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PARTICULAR ASPECTS IN THE DESIGN OF COLD FORMED STEEL MEMBERS AND SHEETING 1.1 Introduction 1.2 Industrial production of cold formed thin gauge sections 1.3. The steel used for cold formed thin gauge members. Characteristics for design 1.4. Influence of cold forming (hammering) 1.5. Maximum Width-to-Thickness Ratios 2.1.Specific Features of the Cross Sections of Cold Formed Thin Gauge Shapes 2.2. Calculation of Sectional Properties

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PARTICULAR ASPECTS IN THE DESIGN OF COLD FORMED STEEL MEMBERS AND SHEETING 1.1 Introduction1.2 Industrial production of cold formed thin gauge sections 1.3.Thesteelusedforcoldformedthingaugemembers.Characteristicsfor design 1.4. Influence of cold forming (hammering) 1.5. Maximum Width-to-Thickness Ratios 2.1.Specific Features of the Cross Sections of Cold Formed Thin Gauge Shapes2.2. Calculation of Sectional Properties 1.1 INTRODUCTION Sheet, strip, plates or flat bars, fabricated in roll-forming machines or by press brake operations; The thickness of the steel sheets or strips excluding the coating 0.5 mm to 4 mm for sheeting and from 1 mm to 8 mm for profiles; also, steel plates and bars as 25 mm may be cold formed into structural shapes Some important advantages: a) cold formed light members are manufactured for relatively light loads and/or short spans; b) various and intricate sectional configurations are produced economically by cold forming operations favourable strength-to-weight ratios may be obtained; c) nestable sections are produced compact packaging and shipping; d) load carrying panels and decks are able to provide useful surfaces for floors, roofs and wall constructions, and in other cases they can also provide enclosedcells for electrical and other conduits; e) panels and decks not only withstand loads normal to their surfaces, but they can also act as shear diaphragms to resist force in their own plans if they are adequately interconnected to each other and to the supporting members. 1.2 INDUSTRIAL PRODUCTION OF COLD FORMED THIN GAUGE SECTIONS A. Continuous process: important series of sections, by continuous forming, in rolling mills. The coil is unrolled and the steel sheet passes through successive pairs of roles and after that the sections are cut at the desired length. Stripped steel may be processed with thickness between 0.3 mm and 18 mm and width between 20 mm and 2000 mm. B.Discontinuous process: small series of sections, either a leaf press brake (folding) of the steel sheets or a coin press brake (press braking) are commonly used for pressing the steel strip in a mould. The thickness of the of the shapes obtained by press folding is relatively small, under 3 mm, and the length of the elements is between 1.5 m and 4.0 m. The shapes obtained by pressing in moulds have the thickness under 16 mm and 6 m length.Types of structural elements:Cold-formed structural members can be classified into two major types:a)- individual structural framing members; used in buildings as beams, columns, trusses, and in the workshop design as purlins, skylights, bracing, structural elements for walls transmission towers, etc b)- panels and decks (corrugated shells); used in facades as external layer for curtain walls, diaphragms, roofs, floors and permanent shuttering. COLD FORMING OF THIN GAUGE SECTIONS Forme diverse realizate din prfile cu pereti subtiri (Trebilcock, 1994)1.3. The steel used for cold formed thin gauge members. Characteristics for design E Continuously hot-dip metal coated sheeting with nominal thickness supplied with half of the normal standard tolerances, the design thickness t may be taken as the nominal core thickness, tc,nom. E In case of continuously hot-dip metal coated steel sheet and strip the core thickness is: tz, the thickness of the zinc protection, usually 0.04 mm both sides of the sheet and 275 g/m2. E Standard grades of steel shall have the properties that conform to the required suitability for cold forming, welding and galvanising. The ratio of the specific minimum ultimate tensile strength fu to the specific minimum yield strength satisfies: E The nominal (characteristic) values of the yield strength fyb and tensile strength fufor the specified steels are presented in table, course notes. EThe basic material used for fabrication of the steel sections consists in flat sheet steel strips and the Romanian standards available are: STAS 908-90, STAS 1945-90, STAS 9236-80, STAS 9150-80, STAS 10896-80, all of them being now harmonized with the european norms (SREN). Generally, all these grades of steel will have the elongation at failure, A (%)>20%. Also, supplementary measures will be adopted for the stripes of 0,28 mm thickness considering cold forming process and sensibility to brittle fracture. 2 . 1 >y uf fz nom ct t t =Examples of profiled sheeting and members (SREN 1993-1-3): a- basic elements; b- structural elements suitable for axial loading; c- structural elements suitable for bending Influence of cold forming (hammering)The manufacturing process modify the mechanical properties of the profiles alteration of the stress-strain curve of the steel.Strain hardening provides an increase of the yield strength and sometimes, of the ultimate strength that is important in the corners and still appreciable in the flanges, while press braking lets these characteristics unchanged in these zones. ( )yb u yb yaf fACntf f ||.|

\|+ =2|.|

\| =902inuiu090 =iu( )u yb yaf f f + s 5 . 0fyb, fu - yield strength, respectively ultimate tensile strength, N/mm2; t - thickness of the steel plate; A - gross area of the cross section (mm2); C =7 for cold rolling and 5 for other methods of cold forming; n - number of folders at 900 having the internal radius r ||.|

\| >4 2 4 1 1min2 , 9266000) ( 83 , 1 tR tbt Ip > stR tat ap > = 8 , 4266000) ( 8 , 262minCold formed shapes with stiffened walls:a)- intermediate stiffeners; b)- with lip and clip (end stiffener) OBSERVATION: The end stiffeners of and C shapes must respect also the condition: amin bp from the total width (excluding the rounded corners) of the wall that is stiffened. Maximum b/t ratios and modelling of the static behaviour Shapes with or without stiffeners, their geometric characteristics and mechanical behaviour, according to EC 3 (SR EN1993-1-1.3) TIPURI DE RIGIDIZARI ALE PERETILOR PROFILELOR FORMATE LA RECE Rigidizari intermediare Rigidizari marginale: a- cu rebord; b cu rebord intarit Rigidizari intermediare longitudinale cu una sau mai multe cute INFLUENTA ROTUNJIRILOR IN STABILIREA LATIMII bp The plane widths bp is measured from the midpoint of the corner. In the case when a cross section is made up from plane elements with sharp corners with r5t and r/bp0.15, rounding of corners is ignored. All the sectional properties may be calculated based on an ideal section and the following approximations:n- number of corners; m- number of flat widths; bi- length of the mid line of the flat widths. PARTICULAR FEATURES FOR THE DESIGN OF THE COLD-FORMED THIN GAUGE SECTIONS Cold-formed (thin gauge) sections may buckle under normal stresses smaller than the yield limit of the steel. The instability of the thin gauge flat sheets subjected to in-plane loading is due to imperfections.The following assumptions are demonstrated to be inconsistent: I. The perfect planarity - the initial deformations of the sheets due to faults of fabrication must be between certain limits. Still, the real plane elements do have initial geometrical imperfections- initial deflection w0, which grows with the increase of loading. Due to the effect of membrane behavior, the ultimate strength of the sheet is bigger than the critical elastic force of buckling, Ncr. This reserve of strength clearly insures a post-critical behavior. Plate in compression: conditions of supports and post-critical reserve II. Reduced deformations out of the plane of the plate this assumption is normally available in the theory of linear buckling in elastic domain. In reality, the ultimate strength of the plate exceeds the critical stress, the deformations being rather important; III. Axial loads - this assumption is impossible from the practical point of view, the planarity of the plate being an ideal assumption. Measurement of residual stresses in a cold-rolled C shape: a) residual flower: b)- slicing method; c)- curvature method;IV. Linear elastic behavior of the material this condition is satisfied up to the yield limit. Still, due to residual stresses caused by rolling, welding, cutting etc, in some fibers the plastic stresses are reached for applied stresses lower than fy. Local buckling in compression and bendingof the thin walled elements Consecutive stages of stress distribution in stiffened compressed elements Winters model (grid) The two distinct stages in the post-critical domain of the behavior of a plate are: Elastic- uniformly distributed stresses, under the critical force; Post-critic - below the critical force, the plate is deformed more and more, the stresses are not anymore uniform. Buckling is reached for a critical value of the normal stress: c cr where the critical stress is ([N/mm2])( )32 22210 1901 12||.|

\| =||.|

\| =p pcrbtkbt Eko ovtoThe coefficient ko depends on the nature and the distribution of the stress on the width of the wall, on the boundary conditions, on the ratio between the dimensions of this wall. - non - stiffened walls: k =0.425; - stiffened walls: k=4.0, the supports are considered articulated. ! It is important to observe that:- in the case of a wall under compression in its plane, the lost of strength capacity will not happen as long as the longitudinal edges will remain rectilinear; - the limits of strength capacity are much increased for certain types of walls. This remark leads to the theory of effective width of the wall. ThedesignconceptthegridmodelproposedbyWinter(1959)fortheinstabilityphenomenon.The cross section for these profiles is made up from flat elements (walls) with constant thickness inter-connected, generating a grid. In the post critical stage (post buckling strength) the central grid do not work anymore while the extreme grids,wherethestrainsaresmaller,areabletotakeoverstressesthatmay reach the design value of strength.Atthemomentwhenthemaximumstrengthvalueofthematerialfy,isreachedintheextreme zones,abiggerportionintheinternalpartofthewallalreadyisntworkinganymore(whereo=0),the deformations being very important. The width of the wall reaches its minimum value, called the effective width beff. From the point of view of the local buckling: -the stiffened compressed elements (walls)are flat elements in compression with both edges parallel to the direction of stress, which are stiffened by web elements, flanges or edge stiffeners of sufficient rigidity;-the non-stiffened compressed elements (walls)are flat elements in compression which are stiffened only at one edge parallel to the direction of the stress. BUCKLING OF THE THIN WALLS-WINTERS GRID MODEL Local buckling in compression and bendingof the thin walled elementsConsecutive stages of stress distribution in stiffened compressed elements Winters model (grid)Effective width of a plate in compression Stiffened walls-marginal and intermediateBucklingis reached for a critical value of the normal stress: c cr where the critical stress is determined with the known relationship: ( )32 22210 1901 12||.|

\| =||.|

\| =p pcrbtkbt Eko ovtoThe coefficient ko depends on the nature and the distribution of the stress on the width of the wall, on the boundary conditions, on the ratio between the dimensions of this wall. non - stiffened walls: k =0.425; stiffened walls: k=4.0, the supports are considered articulated. ! It is important to observethat:- in the case of a wall under compression in its plane, the lost of strength capacity will not happen as long as the longitudinal edges will remain rectilinear; - the limits of strength capacity are much increased for certain types of walls. This remark leads to the theory of effective width of the wall. The design concept the grid model proposed by Winter (1959) for the instability phenomenon. The crosssectionfortheseprofilesismadeupfromflatelements(walls)withconstantthicknessinter-connected, generating a grid. [N/mm2]In the post critical stage (post buckling strength) the central grid do not work anymore while the extreme grids,wherethestrainsaresmaller,areabletotakeoverstressesthatmay reach the design value of strength.At the moment when the maximum strength value of the material R, is reached in the extreme zones,abiggerportionintheinternalpartofthewallalreadyisntworkinganymore(whereo=0),the deformations being very important. The width of the wall reaches its minimum value, called the effective width beff. CLASSIFICATION OF THE WALLS OF A COLD FORMED SECTION From the point of view of the local buckling: -stiffened compressed elements (walls) -flat elements in compression with both edges parallel to the direction of stress, which are stiffened by web elements, flanges or edge stiffeners of sufficient rigidity-non-stiffened compressed elements (walls) -flat elements in compression which are stiffened only at one edge parallel to the direction of the stress. Considering that in the situation of buckling in elastic of a wall having its effective width, beff, the stress cr,eff reaches the maximum stress in the plate in post-critical domain, that is: max =fy. Then the former relationshipbecomes: ( )2 222,1 12||.|

\| =||.|

\|=effpcreffeff crbbbt Ek ovtooFrom this relationship it results that the effective width of the wall depends on the ratio cr/max : maxoocrp effb b =In buckling stage, the averaged stress on the whole width of the wall is u, the equivalence between the stresses will impose the following equation: u p eff u p y effb b b f b o o o = = maxVon Karman determined the following relationship for the effective wall: ( )max22211 12 o vto||.|

\| =pp effbt Ek b bIn the case of the plate articulated all around and uniformly compressed, k = 4.0:max9 . 1oEt beff =in order to simplify the further design specifications EC3 uses the following relationships:relative slenderness (of the plate) referred to bp: oc oktbfpcryp= =4 , 28 reduction factor:yupefff bbo = = influence of the elastic limit: yf240= c11s = andpThe slenderness of a wall, p is the ratio between the flat width of the wall, bp and its thickness, t. It results that:Winter proposed a semi - empirical relationship, derived from that of von Karmans that takes into account the imperfections: |||.|

\| =max max415 . 01 9 . 1o oEtbEt bpeffThis is used byEC3 in the design of the strength of very slender sections.The following annotations are used: 673 . 0 sp1 = 673 . 0 >p||.|

\| =p p 22 . 011Specifications: The effective width of a flat wall in compression and/or in bending is determined considering the relative slenderness referred to the width of the flat wall, bp and also, the limit of yield strength, fyb.In order to identify the way the cross section of a wall is working we have to compare the effective slenderness with the limit slenderness. The recommended values of the maximum slenderness (limit slenderness) for different types of cold-formed sections are presented in table 1. The common experience and the tests in laboratory impose these values. The limit slenderness is defined as the ratio between the width and the thickness of the wall in the case when the normal stresses are uniformly distributed on the whole cross section and equal with the design strength of the material. The values of the limit slenderness depend on the kind of the wall and the grade of the steel. The presence of the imperfections reduces the theoretical values of these limits over which buckling may occur anytime, see table. For:For:DIFFERENCIES BETWEEN BUCKLING OF IDEAL SLENDER MEMBER, HOT ROLLED SECTION MEMBERS AND COLD FORMED SECTIONS STRESSES DEVELOPED IN THE WALLS OF A COLD FORMED SECTION SUBJECTED TO BUCKLING Thin walled C section in compression Buckling ranges depending onslendernessEUROCODE buckling curves BUCKLING MODES OF COLD FORMED SECTIONS Local Flexural+ Flexural Torsionalinteractive buckling a) Flexural + Flexural-Torsional interactive buckling;b) b)- Local+Flexural Torsional interactive buckling Simple buckling modes for a C column (thin walled section) DISTORTION OF OPENED SECTIONES WITH THIN WALLS Combined modes of buckling leading to distortion of thin walled opened sections (wavelength is considered as buckling length in the case of a column) Moduri simple de flambaj ale unui profil C fara rebord: F-flambaj prin incovoiere generala; FT- flambaj prin incovoiere-rasucire; Lw, Lf distorsiunea inimii si respectiv a talpilor Moduri de flambaj prin distorsiune Forme de flambaj, forte critice de flambaj si rezistente la flambaj n functie de lungimea elementului The effective width and effective area of the walls in buckling THE EFFECTIVE WIDTH AND EFFECTIVE AREA OF THE WALLS IN BUCKLING Von Karmans theory mentions that the maximum stress in the wall max systematically reaches the elastic limit fy, so a pattern of the determination of the effective widths comprises: Determination of the stress ratio that shows the distribution of the stresses in the wall considered with its effective width (tab. 2 and 3). For doubly supported elements the stress ratio may be based on the properties of the gross cross section; Considering the supports (internal wall or end wall as cantilever) and again the value of the buckling coefficient is determined k ; Relative slenderness is determined; Reduction factor is determined; The effective width is calculated with the help of tables 2 and 3. ! Specification: In the case when the initial stress applied to the wall is small enough the amplified stress due to the lost of the efficacy max may reach a value much lower than the elastic limit fy. It is rational in this case to determine the effective width on the basis of the compression stress and not based on the limit of elasticity. For that, the parameter is computed by replacing fy with com as a first approximation of the max value. A new, altered value of max is determined for the effective width based on the reiteration of the method and starting from the determination of the relative slenderness of the wall. A procedure of convergence for the stress max , until is reaches the recommended values is based on calculation of the relative slenderness of the effective wall and then using this value in the expression of . FLAMBAJUL PRIN DISTORSIUNE Flambaj prin distorsiune a unui profil Z supus la compresiune (a) si la incovoiere (b) a) Modelul de flambaj prin distorsiune utilizat de SR EN 1993-1-3/2006; b) rigidizare de capat pe fundatia elastica reprezentata de un resort; c) modelul utilizat pentru determinarea coeficientului de rigiditate Aria eficace a unei rigidizari de capat dupa SR EN 1993-1-3/2006 Perete nerigidizat (in consola) Tensiunea critica elastica de flambaj la un element zvelt comprimat prins intr-o fundatie elastica avand coeficientul de pat K este determinata dupa Timoshenko si Gere in 1961Coeficientul de flambaj prin distorsiune: unde zveltetea relativa pentru flambajul distorsional este: ELEMENTS WITHOUT STIFFENERS (PLANE ELEMENTS) I step The reduction factor for the determination of the effective widths according to tab. 4. for doubly supported or 5., for singly supported elements shall be obtained as we have already seen. The value of relative slenderness is determined with: where: com effective stress of compression on the extremities of the wall, 1, determined with respect to the effective area of the transversal section and multiplied with the safety factor, M1; k buckling coefficient according to tab. 4 and 5.. II step The design for the limit state of serviceability, 1-fy: The value of the reduction factor is determined with the relative slenderness obtained as in the I step, where com = 1 M1 and the effective stress calculated is 1 < fy/M1. The following relationships are used: For:we take: =1; For : we take: After determining the values: III stepIn tables 6 and 7 the geometrical width of the flat wall is bp. In the case of the lateral webs without intermediate stiffeners (the folders of the sheeting), the annotation sw is equivalent with bp. ook E tbcompp = 052 . 1673 . 0 >pd0 . 16 . 018 . 022 . 0 1s +||.|

\|=pupd pupdpd ook E tbcomppd = 052 . 1ok Eftby ppu = 052 . 1DETERMINAREA LATIMII EFICACE A PERETILOR COMPRIMATI IN FUNCTIE DE TIPUL LOR SI DE DISTRIBUTIA DE TENSIUNI Perete nerigidizatPerete rigidizat ELEMENTS WITH EDGE OR INTERMEDIATE STIFFENERS Determination of the stiffness (elastic restraint) of the spring determined by the presence of edge stiffeners for C and Z sections: real and equivalent systemAnnotations for edge stiffeners fora)- lipped channel; b) with lip and clip The design is based on the assumption that the stiffener works as a beam on elastic foundation represented by a spring stiffness, depending on the bending stiffness of adjacent parts of plane elements and on the boundary conditions of the element. The determination of the spring stiffness is illustrated in figure 6 for intermediate and edge stiffeners respectively, where: Cs = 1/fs and Cr = 1/fr . The significance of the terms are: f- the deflection of the stiffener due to a force equal with 1; fs and fr are taken as in the figure. For the rotational stiffness in the supports C, C1 and C2 , the effects of other stiffeners are considered if there is the case, for any element that forms the cross section in compression. For an edge stiffener, the deflection fy is determined with the relationship: where: In the case of C and ZIn the case of a intermediary stiffener, C1 and C2 will be conservatory annulled, deflection being thus determined:- reduction factor due to buckling is determined considering the relative slenderness of the wall, and imperfection coefficient according to the table of classification the cross sections by buckling curves, (curve a0): - cr,s the critical stress in the ideal plate (without imperfections).( )3221 123 t Ebb fpp y + =vuuuCbp=1( )322 122211 12) ( 3 Et b bb bfv +=s crybf,o=( )( ) | |22 22 , 0 1 5 , 0 ;1 o | | |_ + + =+ +=Edge stiffeners In order to determine the effective widths that split into several sections a stiffened wall the general method applied follows 7 successive steps; it also may be simplified in a restrained form by imposing initial conditions. Both methods may be developed iteratively.General method: O. An initial effective area of the edge stiffener is determined, based on the fact that it will act as an element infinite rigidly supported and subjected to a stress O. The reduction factor will be determined for this stiffener but this time, the elastic spring will be considered; O. The reduction factor will be improved by iteration. The initial values of the effective widths bef,1 and bef,2 are obtained from the indications in the table, considering that the wall is an intermediary one; The initial values of the effective widths cef si def are obtain as it follows: Lip:in the relationship, andare prior determined and the values of the local buckling coefficient , k is determined as it follows: For:k=0,5; - for: 1,MybEd comfo =c p efb c, = 35 , 0,spc pbb6 , 0 35 , 0,