Experimental and Numerical Analysis of the Behavior of Beam–Column Connections with Reinforced Side Plates

Abstract

This paper describes an experimental and numerical study of the hysteretic behavior of side-reinforced joints of a steel frame manufactured from Q345B steel and welded using an E5015 electrode. The objectives of this study were to observe the mechanical behavior of side-plate reinforced joints under cyclic loads; identify their plastic hinge, skeleton curve, stiffness degradation, ductility, and energy dissipation capacity; and provide useful test data for future damage analysis of steel frames with side-plate reinforced beam–column connections. Two specimens were designed, and both were tested under cyclic loads. The test setup consisted of one beam at the end and a column connected by three groove welds. The cyclic loads were applied to the beam’s free end, and the sizes of the beams and the columns of the two specimens were held constant because the only element studied in the present work was the side-plate reinforcement. In this paper, the responses of these two joints are discussed in terms of their experimentally and numerically obtained failure modes, hysteretic curves, plastic hinge, skeleton curve, stiffness degradation, ductility, and energy dissipation capacity. The results show that the steel frame’s side-plate reinforced joints, compared with normal joints, have smaller plastic hinge displacement and deformation, and higher bearing capacity. Furthermore, if designed according to code, all these welded joints perform satisfactorily.

1. Introduction

Brittle failure was one of the major failure modes of traditional welded and bolted hybrid steel frame beam–column connections in damage caused by the 1994 Northridge earthquake in the United States and the 1995 Kobe earthquake in Japan. This investigation result has caused many scholars from different countries to question the traditional steel frame design theory. Avoiding brittle fracture of beam–column joints has become a popular topic in research on the seismic performance of steel frames. Based on the idea of plastic displacement, new types of ductile beam–column connection were proposed, which are mainly divided into two types: one is a beam–column connection with reinforced beam ends [1,2,3,4]; and the other is a beam–column connection with weakened beam flanges at the ends [5,6,7]. Both can reduce the stress concentration by improving the structural details of the beam–column connection to move the plastic zone outward from the beam end. The beam–column connection with reinforced side plates belongs to the first type. The weld between the reinforced plate and the beam flange bears a large load, and its quality directly affects the mechanical performance of the whole connection.

Many scholars have researched the beam–column connections with reinforced side plates. Ma et al. [8] proposed an improved side-plate reinforced beam–column joint, and used finite element analysis to analyze 11 improved side-plate reinforced joints with different details. Based on the research results of the weak-axis connection of the new type of node field box-reinforced I-shaped column, Lu et al. [9] studied the hysteretic performance of the trapezoidal side-plate reinforced node and used finite element software to carry out low-cycle repeated loads on this type of node. The finite element variable reference simulation analysis was used to understand the action. Yu et al. [10] studied the failure mode and hysteretic performance of the reinforced dog-bone weakened joint of the fabricated beam flange side plate under cyclic loading. Wang et al. [11] studied the side-plate reinforced joints based on testing and finite element analysis under a low-cycle reciprocating load. Kim et al. [12] studied joint fatigue failure modes using five cover-plate and five flange-plate single-sided steel moment-resisting beam–column assemblies tested at full scale. Guo et al. [13] revealed the joints’ failure mechanism and energy dissipation mechanism with different reinforcement forms by testing six Q690 high-strength steel plate-reinforced joints under a low-cycle reciprocating load.

The welding quality of beam–column connections directly affects the mechanical performance of steel structure frames. Nagel [14] et al. carried out ultra-low-cycle fatigue loading on a circular sample of s335 structural steel welded on the base plate under a complex load. Liu et al. [15] conducted a low-cycle reciprocating test on the fatigue fracture of a series of T-shaped welded joints. Zhong [16] et al. studied the fracture behavior of a base metal section of a high-strength welded joint through a uniaxial tensile test of a 45 steel welded specimen. Xiong et al. [17] used uniaxial tensile and tensile compression cyclic tests to study the damage in the welded joint area of a steel frame. Liao et al. [18] conducted a quasi-static test and numerical simulation on the welded joint of a square steel pipe column and an H-shaped steel beam under low-cycle reciprocating action. Wei et al. [19] studied the effect of joint damage under low-cycle reciprocating action when there were cracks in the joint web. Liu et al. [20] conducted finite element analysis on the possibility of cracking in a straight wing expansion joint and flange weakening joint with different parameters. Liu et al. [21] conducted a low-cycle fatigue test on the fracture behavior of beam–column joints of high-strength steel frames. Ma et al. [22] conducted a low-cycle test on the mechanical behavior of welded steel plate joints.

Many of the studies mentioned above focused on joints’ strength and fatigue behavior under monotonic or cyclic loading without considering the influence of welding damage on joint behavior. Therefore, the main focus of this research was to study the effect of welding damage on the performance of welded steel plate joints by analyzing the load-displacement and stress–strain curves of these joints, tested under monotonic and cyclic loading. The degradation process of welding damage was studied using the skeleton curve and damage modulus curve, and the damage model was verified.

2. Experimental Program

2.1. Specimen Design

In this paper, Q345B steel containing carbon alloy steel (C < 0.2%) was selected as the steel of the beam–column specimen. All specimens were made of E5015 weld metal. The material properties of Q345B steel and E5015 weld [23] are shown in

Table 1. Q345B steel and E5015 electrode material test results.

Parmeter	Yield Strength fy/MPa	Tensile Strength fu/MPa	Elastic Modulus E/MPa
Q345B Steel	358.92	589	203,069
E5015 Electrode	382.46	599.87	204,720

. Two T-shaped models between the beam–column inverted points of the side steel frame were designed, namely, one side-plate reinforced node (SRN) and one normal node (NBN) model, and verified by the experiment; the beams and columns of the specimens were HN248 × 12 × 5 × 8 mm and HW250 × 250 × 9 × 14 mm respectively. The total length of the beam was 1400 mm, the full height of the column was 1450 mm, and the beam-to-column section stiffness ratio was 0.32. A bolt-welding hybrid connected the beams and columns. The connecting bolts were 4-M20 8.8-grade friction-type high-strength bolts having a diameter of 22 mm. Full penetration groove welds connected the beam flanges and columns. The structural parameters of the side-plate reinforced node were: l_a = 80 mm, l_b = 80 mm, c = 26 mm, d = 26 mm. The detailed connection structure diagram is shown in Figure 1.

2.2. Test Loading and Measurement

The joint low-cycle reciprocating loading test was carried out in the laboratory of Nanjing Forestry University, using a pseudo-static test scheme [24]. To closely represent the actual situation, the test column was placed vertically during the test, and the side was fixed on the reaction wall by a transfer beam. An end plate was placed at each end of the column having a short plate size of 330 × 330 × 20 mm, and a 100 t hydraulic jack was placed on the upper-end plate through a reaction frame to provide a 500 kN axial force for the frame column; this was equivalent to creating motionless column end boundary conditions for the hinged support. The beam end was vertically equipped with a reaction frame, and a 50 t MTS hydraulic servo actuator was hung at an appropriate position on the upper part of the reaction frame. The beam end was subjected to tension and compression forces (displacement) to apply low-cycle repeated loads until the component was completely destroyed. The computer synchronously collected each measuring point’s load, displacement, and strain values.

During the test, the column was placed horizontally on a hinged support having a height of 60 mm, and the anchor rod was used to reliably connect the column to the rigid ground. Each column end was equipped with a jack and corresponding thrust to form a simply supported boundary condition. The column end had a corner but was not subject to any horizontal or vertical displacement. The beam end was applied with a horizontal cyclic reciprocating load through a MAS-300 actuator manufactured by Hangzhou Bangwei Electromechanical Control Engineering Co., Ltd., Hangzhou, China. having a stroke of 500 mm. The other end was fixed to the reaction wall to keep it level with the rigid ground. The test loading device is shown in Figure 2. Since this actuator is ideal for centering, there is no additional torque, and the use of side supports can be avoided. In the pseudo-static test loading system controlled by the side shift angle between the layers, this side shift angle is approximately equivalent to the beam end rotation angle during the test, and is then converted into the beam end displacement for control. When the bearing capacity of the specimen decreased to 85% of the ultimate bearing capacity, the test stopped. Each cycle period was set to 5 min, and the loading speed was determined according to the cycle period. When the specimen yielded, the loading cycle at each level was completed and paused for 3 min to record the test. The whole loading process took about 3 h. The loading system is shown in Figure 3.

3. Test Results and Analysis

3.1. Test Phenomenon and Failure Form

(1)

NBN specimen

After low-cycle reciprocating loading, the NBN plastic hinge of the test piece was positioned at the beam flange 50 mm from the weld. The length of the crack in the heat-affected zone on side A was about 11.62 cm, and the crack at the toe of the welding hole was the widest, reaching 5.2 mm. Since the cracks on the B-side weld are relatively small, and some were covered by welding slag, the ultrasonic flaw detection instrument was used for inspection. After testing, it was found that the defect wave disappeared 4.56 cm from the left flange of the B-side. The B-side weld was calculated, and the total length of the crack was about 7.84 cm. Figure 4 shows the local deformation diagram of the NBN specimen. The NBN plastic hinge position of the specimen was deformed, and the left and right wings of the A-side had larger crack widths.

(2)

SRN specimen

Figure 5 shows the partial deformation diagram of the SRN specimen. The first stage was loaded to the fourth stage of the loading interval, and the specimen was in the elastic force stage. When the beam end displacement was 60 mm, the end flange of the test specimen SRN showed local buckling deformation, and the end welding seam also had cracks. The plastic deformation was mainly concentrated on the column webs in the node area, indicating that, in the node during the loading process, obvious shear deformation occurred in the domain, followed by the center area of the beam end butt weld. The beam flange at the end of the reinforcing plate appeared to have a small buckling deformation. Due to the stress concentration phenomenon at the plastic hinge where the upper and lower flanges of the beam and the web connect, in the test, cracks first appeared at this location and gradually developed, resulting in a gradual decrease in bearing capacity.

3.2. Hysteresis Curve and Skeleton Curve

Figure 6 shows the hysteresis curves of the side-plate reinforced nodes and ordinary nodes. It can be seen from Figure 6 that the hysteresis curve of the ordinary node is fuller than that of the side-plate reinforced type, indicating that the energy consumption and seismic performance of the ordinary node are better than those of the side-plate reinforced node. Although the hysteresis curve is less full than that of ordinary joints, its extreme value is larger than that of ordinary joints, and the energy consumption degrades faster. This shows that using side-plate reinforced joints improves the ultimate bearing capacity of beams and columns but is not conducive to the overall energy consumption.

The skeleton curve can reflect the relationship between the force and deformation of the component and is an important basis for the dynamic analysis of the component entering the elasto-plastic stage [25]. Figure 7 shows the skeleton curves of the specimens of ordinary joints and side-plate reinforced joints. The skeleton curves of each model show a linear relationship before yielding and a nonlinear relationship after yielding; after reaching the ultimate load, the curve slowly drops, indicating that larger plastic deformation of the beam–column connection occurs at the nodes, and the plasticity of the steel is fully utilized.

3.3. Ductility

Table 2. Load and displacement at characteristic points, and displacement ductility factor.

Specimen	Force Direction	Δy/mm	Py/kN	Δu/mm	Pu/kN	μ
NBN	Positve	20.64	88.56	51.33	114.00	2.04	2.08
	Negative	19.85	89.98	42.02	106.30	2.12
SRN	Positve	23.03	110.18	49.98	129.03	2.17	2.57
	Negative	20.06	100.62	59.36	136.15	2.96

shows the specimens’ characteristic point load, displacement, and displacement ductility coefficients [3]. The experimental data show that the same specimen’s positive and negative ductility coefficients are not significantly different. Nonetheless, the average value of the two represents the ductility of the side-plate reinforced joint. The coefficient was 23.6% higher than that of ordinary joints, which shows that side-plate reinforced joints have better ductility performance than ordinary joints.

The energy dissipation performance of the structure can be used to evaluate the structure’s seismic performance, and the energy dissipation capacity of the steel frame joints can be measured by the equivalent viscous damping coefficient (h_e) [26,27]. The equivalent viscous damping coefficient can be obtained according to the area SABCOA and the S△BOD ratio of the area enclosed by the hysteresis curve ABC and the horizontal axis, as shown in Figure 8. The He of SRN and NBN are 0.306 and 0.290, respectively, indicating that the area of the hysteretic curve of the side-plate reinforced node is larger and fuller. Therefore, the side-plate reinforced node has a strong energy consumption capacity.

3.4. Nodal Damage Analysis

The damage process of metal materials is described with deformation and energy as indicators, which are generally divided into three categories [28]: displacement model, energy model, and combination model. In this study, the energy damage model was used to simulate the damage process of actual nodes, and the damage comparison analysis of ordinary nodes and side-plate reinforced nodes was carried out.

Damage modulus based on energy (energy model) is given by:

$$D={\displaystyle \sum _{i=1}^n{\left(\frac{E_i}{E_{mon}}\right)}^{c_2}}$$

(1)

In the formula, E_i is the energy consumed by the i-th cycle of the specimen; E_mon is the energy consumed by the monotonic tensile specimen; c₂ is the weighted index of the energy damage model.

ABAQUS analysis was used to obtain the load–displacement curve of the same specimen under the single push action, as shown in Figure 9. To calculate the damage modulus value more accurately, the energy consumption of the specimens under the single push action was calculated. The calculation result is that the energy consumption of the NBN specimen was 17,266 J, and the energy consumption of the RRN specimen was 30,626 J. Based on the energy consumption of the two specimens under a single pushing action, the displacement damage model [29] (Equation (1)) was used to calculate the damage modulus of the ordinary joint and the side-plate reinforced joint under the action of a low-cycle reciprocating load. The power function was used for fitting, and the fitting curve is shown in Figure 10.

It can be seen from Figure 10 that the fitting curves of the two specimens are in good agreement with the test values. With the accumulation of plastic displacement, the damage per cycle of each load level increases significantly, and enters the accelerated damage state and the SRN curve. The slope is smaller than that of the NBN curve. However, the final damage modulus of SRN is larger, indicating that the side plate has a noticeable effect on controlling the plastic displacement of the beam end, resulting in a slowdown in the damage process and sufficient energy dissipation.

4. Finite Element Analysis

4.1. Model Building

According to the material performance test of this research group, the beam and column were made of Q345B steel, with E = 2.06 × 10⁵ N·mm⁻² and Poisson’s ratio v = 0.3. The type of welding rod was E5015. The constitutive relationship adopted the three-fold line model considering strengthening and descent, as shown in Figure 11.

ABAQUS finite element software was used to establish the side-plate reinforced steel frame beam–column node analysis model. Generally, the regular block solid model uses the eight-node hexahedron [30] linear reduction integral element (C3D8R). The overall element size is about 30 mm. The area within 180 mm of the node end and the side plate encryption is 9 mm, and the welding seam encryption is set to 2 mm. The specific division is shown in Figure 12.

4.2. Model Validation

4.2.1. Specimen Deformation

Figure 13 uses the side-plate reinforced node (SRN) specimen as an example to show the deformation comparison between the experiment and the finite element analysis. When loaded to the fourth level, the specimen is still in the elastic stage, and the stress cloud diagram is shown in Figure 13a. When loaded to the eighth level, the flanges on both sides of the beam web are deformed significantly, and plastic hinges are generated. The test results are consistent, as shown in Figure 13b. When the tenth level is loaded, the side-plate reinforcement section beam flange is seriously damaged, and the damage positions of the two are the same, as shown in Figure 13c.

4.2.2. Comparison of Test Piece Hysteresis Curve and Skeleton Curve

It can be seen from Figure 14 that, at the initial stage of loading, the hysteresis curves obtained by the test and the finite element calculation are basically consistent; after the peak load is reached, the hysteresis curve of the test specimen is not full enough. This is because the test piece had defects in the welding seam during the test. There were also unstable factors such as the welding heat of the test piece, the uneven machining error, and the material in the test, so the hysteresis curve of the finite element calculation was fuller. The maximum error of the calculated hysteresis curve was 6%. Comparing the hysteresis curves of the two joints, it can be found that the side-plate-reinforced joint specimens are fuller and exhibit good plastic deformation ability.

Figure 15 compares the finite element calculation of the two types of nodes and the skeleton curve obtained from the experiment. Before reaching the yield stage, the skeleton curves of the test and the finite element calculation basically coincide. However, when the load reaches the peak, the two curves begin to separate, and the skeletal curve calculated by the finite element simulation has a relatively small drop. This is because the finite element model does not consider the disadvantages of residual welding stress, and the material is in a relatively ideal state. Comparing the two sets of skeleton curves in Figure 15, it can be seen that the side-plate reinforced nodes have better bearing capacity. Through comparison, it can be found that the finite element simulation of the two specimens is basically consistent with the test results, and the maximum error of the skeleton curve is 8%. The theoretical results are basically consistent with the experimental damage patterns, indicating that the finite element modeling in this paper is effective and can better simulate the real force of the beam–column joints.

4.2.3. Damage Curve Comparison

According to the displacement damage model formula, the damage modulus of the two types of nodes in the finite element analysis was calculated, and the power function was used for fitting. The comparison between the fitting results and the test results is shown in Figure 16. From the outside of the fitting curve [31], the calculated and test values are suitable for fitting with a power function. Corresponding to the hysteresis curve, the model can withstand a larger displacement level during finite element analysis, so the calculation of the two nodes is cumulative. In addition, the plastic damage values are relatively large and the slope of the curve undergoes a process from small to large, which proves that the damage and degradation of the two types of nodes were accelerated. The calculated final damage value of the ordinary joints increases relative to the experimental value, and the slope of the curve at the later stage of loading is significantly reduced.

By comparison, the final damage value of the side-plate reinforced joints and the fitting formula is relatively small, indicating that the finite element analysis of the damage calculation of the side-plate reinforced node was affirmed. However, there are differences in the ordinary node. Nevertheless, the final damage of the side-plate reinforced joint is still higher than that of the ordinary joint, and the energy dissipation time is longer, which is consistent with the conclusion of the experimental damage analysis.

5. Conclusions

(1)

In this test, the beam–column connections buckled at the beam flange and cracking occurred in the welds, and the specimens were then destroyed. The beam–column connections with reinforced side plates can effectively shift the plastic hinge away from the beam end, thus achieving the design goal of outward movement of the plastic hinge.

(2)

The comparison between NBN and SRN showed that SRN has a higher ultimate bearing capacity and a fully developed ductility performance, and a more significant outward movement of its plastic hinge. After the ultimate load was reached, the two connections begin to experience damage, but not stress concentration. This showed that both connections have good seismic performance.

(3)

By comparing the results of the numerical simulation and the structural test of NBN and SRN, the failure mode and the hysteresis curves were basically consistent, thus verifying the validity of the finite element analysis model and the accuracy of the finite element model parameters.