90 -120 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
Displacement (mm) 1-C35 ; 2-C40 ; 3-C45 ; 4-C50 ; 5-C55 ; 6-C60 Fig. 18. The skeleton curves obtained from different concrete strength model.
1-C45 ; 2-C40 ; 3-C35 ; 4-C30 ; 5-C25 ; 6-C20 Fig. 19. The skeleton curves obtained from different concrete strength.
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
Load(KN)
120 90 60 30 0 -30 -60 -90 -120 -50 -40 -30 -20 -10 0 10 20 Displacement(mm)
150 100
7 8 9
Load (KN)
216
50
1 2 3 4 5 6 7 8 9
0 -50 -100
30 40 50
7-S400 ; 8-S335 ; 9-S235
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
1-l=160mm ; 2-l=140mm ; 3-l=120mm ; 4-l=100mm ; 5-l=80mm ; 6-l=60mm ; 7-l=40mm ; 8-l=20mm ;
Fig. 20. The skeleton curves obtained from different rebar strength model.
5. Conclusion The seismic experiment, theoretical derivation and finite element analysis on the RC beam to CFST column joint without welding in the
Load(KN)
150 120 90 10 60 11 30 12 0 13 -30 14 -60 15 -90 -120 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
10-p=3.0% ; 11-p=2.6% ; 12-p=2.2% ; 13-p=1.8% ; 14-p=1.4% ; 15-p=1.0% Fig. 21. The skeleton curves obtained from different reinforcement ratio model.
Fig. 22. The skeleton curves obtained from different steel bracket length model.
field of construction are conducted based on this paper. The hysteretic curve, skeleton curve and ductility coefficient of the joint on the top of the column are obtained under low cyclic loading. The three-stage load–displacement skeleton curve model is put forward on the basis of theoretical research. In order to verify the accuracy of the test and the theory model above, nonlinear finite element analysis method is adopted. According to the diverse parameters of the joints, it discusses the variation of bearing capacity. The follow conclusions can be drawn based on the study about this paper: (1) In this paper, A newly developed RC beam to CFST column joint without welding in the construction field possesses fine energy dissipation capability and ductility request contenting with construction projects, besides the strength and stiffness. (2) The failure of the joints focuses on the steel corbel truncation position, in which the plastic hinge is formed, therefore the failure mode associates with the selection and design of the beam section, regardless of the failure of column. (3) Where the greater design bearing capacity of the beam section is, the longer the length of the corbel and the higher the bearing capacity of the joint. But at the descending stage, it has little effect. (4) The axial compression ratio of the column has a significant impact on the skeleton curves, and the greater the axial compression ratio, the lower the strength and stiffness. When we enter into the descending stage, the decline is faster. (5) In this paper the three-stage skeleton curve theory model was established based on simplifying assumptions, which has proven to be feasible, so it can better describe the bearing capacity and strength degradation process of the joint and such a new joint form is available for design reference.
150 120 90 60 1 2 30 3 0 4 -30 5 6 -60 7 -90 8 9 -120 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50 Displacement(mm)
Load (KN)
in Figs. 17 and 18 and is based on the account of changing different parameters, respectively. From Figs. 17 and 18, it can be found that the effect of steel tube thickness and concrete strength on the skeleton curve is small, and it seems to be ignored approximately. The study result shows that the failure mode of the joint has nothing to do with the design of the column. In addition, the design parameters of the beam are considered as concrete strength, steel strength and steel ratio. Figs. 19–21 show us the different simulation results. The study result shows that the change of the corresponding design parameters can significantly affect the joint skeleton curves. It explains that the failure modes of the joints are directly related to beam design. Based on further research, it shows that the stronger the flexural bearing capacity of the concrete crosssection, the higher the maximum bearing load of the joint, but the slope at the descending stage will remain basically unchanged. Because the corbel designs have a certain impact on the bearing capacity of the joint, this paper simulates the different corbel length of the joint model and obtains the corresponding skeleton curve as shown in Fig. 22. From Fig. 22, the longer the length is, the stronger the bearing capacity of joint, but the slope affected at the descending stage is still small and can be ignored. Moreover, in this project, since the axial compressive ratio of the concrete-filled steel tube has no limits, this paper analyzes the bearing capacity of the joint under the axial compressive ratio, and the corresponding skeleton curve is shown in Fig. 23. The result shows that the greater the axial compression ratio, the less the bearing capacity, and the faster the strength degradation, the worse the ductility.
9-l=0mm
1-nf=0.1 ; 2-nf=0.2 ; 3-nf=0.3 ; 4-nf=0.4 ; 5-nf=0.5 ; 6-nf=0.6 ; 7-nf=0.7 ; 8-nf=0.8 ; 9-nf=0.9 Fig. 23. The skeleton curves obtained from different axial load ratio model.
X. Zha et al. / Journal of Constructional Steel Research 116 (2016) 204–217
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