The aforementioned analyses demonstrate that FE simulation results are consistent with test results, so a series of FE models were established to further analyze how different parameters affect seismic behaviors of the proposed joint type. The selected parameters include constructional details, geometric dimensions, material strength of steel and concrete, and axial compression ratios (n), as shown in Table 4. In every group, the superscript “*” represents the parameter derived from test specimen SPJ2, and other corresponding parameters were changed based on Specimen SPJ2. The first quadrant of P-Δ skeleton curves obtained by FE simulations was used for parametric analyses due to the symmetry based on the origin.
Table 4
Types
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Parameters
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Contents
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Constructional details
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With both ribs and haunches
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SPJ2*
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Only with ribs
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SPJ2-H
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No ribs and no haunches
|
SPJ2-HS
|
Geometric dimensions
|
Beam-to-column bending stiffness ratios per unit length(k)
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0.3, 0.41*, 0.5, 0.6
|
Material strength
|
Steel beam strength
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Q235*, Q345, Q420, Q550
|
Concrete strength
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C40, C50, C60*, C80, No-concrete
|
Compressive force on the column top
|
Axial compression ratios (n)
|
0.04, 0.275*, 0.4, 0.5, 0.6
|
5.1. Influences of constructional details
In the test, haunches and vertical ribbed webs were installed in three joint specimens to build an effective connection, and the influence of stiffening diaphragms was analyzed according to test results. The seismic behaviors of the proposed joint with different constructional details were further studied based on corresponding FE models. Haunches in Model SPJ2-H were removed, and vertical ribbed webs were direct force-transferring components; while all ribs and haunches were removed for Model SPJ2-HS. Figure 14 shows different failure modes obtained from these three models. The bulging column and the plastic hinges near the CFDST column were captured in Model SPJ-HS. For Model SPJ-H, bulges of the column were effectively alleviated, and the plastic hinges were shifted outside in comparison with the failure phenomenon of Model SPJ2-HS. Moreover, the ribs had small bulges along the hypotenuse, which absorbed a part of energy during the cyclic loading process. And for Model SPJ2, an ideal failure mode of plastic hinges formed at beam ends was captured as expected. Meanwhile, the stress concentration at the core area significantly decreased and there was no bulge on the outer steel tube. P-Δ hysteretic curves shown in Fig. 15 present different degrees of full loops. he is 0.139, 0.438, 0.161 respectively for Models SPJ2-HS, SPJ2-H, and SPJ2 at the peak load point. Therefore, the vertical ribbed web joint has the higher energy dissipation capacity, while the joint without ribs and haunches has the lower one. These failure mechanisms and energy dissipation performance have some relationships to the deformation ability, as shown in the skeleton curves in Fig. 16. The initial stiffness of Model SPJ2 was improved by 15.91% than that of Model SPJ2-H, and was improved by 52.96% than that of Model SPJ2-HS. The ultimate bearing capacity of Model SPJ2 was increased significantly (31.42% higher than SPJ2-H and 69.60% higher than SPJ2-HS). The contrastive analysis demonstrates that haunches and ribs have constructive effects on seismic behaviors of the haunched joint with ribbed anchor webs under cyclic loading.
5.2. Influences of beam-to-column bending stiffness ratios per unit length (k)
The beam-to-column bending stiffness ratios per unit length (k) for parametric analyses were 0.3, 0.41, 0.5, and 0.6. Herein k was affected by the length of the steel beam with the same cross-sectional dimension. Hence, the beam length was 5057 mm, 3700 mm, 3034 mm, and 2528 mm respectively, and the cross-sectional dimensions was H350×175×7×11 mm4. The failure mode of all FE models was ideal as plastic hinges were captured at beam ends. Figure 17 shows corresponding P-Δ skeleton curves obtained from FE simulations. It indicates that k controlled by the beam length within a range affected the ultimate bearing capacity and initial stiffness because shortening beam length restricted the rotation radius of the joint under cyclic loading. When k = 0.41, 0.5, 0.6, the ultimate resistance capacity was improved by 9.88%, 15.55%, and 16.77% respectively in comparison with Model of k = 0.3, and initial stiffness was improved by 6.03%, 32.51%, and 42.45%. The differences in the two indexes between Models of k = 0.5 and k = 0.6 were not evident. Therefore, the value of k from 0.3 to 0.5 is fit for this joint type to perform excellent seismic behaviors, and could meet the engineering requirement of “strong column & weak beam”.
5.3. Influences of steel beam strength
The steel grade of the steel beam was Q235 in the test, and Q345, Q420, and Q550 were considered in FE simulations to analyze influences of steel beam strength, and the models were labeled by Q345, Q420, Q550. Figure 18 shows P-Δ skeleton curves of corresponding joint models. The nominal yield displacements increased successively for increasing steel beam strength, and the ultimate resistance capacity of Models Q345, Q420, Q550 was respectively improved by 17.32%, 27.77%, 47.94% than that of Model Q235. However, initial stiffness was almost unchanged since cross-sectional dimensions and Young’s modulus of all steel beams were equal, and the ductility was smaller for the joint model with larger steel beam strength. Figure 19 only contains stress nephograms of Models Q420 and Q550, because Models Q345 and Q420 had similar stress nephograms and the same failure mode that plastic hinges occurred at beam ends and small bulges appeared on outer tube walls. As can be seen in Fig. 14(c) and Figs. 19(a), 19(b), stresses in ribbed anchor webs, steel beams, and outer steel tubes rose significantly when steel beam strength increased, and it caused larger deformations at these positions. For Model Q550, the failure mode was changed to local buckling of steel beams and distinct bulges of the outer tube wall. The growing internal force in steel beams was transmitted to the internal CFST column only via ribbed anchor webs. Therefore, the inner tube and core concrete were less stressed due to an insufficient force transmission, and stresses gradually accumulated and mainly concentrated on steel beams, ribbed anchor webs, until the outer tube.
Besides, according to constructional details of the Specimen SPJ3, stiffening diaphragms was added on Model Q550 to form the new model Q550+, and its failure mode is represented in Fig. 19(c). The whole CFDST column worked as a whole through stiffening diaphragms between two tubes. Meanwhile, the stress concentration area and the bulging part of the outer tube were reduced, and the ductility was better than that of Model Q550 because the internal force from beams was more effectively transmitted to the internal CFST column via stiffening diaphragms. The bearing capacity of Model Q550 + was also improved by 7.65% than that of Model Q550. Therefore, it is practicable to install stiffening diaphragms to enhance ductility and bearing capacity especially when the steel beam strength is large.
5.4. Influences of concrete strength
The uniaxial compressive strength of concrete cubes was selected as 40 MPa, 50 MPa, 60 MPa, and 80 MPa to compute the constitutive relation and model mechanical behaviors of the joint with different concrete strength, and a model without concrete was adopted for a comparison. All the models were labeled by the different concrete C40 ~ C80, and No-concrete. Figure 20 shows the P-Δ skeleton curve of each joint model. There was a sharp degeneration in initial stiffness and ultimate resistance capacity for Model No-concrete, since concrete improved the rigidity of the column and the globality the joint. The initial stiffness and the ultimate resistance capacity of Model C40 were 102.87% and 112.46% respectively higher than those of Model No-concrete. However, for the joint models with CFDST columns, there was a slight improvement in initial stiffness and ultimate bearing capacity when concrete strength increased. The stress nephograms and failure modes of Models C40, C50, C60, and C80 were extremely similar, so only the stress nephogram of Model C40 and that of Model No-concrete are represented in Fig. 21. The column of Model No-concrete bulges, and the bulging position is near the haunch because the hollow thin-walled column under compression is prone to instability and buckling especially for the area of sudden changes in bending stiffness. In the final failure stage, the steel beam was still in a good state without stress concentration and large deformation when the column was failed (Fig. 21(b)). It is concluded from this contrastive analysis that the haunched joint with ribbed anchor webs is applicable for the CFDST structure but not for the steel structure, and using low strength concrete to reduce construction budget based on engineering requirements is practicable.
5.5. Influences of axial compression ratios (n)
The axial compressive force on the CFDST column is an important factor affecting seismic performance of the haunched joint with ribbed anchor webs. Therefore, the values of n (0.04, 0.275, 0.4, 0.5 and 0.6) were considered in FE simulations. Figure 22 presents corresponding P-Δ skeleton curves. The results illustrated that n influenced joint initial stiffness, ultimate resistance capacity, ductility, and deformation resistance. When n = 0.275, 0.4, 0.5 and 0.6, initial stiffness was enhanced by 25.08%, 59.82%, 87.49%, and 162.70% respectively in comparison with that of Model of n = 0.04. As for the ultimate resistance capacity, it enhanced 6.21%, 7.71%, 15.64%, and 21.60%, respectively. It was attributed to that the confinement effect on concrete from double steel tubes was enhanced as the increase of axial compressive force. In addition, there was a sharper fall in the P-Δ skeleton curve after each peak point with the increase of the axial compressive force, accordingly showing a decrease of deformation resistance and ductility. The reason was that the increasing axial compressive force caused larger bending moment once the lateral displacement increased steadily.
When n = 0.04, 0.275, 0.4, failure modes of the joint models were that plastic hinges generated at beam ends, while failure modes of the joint models were the buckling failure of the CFDST column and bulge phenomena on the outer tube wall when n = 0.5 and 0.6. The two different failure modes are represented in Fig. 23. Therefore, the axial compression ratio under 0.5 is better to prevent the buckling failure and bulges of the CFDST column, so as to guarantee sufficient ductility in seismic designs for the haunched joint with ribbed anchor webs.