PSJD-2 4 × C22 A8@65/100 4×C10 + 4×SMA 2.2.1. SMA Materials

bars (10 mm) 0.800 0.25 model test *2.2. Materials*  2.2.1. SMA Materials The Ni–Ti shape memory alloy bar used in this test was customized in Baoji Long Qiangfeng Titanium Industry Co., Ltd (Baoji, China). The chemical composition was approximately as follows: Ni: 54.38%; Ti: 45.575%; others: 0.045%. The length and diameter of the fabricated dumbbell-shaped SMA bar specimens were 130 mm and 10 mm, respectively.

The Ni–Ti shape memory alloy bar used in this test was customized in Baoji Long

Studies have shown that [37,40] heat treatment can greatly improve the super-elas-

ticity of SMA bars. The heat treatment process used in this experiment was as follows: the SMA specimens were placed in a high-temperature furnace with a constant temperature of 400 °C for 25 min, and the water was taken out immediately after the end. In order to further stabilize the mechanical properties of SMA bars, the specimens after heat treatment were placed in boiling water and ice water for 3 min, and the above cold and hot cycles were repeated five times. The cyclic tensile test of SMA bars was carried out according to the strain amplitude (1%, 2%, …, 8%). The cyclic loading and unloading at all levels were carried out once, the strain rate was 0.0015 s−1, and the test room temperature

Qiangfeng Titanium Industry Co., Ltd (Baoji, China). The chemical composition was approximately as follows: Ni: 54.38%; Ti: 45.575%; others: 0.045%. The length and diameter

Studies have shown that [37,40] heat treatment can greatly improve the super-elasticity of SMA bars. The heat treatment process used in this experiment was as follows: the SMA specimens were placed in a high-temperature furnace with a constant temperature of 400 ◦C for 25 min, and the water was taken out immediately after the end. In order to further stabilize the mechanical properties of SMA bars, the specimens after heat treatment were placed in boiling water and ice water for 3 min, and the above cold and hot cycles were repeated five times. The cyclic tensile test of SMA bars was carried out according to the strain amplitude (1%, 2%, . . . , 8%). The cyclic loading and unloading at all levels were carried out once, the strain rate was 0.0015 s−<sup>1</sup> , and the test room temperature was 25 ◦C. The constant temperature heating furnace for heat treatment and the tensile test loading device are shown in Figure 3. The properties of the Ni–Ti alloy after heat treatment are shown in Table 2. *Materials* **2022**, *15*, x FOR PEER REVIEW 5 of 27 was 25 °C. The constant temperature heating furnace for heat treatment and the tensile test loading device are shown in Figure 3. The properties of the Ni–Ti alloy after heat treatment are shown in Table 2.

(**a**) (**b**)

device.

**Material.** 

shown in Table 4.

**Figure 3.** Heating and loading test device: (**a**) Thermostatic heating furnace; (**b**) SMA rod tensile test **Figure 3.** Heating and loading test device: (**a**) Thermostatic heating furnace; (**b**) SMA rod tensile test device.


**Table 2.** Material properties of the Ni–Ti alloy. **Table 2.** Material properties of the Ni–Ti alloy.

Ni–Ti 7800 65.4 600 390 4.5 2.2.2. Steel Plate, Reinforced Steel, and Concrete Materials

2.2.2. Steel Plate, Reinforced Steel, and Concrete Materials The steel plate material used in this test were Q235 (ordinary carbon structural steel and had a nominal design yield strength of 235 MPa), and the specific size of the steel plate is shown in Figure 4. The beam column longitudinal steel bar selection model for HRB400 (its standard value of yield strength is 400 MPa), the stirrup selection of HPB300 (similar as HRB400, its standard value of yield strength is 300 MPa), and the mechanical The steel plate material used in this test were Q235 (ordinary carbon structural steel and had a nominal design yield strength of 235 MPa), and the specific size of the steel plate is shown in Figure 4. The beam column longitudinal steel bar selection model for HRB400 (its standard value of yield strength is 400 MPa), the stirrup selection of HPB300 (similar as HRB400, its standard value of yield strength is 300 MPa), and the mechanical properties of the steel parameters are shown in Table 3. The measured results of the compressive strength of the concrete cube (dimensions: 100 × 100 × 100 mm) test block are shown in Table 4.

properties of the steel parameters are shown in Table 3. The measured results of the compressive strength of the concrete cube (dimensions: 100 ×100 × 100 mm) test block are

**Type of Steel Bar** 

**Figure 4.** Dimensions of the steel plate (unit: mm). **Figure 4.** Dimensions of the steel plate (unit: mm).



**Table 4.** Concrete test block measurement results. **Table 4.** Concrete test block measurement results.


#### *2.3. Load Equipment*

room temperature.

*2.3. Load Equipment*  In order to be close to the actual stress state of the joint, the steel box was set at the lower end of the column, the spherical steel hinge was welded on the steel box in the specimen fabrication process, and the spherical hinge with a loading jack was used at the upper end of the column. At the same time, considering the influence of the beam-column self-weight, the specimen was installed by the vertical beam of the column in the horizontal direction, and the lateral support of the specimen was realized by connecting the scaffolding with the reaction wall. The schematic diagram of the test loading device is shown in Figure 5. Figure 6 shows the scene photos of the loading test. The effect of temperature In order to be close to the actual stress state of the joint, the steel box was set at the lower end of the column, the spherical steel hinge was welded on the steel box in the specimen fabrication process, and the spherical hinge with a loading jack was used at the upper end of the column. At the same time, considering the influence of the beamcolumn self-weight, the specimen was installed by the vertical beam of the column in the horizontal direction, and the lateral support of the specimen was realized by connecting the scaffolding with the reaction wall. The schematic diagram of the test loading device is shown in Figure 5. Figure 6 shows the scene photos of the loading test. The effect of temperature on the performance of the joint is difficult to achieve, so all the tests were carried out at room temperature.

on the performance of the joint is difficult to achieve, so all the tests were carried out at

**Figure 5.** Schematic diagram of the test setup. **Figure 5.** Schematic diagram of the test setup. **Figure 5.** Schematic diagram of the test setup.

**Figure 6.** Photo of the test setup. **Figure 6.** Photo of the test setup. **Figure 6.** Photo of the test setup.

#### *2.4. Layout of Test Points 2.4. Layout of Test Points 2.4. Layout of Test Points*

The resistance strain gauges were affixed to the concrete surface of the longitudinal reinforcement, the SMA reinforcement, and the plastic hinge area of the beam-column member to measure the strain at the corresponding position. The strain gauges used on the steel bar inside the joint specimens were BX120–3AA, and those of the concrete surface The resistance strain gauges were affixed to the concrete surface of the longitudinal reinforcement, the SMA reinforcement, and the plastic hinge area of the beam-column member to measure the strain at the corresponding position. The strain gauges used on the steel bar inside the joint specimens were BX120–3AA, and those of the concrete surface The resistance strain gauges were affixed to the concrete surface of the longitudinal reinforcement, the SMA reinforcement, and the plastic hinge area of the beam-column member to measure the strain at the corresponding position. The strain gauges used on the steel bar inside the joint specimens were BX120–3AA, and those of the concrete surface were BX120–50AA. The strain gauge arrangement of the specimen is shown in Figure 7.

were BX120–50AA. The strain gauge arrangement of the specimen is shown in Figure 7. Considering that the overall size of the component in this test was relatively small, and

were BX120–50AA. The strain gauge arrangement of the specimen is shown in Figure 7. Considering that the overall size of the component in this test was relatively small, and

measure the plastic hinge length of each specimen more accurately, the high-precision non-contact full-field strain measurement system (video image correlate-3d, VIC-3D, Correlated Solutions, Inc., Columbia, SC, USA) based on digital image technology was se-

measure the plastic hinge length of each specimen more accurately, the high-precision non-contact full-field strain measurement system (video image correlate-3d, VIC-3D, Correlated Solutions, Inc., Columbia, SC, USA) based on digital image technology was se-

Considering that the overall size of the component in this test was relatively small, and there was an inevitable slight vibration in the process of low cyclic loading, in order to measure the plastic hinge length of each specimen more accurately, the high-precision noncontact full-field strain measurement system (video image correlate-3d, VIC-3D, Correlated Solutions, Inc., Columbia, SC, USA) based on digital image technology was selected to replace the conventional displacement meter for measurement. The VIC-3D system can measure the full-field three-dimensional displacement and strain of the surface of the object under test and has low environmental requirements. In principle, clear images of the area under the test can be taken indoors and outdoors. The accuracy and feasibility of digital image correlation technology and VIC-3D based on this technology have been proven [41–45]. lected to replace the conventional displacement meter for measurement. The VIC-3D system can measure the full-field three-dimensional displacement and strain of the surface of the object under test and has low environmental requirements. In principle, clear images of the area under the test can be taken indoors and outdoors. The accuracy and feasibility of digital image correlation technology and VIC-3D based on this technology have been proven [41–45]. The measurement range was drawn in the beam-column connection area. Speckles with a diameter not less than 2 mm were arranged in the measurement range, and the correction plate with a side length of 20 mm was selected to correct. The camera was set

The measurement range was drawn in the beam-column connection area. Speckles with a diameter not less than 2 mm were arranged in the measurement range, and the correction plate with a side length of 20 mm was selected to correct. The camera was set up in place and focus, and the vertical displacement value Y at any position in the measurement range can be measured by the measurement system. According to the calculation needs, seven measuring points were selected along the beam end in this experiment, and the distance between each measuring point was 60 mm. The measurement range size and the specific location of the selected measuring points are shown in Figure 8. The vertical displacement of each point is recorded as Y1, Y2, . . . , Y6, Y7. If a plastic hinge is formed between the measuring points marked *n* (1 ≤ *n* ≤ 7) from the beam-column junction, the spacing of each measuring point after the measuring point along the beam length should be the initial 60 mm, and the vertical displacement of the next measuring point is denoted as Yn+1, and so on. If ∆1 = Y*n*+1 − Y*n*, ∆2 = Y*n*+2 − Y*n*, . . . , ∆*K* = Y*n*+*<sup>K</sup>* − Y*<sup>n</sup>* (2 ≤ *K* ≤ 6), then ∆1, ∆2, ∆*K* should satisfy Equation (1) as follows: up in place and focus, and the vertical displacement value Y at any position in the measurement range can be measured by the measurement system. According to the calculation needs, seven measuring points were selected along the beam end in this experiment, and the distance between each measuring point was 60 mm. The measurement range size and the specific location of the selected measuring points are shown in Figure 8. The vertical displacement of each point is recorded as Y1, Y2, …, Y6, Y7. If a plastic hinge is formed between the measuring points marked *n* (1 ≤ *n* ≤ 7) from the beam-column junction, the spacing of each measuring point after the measuring point along the beam length should be the initial 60 mm, and the vertical displacement of the next measuring point is denoted as Yn+1, and so on. If Δ1 = Y*n*+1 − Y*n*, Δ2 = Y*n*+2 − Y*n*, …, Δ*K* = Y*n*+*<sup>K</sup>* − Y*n* (2 ≤ *K* ≤ 6), then Δ1, Δ2, Δ*K* should satisfy Equation (1) as follows: 3 60 60 3 2 60 2 60 <sup>1</sup> sin × <sup>Δ</sup> <sup>=</sup> <sup>=</sup> <sup>×</sup> <sup>Δ</sup> <sup>=</sup> <sup>×</sup> <sup>Δ</sup> <sup>=</sup> <sup>Δ</sup> <sup>=</sup> *<sup>n</sup> K* α. (1)

$$
\sin a = \frac{\Delta 1}{60} = \frac{\Delta 2}{2 \times 60} = \frac{\Delta 3}{3 \times 60} = \dots = \frac{\Delta K}{n \times 60} \tag{1}
$$

Here, *α* is an angle which is between the axis of the undeformed beam outside the end point of the plastic hinge and the horizontal direction, as shown in Figure 9. The *n* value of Equation (1) is the plastic hinge end point. Considering the inevitable measurement error, the absolute value of the sinusoidal difference obtained by Equation (1) is not greater than 1.0 <sup>×</sup> <sup>10</sup>−<sup>4</sup> . It can be approximately equal, and the solution schematic diagram is shown in Figure 9. The measured plastic hinge length calculated for each node is shown in Table 5. value of Equation (1) is the plastic hinge end point. Considering the inevitable measurement error, the absolute value of the sinusoidal difference obtained by Equation (1) is not greater than 1.0 × 10−4. It can be approximately equal, and the solution schematic diagram is shown in Figure 9. The measured plastic hinge length calculated for each node is shown in Table 5.

**Figure 7.** Strain gauge arrangement. **Figure 7.** Strain gauge arrangement.

**Figure 8.** VIC-3D measuring area and the measuring point arrangement. **Figure 8.** VIC-3D measuring area and the measuring point arrangement. **Figure 8.** VIC-3D measuring area and the measuring point arrangement.

**Figure 9.** Schematic diagram of the plastic hinge length judgment principle (unit: mm). **Figure 9.** Schematic diagram of the plastic hinge length judgment principle (unit: mm). **Figure 9.** Schematic diagram of the plastic hinge length judgment principle (unit: mm).

**Table 5.** Measured and calculated value of the plastic hinge length of each node. **Table 5.** Measured and calculated value of the plastic hinge length of each node. **Table 5.** Measured and calculated value of the plastic hinge length of each node.


The vertical load was applied to the top of the column before cyclic loading, and the axial force was kept constant after the axial force was relatively stable. The experimental control of the axial compression ratio was 0.25, while the actual vertical load value was

The vertical load was applied to the top of the column before cyclic loading, and the axial force was kept constant after the axial force was relatively stable. The experimental control of the axial compression ratio was 0.25, while the actual vertical load value was

*2.5. Loading History* 

*2.5. Loading History* 

## *2.5. Loading History*

The vertical load was applied to the top of the column before cyclic loading, and the axial force was kept constant after the axial force was relatively stable. The experimental control of the axial compression ratio was 0.25, while the actual vertical load value was 445 kN. The low cyclic loading test of the joint specimen adopted the whole process displacement control method, and the loading rate was 0.2 mm/s. In this experiment, before the specimen yield, the increment of displacement grading loading was 1 mm, and each stage was recycled twice. After the specimen yield, the yield displacement was denoted as ∆, and it was then loaded by an integral multiple of ∆. Each stage was cycled twice. The loading was terminated when the load dropped to 85% of the ultimate load; otherwise, the component was damaged, as shown in Figure 10. 445 kN. The low cyclic loading test of the joint specimen adopted the whole process displacement control method, and the loading rate was 0.2 mm/s. In this experiment, before the specimen yield, the increment of displacement grading loading was 1 mm, and each stage was recycled twice. After the specimen yield, the yield displacement was denoted as Δ, and it was then loaded by an integral multiple of Δ. Each stage was cycled twice. The loading was terminated when the load dropped to 85% of the ultimate load; otherwise, the component was damaged, as shown in Figure 10.

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**Figure 10.** Loading protocol. **Figure 10.** Loading protocol.

#### **3. Results and Analysis**

#### **3. Results and Analysis**  *3.1. Test Phenomenon*

*3.1. Test Phenomenon*  3.1.1. Comparison Test Piece PJD-1

3.1.1. Comparison Test Piece PJD-1 Specimen PJD-1 was a comparative joint with ordinary steel bars at the beam end. When the loading displacement was 2.0 mm, the first oblique crack appeared in the middle of the beam, with a length of 6.45 cm and a width of 0.10 mm. At the same time, the vertical crack with a length of 4.3 cm and a width of 0.2 mm developed at the root of the beam. The load–displacement curve gradually deviated from the straight line, and the specimen entered the yield stage. When the loading control displacement was one times the yield displacement, the first small crack appears at the bottom of the beam (19 cm away from the core area of the node), and the crack length was 4.16 cm. When the loading control displacement was three times the yield displacement, the vertical cracks at the root of the beam and the oblique cracks in the middle of the beam were successively penetrated from up to down, and were developed in the surroundings, resulting in many small de-Specimen PJD-1 was a comparative joint with ordinary steel bars at the beam end. When the loading displacement was 2.0 mm, the first oblique crack appeared in the middle of the beam, with a length of 6.45 cm and a width of 0.10 mm. At the same time, the vertical crack with a length of 4.3 cm and a width of 0.2 mm developed at the root of the beam. The load–displacement curve gradually deviated from the straight line, and the specimen entered the yield stage. When the loading control displacement was one times the yield displacement, the first small crack appears at the bottom of the beam (19 cm away from the core area of the node), and the crack length was 4.16 cm. When the loading control displacement was three times the yield displacement, the vertical cracks at the root of the beam and the oblique cracks in the middle of the beam were successively penetrated from up to down, and were developed in the surroundings, resulting in many small development cracks. At six times the yield displacement, the peak load of the specimen reached 54.72 kN; at 11 times the yield displacement, the load value of the specimen decreased from 50.08 kN to 37.45 kN, and the test ended. At this point, the vertical main crack at the root of the beam was relatively wide, the concrete at the upper and lower sides of the root was obviously crushed, and the concrete of the protective layer was stripped, as shown in Figure 11a.

velopment cracks. At six times the yield displacement, the peak load of the specimen reached 54.72 kN; at 11 times the yield displacement, the load value of the specimen decreased from 50.08 kN to 37.45 kN, and the test ended. At this point, the vertical main crack at the root of the beam was relatively wide, the concrete at the upper and lower sides

The SJD specimen was the comparison node, where the longitudinal bars at the beam

end were all SMA bars. When the loading displacement was 1.0 mm, the first vertical crack appeared at the root of the specimen, and the length of the crack was about 3.12 cm. When the reverse loading was carried out, the root crack had been quickly penetrated, and the crack width was about 0.3 mm. The load–displacement curve had deviated from the straight line, and the specimen entered the yield stage. When the loading control displacement was four times the yield displacement, the crack width increased, and a small

as shown in Figure 11a.

3.1.2. Comparison Test Piece SJD-1

#### 3.1.2. Comparison Test Piece SJD-1

The SJD specimen was the comparison node, where the longitudinal bars at the beam end were all SMA bars. When the loading displacement was 1.0 mm, the first vertical crack appeared at the root of the specimen, and the length of the crack was about 3.12 cm. When the reverse loading was carried out, the root crack had been quickly penetrated, and the crack width was about 0.3 mm. The load–displacement curve had deviated from the straight line, and the specimen entered the yield stage. When the loading control displacement was four times the yield displacement, the crack width increased, and a small amount of the surface concrete at the root of the beam fell off. At 17 times the yield displacement, a low 'boom' sound was heard, and the load value of the specimen reached 31.66 kN. When the load continued, the load value of the specimen immediately dropped to 16.27 kN, and the test ended. At this point, the vertical main crack at the root of the beam was wider than that at the PJD-1 node, but there was no obvious damage to the upper and lower concrete at the root of the beam, as shown in Figure 11b.

#### 3.1.3. Test Piece PSJD-1 and Test Piece PSJD-2

Both PSJD-1 and PSJD-2 are model test joints with SMA bars and steel endplates. Taking the specimen PSJD-1 as an example, the loading process of this new type of joint was introduced. When the loading displacement was 2.0 mm, the first vertical crack appeared at the root of the beam, with a length of about 9.5 cm and a width of about 0.1 mm. There was no obvious oblique crack in the middle of the beam. When the displacement was controlled to 3 mm, the load–displacement curve begun to deviate from the straight line, the crack width was 0.2 mm, and the crack length reached 10.60 cm; the specimen thus entered the yield stage. When the loading control displacement was three times the yield displacement, the crack width reached 2.0 mm, the residual crack width after unloading was 1.2 mm, and the cracks in the root and middle of the beam were successively penetrated. At seven times the yield displacement, the concrete at the root of the beam showed spalling. At ten times the yield displacement, the load value began to decrease with the low 'boom' sound inside the specimen (which is believed to be the connection fracture between the steel plate and the longitudinal reinforcement), and the final load value of the specimen decreased from 56.11 kN to 46.02 kN. At this point, the crack width of the vertical main crack at the root of the beam was significantly smaller than that of the PJD-1 node, and the compressive area and the stripping volume of the concrete at the upper and lower sides of the root were smaller than those of the PJD-1 node, as shown in Figure 11c.

The first half of the loading process of the PSJD-2 specimen was similar to that of the PSJD-1. When the loading displacement was 2.0 mm, the first vertical crack appeared at the root of the beam, with a length of about 12.0 cm and a width of about 0.1 mm. When the loading displacement was controlled to 4 mm, the root crack width reached 0.5 mm, and the root crack had been penetrated. The first crack appeared in the middle of the beam component, and the crack length was 22.45 cm. The specimen thus entered the yield stage. When the loading control displacement was three times the yield displacement, the core area of the joint specimen began to peel off the concrete block, the root crack width reached 2.0 mm, and the middle crack width reached 1.0 mm. However, when the load was four times the yield displacement, the abnormal sound, similar to that heard in the PSJD-1 experiment, was heard early and originated from inside the specimen, and the load value then immediately decreased from 81.78 kN to 65.80 kN. The specimen thus failed immediately. Due to the relatively early failure of the specimen, the node final crack was smaller than that of the PSJD-1 joint, and there were no obvious signs of concrete compression and spalling, as shown in Figure 11d.

**Figure 11.** Failure modes of the specimens: (**a**) PJD-1; (**b**) SJD-1; (**c**) PSJD-1; (**d**) PSJD-2. **Figure 11.** Failure modes of the specimens: (**a**) PJD-1; (**b**) SJD-1; (**c**) PSJD-1; (**d**) PSJD-2.

#### *3.2. Beam End Load–Displacement Hysteresis Curve 3.2. Beam End Load–Displacement Hysteresis Curve*

The hysteresis curves of each specimen in this test are shown in Figure 12. The hysteresis curves of each specimen in this test are shown in Figure 12.


self-centering ability.

obviously 'flag-shaped'. After each loading stage is completely unloaded, the residual deformation of the node is very small, indicating that the new node has a good

**Figure 12.** Hysteresis loops of the joint specimens: (**a**) PJD-1; (**b**) SJD-1; (**c**) PSJD-1; (**d**) PSJD-2.

#### *3.3. Skeleton Curve*

*3.3. Skeleton Curve* 

As an important basis for restoring the force model and nonlinear seismic response analysis, the skeleton curve reflects the deformation, energy consumption, and stiffness degradation of specimens in different stages. The skeleton curve of each node in this test is shown in Figure 13. As the failure of the PSJD-2 specimen is relatively early, this paper mainly analyzes the skeleton curves of the other three specimens. **Figure 12.** Hysteresis loops of the joint specimens: (**a**) PJD-1; (**b**) SJD-1; (**c**) PSJD-1; (**d**) PSJD-2. As an important basis for restoring the force model and nonlinear seismic response analysis, the skeleton curve reflects the deformation, energy consumption, and stiffness degradation of specimens in different stages. The skeleton curve of each node in this test is shown in Figure 13. As the failure of the PSJD-2 specimen is relatively early, this paper mainly analyzes the skeleton curves of the other three specimens.

**Figure 13.** Envelope curves of the specimens. **Figure 13.** Envelope curves of the specimens.

The following conclusions can be drawn from Figure 13.


#### SJD-1 joint decreases rapidly after yield. However, the bearing capacity of the new *3.4. Residual Displacement of the Beam End*

shown in Figure 14.

joint PSJD-1 is relatively stable after yield and can withstand relatively larger deformation, indicating that the built-in super-elastic SMA reinforcement-steel end plate can delay the yield of the joint to a certain extent and improve the ductility and damage resistance of the joint. The residual displacement of the beam end refers to the residual plastic deformation of the beam end after unloading, and its value can reflect the self-centering ability of the component. The beam end loading-residual displacement curve of each joint specimen is shown in Figure 14.

The residual displacement of the beam end refers to the residual plastic deformation

of the beam end after unloading, and its value can reflect the self-centering ability of the component. The beam end loading-residual displacement curve of each joint specimen is

*3.4. Residual Displacement of the Beam End* 

30

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**Figure 14.** Residual displacement of the beam end after unloading. **Figure 14.** Residual displacement of the beam end after unloading. built-in super-elastic SMA tendons is less than that of the PJD-1 node under the same

It can be seen in the graph that the residual displacement of the three nodes with the built-in super-elastic SMA tendons is less than that of the PJD-1 node under the same loading level. When the peak displacement of the beam end is 30 mm, the recoverable deformation of the PJD-1 joint is 25%, while that of the PSJD-1 joint is 57% (the residual deformation of the beam end is 13 mm); due to the poor anchorage between the SMA bars and the concrete, the failure of the SJD-1 joint occurs earlier (the maximum loading displacement of the beam end is only 20 mm), but the residual displacement of the SJD-1 joint is still less than that of the PJD-1 joint. This shows that, under a certain loading amplitude, the built-in SMA reinforcement can significantly improve the self-centering ability of the It can be seen in the graph that the residual displacement of the three nodes with the built-in super-elastic SMA tendons is less than that of the PJD-1 node under the same loading level. When the peak displacement of the beam end is 30 mm, the recoverable deformation of the PJD-1 joint is 25%, while that of the PSJD-1 joint is 57% (the residual deformation of the beam end is 13 mm); due to the poor anchorage between the SMA bars and the concrete, the failure of the SJD-1 joint occurs earlier (the maximum loading displacement of the beam end is only 20 mm), but the residual displacement of the SJD-1 joint is still less than that of the PJD-1 joint. This shows that, under a certain loading amplitude, the built-in SMA reinforcement can significantly improve the self-centering ability of the node. loading level. When the peak displacement of the beam end is 30 mm, the recoverable deformation of the PJD-1 joint is 25%, while that of the PSJD-1 joint is 57% (the residual deformation of the beam end is 13 mm); due to the poor anchorage between the SMA bars and the concrete, the failure of the SJD-1 joint occurs earlier (the maximum loading displacement of the beam end is only 20 mm), but the residual displacement of the SJD-1 joint is still less than that of the PJD-1 joint. This shows that, under a certain loading amplitude, the built-in SMA reinforcement can significantly improve the self-centering ability of the node. *3.5. Energy Consumption Capacity* 

#### node. *3.5. Energy Consumption Capacity* The structure dissipates the ground motion energy mainly through plastic defor-

*3.5. Energy Consumption Capacity*  The structure dissipates the ground motion energy mainly through plastic deformation, and the seismic performance of the structure can be reflected by the energy dissipation capacity. The energy dissipation value of each specimen under different load dis-The structure dissipates the ground motion energy mainly through plastic deformation, and the seismic performance of the structure can be reflected by the energy dissipation capacity. The energy dissipation value of each specimen under different load displacement can be obtained by calculating the enclosed area of the hysteresis curve in Figure 12, as shown in Figure 15. Figure 15 shows the energy dissipation curve of the four node specimens. mation, and the seismic performance of the structure can be reflected by the energy dissipation capacity. The energy dissipation value of each specimen under different load displacement can be obtained by calculating the enclosed area of the hysteresis curve in Figure 12, as shown in Figure 15. Figure 15 shows the energy dissipation curve of the four node specimens.

0 **Figure 15.** Energy dissipation capacity. The figure shows the following: **Figure 15.** Energy dissipation capacity.

The figure shows the following:

0 5 10 15 20 25 30 35

*Δ*/mm

The figure shows the following: at the beam end of the PSJD-1 node and the PSJD-2 node is greater than that of the

(1) When the specimen is in the elastic stage, the steel bars and SMA bars in the joint do not yield, and the energy dissipation capacity of each joint is very low. PJD-1 node, and the slope of the SJD-1 node is the smallest, indicating that the energy dissipation capacity of the new node is better than that of the ordinary node, while

(1) When the specimen is in the elastic stage, the steel bars and SMA bars in the joint do

(2) When the specimen is in the plastic stage, the slope of the displacement–energy curve

not yield, and the energy dissipation capacity of each joint is very low.

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#### *3.6. Stiffness Degradation* We selected the ring stiffness K as an index to evaluate the stiffness degradation of

We selected the ring stiffness K as an index to evaluate the stiffness degradation of the beam-column joints. The obtained stiffness–ductility coefficient curve is shown in Figure 16. the beam-column joints. The obtained stiffness–ductility coefficient curve is shown in Figure 16.

**Figure 16.** Curves of stiffness degradation. **Figure 16.** Curves of stiffness degradation.

The following conclusions can be drawn from Figure 16:


low. After the concrete cracks, the penetrating cracks are quickly formed, and the stiffness decreases rapidly. When the ductility coefficient is greater than 1, the stiff-

of concrete cracking out of work, the stiffness ratio increases, and the SMA tendons

the ductility coefficient is less than 1, the stiffness degradation rates of the PSJD-1 and

(3) Comparing the PSJD-1 node, the PSJD-2 node, and the PJD-1 node shows that, when

have excellent super-elasticity.

concrete cracking out of work, the stiffness ratio increases, and the SMA tendons have excellent super-elasticity. thus loses comparability, the stiffness of the PSJD-1 node is greater than that of the ordinary node, and the degradation rate is slower. This shows that the stiffness deg-

PSJD-2 nodes are significantly smaller than those of ordinary nodes. When the ductility coefficient is greater than 1, although the premature failure of the internal components of the PSJD-2 node causes the stiffness of the node to rapidly degrade, and

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(3) Comparing the PSJD-1 node, the PSJD-2 node, and the PJD-1 node shows that, when the ductility coefficient is less than 1, the stiffness degradation rates of the PSJD-1 and PSJD-2 nodes are significantly smaller than those of ordinary nodes. When the ductility coefficient is greater than 1, although the premature failure of the internal components of the PSJD-2 node causes the stiffness of the node to rapidly degrade, and thus loses comparability, the stiffness of the PSJD-1 node is greater than that of the ordinary node, and the degradation rate is slower. This shows that the stiffness degradation rate of the node can be delayed with a built-in SMA reinforcement-steel end plate, so that the lateral displacement margin of the structure is larger, which can effectively improve the seismic performance of the structure. radation rate of the node can be delayed with a built-in SMA reinforcement-steel end plate, so that the lateral displacement margin of the structure is larger, which can effectively improve the seismic performance of the structure. **4. Numerical Simulation**  *4.1. Model Establishment and Verification*  4.1.1. Constitutive Model of SMA Material The self-centering 'double flag' constitutive model developed by Ferdinando Auric-

#### **4. Numerical Simulation** chio [46] based on OpenSees is selected, as shown in Figure 17. The constitutive descrip-


The self-centering 'double flag' constitutive model developed by Ferdinando Auricchio [46] based on OpenSees is selected, as shown in Figure 17. The constitutive description of the SMA material is relatively complex, and this model simplifies the constitutive curve of the material into three stages: elasticity, phase transformation and hardening. The corresponding rules are as follows: The corresponding rules are as follows: 1. In the elastic stage, when the stress does not exceed σ *<sup>y</sup>* , the loading and unloading processes develop linearly with stiffness <sup>1</sup> *k* . 2. In the phase transformation stage, when the stress value exceeds σ*<sup>y</sup>* , continuous


The definition of this constitutive model in OpenSees is implemented with seven pa-

**Parameter Physical Significance Value** 

**Figure 17.** Self-centering constitutive model. **Figure 17.** Self-centering constitutive model.

rameters. Parameter values are shown in Table 6.

The definition of this constitutive model in OpenSees is implemented with seven parameters. Parameter values are shown in Table 6. <sup>1</sup> *k* First stiffness (N/mm) 75,000


**Table 6.** SMA simplified constitutive model parameters and values. <sup>2</sup> *k* Second stiffness (N/mm) 1827

4.1.2. Constitutive Model of the Steel Bar and the Steel Plate 4.1.2. Constitutive Model of the Steel Bar and the Steel Plate

The constitutive model of the steel bar and steel plate shown in Figure 18 is the Steel 02 model, proposed by Menegotto and Pinto [47], and modified by Filippou [48]. The model not only considers isotropic strain hardening, but also reflects the influence of the Bauschinger effect. It has a high computational efficiency and good numerical stability. The constitutive model of the steel bar and steel plate shown in Figure 18 is the Steel 02 model, proposed by Menegotto and Pinto [47], and modified by Filippou [48]. The model not only considers isotropic strain hardening, but also reflects the influence of the Bauschinger effect. It has a high computational efficiency and good numerical stability.

where

σ

eq and eq

ε

The constitutive relationship expressions of the Steel 02 model are shown in Equations (2)–(5): The constitutive relationship expressions of the Steel 02 model are shown in Equations (2)–(5):

$$
\sigma\_{\epsilon q} = b \varepsilon\_{\epsilon q} + \frac{(1 - b)\varepsilon\_{\epsilon q}}{\left(1 + \varepsilon\_{\epsilon q}^R\right)^{\frac{1}{R}}} \tag{2}
$$

$$
\sigma\_{\text{eq}} = \frac{\sigma - \sigma\_r}{\sigma\_0 - \sigma\_r}^{'} \tag{3}
$$

$$
\varepsilon\_{eq} = \frac{\varepsilon - \varepsilon\_r}{\varepsilon\_0 - \varepsilon\_r} \tag{4}
$$

(3)

(4)

represent

$$R = R\_0 - \frac{\mathbf{a\_1}\mathbf{\tilde{g}}}{\mathbf{a\_2} + \mathbf{\tilde{g}}} \tag{5}$$
 
$$\mathbf{a\_3} = \mathbf{a\_4} + \mathbf{a\_5} \quad \text{and} \quad \mathbf{a\_6} = \mathbf{a\_1} + \mathbf{a\_2} \tag{6}$$

ξ

σ

<sup>r</sup> and <sup>r</sup>

ε

σ

<sup>0</sup> and <sup>0</sup>

ε

represent the stress and

2

0 a

strain of the rebar at the yield point; <sup>1</sup> a and <sup>2</sup> a represent the curvature degradation coefficients; *R* and *R*0 represent the transition curve curvature coefficient and the initial

*r eq ε ε <sup>ε</sup>* <sup>−</sup> 0 ξ <sup>+</sup> <sup>=</sup> <sup>−</sup> 1 <sup>a</sup> *<sup>R</sup> <sup>R</sup>* , (5) where *σeq* and *εeq* represent the normalized stress and strain; *σ*<sup>0</sup> and *ε*<sup>0</sup> represent the stress and strain of the rebar in the initial state; *σ<sup>r</sup>* and *ε<sup>r</sup>* represent the stress and strain of the rebar at the yield point; a<sup>1</sup> and a<sup>2</sup> represent the curvature degradation coefficients; *R*

and *R*<sup>0</sup> represent the transition curve curvature coefficient and the initial curve curvature coefficient; *b* and *ξ* represent the hardening coefficient of reinforcement and the plastic strain in the semi-periodic cycle. ment and the plastic strain in the semi-periodic cycle. 4.1.3. Theoretical Model of Concrete

ξ

represent the hardening coefficient of reinforce-

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#### 4.1.3. Theoretical Model of Concrete There are three kinds of concrete constitutive models commonly used in OpenSees:

curve curvature coefficient; b and

There are three kinds of concrete constitutive models commonly used in OpenSees: the Concrete 01 model with zero tensile strength, the Concrete 02 model with linear tensile softening, and the Concrete 03 model with nonlinear tensile softening [48]. For the concrete at the joint, its tensile strength can be ignored from a macro perspective. Therefore, for this simulation we selected Concrete 01 as the constitutive model of concrete, as shown in Figure 19. the Concrete 01 model with zero tensile strength, the Concrete 02 model with linear tensile softening, and the Concrete 03 model with nonlinear tensile softening [48]. For the concrete at the joint, its tensile strength can be ignored from a macro perspective. Therefore, for this simulation we selected Concrete 01 as the constitutive model of concrete, as shown in Figure 19.

tions (6)–(10):

the concrete.

In the Concrete 01 model [49], the constitutive relation expression is shown in Equa-In the Concrete 01 model [49], the constitutive relation expression is shown in Equations (6)–(10):

$$\text{when } \varepsilon < \varepsilon\_{0\prime}, f = Kf\_{\varepsilon} \left[ \frac{2\varepsilon\_{\varepsilon}}{\varepsilon\_{0}} - \left( \frac{\varepsilon\_{\varepsilon}}{\varepsilon\_{0}} \right)^{2} \right] \tag{6}$$

$$\varepsilon < \varepsilon < \varepsilon < \dots < \varepsilon < \dots \tag{7}$$

$$\begin{array}{cccc}\downarrow & \downarrow & \downarrow \\ \text{when } \varepsilon\_0 \le \varepsilon \le \varepsilon\_{\varepsilon} & f = Kf\_{\varepsilon}[1 - Z(\varepsilon - \varepsilon\_0)] \end{array} \tag{7}$$

$$\begin{array}{ccccc}\hline\\\text{when}\varepsilon > \varepsilon\_{\text{c}} & f = 0.2Kf\_{\text{c}} \\\hline\\\end{array} \tag{8}$$

$$
\varepsilon\_0 = 0.002K \tag{9}
$$

ε

is the peak pressure and strain of

ε

ε

(7)

*c*

$$Z = \frac{0.5}{\frac{3 + 0.29f\_c}{145f\_c} - 0.002K} \tag{10}$$

ε <sup>0</sup> = 0.002*K* (9) 0.5 where *σ<sup>c</sup>* and *ε<sup>c</sup>* represent the stress and strain of the concrete; *f<sup>c</sup>* is the compressive strength of the concrete cylinder; *K* is the strain increase coefficient caused by the constraint; *Z* is the slope of the strain drop segment; *ε*<sup>0</sup> is the peak pressure and strain of the concrete.

*<sup>f</sup> <sup>Z</sup>*

3 0.29

(nonlinear beam column) was selected for simulation. The element is characterized by allowing the stiffness to change along the length of the rod. At the same time, the resistance and stiffness matrix of the control section can be determined. In the nonlinear simulation,

#### 4.1.4. Types of Beam-Column Elements

*K f c <sup>c</sup>* 0.002 145 <sup>−</sup> <sup>+</sup> <sup>=</sup> , (10) where σ <sup>c</sup> and <sup>c</sup> ε represent the stress and strain of the concrete; c*f* is the compressive strength of the concrete cylinder; *K* is the strain increase coefficient caused by the constraint; *Z* is the slope of the strain drop segment; <sup>0</sup> According to the actual situation of the test, the nonlinear beam-column element (nonlinear beam column) was selected for simulation. The element is characterized by allowing the stiffness to change along the length of the rod. At the same time, the resistance and stiffness matrix of the control section can be determined. In the nonlinear simulation, it has the advantages of fast convergence and high effectiveness [49].

it has the advantages of fast convergence and high effectiveness [49].

4.1.4. Types of Beam-Column Elements

4.1.5. Fiber Model

#### 4.1.5. Fiber Model beam-column section. The fiber model based on the assumption of the plane section dibeam-column section. The fiber model based on the assumption of the plane section di-

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The fiber model, with a wide application and a high accuracy, was selected for the beam-column section. The fiber model based on the assumption of the plane section divides the section of the component into a certain number of grids. The center of each grid is regarded as a numerical integration point. The longitudinal micro-section of the grid is defined as fiber. The section is divided into several types of fiber bundles, such as confined and non-confined concrete, and steel bars. By calculating the strain stress of each fiber, the stiffness of the whole section is obtained [50]. vides the section of the component into a certain number of grids. The center of each grid is regarded as a numerical integration point. The longitudinal micro-section of the grid is defined as fiber. The section is divided into several types of fiber bundles, such as confined and non-confined concrete, and steel bars. By calculating the strain stress of each fiber, the stiffness of the whole section is obtained [50]. *4.2. Model Validation and Parameter Analysis*  vides the section of the component into a certain number of grids. The center of each grid is regarded as a numerical integration point. The longitudinal micro-section of the grid is defined as fiber. The section is divided into several types of fiber bundles, such as confined and non-confined concrete, and steel bars. By calculating the strain stress of each fiber, the stiffness of the whole section is obtained [50]. *4.2. Model Validation and Parameter Analysis* 

The fiber model, with a wide application and a high accuracy, was selected for the

The fiber model, with a wide application and a high accuracy, was selected for the

#### *4.2. Model Validation and Parameter Analysis* 4.2.1. Model Validation 4.2.1. Model Validation

#### 4.2.1. Model Validation According to the test results of material properties, various parameters in the finite

According to the test results of material properties, various parameters in the finite element model were set. Based on the actual displacement of each cycle in the test, the displacement-controlled loading simulation analysis of the model was carried out. The hysteresis curves and skeleton curves of the ordinary concrete joint PJD-1 and the new type of joint PSJD-1 with internal SMA reinforcement were compared with the test results, as shown in Figures 20 and 21. According to the test results of material properties, various parameters in the finite element model were set. Based on the actual displacement of each cycle in the test, the displacement-controlled loading simulation analysis of the model was carried out. The hysteresis curves and skeleton curves of the ordinary concrete joint PJD-1 and the new type of joint PSJD-1 with internal SMA reinforcement were compared with the test results, as shown in Figures 20 and 21. element model were set. Based on the actual displacement of each cycle in the test, the displacement-controlled loading simulation analysis of the model was carried out. The hysteresis curves and skeleton curves of the ordinary concrete joint PJD-1 and the new type of joint PSJD-1 with internal SMA reinforcement were compared with the test results, as shown in Figures 20 and 21.

**Figure 20.** Comparison diagram of numerical simulation and experimental hysteresis curves. **Figure 20.** Comparison diagram of numerical simulation and experimental hysteresis curves. **Figure 20.** Comparison diagram of numerical simulation and experimental hysteresis curves.

**Figure 21.** Comparison diagram of numerical simulation and experimental skeleton curves. **Figure 21.** Comparison diagram of numerical simulation and experimental skeleton curves. **Figure 21.** Comparison diagram of numerical simulation and experimental skeleton curves.

Figures 20 and 21 show that the hysteresis curve and the skeleton curve obtained by

Figures 20 and 21 show that the hysteresis curve and the skeleton curve obtained by

Figures 20 and 21 show that the hysteresis curve and the skeleton curve obtained by simulation are basically consistent with the experimental results, and the established model well reflects the self-centering energy dissipation characteristics of the new type of joints. The peak value of forward loading is slightly smaller than that of the test results. Due to the relatively ideal state of the model in the numerical simulation, and many factors such as constraints and measurement on the test site, there are certain differences. However, from the overall perspective, the obtained hysteresis and skeleton curves still well verify the accuracy and effectiveness of the finite element model.

## 4.2.2. Parameter Analysis

In order to further study the new frame joints to further optimize the design, considering that the PSJD-2 joints failed earlier in the test and failed to fully reflect the influence of SMA reinforcement ratio on the related performance of the new joints, based on the verified finite element analysis model, the parameters such as the reinforcement ratio and the axial compression ratio of the built-in SMA bars in the new joints were simulated and analyzed to further quantify their effects on the mechanical properties, such as hysteretic performance, energy dissipation, and the self-centering ability of the new joints.

Based on the conventional ordinary reinforced concrete frame joints, under the same built-in SMA reinforcement mode, the yield strength of the SMA bars is controlled to be the same, and three new joints (XJD) with different SMA bar diameters were considered, namely, XJD-1 with a diameter of 8 mm, XJD-2 with a diameter of 10 mm, and XJD-3 with a diameter of 12 mm. The diameter of the SMA bars was controlled to be the same (10 mm), and three kinds of SMA bars with different yield strengths were considered to study their effects on the seismic performance of the new joint (XJD): XJD-4 had a yield strength of 300 MPa, XJD-2 had a yield strength of 400 MPa, and XJD-5 had a yield strength of 500 MPa. Specific parameter analysis design is shown in Table 7.


**Table 7.** Model parameter analysis scheme.

#### 1. Effect of the SMA Reinforcement Ratio

Figures 22–25 show that, under the condition of suitable reinforcement, the bearing capacity of the new joint also increases significantly with the increase in the diameter of SMA reinforcement. The S-shaped skeleton curve shows that the new joint has good energy dissipation and ductility. With the increase in the diameter of the SMA bars, the overall stiffness increases, but the increase is small, because the Young's modulus of the SMA bars is smaller than that of ordinary steel bars, and the influence of ordinary steel bars on the overall stiffness is small.

**Figure 22.** Hysteretic force–displacement curve of different diameters. **Figure 22.** Hysteretic force–displacement curve of different diameters. **Figure 22.** Hysteretic force–displacement curve of different diameters. **Figure 22.** Hysteretic force–displacement curve of different diameters.

**Figure 23.** The skeleton curve of different diameters. **Figure 23.** The skeleton curve of different diameters. **Figure 23.** The skeleton curve of different diameters. **Figure 23.** The skeleton curve of different diameters.

**Figure 24.** Stiffness degradation curve of different diameters. **Figure 24.** Stiffness degradation curve of different diameters. **Figure 24.** Stiffness degradation curve of different diameters.

**Figure 24.** Stiffness degradation curve of different diameters.

15 20

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**Figure 25.** Residual deformation curves with different diameters. **Figure 25.** Residual deformation curves with different diameters. In the initial state, increasing the diameter of SMA reinforcement has little effect on the residual deformation of the new node. With the increase in the number of cycles, the

In the initial state, increasing the diameter of SMA reinforcement has little effect on the residual deformation of the new node. With the increase in the number of cycles, the final residual deformation of XJD-3 is reduced by nearly 28% compared with that of XJD-1, indicating that, under the premise of suitable reinforcement, increasing the diameter of SMA reinforcement can significantly improve the self-centering performance of the new In the initial state, increasing the diameter of SMA reinforcement has little effect on the residual deformation of the new node. With the increase in the number of cycles, the final residual deformation of XJD-3 is reduced by nearly 28% compared with that of XJD-1, indicating that, under the premise of suitable reinforcement, increasing the diameter of SMA reinforcement can significantly improve the self-centering performance of the new node. final residual deformation of XJD-3 is reduced by nearly 28% compared with that of XJD-1, indicating that, under the premise of suitable reinforcement, increasing the diameter of SMA reinforcement can significantly improve the self-centering performance of the new node. 2. Effect of Different Axial Pressure Ratio

#### node. 2. Effect of Different Axial Pressure Ratio Figure 26 clearly shows that, when the other parameters of the joint model are exactly

2. Effect of Different Axial Pressure Ratio Figure 26 clearly shows that, when the other parameters of the joint model are exactly the same, within the allowable range, only the axial force applied to the column is changed, and the influence on the seismic performance of the whole joint is almost zero. The main object of the study is the core area of the joint, and the variable parameter object Figure 26 clearly shows that, when the other parameters of the joint model are exactly the same, within the allowable range, only the axial force applied to the column is changed, and the influence on the seismic performance of the whole joint is almost zero. The main object of the study is the core area of the joint, and the variable parameter object of the study is the beam member; therefore, when the axial compression ratio of the column is changed, there is no obvious effect on the mechanical performance of the whole joint. the same, within the allowable range, only the axial force applied to the column is changed, and the influence on the seismic performance of the whole joint is almost zero. The main object of the study is the core area of the joint, and the variable parameter object of the study is the beam member; therefore, when the axial compression ratio of the column is changed, there is no obvious effect on the mechanical performance of the whole joint.

of the study is the beam member; therefore, when the axial compression ratio of the col-


#### *Δ*/mm **5. Conclusions and Discussions**

**5. Conclusions and Discussions** 

**Figure 26.** Comparison of hysteresis curves with different axial compression ratios. **5. Conclusions and Discussions**  In this research, a new type of seismic-resisting self-centering beam-column joint with built-in SMA reinforcement and a steel end plate was designed and investigated ex-In this research, a new type of seismic-resisting self-centering beam-column joint with built-in SMA reinforcement and a steel end plate was designed and investigated experimentally and numerically based on a conventional beam-column edge joint of conventional

In this research, a new type of seismic-resisting self-centering beam-column joint

perimentally and numerically based on a conventional beam-column edge joint of con-


island main buildings in a nuclear power plant. In particular, the seismic performance of the joint was validated through a series of low cyclic loading tests on four models. Good agreement was observed in the comparisons between the experimental and numerical results. The main conclusions and discussions are as follows:


**Author Contributions:** Conceptualization, Q.P. and C.W.; methodology, Q.P. and Z.C.; software, Z.C. and C.W.; validation, Q.P., C.W. and Z.C.; formal analysis, Q.P. and H.G.; investigation, Q.P. and Y.D.; data curation, Y.D. and Q.P.; writing—original draft preparation, C.W. and Z.C.; writing—review and editing, Q.P. and C.W.; supervision, Q.P. and H.G.; project administration, Q.P. and Y.D.; funding acquisition, Q.P., C.W. and Y.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Nature Science Foundation of China, grant number 51878108, and the Department of Science & Technology Guidance Plan Foundation of Liaoning Province, grant number 2019JH8/10100091.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the finding of this study are available from the corresponding author upon request.

**Acknowledgments:** The authors gratefully acknowledge the support from Yang Liu from the College of Environment and Civil Engineering, Chengdu University of Technology, from Xiaofei Xie and Jiangtao Li from Beijing company Beijing Ruituotech Technology Co., Ltd, during the tests conducted for this study.

**Conflicts of Interest:** The authors declare no conflict of interest.
