Study on shear performance of the connection with external stiffening ring between square steel tubular column and unequal-depth steel beams

Abstract

This paper studies the shear performance of the connection with the external stiffening ring between the square steel tubular column and unequal-depth steel beams. Two specimens of interior column connections were tested under low cyclic loading. The deformation characteristics and failure modes exhibited by the test phenomena can be summarized as: (1) two specimens all exhibited shear deformation in steel tube web of the panel zone and (2) weld fracture in the panel zone and plastic hinge failure at beam end were observed. Besides, load-displacement behaviors and strain distributions have been also discussed. The nonlinear finite element models were developed to verify the test results. Comparative analyses of the bearing capacity, failure mode, and load-paths between the equal-depth and unequal-depth beam models have been carried out.

Keywords

connection external stiffening ring load-paths shear performance unequal-depth steel beam

Introduction

Connection with external stiffening ring is one of the most popular connections for keeping the integrity of the steel tubular column and constructing convenience, as described in European Committee for Standardization (CEN, 2004) and American Concrete Institute (ACI, 2014). Krawinkler and Mohasseb (1987) realized that the shear deformation of the panel zone has a significant effect on the strength, stiffness of the frame structures. After the Hyogo-ken-Nanbu Earthquake, Nakashima et al. (1998) found that the shear failure in the panel zone of the connection with the external stiffening ring is one of the main damage forms. The security of the connection in the panel zone has been a vital concern in the design of structure.

In Japan, the initial shear mode of the panel zone was recorded in Architectural Institute of Japan (AIJ, 1997). This method ignores the connection form and uniformly considers the shear bearing capacity provided by the steel tube in the panel zone. Afterward, scholars carried out many researches based on AIJ. According to the test of interior diaphragm connection, Fukumoto (2001) proposed that the shear capacity is composed of three parts: the web in the panel zone, the flange in the panel zone and concrete compression strut. On this basis, the formula of the shear capacity of the connection was derived using the principle of virtual work, and it was also considered to be applicable to the connection with the external stiffening ring. Nishiyama et al. (2004) verified the applicability of the AIJ formula to high-strength materials and proposed an analysis model for restoring force in the panel zone. Fukumoto and Morita (2005) studied the connection with external stiffening ring made of high strength materials. The research parameters are section form, weak component type, the diameter thickness ratio of steel tubular column, and material strength. The shear-shear deformation model in the panel zone of the connection were put forward. Nie et al. (2006, 2007, 2008) studied the seismic performance of the connection with the external stiffening ring and the interior diaphragm connection. Based on the principles of deformation compatibility in the elastic, yield, strengthening and damage stages of the steel, and concrete in the panel zone, the principle of virtual work was used to derive the calculation method of the shear capacity of the connection. Rong et al. (2019a, 2019b) observed the shear failure mode in the panel zone under the low-cycle repeated load test of the connections with external stiffening ring. Two calculation models for the shear capacity of the panel zone were proposed: (1) improved superposition method (the bearing capacity of the ring plate was considered based on the yield line theory and (2) the calculation model of the shear capacity of the panel zone after buckling. However, all the above studies aimed at the connection with external stiffening ring between column and equal-depth beams. When the spans of adjacent beams are different or the loads are very different in the frame structure, the connection with unequal-depths beams can be used. Mou et al. (2018a, 2018b) proposed the connection with external stiffening ring between the square tubular column and unequal-depth beams, and the deformation capacity, hysteresis behavior, and failure modes of specimens with different beam depth ratios were studied.

In this paper, two connections with external stiffening ring between square steel tubular column and unequal-depth steel beams were tested under low cyclic loading to investigate the effect of beam-depth difference on the shear performance of the connection. In addition to test phenomena and failure modes, load-displacement behaviors, and strain distributions were also discussed. Nonlinear finite element models were developed to analyze the bearing capacity, failure mode, and load-paths of the panel zone between equal-depth and unequal-depth beam models.

Experimental programs

Specimens design

To investigate the shear performance on connection with external stiffening ring between the square tubular column and unequal-depth beams, two full-size cruciform specimens subjected to vertical cyclic displacement loads at the beam ends were designed. Upward displacement of deep beam and downward displacement of the shallow beam was defined as the positive loading direction, and vice versa. To observe the deformation characteristics of the panel zone, all specimens were designed according to the principle of “strong member—weak joint failure mechanism.” Specifically, the thickness of the steel tube wall of the panel zone was designed to be thinner than other parts. The two specimens had the same geometries, except for the depth of the shallow steel beam. The details of these two specimens are shown in Figure 1(a) and (b) and Table 1.

Figure 1.

The details of the specimens: (a) TS1, (b) TS2, (c) schematic diagram of the welding details, and (d) photo of the welding details.

Table 1.

Dimensions of specimens.

Specimens	Column (mm)	Shallow beam (mm)	Deep beam (mm)	Thickness of ring plate (mm)	Axial load (kN)
	H × B × t	H × b_f × t_f × t_w	h × b_f × t_f × t_w
TS1	200 × 200 × 12	200 × 150 × 9 × 6	300 × 150 × 9 × 6.5	10	200
TS2	200 × 200 × 12	150 × 150 × 10 × 7	300 × 150 × 9 × 6.5	10	200

Material properties

The steel tubes of the specimens were made of cold-formed square steel tubes and the beams of the specimens were made of H-shaped steel. The strength grade of steel of all the specimens was Q235B, defined in GB/T 221-2008 (2008). The type of the welding rods was E43. The schematic diagram and photos on the welding details of specimens are shown in Figure 1(c) and (d). The following components were welded with groove butt welds: steel tube column and steel tube in the panel zone, steel tube and external stiffening ring, steel beam flange and external stiffening ring. Especially, the steel beam flange and external stiffening ring were provided with backing plates when welding. The following components were welded with fillet welds: steel beam web and steel tube column, steel beam web and external stiffening ring. According to the “Metallic Materials-Tensile Testing-Part 1: Method of test at room temperature” (GB/T 228.1-2010, 2010), standard tensile pieces of steel were cut and the dimension of the coupon specimen was 180 mm × 40 mm, as shown in Figure 2. The stress-strain relationship of steel in the test is shown in Figure 3. The material properties of the steels of various thicknesses are listed in Table 2.

Figure 2.

Details of the coupon specimen.

Figure 3.

Stress-strain relationship of steel in the test.

Table 2.

Material properties of steel.

Thickness (mm)	Position	$f_{y}$ (N/mm²)	$f_{u}$ (N/mm²)	$E_{s}$ (GPa)	$ε_{u}$ (%)	$ε_{c}$ (%)
6	Web of shallow steel beam, square tube of the panel zone	315.7	458.2	200.1	19.7	29.5
6.5	Web of deep steel beam	343.2	473.7	199.2	18.8	28.7
7	Web of shallow steel beam	370.3	489.3	198.3	18.5	28.6
9	Flange of steel beam	387.8	528.9	197.5	20.1	31.5
10	External stiffening ring	350.7	537.4	199.4	21.4	30.2
12	Square tube of the column	327.9	493.7	199.3	19.8	28.5

Test setup and loading procedure

The loading device is shown in Figure 4(a). The boundary conditions are as follows: (1) the top column end was clamped by a fixture with arc plates and (2) the bottom column end and support, the beam end and the actuator were connected by pins, respectively. For explanation, the top column end was restrained from moving in the horizontal direction while the bottom one was restrained both in horizontal and vertical direction, the left and right beam ends were free in the loading direction, and all were allowed to rotate in the loading plane. Before the actual test, specimens were preloaded to ensure good contact with the test device and all test equipment worked properly. Then, the axial compressive load in the vertical direction was applied to the column. In this test, displacement control was used. A reversed cyclic displacement history with monotonically increasing amplitude was applied as illustrated in Figure 4(b), where $θ$ is the displacement angel defined as the ratio of the vertical displacement of the beam end to the length of the beam. Every different displacement amplitude was reversed for two times. The loading was continued until failure occurred or the load-carrying capacity drops to 85% of the peak value. In order to get stable deformation data, the experimental data were collected after keeping the load for 5 min per level. The controlled displacement in the loading process was measured by the LVDT (Linear Variable Differential Transformer) placed at the end of the beam corresponding to the location of a vertical actuator. The displacement data collected by LVDT and the force data collected by force sensor were processed by the computer to form a real-time force-displacement curve.

Figure 4.

Loading devices and loading system. (a) loading devices and (b) loading system.

Test results

Observations

For TS1, the depth difference was 100 mm. Figure 5 shows the details of the test phenomena. No major phenomenon was observed until applied displacement amplitude reached 3%, the two top ring plates originally at the same height occurred misalignment and the web in the panel zone showed slight shear deformation. Linear cracks appeared in the anticorrosive coating of the deep beam flanges while arc cracks in the anticorrosive coating of the web. With the further increase of displacement amplitude, the phenomena described above were more and more obvious, but there were not new phenomena occurred until the specimen suddenly broke at 7%. The butt weld between the bottom column and the bottom ring plate on the side of the deep beam was broken thoroughly and the crack extended to the web of the bottom column. The shear deformation occurred in the whole panel zone, and the shear deformation in the upper part of the steel tube web in the panel zone is larger than that in the lower part.

Figure 5.

The state of specimen TS1 during different loading processes: (a) region 1-misalignment, (b) region 2-arc cracks, (c) region 3-linear cracks, (d) region 4-shear deformation, and (e) region 5-weld crack.

For TS2, the depth difference was 150 mm. Figure 6 shows the details of the test phenomena. The relative height of the two top ring plates began to change when the displacement amplitude reached 2%. The anticorrosive coating on the flange and web of the deep beam cracked at 3% and took on a certain shape with the further increase of the displacement, straight lines on the flanges and arcs on the web. When the displacement reached 5%, the top flange at the end of the deep beam appeared waveform convexity and the deep beam had largely deviated from its planar position, which indicated the specimen had a failure due to the plastic hinge at the end of deep beam. Then, the specimen was not suitable for further bearing. To ensure safety, the test was terminated. At this time, the web in the panel zone had a certain shear deformation, and the upper part of the steel tube web in the panel zone was larger than the lower part as well, but the difference was not as large as that of the specimen TS1.

Figure 6.

The state of specimen TS2 during different loading processes: (a) region 1-misalignment, (b) region 2-arc cracks, (c) region 3-linear cracks, (d) region 4-plastic hinge, and (e) region 5-shear deformation.

Load-displacement relations

The load-displacement hysteresis loops for two specimens are shown in Figure 7(a) and (b). The transverse coordinate is the displacement at the end of the deep beam. The longitudinal coordinate is the sum of the loads applied at the end of the beams on both sides. The shapes of two hysteresis loops were in a plump shuttle type which indicated that both have a certain energy dissipation capacity. Large inelastic deformation observed in both specimens also showed that they had good ductility. The slopes of the loading curves of the specimens decreased with the increasing of the cyclic loads. However, the slopes of the unloading curves were almost unchanged, which indicated bigger loading stiffness degradation and smaller unloading stiffness degradation. Both specimens eventually lost further load-carrying capacity in the negative loading stage, so the negative loading was the weak link of the loading.

Figure 7.

The load-displacement hysteresis loops for two specimens: (a) TS1 and (b) TS2.

The skeleton curves of load-displacement are compared in Figure 8. The ultimate bearing capacity were 275.62 kN and 260.32 kN, for specimens TS1 and TS2, respectively. The curves coincided basically, which indicated that the mechanical properties of TS1 and TS2, including stiffness, ductility, and energy dissipation were similar during loading.

Figure 8.

The skeleton curves for two specimens.

The expected failure mode is a large shear deformation in the panel zone. For TS1 and TS2, there are two different failure modes, which are earlier than the expected failure stage. Reason: The welding of TS1 is defective. The sudden damage of the welding led to the premature failure of the specimen and loss of bearing capacity. The loading point of TS2 may be offset, causing the deep beam to twist and produced a plastic hinge. Based on the above analysis, we believe that the specimens still have greater load-bearing capacity, which is supported by the subsequent analysis of finite element.

Strain distribution

The strain distribution data were obtained during the test using strain gauges. The strain data of TS1 when the clockwise movement of the beam reached the positive maximum displacement were discussed.

Figure 9(a) to (c) show the strain distribution of the top ring plate at the side of shallow beam. Before the displacement amplitude reached 3%, the out-extend length part in the ring plate (points 1–4) was at a low strain level. At 3%, the tensile strain at point 3 increased rapidly, while the other three points did not change much. We analyzed that the strain gauge at point 3 may be attached to the anticorrosive coating, and from the test phenomena of TS1, the anticorrosive coating cracked after the displacement amplitude reached 3%, which cannot represent the true strain level of point 3. With the further increase of the displacement amplitude, the strain distribution became uniformly for the law of “stress redistribution.”Figure 9(c) shows the strain distribution of the out-extend width part in the ring plate (points 5–7). During the whole loading process, the strain value on the outer side of the out-extend width part was less than the strain value on the inner side. With the increase of the displacement amplitude, the tensile strain appeared first and reached its peak value at 2%, then the tensile strain decreased continuously, points 5–7 were in the state of compressive strain at last.

Figure 9.

The strain distribution of the top ring plate at the side of shallow beam. (a) measuring points, (b) strain of points 1-4, and (c) strain of points 5-7.

Figure 10(a) to (c) show the strain distribution of the top ring plate at the side of deep beam. The strain distribution of the out-extend length part in the ring plate (points 8–11) was uniform before 3%, and the tensile strain increased with the increase of the displacement amplitude. However, the strain at point 10 no longer changed after 3%. The steel of the ring plate has material defects. Steel near point 10 has reached the maximum stress after 3%. After that, stress redistribution occurred, and strain values at other points have increased significantly. Figure 10(c) shows the strain distribution of the out-extend width part in ring plate (points 12–14), the strain value of the whole part increased with the increased of the displacement amplitude, and the strain value of the outer side of the out-extend width part was smaller than that of the inner side during the whole loading process.

Figure 10.

The strain distribution of the top ring plate at the side of deep beam. (a) measuring points, (b) strain of points 8-11, and (c) strain of points 12-14.

Figure 11(a) to (c) show the strain distribution of the bottom ring plate at the side of shallow beam. The strain distribution of the out-extend length part in ring plate (points 15–18) became more and more uneven with the increased of the displacement amplitude, showing a state of large in the middle and small on both sides; points 16 and 18 showed a downward trend after 5%, which may be due to the decrease in the bearing capacity of the ring plate on the shallow beam. Figure 11(c) shows the strain distribution of the out-extend width part in ring plate (points 19–21), similar to points 5–7, during the whole loading process, the strain on the outer side was smaller than that on the inner side. With the increase of the displacement amplitude, the tensile strain appeared first and reached its peak value at 1%, then the tensile strain decreased continuously, points 19–21 were in the state of compressive strain at last.

Figure 11.

The strain distribution of the bottom ring plate at the side of shallow beam. (a) measuring points, (b) strain of points 15-18, and (c) strain of points 19-21.

Figure 12(a) to (c) show the strain distribution of the bottom ring plate at the side of deep beam. The out-extend length part in ring plate (points 22–25) was at a low strain level until the displacement amplitude reaches 7%. Figure 12(c) shows the strain distribution of the out-extend width part in ring plate (points 26–28), the strain distribution was uniform. Similar to points 12–14, the strain at each point increased with the displacement amplitude increased.

Figure 12.

The strain distribution of the bottom ring plate at the side of deep beam. (a) measuring points, (b) strain of points 22-25, and (c) strain of points 26-28.

Finite element analysis

Sometimes, the test will not achieve the expected goal due to unexpected conditions. For example, TS1 was damaged in advance due to the quality of the weld. For TS2, the steel beam generated torque due to the deviation of the loading point, and the plastic hinge was generated at the beam end. Before the test, we expected the failure mode to occur in the panel zone. We can also see that the shear deformation of the panel zone changed visually before the failure mode of this test. Thence, the three-dimensional (3D) nonlinear finite element models were developed using the general finite element program Abaqus 6.14–5 to simulate low cycle repeated load test for further research. Firstly, finite element models TF1 and TF2 were established to validate the accuracy of finite element models. Then, equal-depth beam model TF3 was built and compared with unequal-depth beams for bearing capacity and load-paths in the panel zone. TF3 and TF2 had the same geometries, except for the depth of shallow steel beam.

Materials

The stress and strain obtained in Table 2 refer to nominal stress and nominal strain. In ABAQUS, real stress and strain are used. Equations (1) and (2) show the transformation of nominal stress, strain and real stress and strain. Poisson’s ratio was 0.3.

ε_{true} = \ln (1 + ε_{nom})

(1)

σ_{true} = σ_{nom} (1 + ε_{nom})

(2)

where $σ_{true}$ , $ε_{true}$ = real stress, real strain; $σ_{nom}$ , $ε_{nom}$ = nominal stress, nominal strain.

Element type, assembly, and boundary condition

The shell element was used in modeling. The individual steel components were merged to simulate equal strength welds at the connection. During the deformation of the model, there will be no contact between the components, so the interaction was not considered. Boundary conditions: the displacement of three directions was constrained at the bottom of the column, the top of the column was restricted by the displacement in two directions, the displacement in the direction of the column axis was relaxed. Axis pressure was first applied to the column, and the vertical cyclic displacement loads were applied to the end of the beam in the following step.

Verification

The comparison of hysteresis curves between finite element models and tests are shown in Figure 13. The displacement angles of the finite element results are taken to be 7% $θ$ and 5% $θ$ for TF1 and TF2, respectively. Taking the failure stage of the test specimens as reference, the ultimate loads of the tested specimens and the finite element model are listed in Table 3. The shape of the curve and the ultimate loads match well.

Figure 13.

Comparison between test and FEM in load-displacement hysteresis loop: (a) TS1 and TF1 and (b) TS2 and TF2.

Table 3.

The comparison between test and numerical analysis in ultimate load.

Testspecimen	Ultimateload (kN)	FEMspecimen	Ultimateload (kN)	Ratio
TS1	275.62	TF1	276.50	0.99
TS2	260.32	TF2	263.48	0.99

Structural behavior analysis

Since the test expectations were not met, we increased the loading displacement angle of the finite element model to 11% $θ$ . This section carries out the discussion of structural behavior analysis between TF1, TF2, and TF3.

Skeleton curves

Figure 14 shows the comparison of the load-displacement skeleton curves of the three models. The initial stiffness of the equal-depth beam model TF3 is slightly greater than TF1 and TF2. This may be due to the better integrity of the equal-depth beam model. The ultimate bearing capacity of TF2 is slightly larger than that of TF1 and TF3, and it first reaches the turning point of bearing capacity decline. In conclusion, the skeleton curves of the three models are similar, and there is no obvious difference in bearing capacity and rigidity.

Figure 14.

The comparison between test and numerical analysis in skeleton curve.

Failure mode and load-paths

Figure 15 shows the failure mode simulated by the finite element method. All three models produce large shear deformations and buckling in the panel zone. Besides, there is a large stress at the junction of the column and the panel zone, which may be the reason for the TS1 specimen which has poor weld quality being broken at the junction of the column and the panel zone in advance.

Figure 15.

Failure mode in finite element models: (a) TF1, (b) TF2, and (c) TF3.

Although the bearing capacity of three models are similar, the contribution composition of the bearing capacity of the panel zone is different due to differences in the load-paths between equal-depth and unequal depth beam model. The results show that the load-paths of the unequal depth beam model (TF1, TF2) are similar. Therefore, this section only takes TF1 as an example to analyze the load-paths.

The load-path of the unequal depth beam is divided into three stages 1% $θ$ , 3% $θ$ , and 5% $θ$ .

The maximum principal stress nephogram and pattern of TF1 when the displacement amplitude was 1% positive were shown in Figure 16. The top flange of the shallow beam and the bottom flange of the deep beam were under tension at this time. Tensile stress was transferred to the top left corner and bottom right corner of the steel tube web in the panel zone through the top ring plate at the side of the shallow beam and the bottom ring plate at the side of the deep beam. The tension stress between the two corners was transferred through the diagonal region of the web.

Figure 16.

The maximum principal stress nephogram and pattern of SJ1 in 1%.

When the displacement amplitude was 3% positive, the maximum principal stress nephogram and pattern were shown in Figure 17. At this time, there were two ways of transferring the tension stress between the tension parts of the shallow beam and the deep beam through the steel tube web in the panel zone: (1) the tension stress was to transfer along the bottom right corner of the lower part of steel tube web in the panel zone to the vicinity of the bottom ring plate at the side of the shallow beam and then to the shallow beam through the left bottom triangle area of the upper part of the web; (2) the tension stress was to transfer to the top ring plate at the side of shallow beam directly along the top right region of the upper part of the steel tube web in the panel zone and finally to the shallow beam.

Figure 17.

The maximum principal stress nephogram and pattern of SJ1 in 3%.

When the displacement amplitude was 5% positive, as shown in Figure 18, the tension area in the panel zone was further enlarged. The lower part of the steel tube web and the bottom left triangle region in the upper part of the steel tube web in the panel zone constituted a load-path, while the top right triangle region in the upper part of the steel tube web in the panel zone constituted another load-path.

Figure 18.

The maximum principal stress nephogram and pattern of SJ1 in 5%.

In different loading stages, the variation of load-paths in the web of steel tube in the panel zone are shown in Figure 19. Line ① was the diagonal line of the web of steel tube in the panel zone, line ② was the diagonal line of the upper part of the steel tube web in panel zone, and line ③ was the height line of the bottom ring plate at the side of the shallow beam.

Figure 19.

The variation of load-paths in the web of steel tube in the panel zone.

The whole process of the load-paths of the equal depth beam (TF3) is the same as the 1% $θ$ stage, which is to transmit along the diagonal of the web in the panel zone.

Conclusion

Two specimens were tested under low cyclic loading and finite element models were developed to investigate the shear performance of the connection with external stiffening ring between square steel tubular column and unequal-depth steel beams. The following conclusions are obtained:

The hysteresis curve shows that both two specimens have better energy dissipation capabilities. The beam depth difference has little effect on the bearing capacity and initial stiffness of the specimens. In the test, weld fracture in the panel zone (TS1) and plastic hinge failure at beam end (TS2) were observed. Shear deformation occurred to the web in the panel zone.

The stress of the ring plate is basically in a gradual rising stage and has room to rise. The bearing capacity of the shallow beam end may have decreased before the high beam end, but this still needs further investigation.

The shear deformation of the panel zone and the buckling of the web in the panel zone are the failure modes in the finite element models. The effect of beam depth difference on the bearing capacity and stiffness of the panel zone is very small. The load-paths of the equal-depth beam is transmitted along the diagonal of the web in the panel zone in the whole process. The unequal depth beam exhibits three different load-paths at 1% $θ,$ 3% $θ$ and 5% $θ$ , respectively.

Footnotes

Acknowledgements

The entire test was conducted at Tianjin University, China.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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