The Efficiency of Structural Steel Section with Perforated-Corrugated Web Profile Subjected to Shear Loading Condition

The growing popularity of perforated steel plates since 1940’s is due to cost efficiency, ease of fabrication, high strength to weight ratio and suitability for a wide range application [2]. In order to provide better understanding of stress distribution in the vicinity of the web openings, some researches try to examine numerically the web opening shapes of perforated steel sections and identify those that have the best structural behaviour under certain type of loading. [2,3] The aim is to provide the maximum possible web opening area for the integration of services, whilst keeping the minimum possible self-weight for different type of loading.


Introduction
The growing popularity of perforated steel plates since 1940's is due to cost efficiency, ease of fabrication, high strength to weight ratio and suitability for a wide range application [2].In order to provide better understanding of stress distribution in the vicinity of the web openings, some researches try to examine numerically the web opening shapes of perforated steel sections and identify those that have the best structural behaviour under certain type of loading.[2,3] The aim is to provide the maximum possible web opening area for the integration of services, whilst keeping the minimum possible self-weight for different type of loading.
In order to provide data for the development of a design model for the shear capacity of steel girders with web openings, with and without transverse stiffeners and opening reinforcements, a numerical simulation was performed by Hagen et al. (2009) in designing the girder in a state of pure shear at the opening center.Based on the numerical data, a design model is presented that accounts for the reduction in webs shear area, shear buckling of the web and the effect of opening position, vertical stiffeners and opening reinforcement.Darehshouri et al. (2013) reported that the results obtained for circular, square and rectangular openings shows that the ultimate shear capacity was influenced significantly with size of opening, nearly 30% drop of shear capacity when the depth of openings was increased to half the web depth of girders.Meanwhile, Hamoodi (2013) found that the presence of openings in the web section of plate girder had reduced the ultimate shear load about 51%.Shear strength were considerably reduced by the presence of web opening [8] and its decrease with increase the perforation sizes [17].
On the other hand, introduce the corrugated steel web solely provides the shear capacity of the girders where the shear strength is controlled by buckling and/or steel yielding.Eldib (2009) performed finite element analysis to study the geometric parameters affecting the shear buckling strength of curved corrugated steel webs for bridges.The curved corrugated webs produce a tremendous increase in shear buckling strength and considerable weight saving in regard to the corresponding trapezoidal corrugated webs.The corrugation angle has a considerable effect on the behaviour of curved corrugated webs, where higher corrugation angles produce a tremendous increase in the shear buckling strength.The idea of perforated-corrugated web profile in achieving efficient structural steel section can reduce the weight of the steel section and may achieve similar performance to those without opening.Furthermore, the structural capacity of TriWP with perforation not yet studied.Hence, the determination of the structural efficiency of TriWP with the combinations of different perforations shapes, sizes and layouts are needed.A threedimensional finite element model using LUSAS is performed to analyse the structural efficiency and structural behaviour of TriWP with perforation subjected to shear loading.In addition, the effect of section properties and span length on the structural behaviour and performance of TriWP with perforation need to be observed.

Model Description
In this research, the TriWP with perforation is analysed.The model with section properties of 200 mm web depth; 100 mm flange width; 6 mm flange thickness and 4 mm web thickness with 900 mm span length which is used to carry out the study.As illustrated in Fig. 2, TriWP with perforated web consists of two flanges welded to the triangular profile of the perforated web section.

Methodology
There are two stages in this research study; Stage 1 and Stage 2. In Stage 1, the self-weight of TriWP with and without perforation shapes with the dimension of 200 mm × 100 mm × 6 mm × 4 mm and span length of 900 mm is calculated for cases of three different perforation sizes, five different perforation shapes, and three different layouts of perforations.Subsequently, these models have been used in analysis carried out using finite element method to determine the structural efficiency from the ratio of buckling load, Pb to the self-weight under shear loading condition.The increasing load from 0 kN to 120 kN is applied in Stage 1 with the increment of 0 kN, 10 kN, 30 kN, 60 kN, 90 kN and 120 kN.The TriWP with Fatimah De'nan, Hazwani Hasan, Choong Kok Keong / Galeri Warisan Kejuruteraan 1(1) (2017) 29-35 the most efficient perforation shape, size and layout is selected based on highest structural efficiency determined.In the Stage 2, 10 kN of the load applied as a constant parameter with increasing web thickness and span length are used on selected models in Stage 1 to study the structural behaviour and performance.

Finite Element Analysis
For this research, all the material properties are adopted from the tensile test with Young's Modulus, E, of 226.53 N/mm 2 , shear modulus, G of 79 x 10 3 N/mm 2 and Poisson ratio of 0.3.These material properties remain constant throughout the analysis.2013), the critical buckling load factor (kcr) for beams under proportional loading may then be determined directly from the eigenvalue solution.Linear eigenvalue buckling analysis will produce critical loads and buckled shapes.
Thin shell element is used in this study.This is because it is more suitable to structural components which the response is mainly due to flexural or in-plane strains, such as the steel plates making up an I-beam.There are two types of thin shell element, such as quadrilateral thin shell element (QSL8) and triangular thin shell element (TSL6).In this study, quadrilateral mesh is used and it will generally give better results than a triangular mesh due to the higher-order variation of forces and moments across the elements.
In shear loading condition, the loading and supports positions as shown in Fig. 7

Determination of Structural Efficiency
The structural efficiency in Stage 1 is calculated based on the ratio of buckling load to the self-weight by using Equation 1.The buckling load is generated from eigenvalue buckling analysis.Higher value of buckling load would produce higher structural efficiency.The comparison between TriWP with and without perforation is made by calculating the percentage difference of structural efficiency by using Equation 2.

Shear Buckling Capacity
The shear buckling capacity for TriWP without perforation is 39.55 kN.These values come from the shear buckling in the first mode shape.By taking the average of shear buckling capacity, the result of shear buckling capacity for all models is summarized in Table 4.The results of the analysis of TriWP with and without perforation are compared by calculating the percentage difference.The percentage difference is used to present the reduction in shear buckling capacity and it is presented in Table 5.The range of percentage reduction of shear buckling for Layout 1 is 47.9% to 89.05%, 47.9% to 87.69% for Layout 2 and 18.31% to 90.5% for Layout 3. The reduction in shear buckling capacity of TriWP with perforation is found to be more critical when the perforation area increases.Fig. 8 present the shear buckling capacity for all perforation shapes of 0.4D, 0.5D and 0.6D, respectively.It could be observed that the shear buckling capacity for each perforation shape is different.Increasing the perforation area over the web section decreases the shear buckling capacity.It is found that TriWP with perforation of diamond shaped shows the highest shear buckling capacity for Layout 1, Layout 2 and Layout 3 for all three different perforation sizes.However, the perforations are arranged in Layout 3 shows the highest shear buckling capacity due to the reason that the number of perforations in the web section is less than those in Layout 1 and Layout 2. This could be proven that the presence of the perforation in the web section leads to reduction in shear buckling capacity.On the other hand, increasing the perforation size reduces the shear buckling capacity.The percentage of reduction in shear buckling capacity is presented earlier.The lowest reduction in shear buckling capacity recorded is TriWP with perforation of diamond in shape and 0.4D in size arranged in Layout 3 i.e.18.31% (Table 6).That means, the reduction of shear buckling capacity for that model is about 18.31% difference from that of the TriWP without perforation and it shows the lowest drop of shear buckling capacity among other models.The contribution of this research is to explore the reduction of shear in the corrugated web with triangular web profile.The reduction of the shear buckling capacity is presented in term of percentage difference as shown in Table 6.In this study, it has been proven that TriWP with perforation has lower shear buckling capacity than TriWP without perforation and perforation of diamond shape shows largest shear buckling capacity compared to circle, square, hexagon and octagon.

Structural Efficiency
The structural efficiency of TriWP with perforation under shear loading condition can be obtained by dividing the shear buckling capacity by the self-weight of the model (refer Eq.1).Table 7 shows the value of structural efficiency of TriWP with perforation.The results show that the value of structural efficiency decreases with increasing perforation size for all perforation shape.The highest value of structural efficiency is found in Layout 3 which is then followed by Layout 2 and Layout 1.In this case, the highest value of structural efficiency of about 204.75 is TriWP with perforation of diamond in shape and 0.4D in size arranged in Layout 3.Meanwhile, the value of structural efficiency for TriWP without perforation is 244.89.The percentage difference of structural efficiency of TriWP with and without perforation is determined and the results are presented in Table 8.On the other hand, TriWP with perforation of diamond in shape and 0.4D in size arranged in Layout 3 is found to be the lowest percentage difference of structural efficiency which is 16.39%.Among the perforation shapes, the highest structural efficiency occurs in the case of diamond shape.This is then followed by circle, hexagon, octagon and square.Therefore, TriWP with perforation of diamond in shape and 0.4D in size arranged in Layout 3 is selected for further analysis in the Stage 2 under shear loading condition.Section properties have a great effect on the behaviour of beam under shear loading condition.A total of 25 finite element models are analysed under this parametric study to observe the structural behaviour and performance of TriWP with perforation.The model is designed based on the previous stage of numerical analysis where the selected model is chosen based on the structural efficiency i.e.TriWP with perforation of diamond in shape and 0.4D in size arranged in Layout 3. By fixing the depth of the section (D), flange width (B) and the corrugation angle (θ), the models are designed with different web thickness and span length.The constant load applied about 10 kN is used to observe the effect of different section properties.The results of shear buckling capacity of TriWP with perforation of diamond in shape and 0.4D in size arranged in Layout 3 are presented in Fig. 10.The results show that increasing web thickness from 2 mm to 7 mm has improved the shear buckling capacity.However, the shear buckling capacity is not affected by changing the span length of the model.With the increase in the span length, the shear buckling capacity is found to experience only a slight reduction in shear buckling capacity.At the same span length, the model experienced an increasement in shear buckling capacity when the web thickness increased.According to the theoretical part, the nominal shear strength under pure shear,   is given by:   =     √3 Eq. 3 That means that the shear buckling capacity is affected by cross-sectional area, specifically the thickness of the web and the overall web depth.In relation to the research, Equation 3 has proven that the shear buckling capacity is not affected by the length of the model.As reported by Tsavdaris and Mello (2012), they noticed that there was no significant reduction in the shear buckling capacity with any beam span.On the other hand, they also prove that there was no effect on thickness of flange on shear buckling capacity where it produces a small effect which could be ignored.

Conclusion
Seventy-one models of TriWP with and without perforation have been studied.The self-weight of the models was first determined.They were analysed using finite element analysis to investigate shear deformation.Buckling load were investigated to determine the structural efficiency.The following conclusion can be drawn from the present study: a) In the first stage of analysis i.e.Stage 1, TriWP with the perforation of diamond in shape and 0.4D in size arranged in Layout 3 showed the highest buckling moment resistance.Therefore, it contributes to the highest value of structural efficiency (204.75) and leads to the most efficient perforation shape, size and layout.Good agreement can be observed between the result of finite element analysis and previous studies found in the literature.Compared to other researchers, the contribution of the analysis of this study is the structural efficiency of TriWP with perforation.The result of analysis is used to determine the structural efficiency of each model.b) Under shear loading condition, it is found that when the web thickness are increased under the same span length with constant flange and web depth, the value of moment buckling resistance also increased under loading causing shear buckling.Meanwhile, increase in span length of model results in lower shear buckling capacity.
case of trapezoidally corrugated steel web, a few researchers such as Moon et al. (2009), Yi et al. (2008) and Nie et al. (2013) had studied the shear strength and design of this corrugated steel web.Trapezoidally corrugated steel plates have been used as the web of pre-stressed concrete box-girder bridges to reduce dead load and increase structural efficiency.Due to an applied shear stress, the trapezoidally corrugated web can fail by three different shear buckling modes: local, global, and interactive shear buckling as shown in Fig. 1.Local buckling involves a single panel, whereas global buckling involves multiple panels, with buckles extending over the entire depth of the web.

Fig. 4 Fig. 5 2 Fig. 6
Fig. 4 The isometric view of TriWP with perforation of circular shaped arranged in Layout 1 Eigenvalue buckling analysis is used by many researchers such as Valdevit et al. (2006); Moon et al. (2009); Umbarkar et al. (2013); Abidin & Izzudin (2013); Saddek (2015) to obtain critical buckling load by solving the associated eigenvalue problems.The load factors are equivalent to the eigenvalue in an eigenvalue buckling analysis.As mentioned by Abidin & Izzudin ( is adopted from Eldib (2009); Nie et al. (2013); Hamoodi & Gabar (2013).From the Fig., it shows that the condition of the TriWP with perforation after meshing.The symbols of ABCD are presenting the location of the end nodes of TriWP.The nodes for the support are constrained in x, y and z translation direction at one side i.e.AB.Meanwhile, along AC, CD and BD, the supports are constrained in x and z translation.From Eldib (2009); Nie et al. (2013) and Hamoodi & Gabar (2013), the supports are modelled as simply support boundary condition in order to ensure the shear load is applied through the web.On the other hand, the shear loading condition is modelled by applying concentrated load along CD of the vertical stiffener.The concentrated load is applied along one edge of the model to make the web under a pure shear state.Meanwhile, the flanges and stiffeners are replaced with simple support boundary condition for the conservative consideration.However, this study involves the model with and without flanges and their result shows no changes in eigenvalue buckling and buckling modes.

Fig. 7
Fig. 7 Supports and loading position of model for shear loading condition

. Result 4 . 1
efficiency of TriWP without perforation  = structural efficiency of TriWP with perforation 4Percentage weight reduction The self-weight of TriWP without perforation with the dimension of 200 mm × 100 mm × 6 mm × 4 mm and 900 mm of span length is 0.1616 kN.Table1to Table3represent the percentage difference of weight reduction of TriWP with and without perforation for Layout 1, Layout 2 and Layout 3, respectively.The presence of perforations such as circular, square, hexagon, octagon and diamond in TriWP reduces the volume of steel usage.Based on the percentage of weight reduction, TriWP with perforation of square shaped shows the highest weight reduction from 0.4D to 0.6D of perforation size for all three layouts of perforations due to the low self-weight compared to another shapes of perforation.The second highest weight reduction is circle which is then followed by hexagon, octagon and diamond.The trend of reduction is significant because it will affect the value of structural efficiency.TriWP with perforation of diamond shaped shows the lowest percentage of weight reduction since it has the highest self-weight.In terms of the layouts of perforations, perforated TriWP with Layout 1 shows the highest percentage of weight reduction ranging from 5.52% to 24.73%.The corresponding percentage values for Layout 2 range from 3.08% to 13.75% and Layout 3 range from 2.47% to 11.01%, respectively.This is because Layout 1 consists of nine numbers of perforations in the web section while Layout 2 and Layout 3 consist of 5 and 4 numbers of perforations, respectively.

Fig. 9 Fig. 9
Fig.9shows the buckling mode for Layout 3 that occurred in the web of TriWP with perforation size of 0.4D for square, circle, hexagon, octagon and diamond perforation and TriWP without perforation.The buckling modes are similar for all perforation shapes.The contour indicates that shear buckling is significant around the perforation shapes.By referring to the literature, such buckling mode is classified as a local shear buckling mode where the buckling involves a single flat panel(Nie et al., 2013).

4. 4 . 1
Effect of Web Thickness, tw Each model of TriWP steel section with perforation as shown in Table 9 is designed for different span length from 1 m to 5 m.These 25 models are used to study the influence of web thickness on the structural behaviour under increasing length of the section.Other geometric parameters are kept constant i.e.D = 200 mm, B = 100 mm, θ = 45 o and tf = 8 mm.The following web thicknesses are considered; tw = 2 mm, 4 mm, 5 mm, 6 mm and 7 mm.

FatimahFig. 10
Fig. 10 Shear buckling capacity versus web thickness This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited https://doi.org/10.26480/gwk.01.2017.29.35