Effect of openings on cold formed steel shear wall panels

In this paper, the effect of openings on global performance of Cold Formed Steel Shear Wall Panels is investigated numerically using the ABAQUS software. A benchmark model is first validated in terms of lateral shear capacity and nonlinear behaviour of the CFS-SWP. The failure mode of the CFS-SWP with opening is identified and validated. Subsequently, a parametric study on the effect of size and position of openings is conducted, in which the opening position is found to have a significant impact on the CFS-SWP performance. The benchmark model can be used for design purposes to evaluate with good accuracy the reduced ultimate strength of individual CFS-SWPs for any size and position of openings.


Introduction
Cold formed steel (CFS) shear wall panels (SWP) sheathed with corrugated steel sheets have recently gained in popularity as they can resist severe lateral loads in highly seismic areas more effectively compared to others sheathing materials [1]. In addition, experimental research programs have been carried out [2][3][4][5] to evaluate the global behaviour and performance of CFS-SWP with this type of sheathing under lateral load. However, for architectural and functionality design purposes, doors and/or windows openings need to be integrated into the SWP, which has an influence on its performance. The characterization of the lateral behaviour of the CFS-SWP is therefore considered necessary. Fulop and Dubina [6] carried out an experiment with CFS-SWP to get a better insight of the global behaviour and assess the opening effect on the performance of the CFS-SWP under seismic load; they concluded that there is a dependency on the screw-sheathed connections' mode of failure. Other related experiments have also been conducted [7][8][9][10][11]. The AISI North American Standard for Cold-Formed Steel Framing -Lateral Design of 2007 (AISI S213-07) provides design parameters for steel-and wood-sheathing of CFS-SWP to be adopted by engineers. However, due to the diversity of architectural dimensions in light gauge steel construction, the tabulated values of design parameters do not cover the full range of CFS-SWP configurations. Hence, a numerical approach has become necessary and, using finite element (FE) models, it has proven to be a good alternative in predicting the behaviour and assessing the shear strength of the SWP for various geometric and mechanical characteristics. Several FE models have been developed and various modelling techniques have been presented. Bahrebar et al. [12] studied the shear strength of SWP sheathed with steel plate sheets, taking into account buckling failure modes, in addition to buckling of thin steel members [13,14]. In fact, connection failure is a widespread phenomenon in the CFS-SWP. Kechidi et al. [15] developed hysteresis models that consider strength and stiffness degradation as well as the pinching effect observed in the steel-and woodsheathed CFS-SWP. Rouaz et al. [16] presented a comparison between two numerical approaches for shear strength evaluation based on connection shear failure. According to Niari et al. [17], material nonlinearity should be integrated into the FE model, so as to improve its accuracy regarding screw connection which affects global behaviour of the CFS-SWP. Furthermore, Hosseinzadeh et al. [18] suggested that geometric nonlinearity should be introduced in numerical simulation of the CFS-SWP lateral behaviour, which may occur in light gauge steel structural components. Vigh et al. [19] and Kalali et al. [20] also presented a modelling technique of the CFS-SWP sheathed with corrugated steel on a short panel without opening.
As far as the opening effect on the global performance of SWP is concerned, Farzampour et al. [21] investigated, numerically, this aspect on corrugated plate shear walls with hot-rolled steel framing elements (beam and columns). Dai [22] studied the opening effect on CFS-SWP with cassette sheathing, where all members of the SWP were made of cold formed steel, but the cassette sheathing is not in common use in engineering practice. The same author [23] developed a numerical model of CFS-SWP to explore the influence of sheathing boards and fixing boundary conditions. The corrugated steel sheet was modelled with a plain element having two equivalent elastic moduli along the perpendicular and parallel directions of the corrugated steel sheet. In addition, the material nonlinearity, which is a crucial factor in global response, was not taken into account in the FE model [23]. In this paper, a detailed FE model, elaborated and validated using available experimental data, is used to investigate the opening effect on the shear strength of the CFS-SWP sheathed with corrugated steel sheets under lateral load. The nonlinear response and the corresponding ultimate displacement are also explored. The opening effect (door and window) is studied with regard to the change in position and size.

Selection of tested CFS-SWP
A thorough investigation of the effect of openings on the lateral behaviour of SWP would require a tremendous experimental program. In order to overcome these constraints, a detailed FE benchmark model was developed and validated against available experimental data for further sensitivity analyses.
For this purpose, a tested corrugated steel-sheathed SWP performed by Fulop, and Dubina [6], with and without opening, was selected to validate the numerical model. As depicted in Figure 1, the selected specimen without opening, having 3600 mm in length and 2440 mm in height, is composed of two U154/1.5 tracks and nine C150/1.5 studs. The studs are attached to the top and the bottom tracks of each side with two pairs of SPEDEC SL4-F-4.8x16 (d = 4.8 mm) self-drilling, selftapping screws. Built-up cross sections of double stud (toe-totoe) are placed at the ends of the SWP.   In addition, horizontal brace members are installed at midheight of the SWP to reduce twisting and buckling deformations of the stud. Six and four bracing members are placed in the SWP without and with opening, respectively. Table 1 shows main geometrical characteristics of the components of the selected SWPs. An additional chord stud is placed at each end of the opening for the corrugated-steel sheathed SWP, having 1200 x 2100 mm door opening (width x height).

Material properties
in order to characterize basic properties of materials used in SWP tests, mechanical properties of steel members similar to those of the selected panels were adopted from a normalized stress-strain curve in accordance with ASTM A635 G50 ( Figure  4) [25]. The yield stress f y is 344 MPa, the tensile stress f u is 448 MPa and the elastic modulus E s is assumed to be 2.1·10 5 MPa. However, grade 70 steel (f y = 483 MPa and f u = 550 MPa) was used for corrugated steel sheets [26].

Screw connections
In order to take into account nonlinearity behaviour of screw connections, which governs the global response and failure mode of the corrugated steel sheathed SWP, sheathing-to-sheathing and sheathing-to-framing screw connections were tested by Dubina [24]; Figure 5 shows the corresponding loaddisplacement curves. Due to the lack of experimental data related to force-displacement curves of framing connections (stud and track), several series of experiments were undertaken by the author at the CNERIB laboratory, with the same conditions of thickness of members, tensile grade of steel framing, and screw diameter [24]. The screw test was carried out according to European Standards ECCS TC7 TWG 7.10 [27], and dimensions of test specimens ( Figure 6) were selected as recommended in clause 3.2. The minimum number of tests was in compliance with clause 3.1.5 of the ECCS for the single fastener test. As shown in Figure 7, test specimens were placed in the tensile test machine to determine the shear strength capacity and nonlinear behaviour of one connection screw under monotonic load. As reported by Dubina and Fulop [24], the screw tilting and pullout was the dominant failure mode of the sheathingto-sheathing and sheathing-to-framing screw fastener specimens, whereas the failure mode in framing-to-framing connections was dominated by shear of screw fasteners. Figure 8 shows the load-displacement result of the three tested assemblies.

Finite element modelling
SWPs are complex assemblies made of CFS members attached to sheathing using screw-fastened connections. When modelling this subsystem, particular attention is required with regard to the study of its overall behaviour and performance, taking into account main failure modes such as failure of screw-fastened connections, and the local or global buckling limit states of framing members. A detailed description of the FE modelling protocol of the selected SWPs is presented in this section using the commercial ABAQUS software [28].

Element types and meshing
Due to the large strain in SWP elements under horizontal monotonic load, it was deemed important to take into account geometric nonlinearity in the analysis. Hence, all elements, including sheathing, track, stud, and lateral channel bracings, were modelled as S4R shell elements with reduced integration scheme. Each element's node had three translational and three rotational degrees of freedom, which could be restrained according to experimental conditions. Based on similar previous CFS-SWP studies conducted by Dai [22,23] and Rouaz [16], in which sensitivity analysis was performed on mesh size elements, a good compromise in terms of time and accuracy was achieved with a mesh dimension close to 50 mm x 50 mm for all framing members. For the corrugated sheets, each unfastened side was divided into two parts in the horizontal direction, and 40 mm in the vertical direction was adopted as shown in Figure 9. GRAĐEVINAR 72 (2020) 9, 771-780 Effect of openings on cold formed steel shear wall panels The surface-to-surface contact was used to model interaction between element members, namely, contact between track and stud flanges, and sheathing-to-framing contact. Based on sensitivity analysis performed by Dai [23], the results are not greatly affected by friction coefficient. Therefore, a friction factor of 0.3 was adopted in this study.

Mechanical properties of element members
In order to introduce material nonlinearities in the FE model, the engineering stresses (σ) and engineering strains (ε) obtained from normalized curves were converted to obtain the socalled true stress (σ tru ) and true strain (ε tru ) using the following equations [17]: (1) (3)

Tensile strength
The pull-out strength of the sheathing and framing screw connection is estimated using design provisions of the North American Specification for the Design of Cold-Formed Steel Structural Members AISI S100 (section E.4.4.1) [29]. The strength can be obtained using Eq. 4: where d is the nominal screw diameter, t c is the lesser of the depth of penetration and thickness, P not is the nominal pull-out strength per screw, and F u2 is the tensile strength of a member not in contact with the screw head or washer.

Shear mechanical characteristics
The nonlinear shear behaviour of screw fastener is considered as an envelope force-displacement response curve, as shown in Figure 10.
To simulate the damage evolution from point I, which represents the ultimate force, to point D, corresponding to ultimate displacement, each component is defined with ( , F i ) coordinates, where F i is the damaging force, calculated as given in ABAQUS Manual [28]: F effi is the effective force representing the ultimate force, and d i is the damage variable given by equation (6) : where: -equivalent plastic displacement damage at i component -equivalent plastic displacement at damage initiation α -exponential coefficient based on calibration with the experimental data curve -equivalent plastic displacement at damage failure.

Connection modelling
In order to set a connection between two or more elements, ABAQUS has a comprehensive set of connection defining elements such as spot welds, rivets, screws, bolts and other types of mechanical fasteners. Furthermore, as shown in Figure  11, the fixing elements can be located anywhere regardless of the mesh nodes, which are known as "mesh-independent fasteners". Physical characteristics of the connector are then introduced into the "interaction" module and are defined as screws elements taking into account the spacing, diameter, orientation and influence of the radius of screws.

Boundary condition and analysis
Two Tie Multi Point Control "MPC" interactions were used to simulate experimental boundary conditions of the SWP test set-up using the FE models. One was used to fasten the pinned bottom track to the ground in order to model the seven bolts placed in the vicinity of each stud, and the other was adopted to allow the application of displacement at the top track. The test rig that prevents any torsional movement of the wall or out-ofplane translation was modelled by restraints of translations in the out of plane direction. Quasi-static nonlinear analyses were performed, with the initial increment size equal to 0.1 and the minimum increment size limited to 10 · e -8 . The full Newton-Raphson iteration method was used to solve nonlinear equations in the analysis.

Shear strength-lateral displacement assessment
A comparison between numerical and experimental results was made for the selected SWP with and without opening in order to validate the above-described modelling protocol. Figure   12 shows the nonlinear curve of the shear strength-lateral displacement response under monotonic load. As shown in Table 2, the ultimate shear strength (F) and the corresponding lateral displacement (U) are close to the corresponding experimental results, and the difference in shear strength (ΔF) is relatively low (2.40 % and 5.46 %) for SWPs with and without opening, respectively. However, the difference in the initial stiffness and ultimate displacement is more pronounced in the case of the SWP with opening. This is mainly due to some simplistic modelling assumptions which do not take into account some properties such as the real mechanical material properties of the seven bolts installed in the bottom track of the specimen to fix the panel to the ground.

Table 2. Comparison between numerical and experimental results
Introducing the door opening in the SWP led to a decrease of about 24 % and 26 % of the shear strength obtained from experimental and numerical models, respectively, and to a 43 % increase in lateral displacement. The error in predicting the ultimate shear strength and the corresponding lateral displacement is 2.5 % and 5.43 %, respectively. Therefore, this model will be used to investigate the effect of the opening on the shear strength of the SWP. Figure 13 shows the location of material failure of the corrugated steel sheets in order to confirm that the tensile stress developed in the sheathing is absorbed by sheathing-toframing connections. This failure (highlighted in red) is initiated  Effect of openings on cold formed steel shear wall panels at the corner of the SWP and the chord stud having tight screw spacing. The occurrence of failure at these locations means that the tensile stress was absorbed by these connections. On the other hand, framing-to-framing screw-fastened connections did not exhibit any damage over the entire loading range. It is worth noting that this trend has been observed in most of the previous experimental studies on CFS-SWPs.

Figure 13. Failure connections localization of SWP without opening
Failure mode characteristics of the SWP with opening predicted by numerical simulation are illustrated in Figure 14.b. An important local buckling of the corrugated sheathing is clearly absorbed in the lintel region. In addition, a stress concentration appeared around the opening (1) and an uplift of the SWP corners can also be noted (2). Moreover, the failure of screwfastened connections (3 and 4) occurred at two of the lower seams. Similar features characterized the failure mode of the test specimen.

Parametric study
A parametric study was carried out using the above-described modelling protocol in order to evaluate the effect of the opening position and its area ratio on the shear strength of the SWP. Following architectural practice, the dimensions of door and window openings are 1200 mm x 2100 mm and 1200 mm x 800 mm, respectively. Typical positions of these openings are depicted in Figure 15 and, at that, the wall dimensions (3600 mm long and 2440 mm high) and the cross-section properties of the framing members were kept similar to those described in Section 2. The shear strength-lateral displacement curves for the two areas ratios in three different positions are presented in Figure 16.

Effect of opening position
A comparison of the shear strength and the corresponding lateral displacement between the three locations of door and GRAĐEVINAR 72 (2020) 9, 771-780 Idriss Rouaz, Nouredine Bourahla, Smail Kechidi window openings under monotonic load is made in this section. The central opening (position 1 in Figure 15) in the SWP is taken as a benchmark.

Door opening
The results listed in Table 3 show that the SWP with an opening located in position 2 exhibits a higher ultimate shear strength and a large lateral displacement. In fact, two rows of screw connections are installed on the intermediate stud to connect the ends of the corrugated sheets to the SWP framing. This position (2) has an additional row of screw connections compared to others positions (i.e., 1). This configuration with additional screw connections, as compared also to position 3 (due to the lack of screw connections in the chord-stud in the vicinity of the opening), has resulted in an increased shear capacity of the SWP. Moreover, regarding this number of screw connection rows, the SWP with an opening located in position 3 has one screw connection row less than the benchmark case (1), leading to a slightly lower ultimate shear capacity and a larger corresponding lateral displacement due to the reduced number of screw connections. Moreover, a significant distortion appeared at the end of chord stud (Figure 17.a) due to the narrow sheathing lintel at the top of the door.

Window opening
The window opening at different positions was also investigated in the same way as the door opening effect. Table 4 highlights an increase in ultimate shear strength and the corresponding lateral displacement in positions 2 and 3 as compared to the benchmark case. Furthermore, the best performance contribution of this window position is when the opening is between the centre and the end of the SWP (i.e., position 2), which has a greater influence on the ultimate lateral displacement than the shear strength. Despite the small difference in the number of screw connections between position 1 and position 3 (higher in position 1), the shear strength and lateral displacement are higher in position 1 than in position 3. This is due to the fact that, for an opening in position 1, the continuity of the diagonal tension field is no longer ensured compared to position 3. Furthermore, it can be noted that the pull-out screw-fastened connections located in position 3 (Figure 17.b) dominate the main failure mode, due to distortion of the left chord stud of the SWP.

Effect of opening area in different positions
It was found that reducing the opening area by 2.6 times from door to window has not provided the same performance in the three positions. In terms of ultimate shear strength. Figure 18

Conclusions
This paper presents the development and validation of a finite element (FE) modelling protocol for CFS-SWPs with and without openings, based on experimental results as well as a parametric study of the opening's effect on lateral behaviour of CFS-SWPs. It was found that: -Taking into account the material, geometric and connection assembly nonlinearities, a good agreement has been reached between numerical and experimental results in terms of nonlinear behaviour, initial stiffness, ultimate shear strength, and the corresponding displacement. -Discrepancies between numerical and experimental results for specimens with and without openings in terms of ultimate shear strength and displacement are of the order of 2.40 % and 5.46 % respectively. Therefore, the numerical modelling protocol developed for the SWP with opening is considered reliable for the purpose of parametric study.
According to this study, a special attention should be paid to the reducing effect of the opening area and its position on the shear capacity, such as: -The door and window openings, located in the central position, have a tangible effect to decrease the shear capacity of the SWP by up to 26 % and 15 %, respectively, which must be considered by practicing engineers. This study demonstrates the importance of numerical analysis in assessing the effect of openings on the shear strength of the SWPs, and can be a powerful tool to help the design engineer to evaluate with good accuracy the reduced strength capacity of individual CFS-SWPs with any size and position of openings.