Calculation of the effective properties of trapezoidal steel sheets

Calculation of the effective properties of trapezoidal steel sheets Pág. 1 Abstract In the present days, thin-walled structural members are getting used more and more in the industrial domain, that’s why the research of these type of elements demands a lot of attention. One special place between these elements, is occupied by the cold-formed trapezoidal steel sheets. The evolution of this domain concluded in appearance of a numerous manufacturers producing trapezoidal steel sheets, for industrial roofing and structure covering. Due to the high competition, the efficiency and accuracy in determining the load carrying capacity of the sheets has a key role. The methods used to achieve these results have to be conformed with the codes and standards of the country where the sheets are going to be in service. The following study researches the behaviour of trapezoidal steel sheets submitted to bending. The main concept of the paper, is to compare the results of the experimental test, performed at Escola Tecnica Superior d’Enginyeria Industrial de Barcelona with the North-American and European design methods. Aspects, that are examined in the paper are the failure mode and the types of buckling modes that appear in the sheeting. There is a complex presentation of the researches that the project is based on, the software analyses performed in different programs: CUFSM, Ansys-Mechanical APDL; tend to reproduce the real scale experimental test. The FEM analysis appears to be a very good scientific tool to identify the behaviour of trapezoidal steel sheets, given the similarities between the model results and the experimental ones. The design methods use different approaches, but converge to affined results. Pág. 2 Memoria Calculation of the effective properties of trapezoidal steel sheets Pág. 3 ABSTRACT ___________________________________________________ 1 1. INTRODUCTION _____________________________________________ 5 1.1 Origin of the project ........................................................................................ 5 1.2 Motivation ....................................................................................................... 6 1.3 Objectives of the project ................................................................................. 6 1.4 Scope of the thesis ......................................................................................... 7 2. STATE OF THE ART _________________________________________ 9 2.1 Cold formed steel ........................................................................................... 9 2.1.1 Generalities ....................................................................................................... 9 2.1.2 Material ............................................................................................................. 9 2.1.3 Corrosion and protection ................................................................................ 11 2.1.4 Applications of cold formed profiles ................................................................ 11 2.1.5 Advantages & Disadvantages ............................................................................. 13 2.1.6 Specific problems of cold formed profiles ....................................................... 13 2.2 Design procedures ....................................................................................... 15 2.2.1 The Direct Strength Method-AISI (2007) ........................................................ 15 2.2.2 Local Buckling via Finite Strip (Mcrl) ............................................................... 15 2.2.3 Distortional buckling via finite strip (Mcrd)....................................................... 16 2.2.4 Review on the European Approaches ............................................................ 18 2.2.4.1 Approach for unstiffened web and flange ............................................ 18 2.2.4.2 Approach for flange/web with one, two or multiple stiffeners ................ 19 3. REVIEW ON THE EXPERIMENT _______________________________ 27 3.1. Test set-up ................................................................................................... 27 3.2. Real life scaled experiment .......................................................................... 29 4. SOFTWARE _______________________________________________ 35 4.1 CUFSM ......................................................................................................... 35 4.1.1 Defining the material and the section .................................................................. 35 4.1.2 Loads .................................................................................................................. 37 4.1.3 Analysis and results ........................................................................................ 38 4.2 Ansys – Mechanical APDL ........................................................................... 39 4.2.1 Finite element type.......................................................................................... 39 4.2.2 Generating the macros ................................................................................... 40 4.2.3 Analysis........................................................................................................... 43 Pág. 4 Memoria 5. NUMERICAL INVESTIGATIONS AND RESULTS __________________ 46 5.1 Introduction .................................................................................................. 46 5.3 Example of the calculation method using AISI for H150 ................................ 47 5.3 Example of the calculation method using EN-1993 for H-150....................... 51 5.2 Comparison of the results, sheet H150 ....................................................... 59 5.3 Comparison of the results, sheet H55 ......................................................... 59 5.4 Comparison of the results, sheet H68 ......................................................... 59 5.5 Comparison of the results, sheet EUROCOL 60......................................... 60 6. BUDGET __________________________________________________ 61 7. ENVIRONMENTAL IMPACT __________________________________ 63 8. CONCLUSION _____________________________________________ 65 BIBLIOGRAPHY ............................................................................................ 66 Calculation of the effective properties of trapezoidal steel sheets Pág. 5 1. Introduction Cold formed steel sheets, due to its strength and durability is the ideal building material for roofs, facades and partition walls. Their main characteristics are that they are lightweight, easy and economical to fabricate, to deliver and to assembly. An extensive selection of high and low profiles gives the client the opportunity to design in complete accordance with their needs. The trapezoidal steel sheets are mounted on the structure by using fasteners that vary depending on which type of profile is chosen. . Figure 1: Typical trapezoidal sheets 1.1 Origin of the project There are a variety of companies that produce trapezoidal steel sheets for different applications. METALPERFIL and EUROPERFIL are local companies from Catalonia, they have a wide range of products for different applications and different type of structures like: industrial premises, hypermarkets, barns and stables, small residential buildings, carports, advertising panels. This project started as collaboration with METALPERFIL and EUROPERFIL Company in order to improve their list of products, more exactly to find out about the bearing capacity of the steel sheets with different type of sections: H-55, H-68, H-150, Pág. 6 Memoria EUROCOL 60. 1.2 Motivation The motivation to participate in this project comes from a personal, commercial and economical aspect. The personal motivation was born from curiosity towards new types of elements used in civil engineering. The commercial and economical aspects come from the collaboration with METALPERFIL and EUROPERFIL Company, and aim to determine the bearing capacity of the steel sheets. This project also is studying all the parameters that have an influence on the effective properties of the trapezoidal steel sheets. 1.3 Objectives of the project The main object of the project is to assess different a calculation methods for trapezoidal steel sheets by comparing their results with the results from Ansys Mechanical APDL models and the experimental test results. From these models we can get the data necessary to calculate the ultimate bending moment of the sheets, and the ultimate load that they can withstand. To do this it requires a lot of time and resources so, in order to simplify it, one of the objectives is to generate FEM models using macros created with the Ansys Mechanical commands. An experiment is conducted and performed in the laboratory of Escola Tecnica Superior d’Enginyeria Industrial de Barcelona on EUROCOL 60, to determine the bearing capacity and the failure mode of the trapezoidal steel sheet. Furthermore, data from previous experiments will also be used. In the end this study will give us a better understanding about the behaviour of trapezoidal steel sheets with different heights and thickness, with stiffened/ unstiffened webs/flanges; and will allow us to know which is the most efficient design method. Calculation of the effective properties of trapezoidal steel sheets Pág. 7 1.4 Scope of the thesis This particular thesis focuses on assessing the calculation methods in accordance with the North-American, European standards and realize a Finite Element Method model which results together with the calculations converge towards the real scale experimental test results. Pág. 8 Memoria Calculation of the effective properties of trapezoidal steel sheets Pág. 9 2. State of the art 2.1 Cold formed steel 2.1.1 Generalities During the XXth century a new type of element started to appear in the industry, used by American and British engineers the cold formed steel profiles. Their list of application kept growing by the time from purlins, to sheeting for roofs and floor decking which is considered the secondary structure for buildings, but nowadays these profiles are used as primary resistance structures as well. The perspective of cost and efficiency in constructions are being more restrictive than ever, but cold formed profiles excels in resistance/weight ratio, opportunity of rapid transport of the elements, easy and fast assembly and the possibility to recover and recycle the profiles. Being such a new branch in the field of civil engineering, it also created some new and difficult design problems that were rarely encountered in the past. Of course there are similarities in theory, but the use of cold formed steel and small thickness still causes problems for most of the engineers. The problem usually rises from the fact that the component walls of the section are very slender, so the section will be of class 4 or class 3, according to the Eurocode. When using sections of class 4 we have to take into account the fogging (the loss of stability), thus using the active characteristics of sections which are reduced compared to the real characteristics. In this way local instability, buckling, distortion can mix with global instability and generate a higher sensitivity to imperfections and reducing the bearing capacity of the profiles subjected to compression or bending. 2.1.2 Material The stress-strain curve describes the material behaviour. The steel grade used to realize these cold formed profiles is very important in determining their bearing capacity. The stress strain graph of steel can be classified in 2 categories: sharp yielding and gradual yielding (Figure 8 and Figure 9). Pág. 16 Master Thesis - Yield stress - Critical elastic local buckling moment determined by analysis The same calculations can be done with member plastic moment. For (7) (8) For (9) (10) Where (11) (12) - Member plastic moment - Plastic section modulus 2.2.3 Distortional buckling via finite strip (Mcrd) Distortional buckling involves both translation and rotation at the fold line of a member. Distortional buckling involves distortion of one portion of the cross-section and predominantly rigid response of a second portion. The nominal flexural strength, Mnd, for distortional buckling shall be calculated in accordance with the following: For (13) (14) Calculation of the effective properties of trapezoidal steel sheets Pág. 17 For (15) (16) Where (17) (18) - Gross section modulus referenced to the extreme fiber in the first yield - Yield stress - Critical elastic distortional buckling moment determined by analysis The same calculations can be done for the member plastic moment. For (19) (20) For (21) (22) Where (23) (24) - Member plastic moment - Plastic section modulus Pág. 18 Master Thesis 2.2.4 Review on the European Approaches In the project there were 4 type of trapezoidal steel sheets analysed, these sheets had different geometry and thickness, between these sheets were ones with unstiffened and ones with stiffened webs and flanges. During the process multiple parts of the Eurocode-3 were used like: EN 1993-1-5 and EN 1993-1-3. 2.2.4.1 Approach for unstiffened web and flange For unstiffened web and flange the following approach was applied from EN 1993- -1-5. The effective area of flat compression elements should be obtained using Table.1 for internal elements. The effective area of the compression zone of a plate with the gross cross-sectional area Ac should be obtained from: where is the reduction factor for plate buckling (25) The reduction factor may be taken as followsfor internal compression elements: for (26) for (27) Where (28) (29) - is the stress ratio b - is the apropriate width - is the buckling factor corresponding to the stress raio and boundary conditions t – is the thickness Calculation of the effective properties of trapezoidal steel sheets Pág. 19 Table.1 2.2.4.2 Approach for flange/web with one, two or multiple stiffeners Calculation procedure FLANGE Effective width Intermediate stiffener Pos. Centroidal Axis WEB Effective width Web stiffener Interaction of the stiffeners Reduced thickness ratio Pos. Centroidal axis Bending capacity Pág. 20 Master Thesis For flanges with one, two or multiple stiffeners the following approach was investigated and applied. If the flange is subject to uniform compression, the effective area of the cross-section should be reduced using the parameters presented in Figure.4 Figure.4 For one central flange stiffener, the following method should be used to determine the elastic critical buckling stress. (30) Where: - is the notional flat width of plane elements shown in Figure.4 - is the stiffener width, measured around the perimeter of the stiffener Figure.4 , - are the cross-section area and the second moment area of the stiffener according to Figure.4 -is a coefficient that allows for partial rotational restraint of the stiffened flange by the other adjacent elements For two symmetrically placed stiffeners, the elastic critical buckling stress should be calculated as followed. Calculation of the effective properties of trapezoidal steel sheets Pág. 21 (31) With: (32) (33) Where: - is the notional flat width of an outer plane element, Figure.4 - is the notional flat width of the central plane element, Figure.4 - is the overall width of a stiffener, Figure.4 , - are the cross-section area and the second moment area of the stiffener according to Figure.4 For multiple stiffened flange, three or more the effective area of the flange is: (34) Where ρ is the reduction factor according to EN 1993-1-5, the elastic buckling stress should be calculated as follows: (35) Where: - is the sum of the second moment of area of the stiffeners about the centroidal axis - is the width of the flange shown in Figure.4 - is the developed width of the flange shown in Figure.4 The value of kw may be calculated from the compression flange buckling wavelength lb as follows: Pág. 22 Master Thesis -if (36) (37) -if (38) (39) Where sw –is the slant height The value of lb and kwo may be determined from the following: -for a compression flange with one intermediate stiffener: (40) (41) With: (42) -for a compression flange with two intermediate stiffeners: (43) (44) The reduced effective area of the stiffener allowing for distortional buckling should be taken as: Calculation of the effective properties of trapezoidal steel sheets Pág. 23 (45) The reduction factor for distortional buckling resistance should be obtained from the relative slenderness: if (46) if (47) if (48) Where: (49) - is the elastic critical stress for the stiffener The effective cross-section of the compression zone of a web should be assumed to consist of the reduced effective areas. Pág. 24 Master Thesis Fig.5 Effective cross-section of webs The effective areas of the stiffener should be obtained from the following: -for a single stiffener, or for the stiffener closer to the compression flange; (50) -in which the dimensions are showed in Figure.5 Initially the location of the effective centroidal axis should be based on the effective cross-section of the flanges but the gross-section of the webs. In this case the basic effective width seff0 should be obtained from. (51) - is the stress in the compression flange when the cross-section resistance is reached If the web is not fully effective, the dimension should be determined as follows: (52) (53) (54) (55) Where: - is the distance from the effective centroidal axis to the system line of the compression flange see Figure.5, and the dimensions are shown in the same figure If the relevant plane element is fully active the following approach should be used: -in an unstiffened web is Seff1+Seefn > Sn the entire web is effective: (56) Calculation of the effective properties of trapezoidal steel sheets Pág. 25 (57) -in stiffened web, if Seff1+Seff2 > Sa the whole of Sa is effective: (58) (59) -in a web with one stiffener, if Seff3+ Seffn > Seffn the whole of Sn is effective; (60) (61) For a single stiffener, or for the stiffener closer to the compression flange, the elastic critical buckling stress should be determined using: (62) With: (63) (64) - is a coefficient that allows for partial rotational restraint of the stiffened web by the flanges - is the second moment area of a stiffener cross-section - shown in Figure.5 Pág. 32 Master Thesis Figure.11 Load transferring system Before the start of the experiment, the displacement measuring sensors need a calibration, which is realised with the help of a flat surfaced element with all the dimensions known. At the end of the experiment the results from the displacement sensors will be interpreted according to the modifications caused by the calibration. Figure.12 Figure.12 Calculation of the effective properties of trapezoidal steel sheets Pág. 33 After the experimental test the failure mode is analysed, and the data obtained in the process will be necessary to determine the ultimate bending moment of the sheet. Also the results will be compared with the ones obtained from the FEM method and from the numerical analysis that was carried out. This type of experimental test presented for EUROCOL 60 was carried out for sheet H150 and H55 using the same type of set-up. Figure.13 The experimental failure mode Pág. 34 Master Thesis Calculation of the effective properties of trapezoidal steel sheets Pág. 35 4. Software 4.1 CUFSM CUFSM is a software usually used for thin-walled cold-formed steel elements. In the project it is used to determine the multiplication factor for local and distortional buckling that will be used to calculate the critical bending moments of the 4 sheets that has been investigasted. 4.1.1 Defining the material and the section In the software interface the section of the sheets is created by using global coordinates, all the material properties are introduced and the constraints on the two sides of the sheets not allowing translation on the x-x axis and rotation about y-y axis. Figure.14 H150 Pág. 36 Master Thesis Figure.15 H55 Figure.16 H68 Calculation of the effective properties of trapezoidal steel sheets Pág. 37 Figure.17 EUROCOL 60 4.1.2 Loads The applied load/ bending moment is applied in the left side of the interface, on the right side a diagram of stress distribution is shown. Figure.18 Pág. 38 Master Thesis 4.1.3 Analysis and results A buckling analysis was performed to determine the load factor for the critical elastic bending moment for local and distortional buckling. In the interface the buckled shape and the load factor is shown. Figure.19 Local buckling, buckled shape The load factor is used in the numerical analysis by the North-American approach. For sheet H55 the absence of the stiffeners in the web and in the flange concludes in the lack of distortional buckling, that’s why sheet H55 is missing from Figure.20. Calculation of the effective properties of trapezoidal steel sheets Pág. 39 Figure.20 Distortional buckling, buckled shape 4.2 Ansys – Mechanical APDL Ansys Mechanical APDL is a finite element software used in this paper for determining the ultimate bending moment of the sheet. 4.2.1 Finite element type SHELL281 is suitable for analysing thin to moderately-thick shell structures. The element has eight nodes with six degrees of freedom at each node: translations in the x,y,z axes, and rotations about the x,y,z axes. It is well suited for linear, large rotations and large strain non linear applications. Pág. 40 Master Thesis Figure.21 SHELL 281 4.2.2 Generating the macros The macro is a list of command that can be introduced in the interface of the software, it is an easy and efficient way to generate the model, using these types of command gives the user slightly chances to make errors or mistakes. One general macro is created to generate a half web of a trapezoidal steel sheet, which has a length of 1500 mm. This macro can be used to create all types of steel sheets with different geometry, yield stress, mesh. A second material is introduced to avoid local deformations and failure modes in the close environment of the loaded area. This material is assigned just to the loaded parts of the sheet and for the end of the sheet where the supports were positioned in the experimental test. Figure.21 Calculation of the effective properties of trapezoidal steel sheets Pág. 41 Figure.22 Generating the areas In the process 3 different sized elements were used in the mesh, the smallest one 5 mm applied in the area where the yielding was suspected and a 15 mm, 30 mm across the sheet shown in Figure.23. Figure.23 Meshing There were two types of boundary condition system applied on the sheets. One where for the upper and lower flange and for the middle section of the sheet constraints Pág. 48 Master Thesis For l0.776 Mnl 1 0.15 Mcrl Mne       0.4          Mcrl Mne       0.4 Mne 4.263 106 Nmm (Eq.1.2.2.6) Sf - Gross section modulus referenced to the extreme fiber in the first yield Fy - Yield stress Mcrl - Critical elastic local buckling Distorsional Buckling (1.2.2.3) The nominal flexural strength, Mnd , for distortional buckling should be calculated accordingly to: Mcrd 10005352Nmm5.352 106 Nmm MyMne 4.328 106 Nmm d My Mcrd 0.899 (Eq.1.2.2.10) For d0.673 Mnd 1 0.22 Mcrd My       0.5          Mcrd My       0.5 My 3.635 106 Nmm (Eq.1.2.2.9) Mcrd - Critical elastic local buckling The ultimate bending moment should be chosen, from the minimum between, the nominal flexural strength for local, distortional buckling: Mfin min Mnd Mnl     Mfin 3.635 106 Nmm The ultimate bending moment for the whole sheet, with three webs: MSheet 3 Mfin 1.091 107 Nmm Calculation of the effective properties of trapezoidal steel sheets Pág. 49 Mexp 14226750Nmm P%MSheet 100 Mexp 76.66 % Using the member plastic moment for the following calculations: Local Buckling (1.2.2.2) The nominal flexural strength, Mnl , for local buckling should be calculated accordingly to: Mpl ZfFy  Zf Zf17886.46mm 3  Fy327.81 N mm 2  Mpl ZfFy 5.863 106 Nmm Mcrl 10006848Nmm6.848 106 Nmm l Mpl Mcrl 0.925 (Eq.1.2.2.7) For l0.776 Mnl 1 0.15 Mcrl Mpl       0.4          Mcrl Mpl       0.4 Mpl 5.243 106 Nmm (Eq.1.2.2.6) Fy - Yield stress Mcrl - Critical elastic local buckling Mpl - Member plastic moment Zf - Plastic section modulus Distorsional Buckling (1.2.2.3) The nominal flexural strength, Mnd , for distortional buckling should be calculated accordingly to: Mcrd 10005352Nmm5.352 106 Nmm Pág. 50 Master Thesis MyMpl 5.863 106 Nmm d My Mcrd 1.047 (Eq.1.2.2.10) For d0.673 Mnd 1 0.22 Mcrd My       0.5          Mcrd My       0.5 My 4.424 106 Nmm (Eq.1.2.2.9) Mcrd - Critical elastic local buckling Mpl - Member plastic moment Zf - Plastic section modulus The ultimate bending moment should be chosen, from the minimum between, the nominal flexural strength for local, distortional buckling: Mfin min Mnd Mnl     Mfin 4.424 106 Nmm The ultimate bending moment for the whole sheet, with three webs: MSheet 3 Mfin 1.327 107 Nmm Mexp 14226750Nmm P%MSheet 100 Mexp 93.298 % Sheeting with stiffeners in flange and web Calculation of the effective properties of trapezoidal steel sheets Pág. 51 5.3 Example of the calculation method using EN-1993 for H-150 Bending moment capacity of a sheeting with stiffeners in flange and web. Cross-section to be calculated. Values of symbols E210000 N mm2  fy327.81 N mm2  fyb fy  t0.79 mm r3mm bp44.87mm r t3.797 r t51 r bp0.067 r bp0.101 Acording to clause 5.1(3) the influence of rounded corners may be neglected Top flange Pág. 52 Master Thesis Effective width of part of the top flange (see 4.4 of EN 1993-1-5) b1 bp t56.797 235 327.81 0.847 With k.σ assumed:4 k4 p b1 28.4 k 1.181 1 for k4 4.2( )  p0.055 3 ( ) p20.689 be1 0.5 0.68944.87mm15.458mm be2 be1 15.458mm Intermediate stiffener (see clause 5.5.3.4.2) For caculations of As:0.5be=15.458mm For calculation of Is:15t=15*0.79=11.85mm I z Iz Iz2 h Ih2 12 23.7 0 0 0 0 0 32.48 3.02 98.08 296.23 6.83 126.26 _________________________________________________ Sum 56.18 98.08 296.23 z98.08mm2  56.18mm1.746mm As1 2 15.458mm32.48mm 63.396mm As t bp44.87mm bs2 16.24mm32.48mm Calculation of the effective properties of trapezoidal steel sheets Pág. 53 Is170.36mm4  value taken from CUFSM Is1 Is t215.646mm3  The values of lb and kwo may be determined from the following: -for a compression flange with one intermediate stiffener: lb3.07 4 Isbp2 2bp 3bs    t3  5.25( ) kwo sw2bd  sw0.5bd   sw 5.26( ) lb3.07 215.646mm3 0.79mm44.87 2 mm2 2 44.87mm3 32.48mm( ) 0.79 3mm3         1 4 327.947mm sw602mm21532mm2  164.344mm if lb sw1.995 2 bd2bp bs 122.22mm kwo sw2bd  sw0.5bd  1.347 kwkwo kwo 1   2lb  sw lb sw       2           kw1.343 For one central flange stiffener, the elastic critical buckling stress σcr.s should be obtained from: cr.s 4.2kw E   As1 t Is1 t3 t 4bp2 2bp 3bs     176.603 N mm2  5.22( ) Pág. 54 Master Thesis Determination of the position of centroidal axis when the web and the stiffeners in the top flange are fully effective For symbols see figure 5.14 of EN 1993-1-3: l z l*z 30.358 0 0 16.24 3.02 49.0448 31.79 15.6 495.924 16 37.3 596.8 70.46 77.1 5432.466 16 116.89 1870.24 32.21 138.4 4457.864 20.8 153 3182.4 233.858 16084.74 l233.858mm lz 16084.74mm2  eclz l68.78mm ec0.069m -the bending moment capacity is governed by the compression stress at the top flange WEB Effective widths in the web (see clause 5.5.3.4.3) For symbols see figure 5.14 of EN 1993-1-3 Initially the location of the centroidal axis houl be based on the effective cross-section of the flangebut the gross cross-sections of the webs. In this case the basic effective width Seff0 should be obtained from: com.Ed 256.72 N mm2  M0 1 5.32( ) Seff.0 0.76 tE M0com.Ed  17.172mm com.Ed is the stress in the compression flange when the cross-section resistance is reached t0.79mm Calculation of the effective properties of trapezoidal steel sheets Pág. 55 ha31.2 mm hsa 12.21mm 5.33a( ) Seff.1 Seff.0 17.172mm Seff.2 1 0.5 ha ec       Seff.0 21.067mm 5.33b( ) Seff.3 Seff.0 1 0.5 hahsa    ec        22.591mm 5.33c( ) Seff.n 1.5Seff.0 25.758mm 5.33f( ) If S.eff1+S.eff.2 > S.a the whole of S.a is effective, so revise as follows: Sa32 mm Seff.1 Sa 2 0.5 ha ec  14.37mm 5.35a( ) Seff.2 Sa 1 0.5 ha ec        2 0.5 ha ec  17.63mm 5.35b( ) Pág. 56 Master Thesis If S.eff3+S.eff.n > S.n the whole of S.n is effective, so revise as follows: Sn27.175mm Seff.3 Sn 1 0.5 hahsa    ec  2.5 0.5 hahsa    ec  12.697mm 5.36a( ) Seff.n 1.5 Sn  2.5 0.5 hahsa    ec  14.478mm 5.36b( ) Web stiffener (see clause 5.5.3.4.3) Cross section for determination of A.s (see figure 5.15) Cross section for determination of I.s (see figure 5.15) Ssa 16 mm Calculation of the effective properties of trapezoidal steel sheets Pág. 57 Asa1 Ssa Seff.2 Seff.3 46.327mm Is1 16 mm10.34 2mm2  12 2Seff.1    10.34mm 2      2  910.76mm3  For a single stiffener, the elastic critical buckling stress σ.cr.sa should be determined using; Sc115 mm s10.9 SaSsa Sc    146.7mm 5.39b( ) s2s1Sa 0.5Ssa  106.7mm 5.39d( ) kf1 5.39a( ) cr.sa 1.05 kf EIs1 tt3 s1  Asa1 ts2 s1s2    322.027 N mm2  Interaction of flange and web stiffener should be taken into account according clause: 5.5.3.4.4 hha 12.21mm s1ha0.5hha    ec 0.458 for a profile in bending cr.mod cr.s 4 1s cr.s cr.sa        4  176.428 N mm2  5.42( ) Reduced thickness ratio for flange and web stiffener according to clause 5.5.3.1.(7) d fyb cr.s 1.362 5.12d( ) Pág. 64 Master Thesis Calculation of the effective properties of trapezoidal steel sheets Pág. 65 8. CONCLUSION The scope of the thesis is to determine the ultimate bending moment for four type of sheets with different kind of methods. Even though the obtained results show similarities there are advantages and disadvantages that show themselves during the procedure. The North-American approach is an easy way to determine the ultimate bending moment of the sheet. Using the Finite Strip method together with the CUFSM software makes an easy and time saving procedure that show results under 10% of difference from the experimental tests. It gives little room for the user to commit mistakes with the small numbers of variables used during the methods. The European approach is a more complex method that uses a lot of variables and iterations till it arrives to the final results. It gives a lot of room to errors and is more difficult for the user to carry out an analysis. From the software point of view Ansys APDL is the perfect program to this types of researches, the macros make the modelling fast for a variety of sheets, with different geometry and thickness. Furthermore helps the user to generate a multiple type of sheets with slight modifications in the macro. The software seems to be a good scientific tool for the research, but for the designing part its not necessary to use a software with such performance and complexity. Pág. 66 Master Thesis BIBLIOGRAPHY 1. Dan Dubina, V. Ungurean and Raffaele Landolfo “Design of Cold-Formed Steel Structures 2. Eurocode 3 Part 1-3 (ENV 1993-1-3) and Part1-5 (ENV 1993-1-3) General rules-Supplementary rulesfor cold-formed members and sheeting 3. AISI. (2007). North American Specification for the Design of Cold-Formed Steel Structural Members ;American Iron and Steel Institute 4.Esam M. Alawadhi Finite element simulations using ANSYS 5.A. Biegus, D. Czepizak, Research on the interactive resistance of corrugated sheets under combined bending and contact pressure 2006 6.Whei When Yu, Cold-Formed Steel Design, 2000 http://www.EUROPERFIL.es/ http://www.METALPERFIL.es/ https://apps.webofknowledge.com