In this study, the parameters of concave expanded flanges of beam-column connections of steel frames are optimized based on the effects of different sizes of concave expanded flanges on the fracture performance. Firstly, two beam-column connection models with concave expanded flanges are built and analyzed under cyclic loads, which have the same conditions as the specimens during the previous test. Secondly, the validity of the numerical simulation models is verified through analyzing the hysteretic behaviors of the connections with concave expanded flanges, such as the plastic hinge position, the hysteresis curves, the skeleton curves, the stiffness degradation, the ductility coefficient, and the energy dissipation capacity. Thirdly, in order to comprehensively evaluate the fracture status of metal materials, the relevant fracture evaluation index (the stress triaxiality ratio (
The welded steel beam-column moment-resisting connections of steel frames caused widespread damage during the Northridge earthquake in the United States in 1994 and the Kobe earthquake in Japan in 1995, which shows that the design of conventional beam-column connections welded in steel frames has difficulty in meeting the requirements of the standards [
As for beam-column connections with reduced beam section, numerous studies on the mechanical performance of dog-bone connections have been carried out through test and numerical simulation by Pachoumis et al. [
In previous research work, the beam-column connections with concave expanded flanges have better mechanical performance than that of the connections with convex expanded flanges by analyzing the experimental hysteretic behaviors of five full-scale steel beam-column connection specimens (four had expanded beam flanges with different arc shapes, lengths, and widths and the fifth was a control specimen without expanded beam flange) under cyclic loading. Based on the results, two numerical simulation models of the beam-column connections with concave expanded flanges are established and analyzed, wherein the conditions are the same as those used in the test. Afterwards, the validity of the numerical models is verified through comparing the hysteretic behaviors obtained from the test and numerical simulation. According to the fracture index, the parameters of the concave expanded flange (the length of the line (
In previous research work [
In order to verify the validity of the finite element models of beam-column connections by comparing hysteretic behavior between the test and numerical simulation, two connection specimens with a concave arc in the expanded flanges (WF-1A, WF-1B) are designed, which have different lengths of the reinforced section and the transition section of the expanded flanges. And the dimensions of the connections are the same as that in the test, the details of the specimens are shown in Figure
Details of specimens. (a) WF-1. (b) Finite element model.
Specimen parameters.
Specimens | Expansion | Length of line ( | Length of arc ( | Width ( |
---|---|---|---|---|
WF-1A | Concave-arc | 100 | 100 | 40 |
WF-1B | Concave-arc | 200 | 200 | 50 |
The constitutive relation diagram of steel Q235B and weld E4315, which adopt threefold line models, is shown in Figure
Material constitutive model. (a) Q235B steel. (b) E4315 weld.
According to the characteristics of the beam-column connections with concave expanded flanges, the eight-node hexahedral linear reduction integral unit (C3D8R) is suitable for meshing these two numerical simulation models of the connections because of the advantages of computation time and distortion resistance [
Boundary conditions of the finite element model.
Figure
Position of plastic hinge. (a) WF-1A and (b) WF-1B.
A comparison of the 2 hysteresis curves of the connection specimens with concave expanded flanges between the test and numerical simulation is shown in Figure
Hysteretic curves. (a) WF-1A. (b) WF-1B.
From the skeleton curves of the connection specimens with concave expanded flanges between the test and numerical simulation, which is in Figure
Skeleton curves. (a) WF-1A. (b) WF-1B.
The 2 stiffness degradation curves from the test and numerical simulation are shown in Figure
Stiffness degradation curve of WF-1.
The ductility coefficient
Ductility coefficient
Parameter | Test/FE | WF-1A | WF-1B |
---|---|---|---|
Test | 3.46 | 3.22 | |
FE | 4.87 | 3.50 | |
Test | 3.10 | 2.82 | |
FE | 3.26 | 2.95 |
From the above analysis about hysteretic behavior of the test and numerical simulation, the method of establishing the numerical models is reasonable because the trend of the numerical simulation is basically the same as that of the test, and the error between the two results can be accepted, so the method can be used to optimize the parameters of the expansion next. Meanwhile, the optimal range of the expansion can be obtained by comparing the fracture performance because the weld plays an important role in the mechanical performance of the beam-column connections.
If the beam-column connections with concave expanded flanges are to avoid fracture resistance under earthquake loads, it is also necessary to study brittle fractures of the connections. In order to evaluate the effect of different parameters of the expansion on the fracture performance, three groups of numerical simulation models (WF-A, WF-B, and WF-C) are established in ABAQUS, which are different in the length
Path 1.
In damage mechanics, the relevant fracture evaluation indexes are introduced to comprehensively evaluate the fracture status of metal materials [
The macroscopic fracture failure of materials is mainly determined by the combination of stress states at each point and in each direction. Zhu [
The stress triaxiality ratio has an important influence on the shape of the holes in microcosmic materials and determines the generation and development of cracks. The larger the
The material on the surface of the plastic development directly determines the internal development state of microcracks, and the equivalent plastic strain index and the crack development status are positively correlated. EI-Tawil [
The PI value can directly reflect the ductility and fracture tendency of the material. The larger the PI value, the greater the plastic deformation at the point, and the greater the possibility of ductile cracking of the material.
When the stress triaxiality ratio at a certain point is high, the microcracks at that point will develop rapidly and accumulate until forming macroscopic cracks. The process from microcrack accumulation to local crack generation is the ductile cracking process of the metal material. Hancock and Mackenzie [
The cracking index can accurately describe the risk index of fracture at a certain point. The higher the RI value, the greater the possibility of cracking, and the larger the joint damage.
Based on the results of the above test and numerical simulation, the parameters of the expansion of the WF are consistent with those of the above numerical models. In order to investigate the effect of different sizes of concave expanded flanges on the fracture performance of the connections, the range of the parameters of the expansion of WF is selected: the length of the reinforced section
Size of WF-A.
Specimens | |||||||
---|---|---|---|---|---|---|---|
WF-A | WF-A1 | 100 | 0.50 | 100 | 0.25 | 50 | 0.25 |
WF-A2 | 120 | 0.60 | 100 | 0.25 | 50 | 0.25 | |
WF-A3 | 140 | 0.70 | 100 | 0.25 | 50 | 0.25 | |
WF-A4 | 160 | 0.80 | 100 | 0.25 | 50 | 0.25 | |
WF-A5 | 180 | 0.90 | 100 | 0.25 | 50 | 0.25 | |
WF-A6 | 200 | 1.00 | 100 | 0.25 | 50 | 0.25 | |
WF-B | WF-B1 | 100 | 0.50 | 100 | 0.25 | 50 | 0.25 |
WF-B2 | 100 | 0.50 | 120 | 0.30 | 50 | 0.25 | |
WF-B3 | 100 | 0.50 | 140 | 0.35 | 50 | 0.25 | |
WF-B4 | 100 | 0.50 | 160 | 0.40 | 50 | 0.25 | |
WF-B5 | 100 | 0.50 | 180 | 0.45 | 50 | 0.25 | |
WF-B6 | 100 | 0.50 | 200 | 0.50 | 50 | 0.25 | |
WF-C | WF-C1 | 100 | 0.50 | 100 | 0.25 | 25 | 0.125 |
WF-C2 | 100 | 0.50 | 100 | 0.25 | 30 | 0.15 | |
WF-C3 | 100 | 0.50 | 100 | 0.25 | 35 | 0.175 | |
WF-C4 | 100 | 0.50 | 100 | 0.25 | 40 | 0.20 | |
WF-C5 | 100 | 0.50 | 100 | 0.25 | 45 | 0.225 | |
WF-C6 | 100 | 0.50 | 100 | 0.25 | 50 | 0.25 |
In order to study the effect of
WF-A. (a) Triaxiality ratio. (b) Equivalent plastic strain index. (c) Cracking index.
All
Similar to the analysis of
WF-B. (a) Triaxiality ratio. (b) Equivalent plastic strain index. (c) Cracking index.
All
Similar to the analysis of
WF-C. (a) Triaxiality ratio. (b) Equivalent plastic strain index. (c) Cracking index.
Figure
According to the comparison of the experimental results and the finite element analysis, the following conclusions are drawn: The different lengths of the expansion of the beam-column connections can effectively move the plastic hinge away from the beam end. The larger the length and width of the expansion are, the higher the ultimate bearing capacity of the steel structure; however, the ductility of the material cannot be fully developed. When the length and width of the expansion are smaller, the energy dissipation capacity is stronger. According to the direction of the stress triaxiality ratio ( From the comprehensive analysis of the stress triaxiality ratio (
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors appreciate the support of the National Science Foundation of China (51878589 and 51878590), the Production and Research Foundation of Jiangsu Province (BY2016069-01), China Postdoctoral Science Foundation (2019M651762), Six Talent Peaks Project of Jiangsu Province (2017-JZ-038), Science and Technology Planning Project of Yangzhou City (YZ2018068), and the assistance in data processing by the postgraduate students Yake Chen and Ying Zhao, Anhui Provincial Natural Science Foundation (Project no. 1908085QA09), and Natural Science Research Project of Anhui Province (Project no. KJ2019A0591).