Seismic performance and shear bearing-capacity of truss SRC beam-column frame joints

Abstract

The structural performance of a frame joint is particularly important, which can determine the safe state of the global structure. For this reason, the seismic performance of the truss steel reinforced concrete (SRC) beam-column frame joints is investigated by the experimental study and the nonlinear finite element modeling. The main design parameters include the section size of the web rods, the axial compression ratio and the section size of I-steel. The failure mechanism, load-displacement skeleton curve, the ductility and energy dissipation capacity, and shear deformation in the core zone of the truss SRC beam-column joints are studied. A formula is put forward to describe the shear bearing-capacity of the joints. The results indicate that the truss SRC beam-column frame joints generally have good seismic performance. The size of steel and web members have impact on the seismic performance of the truss SRC beam-column joints, and the axial compression ratio is an important factor that impacts the hysteresis behavior and energy dissipation. The proposed shear bearing-capacity formula can objectively reflect the performance of the joints.

Keywords

experimental study nonlinear finite element analysis seismic performance shear bearing-capacity truss SRC beam-column frame joint

Introduction

The beam-column joints are the key nodes of a frame structure, which connect the beam and the column. In the structural design, especially for the seismic design, the beam-column joints are subjected to the combined stresses of bending, shear and torsion. The stress state of the joints is very complex and has great impact on the bearing capacity and rigidity of the structure, and thus the design of beam-column joints is one of the most important issues (Chan et al., 2011; Deng et al., 2018a; Pimpasakdi et al., 2004; Shi et al., 2017; Xiang et al., 2017; Zhou et al., 2017).

Considerable studies have been conducted to understand and improve the seismic performance of the structural joints in recent decades. Lachemi et al. (2009) studied the connecting performance between the steel and the lightweight aggregate concretes (Hamad and Haidar, 2016). Hu et al. (2010) carried out the study on the performance and seismic design of the moment composite frame connected by the steel beam and the steel reinforced concrete (SRC) column. Chou and Uang (2002) established the shear stress model of SRC column-steel beam joints under low cycle reversed load, and proposed suggestions on the parametric design of the joints. Chen et al. (2009) proposed the calculation method of shear bearing-capacity of SRC beam-column joints. A large number of experimental tests on composite structure joints were also carried out (Henriques et al., 2013, 2015; Rong et al., 2012; Seo et al., 2011; Tao et al., 2013; Wang et al., 2018; Zhang and Jia, 2016; Zhang et al., 2012). Since the 21st century, the numerical simulation technology has been rapidly developed and finite element method has been applied to simulate the mechanical behavior of the composite nodes and frames (Chiorean, 2013; El-Tawil and Deierlein, 2001; Hu et al., 2012; Iu, 2016; Liu et al., 2011; Ngo-Huu and Kim, 2012; Wang et al., 2013). The simulation results in good agreement with the experimental results indicate that the finite element analysis can be an effective approach for the study. Yu and Chen (2009) established the ANSYS 3-Dimensional (3-D) finite element model of I-steel tube concrete column-steel beam joint, and studied the nonlinear performance of the composite structure joints under low cycle repeated action.

The truss SRC beam-column frame is a novel structure. The truss SRC structure proposed by SRC research group in Guangxi University has better bearing capacity, ductility, energy dissipation capacity, deformation resilience and seismic performance than these of ordinary reinforced concrete structures (Deng et al., 2018b; Hu et al., 2014; Lin et al., 2011, 2012). However, study on the truss SRC beam-column frame joints has yet to be conducted. Tao et al. (2009) and Fan et al. (2010) carried out the seismic performance test of SRC column-steel truss composite joints and the results showed that the seismic performance at the ends of the beam under the flexural failure model is better than that at the joint zone under shear failure model. Chen (2015) studied the failure mode and mechanical properties of the new truss SRC beam-column frame side joints under low cycle reversed load and proved that truss SRC beam-column frame joints with cross web rods had better damping energy dissipation capacity. Yan et al. (2016) carried out an experimental study on the shear capacity of steel-reinforced high-strength concrete frame joints and relevant theoretical analysis, and proposed corresponding calculation formulas. However, the seismic performance and shear bearing-capacity of the joints have seldom been studied by the experimental study and nonlinear finite element analysis. The full-scale experimental investigation can provide valuable information to understand the failure mechanism, load-displacement hysteretic curve, the ductility and energy dissipation capacity, and shear bearing capacity. The nonlinear finite element analysis also provides valuable information to check the structural behavior of the joints. The failure mechanism and ductility of the frame joints need further investigation, and the mathematical formula to describe the shear bearing-capacity has yet been established.

Given the analysis above, study on the interior joints of the truss SRC beam-column frame structure is performed, taking the section size of the web rods, the axial compression ratio and the section size of I-steel as the main design parameters. The seismic behavior of the truss SRC beam-column frame joints is discussed by exploring the failure mechanism, the load-displacement skeleton curve, the ductility and energy dissipation capacity, the shear deformation in the core area and the shear bearing-capacity. Furthermore, the finite element analysis on the truss SRC beam-column frame joints is conducted and compared with the testing results. Meanwhile, a formula to portray the shear bearing-capacity of the frame joints is proposed through the study.

Experimental design

Testing specimens

A total of six specimens were prepared in the test to simulate the truss SRC beam-column frame joints in the standard layer, numbered JD-1 to JD-6, respectively. Fundamental tests have been conducted to obtain the material parameters of the steel, concrete and reinforcement. The Q235 steel is adopted in the I-steel and the angle steel. The angle steels are welded on the I-steel. The I-steel is fabricated by the hot rolling technology. The design value of tensile, compression and bend strengths of Q235 steel is 205 N/mm², with the Young’s modulus of 2.06 × 10⁵ N/mm², the shear modulus of 0.79 × 10⁵ N/mm² and Poisson’s ratio of 0.28. The HRB400 longitudinal rebars are adopted in the beam and column, and the HPB300 rebar is adopted in the stirrups. The design value of tensile/compression strength of HRB400 rebar is 360 N/mm², and the correlated Young’s modulus is 2.0 × 10⁵ N/mm². The design value of tensile/compression strength of HRB300 rebar is 270 N/mm², and the correlated Young’s modulus is 2.1 × 10⁵ N/mm². The strength grade of concrete is C40. Concrete C40 has a Young’s modulus of 3.53 × 10⁴ N/mm², axial compression strength of 54.89 N/mm² and Poisson’s ratio of 0.2. The reinforcement layout of the truss SRC beam-column frame joints is shown in Figure 1. The length of the beam is about 2.73 m and the height of the column is about 2.20 m. The details of the specimens are listed in Table 1. The main structural design parameters used in this test include the section size of web rod, the section size of I-steel and the axial compression ratio of the SRC column. The bonding condition between the steel and concrete, and the anchorage of the rebars are generally considered according to the design code of reinforcement concretes.

Figure 1.

Reinforcement layout of the beam-column joint in standard layer: (a) geometrical profile of the joint and (b) geometrical profile of the I-steel.

Table 1.

The detail structural information of the specimens.

Specimen number	Beam section b × h (mm)	Column section b × h (mm)	I-steel	Stirrup	Axial compression ratio	Size of web rod
JD-1	200 × 450	350 × 300	I14	A8@100	0.2	L40 × 4
JD-2	200 × 450	350 × 300	I16	A8@100	0.2	L40 × 4
JD-3	200 × 450	350 × 300	I18	A8@100	0.4	L40 × 4
JD-4	200 × 450	350 × 300	I14	A8@100	0.2	L50 × 4
JD-5	200 × 450	350 × 300	I16	A8@100	0.2	L50 × 4
JD-6	200 × 450	350 × 300	I18	A8@100	0.4	L50 × 4

The axial compression ratio n = N/(f_cA), N is the axial pressure applied, f_c is the design value of concrete strength, and A is the area of the column.

Loading modes

Loading device

The column bottom is placed on a simple self-made equivalent hinge, and the column center is aligned with the hinge center. The column cap and foot of the joints are separately fixed to the reaction wall by a reaction force strut. To avoid the lateral instability during loading, an anti-instability device is made at the central section of the SRC beam. The axial pressure is provided by a 1500-kN hydraulic jack. To prevent from the local damage at the top of the column, a 30-mm thick steel plate is fixed on top of the column. The jack is placed on the steel plate during loading. Centers of the steel plate, the column and the jack should be on a straight line to avoid the eccentric pressure. The actuator of electro-hydraulic servo system is placed at both ends of the beam, and low cycle reversed loads are applied on the two ends of the beam to make the joints deformed. The end displacements of the beam are recorded by displacement sensors. Besides, the displacements and the reaction forces of the joints during the loading process are separately collected by the displacement sensors and force sensors. The bottom of the column has been fixed, without displacements in three directions. The loading device of the experiment and the on-site photo follow Figure 2.

Figure 2.

Loading device: (a) design and (b) on-site photo of the experiments.

Loading system

The test adopts the double-control loading system, including load and displacement controls. The load control mode is adopted before yielding, with several step-load stages and one cycle at each load stage. The yield load Py and yield displacement Δy are determined by the obvious transition of the load-displacement (P−Δ) curve. The displacement correlated to the yield load is the yield displacement. After yielding, the displacement control is adopted to test the specimen. The displacement increases step by step with the multiple increment of yield displacement (generally 2~4 times of the yield displacement). Three cycles at each displacement stage is required until the load is dropped to 70% of the maximum load or the specimen cannot bear the predetermined axial pressure. The loading modes used in testing is shown in Figure 3.

Figure 3.

Loading modes.

The specifications of strain gauges used in the tests are steel and rebar strain gauges with a 5-mm gauge length. The foil type adhesive-based resistance strain gauges are selected. The core zone of the joint adopts three-dimensional adhesive-based resistance strain rosette with a 3-mm gauge length. The actuators are placed on surface of the joint. The layout locations and numbers of the strain gauges and displacement sensors are shown in Figure 4. During the analysis, the influence of the bonding state between the steel and concrete has been ignored.

Figure 4.

Layout of strain gauges and displacement sensors: (a) locations and numbers of strain gauges at positive side of the I-steel, (b) locations and numbers of strain gauges at reverse side of the I-steel, (c) measured points and numbers on the steel rebar, and (d) locations and numbers of displacement sensors.

Finite element modeling of the nonlinear analysis

A 3-D solid model is established by using general finite element software ANSYS. To simplify the calculation model and reasonably simulate the actual stress state of the structure, the following assumptions are made during the finite element modeling: (1) the concrete material is considered as isotropy, (2) the reinforcement rebar is considered as macroscopic isotropy, and (3) there is no slip between the steel and the concrete. The geometrical size and material parameters of the finite element models are taken from the measured experimental values of each specimen. ANSYS parametric design language (APDL) modeling technology is adopted to study the parametric effect in the simulation. Different elements are adopted to simulate different concrete and steel components. SOLID65 element is adopted to describe concretes. LINK180 is respect to reinforcement rebar. SHELL181 is respect to I-steel. BEAM188 is respect to angle steel. The constitutive model of the concrete adopts multi-linear Kinematic hardening (MKIN) model and William-Warnke’s five-parameters failure criterion. The constitutive model of the steel is bilinear Kinematic hardening (BKIN) model and Von-Mises yield criterion. The correlated models are displayed in Figure 5.

Figure 5.

Finite element model of reinforcement and steel reinforced cages.

The adopted nonlinear solution is Newton-Raphson (NR) method. The boundary and loading conditions are basically consistent with the tests. The displacement constraints are applied on the bottom of the column. The full bond assumption between the steel and the concrete is made during the numerical model. It means that the influence of the bonding state has been ignored. Considering the Saint-Venant principle, the coupling and rigid-field measures are adopted to deal with the load and boundary. The NR method as a linear method is generally used for solving nonlinear equations.

Analysis on experimental and simulation results

Crack propagation

Six specimens subjected to low cycle reversed load have basically similar crack propagation tracks. It can be seen from the testing and the numerical simulation in Figures 6 to 10 that the expected shear failure in joint core zone occurs in JD-1 to JD-6, and each specimen generally experiences the elastic stage, the stage with cracks, and the destruction. White lime is brushed on the surfaces of the concrete structures, and the square grid with size of 100 mm × 100 mm is drafted on the white surfaces. The cracks in concretes can be straightforwardly detected by the deformed square grid.

Figure 6.

Failure model of JD-1 in testing.

Figure 7.

The first principle stress distribution of JD-1 at failure (Pa).

Figure 8.

Load-displacement hysteresis loop curves of: (a) JD-1, (b) JD-2, (c) JD-3, (d) JD-4, (e) JD-5, and (f) JD-6.

Figure 9.

Moment-rotation hysteresis loop curves of: (a) JD-1, (b) JD-2, (c) JD-3, and (d) JD-4.

Figure 10.

Load-displacement skeleton curve of: (a) JD-1, (b) JD-2, (c) JD-3, (d) JD-4, (e) JD-5, and (f) JD-6.

The testing results of JD-1 and JD-2 indicate that the first microcrack of JD-1 occurs at around 20 kN, and the first microcrack of JD-2 is at about 35 kN, which means that the larger size of the I-steel brings about better performance to resist cracking. The joints with microcracks are still in elastic period. The comparison analysis of JD-4 and JD-5 also validates that the cracking load increases with the sectional size of I-steel. The testing results of JD-3 and JD-6 show that JD-3 cracks at around 18 kN and JD-6 cracks at about 35 kN, which declares that the larger size of the web rod leads to higher cracking load. It also can be obtained from the experimental results that the cracking load decreases with the increase of the axial compression ratio and the relationship appears stable. That is because the larger compression force of the column can lead to cracking at smaller load. The occurrence and propagation of cracks in JD-1 is shown in Figure 11, and the failure mode and correlated numerical results are shown in Figures 6 and 7, respectively.

Figure 11.

Crack propagation state of JD-1.

All the six specimens suffer from the shear destruction of the joints. The failure processes in the core zones of the joints are similar. The vertical crack firstly occurs in the end of the concrete beam at the beam-column junction of the core zone. Secondly, the end of the concrete column at the core zone cracks, along with the I-steel web plate yielding. Thirdly, the main cracks pass through the core zone of the joint along the diagonal. Finally, with the increase of load, the horizontal hoops yield, concretes peel off and the specimen is damaged. When the force decreases to 85% of the maximum load, the joint fails. Splitting the damaged core zone of the joint, it then can be noted that no interfacial slip occurs between the I-steel and the concrete.

Load-displacement skeleton curve

The load-displacement skeleton curve is a curve formed by connecting the peak points of the first cycle of the hysteresis curve corresponding to each load, which reflects the strength, ductility and degeneration characteristics of structures. The load-displacement skeleton curves of the six specimens are shown in Figure 10. It can be obtained that all the truss SRC beam-column frame joints have the elastic, elastic-plastic and plastic stages under the loading action. The load-displacement skeleton curve of the joint with smaller axial pressure is relatively smooth, which indicates that the ductility and deformation capacity of the joint decreases with the increase of axial compression ratio. However, the components with larger axial compression ratio have higher ultimate loads, which indicates that the bearing capacity increases with large axial compression ratio. By comparing the testing data of JD-1 and JD-4, the cross-section size of web rod of JD-1 is smaller, and the shear bearing-capacity of JD-1 is around 192 kN while that of JD-4 is about 201 kN. Therefore, the larger section size of web rod can lead to greater shear bearing-capacity. The measured curves of JD-4 and JD-5 also indicate that the sectional size of JD-4 is smaller and its shear bearing-capacity is around 201 kN, while the shear bearing-capacity of JD-5 is about 229 kN, which indicates that the larger sectional size brings about the greater shear bearing-capacity in the core area.

Characteristic points

Characteristic points of the testing specimen generally include yield point, ultimate point and failure point, which reflect the different states of the structure under different loading stages. The yield point is determined by the equal energy method, and the principle is displayed in Figure 12. A two-fold line with equal deformation energy is adopted to describe the actual load displacement curve, and the global area is equal to the area covered by the original curves. Point B in Figure 12 is the yield point, and the corresponding vertical and horizontal coordinates are the yield load Py and yield displacement ⊿_y, respectively. The failure load of the specimen Pu is defined as 0.85 Pmax, and the corresponding displacement is defined as failure displacement ⊿u. Pmax is the maximum load on the top of the column reached in the testing, and the corresponding displacement is the ultimate displacement ⊿max.

Figure 12.

(a) Equivalent energy method and (b) P−Δ hysteretic curve.

The testing results of the yield and the ultimate points are listed in Table 2. The simulated yield displacement and yield load of each specimen are close to the measured values in testing. The yield points obtained from the experimental study and the simulation match better than that of the limit points, with the maximum error below to 20.22%. Comparing the loads and displacements of the yield and limit states of the joint specimens, the difference between the simulated and experimental loads of the six groups is within 28.67%, and most of them are within 10%. The displacement deviation is a little bigger, because the numerical simulation is based on assumptions. The initial stiffness of the finite element analysis is larger than the testing value, and the calculated bearing capacity is generally higher. When the load approaches the ultimate load, the simulated results rise more smoothly than the experimental curve. Therefore, the limit and yield displacements generally shift to the right, resulting in the differences between experimental and simulated values. Besides, the perfect bonding state between the steel and the concrete along the full length in the numerical model can also lead to the increased load and decreased displacement. It also explains that the measured data are generally smaller than the simulated ones. It is thus convinced that ANSYS accurately simulates the bearing capacity and deformation performance of the joint specimens.

Table 2.

Testing results of characteristic points.

Testing specimen		Load (kN)		Displacement (mm)
		Yield	Limit	Yield	Limit
JD-1	Simulated result	182.16	198.83	12.73	15.28
	Experimental result	179.39	192.51	14.91	17.62
	Difference	1.52%	3.18%	14.62%	13.28%
JD-2	Simulated result	211.21	230.91	9.18	15.24
	Experimental result	178.18	198.03	11.44	19.06
	Difference	15.64%	14.24%	19.76%	20.04%
JD-3	Simulated result	240.25	269.01	11.57	19.53
	Experimental result	232.50	253.87	9.23	13.93
	Difference	3.23%	5.63%	20.22%	28.67%
JD-4	Simulated result	175.66	198.83	10.83	17.01
	Experimental result	167.13	183.59	9.43	17.22
	Difference	4.86%	7.67%	12.93	1.22%
JD-5	Simulated result	195.80	211.49	10.35	14.84
	Experimental result	190.58	211.52	11.92	19.14
	Difference	2.67%	0.01%	13.17%	22.47%
JD-6	Simulated result	241.53	269.60	11.80	20.00
	Experimental result	206.97	229.03	10.38	15.77
	Difference	14.31%	15.05%	12.03%	21.15%

Seismic performance of the joint

Ductility and energy dissipation capacity

Ductility

The ductility reflects the inelastic deformation properties of the structures (components) and the displacement ductility coefficient is adopted to describe the structural ductility. The displacement ductility coefficient can be given by (Tao et al., 2013)

μ_{Δ} = \frac{Δ_{u}}{Δ_{y}},

(1)

where, μ_Δ is the ductility ratio of components, Δ_u is the displacement corresponding to 85% of the maximum bearing capacity and Δ_y is the yield displacement of the joint.

Accordingly, the ductility coefficient of the joint specimens in positive and negative directions can be calculated from the skeleton curves of JD-1 to JD-6, as listed in Table 3. The average ductility coefficients of specimens are obtained by averaging the values in two directions, as displayed in Table 3. Comparing specimens JD-1 with JD-2, when the web size and the axial compression ratio are the same, the section size of I-steel in JD-1 is smaller, and the ductility coefficient of JD-1 is 2.12, which is less than that of JD-2 valued 2.75. It indicates that under certain conditions, the larger the section size of I-steel can bring about better ductility of the joints. Comparing joint JD-2 and JD-5, under the same section size of I-steel and axial compression ratio, JD-2 with a smaller web size has a ductility coefficient of 2.75, which is less than that of JD-5 with a value of 3.22. It indicates that under certain conditions, the larger web size provides the larger ductility coefficient and better ductility of the joint. By comparing JD-5 and JD-6 with ductility coefficients separately equal to 3.22 and 2.82, it is found that the axial compression ratio is inversely proportional to the ductility coefficient of the joint. Large axial compressive ratio has negative impact on the ductility of the frame joint. In addition, the maximum ductility coefficient of the specimen is 3.22 and the minimum value is 2.12. However, the ductility coefficient of solid-web SRC frame joints is about 4.0 (Hamad and Haidar, 2016). Due to the small amount of steel and open spandrel skeleton, the ductility coefficient of the truss SRC frame joints is generally lower than that of the solid-web SRC frame joints.

Table 3.

Ductility coefficients.

Loading direction	JD-1	JD-2	JD-3	JD-4	JD-5	JD-6
Positive	2.18	3.17	3.00	2.91	3.29	2.92
Negative	2.05	2.33	2.07	2.64	3.14	2.72
Average μ_⊿	2.12	2.75	2.54	2.78	3.22	2.82

Energy dissipation

Equivalent damping coefficient and energy dissipation coefficient

The structural components should be able to absorb and dissipate the seismic energy under earthquake actions. The ability of a component to absorb and dissipate seismic energy is defined as the energy dissipation capacity. It is measured through the area surrounded by the P−Δ curves, which is an important parameter for the evaluation of seismic performance of structures. The equivalent damping coefficient (ζ_eq) and the energy dissipation coefficient (I_e) are generally calculated as (Zhang et al., 2012)

ξ_{eq} = \frac{E_{1}}{E_{2}} = \frac{1}{2 π} \frac{S_{ABC} + S_{CDA}}{S_{OBE} + S_{ODF}}

(2)

I_{e} = \frac{S_{ABC} + S_{CDA}}{S_{OBE} + S_{ODF}} = 2 π ξ_{eq}

(3)

where, $E_{1}$ is the area enclosed by the curve ABCD, representing the energy stored in the hysteresis loop for one cycle, as shown in Figure 12(b), and E₂ = 2π (S_OBE+S_ODF) is the elastic deformation energy of the structure. The larger I_e, means the stronger energy dissipation capacity of the structure. The energy dissipation coefficient and equivalent viscous damping coefficient of each joint in the ultimate state are calculated in Tables 4 and 5.

Table 4.

Energy dissipation coefficient and equivalent viscous damping coefficient.

Number	JD-1	JD-2	JD-3	JD-4	JD-5	JD-6
I_e	2.07	1.76	1.76	3.11	3.39	4.78
ζ_eq	0.33	0.28	0.28	0.49	0.54	0.76

Table 5.

Comparison of equivalent damping coefficients of joint specimens.

Number	JD-1	JD-2	JD-3	JD-4	JD-5	JD-6
1Δ	0.16	0.09	0.10	0.19	0.21	0.22
2Δ	0.19	0.13	0.17	0.28	0.29	0.34
3Δ	0.19	0.17	0.21	0.29	0.31	0.39
4Δ	0.23	0.17	0.23	0.32	0.37	0.44
5Δ	0.25	0.20	0.25	0.37	0.41	0.50
6Δ	0.33	0.23	0.28	0.40	0.44	0.57
7Δ	–	0.24	–	0.42	0.48	0.63
8Δ	–	0.28	–	0.45	0.54	0.76
9Δ	–	–	–	0.49	–	–

The load-displacement hysteresis loop curves of the six specimens have been displayed in Figure 8. The moment-rotation hysteresis loop curves of JD-1 to JD-4 have been given in Figure 9. For the displacement sensors on JD-5 and JD-6 are out of work during the testing, the moment-rotation hysteresis loop curves cannot be provided. It can be read from the hysteresis loop curves that the maximum load occurs around the second cycle of each specimen. Table 5 shows that the equivalent viscous damping coefficient of the truss SRC frame joint is around 0.15∼0.34, while that of ordinary reinforcement is 0.1 (Lachemi et al., 2009). It can be concluded that the energy dissipation performance of the truss SRC frame joint is better than that of the ordinary reinforced concrete. The results of Table 4 show that the energy dissipation coefficient of JD-1 is 2.07, obviously lower than that of JD-4 with a value of 3.11 under the same experimental conditions and low-cyclic reversed loading. Similarly, JD-2 and JD-5, and JD-3 and JD-6 follow the same law. It indicates that a larger sectional size of cross web rod results in better energy dissipation capacity and energy dissipation performance of the structure. Under the low-cyclic reversed loading and the same experimental conditions, the average energy dissipation coefficient of JD-4 is 3.11 less than that of JD-5 with a value of 3.39. The results show that a larger size of the section steel will result in a higher energy dissipation coefficient and a better energy dissipation performance of the structure, correspondingly.

Working index

The working index $I_{w}$ is a criterion for evaluating the energy absorbed by components under repeated pressures, bending moments and shear forces. The results are shown in Table 5. The formula is as follows (Rong et al., 2012):

I_{w} = \sum_{i = 1}^{n} \frac{P_{i} Δ_{i}}{P_{y} Δ_{y}}

(4)

where n is the cycle number, i is the number of cycles, P_i is the maximum load of the i-cycle, P_y is the yield load, ⊿_i is the displacement corresponding to the maximum load in the i-cycle, and ⊿_y is the yield displacement. The calculated working indexes for JD-1 to JD-6 are 66.13, 109.02, 76.28, 116.51, 135.94, 125.96, respectively.

Comparing the results of JD-3 and JD-6, the working index of JD-6 is 125.96, which is obviously larger than that of JD-3 with a value of 76.28. The same tendency can be obtained from the comparisons of JD-1 with JD-4 and JD-2 with JD-5. It indicates that the size of the web rod has great influence on the seismic performance, and the seismic performance of components can be enhanced by increasing the web-rob size. Comparing JD-1 with JD-2 and JD-4 with JD-5, the working index of JD-1 (66.13) is less than that of JD-2 (109.02) with the same web-rob size and axial compression ratio. It indicates that the energy dissipation performance of the structure can be enhanced to a certain extent by properly increasing the size of I-steel, so as to improve the seismic performance.

Shear deformation in the joint core zone

Comparison of shear deformation of joint specimens in every characteristic point can be read from Table 6. When the load is relatively small, the concrete does not crack, the shear deformation changes slightly and basically in linear form. With the increase of load, the concrete cracks, and the shear deformation no longer changes linearly and increases with the displacement growth.

Table 6.

Shear angles corresponding to the characteristic points of each joint.

JointCharacteristic point	JD-1 ( $γ$ 10⁻³ rad)	JD-2 ( $γ$ 10⁻³ rad)	JD-3 ( $γ$ 10⁻³ rad)	JD-4 ( $γ$ 10⁻³ rad)	JD-5 ( $γ$ 10⁻³ rad)	JD-6 ( $γ$ 10⁻³ rad)
Yield load	4.6	5.37	3.98	4.71	4.61	4.04
Limit load	5.5	6.47	4.67	5.16	5.88	5.32
Failure load	18.27	27.56	11.4	12.09	19.58	10.02

The unit of the shear angle is 10⁻³ rad.

Table 6 shows the shear angles corresponding to characteristic point of each joint. It can be noted that the shear angles in the core area of the joint are generally small and close to each other, with value basically between 0.004 rad and 0.005 rad. In the ultimate state, the shear angle in the core area of the joint also changes slightly, ranging from 0.005 rad to 0.006 rad. The shear angle changes smoothly from the yield state to the ultimate state. However, the shear angle has abrupt change from the ultimate state to the failure state, and the corresponding shear angle is rather larger than that in the yield and ultimate states.

Bearing capacity degradation

The bearing capacity degradation of the joints can be expressed by the bearing capacity reduction coefficient λ_i, and the formula is (Wang et al., 2018)

λ_{i} = \frac{Q_{j, \max}^{i}}{Q_{j, \max}^{1}}

(5)

where $Q_{j, \max}^{i}$ is the peak load at the j-level load during the i-th cycle, $Q_{j, \max}^{1}$ is the peak load at the j-level load during the first cycle. The strength degradation coefficient λ₃ of the testing specimen in the third cycle of each loading stage is calculated from equation (5), as shown in Table 7.

Table 7.

Strength degradation coefficient λ₃.

Node number		JD-1	JD-2	JD-3	JD-4	JD-5	JD-6
Positive load	1Δ+	0.795	0.942	0.926	0.884	0.919	0.921
	2Δ+	0.741	0.804	0.885	0.843	0.871	0.857
	3Δ+	0.774	0.728	0.825	0.808	0.839	0.783
	4Δ+	0.749	0.71	0.836	0.833	0.783	0.875
	5Δ+	0.724	0.753	0.867	0.799	0.823	0.887
	6Δ+	0.701	0.868	0.813	0.786	0.833	0.821
	7Δ+	–	0.837	–	0.779	0.77	0.808
	8Δ+	–	0.821	–	0.674	0.75	0.772
	9Δ+	–	–	–	0.619	–	–
Negative load	1Δ−	0.813	0.859	0.952	0.887	0.906	0.909
	2Δ−	0.771	0.814	0.809	0.797	0.883	0.86
	3Δ−	0.639	0.813	0.777	0.808	0.824	0.902
	4Δ−	0.726	0.827	0.821	0.825	0.891	0.989
	5Δ−	0.686	0.917	0.799	0.832	0.812	0.967
	6Δ−	0.684	0.878	0.737	0.758	0.877	0.957
	7Δ−	–	0.807	–	0.719	0.847	0.928
	8Δ−	–	0.798	–	0.712	0.749	0.887
	9Δ−	–	–	–	0.701	–	–

The results in Table 7 show that the bearing capacity of the specimens decreases with the increase of displacement and loading cycles, under positive or negative loading. However, in the elastoplastic stage, the descending speed slows down. In the failure stage, the bearing capacity degrades so seriously that the joint cannot continue to bear the load. The comparison of JD-2 and JD-3 shows that the bearing capacity reduction coefficient of JD-2 in each displacement control stage is basically smaller than that of JD-3. Similar to JD-1 and JD-4, the bearing capacity reduction coefficient of JD-1 in each displacement control stage is basically smaller than that of JD-4. The phenomenon indicates that under the same conditions, the bearing capacity degradation of joints can be reduced by increasing the size of the web rod. The bearing capacity reduction coefficient of JD-4 in each displacement control stage is close to that of JD-5, which indicates that the size of I-steel has little effect on the strength reduction coefficient of the frame joints.

Shear bearing-capacity of the joint

The shear bearing-capacity of the joint can be considered as the combined contribution of the truss SRC beam and the SRC column. Before the discussion, the following assumptions are made: (1) the SRC, I-steel web plate and stirrup of the joint support the shear force; (2) when the concrete cracks, the correlated tensile strength is ignored; (3) the I-steel in the core zone of the joint has no local buckling; (4) the interfaces between the I-steel, rebar and concrete well bond without local flaw; (5) the shear contribution of the frame constituted by the flange and the reinforcing rib is ignored, and that of the angle steel outside of the plane is also neglected. The following equation of the shear bearing force of the joint $V_{j}$ can be given (Wang et al., 2018):

\begin{matrix} V_{j} = V_{jc} + V_{jsv} + V_{w} = γ_{s} h_{j} b_{j} f_{c} \\ + \frac{f_{yv} A_{sv} (h_{0} - a_{s}^{'})}{s} + ξ f_{a} t_{w} h_{w} \end{matrix}

(6)

where $V_{jc}$ , $V_{jsv}$ , and $V_{w}$ stand for the shear bearing-capacity of the concrete in the core zone of the joints, the stirrup and the I-steel web plate in the core zone, respectively; $γ_{s}$ and $ξ$ are the shear influence coefficients of the concrete and the I-steel web plate; $h_{j}$ and $b_{j}$ are the height and width of the joint in the core zone ( $b_{j} = \frac{b_{c} + b_{b}}{2}$ , $b_{c}$ and $b_{b}$ are the section width of the column and the beam); $f_{c}$ is the compressive strength of the concrete; $f_{yv}$ is the tensile strength of the stirrup; $A_{sv}$ is the total section area of the stirrup in one section; $(h_{0} - a_{s}^{'})$ is the distance between the rebar at one end of the beam and the rebar at another side of the rebar; $s$ is the interval between the stirrups in the core zone; $f_{a}$ is the yield strength of the I-steel web plate in the core zone; $t_{w}$ and $h_{w}$ are the thickness and height of the I-steel web plate in the core zone.

The linear fit on the numerical simulation results produces the relationship of $t_{w}$ (mm) and $V_{j}$ (kN) as 5.5–843.2 for JD-1, 6.0–907.57 for JD-2, 6.5–1076.48 for JD-3, 5.5–822.43 for JD-4, 6.0–933.71 for JD-5, 6.5–1021.63 for JD-6. The average slop of the $V_{j} - t_{w}$ curve can be figured out as 216.24 kN/mm. According to Table 8, the measured yield strength of web rods is averaged as 374.38 N/mm². The measured compression strength of the concrete is 54.89 N/mm². The average height of the web plate in JD-1 to JD-6 is 160 mm. Thus, the influence coefficient of the I-steel web plate can be calculated out:

ξ = \frac{1}{\sqrt{3}} \frac{\sqrt{f_{a}^{2} - f_{c}^{2}}}{f_{a}} = 0.571

(7)

Table 8.

Properties of steel materials.

Steel material No.	Yield strength (N/mm²)	Ultimate strength (N/mm²)	Elastic modulus (N/mm²)
ϕ8	347.65	465.68	2.01 × 10⁵
14	431.21	581.85	2.04 × 10⁵
18	490.2	638.5	2.06 × 10⁵
I14	425.82	551.73	2.03 × 10⁵
I16	444.44	561.11	2.06 × 10⁵
I18	441.03	543.59	2.05 × 10⁵
L40 × 4	375.62	476.31	2.04 × 10⁵
L50 × 4	373.13	498.54	2.04 × 10⁵

The shear influence coefficient of concrete $γ_{s}$ is figured out by the formula $γ_{s} = α \sqrt{1 - h_{b}^{2} / h_{j}^{2}} \cos θ$ , where $h_{b}$ is the cross-section height of the beam, $θ$ is the angle between the diagonal rod and the horizontal line. Similarly, the linear fit on the numerical simulation results gives $γ_{s}$ with values of 0.222, 0.235, 0.282, 0.216, 0.244, 0.264) for JD-1 to JD-6, respectively. The relationship of influence coefficient $γ_{s}$ and axial compression ratio $α$ can be described by the equation as below:

γ_{s} = 0.185 + 0.218 α

(8)

Given the analysis above, the final formula to explain the shear bearing force of the joint can be expressed as

V_{j} = 0.185 + 0.218 α h_{j} b_{j} f_{c} + \frac{f_{yv} A_{sv} (h_{0} - a_{s}')}{s} + 0.571 f_{a} t_{w} h_{w}

(9)

The comparison of the derived shear bearing forces and the measured forces of JD-1 to JD-6 is listed in Table 9. It can be noted that the two values are very close, with ratio in the range of 0.93-1.04, which validates that the proposed formula can be used as a theoretical basis to predict the shear bearing-capacity of the truss SRC beam-column frame joints. The theoretical values are generally smaller than that of measured ones, which may be attributed to the average processing of some coefficients. However, the proposed formula can still provide guidance to understand the shear bearing force of the joint.

Table 9.

The comparison of calculated and measured shear bearing forces.

Number	Ultimate shear force derived from equation (9) (kN)	Measured ultimate shear force (kN)	Ratio
JD-1	859.07	843.20	1.02
JD-2	868.38	907.57	0.96
JD-3	1008.85	1076.48	0.94
JD-4	859.07	822.43	1.04
JD-5	868.38	933.71	0.93
JD-6	1008.85	1021.63	0.99

Conclusion

The experimental investigation and nonlinear finite element simulation of the truss SRC beam-column frame joints have been conducted to check the seismic performance and shear bearing-capacity. The following conclusions can be drawn from the study:

Both the experimental study and the numerical simulation indicate that the expected shear failure in joint core zone occurs in JD-1 to JD-6, and each specimen generally experiences the elastic stage, the stage with cracks, and the destruction.

The ductility of the truss SRC beam-column frame joints reduces with the increase of the axial compression ratio, but the strength increases. It can be attributed to the effect of P-Δ on the local collapse mechanism. The seismic performance may be increased only by increasing the strength to avoid the local collapse mechanism.

Under the same conditions, the seismic performance of truss SRC beam-column frame joints can be improved by appropriately increasing the sectional sizes of I-steel and web rod, and decreasing the axial compression ratio. Axial compression ratio is a very important factor that impacts the hysteresis behavior and energy dissipation of the truss SRC beam-column frame joints

The derived formula to describe the shear bearing-capacity of the truss SRC beam-column frame joints can be a theoretical instruction for the prediction and evaluation of shear bearing condition.

Footnotes

Authors’ Note

Ping Xiang is also affiliated with Guangdong Provincial Key Laboratory of Building Energy Efficiency and Application Technologies, Guangzhou, China and Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province, Nanchang, 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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work described in this paper was supported by grants from the National Natural Science Foundation of China (Grant Nos. 11972379 and 51908263), Lanzhou University (561220005), Central South University (Grant Nos. 502045006 and 502390001) and Hunan 100-talent plan (420030004), and Key Laboratory of Structures Dynamic Behavior and Control (Ministry of Education) in Harbin Institute of Technology (Grant No. HITCE201901).

ORCID iD

Huaping Wang

Data availability statement

Some data and models that support the findings of this study are available from the corresponding authors upon reasonable request.

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