Mechanical properties of plate type steel bar connectors for prefabricated concrete structures

Abstract

This article presented experimental studies on mechanical properties on Plate Type steel Rebar Connector (PTRC), which is composed of steel plate, thread coupler, and steel tube. This is a new method of mechanical connection of steel bars provided in this article for full-precast concrete shear wall structures. The proposed PTRC was tested under monotonic tensile tests, high-stress cyclic tests and high-deformation cyclic tests according to the code (JGJ107-2016). PTRCs were evaluated as Grade I splice through U₀, U₄, U₈, A_sgt, and U₂₀ according to the code. The stress distribution curves and end section rotation of PTRCs with different parameters were analyzed using verified Finite Element Model. The calculation methods of PTRC initial stiffness, including stiffness of bolt and threads were provided.

Keywords

full-precast concrete shear wall system plate type steel rebar connector monotonic tensile tests high-stress cyclic tests high-deformation cyclic tests residual deformation finite element model calculation method

Introduction

Prefabricated buildings develop rapidly, due to their many advantages such as green construction, labor saving, and factory prefabrication (Yee, 2001; Yee and D, 2001). The most important research subject in fabricated structure is rebar connection method, which would greatly affect the overall safety performance of the whole structure deeply (Qian et al., 2011).

About grouted sleeve connections, Kim (2012) conducted tensile tests on two types of grouted sleeve connectors, Liu C et al. (2020) studied mechanical properties of 15 sleeve specimens for monotonic tensile tests and Fen et al. (2021) investigated dynamic properties of grouted sleeve connections. These studies showed that grouting sleeve technology was an effective method to provide steel bar connection in precast concrete structures. Zhang et al. (2018) conducted high temperature tests on steel sleeve grouting connectors and studied the bearing capacity and failure modes of sleeve grouting connections at different temperatures. Under high temperature, grouted sleeves still could provide enough capability for steel bar connections. However, the connection strength depended on the curing degree of grouting material, which was not conducive to rapid assembly. The assembly needs to wait until the grouting material is solidified.

About steel bar mechanical connections, Jeong et al. (2015) conducted a loading test on reinforced concrete beams connected by tapered threaded steel bars and showed that the mechanical connection of tapered threads could realize equal-strength connection of steel bars. However, this kind of mechanical connection weakened the base material of the steel bar and was not suitable for structures with smaller steel bar diameters. Zhang et al. (2016) and Li et al. (2016), respectively, carried out experimental studies on prefabricated frame column structures and shear wall structures connected by pressed sleeve and showed that the pressed sleeve connection could effectively transmit the tension and pressure of the steel bars. However, the mold size for the pressed sleeve is large, and there are some problems such as high construction intensity and low construction efficiency (Duan et al., 2021).

Bolt connection is a kind of mechanical connection. There are few experimental studies on bolt connection applied to the precast concrete shear wall. Wang et al. (2020) studied the experimental and numerical of precast concrete columns with hybrid bolted splice connections. The study indicated that the PC columns connected by hybrid bolted splice connections exhibited similar seismic performance with the response of cast-in-place columns. James et al. (2004) studied the dynamic performance of bolted connection nodes in prefabricated structures. Liu J et al. (2020) investigated seismic performance of mechanical joints with bolted flange plate for precast concrete column. Test results indicated that this new joint of bolted connection was reliable.

Chen and Guo (2012) carried out low-cycle repeated loading test of a four-floor full-precast concrete shear wall structure. The test specimen kept elastic under moderate earthquake and meet the requirement of no collapsing under strong earthquake. The structure system in this article adopts full-precast shear wall structure system.

This paper provides a new full-precast concrete shear wall structure system, which is connected by Plate Type steel Rebar Connectors (PTRC), as shown in Figure 1. The PTRCs and steel bars are connected by threads. Steel bar threads adopt rib-stripped rolled parallel threads. Chen K et al. (2010) studied the seismic performance of precast shear walls connected by parallel threaded steel bars. The results showed that the vertical steel bars of the precast shear wall connected through parallel threads were effective to transfer the stress.

Figure 1.

New full-precast concrete shear wall system. (a) Plate Type steel Re-bar Connector (b) Steel bars connected by Plate Type steel Rebar Connector.

The PTRC is composed of steel plate, steel tube, and thread coupler, as shown in Figure 1(a). Steel tube and thread coupler are welded with steel plate. Rebar 1 is directly connected to PTRC through thread coupler 1, and rebar 2 is connected to the steel tube through a high-strength bolt, as shown in Figure 1(b). Rebar 2 and high-strength bolts (HSB) are connected by thread coupler 2. High-strength bolts can be replaced by high-strength screws and nuts.

The HSB are inserted from the construction hand holes, through the PTRCs, and screwed into the thread couplers in the bottom shear wall. Then the construction hand holes are filled with prefabricated filler blocks. The connection of steel bars by PTRC is mechanical. The prefabricated components adopting PTRC can receive force immediately after assembly.

Tests

Test specimens and dimensions

This article investigated the monotonic and dynamic mechanical properties of PTRCs. Two types of PTRCs were subjected by yield and ultimate strength tensile tests, monotonic residual deformation tensile tests, high-stress cyclic tests, and high-deformation cyclic tests. Each test contained three specimens. There were 24 specimens in total.

Through these tests PTRCs were evaluated by U₀ which displayed the residual deformation of splice after a normal tensile load, A_sgt which is the total elongation of specimens at maximum tensile force, U₂₀ which displayed the residual deformation of splice after 20times high-stress load circles, U₄ which displayed the residual deformation of splice after 4 times high-deformation load circles, U₈ which displayed the residual deformation of splice after 8times high-deformation load circles, yield strength, maximum strength, etc. Tests and specimens are listed in Table 1 and shown in Figure 2.

Table 1.

List of specimens and tests.

PTRC type	L (mm)	H₁ (mm)	W (mm)	L₁/L₂ (mm)	D₁ (mm)	D₂ (mm)	d₁ (mm)	d₂ (mm)	d₃ (mm)
I	290	50	20	80	24.0	30.0	14.3	16.3	20.0
II	230	50	20	50	24.0	30.0	14.3	16.3	20.0

PTRC type	Yield and ultimate strength tensile tests	Monotonic residual deformation tests	High-stress cyclic tests	High-deformation cyclic tests
I (80 mm)	TLI - A	MI - A	HSI - A	HDI - A
	TLI - B	MI - B	HSI - B	HDI - B
	TLI - C	MI - C	HSI - C	HDI - C
II (50 mm)	TLII - A	MII - A	HSII - A	HDII - A
	TLII - B	MII - B	HSII - B	HDII - B
	TLII - C	MII - C	HSII - C	HDII - C

Figure 2.

The shape and parameters of test specimens. (a) Front view of specimens. (b) Parameters of Plate Type steel Rebar Connector.

As shown in Figure 2, the test specimen consisted of four parts:

1. PTRC. The steel grade for the PTRCs was Q460 C. The PTRCs have three types (named I and II and III). Parameters of the PTRCs including the PTRC length L, the height of steel plate H₁, the width of steel plate W, the length of thread coupler L₁, the external diameter of thread coupler D₁, the nominal inner diameter of thread coupler d₁, the effective inner diameter of thread coupler d₂, the length of steel tube L₂, the external diameter of steel tube D₂, the inner diameter of steel tube d₃ are listed in Table 1 and shown in Figure 2.

2. HSB. The HSB in tests adopted S8.8*M16 standard HSB.

3. Thread coupler. Steel grade of thread couplers was 45Cr. Thread coupler in tests adopted standard thread coupler for φ16 mm rebars according to JGT-163–2013.

4. Rebar1&Rebar2 (φ16 mm, HRB400). The ends of Rebar1&Rebar2 were rib-stripped rolled parallel threads. The thread length on Rebar2 was 20 mm. The thread length on rebars was larger than 1.2 times of rebar diameter to ensure the safety of connections.

Material properties and bolt pre-tension

Mechanical properties of the rebars, PTRCs and parallel threaded couplers were measured through tensile tests for metallic material according to the standard GB/T228-2002 (2002), as listed in Table 2. The elastic modulus of steel took 206 GPa that specified in GB 50017-2003 (2003). Bolts were tighten using the calibrated torque wrench according to the provisions of JGJ82-2011 (2011).

Table 2.

Material properties.

Tested coupons	Materials	Yield strength (f_y/MPa)	Ultimate tensile strength (f_u/MPa)	Strain corresponding to ultimate stress f_u (%)
Rebar	HRB400	507.3	621.7	17
Thread coupler	45Cr	785	880	9.1
PTRC	Q460 C	552.7	614.6	20.3
High strength bolt	S8.8	685.4	885.7	9.7

Test setup and loading regime

The tests were carried out using two machines: a hydraulic testing machine with the maximum loading capacity of 1000 KN; a hydraulic fatigue machine (Instron 8502) with the maximum tensile and press capacity of 250 KN. The Instron 8502 was a high stiffness, 250 KN fatigue rated servo-hydraulic testing system that meets the challenging demands of both static and dynamic testing requirements.

1. Yield and ultimate strength tensile tests

The yield and ultimate strength tensile tests were carried out using hydraulic testing machine. The monotonic loading was controlled by displacement and the loading rate was 1 mm/min.

2. Monotonic residual deformation tensile tests

The monotonic residual deformation tensile tests were carried out using a hydraulic testing machine. The deformations of splice were recorded by butterfly extensometer. The monotonic loading was controlled by force and the loading rate was 2 N/mm² S⁻¹.

Loading steps: 0 → 0.6f_ykA_s → 0 →destroyed. In this step the test recorded ultimate tensile strength and total elongation of splice sample at maximum tensile force. f_yk was standard yield strength of steel bars. A_s was cross-sectional area of steel bars.

3. High-stress Cyclic Tests

In this test, the high-stress cyclic tests were carried out using hydraulic fatigue machine (Instron 8502). The cyclic loading was controlled by force and the loading rate was 5 N/mm² S⁻¹. The frequency of each cycle in this test was 0.0045 HZ.

Loading steps: 0 → (0.9f_ykA_s → −0.5f_ykA_s) 20circles→destroyed. In this step the test recorded ultimate tensile strength and total elongation of splice sample at maximum tensile force.

4. High-deformation Cyclic Tests

In this test, the high-deformation cyclic tests were carried out using hydraulic fatigue machine (Instron 8502). The cyclic loading was controlled by alternate control of deformation and force. The loading rate of deformation was 2 mm· min⁻¹ and the loading rate of force was 5 N/mm² S⁻¹.

Loading steps: 0 → (2ε_yk → −0.5f_ykA_s) 4circles → (5ε_yk → −0.5f_ykA_s) 4circles → destroyed. The frequency of cycles in this test were 0.0047 HZ, 0.002 HZ, respectively. ε_yk was the strain of steel bars when steel bars were under standard yield stress.

Test results

Yield and ultimate strength tests

The splice in tests might fail by five failure modes under tension: (1) Failure mode 1, steel bar fracture; (2) Failure mode 2, fillet weld failure; (3) Failure mode 3, threads slippage; (4) Failure mode 4, PTRC steel plate yielded; (5) Failure mode 5, HSB failure.

In TLI-A, B, C and TLII-A, B, C tests, the steel bar fracture failure occurred in specimens as shown in Figure 3. It could be seen that PTRCs, bolts, thread couplers were fine and had little deformation. The yield strengths of TLI-A, B, C were 104.58 KN, 94.03 KN, 103.17 KN, and the yield strengths of TLII-A, B, C were 102.31 KN, 101.87 KN, and 103.26 KN, which were the yield strength of steel bars. High strength bolts and PTRC steel plates in the tests were proved that they had enough yield strength and stiffness. Also, the rib-stripped rolled parallel threads on steel bars were proved that they had enough strength to connect steel bars. JGJ107-2016 indicated that rib-stripped rolled parallel threads could have the same ability with steel bar. The two types of PTRC splices had similar stiffness and yield strength, as shown in Figure 3. The two types of PTRC could satisfy the connection of steel bars. Then this article researched the monotonic and cyclic mechanical properties of PTRC Type I and II.

Figure 3.

Failure modes and Load - Displacement curves of Plate Type steel Rebar Connector Type I and II. (a) Failure in TLI-A, B, C (b) Failure in TLII-A, B, C

Monotonic residual deformation tensile tests

A_sgt was the elongation of specimens at maximum tensile force

Asgt = [\frac{L_{02} - L_{01}}{L_{01}} + \frac{f_{mst}^{0}}{E}] \times 100

(1)

where d is the diameter of steel bars,

f_{mst}^{0}

is steel bar stress at maximum tensile force, E is elasticity modulus of steel bars, L₀₁ is the length of steel bar deformation measurement zone before loading, L₀₂ is the length of steel bar deformation measurement zone after loading. When the first tensile load 0.6 f_ykA_s was released to 0 KN, the residual deformation of splice U₀ was recorded. Load-deformation curve for specimen MI-A in residual deformation tensile tests was shown in Figure 4. Test results for specimens in residual deformation tensile tests were shown in Table 3.

Figure 4.

Load-deformation curve for specimen MI-A.

Table 3.

Test results for specimens in residual deformation tensile tests.

PTRC type	Specimens	A_sgt-AB, %	A_sgt-CD, %	A_sgt, %	U₀(mm)	Yield load (kN)	Maximum load (kN)	Grade
I	MI-A	6.5	6.7	6.6	0.024	98.0	128.5	I
	MI-B	6.4	6.1	6.25	0.092	105.1	119.8	I
	MI-C	6.6	5.5	6.1	0.074	104.3	123.3	I
II	MII-A	6.3	7.0	6.7	0.079	103.6	117.1	I
	MII-B	7.3	7.2	7.2	0.014	102.1	123.3	I
	MII-C	5.8	6.8	6.3	0.065	104.7	115.5	I

The value of U₀ displayed the residual deformation of splice after a 0.6 f_ykA_s tensile load. The monotonic tensile test performance reflected the basic ability of splices under normal load. The test results showed that the PTRC splices produced a small residual deformation under normal load, thus there would be a small crack width of the concrete structure.

A_sgt-AB was the value of A_sgt for measurement zone which was between A and B in specimens. A_sgt-CD was the value of A_sgt for zone which was between C and D. The value of A_sgt reflected the influence of PTRCs on the ductility of the steel bars. The ductility of structure mainly depends on the ductility of steel bars outside the splices rather than the splices themself. The test results showed that the steel bars connected by PTRCs still had high ductility.

Plate type steel rebar connector type I and type II were evaluated as Grade I splice in which the value of U₀ was required no more than 0.10 mm and the value of A_sgt was required no less than 6.0%, according to the standard JGJ 107–2016. This is the best level in code JGJ 107–2016 and the connectors of Grade I can be used in any situation.

High-stress cyclic tests

In high-stress cyclic tests, a 0.9 f_ykA_s tensile load and a 0.5 f_ykA_s press load were applied 20 times cyclically. Then the residual deformation of splice U₂₀ was recorded, as shown in Figure 5. In the curve, U₂₀ was abscissa of intersection for X axis and the end of the 20th cycle. Load-deformation curve for specimen HSI-A, which was a test result of high-stress cyclic tensile test, was shown in Figure 5. And test data results for specimens in high-stress cyclic tensile tests were shown in Table 4.

Figure 5.

Load-deformation curve for specimen HSI-A.

Table 4.

Test results for specimens in high-stress cyclic tests.

PTRC type	Specimens	U₂₀(mm)	Yield load (kN)	Maximum load (kN)	Grade
I	HSI-A	0.2364	92	124.8	I
	HSI-B	0.2535	95	126.1	I
	HSI-C	0.2317	97	123.2	I
II	HSII-A	0.2668	90	125.7	I
	HSII-B	0.2878	89	126.7	I
	HSII-C	0.2452	91	124.9	I

The curve in stage II displayed the phenomenon that the force remained almost unchanged, and the deformation changed greatly. The theoretical analysis was provided as follows.

The pre-tightening force F_p was applied when connectors were spliced, pre-tightening force was larger than press load, so threads were always in a compressed state and the thread contact surfaces would not separate during initial load cycle. And all parts of connectors were in the elastic stage. Therefore, when the first cycle ended, the joint deformation was almost 0 in load-deformation curve of HSI-A. Because the threads were not uniformly stressed, as shown in Figure 6(b). The slope of axial force curve in actual situation did not remain the same. The force on the thread close to A-A section was the largest. Therefore, under the cyclic load, the threads locally deformed, causing that the pre-tightening force of local thread gradually dropped to 0 after 20 load cycles. When the tensile force turned to press force, the thread contact surface separated, as shown in Figure 6(a). The stage II in Figure 5 shows separating process of thread contact surface, and U₂₀ reflects the residual deformation caused by the thread gap after the local pre-tightening force disappeared.

Figure 6.

Schematic diagram of thread.

In the curves, the hysteresis loop gradually moved to the right. The moves showed that the deformation of splice accumulated in each circle.

The value of U₂₀ displayed the residual deformation of splice after 20times high-stress load circles. The high-stress cyclic tensile test performance reflected the ability of splices under wind load and small seismic load. The test results showed that the PTRC splices produced a small residual deformation under wind load and small seismic load, thus there would be a small crack width of the concrete structure.

Plate type steel rebar connector type I and type II were evaluated as Grade I splice in which the value of U₂₀ was required no more than 0.3 mm, according to the standard JGJ 107–2016.

High-deformation cyclic tests

In high-deformation cyclic tests, a 2ε_yk tensile displacement and a 0.5 f_ykA_s press load were applied 4 times cyclically. After that a 5ε_yk tensile displacement and a 0.5 f_ykA_s press load were applied 4 times cyclically. Then the residual deformation of splice U₄ and U₈ were recorded. S line was the tensile stiffness of splice, as shown in Figure 7

S= F / δ

(2)

F was the force on splice. δ was the deformation of splice.

Figure 7.

Load-deformation curve for specimen HDI-A.

The recorded method of U₄ was: In the 4th circle, draw parallel lines of S line when the tensile force was 0.5 f_ykA_s, and draw parallel lines of S line when the press force was 0.25 f_ykA_s. The parallel lines had intersections with X axis. The distances between intersections in X axis were δ₁ and δ₂, respectively. U₄ was the average of δ₁ and δ₂

U_{4} = (δ_{1} + δ_{2}) / 2

(3)

The recorded method of U₈ was: In the 8th circle, draw parallel lines of S line when the tensile force was 0.5 f_ykA_s, and draw parallel lines of S line when the press force was 0.25 f_ykA_s. The parallel lines had intersections with X axis. The distances between intersections in X axis were δ₃ and δ₄, respectively. U₈ was the average of δ₃ and δ₄

U_{8} = (δ_{3} + δ_{4}) / 2

(4)

Load-deformation curve for specimen HDI-A in high-stress cyclic tests was shown in Figure 7. Test results for specimens in high-stress cyclic tests were shown in Table 5.

Table 5.

Test results for specimens in high-deformation cyclic tests.

PTRC type	Specimens	δ₁(mm)	δ₂(mm)	U₄(mm)	δ₃(mm)	δ₄(mm)	U₈(mm)	Maximum load (kN)	Grade
I	HDI-A	0.2630	0.2651	0.2641	0.5313	0.6482	0.5897	127.2	I
	HDI-B	0.1837	0.2493	0.2165	0.5379	0.5411	0.5395	129.7	I
	HDI-C	0.2149	0.2530	0.2340	0.4772	0.5560	0.5166	126.8	I
II	HDII-A	0.1479	0.1470	0.1475	0.5294	0.6170	0.5732	125.0	I
	HDII-B	0.2335	0.2409	0.2372	0.4358	0.5102	0.4730	126.3	I
	HDII-C	0.2130	0.2207	0.2169	0.4973	0.4611	0.4792	127.5	I

The value of U₄ displayed the residual deformation of splice after 4times high-deformation load circles which were 2 times of steel bar yield strain. The value of U₈ displayed the residual deformation of splice after 4times high-deformation load circles which were 2 times of steel bar yield strain and 4 times high-deformation load circles which were 5 times of steel bar yield strain.

The high-deformation cyclic test performance reflected the plastic ability of splices under strong seismic load. The test results showed that the PTRC splices produced a small residual deformation under strong seismic load, thus there would be a small crack width of the concrete structure.

Plate type steel rebar connector type I and type II were evaluated as Grade I splice in which the value of U₄ was required no more than 0.3 mm and the value of U₈ was required no more than 0.6 mm, according to the standard JGJ 107–2016.

FEM and verification

A 3D Finite Element Model (FEM) developed using the finite element software ABAQUS (2014) was used to study the behavior of steel bar splices connected by PTRC.

Material properties and specimen sizes obtained from the experimental tests were input into the FE model. The yield and ultimate tensile strengths obtained from the experimental tests, as well as the corresponding strain values to ultimate stress listed in Table 2, were considered for the implementation of corresponding constitutive law. The solid element C3D8R, an eight-node linear brick element with reduced integration and hourglass control, was used to mesh the steel bar splices. A fine mesh with the size of 3 mm × 3 mm × 3 mm was used as results of mesh size sensitivity analysis. As shown in Figure 8, the end section of the right steel bar was restrained by U₁ = U₂ = U₃ = 0, the end section of the left steel bar was coupled to point RP-1, and force was applied to point RP-1. The type of the analysis was (static, general). Contact properties between different parts of the connection were all modeled as hard contact in normal direction and finite slip in tangent direction with the tangential friction coefficient of 0.3. Finite element models adopted 1/1 models as shown in Figure 8. The classical Newton–Raphson algorithm was adopted to provide an iterative solution of the problem.

Figure 8.

Finite element model and verification.

The ductile damage of material was considered to steel in FEM. The value of ductile damage was: (fracture strain, stress triaxiality, and strain rate); (2.1938, 0, 1 × 10⁻⁶); (1.6725, 0.05, 1 × 10⁻⁶); (1.2768, 0.1, 1 × 10⁻⁶); (0.9771, 0.15, 1 × 10⁻⁶); (0.7508, 0.20, 1 × 10⁻⁶); (0.5809, 0.25, 1 × 10⁻⁶); (0.4546, 0.30, 1 × 10⁻⁶); (0.3625, 0.35, 1 × 10⁻⁶). And the Gurson–Tvergaard material model was used to describe the stress–strain relationship of the steel. According to research (Amadio et al., 2017), for FE simulations aimed to describe fracture mechanisms of ductile metals, the Gurson–Tvergaard material model available in ABAQUS can be used to explain local strength decrease during damage propagation, in the intermediate phase between the nucleation and coalescence of voids. In it, nucleation and coalescence are considered before homogenization by applying appropriate corrections directly to the stress–strain cell response. The homogenization technique is based on the stress–strain characterization of a representative volume element that is considered to be a cubic volume with voids before the material is stressed. According to research (Amadio et al., 2017), a key role is assigned to the coefficients q₁, q₂, and q₃ representative of the critical yielding surface definition

\emptyset = (\frac{q}{σ_{y}}) + 2 q_{1} f \cos h (- \frac{3}{2} \frac{q_{2} p}{σ_{y}}) - (1 + q_{3} f^{2}) = 0

(5)

where, q is the Von Mises stress, p is the hydrostatic pressure,

σ_{y}

is the yield stress, q₁, q₂, and q₃ are the Tvergaard correction coefficients, while f (0

\leq

\leq

1) is the void volume fraction, which is defined as the ratio of the volume of voids to the total volume of the material and is defined as

f = 1 - r

(6)

where,

r

is the relative density of the material. In accordance with research (Kiran R et al., 2014), the input parameters for the current study were set equal to

r = 0.96

q_{1} = 1.5

q_{2} = 1

and

q_{3} = q_{1}^{2} = 2.25

The 3D FEM connected by PTRC was calculated. Test results from TLI-A and TLII-A were used to verify the FEM. The load-displacement curves obtained from Model-TLI and Model-TLII agreed well with TLI-A and TLII-A tests, as shown in Figure 8. The tension stiffness and tension strength of the connection in FEM simulation were almost equal with those in actual tests. Also, the failure type of FEM simulation which was steel bar fracture, was the same with tensile test.

At the same time, FE model of PTRC was verified by strain test. The local strains of PTRC were measured by seven strain gauges. The measurement position of the strain gauges was shown in Figure 8. The strains at the corresponding position were compared between FE model and strain test, as shown in Figure 8. It could be found that the FE model was in good agreement with the strain test. This FEM could be used to the following parameter analysis of splices.

Parameter analysis of PTRC

The parameters studied in FEM projects, were the height of steel plate H_1, the width of steel plate W, the steel bar diameter D, as shown in Table 6. Totally 13 specimens were analyzed, in which 6 specimens were used for investigating effects of steel plate height, 4 specimens for steel plate width, 3 specimens for the diameter of steel bars. All the steel holes in FEM projects adopt 80 mm. Steel bar material adopts HRB400.

Table 6.

Parameter analysis table of PTRC.

PTRC	H₁ (mm)	W (mm)	D (mm)
302016	30	20	16
402016	40	20	16
452016	45	20	16
502016	50	20	16
602016	60	20	16
702016	70	20	16
501016	50	10	16
501516	50	15	16
502516	50	25	16
503016	50	30	16
502020	50	20	20
502024	50	20	24

The stress distribution curves of PTRCs are recorded and compared under the design yield load of HRB400 steel bars. As shown in Figures 9 and 10, the stress distribution curves were recorded at the position of the X axis, which was the top section of PTRC steel plate. The S.Mises in Y axis showed stress of PTRCs. The yield strength of steel (552.7 Mpa) in the following figures was obtained from the experimental tests. The PTRCs were taken 1/1 model for shown.

Figure 9.

The stress-location curves.

Figure 10.

The stress-location curves.

Effects of steel plate height

Under the design yield load of HRB400 φ16 mm steel bars, it could be seen that in specimens 50*20*16, 60*20*16 and 70*20*16, the stresses of whole steel plate were lower than the actual steel yield strength. They satisfied the using requirements for HRB400 φ16 mm steel bars. The location at 80 mm and 210 mm displayed obvious stress concentration. This phenomenon was caused by eccentric tension in PTRC. The stresses at 80 mm of the three specimens were 510.7 Mpa, 492.1 Mpa, and 468.5 Mpa. The stress ratios at the location of stress concentration were 1, 0.963, 0.917. With the increase of steel plate height, the stresses at the location of stress concentration fell down. The stresses at 145 mm of the three specimens were 442.9 Mpa, 353.2 Mpa, and 291.8 Mpa. The stress ratios at the location of middle section were 1, 0.797, 0.658. With the increase of steel plate height, the stresses at the location of stress concentration fell down obviously. Since the force from steel bar remained the same and the size of the connection between steel tube and steel plate remained the same, the height increase of steel plate only increased the stiffness of PTRC and had little effect on the stress concentration. For stresses at the location of middle section, the steel plate could be regarded as a beam under tension and bending moments. The increase of the section modulus which was caused by the height increase of steel plate, affected the stresses at middle section obviously.

The steel plates in specimens 30*20*16, 40*20*16 and 45*20*16 reached yield strength of steel. The yield part first started from the position of stress concentration, gradually extended to the middle section, and finally formed a yield section between the location of 80–210 mm. And it could be seen that the yield parts of the three specimens were in the initial stage of yield, and the stress remained at the yield strength values(552.7 Mpa), and they had not yet entered the plastic strengthening stage of steel. For 30*20*16, due to the decrease of steel plate stiffness, it could be clearly found that the steel tube rotated and produced a rotation. This phenomenon was studied in End section rotation of PTRC.

Effects of steel plate width

The stresses at 80 mm of the specimens 50*20*16, 50*25*16 and 50*30*16 were 510.7 Mpa, 445.9 Mpa, and 398.2 Mpa. The stress ratios at the location of stress concentration were 1, 0.873, 0.779. With the increase of steel plate width, the stresses at the location of stress concentration fell down. The stress ratios at stress concentration of the specimens 50*20*16, 50*25*16 and 50*30*16 were less than these of 50*20*16, 60*20*16 and 70*20*16. The conclusion was that steel plate width affected the stresses at the location of stress concentration obviously. Because the steel plate width affected the width of the connection between steel tube and steel plate straightly.

The stresses at 145 mm of the three specimens were 442.9 Mpa, 348.2 Mpa, and 290.7 Mpa. The stress ratios at the location of middle section were 1, 0.786, 0.656. For the stresses at middle section, the effects of adding five to width and adding 10 to the height were similar in PTRC.

End section rotation of PTRC

In the specimens 30*20*16 and 50*10*16, there was a rotation occurred at the end section of steel plates. As PTRC was under eccentric tension, the end section of steel plate had a rotation always, as shown in Figure 11(a). When the stiffness of PTRC was large, the angle of rotation was not obvious, such as 70*20*16 and 50*30*16. When the stiffness of PTRC was small, the angle of rotation was obvious, such as 30*20*16 and 50*10*16. For the specimens 50*20*16, 50*20*20 and 50*20*24, when the diameter of steel bars connected by PTRC increased, the angles of rotation also increased gradually, as shown in Figure 11(b). Therefore, the values of rotation angle were related to the ratios between PTRC stiffness and steel bar stiffness. The initial stiffness calculation of PTRC was researched in Initial stiffness calculation method of PTRC.

Figure 11.

Rotation of section A-A. (a) Schematic diagram (b) values for rotation of section A-A.

Initial stiffness calculation method of PTRC

The initial stiffness reflects the stiffness of entire joint of PTRC in the linear elastic range under tensile and pressure force. It can be expressed by the first derivative of the force-deformation curve of joint at the origin

K = {\frac{dF}{d δ} |}_{δ = 0}

(7)

where F is force on steel bar,

δ

is deformation of PTRC joint, K is joint initial stiffness.

For the calculation of joint stiffness, this article adopts the component method. The basic principle of the component method: It splits the joint into multiple basic components. Each component is simulated by a linear or nonlinear spring. The basic components are assembled through the series and parallel combination calculations of the springs to obtain the overall stiffness of the joint.

Based on the experimental phenomenon, the deformation of joint is formed by steel plate deformation, weld deformation, high-strength bolt deformation, threaded coupler deformation, steel tube deformation and threads deformation, as shown in Figure 12(a). The deformation of entire joint is the sum of each part. Each part is regarded as a spring. The equivalent stiffness of joint is composed of six parts, and it is calculated using the spring series formula, as follows

K_{e q} = \frac{1}{1 / K_{p} + 1 / K_{w} + 1 / K_{b} + 1 / K_{c} + 1 / K_{t} + 1 / K_{t h}}

(8)

where

K_{p}

is steel plate stiffness,

K_{w}

is weld stiffness,

K_{b}

is high-strength bolt rod stiffness,

K_{c}

is threaded coupler stiffness,

K_{t}

is steel tube stiffness and

K_{t h}

is threads stiffness.

K_{p}

K_{w}

K_{c}

, and

K_{t}

can be calculated according to European Code of steel structure design EC3ENV-1993-1-1.

Figure 12.

Stiffness calculation of Plate Type steel Rebar Connector. (a) Simplified model of stiffness (b) Load resolution on thread surface.

The calculation method of bolt rod effective length is summarized according to the actual situation of bolts in test. The stiffness calculation of high-strength bolt rod

k_{b} = 1.6 \frac{A_{s}}{L_{b}}

(9)

L_{b} = t_{s t} + t_{t c} + t_{w} + \frac{1}{2} (t_{h} + t_{c})

(10)

where

A_{s}

is cross section area of bolt rod,

L_{b}

is effective length of bolt rod,

t_{s t}

is the length of steel tube;

t_{t c}

is the length of bolt rod in threaded coupler;

t_{w}

is the thickness of steel washer;

t_{h}

is the thickness of bolt head;

t_{c}

is the thickness of cone head.

Regarding the stiffness of thread, the thread is regarded as an elongated triangular prism, which spirals upward. It is assumed that the thread evenly bears the axial force $F_{b}$ . $F_{b}$ is decomposed into normal force and tangential force at thread contact surface. The exploded diagram is as follows:

In the Figure 12(b), φ is the half-angle of thread profile, φ^′ is the half-angle of thread vertical section profile, and γ is the thread rise angle

F_{x^{'}} = F_{b} \cos γ \cos φ^{'}

(11)

F_{y^{'}} = F_{b} \sin γ

(12)

F_{z^{'}} = F_{b} \cos γ \sin φ^{'}

(13)

The thread contact surface area $S_{t h}$ is

S_{t h} = \frac{L_{n}}{\sin γ} \cdot \frac{P \cos γ}{2 \sin φ} = \frac{L_{n} P \cot γ}{2 \sin φ}

(14)

where P is the thread pitch,

L_{n}

is the length of the threaded part.

Assuming that $F_{b}$ has an increment $Δ F_{b}$ , the increments in the direction of x', y', z' are $Δ F_{x^{'}}$ , $Δ F_{y^{'}}$ , $Δ F_{z^{'}}$ . The resulted deformation increments are

δ_{x^{'}} = \frac{Δ F_{x^{'}}}{k_{n} S_{t h}}

(15)

δ_{y^{'}} = \frac{Δ F_{y^{'}}}{k_{τ} S_{t h}}

(16)

δ_{z^{'}} = \frac{Δ F_{z^{'}}}{k_{τ} S_{t h}}

(17)

where

k_{n}

is normal stiffness of contact surface,

k_{τ}

is tangential stiffness of contact surface. The axial deformation is

δ_{z} = (δ_{x^{'}} \cos φ^{'} + δ_{z^{'}} \sin φ^{'}) \cos γ + δ_{y^{'}} \sin γ

(18)

The stiffness calculation of threads

K_{t h} = Δ F_{b} / δ_{z}

(19)

K_{t h} = S_{t h} {(\frac{\cos^{2} γ \cos^{2} φ^{'}}{k_{n}} + \frac{\cos^{2} γ \sin^{2} φ^{'}}{k_{τ}} + \frac{\sin^{2} γ}{k_{τ}})}^{- 1}

(20)

According to handbook (Cheng, 2007), $K_{τ} = (1 - 2 v_{b} / 2 (1 - v_{b})) K_{n}$ , $K_{n} = P_{n}^{β}$ , $P_{n} = F_{x^{'}} / S_{t h}$ . $v_{b}$ , $β$ are coefficients in handbook. $P_{n}$ is average pressure of contact surface, $v_{b}$ is thread tail length, $β$ is surface quality factor.

Because γ is small, $\cos γ \approx 1$ , $\sin γ \approx 0$ , $φ^{'} \approx φ$ . The stiffness calculation of threads is simplified as follows

\begin{array}{l} K_{t h} = S_{t h} {(\frac{\cos^{2} φ}{P_{n}^{β}} + \frac{2 (1 - v_{b}) si n^{2} φ}{(1 - 2 v_{b}) P_{n}^{β}})}^{- 1} \\ = S_{t h} {(\frac{F_{b} \cos φ}{S_{t h}})}^{β} {[co s^{2} φ + \frac{2 (1 - v_{b}) si n^{2} φ}{1 - 2 v_{b}}]}^{- 1} \end{array}

(21)

Conclusion

This article presented experimental and FEM studies on PTRC for prefabricated concrete structures, which is composed of steel plate, thread coupler, and steel tube. The thread coupler and steel tube are welded to the two ends of steel plate, respectively.

• This article provided a new connection method (PTRC) of steel bars for prefabricated concrete structures. The proposed PTRCs were tested under yield and ultimate strength tensile tests, monotonic tensile residual deformation tests, high-stress cyclic tests and high-deformation cyclic tests according to the code (JGJ107-2016).

• Type I and type II of PTRC were evaluated as Grade I splice through U₀, U₄, U₈, A_sgt, and U₂₀ according to the code JGJ 107–2016. This is the best level in code JGJ 107–2016 and the connectors of Grade I can be used in any situation.

• The stress distribution curves of PTRCs with different parameters were analyzed using verified FEM. The steel plate height H₁, steel plate width W, the diameter of steel bars D had effects on stress of weak sections, stress concentration, and end section rotation.

• The calculation methods of PTRC initial stiffness, including stiffness of bolt and threads, were provided.

Footnotes

Declaration of conflicting interests

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

Funding

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

ORCID iD

Peijun Wang

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