DESIGN OF COLD-FORMED STEEL STRUCTURES

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Unformatted text preview: Helsinki University of Technology Laboratory of Steel Structures Publications 15 Teknillisen korkeakoulun tersrakennetekniikan laboratorion julkaisuja 15 Espoo 2000 TKK-TER-15 Seminar on Steel Structures: DESIGN OF COLD-FORMED STEEL STRUCTURES Jyri Outinen, Henri Perttola, Risto Hara, Karri Kupari and Olli Kaitila Helsinki University of Technology Laboratory of Steel Structures Publications 15 Teknillisen korkeakoulun tersrakennetekniikan laboratorion julkaisuja 15 Espoo 2000 TKK-TER-15 Seminar on Steel Structures: DESIGN OF COLD-FORMED STEEL STRUCTURES Jyri Outinen, Henri Perttola, Risto Hara, Karri Kupari and Olli Kaitila Helsinki University of Technology Department of Civil and Environmental Engineering Laboratory of Steel Structures Teknillinen korkeakoulu Rakennus- ja ympristtekniikan osasto Tersrakennetekniikan laboratorio Distribution: Helsinki University of Technology Laboratory of Steel Structures P.O. Box 2100 FIN-02015 HUT Tel. +358-9-451 3701 Fax. +358-9-451 3826 E-mail: srt.sihteerit@hut.fi Teknillinen korkeakoulu ISBN 951-22-5200-7 ISSN 1456-4327 Otamedia Oy Espoo 2000 FOREWORD This report collects the papers contributed for the Seminar on Steel Structures (Rak83.140 and Rak-83.J) in spring semester 2000. This time the Seminar was realized as a joint seminar for graduate and postgraduate students. The subject of the Seminar was chosen as Design of Cold-Formed Steel Structures. The seminar was succesfully completed with clearness in presentations and expert knowledge in discussions. I will thank in this connection all the participants for their intensive and enthusiastic contribution to this Report. Pentti Mkelinen Professor, D.Sc.(Tech.) Head of the Laboratory of Steel Structures DESIGN OF COLD-FORMED STEEL STRUCTURES CONTENTS 1 Profiled Steel Sheeting........................................................................1 J. Outinen Design of Cold Formed Thin Gauge Members.........................................14 R. Hara Design Charts of Single-Span Thin-Walled Sandwich Elements...................34 K.Kupari Numerical Analysis for Thin-Walled Structures.......................................45 H Perttola 2 3 4 5 Cold-Formed Steel Structures in Fire Conditions......................................65 O. Kaitila 1 PROFILED STEEL SHEETING Jyri Outinen Researcher, M.Sc.(Tech) Laboratory of Steel Structures Helsinki University of Technology P.O. Box 2100, FIN-02015 HUT - Finland Email: jyri.outinen@hut.fi (http://www.hut.fi/~joutinen/) ABSTRACT The ligthness of cold-formed thin-walled structures was formerly their most important feature and therefore they were used mostly in products where the weight saving was of great importance, This kind of products were naturally needed in especially transportation industries e.g. aircrafts and motor industry. A wide range of research work during many decades has been conducted all over the world to improve the knowledge about the manufacturing, corrosion protection, materials and codes of practise of thin-walled steel structures. This has led to a constantly increasing use of cold-formed thin-walled structures. Profiled steel sheeting is used in various kind of structures nowadays. In this paper, a short overview of the manufacturing, products, materials and structural design of profiled steel sheeting is given. Also a short overview of some current research projects is given. KEYWORDS Profiled steel sheeting, sheet steel, cold-formed, thin-wall, corrugated, steel, structural design, steel materials, cladding, roof structures, wall structures, floor structures. 2 INTRODUCTION There is a wide range of manufacturers making different kind of profiled steel sheeting products. The manufacturing processes have beensignificantly developed and different shapes of sheeting profile are easy to produce. Steel sheeting is also easy to bend to different shapes e.g. curved roof structures., cylindrical products e.g. culvers etc. The products are delivered with a huge range of possible coatings. Normally the coating is done by the manufacturer and so the products are ready to be used when delivered. Cold-formed steel sheeting can be used to satisfy both structural and functional requirements. In this paper, the structural use is more thoroughly considered. Profiled steel sheeting is widely used in roof, wall and floor structures. In these structures, the profiled steel sheeting actually satisfies both the structural and functional requirements. In floor structures the steel sheeting is often used as part of a composite structure with concrete. In northern countries the roof and wall structures are almost always built with thermal insulation. The sound insulation and the fire insulation have also to be considered, when designing structures. There are several codes for the design of profiled steel sheeting. Almost every country has a national code for this purpose, e.g. DIN-code in Germany, AISI-code in USA, etc. The structural design of profiled steel sheeting in Europe has to be carried out using the Eurocode 3: part 1.3, though there are several national application documents (NAD), where the national requirements are considered with the EC3. An extensive amount of tests has been carried out and analyzed to gather together the existing design codes, and there are numerous formulae in these codes that are based partly on theory and partly on experimental test results. Some of the important aspects of structural design of coldformed profiled steel sheeting is presented in this paper. Numerous different kind of fastening techniques are developed suitable for thin-walled structures. Suitable fasteners are bolts with nuts, blind rivets, self tapping screws, selfdrilling screws and some other kinds of fasteners. The materials used in cold-formed thin-wall members have to satisfy certain criteria to be suitable for cold-forming and usually also for galvanising. The yield strength is normally in the range of 220...350 N/mm2 , but also some high-strength sheet steels with yield strength of over 500 N/mm2 are used in some cases. The practical reasons i.e. transportation, handling etc., limit the range of thickness of the material used in profiled sheeting. A lot of interesting research projects have been carried out concerning the behaviour of profiled steel sheeting all over the world. Some of the current researches are shortly described in this paper. In different parts of the world the focus of the research is naturally on the regional problems. An example of this is Australia, where the main research area of cold-formed steel structures is concentrated on the problems caused by high-wind and storm loads. 3 DEVELOPMENT OF THE PROFILED SHEETING TYPES The profiled sheeting types have been developed significantly since the first profiled steel sheets. The first plates were very simple and the stiffness of these was not very high. The manufacturing process and the materials limited the shape of the profiles to simply folded or corrugated shapes. The height of the profile was roughly in between 15 and 100 mm. Two types of typical simply profiled steel sheet forms are illustrated in figure 1. Figure 1: Simple forms of profiled steel sheeting From the early 1970's the shape of the profiling in steel sheeting developed considerably. This naturally meant possibilities for their widerange usage especially in structural uses. The stiffeners were added to flanges of the profile and this improved notably the bending resistance. The maximum height of the profile was normally still under 100mm. In Figure 2 a profile with stiffeners in flanges is illustrated. Figure 2: More advanced form of profiled steel sheeting. Stifferners in flanges. From the mid 1970's, the development of the shapes of sheeting profiles and also better materials and manufacturing technologies lead to possibilities to provide more complex profiles. This improved substancially the load-bearing capacities of the developed new profiled steel sheets. In figure 3 is shown an example of this kind of more complex profile. 4 Figure 3: Modern form of profiled steel sheeting. Stiffeners in flanges and webs. A huge range of profile types are available nowadays used for structural and other kind of purposes. The thin-walled steel structures and profiled steel sheeting is an area of fast growth. In the next chapter, a few typical examples where cold-formed profiled steel sheeting is used are presented. USE OF PROFILED STEEL SHEETING IN BUILDING Cold-formed profiled sheeting is able to give adequate load bearing resistance and also to satisfy the functional requirements of the design. This aspect is considered in this chapter briefly in relation to the common usage of cold-formed sheeting in floor, wall and roof structures. Floor structures Profiled steel sheeting in floor structures have sheeting, e.g. trapezoidal or cassettes, as load bearing part, either alone or in composite action with other materials such as different kind of board, plywood decking or cast in-situ concrete. In the first case, the composite action is provided by adhesives, and mechanical fasteners, in the second by means of indentation and/or special shear studs. The bending moment resistance is the main requirement, and so the profiles used for flooring purposes are similar to those for roof decking. Figure 4: A Steel-concrete composite floor slab with profiled steel sheeting 5 Wall structures In wall structures, the structure is comprised of an outer layer, the facade sheeting that is usually built with relatively small span, and a substructure which transmits the wind loading to the main building structure. The substructure can be a system of wall rails or horizontal deep profiles, or cassettes with integrated insulation. Another solution combines the load-bearing and protecting function in a sandwich panel built up by metal profiles of various shapes and a core of polyurethane or mineral wool. Figure 5: A facade made with profiled steel sheeting Roof structures The roof structures using steel sheeting can be built as cold or warm roofs A cold roof has an outer waterproof skin with internal insulation if required. The main requirement of preventing the rain water or the melting snow leads to shallow profiles with a sequence of wide and narrow flanges. Sheets fixed using fasteners applied to the crests or the valleys of the corrugations. Figure 6: A roof structure made with profiled steel sheeting of a subway station in Finland 6 The use of few points of fastening means that the forces are relatively high and therefore the spans are usually quite small. A wide range of special fasteners have been developed to avoid the failure of the fasteners or the sheeting e.g. pull-through failure at that point. This is a problem in especially high-wind areas, e.g. Australia. Warm roof includes insulation and water proofing and it is built up using a load-bearing profile, insulation and an outer layer e.g. metal skin, as mentioned before. The loadbearing profiled sheeting in this type of roof normally has the wider flanges turned up in order to provide sufficient support for the insulation. Fasteners are placed in the bottom of the narrow troughs. In this case, the tendency is towards longer spans, using more complex profiles of various shapes and a core of polyurethane. Other applications The highly developed forming tecnology makes it possible to manufacture quite freely products made of profiled steel sheets with various shapes. Such are for example curved roof structures., cylindrical products e.g. culvers etc. There are not too much limitations anymore concerning the shape of the product. In Figure X. a few examples of this are presented. Figure 7: Profiled sheet steel products in different shapes 7 MANUFACTURING Cold-formed steel members can be manufactured e.g. by folding, press-braking or coldrolling. Profiled steel sheets are manufactured practically always using cold-forming. Also the cylindrical products are manufactured by cold cold rolling from steel strips. In figure 8, a steel culvert and a profiled steel sheet is manufactured by cold-rolling. Figure 8: Cold-rolling process of profiled steel products Cold-rolling technique gives good opportunities to vary the shape of the profile and therefore it is easy to manufacture optimal profiles that have adequate load bearing properties for the product. The stiffeners to flanges and webs are easily produced. During the cold-forming process varying stretching forces can induce residual stresses. These can significantly change the load-bearing resistance of a section. Favourable effects can be observed if residual stresses are induced in parts of the section which act in compression and, at the same time, are susceptible to local bucling. Cold-forming has significant strain-hardening effects on ductility of structural steel. Yield strength, ultimate strength and the ductility are all locally influenced by an amount which depends on the bending radius, the thickness of the sheet, the type of steel and the forming process. The average yield strength of the section depends on the number of corners and the width of the flat elements. The principle of the effect of cold-forming on yield strength is illustrated in Figure 9. 8 Figure 9: Effect of cold forming on the yield stress of a steel profile STRUCTURAL DESIGN OF PROFILED STEEL SHEETING Because of the many types of sheeting available and the diverse functional requirements and loading conditions that apply, design is generally based on experimental investigations. This experimental approach is generally acceptable for mass produced products, where optimization of the shape of the profiles is a competitive need. The product development during about four decades has been based more on experience of the functional behaviour of the behaviour of the products than on analytical methods. The initial "design by testing" and subsequent growing understanding of the structural behaviour allowed analytical design methods to be developed. Theoretical or semiempirical design formulae were created based on the evaluation of test results. This type of interaction of analytical and experimental results occurs whenever special phenomena are responsible for uncertainties in the prediction of design resistance (ulimate limit state) or deformations (serviceability limit state). At the moment there are several codes for the structural design of cold-formed steel members. In Europe, Eurocode 3: Part 1.3 is the latest design code which can be used in all european countries. Still, almost every country has a national application document (NAD), in which the former national code of practice is taken into account. In Other parts of the world e.g. in USA (AISI-specifications), Australia, (AS) there are several different codes for the design. All the design codes seem to have the same principles, but the design practices vary depending on the code. 9 The design can basicly be divided in two parts: 1.) Structural modelling and analysis which is normally quite a simple procedure and 2.) Checking the resistances of the sheeting. The values that are needed in the design are: moment resistance, point load resistance and the effective second moments of area Ieff corresponding to the moment resistances. The deflections have to be also considered. The deflections during construction e.g. in steel-concrete composite floors are often the limiting factor to the structure. The load-bearing properties, i.e. moment resistance, point load resistance etc., are almost always given by the manufacturer. Profiled sheeting has basically the following structural functions: 1. To transfer the surface loads (wind, snow,etc.) to the substructure. 2. To stabilise the substructure and the components of it. 3. Optionally to transfer the in-plane loads (e.g. wind load in roofs to the end cables) "Stressed skin design" One important weak point of profiled steel sheeting is the low resistance against transverse point loads as mentioned earlier. The reason is that the load is transmitted to the webs as point loads that create high stress peaks to it. The web is then very vulnerable to lose the local stability at these points. All the manufactures have recommendations for the minimum support width, which has a notable effect on the previous phenomenon. The fire design of cold formed structures is basicly quite simple using the existing codes, but the methods are under new consideration in various research projects, from which a short description is given in chapter "Current research projects". The design for dynamic loading cases is constantly under development in countries, where the wind and storm loads are of high importance. For example in Australia, a large amount of experimental research has been carried out on this subject. Most of this research is concentrated on the connections. Different types of fasteners have been developed to avoid the pull-through, pull-over or pull-out phenomena under dynamic high-wind loading. Figure 10: Examples of pull-through failures under dynamic loading. Local pull-through by splitting and fatigue pull-through (high-strength steel). 10 MATERIALS The most common steel material that is used in profiled steel sheets is hot dip zinc coated cold-formed structural steel. The nominal yield strength Reh (See Fig. 4) is typically 220...550N/mm2 . The ultimate tensile strength is 300...560 N/mm2 . The modulus of elasticity is normally 210 000 N/mm2 . The mechanical properties of low-carbon coldformed structural steels have to be in accordance with the requirements of the European standard SFS-EN 10 147. The mechanical properties are dependent on the rolling direction so that yield strength is higher transversally to rolling direction.. In the inspection certificate that is normally delivered with the material, the test results are for transversal tensile test pieces. In Figure 4, typical stress-strain curves of cold-formed structural sheet steel with nominal yield strength of 350 N/mm2 at room temperature both longitunidally and transversally to rolling direction are shown. The difference between the test results for the specimens taken longitudinally and transversally to rolling direction can clearly be seen. The results are also shown in Tables 1 and 2. 450 Transversally to rolling direction 400 350 Stress [N/mm 2] 300 250 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 Strain [%] 1.4 1.6 1.8 2 Longitudinally to rolling direction Figure 11: Stress-strain curves of structural steel S350GD+Z at room temperature. Tensile tests longitudinally and transversally to rolling direction 11 TABLE 1 MECHANICAL PROPERTIES OF THE TEST MATERIAL S350GD+Z AT ROOM TEMPERATURE. TEST PIECES LONGITUDINALLY TO ROLLING DIRECTION Measured property Modulus of elasticity E Yield stress R p0.2 Ultimate stress Rm Mean value (N/mm2 ) 210 120 354.6 452.6 Standard deviation (N/mm2 ) 13100 1.5 2.3 Number of tests (pcs) 5 5 5 TABLE 2 MECHANICAL PROPERTIES OF THE TEST MATERIAL S350GD+Z AT ROOM TEMPERATURE. TEST PIECES TRANSVERSALLY TO ROLLING DIRECTION Measured property Modulus of elasticity E Yield stress Rp0.2 Ultimate stress Rm Mean value (N/mm2 ) 209400 387.5 452.5 Standard deviation (N/mm2 ) 8800 1.3 1.9 Number of tests (pcs) 4 4 4 The thickness of the base material that is formed to profiled steel sheets is normally 0.5...2.5 mm. The thickness can't normally be less than 0.5 mm. If the material is thinner than that, the damages to the steel sheets during transportation, assembly and handling are almost impossible to avoid. The thickness of the sheet material is not normally over 2.5 mm because of the limitations of the roll-forming tools. The base material coils are normally 1000...1500 mm wide and that limits the width of profiled steel sheets normally to 600...1200 mm. Steel is naturally not the only material that profiled sheeting is made of. Other materials, such as stainless steel, aluminium and composite (plastic) materials are also widely used. Stainless steel products are under development all the time and the major problem seems to be the hardness of the material, i.e. there are problems in roll-forming, cutting and drilling. On the other hand, excellent corrosion resistance and also fire resistance give it big advances. Aluminium profiles are easy to roll-form and cut because of the softness of the material. On the other hand, the ductility is quite restricted, especially at fire conditions. The composite (plastic) materials are also widely used e.g. in transparent roofs, but not usually in structural use. 12 CURRENT RESEARCH WORK A wide range of different kind of research activities concerning profiled steel sheeting is going on in several countries. Most of the studies are based on both experimental test results and usually also modelling results produced with some finite element modelling programs. Usually the aim is to increase the load-bearing capacity of the studied product. Also the materials, coatings and the manufacturing technology are developed constantly. In Finland, there are a lot of small resarch projects concerning the steel-concrete composite slabs with profiled steel sheeting. In these projects, which are mainly carried out in Finnish universities, e.g. Helsinki University of Technology, and in the Technical Research Centre of Finland, the aim is simply to increase the load bearing capacity. This is studied using different profiles and stud connectors. The experiments are normally bending tests, but also some shear tests for the connection between steel sheeting and concrete with push-out tests have ben carried out. During the next few years, several research projects are starting in Finland concerning the design of lightweight steel structures. In these projects, the fire design part is of great importance. In Australia, e.g. in Queensland University of Technology, and also in several other universities, there are numerous on-going research projects concerning mainly the behaviour of the connections of steel sheeting under wind-storm loads e.g. "Development of design and test methods for profiled steel roof and wall claddings under wind uplift and racking loads" and "Design methods for screwed connections in claddings." are recently completed projects. The current situation can be found on their www-site (given in next chapter: References). In these projects a significant amount of small-scale and also large scale tests have been conducted. The small-scale tests are usually carried out to study the pull-out or pull-over phenomena of screwed connections. The large-scale tests aim to study the behaviour of the profiled steel sheeting in wall and roof structures under high-wind loading cases. The research work that is carried out concerning cold-formed steel in USA can be found from the American Iron and Steel Institutes www-site (given in next chapter: References). In this paper, just a few examples of the research work that is currently going on were mentioned. Different research programs concerning the cold-formed profiled steel sheeting are going on in Europe and other parts of the world. A major conference, "The International Specialty Conference on Recent Research and Developments in ColdFormed Steel Design and Construction", where the latest research projects are presented regurarly, is held in St. Louis, Missouri. 13 REFERENCES Eurocode 3, CEN ENV 1993-1-3 Design of Steel Structures- Supplementary rules for Cold Formed Thin Gauge Members and Sheeting, Brussels, 1996 Standard SFS-EN 10 147 (1992): Continuously hot-dip zinc coated structural steel sheet and strip. Technical delivery conditions. (in Finnish), Helsinki Outinen, J. & Mkelinen, P.: Behaviour of a Structural Sheet Steel at Fire Temperatures. Light-Weight Steel and Aluminium Structures (Eds. P. Mkelinen and P. Hassinen) ICSAS'99. Elsevier Science Ltd., Oxford, UK 1999, pp. 771-778. Kaitila O., Post-graduate seminar work on "Cold Formed Steel Structures in Fire Conditions", Helsinki University of Technology, 2000. Helenius, A., Lecture in short course: "Behaviour and design of light-weight steel structures" , at Helsinki University, 1999 Tang, L.,Mahendran, M., Pull-over Strength of Trapezoidal Steel Claddings, . LightWeight Steel and Aluminium Structures (Eds. P. Mkelinen and P. Hassinen) ICSAS'99. Elsevier Science Ltd., Oxford, UK 1999, pp. 743-750. ESDEP Working Group 9 Internet-sites concerning cold-formed steel: http://www.rannila.fi http://www.rumtec.fi http://www.civl.bee.qut.edu.au/pic/steelstructures.html http://www.steel.org/construction/design/research/ongoing.htm 14 DESIGN OF COLD FORMED THIN GAUGE MEMBERS Risto Hara M.Sc.(Tech.) PI-Consulting Oyj Liesikuja 5, P.O. BOX 31, FIN-01601 VANTAA, FINLAND http://www.pigroup.fi/ 15 INTRODUCTION In this presentation, cold formed thin gauge members (for simplicity: `thin-walled members') refer to profiles, which the design code Eurocode 3 Part 1.3 (ENV 1993-1-3) is intended for. These profiles are usually cold rolled or brake pressed from hot or cold rolled steel strips. Due to the manufacturing process, sections of cold formed structural shapes are usually open, singly-, point- or non-symmetric. Most common cross-section types of thin-walled members (U, C, Z, L and hat) are shown in Figure 1.1, see ref. (Salmi, P. & Talja, A.). Other forms of sections i.e. special single- and built-up sections are shown e.g. in ENV 1993-1-3, Figure 1.1. Figure 1.1 Typical cross-section types of thin-walled members. Thin-walled structural members have been increasingly used in construction industry during the last 100 years. They are advantageous in light-weight constructions, where they can carry tension, compression and bending forces. The structural properties and type of loading of thin-walled members cause the typical static behaviour of these structures: the local or global loss of stability in form of different buckling phenomena. To have control of them in analysis and design, sophisticated tools (FEA) and design codes (ENV 1993-1-3, AISI 1996, etc.) may have to be used. Unfortunately, the complexity of these methods can easily limit the use of thin-walled structural members or lead to excessive conservatism in design. However, some simplified design expressions have been developed, see refs. (Salmi, P. & Talja, A.), (Roivio, P.). The main features of the design rules of thin-walled members are described in this paper. The present Finnish design codes B6 (1989) and B7 (1988) are entirely omitted as inadequate for the design of cold formed steel structures. However, the viewpoint is `Finnish-European', i.e. the main reference is the appropriate Eurocode 3 (ENV 1993-1-3) with the Finnish translation (SFS-ENV 1993-1-3) and National Application Document (NAD). The paper concentrates on the analytical design of members omitting chapters 8-10 of the code (ENV 1993-1-3) entirely. Reference is made also to a seminar publication (TEMPUS 4502), where theory and practice for the design of thin-walled members is presented in a comprehensive way. The reference contains also a summary of Eurocode 3 Part 1.3. ABOUT THE STRUCTURAL BEHAVIOUR OF THIN-WALLED MEMBERS The cross-sections of thin-walled members consist usually of relatively slender parts, i.e. of flat plate fields and edge stiffeners. Instead of failure through material yielding, compressed parts tend to loose their stability. In the local buckling mode, flat plate fields buckle causing 16 displacements only perpendicular to plane elements and redistribution of stresses. In this mode the shape of the section is only slightly distorted, because only rotations at plane element junctures are involved. In the actual distortional buckling mode, the displacements of the cross-section parts are largely due to buckling of e.g. flange stiffeners. In both buckling modes, the stiffness properties of the cross-section may be changed, but the member probably still has some post-buckling capacity since translation and/or rotation of the entire crosssection is not involved. In the global buckling mode, displacements of the entire cross-section are large, leading to over-all loss of stability of the member. Global buckling modes depend primarily on the shape of the cross-section. Flexural buckling usually in the direction of minimum flexural stiffness is common also for cold formed members. Low torsional stiffness is typical for open thin-walled members,so buckling modes associated with torsion may be critical. Pure torsional buckling is possible for example in the case of a point symmetric crosssection (e.g. Z-section), where the centre of the cross-section and the shear centre coincide. In torsional buckling, the cross-section rotates around the shear centre. A mixed flexuraltorsional buckling mode, where the cross-section also translates in plane, is possible in the case of single symmetric cross-sections (e.g. U, C and hat). Due to the low torsional stiffness of open thin-walled cross-sections, lateral buckling is a very probable failure mode of beams. Analogy with flexural buckling of the compressed flange is valid in many cases, but does not work well with low profiles bent about the axis of symmetry or with open profiles bent in the plane of symmetry, when the folded edges are compressed (e.g. wide hats). Naturally, plastic or elastic-plastic static behaviour of compressed or bended members are possible when loaded to failure, but with normal structural geometry and loading, stability is critical in the design of thin-walled members. Structural stability phenomena are described in more detail e.g. by (Salmi, P. & Talja, A). BASIS OF DESIGN In cold formed steel design, the convention for member axes has to be completed compared with Structural Eurocodes. According to ENV 1993-1-3, the x-axis is still along the member, but for single symmetric cross-sections y-axis is the axis of symmetry and z-axis is the other principal axis of the cross-section. For other cross-sections, y-axis is the major axis and z-axis is the minor axis, see also Figure 1.1. According to the ENV code, also u-axis (perpendicular to the height) and v-axis (parallel to the height) can be used "where necessary". Depending on the type of contribution to the structural strength and stability, a thin-walled member belongs to one of two construction classes. In Class I the member is a part of the overall stiffening system of the structure. In Class II the member contributes only to the individual structural strength of the element. The Class III is reserved for secondary sheeting structures only. However, this classification for differentiating levels of reliability seems not to have any influence in design. In ultimate limit states (defined in ENV 1993-1-1), the value of partial safety factors (M0 and M1) needed in member design are always equal to 1.1. Factor M0 is for calculation of cross-section resistance caused by yielding and factor M1 is for calculation of member resistance caused by buckling. The serviceability limit states are defined in form of principles and application rules in ENV 1993-1-1 and completed in ENV 1993-1-3 with the associated Finnish NAD. The partial factor in both classes Mser has a value equal to 1.0. 17 The design of adequate durability of cold formed components seems to require qualitative guide lines according to base code ENV 1993-1-3, but also much more exact specifications according to the NAD. The structural steel to be used for thin-walled members shall be suitable for cold forming, welding and usually also for galvanising. In ENV 1993-1-3, Table 3.1 lists steel types, which can be used in cold formed steel design according to the code. Other structural steels can also be used, if the appropriate conditions in Part 1.3 and NAD are satisfied. In ENV 1993-1-3 Ch. 3.1.2, exact conditions have been specified about when the increased yield strength fya due to cold forming could be utilised in load bearing capacity. Fortunately for the designer, Ch. 3.1.2 has been simplified in the NAD: nominal values of basic yield strength f b shall be applied y everywhere as yield strength (hence in this paper fyb is replaced in all formulas by fy ). This can be justified, because on the average, the ratio fya /fyb 1.05 only. Normally yield strengths fyb used in thin-walled members lay in the range 200-400 N/mm2 , but the trend is to even stronger steels. TABLE 3.1 TYPICAL STRUCTURAL STEELS USED IN COLD FORMED STEEL STRUCTURES . 18 Obviously, other material properties relevant in cold formed steel design are familiar to designers: e.g. modulus of elasticity E = 210 000 N/mm2 , shear modulus G = E/2(1+) N/mm2 = 81 000 N/mm2 (Poisson's ratio = 0.3), coefficient of linear thermal elongation = 12 10-6 1/K and unit mass = 7850 kg/m3 . The draft code ENV 1993-1-3 is applicable only for members with a nominal core thickness of 1.0 < tcor < 8.0 mm. In the Finnish NAD, however, the material thickness condition is changed: 0.9 < tcor < 12.0 mm. Up to 12.5 mm core thickness is reached in roll-forming process in Finland by Rautaruukki Oy. The nominal core thickness can normally be taken as tcor = tnom tzin where tnom is the nominal sheet thickness and tzin is the zinc coating thickness (for common coating Z275 tzin = 0.04 mm). Figure 3.1: Determination of notional widths. Section properties shall be calculated according to normal `good practice'. Due to the complex shape of the cross-sections, approximations are required in most cases. Specified nominal dimensions of the shape and large openings determine the properties of the gross crosssection. The net area is reached from gross area by deducting other openings and all fastener holes according to special rules listed in Ch. 3.3.3 of the Eurocode. Due to cold forming, the corners of thin-walled members are rounded. According to the design code, the influence of rounded corners with internal radius r 5 t and r 0.15 bp on section properties may be neglected, i.e. round corners can be replaced with sharp corners. The notional flat width bp is defined by applying the corner geometry shown in Figure 3.1, extracted from the code. If the above limits are exceeded, the influence of rounded corners on section properties `should be allowed for'. Sufficient accuracy is reached by reducing section properties of equivalent cross-section with sharp corners (subscript `sh') according to the formulas: Ag Ag,sh (1-) Ig Ig,sh (1-2) Iw I w,sh (1-4), (3.1a) (3.1b) (3.1c) 19 Where Ag is the area of the gross cross-section, Ig is the second moment area of the gross cross-section and I w is the warping constant of the gross cross-section. Term is a factor depending on the number of the plane elements (m), on the number of the curved elements (n), on the internal radius of curved elements (rj) and notional flat widths bpi according to the formula: n m = 0.43 rj / bpi , j=1 i=1 (3.2) This approximation can be applied also in the calculation of effective cross-section properties. Due to the chosen limits, typical round corners can usually be handled as sharp corners. In order to apply the design code ENV 1993-1-3 in design by calculation, the width-thickness ratios of different cross-section parts shall not exceed limits listed in Table 3.2. In conclusion, they represent such slender flat plate fields that the designer has rather `free hands' in the construction of the shape of the cross-section. However, to provide sufficient stiffness and to avoid primary buckling of the stiffener itself, the conditions 0.2 c/b 0.6 and 0.1 d/b 0.3 for the edge stiffener geometry shall be satisfied. TABLE 3.2 M AXIMUM WIDTH- TO-THICKNESS RATIOS OF PLATE FIELDS . 20 LOCAL BUCKLING One of the most essential features in the design of thin-walled members is the local buckling of the cross-section. The effects of local buckling shall be taken into account in the determination of the design strength and stiffness of the members. Using the concept of effective width and effective thickness of individual elements prone to local buckling, the effective cross-sectional properties can be calculated. The calculation method depends on e.g. stresslevels and -distribution of different elements. The code ENV 1993-1-3 Cl. 4.1. (4-6) states that in ultimate resistance calculations, yield stress fy `should' be used (on the `safe side') and only in serviceability verifications, actual stress-levels due to serviceability limit state loading `should' be used. Thus the basic formulas for effective width calculations of flat plane element without stiffeners in compression could be presented in the general form, in accordance with the complex alternative rules of ENV code, compare to (Salmi, P. & Talja, A.): = 1, when p 0.673 = (p 0.22) / p 2 , when p > 0.673 p = (c / el) = 1.052 (bp / t) (c / E / k) el = k 2 E / 12 / (1 - 2 ) / (bp / t)2 , (4.1a) (4.1b) (4.1c) (4.1d) where is the reduction factor of the width, p relative slenderness, bp width, c maximum compressive stress of the element and k buckling factor. For compressed members c is usually the design stress (fy ) based on overall buckling (flexural or flexural-torsional). For bent members, in an analogical way, c is usually the design stress for lateral buckling (fy ). In special cases, c really can have the value fy in compression or bending. Obviously, the safe simplification c = fy may always be used and to avoid iterations, it is even recommended. The reduction factor shall be determined according to Table 4.1 for internal and Table 4.2 for external compression elements, respectively. The design of stiffened elements is based on the assumption that the stiffener itself works as a beam on elastic foundation. The elasticity of the foundation is simulated with springs, whose stiffness depends on the bending stiffness of adjacent parts of plane elements and the boundary conditions of the element. A spring system for basic types of plate fields needed in analysis is shown in Table 4.3. The determination of spring stiffness in two simple cases is presented in Figure 4.1. For example, in the case of an edge stiffener, the spring stiffness K of the foundation per unit length is determined from: K = u / , where is the deflection of the stiffener due to the unit load u: (4.2) 21 = bp + u bp 3 / 3 12 (1 - 2 ) / (E t3 ), (4.3) Typically for complex tasks, it is not shown in the code how to calculate exactly the rotational spring constant C required in the formula = u bp 3 / C. The spring stiffness K can be used to calculate the critical elastic buckling stress crS: crS = 2 (K E Is) / As, (4.4) where Is is the effective second moment of area of the stiffener taken as that of its effective area As. In the simplified method of (Salmi, P. & Talja, A.), Is and As have been replaced by their full-cross sectional dimensions in consistence of general principles in calculation of elastic buckling forces. The general iterative as well as simplified procedures according to the code to determine the effective thickness of the stiffener teff are in their complexity hard to apply in practical design. Hence, only the simplified, conservative method of (Salmi, P. & Talja, A.) is presented here: teff = S t, (4.5) where S is the reduction factor for the buckling of a beam on an elastic foundation. The factor is determined according to the buckling curve a0 ( = 0.13, see also Figure 6.1) from the equations: S = 1, when s 0.2 S = 1 / ( + ( 2 - s2 )), when s > 0.2 s = (c / crS ) = 0.5 [1 + ( - 0.2) + s2 ], (4.6a) (4.6b) (4.6c) (4.6d) In this study, distortional buckling is considered as a local stability effect. This buckling mode is included in clause 6 of ENV 1993-1-3, where design rules for global buckling are introduced. Distortional buckling is handled only qualitatively in the design code, without any equations. Implicitly it may mean, that FEA is required to be used to analyse this buckling mode in design. However, if in the case of a section with edge or intermediate stiffeners the stiffener is reduced according to the code, no further allowance for distortional buckling is required. Fortunately, distortional buckling mode should not be very probable in thin-walled members with `normal' dimensions. 22 TABLE 4.1 DETERMINATION OF EFFECTIVE WIDTH FOR INTERNAL P LATE FIELDS. 23 24 TABLE 4.3 MODELLING OF ELEMENTS OF A CROSS-SECTION. Figure 4.1 Determination of spring stiffness in two simple cases. 25 LOCAL RESISTANCE OF CROSS-SECTIONS Axial tension The design value of tension Nsd shall not exceed the corresponding resistance of the crosssection NtRd : Nsd NtRd = fy Ag / M0 FnRd, where FnRd is the net-section resistance taking into account mechanical fasteners. Axial compression The design value of compression Nsd shall not exceed the corresponding resistance of the cross-section NcRd : Nsd NcRd = fy Ag / M0, when Aeff = Ag Nsd NcRd = fy Aeff / M1, when Aeff < Ag (5.2a) (5.2b) (5.1) In the equations Aeff is the effective area of the cross-section according to section 4 by assuming a uniform compressive stress equal to fy / M1. If the centroid of the effective crosssection does not coincide with the centroid of the gross cross-section, the additional moments (N sd eN ) due to shifts eN of the centroidal axes shall be taken into account in combined compression and bending. However, according to many references this influence can usually be considered negligible. Bending moment The design value of bending moment Msd shall not exceed the corresponding resistance of the cross-section McRd : Msd McRd = fy Wel / M0, when Weff = Wel Msd McRd = fy Weff / M1, when Weff < Wel (5.3a) (5.3b) In the equations Weff is the effective section modulus of the cross-section based on pure bending moment about the relevant principal axis yielding a maximum stress equal to fy / M1. Allowance for the effects of shear lag to the effective width shall be made, if `relevant' (normally not). The distribution of the bending stresses shall be linear, if the partial yielding of the cross-section can not be allowed. In case of mono-axial bending plastic reserves in the tension zone can generally be utilised without strain limits. The utilisation of plastic reserves in the compression zone is normally more difficult because of several conditions to be met. The 26 procedures to handle cross-sections in bending have been explained e.g. in the code ENV 1993-1-3 and in the paper (Salmi, P. & Talja, A.). For biaxial bending, the following criterion shall be satisfied: MySd / McyRd + MzSd / MczRd 1, (5.4) where MySd and MzSd are the applied bending moments about the major y and minor z axes. McyRd and MczRd are the resistances of the cross-section if subject only to moments about the major or minor axes. Combined tension or compression and bending Cross-sections subject to combined axial tension Nsd and bending moments MySd and MzSd shall meet the condition: Nsd / (fy Ag / M) + MySd / (fy Weffyten / M) + MzSd / (fy Weffzten / M) 1, (5.5) where M = M0 or = M1 depending on Weff is equal to Wel or not for each axis about which a bending moment acts. Weffyten and Weffzten are the effective section moduli for maximum tensile stress if subject only to moments about y- and z-axes. In the ENV code there is also an additional criterion to be satisfied, if the corresponding section moduli for maximum compressive stress Weffycom Weffyten or Weffzcom Weffzten. The criterion is associated with vectorial effects based on ENV 1993-1-1. Cross-sections subject to combined axial compression Nsd and bending moments MySd and MzSd shall meet the condition: Nsd / (fy Aeff / M) + MySd / (fy Weffycom / M) + MzSd / (fy Weffzcom / M) 1, (5.6) where the factor M = M0 if Aeff = Ag, otherwise M = M1. In the case Weffycom Weffyten or Weffzcom Weffzten, an additional criterion has again to be satisfied. In this occasion, reference is also made to the basic steel code ENV 1993-1-1 for the concept of vectorial effects. For simplicity, in the expression above the bending moments include the additional moments due to potential shifts of the centroidal axes. Torsional moment In good design practice of thin-walled open members, torsional effects should be avoided as far as practicable, e.g. by means of restraints or ideal cross-sectional shape. If the loads are applied eccentrically to the shear centre of the cross-section, the effects of torsion "shall be taken into account". The effective cross-section derived from the bending moment defines the 27 centroid as well as the shear centre of the cross-section. Probably, design problems will be expected, because the following criteria have to be satisfied: tot = N + My + Mz + w fy / M tot = Vy + Vz + t + w (fy / 3) / M0 (tot2 + 3 tot2 ) 1.1 fy / M, (5.7a) (5.7b) (5.7c) where tot is the total direct stress having design stress components N due to the axial force, My and Mz due to the bending moments about y- and z-axes and w due to warping. The stress tot is the total shear stress consisting of design stress components Vy and Vz due to the shear forces along y- and z-axes, t due to uniform (St. Venant) torsion and w due to warping. The factor M = M0 if Weff = Wel, otherwise M = M1. To be taken on note that only the direct stress components due to resultants NSd, MySd and MzSd should be based on the respective effective cross-sections and all other stress components i.e. shear stresses due to transverse shear force, uniform (St. Venant) torsion and warping as well as direct stress due to warping, should be based on the gross cross-sectional properties. Shear force The design value of shear Vsd shall not exceed the corresponding shear resistance of the crosssection, which shall be taken as the lesser of the shear buckling resistance VbRd or the plastic shear resistance VplRd. The latter should be checked in the case w 0.83 (fvb / fv ) (M0 / M1) = 0.83 (according to NAD) using the formula: VplRd = (hw / sin) t (fy / 3) / M0, (5.8) where hw is the web height between the midlines of the flanges and is the slope of the web relative to the flanges, see Figure 3.1. The shear buckling resistance VbRd shall be determined from: VbRd = (hw / sin) t fbv / M1, (5.9) where fbv is the shear buckling strength, which depends on the relative web slenderness w and stiffening at the support according to the Table 5.2 in ENV 1993-1-3. The relative web slenderness w is e.g. for webs without longitudinal stiffeners: w = 0.346 (hw / sin) / t (fy / E) 28 Local transverse forces To avoid crushing, crippling or buckling in a web subject to a support reaction or other local transverse force (for simplicity: `concentrated load') applied through the flange, the point load Fsd shall satisfy: Fsd RwRd, (5.10) where RwRd is the local transverse resistance of the web. If the concentrated load is applied through a cleat, which is designed to resist this load and to prevent the distortion of the web, the resistance for concentrated load needs not to be checked. Thin-walled members normally used can be designed for concentrated load according to ENV 1993-1-3 Cl. 5.9.2. The resistance formula to be used in the case of single unstiffened web depends on the number (one or two), the location and the bearing lengths of the concentrated loads. In addition, the resistance depends on the geometry (hw, t, r and ) and material of the web (fy / M1). In the case of two unstiffened webs, the approach is totally different, although the same parameters affect the point load resistance. As a result, only one formula with supplementary parameters is needed. The equations for stiffened webs enforces more the impression that the background of the point load resistance evaluations is rather empirical. Combined forces A cross-section subject to combined bending moment M and shear force Vsd shall be sd checked for the condition: ( Msd / McRd )2 + ( Vsd / VwRd )2 1, (5.11) where McRd is the moment resistance of the cross-section and VwRd is the shear resistance of the web, both defined previously. A cross-section subject to combined bending moment Msd and point load Fsd shall be checked for the cond itions: Msd / McRd 1 Fsd / RwRd 1 Msd / McRd + Fsd / RwRd 1.25, (5.12a) (5.12b) (5.12c) where RwRd is the appropriate value of the resistance for concentrated load of the web, described previously. 29 GLOBAL BUCKLING RESISTANCE OF MEMBERS Axial compression A member is subject to concentric compression if the point of loading coincides with the centroid of the effective cross-section based on uniform compression. The design value of compression Nsd shall not exceed the design buckling resistance for axial compression NbRd : Nsd NbRd = Aeff fy / M1, (6.1) Where, according to ENV 1993-1-3, the effective area of the cross-section Aeff is based conservatively on uniform compressive stress equal to f / M1. The -factor is the appropriate y value of the reduction factor for buckling resistance: = min ( y , z, T ,TF ), (6.2) where the subscripts y, z, T and TF denote to different buckling forms i.e. to flexural buckling of the member about relevant y- and z-axes, torsional and torsional-flexural buckling. The calculation of factor according ENV 1993-1-3 Cl. 6.2.1 is formulated in (Salmi, P. & Talja, A.): = 1, when 0.2 = 1 / ( + ( 2 - 2 )), when > 0.2 = ( fy / cr ) = 0.5 [ 1 + ( - 0.2 ) + 2 ], (6.3a) (6.3b) (6.3c) (6.3d) where is an imperfection factor, depending on the appropriate buckling curve and is the relative slenderness for the relevant buckling mode. 30 Figure 6.1 Different buckling curves and corresponding imperfection factors. In Figure 6.1 is shown the --relationship for different buckling curves and corresponding values of . The buckling curve shall be obtained using ENV 1993-1-3 Table 6.2. The selection of cross-section types in Table 6.2 is very limited. However, the correct buckling curve for any cross-section may be obtained from the table "by analogy" (how?). As a conclusion from the tables (Salmi, P. & Talja, A.), in the case of typical C- and hat profiles European buckling curve b ( = 0.34) for flexural buckling about both principal axes shall be chosen. In the case of other profiles buckling curve c ( = 0.49) shall be used. Regardless of the open cross-section form, the buckling curve b shall be chosen in the case of torsional and flexuraltorsional buckling modes. The critical buckling stress in any mode shall be determined in a traditional way, using equations e.g. from the code ENV 1993-1-3 or reference (Salmi, P. & Talja, A.). These equations for critical buckling stresses are more suitable for everyday design, especially because the cross-sectional properties (iy , iz, It , Iw etc.) can be calculated for gross cross-section. Naturally, in the case of complex cross-sections or support conditions, handbooks or more advanced methods are required. One problem in design may be the determination of buckling length in torsion taking into account the degree of torsional and warping restraint at each end of the member. Lateral-torsional buckling of members subject to bending The design value of bending moment Msd shall not exceed the design lateral-torsional buckling resistance moment MbRd of a member: Msd MbRd = LT Weff fy / M1, (6.4) 31 where Weff is the effective section modulus based on bending only about the relevant axis, calculated by the stress fy / M1 according to code ENV 1993-1-3 or e.g. LT fy (Salmi, P. & Talja A.). Analogically to compressive loading, the reduction factor LT for lateral buckling is calculated by means of buckling curve a ( LT = 0.21): LT = 1, when LT 0.4 LT = 1 / ( LT + ( LT 2 - LT 2 )), when LT > 0.4 LT = ( fy / cr ) LT = 0.5 [ 1 + LT ( LT - 0.2 ) + LT ], 2 (6.5a) (6.6b) (6.6c) (6.6d) where the relative slenderness LT is calculated using elastic buckling stress cr . This stress is the ratio of the ideal lateral buckling moment Mcr and section modulus of gross cross-section. The elastic critical moment Mcr is also determined for the unreduced cross-section. The fo rmula for critical moment Mcry for singly symmetric sections is normal buckling description, but determination of critical moment Mcrz as well as handling of complex sections yields problems for sure. Bending and axial compression In addition to that each design force component shall not exceed the corresponding design resistance, conditions for the combined forces shall be met. In the case of global stability, the interaction criteria introduced in the code ENV 1993-1-3 are extraordinarily complex. For practical design purposes, a more familiar approach for combined bending and axial compression represented by (Salmi, P. & Talja, A) is more practical: Nsd / NbRd + Mysd / MyRd / (1 - Nsd / NEy ) + Mzsd / MzRd / (1 - Nsd / NEz ) 1.0, (6.7) where the meanings of the symbols have been described previously, except the elastic flexural buckling forces NEy and NEz corresponding to the normal Euler flexural buckling formula. In accordance with the code the effective cross-sectional properties can be calculated separately. Naturally, the resistance value shall be taken as smallest if several failure modes are possible. Here again, the additional moments due to potential shifts of neutral axes should be added to the bending moments. For simplicity and for the fact that they usually can be omitted, no additional moments are shown in the formula. Interaction between bending and axial compression are considered thoroughly in Cl. 6.5 of the code, but without any explanations of the backgrounds. SERVICEABILITY LIMIT STATES In the design code ENV 1993-1-3, serviceability limit states have been considered on one page only. The deformations in the elastic as well as in the plastic state shall be derived by 32 means of a characteristic rare load combination. The influence of local buckling shall be taken into account in form of effective cross-sectional properties. However, the effective second moment of area Ieff can be taken constant along the span, corresponding the maximum span moment due to serviceability loading. In the Finnish NAD a more accurate approach is presented, where the effective second moment of area may be determined from the equation: Ie = ( 2 Iek + Iet ) / 3, (7.1) where effective second moments Iek and Iet are to be calculated in the location of maximum span moment and maximum support moment, respectively. On the safe side, ultimate limit state moments may be used. Plastic deformations have to be considered, if theory of plasticity is used for ultimate limit state in global analysis of the structure. The deflections shall be calculated assuming linear elastic behaviour. In stead of strange limit value (L/180) for deflection in the ENV draft code the NAD has defined reasonable limits for different thin gauge structure types. For example, the maximum deflection in the serviceability limit state for roof purlins is L/200 and for wall purlins L/150. CONCLUSIONS In this paper, the main design principles of cold formed thin gauge members (`thin-walled members') have been considered. The manufacturing process results in typical features of thin-walled members: quite slender parts in very different open cross-sections and consequently many local or global failure modes. The desired properties (usually strength to weight ratio) of the members can be reached by optimising cross-sections, but as a by-product, the design procedures can be extremely complicated. The total lack of design codes seems to have been tranformed into a situation, in which some guidelines are available, but they are hard to adapt in practical design. The theoretical background for analytical design should be rather well known, but according to comparative tests, the accuracy of predicted resistance values is still often very poor - sometimes the deviation can even be on the `unsafe side'. However, taking into account several parameters affecting to analytical and test results, this inaccuracy can be expected and kept in mind in every day design. Complex structural behaviour of thinwalled members has produced inevitably complex design codes (e.g. ENV 1993-1-3). Hence all efforts to derive simplified design methods are naturally welcome. Because all manual methods are probably still to laborious, FEA is too heavy a tool and some design programs `already' available may not guarantee sufficient results in practice, the biggest contribution at the moment should be made to reliable calculation programs, which are as simple as possible to use. This challenging task should preferably be carried out by the same institutions, which produce these comprehensive design codes. 33 REFERENCES ENV 1993-1-3. 1996. Eurocode 3: Design of steel structures. Part 1.3: General rules. Supplementary rules for cold formed thin gauge members and sheeting. European Committee for Standardisation CEN. Brussels. SFS-ENV 1993-1-3. 1996. Eurocode 3: Tersrakenteiden suunnittelu. Osa 1-3: Yleiset snnt. Lissnnt kylmmuovaamalla valmistetuille ohutlevysauvoille ja muotolevyille. Vahvistettu esistandardi. Suomen Standardisoimisliitto SFS ry. Helsinki. 1997. NAD. 1999. National Application Document. Prestandard SFS-ENV 1993-1-3. 1996. Design of steel structures. Part 1.3: General rules. Supplementary rules for cold formed thin gauge members and sheeting. Ministry of Environment. Helsinki. ENV 1993-1-1. 1992. Eurocode 3: Design of steel structures. Part 1.1: General rules and rules for buildings. European Committee for Standardisation CEN. Brussels. TEMPUS 4502. Cold formed gauge members and sheeting. Seminar on Eurocode 3 Part 1.3. Edited by Dan Dubina and Ioannis Vayas. Timisoara, Romania. 1995. Salmi, P. & Talja, A. 1994. Simplified design expressions for cold-formed channel sections. Technical Research Centre of Finland. Espoo. Roivio, P. 1993. Kylmmuovattujen tersavoprofiilien ohjelmoitu mitoitus (Programmed design of cold-formed thin gauge steel members). Thesis for the degree of M.Sc.(Tech.), Helsinki University of Technology. Espoo. 34 DESIGN CHARTS OF A SINGLE-SPAN THIN-WALLED SANDWICH ELEMENTS Karri Kupari Laboratory of Structural Mechanics Helsinki University of Technology, P.O.Box 2100, FIN-02015 HUT, Finland ABSTRACT There are four different criteria, which must be determined in order to design a capacity chart for a single-span thin-faced sandwich panel. These criteria are bending moment, shear force, deflection and positive or negative support reaction. The normal stress due to bending moment must not exceed the capacity in compression of the face layer. The shearing stress due to shear force must not exceed the shearing capacity of the core layer. The maximum deflection can be at the most one percent of the span and the reaction force from external loads has to remain smaller than the reaction capacity. This paper presents some details of an investigation using full-scale experiments to determine the estimated level of characteristic strength and resistance of the sandwich panel. KEYWORDS Thin-walled structures, metal sheets, mineral wool core, shear modulus, deflection, normal (Gaussian) distribution, flexural wrinkling, shear failure of the core. INTRODUCTION A typical thin-faced sandwich panel consists of three layers. The top and the bottom surface are usually 0.5 ... 0.8 mm thick metal sheets and covered with a coat of zinc and preliminary paint. The outer surface is coated with plastic. The most commonly used core layers are polyurethane and mineral wool. 35 surface layer, metal sheet core layer h = 100...150 mm b = 1200 mm Figure 1: The cross-section of a typical sandwich panel. Sandwich panels are usually designed to bear only the surface load, which causes the bending moment and the shearing force. The bending moment causes normal stress to the top surface. The core layer must bear the shearing stress and the compression stress from the reaction force. STRUCTURAL FORMULAS AND DEFINITIONS The surface layer is presumed to be a membranous part and its moment of inertia insignificant compared with the moment of inertia for the whole sandwich panel. This gives us the simplification that the compression and tension stresses are uniformly distributed across the surface layer. The value of the modulus of elasticity for the surface layer is more than ten thousand times larger than the value of the modulus of elasticity for the core layer. The influence of the normal stresses across the core layer equals zero when considering the behavior of the whole sandwich panel. The normal stress of the surface layer is 1, 2 = and the shearing stress of the core layer is s = M Q e b Af(1,2) Q eb (2) M eA f (1, 2 ) (1) = bending moment = shear force = the distance between the surface layers center of gravity = the width of the sandwich panel = the area of the surface layers cross section 36 1 s e 2 Figure 2: The approximation of normal and shear stresses. When calculating the deflection in the mid-span of a simply supported sandwich panel we concentrate on two different load cases: Load case A is uniformly distributed transverse loading (Eq. 3 and Fig. 4.) and load case B consist of two symmetrically placed line loads (Eq. 4 and Fig. 5.). 5 qL4 1 gL2 wL = + 2 384 B 8 Geb 23 FL3 FL wL = + 2 1296 B 6Geb DEFINING THE SHEAR MODULUS At the beginning of the testing procedure we can determine the shear modulus. Assuming that the loaddeflection curve is linear and using the Hookes law we can write F = kw + C. After differentiation we get F =k w where k equals the slope of the regression line. load [q] (5) () (3) () (4) k deflection [w] Figure 3: The load-deflection curve. 37 The experimentally defined parameter k leads to the formula that gives us the shear modulus for load case A 1 5L2 G = 8eb 2 - 384B kL and respectively for load case B 1 23L2 G = 6eb - kL 1296 B -1 -1 (6) (7) where B = EAf e2 is the bending stiffness. e is the distance between the centers of the surface layers as shown in the Fig. 2. The value of the modulus of elasticity is E = 210 000 N/mm2 and the area of the surface layer Af = 0.56 1230 mm2. The width of the core layer is 1200 mm. q L Figure 4: Load case A. Uniformly distributed transverse loading. F 2 F 2 L 3 L 3 L 3 Figure 5: Load case B. Two symmetrically placed line loads. 38 FULL SCALE EXPERIMENTS A vacuum chamber was used to produce a uniformly distributed transverse loading of the panels, enabling flexural wrinkling failures to occur in bending. All these experiments were done at the Technical Research Center in Otaniemi, Espoo. Once the panels were positioned in the chamber, the measuring devices for force and deflection were set to zero. A polyethylene sheet was placed over the panel and sealed to the sides of the timber casing. The compression force was produced by using a vacuum pump to decrease the air pressure in the chamber. A total of twelve panels were used in this experiment. This procedure models the distributed load caused by wind. The results of these tests give us the capacity in compression of the surface layer. Polyethene sheet Sandwich Panel Vacuum Chamber Timber Casing Supports The measuring devices = Force = Deflection Figure 6: Experimental Set-up and the positioning of the measuring devices (Vacuum Chamber). For the load case B, two symmetrically placed line loads, all experiments were made at the Helsinki University of Technology in the Department of Civil and Environmental Engineering. From the results of these tests we can calculate both the shearing and reaction capacity. Altogether 28 panels were used in this part. The loading was produced by two hydraulic jacks with deflection controlled speed of 2 mm/min. The testing continued until the sandwich panels lost their load bearing capacity. 39 Force Fu (ultimate force) 0.4 F u 0.2 F u Time Figure 7: The loading history of load case B. THE CHARACTERISTIC STRENGTHS Defining the characteristic strengths is based on the instructions from "European Convention for Constructional Steelwork: The Testing of Profiled Metal Sheets, 1978". It is assumed that all testing results obey the Gaussian distribution The Formulas used in defining the characteristic strengths The value of characteristic strength MK can be calculated from the equation M K = M m (1 - c ) where Mm = average of the test results c = factor related to the number of test results (From Table 1) = variation factor TABLE 1 The relation between factor c and the number of test results n n c 3 2.92 4 2.35 5 2.13 6 2.02 8 1.90 10 1.83 12 1.80 20 1.73 1.65 (8) The square of the variation factor is 40 2 Mi 1 n M - i M i n Mm i =1 2 = i =1 n -1 n 2 (9) where n = the number of test results Mi = the value of test number i Mm = average of the test results The characteristic strengths are calculated based on the test results. The factor related to aging and defining the factor related to temperature The mineral wool core material was tested in three different temperatures. First test was made in normal room temperature +20 oC with the relative humidity RH of 45-50 %. Second test was made after the material was kept for 36 hours in a +70 oC temperature with the relative RH of 100 %. The final part included 36 hours of storage in a +80 oC temperature before testing. The factor related to aging, degradation factors dft and dfc can be calculated from the formulas df t = t 70 and df c = c70 t 20 c20 where t20 t70 c20 c70 = tensile strength at +20 oC temperature, average value = tensile strength at +70 oC temperature, average value = compression strength at +20 oC temperature, average value = compression strength at +70 oC temperature, average value (10) The factors dft and dfc are divided into two groups 0.7 ( I) df t , df c 0.7 ( II ) (11) For the case (I) test results of characteristic strengths for the capacity in compression of the surface layer and the shearing and reaction capacity of the core layer are valid. For the case (II) test result must be multiplied by the following reduction factors ttd = df t + 0.3 and tcd = df c + 0.3. The factor related to temperature can be calculated from Tt = E t80 E and Tc = c80 E t 20 E c20 (13) (12) 41 where Et80 Et20 Ec80 Ec20 = Modulus of elasticity in tension at +80 oC temperature, average value = Modulus of elasticity in tension at +20 oC temperature, average value = Modulus of elasticity in compression at +80 oC temperature, average value = Modulus of elasticity in compression at +20 oC temperature, average value The connection between bending moment and capacity in compression The connection can be given as k ( fw + 0.5 f T ) where ttd f fcK m (14) k = the partial safety factor of external load fw = the normal stress caused by external load fT = the normal stress caused by the temperature difference between inner and outer surface layers ttd = the reduction factor related to aging ffcK = the characteristic strength of the face layers capacity in compression m = the partial safety factor of material In case of a single span, statically determined structure, the term fT = 0. The normal stress caused by external load can be calculated from the formula fw = where e b t qL2 8ebt (15) = the distance between the surface layers' centres of gravity = 1 [m] = the thickness of the surface layer The connection between shear force and shearing capacity The connection can be given as k (Cw + 0.5 CT ) where ttd f CvK m (16) k = the partial safety factor of external load Cw = the shearing stress caused by external load CT = the shearing stress caused by the temperature difference between inner and outer surface layers 42 ttd = the reduction factor related to aging fCvK = the characteristic strength of the face layers shearing capacity m = the partial safety factor of material In case of a single span, statically determined structure, the term CT = 0. The shearing stress caused by external load can be calculated from the formula Cw = where e b qL 2eb (17) = the distance between the surface layers' centres of gravity = 1 [m] The connection between reaction force and reaction capacity The connection can be given as k R wp + 0.5 R T where ( ) tcd R K m (18) k = the partial safety factor of external load Rwp = the reaction force caused by external load RT = the reaction force caused by the temperature difference between inner and outer surface layers tcd = the reduction factor related to aging RK = the characteristic strength of the reaction capacity m = the partial safety factor of material In case of a single span, statically determined structure, the term RT = 0. The reaction force caused by external load can be calculated from the formula R wp = 1 qL 2 (19) The boundary conditions concerning deflection The maximum deflection must remain less than one percent of the span. From external load and temperature difference between inner and outer surface we get two equations: k w q + 0.5 w T ( ( ) ) L 100 (20) k 0.5 w q + w T L 100 (21) 43 k = the partial safety factor of external load in serviceability limit state (=1.0) wq = the deflection caused by external load wT = the deflection caused by the temperature difference between inner and outer surface layers where The deflection caused by external load is mentioned in Eq. (3) and Eq. (4). The deflection caused by the temperature difference between inner and outer surface layer is w T = T T L2 8e (22) where -1 = coefficient of linear thermal expansion for surface layer material, 12 10 - 6 o C = temperature difference between inner and outer surface layers, 60 oC [ ] From equations (20) and (21) we choose the one that gives the larger deflection. DESIGN CHARTS From the four criteria we can construct the design chart by drawing four curves from the equations (14), (16), (18) and (20)&(21). The X-axis represents the span L [m] and the Y-axis represents the external load q [kN/m2]. The area located under all four curves represents the permissible combination of external load and span. 44 Design Chart of a single-span thin-walled sandwich element (example) 4 3.5 External load q [kN/m2] 3 2.5 2 1.5 1 0.5 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 Span L [m] Deflection Bending moment Reaction force Shear force REFERENCES European Convention for Constructional Steelwork, The testing of Profiled Metal Sheets, 1978. CIB Report, Publication 148, 1983. Rakentajain kalenteri (in Finnish), 1985. McAndrew D., Mahendran M., Flexural Wrinkling Failure of Sandwich Panels with Foam Joints, Fourth International Conference on Steel and Aluminium Structures, Finland, Proceedings book: Light-Weight Steel and Aluminium Structures, edited by Mkelinen and Hassinen, pp. 301-308, Elsevier Science Ltd, 1999. Martikainen L., Sandwich-elementin kyttytyminen vlituella, Masters Thesis (in Finnish), 1993. 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The simple calculation procedures given in Eurocode 3 are summarised and advanced calculation models briefly described. The central mechanical and thermal material properties of steel in high temperatures are given based on Eurocode 3 and experimental data. The essential characteristics of the behaviour of cold-formed steel structures in elevated temperatures are discussed. Finally, an overview of different recent research projects in the field is given. KEYWORDS Cold-formed steel, fire design, critical temperature, advanced calculation models, mechanical properties, catenary effects, thermal elongation. INTRODUCTION The use of cold-formed steel structures has become increasingly popular in different fields of building technology. For example, small housing systems using cold-formed steel for wall structures, framing systems and roof structures including trusses and shielding materials have been developed during recent years. Cold-formed steel offers very flexible design using different cross-sectional shapes but 66 can put more demands on the designer because elastic local and global buckling phenomena need to be taken into account in practically all design. At room temperatures, these phenomena are fairly well known, although more research is constantly being done for the optimisation and development of structures. However, the research done on cold-formed steel structures in fire conditions is relatively recent and the behaviour of thin-walled structural members and entities in fire conditions is not sufficiently accurately known. The present design methods thus require the use of expensive fire protection materials to protect the steel structures from excessive heat increase during a fire. This leads to uneconomical, unecological and conservative design. This seminar paper describes and discusses the state of the art in the fire design of cold-formed steel structures. Special features essential to the behaviour of structures in general and cold-formed steel structural members in particular are explained. The present design methods and guidelines given in Eurocode 3 are described. The changes in material properties due to increase of temperature are given based on Eurocode 3 and experimental research. Finally, an overview of recent research projects covering some aspects of the use of cold-formed steel is provided. The applications examined include the behaviour of cold-formed steel wall studs used in small housing, the behaviour of plate members, the local buckling of RHS members and the local buckling of cold-formed steel in composite structural members, such as steel-concrete composite floor slabs DESIGN OF STEEL STRUCTURES IN FIRE CONDITIONS ACCORDING TO EUROCODE 3 General Fire design is an essential part of the design procedure of structural members. Fire design methods are used to insure that a structure designed according to rules used in normal room temperatures can also withstand the additional effects induced by the increase of temperature it is subjected to in the case of a fire, for the demanded duration set for that particular type of structural component. Fire design can be performed either computationally, using tabulated data, or as a combination of the two. Structures can be designed to be unprotected or protected against fire using fire protection materials as long as it is shown that the demands set for the particular design case are met. The criterion commonly used for the resistance of a steel structure against fire is the so-called fire resistance time. The fire resistance time of a load-bearing steel structure is the time from the ignition of a fire to the moment when the capacity of the structure to carry the loads it is subjected to is decreased to the level of the loads or the deflections of the structural member pass the limits set to them [Iso-Mustajrvi et al. 1999]. Fire design is used to verify the resistance of the structure on the basis of the maximum temperature and the loads applied to the structure during a fire. Structures are classified into different groups of required fire resistance time, for example R15-, R30-, R60- and R90-class structures. The classification is based on the type, structural system and intended use of the structure. 67 Structural fire design Simple calculation models for the fire design of steel structures are given in Eurocode 3, Part 1.2 [ENV 1993-1-2:1995] and also presented in this chapter. These rules are restricted to steel sections for which a first-order design theory in global plastic analysis may be used, i.e. class 1 and 2 crosssections. With certain restrictions they can also be used for class 3 and 4 cross-sections. For thin-walled class 4 elements, local buckling phenomena become important. As more precise design methods have not been included in the design code, a quite conservative approach is given, namely that the temperature of cold-formed (class 4) cross-sections should not exceed 350C at any time. In practical terms this means that a relatively thick layer of insulation material need be used, which leads to uneconomical and unenvironmental design. However, Eurocode 3 does allow the use of more advanced calculation models with which it can be shown that the critical temperature of a particular cold-formed steel structure or structural member is higher than the aforementioned 350C. A partial safety factor of 1.0 is used for all loads in load combinations during the fire situation according to Eurocode 1 [ENV 1991-1:1994]. Simple calculation models Fire design can generally be performed using one of two simple calculation models which naturally lead to similar results. The first method is based on the concept of a critical temperature, the second method on the load-bearing function of the structure or structural member. Method based on critical temperature Fire design can be performed using the method based on the critical temperature of the steel structure according to the basic stages laid out in Figure 1. The design procedure begins with the determination of the critical temperature Tcr for the steel structure on the basis of the applied loads, the structural model and the material properties. The critical temperature Tcr is the temperature at which the yield strength of the steel material is decreased to the level of the stresses induced into the structure by external loading [Iso-Mustajrvi et al. 1999]. The critical temperature Tcr is used for the verification of the structure against different limit states. Global and local buckling phenomena should naturally be taken into account. The design is performed by implementing the thermo-mechanical material properties into the basic design formulas used for normal room temperature design. The possible second-order effects, changes in the statical 68 design model of the structure, thermal deformations and deflections and restraint forces should be taken into account as well. The maximum temperature of the steel structure Tsmax reached within its set fire resistance time is determined on the basis of the ISO 834 standard design fire or a natural fire model. In some cases, it can be shown with a reasonable degree of certainty that fire will not spread beyond a localised area even when compartmentation is not used. This type of situation can prevail for example in open car parks, where the effective natural ventilation provided by the large openings in the walls prevent the temperature to rise to a very high level in a larger area around the fire source (e.g. a burning car) within the prescribed fire resistance time. In this type of structure, a local natural fire model can be assumed and design performed accordingly, but this would already fall into the category of "advanced calculation models" (see chapter 2.2.3). However, the different types of natural fire models are beyond the scope of this text and will not be discussed further. Required fire resistance time Structural model Material properties Loads Structural class Design fire Protected steel structure Unprotected steel structure Tcr COMPARED TO Tsmax Tcr > Tsmax Tcr Tsmax Restart design: increase protection or the size of the steel section Design OK: stop design or try reducing protection Figure 1. The fire design of steel structures using the critical temperature criterion. 69 Load-bearing function Another way of determining the fire resistance of a steel structure is given in Eurocode 3, Part 1.2 [ENV 1993-1-2:1995]. The load-bearing function of a steel member shall be assumed to be maintained after a time t in a given fire if Efi,d Rfi,d,t where Efi,d Rfi,d,t is the design effect of actions for the fire design situation according to Eurocode 1, Part 2.2 [ENV 1991-2-2:1995] is the corresponding design resistance of the steel member, for the design fire situation, at time t. The design resistance Rfi,d,t at time t is determined for the temperature distribution in the crosssection by modifying the design resistance for normal temperature design in ENV 1993-1-1 to take account of the mechanical properties of steel at elevated temperatures. Required fire resistance time Calculation of the maximum steel temperature during the required time resistance time Calculation of steel member capacity as function of decreased material properties Rfi,d,t COMPARED TO Efi d Rcrfi,d,t Efi,d Rcrfi,d,t > Efi,d Restart design: increase protection or the size of the steel section Design OK: stop design or try reducing protection 70 Figure 2. The fire design of steel structures using the load-bearing function. Advanced calculation models In Eurocode 3, Part 1.2, it is stated that advanced calculation models can be used for any type of cross-sections of individual members, sub-assemblies and entire structures. Any potential failure modes not covered by the method used should be eliminated by sufficient and appropriate design. The validity of a specific advanced calculation method for a particular design situation should be agreed upon between the client, the designer and the competent authority. Different types of advanced calculation models have been developed. Often they are based on a combination of experimental research and numerical modelling using finite element analysis. MATERIAL PROPERTIES OF COMMON STEEL TYPES USED IN COLD-FORMED STEEL CONSTRUCTION General Eurocode 3, Part 1.2 gives simplified models for the determination of the material properties of structural steel to be used in design practices. An extensive research programme has been carried out at the Laboratory of Steel Structures in Helsinki University of Technology to verify the actual properties of different types of steel in elevated temperatures. The test results have been compared with the values given in the design code. Mechanical properties of steel according to Eurocode 3, Part 1.2 Eurocode 3, Part 1.2 gives the values for the material properties of steel at elevated temperatures. The stress-strain relationship for structural steel is shown in Figure 3. The calculation formulas for the curve of Figure 3 are also given in Eurocode 3, Part 1.2. In Figure 3, f y, is the effective yield strength at temperature , f p, is the effective proportional limit at temperature , Ea, is the slope of the linear elastic range, p, is the strain at the proportional limit, y, = 0.02 is the yield strain, t, = 0.15 is the limiting strain for yield strength and p, = 0.2 is the ultimate strain. 71 Stress fy, fp, Ea, = tan p, y, t, u, Strain Figure 3. Stress-strain relationship for steel at elevated temperatures according to Eurocode 3, Part 1.2. The reduction factors for the stress-strain relationship of steel at elevated temperatures, relative to the appropriate value at 20C, are given in Figure 4. 72 1 0,9 0,8 Reduction factor k 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0 200 400 600 800 1000 1200 Temperature [o C] Effective yield strength Proportional limit Slope of linear elastic range Figure 4. Reduction factors for the stress-strain relationship of steel at elevated temperatures according to Eurocode 3, Part 1.2. Mechanical properties of steel according to tests The mechanical properties of cold-formed hot dip zinc coated structural steel S350GD+Z have been determined experimentally using transient tests at the Laboratory of Steel Structures in Helsinki University of Technology (HUT) [Mkelinen, Outinen 1998]. In transient tests, the test specimen is under constant tensile loading while the temperature is steadily increased. Strain is measured as a function of temperature and thermal elongation is subtracted from the total strain in order to obtain a temperature-strain curve. The transient test method has been found to be a more realistic way of determining the temperature-strain curve than the other commonly used test method, i.e. the steadystate tensile test method. In steady-state tests, the temperature is first increased to a certain level after which a normal tensile test is performed on the specimen. The results of steady-state tests have been found to be strongly dependent on the strain rate and generally the results tend to be too optimistic. The results of the tests performed at HUT are shown in Figures 5 and 6 for modulus of elasticity and yield strength, respectively. The graphs shown include also a comparison of the values given by the design standards of different countries and organisations. A new proposal for the decrease of yield strength as a function of temperature has been made by Outinen [Outinen et al. 2000]. 73 220000 200000 180000 EC3 ECCS B6/B7 Transient state test results Steady state test results Australian/French standards 160000 2) Modulus of elasticity (N/mm 140000 120000 100000 80000 60000 40000 20000 0 0 100 200 300 400 500 Temperature [C] 600 700 800 900 1000 Figure 5. The modulus of elasticity of steel S350GD+Z as a function of temperature, comparison between different design standards and experiments [Outinen et al. 2000]. A distinct yield stress point is difficult to find for structural steels subjected to fire conditions. Therefore the use of different strain limits corresponding to the yield stress have been proposed. These include the use of yield stresses corresponding to 0.1%, 0.2%, 0.5%, 1.0% and 2.0% strains. Eurocode 3 uses the yield stress corresponding to the yield strain y, = 2.0% and the ultimate strain u, = 20.0%. On the basis of his research, Ranby [1999] proposes the use of the 0.2% plastic strain limit to define the yield strength at elevated temperatures. His research shows that the 2.0% limit used by Eurocode 3 is too optimistic when instability governs in cold-formed steel structures. According to Ranby, the design of cold-formed steel structures in fire conditions can be carried out using the equations given for normal room temperature design with the yield stress and modulus of elasticity of the material reduced corresponding to the 0.2% yield strain. 74 450 Eurocode 3: Part 1.2 Transient state test results Steady state test results Proposed curve for the effective yield stength 1998 400 350 Yield strength f [N/mm2] 300 New proposal Australian standard French design recommendations B6 y 250 200 150 100 50 0 0 100 200 300 400 700 a [C] Steel temperature 500 600 800 900 1000 1100 Figure 6. The yield strength of steel S350GD+Z as a function of temperature, comparison between different design standards and experiments [Outinen et al. 2000]. 75 Thermal properties of steel Thermal elongation The coefficient of thermal elongation of structural steel a [dimensionless] can be determined according to the following equations given by Eurocode 3, Part 1.2. These values are valid for all types structural steel. a = l/l = -2.416610-4 + 1.210-5 a + 0.410-8 a2 a = l/l = 1110-3 a = l/l = -6.210-3 + 210-5 a for 20C a 750C for 750C < a 860C for 860C < a 1200C In simplified calculation models, the coefficient of thermal elongation can be assumed to be linear according to the following equation: a = l/l = 1410-6 (a -20) Specific heat The specific heat of structural steel ca [kJ/kgK] can be determined according to the following equations given by Eurocode 3, Part 1.2. ca = 425 + 7.73 10-1 a - 1.69 10-3 a2 +2.22 10-6 a3 13002 c a = 666 - - 738 a 17820 c a = 545 + - 731 a ca = 650 for 20C a < 600C for 600C a < 735C for 735C a < 900C for 900C a 1200C It is worth noting that the specific heat of structural steel grows asymptotically from 600C towards 735C. The value at 735C is thus infinite. When temperature is increased beyond 735C, the value of specific heat is decreased asymptotically and at approximately 800C it reaches the same level it has at 600C. This is due to a phase change in the steel material. However, at 735C, the yield strength of structural steel is negligible, so this is not a critical point in design. In simplified calculation models, the specific heat can be assumed to be independent of steel temperature and may be taken as ca = 600 kJ/kgK. 76 Thermal conductivity The thermal conductivity of structural steel a [W/mK] can be determined according to the following equations given by Eurocode 3, Part 1.2. a = 54 - 3.33 10-2 a a = 27.3 for 20C a 800C for 800C a 1200C In simplified calculation models, the thermal conductivity can be assumed to be independent of steel temperature and may be taken as a = 45 W/mK. ESSENTIAL CHARACTERISTICS OF THE BEHAVIOUR OF COLD-FORMED STEEL STRUCTURAL MEMBERS IN FIRE CONDITIONS The structural use of cold-formed steel structural members can be divided into the following categories: load-bearing profiled sheet steel members load-bearing members in thin-walled steel framed buildings (wall and roof truss structures) sandwich panels with e.g. a mineral wool core and profiled steel sheet covers composite slabs using cold-formed steel sheeting and other cold-formed steel - concrete composite structures The design of cold-formed steel structures usually requires the verification of additional possible failure modes in comparison to the design of e.g. hot-rolled steel beams and columns. Necessary capacity verifications in the elastic range common to all structures include the verification of the ultimate stresses not reaching the yield stress and the verification of the capacity of the structure against different global buckling modes, which include flexural buckling, torsional buckling, torsionalflexural buckling and distortional buckling. Cold-formed class 4 cross-sections need to be checked in addition against local buckling phenomena. In simplified design, a load reduction factor fi for the determination of the load level in the fire design is used. The load reduction factor is dependent on the ratio = Qk,1 / Gk where Qk,1 is the most important live load and Gk is the dead load imposed on the structure. The value of f is usually in the range of 0.6 ... 0.65 for steel and steel-concrete composite structures [Fontana 1994]. The distribution of temperature in the structure is of great importance, not only because of the degradation in material properties in heated zones but also for secondary effects caused by thermal elongation. In simple design models, an even distribution of temperature across the cross-section of the member and also along its length may be assumed. However, this can lead to very conservative or even incorrect design. Beams and columns heated from one side only will usually develop a more 77 or less important temperature gradient across the height of the cross-section, which will lead to the deflection of the beam or column towards the heat source because the hotter side of the member will be subjected to a greater thermal expansion than the cooler side. The overall thermal expansion will possibly also lead to the development of important restraint forces at the ends of the member if the adjacent structural compartments are at a lower temperature and can resist the expansion of the heated parts. This will cause additional normal moments and subsequently also second-order moments into the member. An effect of uneven increase of temperature and different material properties of adjoint members can also be the rupture of connections for instance between gypsum boards and the steel members. The thermally induced elongation of structural members will normally be seen as increased deflections, restraint forces and supplementary stresses on the connections. As the deflection of a beam increases, tensile forces develop along the axis of the member. If the connections are strong enough to withstand these tensile forces and hold the ends of the beam in place, the so-called catenary effects will come into action. When the temperature is increased further, a situation can occur, where the tensile rigidity of the beam will be the main factor against a total collapse of a beam member. Another consequence of catenary effects is the concentration of support forces onto the edge of the support area as shown in Figure 7. Direction of loading Point of support Tensile catenary force Figure 7. Catenary effects on the support [Leino et al. 1992]. 78 EXISTING RESEARCH ON THE BEHAVIOUR OF COLD-FORMED STEEL STRUCTURES IN FIRE CONDITIONS General As mentioned earlier, the research done on the behaviour of cold-formed steel structures in fire conditions is not extensive. The earliest comprehensive scientific articles on the topic date to the late 1970's, when K.H. Klippstein examined the strength of cold-formed steel studs exposed to fire [Klippstein 1978]. During the 1990's, more work has been carried out especially in Finland, Sweden, France, The United Kingdom and Australia. This chapter provides a presentation of some of the research done on the fire resistance of cold formed steel structural members in the above countries. Behaviour and strength of steel wall studs exposed to fire One common use of cold-formed steel structural members is in light-weight steel walls and floors used in residential and office buildings. These walls can be exterior or interior walls, but one general determining design assumption is that the walls act as separating elements between adjacent fire compartments and they should thus resist the spread of fire, heat and toxic fire gases into the next compartment. The walls are generally built using a cold-formed steel stud core as the principal load-bearing system, mineral or glass wool as thermal and sound insulation and gypsum boards on the outsides as sheathing, which has an important structural purpose in providing rigidity to the individual studs. This naturally requires that the gypsum boards be attached to the studs' flanges using screws at regular and sufficiently small intervals. Because of the fire compartment separating function of steel stud walls, there would normally be a great difference in temperature between the two sides of the wall during a fire and thus a steep thermal gradient across the height of the cold-formed steel stud. In a typical case, the fire side of the wall can easily be 200C - 300C hotter than the external side [Ranby 1999]. On the one hand this means that the material properties of the steel parts deteriorate much faster on the fire side than they do on the external side. On the other hand, the fire side of the steel column being hotter, the effect of thermal elongation is also much greater on that side, causing the steel member to deflect towards the heat source. This causes the compressive forces acting on the column to introduce second-order effects, i.e. bending moments which in turn will enhance the development of flexural buckling in the strong axis direction (towards the fire). The structural behaviour of individual studs changes as a function of temperature in this type of a gypsum-boarded wall structure due to changes in their boundary conditions. In normal room temperature and the beginning of the increase of temperature, the restraining effect of the gypsum boards can be made effective use of in design. In practice this means that the only global buckling 79 mode relevant to the design of the cold-formed steel stud is flexural buckling in the strong axis direction. The connection of the stud to the gypsum board prevents not only flexural buckling from taking place in the weak axis direction, but also the torsional or torsional flexural buckling modes. Local buckling may of course still occur and interact with the possible flexural buckling mode. The critical temperature for the functionality of the gypsum boards is approximately 550C, after which they are calcined and their restraining effect is negligible [Ranby 1999]. Cracking and actual destruction of the gypsum boards will also take place. This means that torsional, torsional-flexural and distortional buckling modes become actual. However, the gypsum boards on the external (cooler) side can still stay in place after the fire side boards become calcined, unless the deflection caused by the thermal gradient and second-order effects is strong enough to break also the compressed gypsum boards on the external side. The falling off of gypsum boards on the fire side of the wall will naturally expose the steel studs directly to the fire. This will lead to a rapid reduction of the temperature gradient across the steel section, while other parts of the wall where the gypsum boards are still in place will continue to have a strong temperature gradient. Consequently, adjacent steel studs may be exposed to substantially different conditions towards the later stages of a compartment fire [Klippstein 1978]. Structural fire design model for steel wall studs have been presented by Klippstein [1978], Gerlich [Ranby 1999] and Ranby [1999]. Short descriptions of these models are given in what follows. Klippstein [1978] The design model presented by Klippstein [1978] is based on the allowable stress method given by the AISI design manual and the ASTM-E119 fire test standard. The ASTM-E119 presents the development of a design fire similarly to the ISO 834 standard fire [Ranby 1999]. Klippstein makes the following assumptions: 1. the gypsum board cladding on the internal and external faces of the wall prevent failure by weak axis flexural buckling or torsional buckling 2. the gypsum boards do not carry any vertical loads 3. the stress-strain curve of the steel material is linear up to the yield strength 4. the loads are uniformly applied to all studs in the wall panel 5. all studs have equal temperature gradients, horizontal deflections and average temperatures throughout the duration of the fire. Klippstein emphasises the point that the suggested method is heavily dependent on empirical determination of the variation of the temperature of the stud and the mid-length lateral deflection during the fire. The method is also limited to the type of section used (regular C-section), the amount of insulation, cladding and other physical characteristics. 80 The failure condition given by Klippstein is PT = 1 1 + T 23 Sx FyT A FalT 12 where PT A FalT T Sx FyT is the calculated (predicted) failure load of a particular stud at an elevated temperature T is the gross cross-sectional are of the stud is the allowable stress for axial load at failure temperature is the total mid-length deflection of the stud at the time of failure is the section modulus about the major axis of the C-section is the yield strength at failure temperature. The conclusion drawn by Klippstein is that the proposed design method can be used with reasonable accuracy to predict the failure temperatures of this particular type of studded steel wall up to around 650C. However, it does not take torsional-flexural buckling or moment-induced second-order deflections into consideration. Gerlich [1995] Another method for the determination of the resistance of steel stud walls was given by Gerlich in 1995 and summarised by Ranby [Ranby 1999]. The model uses the equations for the reduction of yield strength and modulus of elasticity given by the AISI design standard. According to the Gerlich method, the stresses in the flanges of a C-section caused by external loads can be calculated using the following equations: if = uf = where N N( e( T ) + e( M )) - A W N N(e (T ) + e( M )) + A W N A e(T) e(M) W for the hot inner flange for the cooler outer flange, is the applied normal force is the gross cross-sectional area of the stud is the mid-length deflection due to thermal effects is the mid-length deflection due to bending moment is the section modulus about the stronger axis of the cross-section 81 Using the above equations, a critical temperature may be found at which the temperature-dependent yield strength of the steel section is equal to the applied stress. The time of failure can then be determined as a function of the increase of temperature. The model presented by Gerlich thus takes the additional deflection caused by bending moment into account, which the other models herein do not. On the other hand, it neglects torsional-flexural buckling. One particular point worth noting in the Gerlich model is that the critical temperature is here determined as the temperature of the cooler outer flange and not the mean temperature of the crosssection. Ranby [1999] Ranby applied the design codes given in Eurocode 3, Part 1.3 for flexural and flexural-torsional buckling in room temperature to elevated temperatures. Based on a number of tests and finite element (FE) modelling, he found that the basic equations of Eurocode 3, Part 1.3 can be directly used in fire design when the decrease of material properties as functions of temperature is taken into account. His proposed design model has two parts. If the temperature stays under the level of calcination of the gypsum boards or the steel members are protected by fire-resistant or incombustible gypsum boards, the design model can be based on equations that consider flexural buckling along the stronger axis only. Because the boards provide lateral support to the steel columns throughout the fire, torsional-flexural buckling does not become a critical failure mode. If, on the other hand, the temperature during the fire rises above the level of calcination of the gypsum boards (say, 550C), the lateral support condition is no longer valid and the torsional-flexural buckling mode should be checked. These assumptions thus lead to the proposed use of the following equations: Nu = f y A ef ey A 1 + x E ef I ef f y A ef e( b - y E ) A ef 1+ x I ef in the case of flexural buckling Nu = in the case of torsional-flexural buckling where = + 2 - 2 = 0.5 1 + ( - 0.2 ) + 2 , 0 .5 [ [ 1 with = 0.34 82 1 l f y A ef i E A gr fy N cr N cr e (b w - y e ) - A ef I ef x Nu 1.5 f y A ef = = in the case of flexural buckling in the case of torsional-flexural buckling x = 1- x = ( 2 M , x - 4) 0.90 M ,x = 1.3 Aef and Ief are the effective area and effective moment of inertia of the steel cross-section, respectively, determined with respect to variations of the modulus of elasticity across the unsymmetrically heated cross-section and are calculated using appropriate area elements weighted according to their modulus of elasticity and summed across the cross section. Ncr is the critical elastic buckling load for torsional-flexural buckling. The eccentricity e used in the above formulas is determined differently from the methods proposed by Klippstein and Gerlich. While Klippstein used the value of mid-length deflection and Gerlich the sum of thermal and moment-induced deflections, Ranby uses a so-called effective eccentricity. The effective eccentricity is determined as e = e(T) - y = e(T) - bw / 2 - yE where e(T) yE is the thermal deflection caused by the temperature gradient across the steel section is the distance in the y - direction between the supported (compressed) flange and the modified centre of gravity, which is shifted towards the compression flange due to the variation of elastic properties across the section. is the width of the web bw Distortional buckling is not considered in Ranby's work. Comparison of the methods proposed by Klippstein, Gerlich and Ranby Ranby made a comparison of the three methods in his Licenciate Thesis [Ranby 1999]. He found that for a C-section with a web height bw = 100 mm, Klippstein's method gives higher resistance values when compared to the other two methods, more in tune with each other. On the other hand, 83 when the web's height is doubled, bw = 200 mm, Klippstein's method is conservative in comparison with Gerlich's model. Ranby's own model generally gives values between the two other models. All three models use the ISO 834 standard fire development model, or similar. Strength of plates subjected to localised or global heat loads Guedes Soares et al. [1998, 2000] have examined the behaviour of thin plates under global and localised heat loads using a parametric study carried out on a general-purpose non-linear finite element code ASASNL. The plates are considered as parts of a larger structural entity and not as individual structural components independent of any external boundary conditions. Thus the surrounding structures will oppose to the expansion caused by thermal loads. The boundary conditions are modelled as springs at the edges of the plates. Five different geometries were considered using 1000 1000 mm2 square plates with thickness varying from 10.0 mm to 50.0 mm. The b/t ratios used were 100, 80, 60, 40 and 20. The heated area was also square and central to the plate, with its size varying between 6% and 77% of total plate area. Five different temperature levels were used, i.e. 100C, 200C, 400C, 600C and 800C. In practical situations, a plate would normally be subjected to an operational loading condition after which thermal loads might occur. However, for reasons of simplicity in the analysis procedure, this sequence was reversed in this study so that the plates were first heated locally to the particular temperature level after which a biaxial stress was applied. When working in the elastic range, it was shown by Guedes Soares et al. that both approaches lead to the same results in terms of plate capacity. When the plates were first examined without heating under biaxial loading, it was seen that the plate with b/t = 20 collapsed plastically while the other plates had important out-of-plane deformations (local buckling) at the time of collapse. The thickest plate had also a much higher strength than the other plates. 84 Figure 8. Axial stress for a plate with 25% heated area (b/t = 60). When a 6% portion of total plate area was heated to the five different temperatures mentioned above, it was seen that the buckling stress was slightly reduced but post-buckling behaviour was not affected. When 25% of total area was heated, the buckling stress was reduced a little more, but in the post-buckling area stresses were actually slightly increased. An interesting phenomenon is that a high localised temperature area in a plate can actually induce tensile stresses into the plate. Although thermal expansion will produce compressive stresses across the whole plate area due to edge restraints in the first part of temperature increase, the material properties of the local high temperature area will later on be reduced so much that the compressive stresses in this area will be reduced as well and they can actually turn into tensile stresses, as seen from Figure 8 for temperatures above 400C. For larger heated areas up to 100%, the thermal stresses will induce a generalised compressive stress in the plate and a general degradation of material properties, which together will cause the collapse of the plate. When the whole plate is heated, there is no post-buckling strength. The main conclusion drawn from the study is that the collapse load of the plates decreases rapidly when the heated area is more than 50% of total plate area. Ranby also included a chapter on the local buckling of cold-formed steel plates in his Licenciate Thesis [Ranby 1999]. He found that with the use of the 0.2% yield stress, and a typical value of load reduction factor equal to 0.6, the maximum steel temperature corresponding to the load bearing resistance is closer to 450C than the 350C proposed by Eurocode 3. Local buckling of RHS columns Rectangular hollow sections (RHS) are commonly used as columns in buildings and members in roof trusses, among other things. Ala-Outinen and Myllymki [1995] carried out an experimental and numerical (FEA) research on the local buckling of unprotected RHS members in high temperatures with the aim of developing a simple design procedure. Tests were performed on 900 mm long RHS 2002005 and RHS 1501003 sections. The tests were transient state tests where the furnace temperature was first raised to 300C in three minutes and then kept at a constant increase rate of 10C / minute. It was found that concentrically loaded columns lost their bearing capacity through local buckling at mid-length of the column. Eccentrically loaded columns (e = 28 mm) failed similarly except that the buckle appeared near the top of the column. 85 The calculation method proposed by Ala-Outinen and Myllymki [1995] is based on the equations of Eurocode 3, Part 1.3 for normal room temperature design. The effective width of plate parts should be calculated using the same formulas in fire conditions as for ambient temperature conditions, with the exception that the values of the yield strength and the modulus of elasticity should be reduced according to Eurocode 3, Part 1.2. The stress of the plate element should be set equal to the yield strength y corresponding to the 0.2% proof strain. The load reduction factor fi should be determined according to Eurocode 1, Part 2.2 and is usually in the range of 0.6 - 0.7. After this, the critical temperature of a cross-section can be determined from the calculated load-bearing capacity curve using the appropriate load reduction factor. The authors found that for the tested columns, the critical temperature with fi = 0.7 will be around 400C using this calculation method. This is higher than the 350C suggested by Eurocode 3, Part 1.2 but less than the actual collapse temperatures observed in the tests. Thus the method gives conservative results. Cold-formed steel used in composite structural elements Composite slabs using profiled cold formed steel sheets as steel parts and encasement for casting have become more and more popular in recent years. Uy and Bradford [1995] studied the elastic and inelastic local buckling behaviour of the steel parts of such structures using a finite strip method (FSM). They found simple equations for the determination of local buckling stresses ol(T) at any temperature T. In the elastic range, ol ( T) = ol (20) E( T) E( 20) f yp ( T) f yp ( 20) when ol(T) f yp(T) ol ( T) = ol (20) when ol(T) f yp(T) where ol(20) ol ( 20) = is the elastic local buckling stress at room temperature given by k 2 E b 12(1 - ) t 2 2 E(T) E(20) fyp(T) fyp(20) is the modulus of elasticity of steel at temperature T is the modulus of elasticity of steel at temperature T = 20C is the yield stress of steel at temperature T is the yield stress of steel at temperature T = 20C. As was seen in the analyses by Guedes Soeres et al. [1998, 2000] in the case of a plate being heated locally, the decrease of the value of the modulus of elasticity and the yield strength can lead to 86 a decrease in compressive stresses in the element. This in turn will naturally prevent local buckling from occurring as rapidly as in room temperature. This same rather paradoxical phenomenon was observed by Uy and Bradford as well. They found that the required slenderness limits at elevated temperatures are much higher to avoid local buckling than those that exist at room temperature. In practice this means that the design against local buckling at room temperature will be adequate also for fire temperatures. 87 REFERENCES ENV 1991-1:1994, Eurocode 1: Basis of Design and Actions on Structures, Part 1:Basis of Design, Brussels, Belgium, 1994. ENV 1991-2-2:1995, Eurocode 1, Part 2.2: Actions on structures. Actions on structures exposed to fire, Brussels, Belgium 1995. ENV 1993-1-2:1995, Eurocode 3, Part 1.2, Design of Steel Structures, General rules. Structural fire design, European Committee for Standardization, Brussels, Belgium 1995. ENV 1993-1-3:1996, Eurocode 3, Part 1.3, Design of Steel Structures, General rules. Supplementary rules for cold formed thin gauge members and sheeting, European Committee for Standardization, Brussels, Belgium 1996. Klippstein, K.H., Strength of Cold-Formed Steel Studs Exposed to Fire, Proceedings of the Fourth International Speciality Conference on Cold-Formed Steel Structures, St.Louis, Missouri, U.S.A., June 1-2, 1978. Mkelinen, P., Miller, K., Mechanical Properties of cold-rolled hot-dip zinc coated sheet steel Z32 at elevated temperatures, Helsinki University of Technology Division of Structural Engineering, Julkaisu/Report 58, Otaniemi, Espoo, Finland 1983. Mkelinen, P., Outinen, J. Results of the High-Temperature Tests on Structural Steels S235. S355. S350GD+Z and S420M, Helsinki University of Technology Laboratory of Steel Structures Report 2, Espoo, Finland 1998. Outinen, J., Material Properties of Steel and Concrete at Fire Temperatures, Seminar presentation in Malaska et al., Design of Steel-Concrete Composite Structures, Helsinki University of Technology Laboratory of Steel Structures Report , Espoo, Finland 1998. Leino, T., Salmi, P., Myllymki, J., Ohutlevyrakenteiden palonkesto, Rakenteiden analysointi tietokoneella, Ohjelmat ja menetelmt [The fire resistance of profiled thin steel sheet structures]. VTT Tiedotteita 1320, Espoo, Finland 1992 (in Finnish). Ala-Outinen, T., Myllymki, J., The local buckling of RHS members at elevated temperatures, VTT Research notes 1672, Espoo, Finland 1995. Ranby, A., Structural Fire Design of Thin Walled Steel Sections, Licenciate Thesis, Division of Steel Structures, Department of Civil and Mining Engineering, Lule University of Technology, Sweden 1999. 88 Grages, H., Simulated fire tests on walls with slotted studs, Master Thesis, Department of Structural Engineering, Royal Institute of Technology KTH, Stockholm, Sweden 1999. Uy, B., Bradford, M.A., Local Buckling of Cold Formed Steel in Composite Structural Elements at Elevated Temperatures, Journal of Constructional Steel Research 34 (1995) 53-73. Guedes Soares, C., Teixeira, A.P., Strength of plates subjected to localised heat loads, Journal of Constructional Steel Research 53 (2000) 335-358. Iso-Mustajrvi, P., Inha, T., Kantavien tersrakenteiden palosuojaus (The fire protection of loadbearing steel structures), Tersrakenneyhdistys r.y. ja Rakennustieto Oy, Helsinki, Finland 1999 (in Finnish). Guedes Soares, C., Gordo, J.M., Teixeira, A.P., Elasto-plastic behaviour of plates subjected to heat loads. Journal of Constructional Steel Research 1998; 45(2): 179-198. Outinen, J., Kaitila, O., Mkelinen, P., Tersrakenteiden palomitoituksen kehitystutkimus (A Study for the Development of the Fire Design of Steel Structures), Fifth Finnish Steel Structures R&D Days, 18-19 January 2000, Helsinki University of Technology Laboratory of Steel Structures Publications 13, Espoo, Finland 2000 (in Finnish). TRY Tersnormikortti 13/2000. Terksen materiaalimallit mitoitettaessa palosuojaamattomia tersrakenteita. (The material models of steel for the design of unprotected steel structures) TRY, Helsinki, Finland 2000 (in Finnish). Fontana, M., Fire Engineering Design of Steel Structures, Lecture notes for a short course held at Helsinki University of Technology 22-23.8.1994. HELSINKI UNIVERSITY OF TECHNOLOGY LABORATORY OF STEEL STRUCTURES PUBLICATIONS TKK-TER-2 TKK-TER-3 TKK-TER-4 TKK-TER-5 TKK-TER-6 TKK-TER-7 TKK-TER-8 TKK-TER-9 TKK-TER-10 TKK-TER-11 TKK-TER-12 TKK-TER-13 TKK-TER-14 TKK-TER-15 Mkelinen, P., Outinen, J., Results of the High-Temperature Tests on Structural Steels S235, S355, S350GD+Z and S420M, 1998. Ma, Z., Damage Evaluation and Aseismic Repair of R.S. Structures After Fire, 1998. Malaska, M., Korhonen, E., Vuolio, A., Lu, W., Outinen, J., Myllymki, J., Ma, Z., Seminar on Steel Structures: Design of Steel-Concrete Composite Structures, 1998. Tenhunen, O., Ohutlevyorsien asennustarkkuus, 1998. 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