Analyzing the Flexural Performance of Cold-Formed Steel Sigma Section Using ABAQUS Software

Abstract

Cold-formed steel structures are a type of steel fabrication that is commonly employed in building construction. Before manufacture, they are designed precisely to the appropriate dimensions using the ABAQUS software. Both the strength of the cross-section and distortional buckling determine the load-carrying capability of the section. It was found that thin walls in some cold-formed sections suffered distortional buckling under light loads, and that these elements continued to be strong even after the members buckled. To prevent local buckling, stiffness is offered by the web part. There are several methods for determining the modes and elastic buckling stress. They are finite element analysis, finite strip analysis, and conventional Fourier series solutions. The thickness of the specimen and types of stiffener selection which influence the ultimate strength and deflection should be the issue in the design of the appropriate sigma section. The non-linear numerical analysis of the web-stiffened triangular section was performed using ABAQUS v6.4. It has been demonstrated that sections with height-to-thickness (h/t) ratios have load-bearing capacities. When compared to the lower h/t ratio sections, they demonstrated an improvement in load-carrying capability from 35.13% to 37.2%.

1. Introduction

Cold-formed steel flexural members’ ability to support loads are constrained by both the distortional member’s distortional buckling and the cross-section’s section strength. A slight change in shape can significantly alter the section’s strength properties in cold-formed sections [1]. It is vital to create certain minimum standards and legislation to regulate the buckling and strength properties. Additionally, it has been noted that in some places, thin walls have experienced distortional buckling at light pressures and that even after the members buckled, these elements could still support heavier loads. Therefore, stiffness is added to the web part to lessen local buckling [2]. There are a variety of ways for calculating the elastic buckling stress and modes. Three common techniques are classical Fourier series solutions, finite element analysis, and finite strip analysis. Finite element analysis is presented here.

On buckling occurs in the CFS section to prove distortional buckling using hardened flanges [3]. From the article, it is learned how the systematic representation to examine the distortions collapse performance of CFS-lipped channel segment by taking into consideration of two consignment circumstances. The technique, which is an analytical explanation intended to influence the distortional buckling throughout the significant stress of the CFS segments consequential lying on the resource of the entire based on the energy theory. The projected mould is comprehensive in the direction of the channel segment beams and columns using section. Here, the General Beam Theory (GBT) is worn in the direction of conducting many channel segment beams and columns on the way to authenticate the projected technique.

Experimented with cross-sectional the CFS channel’s deflection ability, focusing on the way to the limited distortional buckling dealings [4]. This manuscript describes an investigational program which was completed at the University of Sheffield for the examination of the interaction of buckling in CFS-lipped channel beams. The channels were prearranged into an end-to-end pattern such that a total of six tests, including three unusual cross-sectional geometries, could be undertaken. The different specimens were experienced with a four-point deflection pattern using sustained limit situation, whereas being across braced on the load point. The beams will be observed to be unsuccessful in the stable instant span by the dealings of local in addition to the distortional buckling. The numerical imperfection of the column will be recorded before the experiment using a specifically planned computer rig making use of laser sensors. The tensile coupon will be in addition to extract from the flat segment as well as the bent areas of the cross-sections are organized to decide the material property.

The axial compression strength of gypsum plasterboard and sheathed web-stiffened stud walls [5]. Cold-produced steel-framed walls ruled with suitable sheathing materials are increasingly being utilized as vertical load-bearing systems owing to their many benefits. Despite this widespread use, attempts at improving their structural efficiency using either optimized studs or novel sheathing elements have been scarce. Arguably, the sustained use of lipped channel studs and conventional sheathing materials has long forestalled such improvements. Firstly, this study provides experimental evidence on the superior characteristics of the web-stiffened studs, developed specifically for load-bearing steel-framed wall applications, and their ability to utilize sheathing restraints to achieve higher axial compression strengths. Secondly, it shows that the use of steel sheathing, either in isolation or together with gypsum plasterboards, significantly increases the strength of the web-stiffened stud. Thirdly, single plasterboard web-stiffened stud walls are found to be highly efficient due to the monolithic nature of the sheathing that leads to greater degrees of composite action between the studs and the sheathing. Finally, it presents a spring-based analytical model capable of conveniently estimating the failure loads of sheathed web-stiffened studs. The model particularly focuses on the out-of-plane restraints provided by the sheathing, the contribution of which to the overall strength of the wall has traditionally been considered trivial but is shown to be substantial in the case of web-stiffened studs.

The distortional buckling behaviour of CFS sigma and zed-section members consider the deflection of the flange due to bending [6]. Moreover, a model and derive formulas for calculating the distortional buckling critical load of a CFS channel section subjected to pure bending [7]. In addition, a simplified semi-analytical model to predict the distortional buckling significant tension of CFS flexural components [8].

On the source of the whole prospective power principle, a stiffened-plate buckling model (SPBM) was used to calculate the distortional buckling critical stress of CFS channel section beams, and verified through the finite strip method (FSM) [9]. Extended SPBM to the distortional buckling analysis of the CFS channel section columns was based on symmetrical deformation.

To enhance the seismic nature of Cold-Formed Steel (CFS) shear walls, Cold-Created Steel High-Strength Lightweight Foamed Concrete (CSHLFC) shear walls with straw boards are proposed [10]. This study conducted tests of six full-scale shear wall specimens to investigate the failure mode, load-bearing capacity, ductility, stiffness characteristic and energy dissipation capacity. The test characteristics included HLFC density grade, stud section area, wall width and vertical stack. Test results specified that HLFC has a higher effect on seismic implementation and failure approach of the shear walls. The failure modes were cracking and crushing of HLFC, cracking of straw boards, local buckling of studs, and relative slippage between HLFC and studs, which made the wall exhibit good ductility and energy dissipation capacity. The compressive bearing capability of HLFC and the restrictive outcome of HLFC on a steel frame raised the shear strength and firmness. The most effective way of improving seismic performance was to increase wall thickness, followed by increasing HLFC density grade and stud section area, but increasing vertical load had an adverse effect on seismic performance.

The seismic implementation of an innovative cold-formed steel (CFS) moment-resisting frame experimentally and systematically [11]. A short-scale CFS moment-resisting portal frame has been experimented with under static monotonic loading until failure. The frame contains two box-shaped columns (face-to-face channels associated with inside plates), a back-to-back attached channel beam segment, and completely moment-resisting CFS bolted links. During experimental tests, the damage was mostly concentrated at the top and bottom of the CFS columns due to the web crippling of the channels close to the connections, whereas no fracture or noticeable slippage was viewed at the connection zones. A detailed finite element (FE) model was developed using ABAQUS by taking into account the material non-linearity and geometrical imperfections. The lateral load-displacement behaviour, ultimate strength and failure modes predicted by the model were in very good agreement with the experimental results. The validated FE model was then used to assess the effects of key design parameters on the lateral load capacity, ultimate displacement, energy dissipation, ductility, and ductility reduction factor of the frame. It is shown that the proposed system can provide good seismic performance subjected to the appropriate design of the main structural elements. Increasing the axial load ratio of the columns by 50% resulted in a 26%, 62%, and 50% decrease in the ultimate lateral load, energy dissipation capacity, and ductility ratio of the CFS frame, respectively. However, the energy dissipation capacity and the ductility ratio of the proposed system increased significantly by decreasing the width-to-thickness ratio of the columns. The typical CFS bolted moment connections may exhibit very low ductility and energy dissipation capacity, especially when the width-to-thickness ratio of the CFS elements increases.

Local-flexural inter-active buckling of customary in addition to customized CFS components [12]. The work plans in the direction of observed dealings of confined in addition to mostly flexural buckling within CFS components underneath axial firmness. Comprehensive nonlinear finite element structure will be developed, as well as authentic aligned with a whole of 36 axial firmness experimentation on CFS simple as well as lipped channel components using marginal limitations. Numerical representation included the differential stress-strain performance of CFS fabric in addition to improved possessions of cold employment edge sections get hold of coupon investigations. The convergences of preliminary arithmetical defect of the samples are designed via in particularly intended set-up using laser disarticulation transducers will be also in use and interested in contemplation. The formed FE representations created an exceptional forecast of the imperative potency of the samplings accomplished from the investigational experiments.

The authenticated FE representations as well as investigational results will be then worn to review the sufficiency of the efficient breadth technique into Eurocode 3 (EC3) in addition to the Direct Strength Method (DSM) is similar to the planning ability of an extensive variety of conventional as well as optimized propose of CFS channel feature section. The consequences represented by Eurocode 3 give traditional forecast (on an average of 21% divergence) intended used for the compressive ability of simple in addition to lipped component segments, at the same time as in the general, DSM forecast will be made additional particular intended for lipped components.

Structural performance of cold-formed steel composite beams [13]. This learning planned a work of fiction technique of attracting the power in addition to the rigidity of CFS beams. Flexural members will be the principal components in the majority of construction. Therefore, the present will be vital necessitates in the CFS business in the direction of giving the impression of being further than the conservative CFS beam segments in addition to expanding the work of fiction method to address the worse local buckling troubles that survive in CFS flexural components. The most important objective of this learning was in the direction of producing novel CFS amalgamated beam segments with enhanced structural presentation as well as financing schemes. This learning gives an investigational learning behaviour on dissimilar CFS amalgamated beams using purely maintain ending circumstances with fewer than four loading points. Fabrications belonging in addition to the numerical limitation of the representation will be considered. The examination strengthens the representation and is evaluated using the intended potency forecasted through Australian/New Zealand Standards intended for CFS arrangements.

2. Experimental Investigation

2.1. Introduction

The C-section, sigma section with single triangle web stiffener, sigma section with double triangular web stiffener, and sigma section with trapezoidal web stiffener were employed in the current study [14]. Cold-formed steel beams’ flexural buckling strength plays a major role in the failure of flexural members when determining the flexural behaviour of stiffened web sections through experimental investigation. Section flexural capacity is primarily determined by the three types of buckling failure modes: lateral torsional buckling, distortional buckling, and local buckling, along with their interactions [15]. Local buckling stresses remained reduced through incorporating the stiffeners in addition to the section. In addition, further distortional buckling modes appear in section [16]. The tests were performed on the sigma section with a single triangular web stiffener and the sigma section with a trapezoidal web stiffener.

2.2. Types of Buckling

2.2.1. Local Buckling

The vital aspect of cold-formed steel sections is in the local buckling, and it is a major feature of cold-formed steel sections, as the reason the path to the emaciated mechanism which is employed everlastingly grasp before the yielding. Furthermore, the inferior will resolve the mound by the side of which the buckle decides the frame for willowy the plate. At short wavelengths, the local mode repeats, usually requiring simple rotation at element junctions [17].

2.2.2. Distortion Buckling

Unlike local or lateral buckling, distortion buckling may influence the design of some laterally braced, cold-formed steel sections. If distortional buckling occurs, these regions truly twist while fizzling, which is unusual for both local and lateral buckling. For the most part, the distortional mode recurs at wavelengths ranging from short to long, depending on geometry and stacking, and it involves rotation and interpretation of various components [18].

2.2.3. Lateral-Torsional Buckling

When cold-formed steel members are loaded, they may get twisted and deflected laterally as well as vertically. It is because the bracing is not properly abounding. The moment of the flexural members is resolute not only due to the structure of the section strength of the cross-section, but that it is also restricted by the member’s lateral buckling strength. At long wavelengths, the lateral-torsional mode often involves the translation of the whole cross-section [19].

3. Material Property

3.1. Coupons Test

Material abilities are important in the performance of structural members, so before designing parameters for the type of steel structural member in cold-formed steel construction, it is significant to be aware of the mechanical properties of the steel sheets, strips, plates, or flat bars which are commonly employed. The creation of an acceptable analytical paradigm for predicting the behaviour of cold-formed steel structural elements necessitates an accurate description of the related material properties [20].

3.2. Mechanical Properties of Cold-Forming Steel Sections

For testing, the mechanical properties of the cold-formed steel (CFS) channel sections were assessed and established on the uniaxial tensile. Given the structural point, the belongings of the steel that were of concern included [21]:

✓

Yield point or yield strength

✓

Ultimate load

✓

Stress-strain characteristics

✓

Modulus of elasticity

✓

Tangent modulus and shear modulus

3.3. Tensile Coupons Preparation and the Procedure of the Test

For the cross-section, the tensile specimen was a standardized sample, as presented below. The standard flat coupon dimensions were fabricated according to the IS 1608:2005 and ISO 6892:1998: “Metallic materials—Tensile Testing at Ambient Temperature” [22]. The flat specimens were cut along the longitudinal length of the specimen. Figure 1 shows the details of the coupon test specimen and machine, and Figure 2 shows the sketch of the coupon test specimen.

The tensile coupons were put through their paces on a KN UTM machine. For the test, a load range of up to 10% (full load capacity of 1000 kN) was used. With the help of gripping devices, the coupons were placed for testing, and they were aligned according to the machine’s vertical axis. A constant rate of the axial load was applied. Strain indicators created with the data collecting system were used to record strains. The load-elongation relationship was used for the relationship calculation, along with the stress-strain of the tensile coupon, by using the initial cross-sectional area as well as gauge length. Similarly, the flat coupon cross-sections were planned by measuring the definite minimum width as well as the thickness inside the gauge length to the closest 0.01 mm. By eliminating the coating thickness, the minimal base thickness was established; the resultant manufacturing stress-strain curves for sections are shown. All the tensile coupons were found to have similar curves. The yield point was calculated using 0.2% proof stress. Figure 3 depicts the stress-strain curve of a flat specimen through a thickness of 2 mm.

3.4. Tensile Coupon Test Results

Tensile studies revealed tensile coupons made from flat components with almost equal stress-strain relationship, then yield strength, and similarly, ultimate strength, and elongation as tensile coupons made from round parts. The yield point was found via the offset technique, with a 0.2% offset, and the graph demonstrates progressive yielding. True stress values were determined by dividing the force observed during the tensile test by the specimen’s real or instantaneous cross-section. In addition, the real strain should be converted to plastic strain for use in the analytical investigation. Although real data on the qualities of the unmixed steel is not available, the behaviour of the flat portions implies that the cold-roll forming procedure did not affect the section’s flat parts [23].

4. Experimental Set-Up

Specimen Details

Sigma sections of single triangular stiffeners and trapezoidal stiffeners with heights of 100 mm, flange widths of 50 mm, thicknesses of 1.2 mm, 1.6 mm, and 2 mm, and specimen lengths of 1.5 m, were evaluated to compare their acquired capacity with analytical data. The triangular stiffener was roughly 20 mm long, while the trapezoidal stiffener was about 40 mm long. A loading frame was put up in the strength of the material laboratory to evaluate the flexural behaviour of cold-formed steel sections. The loading arrangement had a total height of 1.5 m. The boundary criteria were set by the IS 800-2007 universal steel code of practice [24]. Examples had triangular and trapezoidal stiffening in the web, as well as an angle section, joined at the two-point loading to prevent lateral torsional buckling. At the top of the compression flange, two-point loading was used. The specimen was labelled with the end offset and the one-third and two-thirds span distances. The spreader beam was attached to the specimen with ropes. By appropriately balancing the loading in horizontal bars that were projected ordinarily to the plane of loading, the danger of eccentric moment actions was prevented. The stresses were measured with foil-type electronic strain gauges attached to the top, in addition to the bottom of the central part. LVDT with a range of 0.01 mm was then utilized to measure the vertical and lateral deflections, which were fixed at the bottom centre and middle of the web, respectively. Figure 4 depicts the two-point flexure loading set-up, Figure 5 shows trapezoidal segments for testing, and Figure 6 shows triangle segments for testing. Similarly, Figure 7 shows the test set-up for profile testing. Figure 8 shows LVDT, Figure 9 shows the strain gauge, and Figure 10a,b shows different views of the profile 3 test set-ups.

5. Test Procedure

First, the location of a space which has the requirements for executing the test is met. The specimen’s surface is then cleaned to remove any dust. In cold-formed steel fabrication, the dimensions at cross-sections are examined for any errors that may be present. Electronic foil-type strain gauges are used to detect strain at the specimen’s mid-span bottom. The vertical and lateral deflections are then measured using an LVDT with a range of 0.01 mm. The measurements are taken in the middle of the span. The beam is positioned on the base platform, end conditions are established, and supports with hinges and rollers are installed. The load is applied in small increments. The strain gauge is fine-tuned for zero at the start, and similarly, adjustments for bend measurements are made. The loading is undertaken using the eight-tonne capacity hydraulic jack and the strain observations are noted as deflections are tabulated.

6. Details of Experimental Test Results

The specimens that remained were tested with two-point flexure from which the outcomes were acquired. A comparison of vertical and lateral displacement and ultimate load for various sections that were experimentally tested is shown in the figures below. Figure 11 shows the ultimate load for profile 2, while Figure 12 shows the ultimate load for profile 3. Figure 13 shows the load vs. vertical deflection for a 1.2 mm-thick specimen, Figure 14 shows the load vs. lateral deflection for a 1.2 mm-thick specimen, Figure 15 shows the load vs. vertical deflection for a 1.6 mm-thick specimen, Figure 16 shows the load vs. lateral deflection for a 1.6 mm-thick specimen, Figure 17 shows the load vs. vertical deflection for a 2 mm-thick specimen, and Figure 18 shows the load vs. lateral deflection for a 2 mm-thick specimen.

7. ABAQUS Programme

ABAQUS is a commercial finite element analysis (FEA) software tool. It is a general-purpose finite element modelling package that can solve a wide range of mechanical and civil problems numerically [25]. Static and dynamic structural analysis (both linear and non-linear), steady-state and transient difficulties, mode frequency and buckling studies, acoustic and electromagnetic challenges, and many forms of field and coupled-field applications are among the topics addressed. The software has numerous unique characteristics that allow non-linearity or secondary effects which will be incorporated into the solution, such as hyperelasticity, creep, plasticity, strain hardening, swelling, large deflections, big strain, material anisotropy, and radiation. The finite element model ABAQUS v.6.4 is used to analyse the behaviour, in addition to the strength, of cold-formed steel sigma purlins for various profiles with changing h/t and b/t ratios with an open boundary condition [26].

7.1. Program Overview

The ABAQUS v6.4 element collection includes multiple static elements in addition to dynamic ones, over the 20 heat transfer elements, in addition to the several magnetic fields and special purpose elements. The ABAQUS v6.4 programme can analyse two- and three-dimensional frame structures, piping systems, two-dimensional plane and axis-symmetric solids, flat plates, axis-symmetric and three-dimensional shells, and non-linear problems such as contact, interface, and cables, thanks to this wide range of elements. The processors work together to construct a programme, with each processor assigned a certain task. They are:

Part: This builds the model

Property: This is used to select materials from the library, and to change their properties. Materials can be assigned to behave in a linear or non-linear way.

Assembly and Mesh: This is used to mesh the model with different sizing and also to assign contacts and their corresponding mesh.

Step and Load: Assigning the loads, and the constraints, in addition to finally getting a finite element result.

Job: This is used to assign the various output requirements.

Results: For additional processing, in addition to viewing the results over the entire modal at specific time points.

Throughout the software, a Graphical User Interface (GUI) is situated to allow access in order to support novice users’ learning, in addition to providing more experienced users with several windows, pull-down menus, conversation boxes, toolbars, user-defined outcomes, and online documentation.

7.2. Element Type

S8R elements were used to simulate the specimens [27]. Elements are composed of 20 different nodes, each with three degrees of freedom: translations in the nodal x, y, and z directions, as well as rotations about the x, y, and z axes. Because of their qualities such as stress stiffening, plasticity, creep, big deflection, and enormous strain, the elements are suitable for linear, large rotation, and/or massive strain nonlinear applications.

8. Materials and Methods

Both the linear and non-linear material characteristics were provided for each specimen.

Table 1. Linear properties of the specimen.

Description	Value
Young’s modulus	2.06 × 105 N/mm2
Poisson’s ratio	0.3
Yield stress	230 N/mm2

includes information on the specimen’s linear qualities, while

Table 2. Non-linear properties of the specimen.

Yield Stress	Plastic Strain
230	0
246	0.02374
294	0.04784
374	0.09436
437	0.1388
480	0.1814

includes information on its non-linear features. The stress-strain information must be put into ABAQUS as actual stress and true plastic strain. The investigation’s goal was to create an effective and cost-effective section in comparison to other sections. The finite element analysis was performed using the stress-strain data using the tensile coupon test that was available in the lab.

Modelling and Meshing

To begin modelling the beam, three-dimensional, deformable solid pieces were created in ABAQUS. All of the finite element models utilized the quadratic shell element. Two-point loading and simply supported boundary conditions finite element models were created. The eight-node shell element (S8R) type was used to carry out the model’s structured meshing. Using the 20 × 20 mm element produced better simulation results.

9. Specimen Details

Figure 19 shows various profiles like Figure 19a C-section, Figure 19b trapezoidal section, Figure 19c triangular section, and Figure 19d double triangular section. The sigma section examples have heights of 100 mm, 150 mm, and 200 mm. For 1.5 m length, flange widths of 50 mm, 75 mm, and 100 mm were employed, with thicknesses of 1.2 mm, 1.6 mm, 2 mm, 2.3 mm, 2.5 mm, 3 mm, 4 mm, 5 mm, and 6 mm. The appropriate cold-forming process stiffens the web. To explore the buckling modes, all of the specimens were studied without distortional restriction. Appendix A contains the specimen’s geometric features.

Figure 20 shows various profiles as follows: (a) C-section; (b) triangular section; (c) trapezoidal section; and (d) double triangular section constructive views, as (i) mesh view; (ii) elevation; and (iii) load and support, respectively.

Boundary Conditions

The goal of the ideal finite element models was to explore the flexural behaviour of these ideals with simply supported boundary conditions. The support configurations were almost symmetric around the mid-plane, although one support constrains X-axis movement. The finite element model’s simply supported boundary conditions are given as follows:

The pin support at one end was modelled by restraining degrees of freedom. The pin support at the other end was modelled by the restraining degree of freedom where the set of nodes represents displacement ‘ur’ which represents the rotation.

1. Pin support at one end was represented by degrees of freedom ‘ux’, ‘uy’, ‘uz’, ‘ury’, or ‘urz’ for the set of nodes.

2. The pin support at the other end was simulated by restricting degrees of freedom ‘ux’, ‘uy’, ‘ury’, or ‘urz’ for the set of nodes, where ‘u’ denotes displacement and ‘ur’ rotations.

10. Loading of Specimen

For all specimens 1.5 m in length with various characteristics, the boundary conditions were modelled and analysed for load-carrying capability and buckling performance. The specimens’ ends were simply supported, and neither end was restricted from buckling. The beam sample was constrained by its one-fourth width until breakdown happened, and the results would be collected by non-linear research. Loads were applied in the inverse Y direction. The weights were applied in increments with a 0.05 increment size at first. The highest increment size remained at 1.0, while the smallest increment size remained at 0.00001. A static general analysis was performed.

11. Analytical Results

Finite element software ABAQUS v6.4 was employed in the analysis of all the specimens using variable thickness, height-to-thickness ratio, and b/t ratio. From this analysis, vertical deflection and ultimate load were determined. Encumbered by its one-fourth width until the breakdown occurs, the consequences would be obtained through non-linear investigations. They were tabulated below. From the chart, the difference in percentage values for deflection and ultimate load were derived.

Result and Discussion for Profile-1, -2, -3, and -4 Specimens

From the non-linear analysis, vertical deflection and ultimate load were determined for all the profile 1 specimens. Their corresponding load-deflection pattern and ultimate load-carrying capacity were plotted, and their behaviour was studied [28].

Figure 21 shows profile 1 C-section: (a)(i) x,y,z deflection contour; (a)(ii) x,y deflection contour; and (a)(iii) stress contour. Figure 22 shows profile 1 C-section parameters as load vs. deflection for (a)(i) P1HF1; (a)(ii) P1HF2; (a)(iii) P1HF3; and (a)(iv) ultimate load.

Figure 23 shows profile 2 triangle section: (a)(i) x,y,z deflection contour; (a)(ii) x,y deflection contour; and (a)(iii) stress contour. Figure 24 shows profile 2 triangle section parameters as load vs. deflection for (a)(i) P2HF1; (a)(ii) P2HF2; (a)(iii) P2HF3; and (a)(iv) ultimate load.

Figure 25 shows profile 3 trapezoidal section: (a)(i) x,y,z deflection contour; (a)(ii) x,y deflection contour; and (a)(iii) stress contour. Figure 26 shows profile 3 trapezoidal section parameters as load vs. deflection for (a)(i) P3HF1; (a)(ii) P3HF2; (a)(iii) P3HF3; and (a)(iv) ultimate load.

Figure 27 shows profile 3 double triangle section: (a)(i) x,y,z deflection contour; (a)(ii) x,y deflection contour; and (a)(iii) stress contour. Figure 28 shows profile 3 double triangle section parameters as load vs. deflection for (a)(i) P4HF1; (a)(ii) P4HF2; (a)(iii) P4HF3; and (a)(iv) ultimate load.

12. Results and Discussion

The web-stiffened sigma sections and channel sections in transverse two-point loads with simply supported circumstances were numerically analysed using ABAQUS v6.4. Loading was gradually added until failure. In the incremental loading, ultimate values were estimated using ABAQUS v6.4 for all specimens.

Examination of the section concerning the various variables is essential to identify which one is significant. The important factors are:

(a) Thickness of the specimen

(b) Type of stiffener

The effect of the aforementioned variables on the ultimate strength, as well as the deflection, is discussed below.

Ultimate Strength

Influence of Thickness of the Specimen

When the thickness of the specimen increased, so did its ultimate strength. The maximum strength of profile 2 improved by 194% when the thickness increased from 1.6 mm to 2 mm, but remained unchanged at 1.2 mm [29]. Similarly, when the thickness of profile 3 was increased from 1.2 mm to 2 mm, the ultimate strength improved from 22.72% to 45%. Figure 29 shows a comparative ultimate load study of profile 2 and profile 3: (a)(i) profile 2 triangular section; and (a)(ii) profile 3 trapezoidal section.

In the analytical analysis, all of the specimens revealed an 11.11% drop in strength when the stiffener was changed from triangular to trapezoidal [30]. However, during the experimental investigation, 1.2 mm- and 1.6 mm-thick specimens exhibited a 25% increase in strength when the stiffener was altered, whereas the 2 mm-thick specimen showed a 25% gain in strength. Figure 30 depicts the ultimate load for the diameters measuring 1.2, 1.6, and 2 mm.

13. Load vs. Vertical Deformation

Figure 31 shows a comparison of load versus deformation with various thicknesses of profile 2 and 3: (a)(i) P2HF1 1.2 mm; (a)(ii) P3HF1 1.2 mm; (a)(iii) P2HF1.2 mm; and (a)(iv) P3HF1.2 mm. The vertical deformations were compared to the findings of the analysis. Because of the support circumstances and diverse equipment involved in the measurement, the values of the vertical deformation from experimental work differed somewhat from the analytical results.

14. Conclusions

The experimental investigation was carried out utilizing a two-point flexure test, which provides the maximum load-carrying capability. The non-linear numerical analysis of the web-stiffened triangular section was performed using ABAQUS v6.4. The pieces were evaluated under simply supported circumstances for pure bending. Members were studied for ultimate load capacity and deflection. The greater the value of the h/t ratio in the section, the lower the load-carrying capability. When compared to lower h/t ratio sections, they increased load-carrying capacity from 35.13% to 37.2%.

• A higher value of h/t ratio in the section was associated with low load-carrying capacity. They showed an increase in load-carrying capacity from 35.13% to 37.2% when compared with the lesser h/t ratio sections.
• The results obtained from the numerical analysis showed the ultimate load-carrying capacity of profile 2 of the sigma section was increased to an average of about 11.11% compared to profile 3 of the sigma section.
• Load-carrying capacity was increased for profile 2 of the sigma section compared to profile 3 of the sigma section, due to the provision of stiffeners in the web of the sigma section.
• Lateral and vertical displacements for profile 2 of the sigma section were more than for profile 3 of the sigma section.
• For profile 1, the ultimate load-carrying capacity of HF1 was increased by 10% compared to HF2 and 60% compared to HF3 gradually for 4 mm, 5 mm, and 6 mm thicknesses, while for other specimens it started to decrease.
• For profiles 2 and 3, the ultimate load-carrying capacity of HF1 was increased by 5% compared to HF2 and 59% compared to HF3 gradually for 5 mm and 6 mm thicknesses, while for other specimens it started to decrease.
• For profile 4, the ultimate load-carrying capacity of HF1 was increased by 5.5% compared to HF2 and 55.55% compared to HF3 gradually for the 6 mm thickness, while for other specimens it started to decrease.
• From the experimental investigation, profile 2 had more load-carrying capacity than profile 3 for the d/t ratios of 83.33 and 62.5, while it decreased for the d/t ratio of 50.
• Specimens with an h/t ratio of 62.5 showed the least vertical displacement and lateral displacement in mid-span compared to those specimens with an h/t ratio of 83.33 and 50.
• As per the numerical and experimental analysis, the capacity of the section in profile with triangular stiffener was greater in all aspects when compared to the profile with trapezoidal stiffener, profile with double triangular stiffener and C-section. Thus, significant cost reduction in constructions can be made when a section with triangular stiffener is used.