In this paper, a nonlinear finite element (FE) analysis of high-performance hybrid system (HPHS) beam-column connections is presented. The detailed experimental results of the ten half-scale hybrid connections with limited seismic detailing have been discussed in a different paper. However, due to the inherent complexity of HPHS beam-column joints and the unique features of the tested specimens, the experimental study was not comprehensive enough. The new connection (HPHS) detail suggested in this study is characterized by ductile connection, steel connectors, and engineered cementitious composite (ECC) which is a kind of high-performance fiber reinforced cement composite with multiple fine cracks (HPFRCCs). Therefore, in this paper, FE analysis results are compared with experimental results from the cycle tests of the two specimens (RC and PC) to assess model accuracy, and detailed model descriptions are presented, including the determination of stiffness and strength. The critical parameters influencing the joint’s behavior are the axial load on column, beam connection steel plate length, inner bolt stress contribution, and plastic hinge area.
Precast concrete has not been used widely as a framing system for buildings located in several seismic regions. Precast concrete joints between the prefabricated members have some issues. Connections, in particular beam-to-column connections, are the vital part of precast concrete construction. To satisfy the structural requirements of the overall frame, each connection must have the ability to transfer vertical shear, transverse horizontal shear, axial tension and compression, and occasionally bending moment and torsion between one precast component and another, safely. The transfer of forces between the components and eventually the behavior of frames are governed by the characteristics of the connections. However, in practice, the behavior of precast connections is not well established and not fully understood to fulfill the requirements needed in the design and construction development of precast technology [
Current technology is widely available to satisfy the growing demand required of engineers to provide communities with superior levels of structural performance during an earthquake. As more advances are made in seismic engineering, the available technology becomes more cost-competitive when compared to traditional construction practice: further financial benefits can be associated with the improved response of the system considering the seismic risk applied over the working life of the structure. High performing systems will be designed to operate more efficiently as they are tuned to their direct application. As a result, the seismic demand imposed onto a structure (maximum displacements and accelerations) can be significantly reduced, thereby reducing material costs and construction time. However, in developing this new technology, design recommendations are required to ensure the technology is appropriately utilized.
This paper focuses on understanding the behavior of the HPHS (high-performance hybrid system) under seismic action. The validity of the HPHC system was demonstrated by a series of experimental tests, which proved the system has good performance under lateral loading. For application of the HPHS to the real structure, the seismic performance of single connections for several primary variables has to be assessed. In this study, parametric study for the HPHS connection was carried out based on test and FEM analysis. Investigated parameters include (1) axial load on column, (2) beam connection steel plate length, (3) inner bolt stress contribution, and (4) plastic hinge area. Therefore, this paper is aimed at developing and calibrating a nonlinear FE model and further uses it to investigate the behavior of HPHS by varying the main control parameters [
The new connection detail suggested in this study is characterized by ductile connection, steel connectors, and engineered cementitious composite (ECC) which is a kind of high-performance fiber reinforced cement composite with multiple fine cracks (HPFRCCs) and used in order to improve the constructability of joint and efficiently transfer stress between discontinued precast members. Making steel connector consists of bolting steel tubes and steel plates which are usually placed inside the precast column and beam and casting the ECC to some parts of the beam and joint in the field (refer to Figures
Description of development of precast concrete beam-to-column connection.
Proposed connection type. (a) Inside connection. (b) Outside connection.
The dimensions and details of reinforcements of the specimens are shown in Figure
Details of specimens. (a) RC-control. (b) PC-I50-0.2.
Details of test specimen and material properties.
Specimens | Connection method (axial force) | Hoop bar of joint area | ECC area (mm) | Column size (mm) | Beam size (mm) | Column | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Reinforcing bar (upper and lower) | Hoop | ||||||||||||||
RC-control | Cast-in-place (0.1) | O | — | 350 × 350 | 350 × 400 | 508 | 0.038 | 12-D22 | 475 | 0.011 | 50 | D13 | |||
PC-I50-0.2 | Inside connection (0.2) | 500 (1.4 d) | |||||||||||||
Specimens | Beam | ||||||||||||||
Reinforcing bar (upper and lower) | Stirrup | PC member | ECC member | ||||||||||||
RC-control | 437 | 0.012 | 8-D16 | 475 | 0.014 | 100 | D13 | 27.5 | — | 1.6 | 1,056 | 792 | 629 | 1.68 | 1.53 |
PC-I50-0.2 | 461 | 0.016 | 8-D19 | 27.5 | 40.5 | 1.6 | 1,286 | 965 | 628 | 2.04 | 1.53 |
Test results.
Specimen | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
RC-control | Pos | 89 | 119 | 114 | 1.5 | 3.5 | 4.25 | 2.3 | 125 | 285 | 206 | 792 | 540 | 572 | 1.06 |
Neg | 95 | 127 | 120 | 1.9 | 3.5 | 4.25 | 1.8 | 219 | 611 | 1.13 | |||||
PC-I50-0.2 | Pos | 111 | 148 | 114 | 1.3 | 3.5 | 4.25 | 2.7 | 125 | 346 | 255 | 964 | 583 | 711 | 1.22 |
Neg | 124 | 166 | 110 | 1.3 | 3.5 | 4.25 | 2.7 | 286 | 798 | 1.36 |
All estimates associated with moment and shear are computed based on actual material properties.
Test and analysis results. (a) RC-control. (b) PC-I50-0.2.
The proposed connection system (HPHS) has various types of structural elements such as concrete, steel plate, and ECC. It is very difficult to investigate design variable experiment, so nonlinear finite element analysis was conducted based on the experimental results. To improve understanding of the proposed connection system of local stress-strain behavior and joint strength in the vicinity of beam-to-column connection, a total of three concrete models were adopted and analyzed. These innovative high-performance hybrid systems (HPHSs) make use of steel, bolt sections, and ECC into the beam-column joint region to facilitate the connection of precast elements. In the experimental study, two cast-in-place and ten PC specimens, whose connection configurations slightly differed from each other, were tested. However, due to unique features of the tested specimens and material heterogeneity, it was difficult to understand the complex seismic behavior of beam-column connections. Furthermore, the effect of several influencing parameters such as flexural strength ratio and axial load cannot be varied in a limited number of experiments. The ABAQUS (ABAQUS version 6.6-1, 2006) finite element code was used to analyze the proposed precast beam-column connections. These numerical models consisted of a combination of elements, springs, and constraint conditions. Amongst these were refined 2D plane stress elements incorporating the full nonlinear material/geometric properties, contact elements, surface interaction with friction, constraint conditions using equation points, concrete crack conditions, and elastic foundation springs. These advanced modeling methods were intended to provide a detailed and accurate understanding of the overall behavior of the connections, including the stress distributions on the contact surfaces in spite of the high computational cost typically associated with this type of data [
The longitudinal reinforcement of the beam and column was deformed bars of yield strength 437 MPa and 508 MPa, while the beam stirrups and column transverse ties were applied with yield strength 475 MPa and 400 MPa. The slump value of the concrete mix was 75 ± 25 mm. The average compressive strength of concrete calculated using the cylinder tests was found to be 27.5 MPa (joint area ECC = 40.5 MPa). Steel connector, used in the construction of the specimens, was confirmed to be SS400. Average values of steel section properties were obtained from the samples of tensile coupon tests. However, for the wide range of parametric study, proposed equations were used and compared with test results. Used stress-strain models of concrete were the modified Kent–Park model and Collins model accounting for the confinement effect of steel tube embedded in the column. Additionally, the concrete damaged plasticity model was provided by ABAQUS; it needs the true stress-logarithmic stress-strain relation for tension and compression. Therefore, in this research, an equivalent uniaxial constitutive model for concrete in tension suggested by Torres [
Stress-strain curve of concrete in uniaxial stress state.
Stress-strain curve of steel in uniaxial stress state.
Stress-strain curve for confined concrete.
ABAQUS input values for confined concrete.
Plastic stress (MPa) | Plastic strain | Compression damage |
---|---|---|
28.21 | 0 | 0 |
32.03 | 0.000110 | 0.01 |
35.23 | 0.000221 | 0.02 |
39.80 | 0.000493 | 0.05 |
41.92 | 0.000834 | 0.1 |
41.99 | 0.001032 | 0.15 |
41.29 | 0.001450 | 0.2 |
39.89 | 0.002287 | 0.5 |
21.22 | 0.01331 | 0.9 |
The last set of material properties is ECC in compression and tension. As previously discussed, ECC has very large capacity in tension. Using stress-strain data from the test, equivalent perfectly plastic material behavior was used for material modeling in tension (refer to Figure
Stress-strain curve for ECC in uniaxial stress state in tension.
In the present study, the specimens were analyzed using the ABAQUS software. Two-dimensional (2D) plane stress elements were applied to simulate the concrete and steel plates, while reinforcing bars were modeled as truss elements. In material modeling, the concrete models were based on nonlinear fracture mechanisms to account for cracking, and plasticity models were used for the concrete in compression and steel reinforcement. The ABAQUS (ABAQUS version 6.10-1, 2010) finite element code was used to analyze the effect of variables of the proposed connection system (refer to Figure
Partitioned 2D models for proposed connection system (hybrid connection).
Generally, in the composite structure, there are many problems with contact area of concrete and steel. Therefore, all interfaces between two contact surfaces were constrained with each other. The general contact formulation used in ABAQUS involves a master-slave algorithm. This formulation considers the hard contact for normal direction of each surface and frictional contact behavior for tangential direction. Surface interactions and constrained area are shown in Figure
Constrained model.
Boundary condition.
Loading sequence.
To verify the finite element model, the analytical results were compared with the experimental results. The specimens were modeled with a truss elements and the remaining plane stress 2D elements. Concrete was modeled using 2D plane stress elements which were isoparametric elements. On the other hand, the reinforcing steel bars were modeled as two-node truss elements. At the joint core region, the area of truss elements close to the boundary was increased appropriately to simulate their corresponding steel area contributions. The beam bottom bars were discontinued at the face of the column. Steel plates, which were used for the connection at the joint, extended inside the beam at one side and abutted with the column face on the other side. These plates were simulated as 2D plane stress elements. These elements were assigned with steel plate thickness and its material properties. The concrete on the front and rear side of these elements was neglected in the analysis as it was filled up after the connections were fastened. Four rows of 2D elements at the bottom of the joint were treated as being connected by the steel plates, and their equivalent area was transferred to the column main bars and transverse links.
The predicted and observed responses of the specimens are presented in Figure
Predicted story shear forces versus horizontal displacement and crack pattern. (a) RC-control. (b) PC-I50-0.2. (c) PC-50H-0.1. (d) PC-I25H-0.1. (e) PC-O50-H-0.1. (f) PC-O25-H-0.1 (exterior).
Comparison of the analytical and experimental results of all the specimens showed that the lateral load-displacement hysteresis loops obtained from the FE analyses were quite similar to the experimental observations. Besides, the failure modes and the ultimate ductility capacities correlated well with the experimental results. The FE analyses also showed that results of the deformations and cracking patterns matched well with the experimental observations. From the aforementioned observations and predictions of both the global and local behaviors using the FE analysis, the use of FE modeling techniques can, therefore, be further extended to study the joint performance by varying different parameters.
Axial loading is a critical parameter in the studies of beam-column joints, but its effect on seismic behavior of beam-column joints has not been fully understood. Previous investigations have shown that axial force is beneficial to the joint shear resistance [
Lin and Restreop’s investigations [
In this study, the influence of axial loading on the seismic behavior of hybrid-steel concrete joints is investigated. Axial load was applied in first step at the column, and lateral load was applied to the same location in second step, cyclically. The same loading histories as those used in the analysis of specimens without axial loading were applied, and the story shear force versus horizontal displacement plots corresponding to different axial load levels were plotted for specimen PC-I50-0.2. It can be seen that Specimen inter series attained an optimum value of ultimate story shear when axial load ratio was
Load-displacement predictions under different axial loading levels (specimen PC-I50-0.2).
When designing the reinforced concrete frame, the most important design consideration is the moment strength ratio of beam and column and plastic hinge location. Furthermore, steel plates would be a very important design parameter because this parameter determines the strength and stiffness of beams.
The moment strength ratio is defined as the ratio of the sum of the nominal moment strengths of the column above and below the joint to the sum of the nominal moment strengths of all the beams in one plane framing into the joint. Theoretically, a moment strength ratio greater than one should cause the plastic hinges to form in the beams and not in the column. However, ACI318 Building Code [
As a result of finite element analysis, the capacity of beam-to-column joint specimen could be determined by the strength of beam for most cases. However, the failure mode of the beam-to-column specimen for the case of moment capacity ratio 1 had shown beam-joint failure. Other test specimens which have a moment strength capacity of 1.2 ∼ 1.6 have shown beam failure mode. As the moment capacity ratio increased, the plastic hinge location moved to the outside of the joint. And cracks were more concentrated to plastic hinge. It is shown in Figures
Crack pattern by axial load (specimen PC-I50-0.2). (a) Axial load ratio of 0.1. (b) Axial load ratio of 0.2. (c) Axial load ratio of 0.3. (d) Axial load ratio of 0.5.
Crack pattern according to moment strength ratio (specimen PC-I50-0.2). (a) Moment strength ratio of 1.0. (b) Moment strength ratio of 1.2. (c) Moment strength ratio of 1.4. (d) Moment strength ratio of 1.6.
Strain distribution is very important information for plastic hinge location; from the strain information of FEA results, plastic hinge location was clearly observed. All specimens have experienced yielding of reinforcements. However, decreasing the moment strength ratio decreases the stress in plastic hinge region. At low level of moment strength ratio yielding of reinforcement was shown latterly, than other cases of specimens. It is shown in Figure
Stress distribution according to moment strength ratio (specimen PC-I50-0.2). (a) Moment strength ratio of 1.0. (b) Moment strength ratio of 1.2. (c) Moment strength ratio of 1.4. (d) Moment strength ratio of 1.6.
Plastic hinge location according to plate length. (a) Tested length. (b) Half of tested length.
To determine the moment capacity of bolt connection, the strain distribution of bolts and connecting plates should be investigated. Because bolt strain cannot be measured from the test, 3D finite element analysis was performed. Because too many components were needed to compensate details of the proposed connection system, analysis was performed in monotonic loading, only. The finite element model consisted of 3 parts: concrete parts, steel parts, and reinforcement. For the reality of finite element modeling, each part was modeled separately. And reinforcements were embedded in concrete components. These models are illustrated in Figure
Finite element modeling (embedded components). (a) Concrete part. (b) Steel plate part. (c) Reinforcement part. (d) Total modeling.
As a result of finite element analysis, stress contour and strain field were provided. Especially, stress and strain of bolts components were investigated for the distribution of resultants forces for connecting area. The stress distribution is illustrated in Figure
Stress distribution of total model.
Stress distribution of reinforcements.
Stress distribution. (a) Steel plates. (b) Connection bolts.
Neutral axis was formed at the third bolt from the compressive extreme fiber. Because stiffness could be increased with the composite action at compressive area, compressive stress area was bigger than tensile one. Provided stress is shown in Table
Stress distribution and resultant force results.
Element ID | Stress type | Strain compatibility | FEM | ||
---|---|---|---|---|---|
Stress (MPa) | Resultant force (kN) | Stress (MPa) | Resultant force (kN) | ||
El. 1 | Tension | 400 | 624 | 368 | 574 |
El. 2 | Tension | 280 | 302 | 253 | 272 |
El. 3 | Tension | 180 | 151 | 150 | 125 |
El. 4 | Tension | 90 | 76 | 65 | 54 |
El. 5 | Compression | 92 | 77 | 113 | 94 |
El. 6 | Compression | 200 | 73 | 253 | 92 |
Cc | Compression | 30 | 770 | 36 | 720 |
FE models used in this study well predict the behavior of test specimens. However, the initial stiffness problems encountered by the embedded truss model should be solved for the more wide parametric study such as serviceability check in design process.
According to the parametric study, the effect of axial load was investigated. There is a reduction in story shear and ultimate number of cycles after enhancement in axial load ratio beyond 0.3 (i.e.,
Plastic hinge region is very important design criteria for frame action. From the result of the parametric study, plastic hinge location is determined by the moment strength ratio and plate length. Generally, plastic hinge was formed far from the column face with the increase of moment strength ratio. It was clarified by investigating the stress distribution of reinforcement. For low value of moment strength ratio, reinforcement is hard to yield and plastic hinge cannot be formed easily, in the area of plate installed area. However, the length of plates is an important parameter for location of plastic hinge. Investigation from the test and FE model revealed that plastic hinge occurred at the end of steel plates. Therefore, using the proposed connecting system, plastic hinge location can be controlled by the designers.
Complicated 3D model for the proposed connecting system would be used for design strength calculation for connection. The stress distribution of bolt elements is similar to the stress distribution resulted from strain compatibility methods. Therefore, the proposed connection can be designed using conventional design methods.
The data used to support the findings of this study are included within the article. Any additional data related to the paper may be requested from the corresponding author.
The author declares that there are no conflicts of interest.
This study was supported by Kyungnam University Foundation Grant, 2016.