1 Introduction

Over the years, the application of CFS in construction has increased due to more researches done to ensure the stability and quality of the structure. Even though CFS was widely used in structural components such as roof trusses, wall panels, frames, etc., the connection problems in cold formed was an issue that caused buckling and instability due to thin-wall behavior [1–3]. This relates to the safety issues of structure, stiffness of members, the failure modes of steel members and the strength of CFS. Besides that, more research began to take place in the design of cold formed members, wall and systems and seismic design of CFS structure. CFS were then utilized in important structural members and low rise building as well as mid-rise construction [4]. For this analysis, exact dimension used of LCS and RHS for FEA were tabulated in Table 1.

Table 1 Exact dimension of cold formed LCS and RHS
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As the demand of CFS connection increased for roof truss, there was a need to analyze the suitable connection for trusses to ensure an effective connection between truss members. Pitched roof such as Fink truss and Howe truss were very commonly used as it transfers the applied load to the supports without the need for web members. Self-drilling screws was very effective in CFS connection because it can be operated easily and clamped two or more thin steel sheets without any special tools. CFS is chosen as building material due to many advantages like lightweight, high strength and stiffness, ease of prefabrication and mass production, fast and easy erection and installation, economy in transportation and handling, recyclable, energy efficiency and durable [5]. The thickness of CFS was from 1.2 to 3.2 mm with yield strength from 250 to 450 N/mm2 [6].

Connection in steel structure was very important. If the connection was not designed properly, it can lead to weak links of the structure which can affect its serviceability due to large deflections [7]. The earthquake in Northridge, California (1994) and later the Kobe, Japan (1995) caused many cases of structural failure due to failure of connection [8].

It was revealed that connection strength per screw of a connection decreases as the number of screws in the connection increases [9]. This was caused by ‘group effect’ reduction, which was defined as the ratio of the connection strength per screw to the average strength for a single screw connection of the same thickness of steel sheet and same screw size. Besides, tilt fastener was recommended to be eliminated during screw shear strength tests for more accurate shear strength of a fastener [10]. Due to the thin-walled behavior, CFS exhibited different failure mode and large deformation as the buckling was the major concern of the connection structural analysis [10].

Web crippling at points of concentrated load and supports can be a critical problem in CFS structure. It often occurs in cold formed members because the loads eccentric from the web centerline due to the rounded corners of the sections. The webs were slender and unstiffened in CFS, unlike hot rolled where web stiffeners are used [11]. Often, this was the case for beams such as Z purlins and C purlins which may undergo flexural-torsional buckling because of low torsional stiffness, if not properly braced. Moreover, the section was mainly experience torques and distortional buckling because the sections were usually loaded eccentrically from it shear center [12].

The shear increased when the number of screws increased [13]. Similar to the study in LaBoube and Sokol [9], it has shown a declining trend that the connection strength per screw will decrease as the number of screws in a connection increases due to the group effect in screw connection. The arrangement of screws did not significantly influence the strength of the screws as the group effect only varied less than 10% [14]. However, the screw connection strength for multiple screws was lower than the strength of single screw connection.

Due to the raining season in Malaysia, these pitched roofs were very commonly used because the roofs were well designed for water evacuation. Screws were very effective to fasten structural members and to connect individual panels. It was a convenient method for joining thin steel section as it does not require heavy and precise tools at the site [3]. Recently, Hamid and Harsad [14] carried a study on CFS single shear connection by setting the design parameters of screws number from two to six screws. Similar to the study in LaBoube and Sokol [9] it has shown a declining trend that the connection strength per screw will decrease as the number of screws in a connection increases due to the group effect in screw connection. Randy and LaBoube [15] explained that screws might experience secondary stresses and lead to premature failure that caused the reduction of shear in connection. Due to the deformation of screws, Koka et al. [16] suggested a connection of screws with not more than three screws to avoid disproportional load distribution on the screw connection.

2 Finite Element Analysis

This study was done by using LUSAS to understand the behaviour of connection in truss system. By assigning different number of screws, the results of all these cases was compared. The connection for Howe and Fink truss were investigated at side and peak location of the truss system for LCS and RHS. It is known as a pitched truss and very efficient to transfer the applied loads directly to the support through top chord members without the need for web members. During heavy rain, pitched roofs were also better when dealing with water evacuation due to the ‘A’ frame slopes. It was very durable if designed properly as compared to other types of truss system.

As stated in BS 5534, a minimum roof pitch of 20° was recommended. For this analysis, the angle for both types of truss was 25° with a span of 9 m. The overall height of the truss was 2.1 m. The details of truss dimension for Howe truss and Fink truss are shown in Figs. 1 and 2, respectively.

Fig. 1
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Dimension of Howe truss

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Fig. 2
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Dimension of Fink truss

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2.1 Section Properties

More research began to take place in the design of cold formed members, wall and systems and seismic design of CFS structure. CFS were then utilized in important structural members and low rise building as well as mid-rise construction [4].

The smooth surface of CFS was presented with grey finishes. Compared to hot-rolled, CFS gives aggregable surface finish, and has better tolerant in terms of concentricity, and straightness. There were different shapes and types of CFS including the open sections, closed sections and built-up sections, for example lipped channels (C sections), Z section, double channel I beams, hat sections, box sections and etc. The shape used for this analysis as shown in respective figure. The entire buildings and for roof, floor and wall systems normally involved with this type of section. Besides, CFS was normally applied for individual framing members such as studs, joists and truss members.

For this analysis, the section properties for the cold formed LCS and cold formed RHS are shown in Table 2a, b. Both sections used the same thickness of 0.75 mm. The steel grade was hot dip galvanized steel. The yield stress was a minimum of 550 MPa for thickness less than 1.2 mm. The coating of steel was galvanized iron or real zinc or zincalume to avoid corrosion.

Table 2 (a) LCS properties, (b) RHS properties
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2.2 Screw Specification

The self-drilling screw used in the cold formed connection of truss was 4 mm hex washer head with drilling point, hardened, chromium VI Free Zinc Plated. The screw specification is shown in Fig. 3. However, in modelling, screw connection was simplified to pinned support for ease of interpretation.

Fig. 3
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Self-drilling screw dimension

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Table 3 show the different number of screws that have been modelled using LUSAS. Case 1 was the typical of screws used at the site while Case 2 and Case 3 were modified by adding more screws.

Table 3 Cases for number of screw connection
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The surface mesh with element size 10 mm was assigned to all the truss members. The self-drilling screw used in the cold formed connection of truss was 4 mm. All the supports were set as fixed support and pinned support. The loads assigned include live load of 0.25 kN and dead load of 0.598 kN. The material assigned to the model was similar to the actual truss member which was CFS with Young’s Modulus of 200 GPa.

2.3 Convergence Analysis

LUSAS 14 was used for finite element analysis in this research. All the dimension and other parameters of the models were mentioned in Sect. 1. In order to determine the meshing size, the side location of RHS is used to determine the effect of different meshing. An analysis was run by using different element size of 30, 10 and 5 mm, while other attributes of the model remained the same. The overall time taken to run the analysis becomes longer when the element size gets smaller, this is because it leads to more accurate result of FEA. As shown in Fig. 4, it can be seen that the denser the meshing of models, the smaller the element size.

Fig. 4
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The meshing of different element size a 30 mm, b 10 mm, c 5 mm

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Figure 5 shows the contours for these three different meshing. Similarly, the smaller the element size, the smoother the contours as shown in the figure.

Fig. 5
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The contour of different element size a 30 mm, b 10 mm, c 5 mm

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It is also found that the element size affects the deformed mesh. When the meshing is too big, the deformed shape is not too obvious as shown in Fig. 6.

Fig. 6
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The deformed mesh of different element size a 30 mm, b 10 mm, c 5 mm

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Through convergence study of the meshing size, it is found that the size of 10 mm is suitable in this research because the analysis results for 10 mm is very accurate with the percentage difference of less than 5% as compared to 5 mm. The surface mesh with element size 10 mm is assigned to all the truss members. The quadrilateral thin shell element (QSI4) is set for the models and illustrated in Fig. 7a, b.

Fig. 7
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a Thin shell mesh of truss member, b close up of element QSI4 mesh

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2.4 Verification of FEA

Theoretical calculation using the virtual work method was used to calculate the displacement of the truss to verify the results of finite element analysis in LUSAS. An example of a truss is shown in Fig. 8. The truss was simplified to A frame with 9 m long and 2.1 m height similar to the truss used in this research. The cross-sectional area of each member was 400 mm2 and E = 200 GPa. It was required to know the vertical displacement at point C when a load of 5 kN was applied to the truss by manual calculation and compared with the result obtained from LUSAS.

Fig. 8
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Truss used for verification work

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By applying the formula of virtual work method, the solution for displacement is shown in Fig. 9a–d for better understanding. By applying nNL force from Fig. 9d, the vertical displacement at point C was calculated. The vertical displacement at point C using virtual work method was 0.141 m (141 mm) downwards.

Fig. 9
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a Virtual force of truss member, b real force of truss member, c Length of truss member, d nNL force of truss member

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Since the virtual work method only applicable for deflection checking, the displacement of the truss system has been obtained from LUSAS for verification purpose. Similar truss as shown in Fig. 8 was modelled in LUSAS and the vertical displacement, Dy at Point C obtained at node 198 was −0.155629 m (155.6 mm) downwards. As compared to the answer from calculation which was 140.6 mm, it shows a difference of 10.6% from displacement in LUSAS.

3 Results and Discussion

The outcomes of the research were based on the parametric study of the arrangement and number of screw connection. Rectangular hollow section (RHS) and lipped channel section (LCS) were used in the cross section of the truss system. It was predicted that the screw number will affect the performance and strength of screw connection in truss system. As such, discussions were made in accordance with the results obtained such as displacement, stress, shear and moment after all analysis have been done using LUSAS software as shown in Fig. 10.

Fig. 10
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a Displacement analysis, b stress analysis, c shear analysis, d moment analysis

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The number of screws will affect the behavior of screw connection [17, 18]. The screw connection will experience failure when the ability to resist the applied load was exceeded. If the number of screws was increased, the connection strength should be increased. Various tests such as shear and moment test can be done to investigate further on the behavior of connection strength. However, there were some studies found that the strength of screw connection did not improve with the increasing number of screws.

One of the parametric studies in this research was based on different number of screws.

The effects of screw connection in terms of displacement, stress, moment and shear were compared and discussed based on different numbers of screws added to the connection. Overall, when screws number was higher, the displacement becomes lower (the displacement increased slightly for RHS but it was not remarkable because the deflection was less than 1 mm); the stress decreases; there was also a drop-in shear strength but the increment of the moment did not happen in all cases.

In general, typical number of screws show lowest deflection in RHS. For the LCS truss system, the most significant drop of deflection happened at the side location by 99%. In other cases, the results were not as remarkable although the percentage changed were between 1 and 45%.

From the table, it was found that the overall trend of deflection increased slightly but not significant in RHS (the negative sign signifies downward direction) and decreased in LCS when more number of screws are added to the connection. As shown in Figs. 11 and 12, the typical number of screws in RHS generally has the lowest deflection as compared to other cases. The maximum number of screws was most suitable for LCS. In terms of deflection, it should be as small as possible to ensure the safety of the structure and improve the connection strength. This was referring to the action of tension field. The compression about diagonal direction were unable resisted by web section, when the web section started to buckle. The compression about diagonal direction was then directly swapped to the flanges section. This was due to the action of tension filed where the web section resists only the tension about diagonal direction. This behaviour pattern was almost identical to a pratt truss system, where the compression forces were resisted by vertical members and tension forces were resist by the diagonal member.

Fig. 11
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Displacement for different number of screws in RHS

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Fig. 12
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Displacement for different number of screws in LCS

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For the principal stress comparison as found in Figs. 13 and 14, it is shown that the principal stress declined with more screws inserted to the connection. The lowest stress in the RHS for all locations occur with the maximum number of screws which the percentage dropped around 25–43% from typical case. The principal stress also declined more than half in LCS except its peak location of Fink truss which remained unchanged.

Fig. 13
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Stress for different number of screws in RHS

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Fig. 14
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Stress for different number of screws in LCS

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From the LUSAS analysis result, throughout the shear zone the stresses were truly found distributed across the web opening and therefore the occurrence of shear failure was more pronounced near the opening compare to the web of solid I-beam.

To sum up all the cases for stress analysis, maximum number of screws displayed the best performance in RHS and LCS. To increase the connection strength, the principal stress should be lower when the number of screws was higher. There was a need to identify the maximum principal stress because failure will occur if the maximum strength value reached the elastic limit in simple tension. When one or two more screws were added to the peak location of truss, the shear force increased. The similar trend at the peak location of Howe truss where the shear force raised from 7 to 17 N. In the meantime, it shows declining trend of shear force in other cases when more screws were inserted into the connection.

The connection with double screw normally failed due to bearing or tilting failure. Another observation from the connection of double screw was that the shear capacity of a single screw using was not definitely yield twice. By using the multiple fasteners, secondary stresses on connections from the connection deformation. Subsequently, the reduction of connection performance was noticed. Thus, the steel with low ductility performed better than the steel with normal ductility due to less redistribution of stress capacity.

On the whole, the shear force for both RHS (see Fig. 15) and LCS (see Fig. 16) became smaller when more screws number was added to the connection. The maximum number of screws was designed for all the cases of RHS and LCS in accordance with the lowest shear result shown in the graphs. Lower shear strength signified higher connection strength of screws.

Fig. 15
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Shear for different number of screws in RHS

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Fig. 16
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Shear for different number of screws in LCS

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As seen in other cases, the higher the number of screws, the smaller the moment at the connection. By using maximum number of screws in the connection, the moment of RHS reduced by more than 50%. As demonstrated in Figs. 17 and 18, the maximum moment occurs when the typical number of screws was used for LCS at the side location and peak location of Howe truss. When one or two more screws were added at the peak location of Fink truss, the moment increased slightly but not as crucial as other cases.

Fig. 17
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Moment for different number of screws in RHS

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Fig. 18
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Moment for different number of screws in LCS

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It signified that when screws number increases, it was not necessarily that the connection strength will increase [9, 14]. It was revealed that the reduction of connection strength happened as the number of screws increased. The strength of screw connection was not proportioned to the number of screws. For example, when four screws were used, the load capacity was not four times better than the single screw connection. This was caused by group effect reduction when more number of screws were used in connection.

Since the group effect will reduce the connection strength, it was proposed that the typical number of screws was the most appropriate to be applied to the side and peak location of truss system of RHS and LCS. The typical number of screws was safe and sufficient to support the truss system without causing tilting and bearing failure modes under applied load.

4 Conclusion

Through FEA, the screws behaviors at the side and peak location of RHS and LCS truss system were compared based on different screws number and screw arrangement. To conclude, different screws number arrangement did not necessarily enhance the connection strength of screws in the CFS truss system. Even though there were some cases that made the connection better, a reasonable consideration should be done to check the conservative of screws design. Since the connection did not show a large improvement in strength, it was advised to apply the typical number and arrangement of screws used on the site after cost and economic consideration. This achieved the objective by determining the screws behavior based on different screws number and arrangement using FEA.

It was recommended to carry out a nonlinear analysis by considering the material, boundary and geometric nonlinearity so that it can establish the factual results. The modelling process in LUSAS should be made easier so that the models can represent the real structure in the simplest form like line elements, in turn save the time of checking procedure in the design process.

In addition, with the permissions of time and financial considerations, it was strongly advised to get the proper model for material testing to compare the analysis in FEA software. Models with different number and different arrangements of screws can be modelled for testing to check the behavior of connection.