Experimental investigation of typical connections for fabricated cold-formed steel structures

Abstract

This article presents a comparative investigation on mechanical behavior and construction characteristics of some typical connections in cold-formed thin-walled steel. The lap shear tests of 96 specimens considering four typical connections with a self-piercing rivet, clinching, self-drilling screw, and blind rivet were conducted. The effects of sheet thickness and thickness ratio on failure modes and mechanical behavior of the four types of connections were investigated. Through analyzing the feasibility of mechanic and construction, the applicability of the four types of connections in fabricated cold-formed steel structures was comprehensively evaluated. The result of the research shows that compared with the other three connections, self-piercing rivet connections are more suitable for modularly fabricated cold-formed steel structures because of its superior mechanical properties, well-formed quality, high efficiency, and potential industrialization. Based on the design methods of fasteners in North American (AISI S100-16) and European standards (prEN1999-1-4) on cold-formed steel structures, an appropriate design method is proposed for self-piercing riveting connections.

Keywords

design method fabricated cold-formed steel structure feasibility of construction feasibility of mechanics typical connections

Introduction

Fabricated cold-formed steel (CFS) structures with lightweight and good seismic performance have been valued and promoted in the industrialization of fabricated buildings because of its suitability for modular design, industrial production, and mechanized assembly (Zhu, 2013). The strength and assembly efficiency of CFS members are largely dependent on fasteners (Lennon et al., 1999). Therefore, an optimal connection technique can significantly improve the competitiveness of CFS structures in the construction market (Davies, 2000). Nowadays, self-drilling screw and welding are commonly used traditional connections in the CFS structural components (Iuorio et al., 2014; Velchev et al., 2010). Blind rivet, bolt, clinching, and self-piercing riveting (SPR) are the main joining technologies in the field of mechanical and automotive engineering (Davies, 2000; Mäkeläinen and Kesti, 1999; Moroni et al., 2010; Pedreschi et al., 1997). Especially, clinching and SPR were used in industrial production lines for joining multiple materials (Meschut et al., 2014). Fiorino et al. (2016, 2017) presented the response of ballistic nails and clinching under monotonic and cyclic shear tests for CFS structures and investigated the seismic behavior of CFS strap-braced stud walls with self-drilling screws. A finite element model was established for single mechanically fastened joints to predict the bearing response of composite plates with different stacking sequences and determine the influence of the failure criteria (Dano et al., 2000). The shear failure of bolted connections used aluminum alloy connecting elements was presented by Menzemer et al. (1999). Failure reasons of overhead power line yoke connector were investigated by Dzǔpona et al. (2013). According to the rivet type, the SPR joints involve SPR, clinch riveting (CR), and solid self-piercing riveting (SSPR) (Mucha, 2015). The mechanical behavior and failure mechanism of riveting joints with various sheet materials were analyzed (Mucha, 2013; Mucha and Witkowski, 2015).

The selection of connection type lies on many factors related to material, strength, process, and others. Some connection types and comparison can be supported by corresponding research (Lorenzo and Landolfo, 2004; Mucha and Witkowski, 2013; Xie et al., 2018). For modularly fabricated CFS structures, the characteristics of steel sheet, mechanical property, construction efficiency, and cost of connection joints must be considered to choose the appropriate connection type. SPR, clinching, blind rivet, and self-drilling screw are selected in this research. The selected connections were also based on the similar specimen geometry, as shown in Figure 1.

Figure 1.

Four types of connections used in cold-formed thin-walled steel sheets: (a) self-piercing rivet, (b) clinching, (c) self-drilling screw, and (d) blind rivet.

SPR connection, one of the main connection techniques used in thin sheets, is a kind of mechanical joining being widely applied to automotive production, which can not only be used for the connection of different metal sheets (Pickin et al., 2007; Sun and Khaleel, 2005) but also produce a joint with smooth surface. The forming process of SPR joints involves driving a separate rivet into the layer of steel sheets, piercing, clinching, and forming an interlock mechanism (Pickin et al., 2007; Yan et al., 2017). In most cases, SPR joints connecting steel sheet feature a high stiffness and strength (Moss and Mahendran, 2002; Mucha and Witkowski, 2013). Haque and Durandet (2016) conducted an experimental investigation of cross tension and lap shear on SPR joints. They concluded that shear strength was greater than tensile strength, and the relationship between shear strength and tensile strength was proposed based on cross-sectional dimensions of SPR joints. Yan et al. (2017) established a constitutive model of SPR connections in CFS and proposed the shear strength design method.

The simplest and most economic connection is clinching without any additional fasteners, which also belongs to the mechanical joint. By means of special clinching tools with the highest stiffness, the sheets generate local cold deformation until interlocking projection is achieved (Mucha, 2011; Mucha and Kaščák, 2010). Mucha and Witkowski (2014) studied the advantages and disadvantages of clinching connections and analyzed the influences of different forming techniques and loading directions on strength of joints. Coppieters et al. (2013) indicated that the axial shear strength was greater than tension strength through analysis of strength on clinching joints. Clinching connection has been used in the fabrication of CFS building systems, which was studied by Pedreschi and Sinha (2006). They conducted a large number of tests on mechanical clinching and predicted its shear strength in CFS structures based on the failure mode.

Self-drilling screws feature high load-carrying capacity and ductility in cold-formed structures, but such connections have a complex working process. Manifold research activities achieved the mechanical behavior and mechanism of screws (Babalola and Laboube, 2004; Laboube and Sokol, 2002; Rogers and Hancock, 1999). Serrette and Peyton (2009) had carried out a series of experimental studies on the shear strength of screws. Lu et al. (2013) introduced the whole test process of both single and multiple self-drilling screw connections and summarized the failure modes of joints.

The most frequently used connection technique is blind rivet in machinery field, which requires pre-drilling and positioning in the sheets. The rivet is inserted into a hole drilled and a special rivet gun is used to pull the rivet mandrel into the rivet body. That makes the rivet body expand and consequently the rivet mandrel snaps off. Such a connection can be inserted and fully installed from only one side of an element or structure. Lorenzo and Landolfo (2004) presented shear experimental response of blind rivets for CFS structures; they concluded that blind rivets have higher performances, both in terms of ductility and strength. Mucha (2015) discussed the influence of sheet material type on blind rivet joints and analyzed its fracture mechanism. Wang et al. (2017) presented a classification of failure modes in friction stir blind riveted lap shear joints with dissimilar materials.

The article presents a comparative investigation on mechanical properties and construction characteristics of the four types of connections which connected overlapped steel sheets. The effects of sheet thickness and thickness ratio on failure modes and mechanical behavior of considered connections are observed. According to the test results and construction characteristics of fabricated CFS structures, the feasibility of the four connections for fabricated CFS structures is comprehensively evaluated.

There is no design method of SPR connection in current standards of civil engineering, and some existing papers have limitations for strength calculation of SPR connections. Based on cross-sectional dimensions, Haque and Durandet (2016) proposed the shear strength formulation of SPR joints, but this method is not suitable for actual engineering design and only considers the case of rivet tail pull-out from the bottom sheet. The shear strength formula of SPR developed by Yan et al. (2017) has too complicated parameters, and it only considers the failure mode of pull-out of the SRP. Therefore, based on the design methods of fasteners in North American and European standards (AISI S100-16:2016, 2016; prEN1999-1-4:2004, 2004) on CFS structures, an appropriate design method is proposed herein for SPR connections.

Experimental investigation

Material property

Galvanized cold-formed thin-walled steel sheets were used for the test specimens. Five different thicknesses (0.8, 1.0, 1.2, 1.5, and 2.0 mm) were used in the research, and their material properties were determined via tests. Based on the method of Metallic Materials—Tensile Testing at Ambient Temperature (GB/T228:2002, 2002), three samples of each thickness were tested to obtain average values of each parameter which are described in Table 1.

Table 1.

Mechanical property of steel sheets.

Material thickness, t (mm)	Yield strength, f_y (MPa)	Tensile strength, f_u (MPa)	Strength yield ratio, f_u/f_y	Young’s modulus, E (10⁵ MPa)	Elongation (%)
0.8	267	365	1.37	2.0	26.56
1.0	240	349	1.45	2.1	35.89
1.2	285	363	1.27	2.1	31.45
1.5	240	330	1.40	2.1	26.43
2.0	234	331	1.42	2.1	38.36

Specimens design and loading scheme

Combination thickness of two sheet strips of 0.8, 1.0, 1.2, 1.5, and 2.0 mm were connected by the considered fasteners to conduct a series of lap shear tests. All galvanized CFS made of DX51D+Z25 were 200 mm long × 60 mm wide with an overlap length of 30 mm (AISI TS-4-02:2002, 2002), as shown in Figure 2. t₁ and t₂ are thickness values of the top sheet and thickness of bottom sheet, respectively. Based on the provisions of screw connections in AISI S100-16:2016 and the research reported by Li et al. (2012), 15 mm end distance was specified for all specimens in this research. Nine different combination thicknesses for each connection and three specimens of each combination were well prepared and labeled. For the size selection of SPR, clinching, self-drilling screw, and blind rivet, the common types used in engineering were selected. The diagram of the bottom dies used for SPR and clinching joint are defined in Figure 3, and the dimension of die is presented in Table 2. Through a large number of pre-tentative strength tests, the dimensions of the fasteners that match the performance of the test steel sheets were determined, as shown in Table 3.

Figure 2.

Diagram of specimens for lap shear test (unit: mm).

Figure 3.

Diagram of the bottom die: (a) the die for SPR joints and (b) the die for clinching joints.

Table 2.

Parameters of the bottom die.

Self-piercing rivet					Clinching
Mold label	H (mm)	h (mm)	D₁ (mm)	D₂ (mm)	Mold label	D_d (mm)	H_d (mm)
RM1	1.70	1.70	7.00	6.00	CM1	5.0	0.7
RM2	1.67	0.55	8.50	5.00	CM2	8.5	1.8
RM3	1.85	0.55	9.00	5.00

Table 3.

Main dimensions for fasteners used in sheet joints.

Sheet combination	Self-piercing rivet				Clinching			Self-drilling screw		Blind rivet
t₁+t₂ (mm)	L₁ (mm)	d_w (mm)	d_s (mm)	Mold	d_p (mm)	d_d (mm)	Mold	L₂ (mm)	d_z (mm)	L₃ (mm)	d_b (mm)
0.8+0.8	4	7.6	5.3	RM1	4.2	5.0	CM1	22	4.2	11	5
1.0+1.0	4.5	7.6	5.3	RM1	4.2	5.0	CM1	22	4.2	11	5
1.2+1.2	5	7.6	5.3	RM3	5.3	8.5	CM2	22	4.2	11	5
1.5+1.5	5.5	7.6	5.3	RM3	5.3	8.5	CM2	22	4.2	11	5
2.0+2.0	6	7.6	5.3	RM2	5.3	8.5	CM2	22	4.2	11	5
0.8+1.5	5	7.6	5.3	RM3	5.3	8.5	CM2	22	4.2	11	5
1.0+1.5	5	7.6	5.3	RM3	5.3	8.5	CM2	22	4.2	11	5
1.2+1.5	5.5	7.6	5.3	RM3	5.3	8.5	CM2	22	4.2	11	5

L₁is the rivet length. d_w and d_s are the diameters of SPR head and tail, respectively. d_p and d_d are the inter diameter and outer diameter. L₂ and d_z are the length and diameter of self-drilling screw. L₃ and d_b are the length and diameter of blind rivet.

The measuring equipment and automatic extensometer were checked and calibrated before the shear test was performed on Zwick Roell Z10 (Figure 4) tensile testing machine with 100-mm long gauge length. The load applied by the machine (maximum tensile force of 30 kN) was controlled by displacement mode. In order to keep performed specimens in a static load condition, the speed of the tensile testing machine was 3 mm/min. The joint deformation was measured by a supporting automatic extensometer in shear tests.

Figure 4.

Loading system on the examined specimen in lap shear test.

Test results and analysis

Failure modes

SPR

The type of failure mode affects the shear response of the lap shear test (Yu, 2000). In CFS structural systems, the effects of thickness ratio (t₂/t₁) on the failure modes of SPR joints can be summarized as: (SPR1) pull-out of rivet tail from the bottom sheet for t₂/t₁ = 1.0 (Figure 5(a)), (SPR2) bearing of the top sheet and pull-out of rivet head from the top sheet for t₂/t₁ ≥ 1.5 (Figure 5(b)), (SPR1+SPR2) mix failure mode, the rivet tail pulled out from the bottom sheet with pull-out of the partial rivet head from the top sheet for 1.0 < t₂/t₁ < 1.5 (Figure 5(c)). The failure mechanism of SPR1 was that the interlocking mechanism failed first due to its shear capacity was less than bearing ability between rivet head and the top sheet, and whole rivet still joined with the top sheet. For SPR2, rivet head extruded the top sheet and led to the expansion of the top sheet hole-wall, in which the shear capacity of interlocking mechanism was greater than the bearing ability of top sheet.

Figure 5.

Failure modes of self-piercing rivet joints: (a) failure mode SPR1, (b) failure mode SPR2, (c) mix failure mode of SPR1 and SPR2.

Clinching

The thickness ratio (t₂/t₁) has less influence on the failure modes of clinching joints. Mucha and Witkowski (2014) have observed that a different destruction mechanism of clinching depends on the interlock shape and values of parameters (thickness of the embossment, width of the interlock in the upper sheet, and width of the interlock in the lower sheet) during the shearing test. In clinching lap joint shear test, the following failure modes were observed: (C1) neck fracture (Figure 6(a)), fracture occurred in the neck thickness under the action of horizontal shear force. (C2) the separation of the top sheet and the bottom sheet (Figure 6(b)), failure mode occurred due to the insufficient interlocking between two sheets.

Figure 6.

Failure mode of clinching joints: (a) failure mode C1 and (b) failure mode C2.

Self-drilling screw

In cold-formed shear connections made of self-drilling screws, three basic types of failure modes usually occur: (SDS1) titling and bearing (Figure 7(a)) for t₂/t₁ = 1.0, (SDS2) shearing of fastener (Figure 7(b)), and (SDS3) shearing of the top sheet (Figure 7(c)) for t₂/t₁ ≥ 1.5. For the failure mode SDS1, self-drilling screw underwent severe titling and the top sheet was extruded by screw head. For the failure mode SDS2, the self-drilling screw was sheared when the combination thickness was 2.0+2.0 mm. This is due to the higher shear strength of steel sheet than the self-drilling screw. The top sheet was sheared by screw head along the length of sheet where the bearing ability of steel sheet is lower for the failure mode SDS3.

Figure 7.

Failure modes of self-drilling screw joints: (a) failure mode SDS1, (b) failure mode SDS2, and (c) failure mode SDS3.

Blind rivet

The failure mode of blind rivet joints can be concluded as three types under different thickness ratio (t₂/t₁) as follows: (BR1) titling and bearing of rivet for t₂/t₁ = 1.0 (Figure 8(a)), (BR2) shearing of rivet for 2.0+2.0 mm (Figure 8(b)), (BR3) pull-out of rivet head from the top sheet for t₂/t₁ ≥ 1.5 (Figure 8(c)). The mechanism of failure mode BR1 and BR2 were, respectively, similar with failure mode SDS1 and SDS2 of the self-drilling screw. For the failure mode BR3, the rivet occurred tilting and the rivet head pulled out from the top sheet. This is due to the lower bearing ability of the top sheet.

Figure 8.

Failure modes of blind rivet joints: (a) failure mode BR1, (b) failure mode BR2, and (c) failure mode BR3.

To summarize, the thickness ratio (t₂/t₁) has less influence on the failure mode of clinching joints, but it has a greater influence on that of SPR, self-drilling screws and blind rivet joints. Table 4 shows designation of failure modes for the four connections. It can be concluded that the failure modes of the foregoing three types were mainly manifested as tilting and bearing when the thickness ratio (t₂/t₁) was equal to 1, and pull-out of fastener or shearing of the top sheet usually occurred when the thickness ratio (t₂/t₁) was greater than or equal to 1.5. The shear failure mode appeared on self-drilling screw and blind rivet joints for the combination thickness of 2.0+2.0 mm in which the fastener was snipped. This mode belongs to brittle failure where the fastener abruptly failed before the sheets, which caused the joint to not make full use of its mechanical properties. The fastener, therefore, needs to consider the performance matching with the sheet material.

Table 4.

Designation of failure modes for all specimens joint.

Sheet combination, t₁+t₂ (mm)	Failure modes of shear specimen
Sheet combination, t₁+t₂ (mm)	Self-piercing rivet	Clinching	Self-drilling screw	Blind rivet
0.8+0.8	SPR1	C1	SDS1	BR1
1.0+1.0	SPR1	C1	SDS1	BR1
1.2+1.2	SPR1	C1	SDS1	BR1
1.5+1.5	SPR1	C1	SDS1	BR1
2.0+2.0	SPR1	C1	SDS3	BR3
0.8+1.5	SPR2	C2	SDS2	BR2
1.0+1.5	SPR2	C1	SDS2	BR2
1.2+1.5	SPR1+SPR2	C1	SDS1	BR1

The curves of load–deformation

The comparison among the average shear load–deformation responses of the considered connecting systems under the combination of the same sheet thickness and different thicknesses are shown in Figures 9 and 10. In regard to shear specimens of SPR connections, it can be concluded that the curves of load–deformation can be divided into four stages: elastic stage (linear relationship between load and deformation), elastic–plastic stage (nonlinear increase relationship between load and deformation), plastic stage (nonlinear slow drop relationship between load and slip), and failure stage (sharply drop relationship between load and deformation), see Figures 9 and 10. Comparing to the shear responses of SPR, clinching has a shorter plastic stage, and self-drilling screw and blind rivet have a longer elastic–plastic stage.

Figure 9.

Typical load–deformation curves of four connections: (a) 0.8+0.8 mm, (b) 1.0+1.0 mm, (c) 1.2+1.2 mm, (d) 1.5+1.5 mm, and (e) 2.0+2.0 mm.

Figure 10.

Typical load–deformation curves of four connections: (a) 0.8+1.5 mm, (b) 1.0+1.5 mm, and (c) 1.2+1.5 mm.

It can be seen from Figure 9 that the shear capacity of SPR and self-drilling screw connections have strong increments with the increase in the sheet thickness, and the shear capacity of SPR was superior to the other three. SPR and clinching, both of which have high stiffness, provided much larger slopes than the other two. However, both the self-drilling screw and blind rivet showed a higher deformability, and their ultimate deformation in shear responses were greater than SPR and clinching. The shear capacity of the four connections increased with a decrease in sheet thickness ratio (Figure 10). The biggest increment in SPR was achieved in comparison with all other connection types tested, see Figure 10.

Analysis and evaluation of feasibility of the four connections

Comparison analysis of mechanical behavior

In order to investigate the mechanical feasibility of the considered connections in fabricated CFS structures, the performances of all specimens tested including shear stiffness, peak load, ductility, and separation energy were made a contrastive analysis. Figure 11 shows the simplified load–deformation curve of shear test on connection, and the parameters were used to describe the shear behavior as follows: P_max is peak load on shear load–deformation curve; u_p is deformation corresponding to P_max; P_y is yield load equals to 0.8P_max (Shi et al., 2009); u_y is yield deformation corresponding to P_y; P_u is ultimate load equals to 0.8P_max; u_u is ultimate deformation corresponding to P_u; K_e is shear stiffness equals to P_y/u_y; μ is ductility factor equals to u_u/u_y; and E is separation energy defined as the area between load–deformation curve and the u axis (0 < u < u_u).

Figure 11.

Definition of parameters for shear behavior of connections.

Table 5 shows the comparison of shear stiffness for four types of connections. The average stiffness of SPR connections was 11 times greater than self-drilling screws and about 7 times greater than the specimens joined by blind rivets. The average stiffness of clinching connections was 14 times greater than self-drilling screws and about 9 times greater than blind rivets. What’s more, the shear stiffness of four types of connections increased with the increase in the combined sheet thickness or the decrease in the thickness ratio (t₂/t₁). Compared with self-drilling screw and blind rivet, SPR and clinching had higher shear stiffness due to their especial forming mechanism.

Table 5.

The comparison of shear stiffness for four type connections.

Sheet combination	Self-piercing rivet	Clinching	Self-drilling screw	Blind rivet
t₁+t₂ (mm)	K_se (kN/mm)	K_ce (kN/mm)	K_ze (kN/mm)	K_be (kN/mm)
0.8+0.8	12.45	8.88	0.80	3.77
1.0+1.0	14.34	12.12	0.66	2.44
1.2+1.2	16.95	16.49	1.29	1.65
1.5+1.5	27.93	20.28	2.60	1.58
2.0+2.0	12.90	55.17	1.89	3.10
0.8+1.5	8.54	9.19	1.02	1.34
1.0+1.5	10.43	16.24	0.93	1.40
1.2+1.5	19.91	18.27	1.79	1.61
Average	15.43	18.27	1.37	1.61

Table 6 lists the peak load of the four connections with different steel thicknesses. The average peak load of all specimens connected by SPR was about one time greater than self-drilling screws and blind rivets and two times greater than clinching. In addition, the shear strength of the four connections increased with the increase in the combined sheet thickness or the decrease in the thickness ratio (t₂/t₁). Compared with clinching, the connection of SPR, self-drilling screw and blind rivet had higher shear strength because of the existing fastener in their joints. In particular, the shear strength of SPR was highest than the others.

Table 6.

Peak load of four connections with different steel thicknesses.

Sheet combination	Self-piercing rivet	Clinching	Self-drilling screw	Blind rivet
t₁+t₂ (mm)	P_max (kN)	P_max (kN)	P_max (kN)	P_max (kN)
0.8+0.8	3.54	0.94	2.53	3.22
1.0+1.0	4.57	1.53	3.00	4.81
1.2+1.2	6.34	2.22	3.72	5.52
1.5+1.5	7.35	2.73	5.74	5.96
2.0+2.0	9.39	2.49	7.27	6.21
0.8+1.5	4.34	3.67	4.42	4.78
1.0+1.5	5.46	3.53	5.25	5.26
1.2+1.5	6.63	3.13	5.44	5.55
Average	5.95	2.53	4.67	5.16

Table 7 shows the comparison of ductility and ultimate deformation for four types of connections. The ductility factors of SPR and clinching connections were superior to self-drilling screw and blind rivet connections, but their ultimate deformation was inferior to self-drilling screws and blind rivets, as shown in Table 7. Energy values of the four connections are illustrated in Figure 12. The mean energy of each type of connection increased with the increase in the sheet thickness. Clinching connections show the worst ability of energy dissipation. For self-drilling screws and blind rivets, tilting and slipping of the fastener lead to larger deformation and good separation energy. For SPR and clinching connections, forming mechanism of joint caused smaller deformability and larger ductility.

Table 7.

Ductility and ultimate deformation of four connections for different steel thicknesses.

Connections	Mechanical parameters	Sheet combination, t₁+t₂ (mm)
Connections	Mechanical parameters	0.8+0.8	1.0+1.0	1.2+1.2	1.5+1.5	2.0+2.0	0.8+1.5	1.0+1.5	1.2+1.5
Self-piercing rivet	u _y	0.23	0.26	0.31	0.21	0.59	0.41	0.42	0.27
	u _u	2.13	2.70	3.05	3.87	3.77	3.80	4.16	2.79
	μ	9.36	10.64	12.17	18.46	6.47	9.21	9.95	10.49
Clinching	u _y	0.05	0.10	0.10	0.11	0.14	0.32	0.17	0.14
	u _u	0.25	0.56	0.60	0.66	0.86	1.20	0.96	0.81
	μ	5.01	5.56	5.80	6.08	20.25	3.75	5.54	5.92
Self-drilling screw	u _y	2.53	3.63	2.11	2.60	3.11	3.48	2.43	3.94
	u _u	4.88	6.57	6.46	7.30	5.92	8.83	9.03	7.80
	μ	1.93	1.81	3.06	2.80	1.91	2.54	3.72	1.98
Blind rivet	u _y	0.69	1.58	2.76	3.13	1.61	2.89	3.03	3.04
	u _u	5.76	8.04	9.18	9.30	5.07	11.58	9.18	8.47
	μ	8.40	5.12	3.43	3.05	3.15	4.04	3.04	2.74

Figure 12.

Energy values of same sheet combination.

According to the above analysis, the forming mechanism of SPR and clinching joint is dissimilar with the self-drilling screw and blind rivet. The interlocking mechanism with outstanding shear stiffness in SPR or clinching joints gave two steel sheets stronger connection and better integrality. However, the interlocking mechanism has low deformability, which causes relatively worse separation energy in shear test. For the connections of self-drilling screw and blind rivet, there was bad integrality between steel sheet and fastener. As the load was applied, the fastener began to tilt and extrude the sheet that has made such connections generated low stiffness, but deformability and separation energy were great. In summary, compared with self-drilling screw and blind rivet, SPR and clinching connections have high shear stiffness. Self-drilling screw and blind rivet own outstanding deformability and separation energy.

The analysis of construction feasibility

To study the construction feasibility of the considered connections in fabricated CFS structures, Table 8 gives the contrast results of the construction characteristic or cost of the four connections. It can be known that (1) from the point of view of the construction process and connection efficiency, self-drilling screw and blind rivet need some pre-processing for a preliminary clamping, and positioning and drilling of sheets in a specified way to place in the fasteners, which would be time-consuming and may reduce efficiency of industrial production. SPR and clinching were installed on the two overlapped sheets by special mechanical devices, which do not require any pre-processing and also enable quick assembly of CFS components. (2) From the formed quality and appearance of joints perspective, SPR joints were tightly interlocked with the sheets, and the joints have a high quality and good appearance with smooth surfaces. However, the joints of self-drilling screws and blind rivets were relatively loose with the micro-size of clearance between sheet hole-wall and fastener and have an uneven surface with a protruding fastener head or tail. (3) Self-drilling screws and blind rivets were mainly suitable for on-site construction of CFS structures due to their simple and convenient tools: electric drill and air riveter which have high construction flexibility. SPR and clinching require special riveting equipment which has the problem of space interference when riveting. Therefore, both of which are only suitable for industrial production lines and are very suitable to be used in fabricated modular constructions. (4) Clinching, without additional fasteners, has the lowest cost. Self-drilling screws also have low cost because of their cheapness. SPR and blind rivet connections demand for special fasteners and equipment, so high cost will be taken.

Table 8.

Comparison of construction feasibility for the four connections.

Connections	Construction characteristics
Connections	Procedure	Connection efficiency	Formed quality	Appearance	Flexibility	Cost
Self-piercing rivet	Simple	A	A	A	D	A
Clinching	Simple	B	A	B	D	D
Self-drilling screw	Complex	C	D	D	B	C
Blind rivet	Complex	C	B	D	C	A

A represents high or excellent. B represents good. C represents middle. D represents low or poor.

Feasibility evaluation

Based on the feasibility analysis of mechanical behavior and construction characteristics, the four connection types, SPR, clinching, self-drilling screw, and blind rivet, were evaluated and their feasibility in fabricated CFS structures is given as follows:

SPR connections with a simple process, good formed quality and appearance, high connection efficiency, and potential industrialization are appropriate for fabricated CFS structures. High shear capacity, stiffness, and ductility are achieved in comparison with all other types in spite of existing disadvantages of high cost and poor flexibility. According to current state of art (He et al., 2008; Yan et al., 2017), SPR connections are not suitable for the construction on site because of limits from construction techniques and space interference of riveting equipment, but it can be used in components assembly on production lines. The walls or floors of the overall CFS structures are divided into a multiple number of standard modules based on building modular, in which components are accomplished by SPR connections on production lines. In addition, for achieved modules, a small number of fasteners with high flexibility are used to assemble on site.

Clinching connections have some obvious advantages which include high stiffness, efficiency, simple process, and low cost. However, it is not advised to join stress components in CFS structural systems using this connection type due to its lower shear ability, deformability, and construction flexibility.

Self-drilling screw connections with high ductility, deformability, and low cost can be used on the construction site because of its high flexibility. But the disadvantages of complicated process, low efficiency, poor quality, and appearance, still exist in this type of connection. This connection is not suitable to be used in fabricated modular assembly at the factory.

Similar to self-drilling screw connections, blind rivet connections have high shear capacity, ductility, and construction flexibility, and have some disadvantages which include complicated processes, low efficiency, difficulty in automation, poor quality and appearance, and is more expensive. Therefore, it is less used in CFS structures.

The shear strength design for SPR connections

According to the analysis of the preceding context, the mechanical property and potential industrialization of SPR in comparison to the other types of connections tested are the greatest.

For the shear strength design of fasteners on CFS structures, the shear design method of screws, power-actuated fasteners (PAFs) and others were recommended in American standard AISI S100-16:2016. European standard prEN1999-1-4 on CFS structures adopted the design rules of blind rivets to SPR connections. There was no corresponding design method for SPR in current specifications.

The provisions of screws were recommended by American standard AISI S100-16:2016. For failure modes of tilting and bearing, the nominal shear strength of sheet per screw, P_nv, was determined in accordance with the following section. For t₂/t₁ ≤ 1.0, P_nv shall be taken as the smallest of

P_{nv} = 4.2 (t_{2}^{3} d)^{0.5} F_{u 2}

(1)

P_{nv} = 2.7 t_{1} d F_{u 1}

(2)

P_{nv} = 2.7 t_{2} d F_{u 2}

(3)

For t₂/t₁ ≥ 2.5, P_nv shall be taken as the smaller of

P_{nv} = 2.7 t_{1} d F_{u 1}

(4)

P_{nv} = 2.7 t_{2} d F_{u 2}

(5)

For 1.0 < t₂/t₁ < 2.5, P_nv shall be calculated by liner interpolation between the above two cases. Where P_nv is the nominal shear strength of sheet per screw (N), t₁ is thickness of sheet in contact with screw head or washer, t₂ is thickness of sheet not in contact with screw head or washer, d is nominal screw diameter, F_u1 is tensile strength in contact with screw head or washer (N/mm²), and F_u2 is tensile strength not in contact with screw head or washer (N/mm²).

The provisions of PAFs were recommended by American standard AISI S100-16:2016. Shear strength of PAFs on the basis of different failure modes:

For bearing and tilting strength

P_{nb} = α_{b} d_{s} t_{1} F_{u 1}

(6)

For pull-out strength

P_{nos} = \frac{d_{ae}^{1.8} t_{2}^{0.2} {(F_{y 2} E^{2})}^{1 / 3}}{30}

(7)

where P_nb is nominal bearing and tilting strength of per PAF (N), P_nos is nominal pull-out strength in shear per PAF (N), d_s is nominal shank diameter, d_ae is average embedded diameter, α_b is calculation coefficient (α_b = 3.2), t₁ is thickness of sheet in contact with PAF head or washer, t₂ is thickness of sheet not in contact with PAF head or washer, F_u1 is tensile strength in contact with PAF head or washer (N/mm²), and F_u2 is tensile strength not in contact with PAF head or washer (N/mm²).

The failure modes of SPRs are similar with PAFs in shear. This method could be utilized to calculate SPR shear strength. At present, based on European standard prEN1999-1-4, Europe adopted the design rule of blind rivets as follows

F_{b} = α f_{u} dt / γ_{M}

(8)

where F_b is bearing strength of per blind rivet, d is rivet diameter (N), f_u is tensile strength of parent material (N/mm²), t is thickness of thinner sheet, t₁ is thickness of thicker sheet, α is calculation coefficient (for t₁/t = 1, α = 3.2(t/d)^0.5 and α ≤ 2.1; for t₁/t ≥ 1, α = 2.1; for 1 < t₁/t < 2.5, α is liner interpolation of the above two cases), and γ_M is influence coefficient (γ_M = 1.25).

This method is only considered for bearing failure. The mechanical mechanism and failure mode of SPR are different from blind rivet in shear.

Adopting the above three methods to calculate shear strength of SPR connections, the calculation values under different combinations of sheet materials are tabulated in Table 9. The mean values of test strength and nominal strength ratio of SPR connections are 1.24, 2.15, and 1.99, respectively. It can be seen that the values calculated by screw design method recommended by American Standard AISI S100-16:2016 are closer to the actual values of SPR. When SPR connections with bearing failure use the PAFs design method of bearing and tilting strength, the test results are the nearest to calculation values.

Table 9.

Calculated results of shear strength for different design methods.

Sheet combination, t₁+t₂ (mm)	Design methods
	North American		European standard	Proposed	Failure mode of SPR
	P_max/P_nv	P_max/P_nb (P_nos)	P_max/F_s	P_max/P_s	Failure mode of SPR
0.8+0.8	1.40	0.23	2.30	1.02	SPR1
1.0+1.0	1.35	0.27	2.22	0.98
1.2+1.2	1.37	0.36	2.25	1.00
1.5+1.5	1.30	0.43	2.14	0.95
2.0+1.5	1.05	0.50	1.72	1.06
1.2+1.5	1.29	0.37	1.76	1.00
1.5+2.0	1.28	0.43	1.77	1.01
0.8+1.5	1.04	0.88	1.88	0.98	SPR2
1.0+1.5	1.09	0.92	1.88	1.03	SPR2
Mean value	1.24	0.49	1.99	1.00	–
Coefficient of variation	0.12	0.51	0.12	0.04	–

SPR: self-piercing rivet.

According to the above analysis and referring to the design principle of screws and PAFs, a design method of shear strength for SPR CFS was proposed in this article under failure mode SPR1 and failure mode SPR2:

For t₂/t₁ ≤ 1.0

P_{s} = α_{a} (t_{2}^{3} d_{s})^{0.5} F_{u 2}

(9)

For t₂/t₁ ≥ 1.5

P_{s} = α_{b} d_{w} t_{1} F_{u 1}

(10)

For 1.0 < t₂/t₁ < 1.5, P_s shall be taken as the smaller of the above two cases. Where P_s is nominal shear strength of sheet per SPR (N); t₁ is thickness of sheet in contact with rivet head; t₂ is thickness of sheet in contact with rivet tail; d_s is nominal rivet diameter; d_w is nominal rivet head diameter; F_u1 is tensile strength in contact with rivet head (N/mm²); F_u2 is tensile strength in contact with rivet tail (N/mm²); α_a and α_b are calculation coefficient defined in Table 10, and α_a = 5.8, α_b = 2.0.

Table 10.

Definition of calculated coefficient for SPR connection.

Sheet combination, t₁+t₂ (mm)	$α_{a} = P_{\max} / ((t_{2}^{3} d_{s})^{0.5} F_{u 2})$
Sheet combination, t₁+t₂ (mm)	Specimen 1	Specimen 2	Specimen 3	Average value	Standard deviation	Variation coefficient	α
0.8+0.8	5.64	6.04	6.00	5.89	0.22	0.04	5.8
1.0+1.0	5.49	5.81	5.76	5.69	0.17	0.03
1.2+1.2	5.76	5.77	5.78	5.77	0.01	0.00
1.5+1.5	5.43	5.50	5.47	5.46	0.03	0.01
2.0+1.5	6.12	6.09	6.10	6.10	0.01	0.00
	$α_{b} = P_{max} / (d_{w} t_{1} F_{u 1})$
0.8+1.5	1.91	1.94	2.02	1.95	0.05	0.03	2.0
1.0+1.5	2.10	2.01	2.06	2.06	0.05	0.02	2.0

SPR: self-piercing rivet.

Table 9 lists the results of the four design methods (AISI S100-16:2016, prEN1999-1-4, and this article) for tested value and calculated value ratio. The average values of the four connections’ ratios under different sheet combinations are 1.24, 0.49, 1.99 and 1.00, respectively, and the coefficient of variations (COVs) are 0.12, 0.51, 0.12, and 0.04. After amending existing methods in standards, the proposed method in this article is more accurate and reasonable than other calculation methods.

In accordance with Chapter B3.2 of AISI S100-16:2016, connections shall be designed to have strength such that the available strength equals or exceeds the required strength. Based on the provisions of Chapter K in AISI S100-16:2016 to determine the resistance factor, ϕ, for load resistance factor design (LRFD) and the safety factor, Ω, for the allowable strength design (ASD), the resistance factor and safety factor for the proposed shear strength method can be defined by equations (11) and (12)

ϕ = C_{ϕ} (M_{m} F_{m} P_{m}) e^{- β_{o} \sqrt{V_{M}^{2} + V_{F}^{2} + C_{P} V_{P}^{2} + V_{Q}^{2}}}

(11)

Ω = 1.6 / ϕ

(12)

where C_ϕ = a calibration coefficient = 1.52; M_m = material factor = mean value = 1.10 (AISI S100-16:2016, Table K2.1.1-1); F_m = fabrication factor mean value = 1.0 (AISI S100-16:2016, Table K2.1.1-1); P_m = professional factor mean value = 1.0; β_o = target reliability index = 3.5 (for connections for LRFD); V_M = material factor COV = 0.10 (AISI S100-16:2016, Table K2.1.1-1); V_F = fabrication factor COV = 0.15 (AISI S100-16:2016, Table K2.1.1-1); C_p = correction factor (5.7 for n = 3 and (n+1)(n−1)/(n(n − 3)) for n ≥ 4); V_p = test results COV = 0.07; V_Q = load effect COV = 2.1 (for LRFD and least significant difference (LSD)); and e = 2.718. Table 11 shows data of all relevant parameters as well as the calculated values of the resistance factor and safety factor.

Table 11.

Statistical data for resistance factor and safety factor.

Statistical data	Shear design for failure mode (SPR1) (equation (9))	Shear design for failure mode (SPR2) (equation (10))
Quantity	15	6
Mean	1.00	1.00
Standard deviation	0.04	0.04
COV	0.04	0.04
M _m	1.10	1.10
F _m	1.00	1.00
P _m	1.00	1.00
β_o (LRFD)	3.5	3.5
V _M	0.10	0.10
V _F	0.15	0.15
C _P	1.24	1.94
V _P	0.07	0.07
V _Q	0.21	0.21
ϕ (LRFD)	0.61	0.60
Ω (ASD)	2.60	2.65

COV: coefficient of variation; LRFD: load resistance factor design; ASD: allowable strength design.

Conclusion

Shear tests were conducted on SPR connections, clinching connections, self-drilling connections, and blind rivet connections for nine thicknesses of two layers steel sheets. The characterization of mechanical behavior and construction characteristics of each fastener were done. This analyzed their feasibility and applicability in fabricated CFS structural systems. A design method of SPR connections was developed based on the methods of other fasteners in available standards:

The thickness ratio (t₂/t₁) has less influence on the failure mode of clinching connections, but has great influence on that of SPR, self-drilling screw, and blind rivet connections. When the thickness ratio (t₂/t₁) was equal to 1, the failure modes of SPR, self-drilling screw, and blind rivet connections were mainly manifested as the fastener tilting and pulling out. When the thickness ratio (t₂/t₁) was greater than or equal to 1.5, bearing of the top sheet usually occurred.

Compared with self-drilling screw and blind rivet, SPR connections show higher shear strength, stiffness, and ductility, but its deformability and separation energy are smaller. The above mechanical performance parameters increase with the increase in the sheet thickness or the decrease in the thickness ratio.

Self-drilling screw and blind rivet connections have a high shear strength and ductility but also have some disadvantages such as complex procedures, low connecting efficiency, difficulty in automation, and poor formed quality and appearance. They are suitable for construction sites of CFS structures due to their construction flexibility.

Clinching connections show high stiffness, connecting efficiency, simple procedures, and the lowest cost, but its shear capacity and deformability are low and construction flexibility is poor. Therefore, it cannot be used as stress components in cold-formed thin-walled steel structures.

SPR connections had poor construction flexibility and high cost. However, SPR connections are very suitable to be used in the fabricated modular assembly for CFS structures because of its simple process, good formed quality, appearance, high connection efficiency, and potential industrialization.

Based on different failure modes, the design method of shear strength is proposed for SPR connection. Compared with the design methods of fasteners in existing standards, the design method proposed in this article has higher accuracy and gives more reasonable predictions.

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant No. 51678008). The authors express their gratitude for this financial support.

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