THE PRELIMINARY UNIAXIAL COMPRESSION BEHAVIOR OF CORRUGATED COLD FORMED STEEL MEMBERS

In today’s construction industry, the economic conditions are at the forefront, and fast-to-implement cheap solutions have become widespread. This has been evidenced by RFM (Roll Forming Machine) technology, especially in the light of the steel construction sector. With the machine called RFM, steel or aluminum sheet / sheet sections are inserted in a self-tapping fashion to produce k-span elements. The vault construction systems formed by means of joining and clamping the elements produced have become very common thanks to this technology. As an example, a k-span manufactured with this technology and produced in the United States of America is shown in Figure 1 (M.I.C. Industries Inc., Gençler Metal Ltd. Inc.). The precise process of construction of RFM arch steel roofs and buildings is described in Refs. [1] and [2]. The corrugated members are formed by themselves while giving a belt shape to the flat hair panels [3–4]. Thus, the inertia is increased at a high degree, and economic vault construction elements are produced. It has been proven by analytical and experimental findings that the performance of lightweight structures against earthquakes is much better due to the reduction in construction weight and less damage during earthquakes. For this reason, the vault systems designed and constructed with corrugated light steel panels; geometric shapes, horizontal (earthquake, wind, etc.) loads, and extremely good performance under vertical loads. This technique, inspired by the behavior of arch structures, is almost identical with the freight transport system of centuries. Furthermore, irregularities in interior volume, visual disturbance, negativistic affects; such as columns and beams, which cause workspace restrictions are reduced. Unlike conventional steel and reinforced concrete structures, and their standard form, the manufacturing and installation faults are close to none for the k-span structures. Thus, more secure large-volume designs became possible with fewer structural irregularities and application errors. In recent years, a number of researches were carried out to study the behavior of arch-shaped steel sheet sections, including the work of Cybulski et al., who studied the influence of surface transverse geometric imperfections called corrugations on the local stability of cold-formed elements and two types of thin-walled elements are considered: a panel with smooth walls and panels with corrugations on their surfaces. Finally, the conclusions are made, which can be useful for design purposes [5–6]. Piekarczuk and Malowany have worked on the comparative analysis of numerical models of arch-shaped steel sheet sections. As a result, an acceptable reduction of FEM model complexity is proposed for the analyzed structure [7]. Malesa et al. have described two practical applications of the multi-camera digital-image correlation system in order to show its feasibility in engineering failure analysis [8]. Piekarczuka et al. refer to thin-walled corrugated steel profiles as arched roofing in architectural structures. They have proposed a method of analyzing the results of numerical calculations based on the identification of a perturbation component of displacement in selected points of the profile. The method is based on a discrete Fourier transform and allows the establishment of an estimation criterion for the lower limit of a profile’s load capacity [9].

Figure 1.

For the construction of the k-span in the design, light steel sheets are transported to the building site via RFM truck for application on site. First, panels are manufactured and cut to get the required spacing. These panels are then given an accurate shape to form the designed arch, and brought together to form the structure. In the case of restricted data obtained from the literature, all calculations are made according to the relevant American Standards. However, this situation brings with it a number of limitations, especially since the different loads considered in European specifications are ignored. Furthermore, there is a lack of a suitable theoretical model for such lightweight steel elements, and the folding formations that occur during panels that can be bent into a belt include uncertainties [10]. Particularly, it is not entirely true that the pattern serves as a barrier against local collapses. This research is a starting point for the investigation of the effect of the teeth on the k-span (super span model 600) panels under uniaxial loading. General introduction to RFM technology and its problems are described by Walentyński (2004) [2] and Cybulski and Kozieł (2011) [11]. The corrugated and un-corrugated cold formed steel members are modeled with finite-elements (ANSYS-Workbench Ver. 17) to analyze the behavior of relevant members subjected to uniaxial load. Three types of analyses are achieved: the linear buckling analysis based on eigenvalue problem [12], the Riks Method analysis based on arc length iteration method [13], and the Automatic Stabilization analysis based on the Newton–Raphson iteration method and on the artificial mass proportional damping [14]. Thus, the aim of the study was to analyse the influence of the corrugation on the behavior of cold formed steel members in the structure roofs. The load-displacement and loadstrain curves were used to evaluate the main parameters characterizing the behavior of the tested cold-formed steel members under uniaxial load, such as the maximum load and the maximum displacement.

Once the RFM has taken to the site on a track, the construction process can be carried out by a small group of trained personnel. The Figure 2 shows the shape of the RFM.

Figure 2.

Panels are cut at the site, squeezed together with the sewing machine, secured to the lifting platform and transported to the application site with a crane. Figure 3 shows the application of a k-span vault-type structure made of light steel plates on the site.

Figure 3.

In this study, load-displacement and load-strain curves under axial load of two types of sectioned members made of light steel plate are investigated. In the first type, a non-feminine lightweight steel sheet section was investigated. The second type is the light steel plate section which is regarded as corrugated. Two types of models were obtained using RFM technology. Another point to note is that in both samples, there are parallel folds for the folding direction, while the second type corrugated vertically. In both types of members, the plate thickness is 0.6 mm, and the member height is 1200 mm. In this research, the k-span (super span model 600) is attempting to provide a basis for a better understanding of the dental (folding/bending) effect on panels. The coupon tension test of the structural steel material of the light steel plate were performed complying with UNE-EN 10002-1 [15]. Material properties of both types of steel panels are as follows:

All the models are manufactured from the same steel roll. Thus, the material properties are same for all and presented in Table 1. Furthermore, two types of experimental models are shown in Figure 4.

Figure 4.

This study was carried out at Atatürk University. The hydraulic jack was used here to assess the static load of the test models. The maximum load of the setup was 900 kN, which was employed with a maximum stroke of 300 mm, and a constant speed of 0.016 mm/s, up to the collapse of the specimens [16–27]. Two linear variable displacement transducers with a maximum displacement of 100–300 mm (locations of LVDTs are shown as DT in Figure 5) were used. Two strain gauges (presented as ST1 and ST2; TML YEFLA-5, resistance: 121Ω ± 0.5%; sensitivity coefficient: 2.1 ± 2%; size: 5 mm × 3 mm) [16–27] are added to the system to survey the strain distribution. Furthermore, pinned support was used in all tests. The locations of the strain gauge, and LVDTs are shown in Figure 5. Experiments were prepared with the support of a steel construction company (Gençler Metal Ltd. Şti.) [28]. the aim of the study was to examine the behavior of the teeth perpendicular to the load on the k-span (super span model 600) panels under axial load. Deformation measuring instruments and test setup are shown in Figure 5.

Figure 5.

Three tensile coupon tests were performed to obtain the shell material properties. Average yield strength was found 352.8 MPa. The Young’s modulus was calculated 201GPa, and the Poisson’s ratio was obtained 0.29. The analytical solution for the ultimate load of straight and corrugated panels is based on Eurocode 3 Part 1-5 [29]. Due to future experimental investigations of both types of panels, where local stability will be examined, distortional buckling is neglected. Thus, the use of Eurocode 3 Part 1-3 [10] for cold-formed elements is omitted and only cross sections of effective widths are used to make the necessary allowances for reductions in resistance due to the effects of local buckling. The post-critical load carrying capacity for cold-formed element is described in the Cybulski et al [5]. They used the Eurocode 3 to calculate the post-critical load carrying capacity [10, 29]. In this research, the post-critical load carrying capacity was calculated same as Cybulski’s et al [5]. So, the post-critical load carrying capacities are equal to 57.96 kN and 79.38 kN for with and without corrugated models, respectively. The effective cross-section area is given in Figure 1.

The load-displacement curves are discussed, shown in Figures 6 and 7 for the members with and without corrugation to the loading direction. Table 2 presents not only the maximum load (limited load = P_U), first buckling load (P_cr) and displacement values for both experiments, but also gives comparative results for both experiments. The behaviors of axially loaded, with and without corrugated (super span model 600) members are investigated throughout this study. It is seen that the first buckling load of the member perpendicular to the load direction (orthogonal to horizontal load) is 1.59 times greater than the member perpendicular to the load (perpendicular to the load without vertical folding). Also, the load carrying capacity of the member perpendicular to the load direction (orthogonal to horizontal load) is 4.13 times greater than the member perpendicular to the load (perpendicular to the load without vertical folding) (Table 2). Moreover, when the displacements of the members are compared, the first buckling load displacement of the member perpendicular to the load direction (orthogonal to horizontal load) is 0.06 times lower than the member perpendicular to the load (perpendicular to the load without vertical folding). Also, the horizontal gear member deforms 4.25 times less. Also, the displacement at Pu of the member perpendicular to the load direction (orthogonal to horizontal load) is 0.27 times lower than the member perpendicular to the load (perpendicular to the load without vertical folding). As a result, teeth perpendicular to the load direction increase the load carrying capacity while reducing the displacement. Table 2 shows the comparison of the first buckling load (P_cr), and maximum load (P_u) of experimental model. Table 2 shows that, after the first buckling load (P_cr) of the models, they resisted the models themselves. They entered the stage of post-buckling. A fading effect is about 33.03% and 75.56% for the uncorrugated model and corrugated model, respectively. Thus, a fading effect of the corrugated model was greater than of the uncorrugated model. Furthermore, when the maximum load (P_u) of the experimental compared to analytical one from the EC3, the first buckling load (P_cr) of the uncorrugated experimental model is 0.039 times lower than the EC3 based one. And the first buckling load (P_cr) of the corrugated experimental model is 0.045 times lower than the EC3 based one. The maximum load (P_u) of the uncorrugated experimental model is 0.059 times lower than the analytical load of EC3. And the maximum load (P_u) of the corrugated experimental model is 0.178 times lower than the analytical load of EC3. Thus, Table 2 shows that analytical load based on EC3 is greater than the experimental first buckling load (P_cr) and experimental maximum load (P_u). On the other hand, if anyone wants to get the first buckling load (P_cr) and the maximum load (P_u) times according to theoretical formulas, it must multiply the coefficients to obtain the first buckling load (P_cr) and the maximum load (P_u).

Figure 6.

Figure 7.

The load-strain curves are discussed and shown in Figures 8, and 9. The both tension pulleys showed the same behavior at the same time. They transitioned from elastic to the plastic region. In addition, the displacement was about twice as big in the section of steel plate with horizontal corrugated belt as compared to the other one.

Figure 8.

Figure 9.

The greatest stress of the sections of the arched steel plate can be evaluated as the flaw and lateral buckling sensitivity that can occur during construction. As shown in Fig. 10, in the experiments carried out corrugated and without corrugated elements perpendicular to the load direction, the elements are buckled parallel and outward to the wings. It is seen that the damages of the V shape in both elements are more numerous in the elements which are perpendicular to the load. Considering the resulting damage, it is seen that a small number of V-type damage is effective on a larger length in a horizontal without corrugated, whereas more V damage in a horizontal gear is effective on shorter direction.

Figure 10.

In this study, it is aimed to compare the stress distributions on the corrugated and without corrugated by modeling in the ANSYS Workbench v16 program [30]. Three different types of analyses are used: linear buckling analysis [12] based on eigenvalue problem, Riks Method [13] analysis based on arc length iteration method, and Automatic Stabilization [14] analysis based both on the Newton–Raphson iteration method and on the artificial mass proportional damping. Three tensile coupon tests were performed to obtain the shell material properties. Average yield strength was found 352.8 MPa. Young’s modulus was calculated 201GPa, and Poisson’s ratio was obtained 0.29. For with and without corrugated panels boundary conditions are the same and are presented in Fig. 11 in terms of a straight panel. Such boundaries are chosen due to future laboratory compression tests. Length of support was 250 mm in all models.

Figure 11.

One of the most important steps in finite-element (FE) analysis is the creation of mesh structure. The sweep, automatically generated, tetrahedrons and hex-dominant are meshing method in ANSYS Workbench program. The sweep method cannot be used in plate or concrete models. The non-sweep able bodies force the sweep method controlling. The automatically generated, tetrahedrons and hex-dominant method meshing compare their created nodes and elements for the same sizing [22]. The mesh size is taken as 5 mm for each method. It is observed from the Table 4 that, automatically generated tetrahedrons and hex-dominant meshing methods give different values for nodes and elements.

Therefore, tetrahedron meshing with 10-node (every node of this volume has three degrees of freedom) selected for solving FE models. Mesh sizing is important for accurate stress value. For this purpose, selected meshing type, the tetrahedron mesh divides various sizing mesh starting with 10 mm. When the stress and displacement values are stable, this mesh sizing can be applicable for FE analysis. Fig. 12 illustrates that mesh sizing is important to find the exact stress values.

Figure 12.

Furthermore, Fig. 12 shows the maximum stress values of the models, and 1–3 mm mesh sizing results are similar. The variation of the stress values is becoming very rough, and as seen from the Fig. 12, the curve is becoming asymptotic for less than 1 mm mesh size. Because of the memory allocation and computer analysis time problems, the mesh size is decided as three mm for FE analysis. The finite-element mesh size is a phenomenon for divergence of the results. Thus, the above mentioned sensitivity analysis is evaluated to predict optimum mesh size. Figure 13 shows the numeric model.

Figure 13.

A post-buckling analysis of a geometrically perfect structure may exhibit a sharp bifurcation at the buckling load, which may be missed in the Riks Method [35]. Adding geometric imperfections smoothed out the discontinuous response at the point of buckling and allows the solution to follow the response more easily [31–35]. The Risk method and imperfections type used for analyses of all models in this research, and the analysis path is same as section 3.5 and 3.6 as in the ref [5].

Figs. 14 and 15 show the load-displacement curves predicted from the finite-element models. There appears to be good agreement between the experimental and FE model results. Table 5 shows the comparison of FE and experimental models. The average ratios for the experimental maximum loads (P_u) / the maximum loads of FE models (P_m) for uncorrugated, and the corrugated ones are changed between 0.95 and 1.38. The average ratios for the experimental maximum displacements / the maximum displacements of FE models for uncorrugated and the corrugated ones are changed between 0.35 and 2.42. The uncorrugated member values were close for the experimental and numerical ones, unlike for the corrugated ones.

Figure 14.

Figure 15.

Figure 16 shows the maximum shear strains by FE analysis for with and without corrugated models. The numerical models are consistent and show local and distortional buckling in the models. The failures of the numerical models are same as the experimental ones.

Figure 16.

In this research, an experimental study was carried out to determine the load-strain and load-displacement curves representing the behavior of steel plate sections with k-span (super span model 600). Thus, the aim of the study was to analyse the influence of the corrugation on the behavior of cold formed steel members in the structure roofs. The key findings and observations are presented as follows:

The first buckling load of the member perpendicular to the load direction (orthogonal to horizontal load) is 1.59 times greater than the member perpendicular to the load (perpendicular to the load without vertical folding). Furthermore, the load carrying capacity of the member perpendicular to the load direction (orthogonal to horizontal load) is 4.13 times greater than the member perpendicular to the load (perpendicular to the load without vertical folding).