Shear stiffness of inclined screws in timber–concrete composite beam with timber board interlayer

Abstract

The timber board interlayer is applied as the formwork for the pouring of concrete slab in various practical applications of timber–concrete composite structures, with the rehabilitation of timber buildings, in particular. At present, there are few studies performed to study the shear stiffness of inclined screws in timber–concrete composite beams with timber board interlayer. In this article, eight groups of shear tests were carried out to study the shear stiffness of inclined screws in timber–concrete composite beams with timber board interlayer. The key parameters included the embedment depth of the screw connector into timber, screw diameter, the thickness of concrete slab, and concrete strength. As indicated by the test results, the shear stiffness of the inclined screws was improved as the embedment depth of screw into timber and screw diameter increased. When the embedded depth of screw into concrete remained unchanged, the thickness of concrete slab and concrete strength exhibited no significant impact on the shear stiffness of inclined crossing screws. On the basis of the theory of a beam on a two-dimensional elastic foundation, the calculation method for predicting the shear stiffness of inclined screw in timber–concrete composite beams with interlayer was proposed. The comparisons demonstrated that the shear stiffness of inclined screw can be well predicted using the calculation method.

Keywords

calculation method inclined screws shear stiffness timber board interlayer timber–concrete composite

Introduction

The timber–concrete composite (TCC) structure is a composite structural system in which the timber beam and the concrete slab can work together as one unit due to the sufficient composite action, and the mechanical properties of each structural component are utilized efficiently. The TCC beam has many advantages in comparison with the conventional timber beam, including increased load carrying capacity and bending stiffness, improved sound insulation property and vibration performance (Hong et al., 2020; Jiang et al., 2017; Zhang et al., 2020). The timber board interlayer is applied as the formwork for the pouring of concrete slab in various practical applications of TCC structures, with the rehabilitation of timber buildings, in particular (Ahmadi and Saka, 1993; Dias, 2005).

The longitudinal shear forces at the timber–concrete interface are transferred through the shear connectors. Therefore, the shear strength and stiffness of the shear connectors play a significant role in both load-bearing capacity and the rigidity of TCC beams (Yeoh et al., 2011). The inclined screws are extensively applied as the shear connectors in the TCC beams due to the excellent mechanical behavior, speedy installation process, and easy accessibility (Du et al., 2019a; Symons et al., 2010b). Therefore, plenty of research works have been carried out to study the shear stiffness of inclined screw connectors in TCC beams (Deam et al., 2008; Fragiacomo, 2012; Kavaliauskas et al., 2007; Khorsandnia et al., 2012, 2016). Lukaszewska et al. (2008) and Symons et al. (2010a) performed push-out tests on the inclined screws with different inclination angles. As revealed by the test results, the shear stiffness of the screw connector inserted vertically was smaller than that of the inclined screw connector. In the experimental studies conducted by Steinberg et al. (2003), the mechanical behavior of inclined screw connectors with different screw arrangements was investigated. According to the research results, the shear stiffness of the inclined screw working exclusively under shear-tension stress was smaller compared to the crossed screws. Du et al. (2019b) performed shear tests to study the impact of concrete strength and screw inclination angle on the shear stiffness of inclined crossing screws in TCC beams without interlayer. The experimental results demonstrated that the shear stiffness of inclined crossing screws was improved as the inclination angle between the screw connector and the shear plane was reduced. However, the concrete strength showed no considerable impact on the shear stiffness. Jorge et al. (2011) and Mirdad and Chui (2019) studied the effect of interlayer on the shear performance of the inclined screws. The results demonstrated that the installation of an interlayer between timber beam and concrete slab resulted in a decline in the shear stiffness of inclined screw connectors. Berardinucci et al. (2017) performed push-out tests on the inclined screws in TCC beams with the timber board interlayer of different thicknesses. As indicated by the results, the shear stiffness of the inclined screws decreased as the ratio between the interlayer thickness and the screw length increased.

At present, there are several calculation methods for calculating the shear stiffness of the inclined screws in TCC beams without interlayer. Symons et al. (2010a) suggested an analytical model based on the theory of a beam on a two-dimensional elastic foundation. According to the model, the screw connector and the timber component were regarded, as the elastic material and rigid concrete clamped the screw at the interface between the timber beam and the concrete slab. The comparisons performed between the experimental and theoretical results revealed that the shear stiffness of the inclined screws was overestimated by approximately 20% using this model. Moshiri et al. (2014) proposed the analytical model for the prediction of the shear stiffness of inclined screws. In this model, the timber was considered as the elastic foundation which consisted of orthogonal springs with different foundation stiffnesses in the parallel and transverse to the timber grain, but the friction between the timber beam and the concrete slab was neglected. Furthermore, Marchi et al. (2017) developed the simplified calculation method for predicting the shear stiffness of inclined screws. As shown by the theoretical results, the shear stiffness of the inclined screw was mainly contributed by the lateral stiffness and the axial stiffness of the screw connector. Nevertheless, few researches have been performed on the shear stiffness of inclined screws in TCC beams with timber board interlayer.

In this article, eight groups of shear tests were performed to study the shear stiffness of inclined screws in TCC beams with timber board interlayer. The studies focused on the impacts of the embedment depth of screw into timber, thickness of concrete slab, screw diameter and concrete strength on the pattern of failure, load–slip behavior, and shear stiffness. Based on the theory of a beam on a two-dimensional elastic foundation, the theoretical method for predicting the shear stiffness of inclined screw in TCC beams with interlayer was proposed.

Shear tests

Description of test specimens

To study the shear stiffness of the inclined screws in the TCC beam with the timber board interlayer, eight groups of shear test specimens were designed and tested, with two replicate specimens assigned to each group. The critical parameters of test specimens under investigation included the embedded length of screw into glulam, thickness of concrete slab, screw diameter, and concrete strength, as shown in Table 1. Each test specimen consisted of a timber beam connected to one concrete slab through three pairs of inclined crossing screws. The timber board interlayer was installed on the top of the timber beam and applied as a formwork for the pouring of concrete slab. The timber board had a width of 400 mm, a thickness of 15 mm, and a length of 1500 mm. The concrete slab had a width of 400 mm, a length of 1500 mm, and different thicknesses. In each test specimen, three horizontal crosswise pairs of screw connectors were installed into the timber beam with the inclination angle of 45° to the timber grain. To prevent the cracking of both the timber beam and the timber board interlayer, the screw connectors were driven with predrilling. Based on the applicable rules of screw connectors from Eurocode 5 (EN 1995-1-1:2004, 2004), the screw connectors had an embedment length into concrete of 70 mm and transverse spacing of 50 mm. The configuration of the shear test specimen 12-100-T80-C40 is shown in Figure 1.

Table 1.

Main parameters of test specimens.

Test series	Screw diameter d (mm)	Penetration length into timber l (mm)	Thickness of concrete slab t (mm)	Concrete grade
12-100-T80-C40	12	100	80	C40
10-100-T80-C40	10	100	80	C40
8-100-T80-C40	8	100	80	C40
12-80-T80-C40	12	80	80	C40
12-120-T80-C40	12	120	80	C40
12-100-T60-C40	12	100	60	C40
12-100-T100-C40	12	100	100	C40
12-100-T100-C50	12	100	80	C50

Figure 1.

Configuration of shear test specimen 12-100-T80-C40: (a) elevation view and (b) side view.

Materials

The timber beam used in the tests was made of homogeneously glued laminated larch timber. The average density of the timber was 0.578 g/cm³, and the average moisture was 11.3%. The material tests on the timber were performed following the standard (ISO 3787:1976, 1976). The mean compression elasticity modulus of the timber was 12570 N/mm², and the compression strength parallel to the timber grain was 57.6 N/mm². The cubic compression tests on the concrete were conducted according to GB/T 50081 (2002). The average compressive strength was 39.8 and 50.4 N/mm² for concrete strength grade C40 and C50, respectively. Besides, the material tests on the lag screw were conducted according to ISO 898-1:2013 (2013). The yield strength of the screw connector measured from material tests was 375 N/mm², and the ultimate tensile strength was 462 N/mm².

Test setup

The shear tests setup and measurements are shown in Figure 2. The self-balancing frame was utilized to apply longitudinal shear force on the test specimens, and a 300 kN hydraulic jack was employed to implement the horizontal load on the concrete slab. To measure the relative slips between the timber beam and the concrete slab, one displacement transducer was mounted at the end of the shear test specimens, and two displacement transducers were installed at both sides of the middle specimens. The loading protocol was implemented according to EN 26891:2000 (2000). First of all, the test specimens were loaded to 40% of the estimated ultimate load (F_est) at a speed of 20% F_est per minute. The applied load was maintained at the same level for 30 s. Then, the load was reduced to 10% F_est with a speed of 20% F_est per minute. Afterward, the load was increased to 70% F_est with a rate of 20% F_est per minute. Finally, the further load was increased with a speed of 2 mm/min until the occurrence of either failure or a 15-mm displacement.

Figure 2.

Shear test setup and measurements.

Test results and discussion

Test results

The test results and the patterns of failure occurring to the shear test specimens are presented in Table 2. According to EN 26891:2000 (2000), the shear bearing capacity F_max is defined as the maximum load during the shear tests. The serviceability shear stiffness K_s is determined by the slope of the load–slip curve between 10% and 40% of the estimated ultimate load F_est. In the initial period of loading, the relative slip was small due to the excellent bond between the timber beam and the concrete slab. The ratio between the ultimate slip and yield slip u_u/u_y is used to evaluate the ductility performance of inclined screws (Jorissen and Fragiacomo, 2011). As the applied load increased, the relative slip increased linearly. When the load reached nearly 70% of the maximum load, some horizontal cracks at the position of the inclined screws occurred on the concrete slab. Two types of failure mechanisms were observed from the shear tests: cone expulsion failure of the concrete layer around shear-compression screw and pull-out failure of shear-compression screw, as shown in Figure 3.

Table 2.

Shear test results.

Test series	F_max (per pair)		K_s (per pair)		u_u/u_y	Failure mode
Test series	Average (kN)	Cov (%)	Average (kN/mm)	Cov (%)	u_u/u_y	Failure mode
12-100-T80-C40	45.98	1.7	22.72	7.8	2.51	P
10-100-T80-C40	34.65	2.9	18.02	6.6	2.68	P
8-100-T80-C40	23.75	1.1	13.13	4.1	2.08	P
12-80-T80-C40	42.68	1.4	17.09	6.2	1.95	P
12-120-T80-C40	52.49	1.4	24.79	5.5	2.21	C
12-100-T60-C40	28.26	3.8	21.48	6.5	1.94	C
12-100-T100-C40	44.61	0.8	23.04	6.9	2.07	P
12-100-T80-C50	47.05	3.5	23.55	4.9	1.70	P

u _u: ultimate slip; u_y: yield slip; P: pull-out failure of shear-tension loaded screw; C: cone failure of concrete layer around the shear-compression loaded screw.

Figure 3.

Failure modes of inclined screws. (a) Cone failure of concrete layer and (b) pull-out failure of shear-tension loaded screw.

The load–slip curves are indicative of the shear performance of shear connectors. Figure 4 shows the load–slip curves of inclined screws from the shear tests. During the initial period of loading, the relative slip at the interface showed a linear increase with the rise of load applied. As the load increased to nearly 70% of the ultimate load, the relative slip increased rapidly with the increase in the applied load. In this process, the shear stiffness of inclined screws decreased on a continued basis. After reaching the ultimate load, the load was slowly reduced with the increase in the slip. Overall, the inclined screws in the TCC beams showed a ductility performance, which was attributed to the bending deformation of the screw connectors.

Figure 4.

Load–slip curves of shear test specimens.

Discussion

According to the shear test results (Figure 5), the impacts of the embedment depth of screw into timber, thickness of concrete slab, screw diameter, and concrete strength on the shear stiffness of the inclined screws in TCC beams with timber board interlayer were obtained as follows:

Figure 5(a) shows the experimental results of inclined screws with an embedment length of 80, 100, and 120 mm. As for the screw connectors with an embedment length of 100 and 120 mm, the shear stiffness was increased by 32.9% and 44.4% compared to the screw connectors with an embedment length of 80 mm, respectively. Thus, it can be concluded that, with the increase in the embedment length of screw connectors in timber, the shear stiffness of the inclined screws was increased due to the improved withdrawal capacity of the screw connector.

Figure 5(b) presents the shear test results of inclined screws using a screw diameter of 8, 10, and 12 mm, respectively. The shear stiffness of inclined screws using a screw diameter of 10 and 12 mm was increased by 37.2% and 73.0% compared to the screw connectors using a screw diameter of 8 mm, respectively. It can be summarized that with increase in the screw diameter, the shear stiffness of inclined screws was improved due to the increased lateral stiffness and axial stiffness of the screw connector.

The experimental results of inclined screws with the concrete slab of different thicknesses are presented in Figure 5(c). The shear stiffness of inclined screws was 21.48, 22.72, and 23.04 kN/mm when the thickness of concrete slab was 60, 80, and 100 mm, respectively. It was found that when the embedment depth of screw into concrete remained unchanged, the thickness of concrete slab had no significant impact on the shear stiffness of inclined crossing screws.

The shear stiffness of inclined screws was 22.72 and 23.55 kN/mm for the concrete strength of 40 and 50 MPa, respectively. As the Young modulus of the concrete was considerably larger compared to the timber, the concrete strength exhibited no significant impact on the shear stiffness of inclined crossing screws.

Figure 5.

Influences of different parameters on shear stiffness of inclined crossing screws. (a) Embedment length of screw into timber, (b) screw diameter, and (c) thickness of concrete slab.

Calculation method for predicting shear stiffness

Analytical model for shear stiffness

It is essential to estimate the shear stiffness of connection as the deflection of the TCC beams is significantly affected by the relative slip between the timber beam and the concrete slab. From the experimental and theoretical research works, it can be seen that the shear performance of the inclined screw connector was contributed by the bending resistance and the withdrawal capacity of the screw connector (Du et al., 2019b; Kavaliauskas et al., 2007). In the initial elastic range, the timber beam and the concrete slab can be assumed as the elastic foundation in which the elements of continuous beam are displaced vertically perpendicular to the axis of the screw connector parallel to the compressive force. Therefore, the stiffness and deformation of the screw connector in the surrounding timber and concrete can be regarded as a continuous beam attached to the springs along the embedment length of the screw connector. The compressive stresses P distributed along with the screw connector at any point are directly proportional to the settlement deformation of the foundation y at this point. The formula for calculation is expressed as follows

y = \frac{P}{k}

(1)

The homogeneous differential equation of beam deflection on the elastic foundation can be calculated as

EI \frac{d^{4} y}{d x^{4}} + ky = 0

(2)

Therefore, the deformation of the semi-infinite long beam at the end is determined by

y = - \frac{2 ω}{k} (V + ω M)

(3)

The rotation of semi-infinite long beam at the end is calculated by

φ = - \frac{2 ω^{2}}{k} (V + 2 ω M)

(4)

where y is the settlement deformation of the foundation, P is the compressive stress, k is the foundation modulus, E is the Young modulus of the screw connector, I is the second moment of the cross-sectional area of the screw connector, and $ω = \sqrt[4]{k / 4 EI}$ .

The flexibility coefficients were obtained from the solution of the semi-infinite long beam on elastic foundation, which is loaded by the shear force V and the axial force at the interface between the timber beam and the concrete slab. The analytical model of inclined screw on the elastic foundation is presented in Figure 6. The axial force of the inclined screw embedded in timber beam N can be determined as

N = F_{ax} = k_{ax} π d l_{ax} δ_{ax}

(5)

Thus, the derivation of axial displacements of inclined screw inserted into timber δ_ax can be calculated by

δ_{ax} = \frac{N}{k_{ax} π d l_{ax}}

(6)

where N is the axial force of the inclined screw at the interface, k_ax is the withdrawal stiffness of the inclined screw embedded into the timber beam, d is the diameter of the screw connector, l_ax is the embedded length of the screw connector into timber, and δ_ax is the axial displacements of inclined screw embedded into timber.

Figure 6.

Analytical model for inclined screw in TCC beams with interlayer.

The shear stiffness of the inclined crossing screw can be determined through imposing the continuity of the flexural deformations of the screw connector. With the applied flexibility method, the compatibility equations of the cross-sectional area of the screw connector can be written as

{\begin{matrix} η_{11} V \sin α + η_{12} M \sin α + λ N \cos α = S \\ - η_{11} V \cos α - η_{12} M \cos α + λ N \sin α = 0 \\ φ_{21} V + φ_{22} M = 0 \end{matrix}

(7)

where the flexibility coefficients are

η_{11} = \frac{2 ω_{w}}{k_{w}} + \frac{2 ω_{c}}{k_{c}} + \frac{t^{3}}{3 E_{S} I_{S}} φ_{22} = \frac{4 ω_{w}^{3}}{k_{w}} - \frac{4 ω_{c}^{3}}{k_{c}} - \frac{t}{E_{S} I_{S}}

η_{12} = φ_{21} = - \frac{2 ω_{w}^{2}}{k_{w}} + \frac{2 ω_{c}^{2}}{k_{c}} + \frac{t^{2}}{2 E_{S} I_{S}}

with

λ = \frac{1}{k_{ax} π d l_{ax}}, ω_{w} = \sqrt[4]{k_{w} / 4 E_{S} I_{S}}, ω_{c} = \sqrt[4]{k_{c} / 4 E_{S} I_{S}}

After simplifying equation (7), the compatibility equations can be expressed as

{\begin{matrix} (η_{11} - \frac{η_{12}^{2}}{φ_{22}}) V \sin α + λ N \cos α = S \\ (\frac{η_{12}^{2}}{φ_{22}} - η_{11}) V \cos α + λ N \sin α = 0 \end{matrix}

(8)

The shear stiffness of the inclined screw K_s is calculated by

K_{s} = \frac{F}{S} = \frac{V \sin α + N \cos α}{S}

(9)

Substituting equation (8) into equation (9), the shear stiffness of the inclined screw is calculated as

K_{s} = \frac{φ_{22} \sin^{2} α}{η_{11} φ_{22} - η_{12}^{2}} + \frac{\cos^{2} α}{λ}

(10)

It is worth noting that the theoretical model is premised on the simplifying assumption of the screw connector on a perfectly elastic foundation, ignoring the gap between the screw connector and the composite components (timber beam and concrete slab) and the uneven distribution of the foundation stiffness of the timber and the concrete along with the screw connector. To consider the impacts of these factors on the shear stiffness of the inclined screw, the modified factor γ was introduced into equation (10). The value for γ was obtained by performing the regression of the shear test results from this article and the references (Table 3). Therefore, the calculation formula of the shear stiffness can be expressed as follows

K_{s} = γ (\frac{φ_{22} \sin^{2} α}{η_{11} φ_{22} - η_{12}^{2}} + \frac{\cos^{2} α}{λ})

(11)

where E_s is the Young modulus of the screw connector, I_s is the second moment of cross-sectional area of the screw connector, α is the inclination angle of the screw connector with respect to the timber grain, V is the shear force at the interface, t is the thickness of timber board interlayer, k_w is the foundation stiffness of the timber, $k_{w} = k_{p} \cos α - k_{t} \sin α$ , k_p is the foundation stiffness of timber parallel to the grain, k_t is the foundation stiffness of timber transverse to the grain, k_c is the foundation stiffness of the concrete, and γ= 0.163.

Table 3.

Summary of shear test results of inclined screws.

Authors	Specimens	d (mm)	l _ax (mm)	α (degree)	t (mm)	K _s (kN/mm)
Steinberg et al. (2003)	A	6	100	45	0	15.08
Steinberg et al. (2003)	B	6	100	45	0	9.93
Jorge et al. (2011)	H	7.4	100	45	0	15.90
	Q	7.4	100	45	0	14.60
	P	7.4	100	45	0	15.70
	U	7.4	100	45	0	17.30
	B	7.4	100	45	25	10.50
	V	7.4	100	45	25	10.10
	T	7.4	100	45	25	11.85
	S	7.4	100	45	25	11.90
Mirdad and Chui (2019)	CLP-L80-I5-45°	11	80	45	5	14.88
	CLP-L80-I5-30°	11	80	30	5	20.03
	CLP-L100-I5-45°	11	100	45	5	16.64
	CLP-L100-I5-30°	11	100	30	5	26.31
	CLT-L80-I5-45°	11	80	45	5	14.70
	CLT-L80-I5-30°	11	80	30	5	25.88
	CLT-L100-I5-45°	11	100	45	5	17.21
	CLT-L100-I5-30°	11	100	30	5	27.31
Berardinucci et al. (2017)	CLC8160	8	128	45	44	15.21
Berardinucci et al. (2017)	CLC8240	8	79	45	22	11.21
Kavaliauskas et al. (2007)	Specimen	6	50	45	0	10.87
Fragiacomo (2012)	Specimen	7.5	100	45	0	11.98
Deam et al. (2008)	Specimen17	7.5	100	45	0	14.40
Khorsandnia et al. (2016)	A3	16	160	45	0	33.75
Khorsandnia et al. (2016)	A4	16	160	45	0	35.80

Comparison between test results and theoretical results

The comparisons drawn between the test results and the calculated results are presented in Table 4, where K_s,t is the test results of the shear stiffness of inclined screws and K_s,c is the calculated results of the shear stiffness of inclined screws. The calculation method presented in this article considers the impacts of the material property, screw diameter, embedment length of screw connector into the timber beam, thickness of timber board interlayer, and screw inclination angle on the shear stiffness of the inclined screw. As revealed by the comparison results, the shear stiffness of inclined screws in the TCC beams with timber board interlayer can be well predicted.

Table 4.

Comparison between test results and theoretical results.

Authors	Specimens	K _s,t (kN/mm)	K _s,c (kN/mm)	K _s,t/K_s,c
This article	12-100-T80-C40	22.72	18.38	1.24
	10-100-T80-C40	18.02	16.14	1.12
	8-100-T80-C40	13.13	13.19	0.99
	12-80-T80-C40	17.09	14.70	1.16
	12-120-T80-C40	24.79	22.07	1.12
	12-100-T60-C40	21.48	18.39	1.17
	12-100-T100-C40	22.79	18.39	1.24
	12-100-T80-C50	23.55	18.39	1.28
Steinberg et al. (2003)	A	15.08	16.08	0.94
Steinberg et al. (2003)	B	9.93	16.08	0.62
Jorge et al. (2011)	H	15.90	13.46	1.18
	Q	14.60	13.46	1.08
	P	15.70	13.46	1.17
	U	17.30	13.46	1.28
	B	10.50	11.79	0.89
	V	10.10	11.79	0.86
	T	11.85	11.79	1.01
	S	11.90	11.79	1.01
Mirdad and Chui (2019)	CLP-L80-I5-45°	14.88	18.74	0.79
	CLP-L80-I5-30°	20.03	21.80	0.92
	CLP-L100-I5-45°	16.64	22.12	0.75
	CLP-L100-I5-30°	26.31	26.87	0.98
	CLT-L80-I5-45°	14.70	18.74	0.78
	CLT-L80-I5-30°	25.88	21.80	1.19
	CLT-L100-I5-45°	17.21	22.12	0.78
	CLT-L100-I5-30°	27.31	26.87	1.02
Berardinucci et al. (2017)	CLC8160	15.21	15.85	0.96
Berardinucci et al. (2017)	CLC8240	11.21	10.39	1.08
Kavaliauskas et al. (2007)	Specimen	10.87	10.91	1.00
Fragiacomo (2012)	Specimen	11.98	13.64	0.88
Deam et al. (2008)	Specimen17	14.40	13.65	1.06
Khorsandnia et al. (2016)	A3	33.75	43.86	0.77
Khorsandnia et al. (2016)	A4	35.80	43.86	0.82
Mean				1.00
Coefficient of variation				0.17

Conclusion

The experimental and theoretical research studies were performed to study the shear stiffness of inclined screws in TCC beams with timber board interlayer. The experimental program involved eight groups of shear tests. Besides, the calculation method was proposed to calculate the shear stiffness of inclined screws in the TCC beams with timber board interlayer. Based on the results, the following conclusions are drawn:

The test results indicated that the shear stiffness of the inclined screws with an embedment length of 100 and 120 mm was increased by 32.9% and 44.4% compared to the screw connectors with an embedment length of 80 mm, respectively. When the embedded depth of screw into concrete remained unchanged, the thickness of concrete slab showed no considerable impact on the shear stiffness of inclined crossing screws.

The shear stiffness of inclined screws using the screw diameter of 10 and 12 mm was increased by 37.2% and 73.0% compared to the screw connectors using a screw diameter of 8 mm, respectively. As the Young modulus of the concrete was substantially larger compared to the timber, the concrete strength exhibited no significant impact on the shear stiffness of inclined crossing screws.

Based on the theory of a beam on a two-dimensional elastic foundation, the calculation method for predicting the shear stiffness of inclined screw in TCC beams with timber board interlayer was proposed. The comparison results demonstrated that the shear stiffness of inclined screw can be well predicted using the calculation method as suggested.

Footnotes

Acknowledgements

The author(s) also thank Associate Mrs Tong Zhang for revising and proofreading this article.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research was supported by National Natural Science Foundation of China (Nos. 51678295 and 51478220) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_0914).

ORCID iD

Xiamin Hu

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