Design of composite beams using light steel sections

DESIGN OF COMPOSITE BEAMS USING LIGHT STEEL SECTIONS AUTHOR: AIDA RODERA GARCÍA TUTOR: MIRAMBELL ARRIZABALAGA, ENRIQUE POPO-OLA, SUNDAY O. ii PROYECTO DE VIGAS MIXTAS EMPLEANDO PERFILES DE ACERO LIGERO Autor: RODERA GARCÍA, AIDA Tutor: MIRAMBELL ARRIZABALAGA, ENRIQUE POPO-OLA, SUNDAY O. RESUMEN La construcción mixta se viene empleando como un método de construcción desde hace décadas, sin embargo tradicionalmente se han utilizado secciones de acero laminado en caliente en lugar de perfiles ligeros (conformados en frío). Los principales componentes de la tradicional construcción mixta han sido las estructuras de acero laminado en caliente, las chapas de acero, los conectores y el hormigón in-situ con armadura pasiva. Las ventajas de este método de construcción son varias entre las que destacan la velocidad de la construcción gracias al rápido montaje de la estructura metálica, la economía en el uso de materiales, su resistencia última y su buen comportamiento en servicio. A estas ventajas pueden añadirse otras más si se emplean secciones de acero ligero en lugar de las tradicionales conformadas en caliente. Las mejoras que el acero ligero incorpora son básicamente su menor coste y peso debido al ahorro de material. Las estructuras de acero ligero abarcan secciones C, Z o con otras formas similares, de acero galvanizado y conformado en frío, con unos espesores entre 1.2 y 3.2 mm. Trabajos previos han estudiado el comportamiento de estas secciones actuando como vigas o columnas bajo diferentes estados de cargas, pero la presencia conjunta de este tipo de secciones y del hormigón in-situ es un campo que aún no se conoce en profundidad. En el caso particular de las vigas mixtas de acero ligero se emplean secciones doble C en lugar de perfiles I de acero laminado en caliente, pero la forma general de construcción es similar a la llevada a cabo en la construcción mixta convencional. Es importante resaltar el hecho de que no pueden ser empleados conectadores soldados debido al relativamente pequeño espesor de la sección de acero conformado en frío, y por tanto ha sido necesario desarrollar otras alternativas para los conectadores. Dichos conectadores constan de elementos de acero perfilados, fijados mediante espigas que pueden ser conducidas neumáticamente. Para conocer el comportamiento de estos conectadores se han llevado a cabo algunos ensayos que ofrecen una serie de valores de sus resistencias de cálculo. Con el objetivo de ofrecer una guía para el dimensionamiento de vigas mixtas empleando perfiles ligeros, se ha llevado a cabo un cuidadoso estudio, desarrollándose ejemplos de cálculo, los cuales se pueden adaptar con facilidad a una condiciones de proyecto determinadas, y tablas para facilitar la rápida selección de un perfil adecuado, en función de la carga, el grado de acero empleado, y la luz a salvar. Para alcanzar este objetivo global, en primer lugar se ha realizado un análisis de las formas genéricas de la construcción mixta a través de documentación existente, lo cual permite conocer las posibilidades de las losas y vigas mixtas así como las propiedades que son requeridas en los materiales involucrados. Posteriormente se ha centrado el estudio en el caso particular de la construcción mixta usando secciones de acero ligero. Una vez se conocen la resistencia de los materiales y las dimensiones de los elementos, se estudia el comportamiento de las losas mixtas y de las vigas mixtas. Empleando perfiles ligeros conformados en frío (esbeltos), debido a su pequeño espesor, hay algunas diferencias en el modo de cálculo de la resistencia de la viga mixta. Estas diferencias han sido tenidas en cuenta, y para clarificar como se ha de llevar a cabo el dimensionamiento y la verificación de una viga mixta, dos ejemplos de cálculo han sido desarrollados paso a paso. Uno muestra el caso en el que la viga carece de apoyos provisionales durante la etapa de construcción y otro en el que si los tiene. Siguiendo el mismo procedimiento de los ejemplos, se han realizado diferentes tablas para los casos de empleo de apoyos provisionales y de ausencia de los mismos, variando el grado del acero empleado y la carga variable aplicada. En las tablas resulta complejo obtener una idea general de cuales son las relaciones entre las distintas variables, por eso se presentan unos gráficos que las muestran con claridad. Estas tablas y gráficos pretenden ser útiles en la etapa de diseño facilitando al ingeniero la elección del perfil ligero adecuado en base a las cargas existentes y a la luz requerida. iii ABSTRACT Composite construction is well established for some decades as a construction method but it has traditionally used hot rolled steel sections rather than light steel (cold formed) sections. The main components of traditional composite construction have been hot rolled steel framework, steel decking, shear connectors and in-situ concrete with mesh reinforcing steel. The benefits of this construction method are several and the most important of them are speed of construction due to the rapid erection of the steel framework, economy in use of materials, robustness to damage and good performance in service. To these benefits some more can be added if light steel sections are used instead of the traditional hot rolled. The advantage that light steel gives are basically two: that cold formed steel is cheaper that hot rolled and that is also lighter in weight. Light steel framing comprises galvanized cold formed steel sections of C or Z or similar forms of 1.2 to 3.2 mm thickness. Previous works have studied how these sections behave as beams or columns under different loads cases, but the composite action of light steel sections with in-situ concrete is a field not yet fully explored. Composite light steel beams use back to back double C sections rather than hot rolled steel I beams, but the general form of construction is similar to conventional composite construction. Importantly, welded shear connectors cannot be used for the relatively thin steel used in light steel construction, and therefore it has been necessary to develop alternative forms of shear connectors using powder actuated, or pneumatically driven pins. These shear connectors use profiled strip steel elements which are fixed by pins. To know the resistance and behaviour of these innovative shear connectors some tests have been carried out determine the design resistance of these connectors. The aim of this project is to provide guidance on the design of composite beams using light steel sections, a carefully study has been carried out getting eventually design examples which illustrate the calculus method and can be adapted in a easy way to a design particular characteristic, and design tables to aid rapid selection of light steel sections, depending on the span, the loading and the steel grade used. To be able to achieve the objectives a progressive work has been carried out. First a literature review on generic forms of composite construction such as composite slabs and beams as well as the types of shear connectors was carried out. The review also types of the materials involved and their properties. With the information already available from previous studies it was possible to get deeper knowledge of the specific shear connectors and beams sections used in composite light steel construction. Once the materials resistance values and elements dimensions are known, the design of the composite slabs and composite beams was studied. However using cold formed steel sections (slender), the thin thickness of the steel, means that there are some differences in the calculation of the resistance capacity of the composite beam. These differences have been taken into account and to show how the design process of a composite beam works, two design examples have been developed step by step. One is for the case when the beam is not propped during the construction stage and the other one for when the beam is propped. Following this process design tables have been computed for the cases of propped and unpropped and using different steel grades and imposed load. With tables is quite difficult to get a general idea of which relations exist between the different variables, this is the reason why some graphs are presented which show the relations with clarity. The objective of these design tables and graphs are for use during the design stage, making it easier for engineer selection the light steel section base on loading and the span required. iv INDEX Page No. Notation 1 1. Introduction 3 1.1 Background 3 1.2 Objectives 4 2. Literature review on forms of composite constructions 5 2.1 Types of composite slabs 5 2.2 Types of composite beams 7 2.3 Types of shear connectors 8 2.3.1 Headed stud shear connector 8 2.3.2 Oscillating perfobondstrip 8 2.3.3 Continuous perfobondstrip 8 2.3.4 Waveform strips 8 2.3.5 T-shape connector 9 2.3.6 Hilti HVB shear connectors 9 2.3.7 Profiled shear connectors 9 2.3.8 Shear connectors’ strength and ductility 11 2.4 Material properties 11 2.4.1 Structural steel 11 2.4.2 Profiled steel decking 12 2.4.3 Concrete (NWC and LWC) 12 2.4.4 Reinforcement bars 13 2.4.5 Shear connectors 14 2.5 Comparison between BS 5950 and EC4 Part 1.1 14 2.5.1 Structural steel 14 2.5.2 Profiled steel decking 14 2.5.3 Concrete 14 2.5.4 Reinforcement bars 15 2.5.5 Shear connectors 15 2.5.6 Partial safety factors 15 3. Literature review on forms of composite construction using light steel sections 18 3.1 Generic forms 18 3.2 Types of light steel composite frames, floors, beams and walls 19 3.2.1 Light steel composite frames 19 3.2.2 Light steel composite floors 20 3.2.3 Light steel composite beams 21 3.2.4 Light steel composite wall 22 3.3 Types of shear connectors 22 3.3.1 Hilti HVB shear connectors 23 3.3.2 Profiled shear connectors 23 3.4 Material properties 25 3.4.1 Light steel sections 25 3.4.2 Profiled steel decking 27 v 4. Basis of design of composite slabs 29 4.1 Definition 29 4.2 Construction stage condition 29 4.3 Composite stage condition 30 4.4 Fire resistance 32 4.5 Example guide 34 5. Basis of design of composite beams 37 5.1 Construction condition 37 5.2 Effective slab width 38 5.3 Plastic analysis of composite action 38 5.4 Shear resistance 41 5.5 Shear connection (full and partial) 42 5.6 Transverse reinforcement 46 5.7 Local buckling 47 5.8 Serviceability conditions 49 5.8.1 Control of deflections 50 5.8.2 Crack control 52 5.8.3 Vibration response 52 6. Design examples 54 6.1 Unpropped beam 54 6.2 Propped beam 64 7. Load-span design tables for composite beams using light steel section and profiled shear connectors 77 7.1 Properties of light steel sections 77 7.1.1 Class classification 77 7.1.2 Shear buckling 78 7.2 Design criteria 81 7.3 Propped and unpropped beams 81 7.4 Use of design tables 86 8. Conclusions 89 9. Bibliographic references 91 10. Supplementary bibliography 92 Annex 1: Generic C sections properties 93 Annex 2: Section class classification 96 A2.1 Single generic C section class classification 97 A2.2 Composite beams cross sections class classification 98 Annex 3: Heavy cold formed steel sections 103 A3.1 Heavy cold formed sections 104 1 NOTATION EC4 Definition Aa cross-sectional area of the steel section Acv cross-sectional area of concrete per unit length in any shear plane Aε amount of the reinforcement crossing each shear plane b beams spacing b width of the steel section flange beff effective breadth of slab E elastic modulus fck characteristic strength of concrete or cylinder strength fcu cube strength of concrete fd design tensile strength of steel fsk yield strength of the reinforcement fy yield strength of structural steel fyp yield strength of the deck F action or force G permanent loads h height of the steel section hc height of concrete slab above deck profile hp deck profiled height ht slab depth I second moment of area L length of beam, beam span MRd design value of moment resistance MSd design value of applied moment n modular ratio of steel to concrete N number of shear connectors Nf number of shear connectors for full shear connection PNA plastic neutral axis PRd resistance of a shear connector Q variable loads r ratio of cross-sectional area of the steel section relative to the concrete section Rc plastic axial compressive resistance of the slab Rq longitudinal shear force transfer Rs plastic axial tensile resistance of the steel section tf thickness of the steel section flange tw thickness of the steel section web V shear force W section modulus γG partial safety factor on permanent loads γQ partial safety factor on variable loads γ partial safety factor on materials δ deflections ε √(235/fy) ρ dry density of concrete ζRd basic shear strength of concrete 2 The subscripts to the above symbols are as follows: a steel c concrete s reinforcement p steel deck pl plastic resistance of section Rd design value of resistance Sd design value of action or force The member axes in all Eurocodes are: x axis along member y major axis bending z minor axis bending 3 1. Introduction 1. INTRODUCTION 1.1 BACKGROUND Composite construction achieves important benefits by making steel and concrete work together, but these advantages can be improved if light cold formed steel sections instead of hot rolled sections are used. The advantages of the light steel composite construction are: • to get a rapid erection of the steel framework. • robustness to damage and good performance in service. • weight and cost of materials are reduced. In modern composite construction, the steel framing elements are erected first and provide a stable structure that is capable of supporting construction loads. The composite action that developed later with the concrete or other material serves to provide resistance to imposed loads, and importantly, to improve the stiffness of the construction. Often serviceability criteria dominate in modern design and therefore control of deflections and vibration response are as important as load resistance. After several years of experience on composite construction as a construction method, light steel sections have been introduced in this type of construction. The general principles of composite design using light steel sections are the following: • During construction light steel beams are designed ELASTICALLY to support the construction loads. Sometimes it is necessary to use single temporary props to control deflections at this stage. • Once the steel and concrete are acting compositely, composite light steel beams are design PLASTICALLY to support the loads acting at the ultimate limit state. It is possible to carry out plastic design because the steel section acts entirely in tension. • A minimum degree of shear connection is required. This must be compatible with the deformation capacity of the shear connectors. Light steel sections introduce some particularities in composite construction. Composite light steel beams use double C sections rather than hot rolled I, and profiled strip steel connectors fixed by powder actuated pins instead of welded shear connectors. The main objective is therefore to explore innovative composite construction technology where light steel sections act compositely with in-situ concrete. This will lead to increase speed of construction, longer spans, economy of materials and good performance in service, particularly in low and medium-rise buildings (which means buildings with no more than 6 levels). 4 1. Introduction 1.2 OBJECTIVES The purpose of this study is to find out the possibilities of light cold formed sections in composite construction to clarify in which designs can be considered and make use of all the benefits they incorporate. To achieve this final objective requires a determinate process: • Review the general forms of composite construction and the properties of the materials involved. • Review various opportunities for composite construction using light steel frames and components. • Knowledge of innovative shear connectors, based on strip steel and powder actuated pins, for use with light steel composite construction. • Definition and behaviour of a composite slab. • Design and analyse a typical light steel composite beam. • Complete work example for light steel sections composite beams propped and unpropped during construction. • Prepare design tables for light steel composite beams to be used by design engineers. 11 2. Literature review on forms of composite constructions Figure 2.11 Profiled shear connector 2.3.8 Shear connectors’ strength and ductility The results of some push-out tests on shear connector devices for steel-concrete structures are presented by Galjaard and Walraven (2001). The tests are carried out in accordance with Eurocode 4 (1997) for standard push-out tests. Large differences in ductility and strength between the various connector devices and concrete types have been observed. Table 2.1 Strength of different shear connectors Normal weight concrete Concrete grade 30/37 Light weight concrete Concrete grade 30/37 Strength PRk (kN) Ductility δuk (mm) Strength PRk (kN) Ductility δuk (mm) Headed studs 102 5.0 92 4.9 Continuous perfobondstrip 653 0.8 485 2.9 Oscillating perfobondstrip 974 1.9 858 2.7 Waveform strip 200 1.8 N/A N/A T-shape connector 633 16.1 657 38.8 Hilti HVB 28 N/A 25 N/A Profiled Strip Shear 20 > 6 N/A N/A 2.4 MATERIAL PROPERTIES 2.4.1 Structural steel In composite construction design, the two grades of steel that can be used are: S275 and S355. This nomenclature means that minimum yield strength of 275 N/mm2 and 355 N/mm2 respectively, is guaranteed. 12 2. Literature review on forms of composite constructions Table 2.2 Steel properties Nominal thickness of element, t (mm) t ≤ 40 mm 40 mm < t ≤ 100 mm Nominal steel grade fy (N/mm2) fu (N/mm2) fy (N/mm2) fu (N/mm2) S275 275 430 255 410 S355 355 510 335 490 2.4.2 Profiled steel decking The way in which the grades of steel for profiled steel sheeting or decking are specified is in terms of the yield strength of the steel. Yield strength of 280 and 350 N/mm2 are the common grades for sheet steel used (see 3.4.2). 2.4.3 Concrete (NWC and LWC) The concrete grade in Eurocode is specified in terms of the cylinder strength, fck. Hence C30 concrete means that the concrete compression strength is 30 N/mm2. If cubes were used instead of cylinders, then the resulting strength from testing (fcu) would be different. The approximate conversion to become cylinder strength to cube strength is: fck ≈ 0,8 fcu (2.1) The mean compression strength (fck and fcu), tensile strength (fct) and elastic moduli of concrete (Ec) are presented in the following table for various concrete strengths: Table 2.3 Concrete properties Strength class of concrete Properties of concrete C20 C25 C30 C35 C40 C45 C50 fck (N/mm2) 20 25 30 35 40 45 50 fcu (N/mm2) 25 30 37 45 50 55 60 fct (N/mm2) 2.2 2.6 2.9 3.2 3.5 3.8 4.1 Ec (kN/mm2) 29 30.5 32 33.5 35 36 37 For both, normal weight concrete (NWC) and light weight concrete (LWC), a concrete grade between C25 and C35 is normally chosen, in accordance with the design requirements. Light weight concrete is commonly used because of the obvious advantages of approximately 25% weight saving (dry densities: NWC density 2350 kg/m3, LWC density 1850 kg/m3), and also because LWC has better insulation qualities than NWC. 13 2. Literature review on forms of composite constructions The concrete grade is normally chosen on the following basis: - overall structural requirements - exposure conditions - flooring to be laid on the slab As a minimum standard, grade C30 should be specified. In case of concrete used as a wearing surface, the minimum grade should be C35 (although C40 is preferred). Because the concrete is only exposed on one surface of the composite floor, it can take a longer period of time to cure and dry than a traditional reinforced concrete slab. If moisture sensitive floorings or adhesives are to be applied, many months may be needed before the slab is sufficiently dry to accept them. If the time for drying allowed in the contract programme is inadequate, measures such as the specification of special ”quick dry” concrete may need to be considered. 2.4.4 Reinforcement bars The reinforcement used in composite slabs construction is usually reinforcement which takes the form of a relatively light mesh, commonly supplemented by some bar reinforcement. The mesh reinforcement is required to perform a number of different functions: • Provide bending resistance at the supports of the slab in the fire condition. • Control and reduce cracking at the supports. This cracking occurs because of flexural tension and differential shrinkage effects. • Distribute the effects of localised point loads and line loads along a greater area. • Increase the strength at the edges of openings. • Acts as transverse reinforcement to the composite beams The most common mesh sizes are A142 and A193, where the numbers indicate the cross-sectional area (mm2) of reinforcing bars per metre width. The mesh is normally manufactured in “sheets” that are 2.4 m wide and 4.8 m long. Mesh with layers of bars equally spaced in both directions is normally used. Mesh sizes less than A142 are not recommended because of their poor performance as fire reinforcement and inability to control shrinkage. But A142 is more common than A193. Sometimes bar reinforcement may be used to supplement the mesh. With the use of these supplement bars it is possible to achieve some benefits as: • To increase the fire resistance periods. • To reinforce the slab around significant openings. • When additional transverse reinforcement is needed. • To achieve better crack control. In shallow composite slabs, the reinforcement should be supported sufficiently high above the top of the deck to allow concrete placement around the bars. It is necessary to have a proper cover. In practice, for the “mild” exposure conditions that exist internally 14 2. Literature review on forms of composite constructions in most buildings, this means that the mesh should be placed ideally in a zone between 20 mm and 40 mm from the upper surface of the slab. 2.4.5 Shear connectors The properties and proportions of shear connectors used depend mainly on the thickness and shape of the steel sheet and the concrete grade used. Normally the steel used to fabric shear connectors is of 500 N/mm2 ultimate tensile strength. The characteristic resistances of the shear connector are tabulated in function of their dimensions and the characteristic strength of the concrete used. 2.5 COMPARISON BETWEEN BS5950 AND EC4 PART 1.1 There are quite differences between Eurocode (EC) 4 and British Standard (BS) 5950, not only about design equations, also about materials properties and partial safety factors. 2.5.1 Structural steel The properties of structural steels are in accordance with Eurocode 4 and BS after the EN 10025 (which replaces BS 4360 for these grades). In this case both of them agree that the two grades of steel that can be used in composite construction like structural steel are S275 and S355. Since 1993 the nomenclature for strength grades used are the same for both codes, when BS adopt the Eurocode. 2.5.2 Profiled steel decking The profiled steel sheeting or decking are classified based on the grade of the steel used. Eurocode and BS agree that the yield strength of 280 and 350 N/mm2 are the most appropriate. In BS these are known as Z28 and Z35 respectively. 2.5.3 Concrete There is a significant difference in how the concrete grade is specified in Eurocode and in BS. The concrete grade is specified in terms of the cylinder strength, fck in Eurocodes, instead of the cube strength fcu as in BS. The approximate conversion to be able to change from one of them to another one is: fck ≈ 0,8 fcu (2.2) Hence C30 concrete based on cylinder strength is 37 N/mm2 cube strength. The designation of concrete grade is therefore C30/37 defining the cylinder/cube strength. 15 2. Literature review on forms of composite constructions 2.5.4 Reinforcement bars The most common tensile grade used is 500 N/mm2. Reinforcement is normally used like mesh. Meshes of around 2.4m x 4.8m are fabric to use. The most common mesh sizes are A142 and A193, where the numbers indicate the cross-sectional area (mm2) of reinforcing bars per metre width. These values are the same in Eurocode and BS. 2.5.5 Shear connectors The dimensions and properties of the different shear connectors are defined in Eurocode and also in BS. The commonly ultimate tensile strength used in the fabrication of the connectors is 500 N/mm2. This is common in both codes, but it has to be taken into account that many forms of shear connectors are permitted and they have different resistances. 2.5.6 Partial safety factors Partial safety factors are applied to each of the materials involved in the composite construction. Also some factors are applied to the loads and they are different between the Eurocode 4 and BS. Table 2.4 Partial safety factor according to Eurocode 4 ENV 1994 (1994) (*) Limit State Partial safety factors on: Ultimate Serviceability Fire Structural steel 1.05 1.0 0.9 Concrete 1.5 1.3 1.0 Shear connectors 1.25 1.0 1.0 Shear bond 1.25 1.0 0 Materials Reinforcement 1.15 1.0 1.0 (*) Nowadays the ENV is in a changing process into the EN 16 2. Literature review on forms of composite constructions Table 2.5 Loads factors according to Eurocode 4 and BS Limit state Loads factors Ultimate Serviceability Imposed (variable) load 1.5 1.0 Eurocode 4 Dead (permanent) load 1.35 1.0 Imposed (variable) load 1.6 1.0 BS Dead (permanent) load 1.4 1.0 To illustrate the differences between both codes the following table summaries the main points where EC4 Part 1.1 has a criteria and BS5950 a different one on the design of composite beams. 17 Table 2.6 Summary of code designs of composite beams (*) Design value for 19 mm diameter headed studs (100 mm high) in Grade 25 (cylinder) normal weight concrete (**) Design value for lightweight concrete (density = 1800 kg/m3) Stress blocks Headed stud shear connector design resistance (kN) Serviceability limits Code/Method Load factors Effective breadth Steel Concrete NWC(*) LWC(**) Minimum shear connection Steel Concrete BS 5950 Part 3 1.6Q + 1.4G Span/4 but < 0.8b primary beams fy 0.57fck 80 72 0.4 for L < 10 m fy 0.5fcu Eurocode 4 1.5Q + 1.35G Span/4 0.95fy 0.57fck 73 66 0.4 for L < 5 m None None 18 3. Literature review on forms of composite construction using light steel sections 3. LITERATURE REVIEW ON FORMS OF COMPOSITE CONSTRUCTION USING LIGHT STEEL SECTIONS 3.1 GENERIC FORMS Composite construction using hot rolled steel elements has been carefully studied and is properly established. But light steel construction comprises cold formed steel sections instead of hot rolled steel sections, and there are quite big differences in their behaviours. It is important to understand the design principles and practical considerations taken into account, because if not the design of cold rolled sections may appear to be more complicated than the design of hot rolled sections. One of the most important aspects that have to be considered carefully working with these thin cold formed elements are the methods of cutting, joining and attachment of other members and materials Nowadays cold formed steel sections are widely used in building applications and decking is used in composite floors and also in flat roofs. Some of the most important advantages related with the used of cold formed elements are: • For a given section depth, a high load resistance may be achieved • Long span capability • Good dimensional accuracy • Good durability response in internal environments • Freedom for long term creep and shrinkage • Lighter constructions Composite construction using light steel frames and components has different applications: - Composite beams using double-C sections, also called back to back, with steel decking and in-situ concrete working composite due to strip shear connectors attached by powder actuated pins. - Composite frames using C and Z sections with steel decking and in-situ concrete in which the framework acts as permanent formwork. - Vertically orientated steel decking acting with in-situ concrete to form a double skin composite wall. - Heavy duty flooring acting compositely with light steel floor joists to improve the stiffness of the floor. - Heavy duty walling acting compositely with light steel wall panels to improve the diaphragm action of the wall. 19 3. Literature review on forms of composite construction using light steel sections 3.2 TYPES OF LIGHT STEEL COMPOSITE FRAMES, FLOORS, BEAMS AND WALLS 3.2.1 Light steel composite frames In different places around the world is possible to find cold-formed sections or decking used to provide the formwork to in-situ concrete frames. In France a system of slim floor construction is used in which the Z sections used as secondary beams span between the primary slim floor beams. The secondary beams dimensions might be chosen to match with the slab requirements of the construction (see Figure 3.1). A wide ribbed U section which acts compositely with in-situ concrete, has been developed in Finland by a steel company. The U section is propped during the construction stage and incorporates composite concrete-filled hollow sections with saddles on which the U section beam is supported. If additional bar reinforcement is placed, no fire protection is required, as in a common T beam (see Figure 3.2). Other different composite frame which has some disadvantages has been developed in Australia. A profiled decking is used to provide permanent formwork to the sides and soffit of deep beams and large columns. But secondary frames are required to support the decking and to resist concrete pressures, which may be considered a disadvantage (see Figure 3.3). Composite frames consisting in C and Z sections combined forming primary and secondary beams, and complete frameworks which support in-situ concrete have been developed in New Zealand and Canada. This system achieves excellent seismic resistance by confining the in-situ concrete (see Figure 3.4). Figure 3.1 Slim floor beam using composite Z sections as secondary beams Figure 3.2 Finnish system of light steel composite construction 20 3. Literature review on forms of composite construction using light steel sections Figure 3.3 Profiled sheeting used as permanent formwork to deep beams and columns Figure 3.4 Light steel framework as permanent formwork to in-situ concrete 3.2.2 Light steel composite floors In housing and in low-rise building construction is very common to use light steel floor joints. They comprise C sections which are placed 400 to 600 mm apart. Floor boarding attached to the joints improved their stiffness considerably. Layers of board, plasterboard and suspended ceilings are often used to increase the acoustic insulation of the floor. A system which provides a very stiff construction comprise profiled decking as part of a composite flooring system in which boarding is fixed by frequent pins and screws. The high stiffness of this construction improves the lateral transfer of loads across the decking (see Figure 3.5) Figure 3.5 Composite floor system 27 3. Literature review on forms of composite construction using light steel sections There are also some benefits of cold forming on material properties as the increase in average yield strength. This increase in strength is typically 3 to 10%. Geometrical properties of cold rolled sections are divided in two big groups, the gross section properties and the reduced section properties which take into account the effect of local buckling. These two different properties are used in different cases. The gross section properties are used to calculate the elastic stiffness of members or the moments in continuous structures. However reduced properties are used to calculate the load capability of the sections. Light steel section properties have been tabulated by Lawson, Chung and Popo-Ola (2002). 3.4.2 Profiled steel decking Profiled steel decking dimensions are in range of 45 to 80 mm height and 150 to 300 mm trough spacing, (rib spacing). This type of decking typically spans until 3 m or 4.5 m. There are two well known types of decking profiles, the re-entrant profile and the trapezoidal profile. These two types are the most common (see Figure 3.10 and Figure 3.11). Decking is generally rolled from 0.9 to 1.5 mm thick strip steel. Steel grades for this application are typically S280 or S350 (steel yield strengths of 280 or 350N/mm2). The steel is galvanized before forming, in the same way as light steel sections. In composite slabs the steel decking has two main structural functions: 1. During concreting, the decking supports the weight of the wet concrete and reinforcement, together with the temporary loads associated with the construction process. It is normally designed to be used without temporary propping. 2. In service, the decking acts “compositely” with the concrete to support the loads on the floor. Composite action is obtained by shear bond and mechanical interlock between the concrete and the decking. The decking has also other important functions. The decking may also be used to stabilise the beams against lateral torsional buckling during construction, and to stabilise the building as a whole by acting as a diaphragm to transfer wind loads to the walls and columns. The decking, together with the fabric mesh reinforcement placed in the top of the slab, also helps to control cracking of the concrete caused by shrinkage effects. 28 3. Literature review on forms of composite construction using light steel sections Figure 3.10 Re-entrant profiled steel decking Figure 3.11 Trapezoidal profiled steel decking 29 4. Basis of design of composite slabs 4. BASIS OF DESIGN OF COMPOSITE SLABS 4.1 DEFINITION Composite slabs construction comprises two different elements, steel decking or sheeting, and in-situ concrete. The steel decking is considered as the permanent formwork to the in-situ concrete. The most efficient use of composite slabs is for spans between 3 and 4 m, and the most common is 3m. The ability of the decking to support the construction loads, without the need for temporary propping, normally dictates these spans. If props are used, longer spans are possible. Also some of the deeper profiles can achieve spans of up to 4.5 m without propping during construction. The maximum span to depth ratio for the deck will normally be 60. The slab depths largely depend on fire insulation requirements and are usually between 100 and 200 mm. It depends on the time of fire resistant expected. To choose the concrete type it has to take into account that it affects the stiffness of the section and the strength of the shear connectors. Normal weight concrete (NWC) and light weight concrete (LWC) are both used. When the concrete has gained sufficient strength it acts as a composite slab with the tensile strength of the decking. A light mesh of reinforcement is placed in the concrete to reduce the severity of cracking and to increase the fire resistance. Support beam in-situ concrete slab reinforcement Support beam Figure 4.1 Composite slab 4.2 CONSTRUCTION STAGE CONDITION If the slab is unpropped during construction, the decking alone has to resist the selfweight and the construction loads. In this case subsequent loads are applied to the 30 4. Basis of design of composite slabs composite section. If the slab is propped during construction, all of the loads have to be resisted by the composite section. This can lead to a reduction in the imposed load that the slab can support, due to the increase of the shear in the interface between the concrete and the decking. The construction load, taken to act in addition to the self-weight of the slab and beam, for the decking design is: • An intensity of load of 1.5 kN/m2 acting over a plan area of 3m × 3m • Elsewhere, a reduced load of 0.5 kN/m2 The construction loads take account of the sequential nature of the concreting and the operations on the decking. Therefore, design cases to be considered are: 1. single span loaded to 1.5 kN/m2 plus self-weight; adjacent spans loaded to 0.5 kN/ m2 plus self-weight, or 2. single span loaded to 1.5 kN/ m2 plus self-weight; adjacent spans not loaded. Case 1 is maximum elastic moment at the supports, and 2 correspond to the maximum elastic moment in mid-span. The design of continuous decking is based on an elastic distribution of moments for the construction loads. The elastic moment resistance of the section is established taking account of the effective breadth of the thin steel elements in compression. No moment redistribution is allowed and the common critical conditions would be the negative moment at the supports. 4.3 COMPOSITE STAGE CONDITION The most common mode of failure of the composite slab is due to the breakdown of shear bond. The ultimate moment resistance of composite slabs is determined by the breakdown of bond and mechanical interlock between the decking and the concrete, known as shear bond. Composite slabs are usually designed as simply supported members, and the slip between the decking and the concrete usually occurs before the plastic moment resistance of the composite section is reached. Eurocode 4 permits the design of composite slabs as continuous slabs by placing reinforcement in the negative moment region. There are two methods of design of composite slabs permitted by Eurocode 4. The traditionally used which is called “m” and “k” method, and an alternative method based on the principles of partial shear connection. The performance of a particular deck profiled in a composite slab can only be well assessed by test. Design by testing consists of two main parts with different purposes. 31 4. Basis of design of composite slabs The test is carried out in two states: • A dynamic part to identify those cases where there is an inherently brittle bond between the concrete and the steel. (10,000 load cycles up to 1.5 times the working load). • Following the dynamic part, a static load is applied and increased until failure occurs. The test results are then presented in terms of empirical constants (m and k) that can be used to quantify the interaction between the steel and concrete. The constants, m and k, are not normally provided by the decking manufacturers, they use this information themselves to present to the designers a range of load-span tables for their specific products. For the alternative method in the EC4, tests are required too. A characteristic longitudinal shear resistance is defined based on tests. Then this resistance is used in a modified partial shear connection analysis. The design for serviceability is based on deflection limits but no deflection limits are specified in Eurocode 4 for the deflection of the deck after concreting. As a further check, it is recommended that the increased weight of concrete due to ponding should be included in the design of the support structure if the predicted deflection, without including the effect of ponding, is greater than one tenth of the overall slab depth. The use of simple design rules to ensure adequate deflection behaviour of a composite slab is accepted practice. Limits for span-to-depth ratios for slabs using NWC and LWC are given. Confirming that the slab satisfies these limits will ensure that excessive deflections are avoided. The effective span of the decking is defined as the smaller of: • The distance between the centres of the supports. • The clear span between the supports plus the effective depth of the concrete slab. The values in the table 4.1 apply to slabs under uniformly distributed loading, with nominal continuity reinforcement (0.1%) over the intermediate supports, and not for slabs with full continuity reinforcement over the supports. Deflections should be calculated explicitly for slabs that fail to satisfy span-to-depth ratio limits. The stiffness of the slab can be determined using normal reinforced concrete design rules (assuming fully effective bond between the decking and the concrete). 32 4. Basis of design of composite slabs Table 4.1 General rules for the slab: maximum span-to-depth ratios(*) NWC LWC Single spans 30 25 End spans 35 30 Internal spans 38 33 (*)Values apply to supported spans with nominal continuity reinforcement, subject to uniformly distributed loading. There is always a risk of cracking in the concrete in all composite slabs. This is due to the restraint to drying shrinkage provided by the steel decking and primary steelwork, even though the decking effectively acts as reinforcement and helps to distribute the shrinkage strains so that large cracks do not form. However, cracks do not normally mean a durability or serviceability hazard. Only when the surface of the slab is used as a wearing surface, or where terrazzo or other “rigid” floor covering are to be used, may specific reinforcement be required in order to control the cracking. When cracking is an issue, reinforcement percentages in excess of 0.3% will normally be required in order to limit crack widths to the typically specified limit of approximately 0.3 mm. In composite slabs mesh, rather than bars, is generally used to control cracking. The greatest risk of cracking is normally over supporting beams, owing to the combination of drying shrinkage and flexural action. Induced joints may be used to reduce the risk of random cracking at these locations. With the induced joints it is possible to control where the crack will be form. It is possible that larger crack widths over the intermediate supports will occur with propped construction, because the full self-weight of the slab is applied in the composite slab on removal of the props. Reinforcement of 0.5% of the slab cross-sectional area should be sufficient in these cases to control cracking. 4.4 FIRE RESISTANCE The measure to improve the fire resistance is to increase the reinforcement. To satisfy requirements for the fire condition, an increased size of mesh may need to be used, or extra bars may need to be placed in the troughs of the deck. In either case, the additional reinforcement is used to compensate for the loss of strength of the decking at elevated temperatures. A design guidance covering this aspect is normally given by the decking manufacturers in their design tables. However, established guidance on minimum slab thicknesses, minimum decking thickness, and the corresponding mesh sizes, for particular fire resistance periods is given in the following tables for trapezoidal decking and for re-entrant decking. The data in table 4.2 may be used directly for trapezoidal decking profiles of 45 to 60 mm nominal depth (hp is the differential height between the thin and the most depth 33 4. Basis of design of composite slabs parts of the decking). For decking profiles greater than 60 mm deep, slab depths given in the table should be increased by (hp – 60) mm. For decking profiles that are between 45 and 55 mm deep, when spans are not greater than 3 m, the specified minimum slab depths may be reduced by (55 – hp) mm. Figure 4.2 Composite slab cross section Table 4.2 Fire resistance specifications for trapezoidal decking Minimum dimensions Slab thickness ht (mm) Maximum Span (m) Fire resistance (hours) Deck thickness t (mm) NWC LWC Mesh Size 2.7 1 0.8 130 120 A142 3.0 1 0.9 130 120 A142 3.0 1 1/2 0.9 140 130 A142 3.0 2 0.9 155 140 A193 3.6 1 1.0 130 120 A193 3.6 1 1/2 1.2 140 130 A193 3.6 2 1.2 155 140 A252 The data in table 4.3 applies to re-entrant decking profiles of 38 to 50 mm nominal depth. For profiles greater than 50 mm deep, the specified minimum slab depth should be increased by (hp – 50) mm. Table 4.3 Fire resistance specification for re-entrant decking Minimum dimensions Slab thickness ht (mm) Maximum Span (m) Fire resistance (hours) Deck thickness t (mm) NWC LWC Mesh Size 2.5 1 0.8 100 100 A142 2.5 1 1/2 0.8 110 105 A142 3.0 1 0.9 120 110 A142 3.0 1 1/2 0.9 130 120 A142 3.0 2 0.9 140 130 A193 3.6 1 1.0 125 120 A193 3.6 1 1/2 1.2 135 125 A193 3.6 2 1.2 145 130 A252 34 4. Basis of design of composite slabs 4.5 EXAMPLE GUIDE In composite slabs there are three possible modes of behaviour based on the level of interaction between the concrete and the steel decking: — Complete interaction — Partial interaction — Zero interaction And there are also three likely collapse mechanisms depending on the characteristics of the slab: • Failure type 1: applied moment exceeds moment resistance. • Failure type 2: ultimate load resistance is governed by the steel concrete interface. • Failure type 3: applied vertical shear exceeds shear resistance. EXERCICE 1. Check metal deck during construction Consider the self-weight of the deck and the wet concrete, and these loads have to be over all the deck. Consider the construction loads and distribute them to have the more unfavourable situation for both, maximum sagging bending moment, and maximum hogging bending moment (positive and negative moments). They have to be less than the moment resistance of the deck, Mp.Rd+ and Mp.Rd-. 2. Check deck deflection in construction eff IE Lpk × ××××= 1 384 54 δ (4.1) k=1.0 for simply supported decking k=0.41 with two equal spans (3 supports) k=0.52 with three equal spans k=0.49 with four equal spans Ieff is the second moment of area of the effective section Limit: L/180 or 20 mm (4.2) 3. Check design of composite slab – at ULS Assume that slab acts as a series of simply supported beams. The moment resistance of the slab has to be greater than the applied moment. 35 4. Basis of design of composite slabs Design bending moment: [ ] 8 2 LQG MQG Sd ××+× = γγ (4.3) Position of plastic neutral axis: X c ck ap ypp fB fA X γ γ ×× × =85.0 (4.4) where p A is the area of the deck (mm2/m) B width took as 1000 mm yp fis the tensile strength of the deck 10.1= ap γ is the partial safety factor of the deck Xdz p × −= 5.0 (4.5) where p dis the total depth of the slab without half of the deck height plus the deck thickness. Moment resistance of the slab: z f AM ap yp pRdps ××= γ , (4.6) 4. Check longitudinal shear (m-k method) Design shear force: [ ] 2 LQG VQG sd × × + × = γ γ (4.7) Longitudinal resistance is: vss p pRdL k LB A mdBv γ 1 ,×        + × ×××= (4.8) The m-k method is semi-empirical. Direct relationship is established with the longitudinal shear load capacity of the sheeting. Ls depend on the type of loading. Uniform load applied to the entire span L simply supported beam, Ls = L/4 25.1 = vs γ is the partial safety factor of longitudinal shear 36 4. Basis of design of composite slabs 5. Check vertical shear Design shear force: [ ] 2 LQG VQG sd × × + × = γ γ (4.9) Vertical shear resistance is: RdpoRdv kkdbV τ ××××= 21. (4.10) where bo is the average concrete rib width (over 1 m) p dk −= 6.1 1 (4.11) ρ ×+= 402.1 2 k (4.12) po p db A × = ρ (4.13) c ck Rd f γ τ 25.0= (4.14) 6. Serviceability limit state Calculate the deflections with the average second moment of composite slab. Deflections would not be design criteria for slabs that satisfy span-to-depth ratio limits. 43 5. Basis of design of composite beams 0,112,0 ≤      += d h α takes into account the height and diameter of the stud γv = 1,25 is the partial safety factor at the ultimate limit state These formulae apply for stud diameters smaller than 22 mm. Degree of shear connection In the plastic design of composite beams, the longitudinal shear force to be transferred between the points of zero and maximum moment should be the smaller of Rc or Rs. If so, full shear connection is provided. If less shear connectors than the number required for full shear connection are provided it is not possible to develop the full plastic moment resistance of the composite section. In this case the degree of shear connection may be defined as: s q fR R N N= for Rs < Rc (5.25) c q fR R N N= for Rc < Rs (5.26) where Rq is the total shear force transferred by the shear connectors between the points of zero and maximum moment Nf is the number of shear connectors for full shear connection N is the number of shear connectors provided over the relevant part of the span. Moment resistance of a composite section with partial shear connection When Rq, resistance of shear connection, is less than both Rc and Rs there is no full shear connection and the moment resistance is reduced. paq QNR ×= (5.27) There are two different methods to determining the reduced moment resistance: 1. “Linear-interaction” approach () RdaplRdpl f RdaplRd MM N N MM ,,, −+= (5.28) where Mpl,Rd is the moment resistance of the composite section for full shear connection Mapl,Rd is the moment resistance of the steel section 44 5. Basis of design of composite beams An adequate design is that which satisfies MSd ≤ MRd. This check may be repeated at point load positions by redefining N as the number of shear connectors from the support to the point considered. 2. Stress block method This method is exact in that the equilibrium of the section is solved by equating the force in the concrete to the force transferred by the shear connectors Rq. No design formulae are given in Eurocode 4. The stress block method leads to significantly higher moment resistance than the linear interaction method for degrees of shear connection between 0.4 and 0.7. a) Plastic neutral axis in flange of steel beam: Rq ≥ Rw () ( ) y qs c q pcqsc Bp RR R R hhR h RM 42 1 2 2 − −        −++= (5.29) That is the same as: () ( ) y qs f pcc f sc Bp RR N N hhR N Nh RM 4 5,01 2 2 − −        −++= (5.30) b) Plastic neutral axis within the web: Rq < Rw 1) Web Class 1 or Class 2 ε 76≤ w t d or vqw RRt d − ≤1 76 ε (5.31) () 42 1 2 2 , d R R R R hh h RMM v q c q pcqRdaplc −                  −+++= (5.32) That is the same as: () 4 5,01 2 2 2 , d R R N N N N hh h R N N MM v c ff pcc f Rdaplc         −                  −+++= (5.33) 2) vqw RRt d − >1 76 ε (5.34) () ( )( ) 4 2 2 1 2 2 , d R RRRRRR R R hh h RMM v oqvqvq c q pcqRdaplc −−−+ −                  −+++= (5.35) 45 5. Basis of design of composite beams where Mc is the reduced moment resistance d is the clear depth of the steel web tw is the thickness of the steel web ε = (275/py)0,5 ywv ptdR × × = is the resistance of clear web depth yo ptR w×××= 2 38 ε is the resistance of slender web Minimum degree of shear connection A minimum degree of shear connection limit is introduced in order to ensure adequate deformation capacity of the shear connectors. In principle, the use of stress-block method imposes greater deformations on the shear connectors at failure and therefore, any general limit is conservative for the linear interaction method. The general limits on the degree of shear connection for a composite slab (with bo/hp ≥ 2 and hp ≤ 60mm): L ≤ 25 m N/Nf ≥ 1-(355/fy ) (1-0,04 Le) ≥ 0,4 L > 25 m N/Nf ≥ 1.0 L is the beam span Influence of deck shape The deck shape influence on the strength of shear connectors. Strength reduction factor kt for shear connectors is calculated with the following equation: ( ) p p p r th hh h b N k − ××= 0 7,0 (5.36) with kt ≤ 1.0 for Nr = 1 kt ≤ 0.8 for Nr = 2 where Nr is the number of studs per trough (Nr < 3) b0 is the average trough width h is the stud height This formula applies to the strength of the shear connectors when the steel decking crosses the beams and where the shear connectors project at least 35 mm above the top of the decking. A further limit is that h < hp + 75 mm in evaluating kt. 46 5. Basis of design of composite beams The coefficient 0.7 has been established on basis of test evidence. It is a reduction from the coefficient 0.85 used in previous guidance. It is also recognised that the formula may be unconservative for shear connectors in pairs and therefore the upper limit on kt is 0.8. For primary beams, where the decking is placed parallel to the beams, the constant in the above equation is reduced from 0.7 to 0.6. However, no further reduction is made for the number of shear connectors in this case and the limit on kt is 1.0 for Nr =1 or 2. 5.6 TRANSVERSE REINFORCEMENT The longitudinal shear strength of the concrete slab should be checked in order to ensure transfer of force from shear connectors into the slab without splitting the concrete. This may require provision of transverse reinforcement perpendicular to the beam. Potential shear planes through the slab lie on either side of the shear connectors. The shear resistance per unit length of shear plane along the beam is: νRd = 2.5Acv η τRd + Ae fsk /γs ≤ 0.2 Acv η fck /γc (5.37) where Acv is the cross-section area of concrete per unit length in any shear plane τRd is the basic shear strength of concrete (see table 5.1) Ae is the amount of the reinforcement crossing each shear plane fsk is the yield strength of the reinforcement η is taken as 1,0 for normal weight concrete and 0.3+0.7(ρ/2400) for lightweight concrete. Table 5.1 Basic shear strength of concrete (ENV 1994 (1994)) Strength class of concrete C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 fck (N/mm2) 20 25 30 35 40 45 50 τRd (N/mm2) 0.26 0.30 0.34 0.38 0.42 0.46 0.50 A component arising from the tensile strength of the deck may be added to the longitudinal shear resistance. Its full strength can be used when the deck crosses the beam (secondary beams), and is continuous. When the deck is discontinuous, the anchorage force developed by the shear connectors may be included, provided both ends of the deck are properly attached. The anchorage force per unit length of the beam is given as: 47 5. Basis of design of composite beams ( ) ap yps r pd fdt s N γ ν 4 = (5.38) where Nr is the number of shear connectors in each group on the beam flange d is the stud diameter ts is the sheet thickness fyp is the design strength of the sheet steel used to form the profile decking s is the shear connecting spacing The coefficient 4 should be replaced by (1+ a /(1.1d)) where "a" is the distance of the edge of the sheet from the centre of the stud. This approach is very conservative and full end anchorage is achieved when the edge distance, a, exceeds 2d. In practice the edge distance should exceed 40 mm. The total longitudinal shear resistance, for an internal beam, per unit length of the beam is determined by shear failure along two shear planes and is therefore equal to 2(νRd + νpd). Where the decking is not properly anchored or where longitudinal sheet overlaps are close to the beam, the contribution of the decking should be neglected. 5.7 LOCAL BUCKLING In the ultimate limit state analysis of composite beams, it is important to consider the possibility of local buckling. This is done by defining the class of cross-section. As the plate elements in structural sections are relatively thin compared with their width, when loaded in compression (as a result of axial loads applied to the whole section and/or from bending) they may buckle locally. The disposition of any plate element within the cross section to buckle may limit the axial load carrying capacity, or the bending resistance of the section. Avoidance of premature failure arising from the effects of local buckling may be achieved by limiting the width-to-thickness ratio for individual elements within the cross section. This is the basis of the section classification approach. The composite beam section classification is based on an effective width of slab acting together with the steel beam. Properties of each section class: Class 1 and 2: capable of developing the full plastic bending moment. Class 1 sections can also rotate after formation of a plastic hinge, but this is not important for simply supported beams. Class 3: because of local buckling in the part of the steel section under compression, full plastic moment resistance cannot be achieved, although stresses in the extreme fibres of the steel section can reach yield. Class 4: local buckling occurs before yield is reached in the extreme fibres. 48 5. Basis of design of composite beams Classification of composite section: Compression flange: For simply supported beams the compression flange is the top flange, and it is restrained from buckling by the concrete slab to which it is attached by shear connectors. Flange buckling is assumed to be prevented, and the flange may be defined as Class 1. Web: If the plastic neutral axis (PNA) lies in the concrete slab or the upper flange of the section, the composite section can be considered as Class 1 since the web is in tension throughout. When the PNA is in the web, the slenderness of the web should be checked to determine the classification of the web, and hence the classification of the crosssection. But this condition is not common in simply supported beams. Therefore in composite beams, to know if it is possible that local buckling occurs or not, it is necessary to analysis where the PNA lies. The plastic axial resistance of the steel beam, in tension, is represented by Rs and of the concrete slab, in compression, by Rc: a ya s fA R γ × = (5.39) ceff c ck chb f R××= γ 85,0 (5.40) where a γ =1.05 c γ =1.5 a A is the area of the steel beam eff bis the effective width of the slab The concrete in the ribs is ignored so the maximum depth of concrete in compression is limited to the thickness of the slab above the profiles hc. Considering the longitudinal equilibrium of the composite section it can be seen that the PNA is located in the thickness hc of the concrete of the slab if Rc > Rs. 49 0,85 f ck / γ c (compression) Rc Rs yp P.N.A. h/ 2 h/ 2 f / γ ya b eff + (tension) h c h p h 5. Basis of design of composite beams Figure 5.5 Plastic distribution of the normal stresses (example of plastic neutral axis in the slab). The depth of the plastic neutral axis yp measured from the upper surface of the concrete slab is given by: c c s ph R R y×= (5.41) If cp hy <, the PNA lies within the concrete slab and the composite section is classified as Class 1, so it is capable of developing the full plastic bending moment, and the local buckling is not considered in the design of the composite beam. 5.8 SERVICEABILITY CONDITIONS Serviceability limit states concerns three different aspects: a) Control of deflections b) Cracking control c) Vibration response It is common to base assessments at the limit state study on elastic behaviour. To do not be necessary to take considerations of post-elastic effects, limits are usually placed on the stresses existing in beams at the serviceability limit state. However no stress limits are given in Eurocode 4, because it is argued that: • Slight yielding in the positive moment region has a limited effect on deflections • The beneficial effects of continuity on deflection are ignored. Deflection limits are not specified in Eurocode 4 and reference is made to Eurocode 3 for limits on deflections due to permanent and variable loads. Nowadays there are no limits on deflections in Eurocode 4 and either in Eurocode 3. 50 5. Basis of design of composite beams 5.8.1 Control of deflections Deflections are calculated using the second moment of area of the composite section based on elastic properties. So first of all the second moment of area has to be calculated. Under positive moment the concrete may be assumed to be uncracked. To calculate the second moment of area, the composite section is considered as a transformed steel section. The second moment of area of the composite section, expressed as a transformed steel section, is: () () ay ceffpca cI n hb nr hhhA I++ + ++ =1214 23 2 (5.42) where n is the ratio of the elastic moduli of steel to concrete, taking into account the creep of the concrete when it is relevant r is the ratio of the cross-sectional area of the steel section relative to the concrete section Iay is the second moment of area of the steel section The common value of the ratio Ic/Iay is in the range of 2.5 to 4.0. These values indicate that one of the main benefits we can get with the composite action is in terms of reduction of deflections. Table 5.2 Deflection limits (ENV 1993-1-1 (1993)) Conditions δmax (sagging in the final state) δQ (due to variable loading) Roofs generally L/200 L/250 Roofs frequently carrying personnel other than for maintenance L/250 L/300 Floors generally L/250 L/300 Floors and roofs supporting brittle finish or nonflexible partitions L/250 L/350 Floors supporting columns L/400 L/350 The modular ratio, n, represents the ratio of the elastic modulus of steel to the timedependent modulus of concrete. For normal weight concrete the typically modular ratios that may be used are 6.5 for short term (variable) loading, and 20 for long term (permanent) loading in an internal environment. The values of secant elastic modulus of concrete under short term loads are given in table 5.3. The elastic modulus under long term loads is affected by creep, which causes a reduction in the stiffness of the concrete. 51 5. Basis of design of composite beams Table 5.3 Secant elastic modulus of concrete Strength Class of Concrete 20/25 25/30 30/37 35/45 40/50 45/55 50/60 Ecm (kN/mm2) 29 30,5 32 33,5 35 36 37 Influence on deflections of partial shear connection This effect is very important because deflections increase due to the effect of slip in the shear connectors. However these effects are ignored in composite beams designed for full shear connection. For cases of partial shear connection using shear connectors, the deflection, δ, is increased according to:        −×        −×+= 111 c a fc N N C δ δ δ δ (5.43) where N/Nf is the degree of shear connection δc is the deflection of the composite beam with full shear connection δa is the deflection of the steel beam under the same loads C is a coefficient, taken as 0.3 for unpropped construction and 0.5 for propped construction. This coefficient, C, is different for unpropped and propped construction due to the higher force in the shear connectors at serviceability state in propped construction than in unpropped construction. In Eurocode 4 no account of slip is taken in umpropped beams when N/Nf ≥ 0.5 because it is argued that deflections are already conservative. Shrinkage induced deflections Deflections produced by shrinkage are considered only in some specific cases. Eurocode 4 is ambiguous about deflections arising from shrinkage of the concrete slab. It states that shrinkage deflections need only be calculated for simply supported beams when span to depth ratio of the beam exceeds 20, and when the free shrinkage strain of the concrete exceeds 400 x 10-6. In practice, these deflections will only be significant for spans greater than 12 m in exceptionally warm dry atmospheres. The curvature, Ks, due to a free shrinkage strain, εs, is: ( ) () c apcs sInr Ahhh + ++ =12 2 ε ϕ (5.44) 52 5. Basis of design of composite beams where n is the modular ratio appropriate for shrinkage calculations, n ≈ 20. The deflection due to this curvature for simple supported beams is: δs = 0.125 ks L2 (5.45) This formula to calculate the deflection due to shrinkage ignores continuity effects at the supports; hence it probably over-estimates shrinkage deflections by a considerable margin. 5.8.2 Crack control Crack control is not always necessary, only where the proper functioning of the structure or its aesthetic aspects, appearance, would be impaired. Where it is necessary to control cracking, the amount of reinforcement should exceed a minimum value. Due to this extra reinforcement cracks are distributed uniformly in the negative moment region. This minimum percentage of reinforcement, ρ, is given by: %100%100 ×××=×= s ct c c Sf kk A A σ ρ (5.46) where kc is a coefficient due to the bending stress distribution in the section with a value between 0.4 and 0.9. k is a coefficient accounting for the decrease in tension strength (k ≈ 0.8). fct is the effective tensile strength of concrete. A value of 3 N/mm2 is the minimum adopted. σs is the maximum permitted stress in the reinforcement. A typical value of ρ is 0.4% to 0.6% which is well in excess of the minimum of 0.2% necessary for shrinkage control and transverse load distribution. These bars do not need to be placed along the entire beam, only in the negative moment region of the beams or slabs. 5.8.3 Vibration response Potential vibration response may be necessary to be check especially for long span beams. Natural frequency of a beam is: sw f δ 18 = cycles/sec (5.47) where δsw is the instantaneous deflection (in mm) caused by the self weight of the floor and other permanent loads on to the composite beam. 59 6. Design examples 5. Degree of shear connection: There is a minimum degree of shear connection which for beams with a span equal or less than 5 m is 0.4. 449.0 4813.288 6.129 === s q fR R N N > 0.4 The degree of shear connection cannot be higher than 1 and less than a minimum equal to 0.4. 4.0449.01 >> 6. Moment resistance with partial shear connection: Using the linear interaction method, the moment resistance of a composite beam is obtained as follows: () RdaRdpl f RdaRd MM N N MM ... −×+= where 24.17 .=×= dxxRda fWM kNm = f N N Degree of shear connection = Rdpl M. Moment resistance based on full shear connection () 3254.3824.171750.64449.024.17 = −×+= Rd M kNm 6920.303254.38 =>= SdRd MM kNm Increase in moment resistance due to composite action: 223.2 24.17 3254.38 . == Rda Rd M M 7. Vertical shear: Beam + slab = 2.71 x 1.35 x 4.5 x 1.5 / 2 = 12.3474kN Ceiling + services = 0.5 x 1.35 x 4.5 x 1.5 / 2 = 2.2781 kN Imposed load = 2.5 x 1.5 x 4.5 x 1.5 / 2 = 12.6563 kN Total shear force: Sd V = 27.2818 kN 60 6. Design examples Shear resistance: Vpl,Rd 3 . d vRdpl f AV ×= where wv htA = 45826.98534 3 267 2.3200 .=××= Rdpl V N 5344.98 .= Rdpl V kN 2818.27= Sd V kN ≤ 5344.98 .= Rdpl V kN 267.495.0 .=× Rdpl V kN > 2818.27= Sd V KN (there is no interaction bending momentshear force) 8. Shear buckling resistance: Shear buckling resistance must be checked if the web slenderness (d/tw) exceeds 69ε: w t d> 69ε where dis the height of the web w t is the thickness of the web ε280 235235 == y f 8.1966.122002 =× − =×−= f thd mm 2.36.12 =×= w tmm 5.61 2.3 8.196 = 69ε = 63.2 61.5 < 63.2 → therefore the possibility of buckling in shear is not necessary to be checked. 61 6. Design examples Serviceability limit stage 1. Elastic stress In Eurocode 4, ENV 1994 (1994), no stress checks are required for normal conditions, so no stress limits are given. 2. Deflections • Non-composite stage deflection: δ Self weight of slab and beam = 2.71 kN/mm2 Design load F = 2.71 x 4.5 x 1.5 = 18.2925 kN a E= 205 kN/mm2 xxa IE FL 384 53 = δ () 3802.16 104.646205384 105.418.29255 4 3 3 = ××× ××× = δ mm • Composite stage deflection: δc Imposed load = 2.5 kN/mm2 Design Load F = 2.5 x 4.5 x 1.5 = 16.875 kN () () xx ceffcpa cI n hb nr hhhA I+ × + + ++ =1214 23 2 01202006.0 801125 1082.10 2 = × × = × = ceff a hb A r n = Modular ratio = 10, for normal weight concrete () () 5.46126288104.646 1012 801125 01202006.01014 805022001082.10 4 3 2 2 =×+ × × + ×+× +×+×× = c I mm4 7 1061262885.4 ×= c I mm4 62 6. Design examples Deflection with full shear connection ca cIE FL 384 53 = δ ( ) 1175.2 1061262885.4205384 105.4875.165 7 3 3 = ××× ××× = c δ mm As partial shear connection exists, the effect of slip has to be taken into account:      −×        −+= 113.01 c a fc N N δ δ δ δ 1109.15 104.646 1061266505.41175.2 4 7 = × ×× = × = xx cc aI I δ δ mm () 2643.41 1175.2 1100.15 449.013.011175.2 =           −×−+×= δ mm 4.2643 ≈ 1055 L < 350 L The deflection due to imposed load is satisfactory • Total deflection: Construction stage = 16.3802 mm Imposed load = 4.2643 mm Ceiling + services ≈ 8529.0 5.2 2643.45.0 = × mm Total = 21.4973 mm The limit on the maximum total deflection for a composite beam is the following: 5.22 200 4500 200 == Lmm > total deflection = 21.4973 mm The total deflection is also satisfactory. 3. Transverse reinforcement The resistance of concrete flange to splitting will be check, using A142 mesh reinforcement in the slab. 63 6. Design examples • Shear resistance per shear surface, Rd v c ck cv s ske RdcvRd f A fA Av γ η γ ητ 2.05.2 ≤+= e A = 142 mm2/m η = 1 for normal weight concrete cv A= 105 x 103 mm2/m ck f= 30 N/mm2 sk f= 460 N/mm2 5.1 8.1 25.025.0 05.0 ×=×= c ctk Rd f γ τ = 0.3 c γ = 1.5 s γ = 1.15 55.13510 15.1 460142 3.01101055.2 33 =×      × +××××= − Rd v kN/m 42010 5.1 301 101052.02.0 33 =×      × ×××= − c ck vc f A γ η kN/m > 135.55 kN/m • Shear force per unit length, v Placing the top-hat connectors in the way there are four studs per trough: 96 3.0 5.06.57 = × = Sd v kN/m < Rd ν = 135.55 kN/m A142 mesh is satisfactory 4. Vibration (Simplified approach) Loading: Beam + slab = 2.71 kN/m2 Ceiling + services = 0.50 kN/m2 10% of imposed load = 0.25 kN/m2 Total = 3.46 kN/m2 Total weight of floor, F = 3.46 x 4.5 x 1.5 = 23.355 kN 64 6. Design examples Increase of second moment of area of the composite section based on elastic properties c I, by 10% to allow for the increased dynamic stiffness of the composite beam, 1c I 77 11007389174.51061262885.41.1 ×=××= c I mm4 Instantaneous deflection caused by re-application of the self weight of the floor and the beam to the composite beam, a δ 1 3 384 5 ca aIE LF ×× ×× = δ () 6642.2 1007389174.5205384 105.4355.235 7 3 3 = ××× ××× = a δ mm Natural frequency ≈ 0279.11 6642.2 1818 == a δ Hz > 4 Hz 5. Conclusion The design is limited basically by the moment resistance of the beam in the construction stage rather than serviceability criteria. The maximum span of the secondary beams that is possible to consider in the design is limited by moment resistance at the construction stage, if the span would be increased the beam would fail before the composite behaviour. 6.2 DESIGN EXAMPLE OF A 4.5 m SPAN BEAM, PROPPED DURING CONSTRUCTION The main differences on the design of a composite beam propped during construction are the following: • The beam functions exclusively as composite • Deflections: Sum of: - Dead loads on composite section - Imposed loads on composite section Using props during construction sometimes it is possible to get a greater span, but not in all cases, it depends on the imposed loads because all of the loads have to be resisted by the composite section. 65 6. Design examples Design data Imposed load: Imposed load 2.5 kN/m2 Floor dimensions: Span L = 4.5 m Beam spacing b = 1.5 m Slab depth ht = 130 mm Depth above profile hc = 80 mm Deck profiled height hp = 50 mm Beam propped during construction. Props are placed in the middle of the span. Shear connectors: Top-hat shear connectors attached with 4 studs to the beam. Materials: Steel: Grade S280 Nominal value of yield strength y f= 280 N/mm2 Partial safety factor a γ = 1.05 Design strength 267 05.1 280 === a y d f f γ N/mm2 Concrete: Normal weight concrete strength class C30/37 Density = 2400 Kg/m3 (23.55 kN/m3) 66 6. Design examples Loading: Self weight of the concrete slab Weight = = () 6 993 3 31047275.2 10 55.23 150 10 55.23 10 1 300 10 301205010130 − ×=×=××      ×+−× kN/mm2 Weight = 2.47275 kN/m2 Construction Stage: Concrete slab = 2.47 kN/m2 Steel deck = 0.15 kN/m2 Reinforcement (allow) = 0.04 kN/m2 Steel beam (allow) = 0.05 kN/m2 Total = 2.71 kN/m2 Construction Load = 0.50 kN/m2 Composite Stage: Concrete slab = 2.47 kN/m2 Steel deck = 0.15 kN/m2 Reinforcement (allow) = 0.04 kN/m2 Steel beam (allow) = 0.05kN/m2 Total = 2.71 kN/m2 Ceiling and services = 0.50 kN/m2 Imposed: Total imposed load = 2.5 kN/m2 Initial selection of beam size The response of a DOUBLE GENERIC C SECTION is going to be studied. A suitable section for imposed load of 2.5 kN/m2 would be a 200 x 65 x 1.6 Grade S280 Section properties and dimensions: 200=h mm 130652 =×=b mm 67 6. Design examples 2.36.12 =×= w t mm 6.1= f t mm 82.10= a A cm2 646.4= xx I cm4 64.65= xx W cm3 Nominal value of yield strength 280 = y f N/mm2 ( f t< 40 mm) Construction stage design During the construction stage the span of the beam is half of the final span, due to the prop placed in the middle span. Ultimate limit stage loading Dead load factor 35.1= G γ Imposed load factor 5.1= Q γ Slab + beam = 2.71 x 1.35 = 3.6585 kN/m2 Construction = 0.50 x 1.5 = 0.75 kN/m2 Total = 4.4085 kN/m2 Total design load = F = 4.4085x 2 5.4 x 1.5 = 14.8787 kN Design moment = 4.1846 8 2 5.4 8787.14 = × = sd M kNm It is assumed that the beam in the construction stage is laterally restrained by the decking since the decking spans perpendicular to the beam and is directly attached to it. Moment resistance of the steel beam = Rda M. 24.17 10 26765.64 3 .= × =×= dxxRda fWM kNm > 4.1846 kNm Composite stage design In the composite stage the props have been removed and the beam span is 4.5 m. 68 6. Design examples Ultimate limit stage loading Slab + beam = 2.71x 1.35 = 3.6585 kN/m2 Ceiling + services = 0.50 x 1.35 = 0.675 kN/m2 Imposed load = 2.5 x 1.5 = 3.75 kN/m2 Total = 8.0835kN/m2 Total design load = F = 8.0835 x 4.5 x 1.5 = 54.5636 kN Design moment = 6920.30 8 5.4 54.5636 = × = sd M kNm Effective width of compression flange: beff 125.1 8 5.42 8 2= × = × =o eff l b m 1. Compressive resistance of slab: Rc ceff c ck chb f R××= γ 85,0 where ck f is the characteristic strength of concrete = 30 N/mm2 c γ is the partial safety factor for concrete = 1.5 1530 10 80 1125 5.1 3085.0 3=×× × = c R kN 2. Tensile resistance of steel section: Rs das fAR ×= 4813.288 10 10 26782.10 3 2 =××= s R kN 75 6. Design examples 55.13510 15.1 460142 3.01101055.2 33 =×      × +××××= − Rd v kN/m 42010 5.1 301 101052.02.0 33 =×      × ×××= − c ck vc f A γ η kN/m > 135.55 kN/m • Shear force per unit length, v Placing the top-hat connectors in the way there are four studs per trough: 96 3.0 5.06.57 = × = Sd v kN/m < = Rd ν 135.55 kN/m A142 mesh is satisfactory 4. Vibration (Simplified approach) Loading: Beam + slab = 2.71 kN/m2 Ceiling + services = 0.50 kN/m2 10% of imposed load = 0.25 kN/m2 Total = 3.46 kN/m2 Total weight of floor, F = 3.46 x 4.5 x 1.5 = 23.355 kN Increase of second moment of area of the composite section based on elastic properties c I, by 10% to allow for the increased dynamic stiffness of the composite beam, 1c I 77 11007389174.51061262885.41.1 ×=××= c I mm4 Instantaneous deflection caused by re-application of the self weight of the floor and the beam to the composite beam, a δ 1 3 384 5 ca aIE LF ×× ×× = δ () 6642.2 1007389174.5205384 105.4355.235 7 3 3 = ××× ××× = a δ mm 76 6. Design examples Natural frequency ≈ 0279.11 6642.2 1818 == a δ Hz > 4 Hz 5. Conclusion When the beam is propped during the construction stage, its span is not limited by the moment resistance at the construction stage rather than in the case of an unpropped construction. If props are used, the design is limited basically by the total deflection which is a serviceability criterion. 77 7. Load-span design tables 7. LOAD-SPAN DESIGN TABLES FOR COMPOSITE BEAMS USING LIGHT STEEL SECTION AND PROFILED SHEAR CONNECTORS 7.1 PROPERTIES OF LIGHT STEEL SECTIONS 7.1.1 Class classification The particular cold formed sections analysed are Generic C sections which properties have been tabulated by Lawson, Chung and Popo-Ola (2002) (see Annex 1). If we check the class classification for the single light steel sections according to the criteria of Eurocode 3, showed in table 7.1, the result is that all sections are slender (see Annex 2.1). The following table gives the limiting proportions for compression elements of Class 1 to 3. When any of the compression elements within a section fail to satisfy the limit for Class 3 the whole section is classified as Class 4 (commonly referred to as slender), and local buckling should be taken into account in the design using an effective cross section. Table 7.1 Maximum slenderness ratios for the elements of a rolled section in compression and bending Element Class 1 Class 2 Class 3 Flange c / tf = 10 ε c / tf = 11 ε c / tf = 15 ε Web subject to bending d / tw = 72 ε d / tw = 83 ε d / tw = 124 ε Web subject to compression d / tw = 33 ε d / tw = 38 ε d / tw = 42 ε As the Annex 2.1 tables show, all the single sections are Class 4, and this means that local buckling may occur in compression elements before yield is reached. However in composite construction the sections used are back to back double sections, not single sections, and working compositely with a concrete slab. In this case the class classification of the section is different. In calculation for the construction stage of a composite beam the classification of the cross section should be based on the plain steel section, but secondary beams are laterally restrained by the steel decking and can develop their full moment resistances. 78 7. Load-span design tables Once the composite action is achieved, to know if local buckling can occur or not, the position of the plastic neutral axis has to be checked. These calculations have been carried out for all the cases treated in this project, with the different sections and imposed loads (see Annex 2.2). The plastic neutral axis lies within the concrete slab in all the combinations studied; hence the composite sections are classified as Class 1 and local buckling has not to be considered in the design. 7.1.2 Shear buckling Working with light steel sections it is important to consider the possibility of buckling in shear. Shear buckling resistance must be checked if the web slenderness (d/tw) exceeds 69ε: w t d> 69ε (7.1) where d is the height of the web w t is the thickness of the web y f 235 = ε The possibility of buckling in shear has been checked for all the Generic C double sections studied in this project as the table 7.2 shows. Only with two of the Generic C double sections studied and in the case that steel grade S350 is used, shear in buckling may happed. These two sections are 200x65x1.6 and 300x65x2.4 back to back double sections. The shear buckling resistance of these two sections has to be calculated to know if that means a hazard or not. 79 7. Load-span design tables Table 7.2 Study of the possibility of buckling in shear of the different sections D (mm) t (mm) tw (mm) d (mm) d/tw 69ε (fy=280 N/mm2) 69ε (fy=350 N/mm2) 100 1,2 2,4 97,6 40,667 63,213 ok 56,539 ok 125 1,2 2,4 122,6 51,083 63,213 ok 56,539 ok 125 1,6 3,2 121,8 38,063 63,213 ok 56,539 ok 150 1,6 3,2 146,8 45,875 63,213 ok 56,539 ok 150 1,8 3,6 146,4 40,667 63,213 ok 56,539 ok 165 1,6 3,2 161,8 50,563 63,213 ok 56,539 ok 165 1,8 3,6 161,4 44,833 63,213 ok 56,539 ok 180 1,6 3,2 176,8 55,250 63,213 ok 56,539 ok 180 1,8 3,6 176,4 49,000 63,213 ok 56,539 ok 180 2,0 4 176 44,000 63,213 ok 56,539 ok 200 1,6 3,2 196,8 61,500 63,213 ok 56,539 Buckli. 200 1,8 3,6 196,4 54,556 63,213 ok 56,539 ok 200 2,0 4 196 49,000 63,213 ok 56,539 ok 220 2,0 4 216 54,000 63,213 ok 56,539 ok 220 2,4 4,8 215,2 44,833 63,213 ok 56,539 ok 250 2,4 4,8 245,2 51,083 63,213 ok 56,539 ok 300 2,4 4,8 295,2 61,500 63,213 ok 56,539 Buckli. 300 3,0 6 294 49,000 63,213 ok 56,539 ok Shear buckling resistance has been calculated with the simple post-critic method for these two sections: a baw Rdba td V γ τ ×× = . (7.2) where the value of the simple post-critic resistance ba τ depend on the value of the web slenderness w λ _ τ ε λ k td w w×× =4.37 / _ (7.3) 80 7. Load-span design tables where τ k= 5.34 is the shear buckling coefficient For both sections, 200x65x1.6 and 300x65x2.4, the value of the web slenderness is: w λ _ = 0.868 Therefore 0.8 < w λ _ < 1.2 And according to the simple post-critic method                     −−= 3 8.0625.01 _y w ba f λ τ (7.4) With the simple post-critic resistance the shear buckling resistance is calculated for each section, showed in table 7.3, and it can be compared with the shear force Sd V to know if the buckling in shear may be a problem or not with these sections. As it is possible to see in table 7.4, shear force in the cases studied is always lower than the shear buckling resistance of the section, hence shear buckling will never happen. Table 7.3 Shear buckling resistance Generic C section w λ _ ba τ (N/mm2) Rdba V. (kN) 200x65x1.6 0.868 193.43 116.014 300x65x2.4 0.868 193.43 261.032 Table 7.4 Shear force values 200x65x1.6 Unpropped (S350) 200x65x1.6 Propped (S350) 300x65x2.4 Unpropped (S350) 300x65x2.4 Propped (S350) Imposed load (kN) L (m) VSd (kN) Imposed load (kN) L (m) VSd (kN) Imposed load (kN) L (m) VSd (kN) Imposed load (kN) L (m) VSd (kN) 1.5 4.7 23.2 1.5 5.3 26.3 1.5 7.3 35.9 1.5 7.9 38.9 2.5 4.6 27.8 2.5 4.9 29.7 2.5 7.0 42.4 2.5 7.3 44.3 3.5 4.4 31.6 3.5 4.6 33.1 3.5 6.8 48.9 3.5 6.9 49.6 4.5 4.3 35.7 4.5 4.4 36.6 4.5 6.6 54.9 4.5 6.6 54.9 81 7. Load-span design tables 7.2 DESIGN CRITERIA Design tables have been calculated for double Generic C light steel sections (see tables 7.5 to 7.8). These tables contain a wide range of cases although one of the parameters involved has been considered fixed, the beam spacing. On this way the design tables can be used to design composite beams and also to compare how sections span capacity vary with the construction conditions, steel grade and imposed load applied. Design criteria: - a: moment resistance of the beam exceeded in the construction stage - b: interaction between shear force and bending moment - c: moment resistance of the composite beam with full shear connection exceeded - d: moment resistance of the composite beam with partial shear connection exceeded - e: limit on the degree of partial shear connection not satisfied. This is not a failure criterion but it is a warning that the shear connection provided is less than the Eurocode limit of 40%. - g: total deflection of LE/200 exceeded for unpropped, (equal to LE /250 for propped) - h: imposed load deflection of span/350 exceeded - i: natural frequency is less than 4 Hz 7.3 DESIGN TABLES. PROPPED AND UNPROPPED BEAMS The two first tables are for unpropped beams during construction (tables 7.5 and 7.6) and the second ones are for propped beams (tables 7.7 and 7.8). The parameters showed in the tables are the maximum span that each section can achieve followed by the design criteria which limits this maximum span. The number of connectors required for these conditions and the deflection that the beam self weight and the imposed loads mean. Tables’ notation: LE: span of the beam (secondary beam) δE: deflection due to imposed loads δS: deflection due to beam self weight N: number of shear connectors 82 BEAM DATA • Internal beam • Uniform load • Beam spacing 1.5 m • Steel strength S 280 • Stud resistance 18 kN SLAB DATA • Slab depth 130 mm • Concrete strength C30/37 Beam is unpropped during construction Table 7.5 Load-span design table for double Generic C section: unpropped – fy = 280 N/mm2 IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGNATION LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N 100x55x1.2 2,4 a 1,1 9,7 8 2,4 a 1,9 9,7 8 2,4 g 2,5 9,0 7 2,2 b 2,7 7,2 7 125x55x1.2 2,8 a 1,3 10,3 9 2,8 a 2,2 10,7 9 2,8 a 3,0 10,3 9 2,7 g 3,6 9,7 9 125x55x1.6 3,2 g 1,8 13,4 10 3,1 g 2,8 12,3 10 3,0 g 3,6 11,1 10 3,0 g 4,2 10,1 9 150x65x1.6 3,8 g 2,3 15,8 12 3,7 g 3,5 14,6 12 3,6 g 4,5 13,0 11 3,5 g 5,3 11,7 11 150x65x1.8 3,9 g 2,4 16,3 13 3,9 g 4,0 16,2 13 3,7 g 4,7 13,2 12 3,6 g 5,6 12,0 12 165x65x1.6 4,0 g 2,4 16,3 13 4,0 g 4,0 16,0 13 3,9 g 4,8 13,8 12 3,8 g 5,7 12,5 12 165x65x1.8 4,2 g 2,7 17,6 14 4,1 g 4,1 15,8 13 4,0 g 5,1 14,1 13 3,9 g 6,1 12,8 12 180x65x1.6 4,3 g 2,5 16,8 14 4,2 g 4,1 16,2 14 4,1 g 5,2 14,6 13 4,0 d 6,1 13,0 13 180x65x1.8 4,5 g 2,9 18,6 14 4,4 g 4,5 17,1 14 4,3 g 5,5 14,9 14 4,1 d 6,4 13,3 13 180x65x2.0 4,6 g 3,1 19,1 15 4,5 g 4,6 17,0 15 4,4 g 5,8 15,3 14 4,3 d 6,8 13,7 14 200x65x1.6 4,6 a 2,7 17,4 15 4,6 a 4,5 17,4 15 4,5 g 5,8 15,8 14 4,2 d 6,1 12,7 14 200x65x1.8 4,8 g 3,1 19,4 16 4,8 g 5,1 19,0 16 4,6 g 6,1 16,1 15 4,4 d 6,5 13,0 14 200x65x2.0 5,0 g 3,4 20,7 16 4,9 g 5,1 18,7 16 4,8 g 6,4 16,5 15 4,5 d 6,9 13,4 15 220x65x2.0 5,4 g 3,7 22,1 18 5,3 g 5,5 19,6 17 5,1 g 7,0 17,6 17 4,8 d 7,0 13,4 15 220x65x2.4 5,7 g 4,0 23,1 19 5,5 g 6,0 20,6 18 5,4 g 7,6 18,3 17 5,0 d 7,7 14,1 16 250x65x2.4 6,3 g 4,6 25,5 21 6,1 g 6,8 22,6 20 5,9 g 8,5 20,0 19 5,5 d 8,0 14,2 18 300x65x2.4 7,3 g 5,4 29,3 24 7,1 g 8,0 25,8 23 6,7 d 9,4 21,2 22 6,1 d 8,5 14,5 20 300x65x3.0 7,8 g 6,0 31,0 25 7,5 g 8,8 27,1 25 7,2 d 10,6 23,0 24 6,6 d 9,6 15,9 21 83 BEAM DATA • Internal beam • Uniform load • Beam spacing 1.5 m • Steel strength S 350 • Stud resistance 18 kN SLAB DATA • Slab depth 130 mm • Concrete strength C30/37 Beam is unpropped during construction Table 7.6 Load-span design table for double Generic C section: unpropped – fy = 350 N/mm2 IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGNATION LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N 100x55x1.2 2,5 g 1,4 10,5 8 2,4 g 2,1 9,5 7 2,3 g 2,7 8,6 7 2,3 g 3,2 7,9 7 125x55x1.2 2,9 g 1,7 12,4 9 2,8 g 2,6 11,2 9 2,8 g 3,3 10,1 9 2,7 g 3,9 9,3 9 125x55x1.6 3,2 g 2,0 13,3 10 3,1 g 3,0 11,8 10 3,0 g 3,8 10,8 10 2,9 g 4,4 9,7 9 150x65x1.6 3,8 g 2,5 15,6 12 3,7 g 3,7 13,9 12 3,6 g 4,7 12,5 11 3,5 g 5,5 11,3 11 150x65x1.8 3,9 g 2,6 16,0 12 3,8 g 3,9 14,3 12 3,7 g 4,9 12,8 12 3,6 g 5,8 11,6 11 165x65x1.6 4,1 g 2,8 17,7 13 3,9 g 4,0 14,9 13 3,8 g 5,1 13,3 12 3,7 g 6,0 12,1 12 165x65x1.8 4,2 g 2,8 17,3 13 4,1 g 4,2 15,2 13 4,0 g 5,4 13,6 13 3,9 g 6,3 12,3 12 180x65x1.6 4,3 g 2,9 17,8 14 4,2 g 4,3 15,8 13 4,1 g 5,6 14,4 13 4,0 g 6,5 12,8 13 180x65x1.8 4,5 g 3,1 18,3 14 4,3 g 4,6 16,2 14 4,2 g 5,8 14,5 14 4,1 g 6,8 13,1 13 180x65x2.0 4,6 g 3,2 18,9 15 4,5 g 4,8 16,7 14 4,4 g 6,1 14,9 14 4,2 g 7,1 13,4 14 200x65x1.6 4,7 g 3,2 19,2 15 4,6 g 4,8 17,1 15 4,4 g 6,1 15,2 14 4,3 g 7,1 13,8 14 200x65x1.8 4,9 g 3,4 19,8 16 4,7 g 5,1 17,6 15 4,6 g 6,4 15,6 15 4,5 g 7,5 14,1 14 200x65x2.0 5,0 g 3,6 20,4 16 4,9 g 5,3 17,9 16 4,7 g 6,7 16,1 15 4,6 g 7,8 14,4 15 220x65x2.0 5,4 g 3,9 21,8 17 5,2 g 5,8 19,2 17 5,1 g 7,3 17,1 16 4,9 g 8,5 15,4 16 220x65x2.4 5,7 g 4,2 22,9 18 5,5 g 6,3 20,1 18 5,4 g 7,9 17,9 17 5,2 g 9,1 16,0 17 250x65x2.4 6,3 g 4,8 25,2 20 6,1 g 7,0 22,1 20 5,9 g 8,8 19,6 19 5,7 g 10,2 17,5 19 300x65x2.4 7,3 g 5,6 28,9 24 7,0 g 8,3 25,2 23 6,8 g 10,4 22,4 22 6,6 g 11,9 19,9 22 300x65x3.0 7,8 g 6,2 30,6 25 7,5 g 9,1 26,7 25 7,3 g 11,3 23,6 24 7,1 g 13,0 20,9 23 84 BEAM DATA • Internal beam • Uniform load • Beam spacing 1.5 m • Steel strength S 280 • Stud resistance 18 kN SLAB DATA • Slab depth 130 mm • Concrete strength C30/37 Beam is propped during construction Table 7.7 Load-span design table for double Generic C section: propped – fy = 280 N/mm2 IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGNATION LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N 100x55x1.2 3,3 g 4,2 7,7 11 3,0 g 5,2 5,6 9 2,6 b 4,8 3,7 8 2,2 b 3,9 2,3 7 125x55x1.2 4,0 g 5,2 9,3 13 3,6 g 6,2 6,8 11 3,2 b 6,6 5,1 10 2,8 b 5,4 3,3 9 125x55x1.6 3,9 g 4,9 8,9 12 3,5 g 6,2 6,7 11 3,3 g 6,9 5,3 11 3,1 g 7,3 4,4 10 150x65x1.6 4,5 g 5,8 10,4 15 4,2 g 7,3 7,9 13 3,9 g 8,2 6,3 12 3,6 d 8,3 5,0 12 150x65x1.8 4,6 g 5,9 10,6 15 4,2 g 7,4 8,0 14 4,0 g 8,3 6,4 13 3,7 g 8,7 5,3 12 165x65x1.6 4,9 g 6,2 11,2 16 4,5 g 7,8 8,5 14 4,2 g 8,7 6,7 13 3,8 d 8,2 4,9 12 165x65x1.8 4,9 g 6,3 11,4 16 4,5 g 8,0 8,6 15 4,3 g 8,9 6,9 14 3,9 d 8,8 5,3 13 180x65x1.6 5,2 g 6,6 12,0 17 4,8 g 8,4 9,1 15 4,4 d 9,1 7,0 14 4,0 d 8,2 4,9 13 180x65x1.8 5,3 g 6,7 12,1 17 4,9 g 8,5 9,2 16 4,5 g 9,5 7,4 15 4,1 d 8,8 5,3 13 180x65x2.0 5,3 g 6,8 12,3 17 4,9 g 8,6 9,4 16 4,6 g 9,6 7,5 15 4,3 d 9,3 5,6 14 200x65x1.6 5,6 g 7,2 13,0 18 5,2 g 9,0 9,8 17 4,7 d 9,1 7,0 15 4,2 d 8,2 4,9 14 200x65x1.8 5,7 g 7,3 13,1 18 5,3 g 9,2 10,0 17 4,8 d 9,7 7,5 16 4,4 d 8,8 5,3 14 200x65x2.0 5,8 g 7,4 13,3 19 5,3 g 9,4 10,2 17 5,0 d 10,3 8,0 16 4,5 d 9,3 5,6 15 220x65x2.0 6,2 g 7,9 14,3 20 5,7 g 10,1 10,9 19 5,3 d 10,4 8,0 17 4,8 d 9,4 5,7 15 220x65x2.4 6,4 g 8,2 14,7 21 5,9 g 10,4 11,3 19 5,6 d 11,5 8,9 18 5,0 d 10,4 6,2 16 250x65x2.4 7,1 g 9,0 16,3 23 6,6 g 11,5 12,5 21 6,0 d 11,8 9,1 20 5,5 d 10,6 6,4 18 300x65x2.4 8,1 g 10,3 18,7 27 7,5 d 13,2 14,3 25 6,7 d 12,3 9,5 22 6,1 d 11,2 6,7 20 300x65x3.0 8,5 g 10,8 19,6 28 7,9 g 13,8 15,0 26 7,2 d 14,0 10,8 24 6,6 d 12,7 7,7 21 91 9. Bibliographic references 9. BIBLIOGRAPHIC REFERENCES 1. Galjaard, H. C., Walraven, J. C. (2001), Static tests on various types of shear connectors for composite structuresConnections between Steel and Concrete, edited by R. Eligehausen, Vol. Two. University of Stuttgart, Germany. 2. ENV 1993-1-1 (1993) Eurocode 3. Design of steel structures. Part 1-1: General Rules and Rules for Buildings. European Committee for Standardisation (CEN). 3. ENV 1994-1-1 (1994) Eurocode 4. Design of composite steel and concrete structures. Part 1-1: General Rules and Rules for Buildings. European Committee for Standardisation (CEN) . 4. ENV 1994-2 (1997) Eurocode 4. Design of composite steel and concrete structures. Part 2: Composite bridges. European Committee for Standardisation (CEN). 5. Fontana, M., Beck, H., Bärtschi, R. (2001), Experimental investigation on the behaviour of strip shear connectors with powder actuated fasteners-Connections between Steel and Concrete, edited by R. Eligehausen, Vol. Two. University of Stuttgart, Germany. 6. Lawson, R.M., Chung, K.F., Popo-Ola, S.O. (2002), Building Design Using Cold Formed Steel Sections-Section Properties and Load Tables, The Steel Construction Institute. 7. Lawson, R.M., Popo-Ola, S.O. (2002), Opportunities for Heavy Cold Formed Steel Sections, The Steel Construction Institute. 8. Lawson, R.M., Popo-Ola, S.O. (1998), Push-out tests with strip connector fastened with HILTI X-EDNK22 pins into cold formed steel sections, The Steel Construction Institute. 92 10. Supplementary bibliography 10. SUPPLEMENTARY BIBLIOGRAPHY • “Cold-Formed Steel Design”, Second Edition. Edited by Wei-Wen, Yu, 1991. New York. Wiley Publications. • “Composite Beam Design to Eurocode 4”. Edited by R. M. Lawson and K. F. Chung, 1994. Steel Construction Institute. • “Composite Slabs and Beams using Steel Decking: best practice for design and construction”. Edited by G. H. Couchman, D. L. Mullett and J. W. Rackham, 2000. The Metal Cladding & Roofing Manufacturers Association. • “Design of Composite Beams Using Precast Concrete Slabs”. Edited by S. J. Hicks and R. M. Lawson, 2003. Steel Construction Institute. 93 ANNEX 1 GENERIC C SECTIONS PROPERTIES 94 GENERIC C SECTIONS GROSS SECTION PROPERTIES Single section Table A1.1 Section properties of Generic C single sections D (mm) B (mm) T (mm) Area (cm2) Weight (kg/m) Ix x (cm4) Iy y (cm4) rx x (cm) ry y (cm) Wx x (cm3) Wy y (cm3) J (cm4) Cw (cm6) es (mm) 100 55 1,2 2,67 2,09 44,3 11,5 4,07 2,07 8,87 3,22 0,0120 255 -26,6 125 55 1,2 2,96 2,32 73,9 12,4 5,00 2,05 11,83 3,31 0,0133 401 -25,1 125 55 1,6 3,93 3,08 97,0 16,1 4,97 2,02 15,52 4,28 0,0319 513 -24,6 150 65 1,6 4,63 3,63 165,4 25,6 5,98 2,35 22,06 5,66 0,0376 1127 -28,1 150 65 1,8 5,19 4,08 184,7 28,4 5,96 2,34 24,63 6,27 0,0536 1244 -27,8 165 65 1,6 4,86 3,82 206,2 26,4 6,51 2,33 25,00 5,72 0,0394 1387 -27,3 165 65 1,8 5,46 4,28 230,4 29,3 6,50 2,32 27,93 6,34 0,0563 1532 -27,1 180 65 1,6 5,10 4,00 252,5 27,1 7,04 2,31 28,06 5,77 0,0413 1681 -26,6 180 65 1,8 5,72 4,49 282,2 30,1 7,02 2,29 31,36 6,40 0,0591 1856 -26,4 180 65 2,0 6,34 4,98 311,2 33,0 7,01 2,28 34,59 7,00 0,0812 2023 -26,1 200 65 1,6 5,41 4,25 323,2 28,0 7,73 2,28 32,32 5,83 0,0439 2125 -25,7 200 65 1,8 6,07 4,77 361,3 31,1 7,71 2,26 36,14 6,47 0,0627 2348 -25,5 200 65 2,0 6,73 5,28 398,7 34,0 7,70 2,25 39,87 7,08 0,0862 2560 -25,2 220 65 2,0 7,12 5,59 499,6 35,0 8,37 2,22 45,43 7,14 0,0912 3174 -24,4 220 65 2,4 8,50 6,67 590,9 40,7 8,34 2,19 53,73 8,30 0,1578 3664 -23,8 250 65 2,4 9,21 7,23 802,8 42,1 9,34 2,14 64,23 8,40 0,1709 4903 -22,7 300 65 2,4 10,39 8,15 1249,4 44,1 10,97 2,06 83,31 8,53 0,1928 7444 -21,0 300 65 3,0 12,88 10,11 1531,2 52,4 10,90 2,02 102,09 10,14 0,3762 8780 -20,2 xx t D B 95 Double section Table A1.2 Section properties of double Generic C sections D (mm) B (mm) T (mm) Area (cm2) Weight (kg/m) Ix x (cm4) Iy y (cm4) rx x (cm) ry y (cm) Wx x (cm3) Wy y (cm3) J (cm4) Cw (cm6) es (mm) 100 55 1,2 5,34 4,19 88,6 42,8 4,07 2,83 17,73 7,79 0,0239 1135 - 125 55 1,2 5,92 4,64 147,8 42,9 5,00 2,69 23,66 7,79 0,0265 1733 - 125 55 1,6 7,85 6,17 194,0 55,9 4,97 2,67 31,05 10,17 0,0637 2198 - 150 65 1,6 9,26 7,27 330,9 87,0 5,98 3,07 44,13 13,39 0,0751 4869 - 150 65 1,8 10,39 8,15 369,4 96,9 5,96 3,05 49,27 14,90 0,1072 5353 - 165 65 1,6 9,73 7,63 412,5 87,0 6,51 2,99 50,01 13,39 0,0789 5859 - 165 65 1,8 10,91 8,57 460,7 96,9 6,50 2,98 55,86 14,90 0,1127 6443 - 180 65 1,6 10,19 8,00 505,0 87,0 7,04 2,92 56,13 13,39 0,0827 6940 - 180 65 1,8 11,44 8,98 564,3 96,9 7,02 2,91 62,72 14,91 0,1181 7634 - 180 65 2,0 12,68 9,95 622,4 106,4 7,01 2,90 69,17 16,37 0,1623 8285 - 200 65 1,6 10,82 8,49 646,4 87,1 7,73 2,84 64,65 13,39 0,0878 8524 - 200 65 1,8 12,15 9,54 722,6 96,9 7,71 2,82 72,27 14,91 0,1254 9379 - 200 65 2,0 13,46 10,57 797,3 106,4 7,70 2,81 79,75 16,38 0,1724 10183 - 220 65 2,0 14,25 11,18 999,2 106,5 8,37 2,73 90,85 16,38 0,1824 12277 - 220 65 2,4 17,00 13,34 1181,9 124,7 8,34 2,71 107,46 19,18 0,3155 14042 - 250 65 2,4 18,41 14,45 1605,5 124,7 9,34 2,60 128,46 19,19 0,3418 18067 - 300 65 2,4 20,77 16,31 2498,9 124,8 10,97 2,45 166,61 19,19 0,3857 25902 - 300 65 3,0 25,76 20,22 3062,3 150,1 10,90 2,41 204,18 23,09 0,7523 30070 - NOTE: Gross sections properties are independent on the design yield strength, so these properties tables can be used for steel grade S280 and S350 N/mm2. D B y y xx B t 96 ANNEX 2 SECTIONS CLASS CLASIFICATION 97 Annex 2. Sections class classification A2.1 SINGLE GENERIC C SECTION CLASS CLASSIFICATION: The elements of the single Generic C sections, flange and web, have been class classification according to the Eurocode limits. Table A2.1 Single Generic C section class classification (fy= 280 N/mm2,92.0= ε ) D (mm) B (mm) t (mm) c (mm) c/tf Flange d/tw Web under Bending Web under Compres sion CLASS 100 55 1,2 27,5 22,92 class4 83,33 - class4 class4 125 55 1,2 27,5 22,92 class4 104,17 - class4 class4 125 55 1,6 27,5 17,19 class4 78,13 - class4 class4 150 65 1,6 32,5 20,31 class4 93,75 - class4 class4 150 65 1,8 32,5 18,06 class4 83,33 - class4 class4 165 65 1,6 32,5 20,31 class4 103,13 - class4 class4 165 65 1,8 32,5 18,06 class4 91,67 - class4 class4 180 65 1,6 32,5 20,31 class4 112,50 - class4 class4 180 65 1,8 32,5 18,06 class4 100,00 - class4 class4 180 65 2,0 32,5 16,25 class4 90,00 - class4 class4 200 65 1,6 32,5 20,31 class4 125,00 class4 class4 class4 200 65 1,8 32,5 18,06 class4 111,11 - class4 class4 200 65 2,0 32,5 16,25 class4 100,00 - class4 class4 220 65 2,0 32,5 16,25 class4 110,00 - class4 class4 220 65 2,4 32,5 13,54 - 91,67 - class4 class4 250 65 2,4 32,5 13,54 - 104,17 - class4 class4 300 65 2,4 32,5 13,54 - 125,00 class4 class4 class4 300 65 3,0 32,5 10,83 - 100,00 - class4 class4 98 Annex 2. Sections class classification Table A2.2 Single Generic C section class classification (fy= 350 N/mm2,82.0= ε ) D (mm) B (mm) t (mm) c (mm) c/tf Flange d/tw Web under Bending Web under Compres sion CLASS 100 55 1,2 27,5 22,92 class4 83,33 - class4 class4 125 55 1,2 27,5 22,92 class4 104,17 class4 class4 class4 125 55 1,6 27,5 17,19 class4 78,13 - class4 class4 150 65 1,6 32,5 20,31 class4 93,75 - class4 class4 150 65 1,8 32,5 18,06 class4 83,33 - class4 class4 165 65 1,6 32,5 20,31 class4 103,13 class4 class4 class4 165 65 1,8 32,5 18,06 class4 91,67 - class4 class4 180 65 1,6 32,5 20,31 class4 112,50 class4 class4 class4 180 65 1,8 32,5 18,06 class4 100,00 - class4 class4 180 65 2,0 32,5 16,25 class4 90,00 - class4 class4 200 65 1,6 32,5 20,31 class4 125,00 class4 class4 class4 200 65 1,8 32,5 18,06 class4 111,11 class4 class4 class4 200 65 2,0 32,5 16,25 class4 100,00 - class4 class4 220 65 2,0 32,5 16,25 class4 110,00 class4 class4 class4 220 65 2,4 32,5 13,54 class4 91,67 - class4 class4 250 65 2,4 32,5 13,54 class4 104,17 class4 class4 class4 300 65 2,4 32,5 13,54 class4 125,00 class4 class4 class4 300 65 3,0 32,5 10,83 - 100,00 - class4 class4 A2.2 COMPOSITE BEAMS CROSS SECTIONS CLASS CLASSIFICATION If the plastic neutral axis depth since the upper surface of the slab, yp, is smaller than the concrete depth above the steel decking, 80 mm, the composite cross section is classified as Class 1. With the compressive resistance of the concrete slab (Rc) and the tensile resistance of the steel section (Rs) is possible to calculate the depth of the plastic neutral axis yp. 99 Table A2.3 Composite cross section class checking: unpropped - fy = 280 N/mm2 IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGNATION LE (m) Rc (kN) Rs (kN) yp (mm) LE (m) Rc (kN) Rs (kN) yp (mm) LE (m) Rc (kN) Rs (kN) yp (mm) LE (m) Rc (kN) Rs (kN) yp (mm) 100x55x1.2 2,4 816 142,3 14,0 2,4 816 142,3 14,0 2,4 816 142,3 14,0 2,2 748 142,3 15,2 125x55x1.2 2,8 952 157,8 13,3 2,8 952 157,8 13,3 2,8 952 157,8 13,3 2,7 918 157,8 13,8 125x55x1.6 3,2 1088 209,4 15,4 3,1 1054 209,4 15,9 3,0 1020 209,4 16,4 3,0 1020 209,4 16,4 150x65x1.6 3,8 1292 246,9 15,3 3,7 1258 246,9 15,7 3,6 1224 246,9 16,1 3,5 1190 246,9 16,6 150x65x1.8 3,9 1326 277,0 16,7 3,9 1326 277,0 16,7 3,7 1258 277,0 17,6 3,6 1224 277,0 18,1 165x65x1.6 4,0 1360 259,4 15,3 4,0 1360 259,4 15,3 3,9 1326 259,4 15,6 3,8 1292 259,4 16,1 165x65x1.8 4,2 1428 291,1 16,3 4,1 1394 291,1 16,7 4,0 1360 291,1 17,1 3,9 1326 291,1 17,6 180x65x1.6 4,3 1462 271,8 14,9 4,2 1428 271,8 15,2 4,1 1394 271,8 15,6 4,0 1360 271,8 16,0 180x65x1.8 4,5 1530 305,1 16,0 4,4 1496 305,1 16,3 4,3 1462 305,1 16,7 4,1 1394 305,1 17,5 180x65x2.0 4,6 1564 338,1 17,3 4,5 1530 338,1 17,7 4,4 1496 338,1 18,1 4,3 1462 338,1 18,5 200x65x1.6 4,6 1564 288,5 14,8 4,6 1564 288,5 14,8 4,5 1530 288,5 15,1 4,2 1428 288,5 16,2 200x65x1.8 4,8 1632 323,9 15,9 4,8 1632 323,9 15,9 4,6 1564 323,9 16,6 4,4 1496 323,9 17,3 200x65x2.0 5,0 1700 359,0 16,9 4,9 1666 359,0 17,2 4,8 1632 359,0 17,6 4,5 1530 359,0 18,8 220x65x2.0 5,4 1836 379,9 16,6 5,3 1802 379,9 16,9 5,1 1734 379,9 17,5 4,8 1632 379,9 18,6 220x65x2.4 5,7 1938 453,2 18,7 5,5 1870 453,2 19,4 5,4 1836 453,2 19,7 5,0 1700 453,2 21,3 250x65x2.4 6,3 2142 491,0 18,3 6,1 2074 491,0 18,9 5,9 2006 491,0 19,6 5,5 1870 491,0 21,0 300x65x2.4 7,3 2482 553,9 17,9 7,1 2414 553,9 18,4 6,7 2278 553,9 19,5 6,1 2074 553,9 21,4 300x65x3.0 7,8 2652 686,9 20,7 7,5 2550 686,9 21,6 7,2 2448 686,9 22,4 6,6 2244 686,9 24,5 100 Table A2.4 Composite cross section class checking: unpropped - fy = 350 N/mm2 IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGN. LE (m) Rc (kN) Rs (kN) yp (mm) LE (m) Rc (kN) Rs (kN) yp (mm) LE (m) Rc (kN) Rs (kN) yp (mm) LE (m) Rc (kN) Rs (kN) yp (mm) 100x55x1.2 2,5 850 177,9 16,7 2,4 816 177,9 17,4 2,3 782 177,9 18,2 2,3 782 177,9 18,2 125x55x1.2 2,9 986 197,2 16,0 2,8 952 197,2 16,6 2,8 952 197,2 16,6 2,7 918 197,2 17,2 125x55x1.6 3,2 1088 261,8 19,3 3,1 1054 261,8 19,9 3,0 1020 261,8 20,5 2,9 986 261,8 21,2 150x65x1.6 3,8 1292 308,6 19,1 3,7 1258 308,6 19,6 3,6 1224 308,6 20,2 3,5 1190 308,6 20,7 150x65x1.8 3,9 1326 346,2 20,9 3,8 1292 346,2 21,4 3,7 1258 346,2 22,0 3,6 1224 346,2 22,6 165x65x1.6 4,1 1394 324,2 18,6 3,9 1326 324,2 19,6 3,8 1292 324,2 20,1 3,7 1258 324,2 20,6 165x65x1.8 4,2 1428 363,8 20,4 4,1 1394 363,8 20,9 4,0 1360 363,8 21,4 3,9 1326 363,8 21,9 180x65x1.6 4,3 1462 339,8 18,6 4,2 1428 339,8 19,0 4,1 1394 339,8 19,5 4,0 1360 339,8 20,0 180x65x1.8 4,5 1530 381,4 19,9 4,3 1462 381,4 20,9 4,2 1428 381,4 21,4 4,1 1394 381,4 21,9 180x65x2.0 4,6 1564 422,6 21,6 4,5 1530 422,6 22,1 4,4 1496 422,6 22,6 4,2 1428 422,6 23,7 200x65x1.6 4,7 1598 360,6 18,1 4,6 1564 360,6 18,4 4,4 1496 360,6 19,3 4,3 1462 360,6 19,7 200x65x1.8 4,9 1666 404,9 19,4 4,7 1598 404,9 20,3 4,6 1564 404,9 20,7 4,5 1530 404,9 21,2 200x65x2.0 5,0 1700 448,7 21,1 4,9 1666 448,7 21,5 4,7 1598 448,7 22,5 4,6 1564 448,7 23,0 220x65x2.0 5,4 1836 474,9 20,7 5,2 1768 474,9 21,5 5,1 1734 474,9 21,9 4,9 1666 474,9 22,8 220x65x2.4 5,7 1938 566,6 23,4 5,5 1870 566,6 24,2 5,4 1836 566,6 24,7 5,2 1768 566,6 25,6 250x65x2.4 6,3 2142 613,8 22,9 6,1 2074 613,8 23,7 5,9 2006 613,8 24,5 5,7 1938 613,8 25,3 300x65x2.4 7,3 2482 692,4 22,3 7,0 2380 692,4 23,3 6,8 2312 692,4 24,0 6,6 2244 692,4 24,7 300x65x3.0 7,8 2652 858,6 25,9 7,5 2550 858,6 26,9 7,3 2482 858,6 27,7 7,1 2414 858,6 28,5 107 Table A3.2 Section properties of heavy cold formed double extended C sections D (mm) Btop (mm) Bbot (mm) t (mm) Area (cm2) Weight (kg/m) Ix x (cm4) Iy y (cm4) rx x (cm) ry y (cm) Wx x (cm3) Wy y (cm3) J (cm4) Cw (cm6) 200 75 100 4,0 28,66 22,50 1745,1 375,9 7,80 3,62 163,5 43,0 1,4980 29133 200 75 100 5,0 35,57 27,92 2138,5 471,4 7,75 3,64 200,3 53,9 2,9169 34727 200 75 100 6,0 42,35 33,24 2513,6 567,3 7,70 3,66 235,3 64,8 5,0143 39661 250 75 100 4,0 32,62 25,61 2951,3 376,1 9,51 3,40 222,8 43,0 1,7050 46297 250 75 100 5,0 40,53 31,82 3627,2 471,8 9,46 3,41 273,8 53,9 3,3236 55358 250 75 100 6,0 48,31 37,92 4275,9 568,0 9,41 3,43 322,7 64,9 5,7200 63436 300 75 100 4,0 36,58 28,71 4564,9 376,3 11,17 3,21 288,9 43,0 1,9120 67503 300 75 100 5,0 45,59 35,71 5622,1 472,2 11,12 3,22 355,8 54,0 3,7304 80885 300 75 100 6,0 54,27 42,60 6641,7 568,7 11,06 3,24 420,2 65,0 6,4257 92900 400 75 100 4,0 44,50 34,93 9213,0 376,8 14,39 2,91 441,3 43,1 2,3260 122117 400 75 100 5,0 55,41 43,50 11379,2 473,0 14,33 2,92 544,9 54,1 4,5439 146726 400 75 100 6,0 66,19 51,96 13482,1 570,1 14,27 2,93 645,5 65,1 7,8371 169022 108 HEAVY COLD FORMED DOUBLE LIPPED C SECTIONS BEAM DATA • Internal beam • Uniform load • Beam spacing 2.4 m • Steel strength S350 • Pin resistance 18 kN SLAB DATA • Slab depth 130 mm • Concrete strength C30/37 Beam is unpropped during construction Table A3.3 Design table for composite beam with double lipped C, H-CFS. IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGNATION LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N 200x75x3.0 5,0 g 3,9 19,6 16 4,8 g 5,7 17,2 15 4,6 g 7,1 15,2 15 4,3 d 6,7 11,0 14 200x75x4.0 5,4 g 4,3 21,1 17 5,2 g 6,3 18,4 17 5,0 g 7,8 16,2 16 4,7 d 8,0 12,7 15 200x75x4.5 5,5 g 4,5 21,7 18 5,3 g 6,6 18,9 17 5,2 g 8,1 16,6 17 4,9 d 8,6 13,5 16 250x75x3.0 5,9 g 4,8 23,2 19 5,7 g 7,0 20,1 18 5,4 d 7,9 16,0 17 4,9 d 7,2 11,3 16 250x75x4.0 6,4 g 5,3 24,9 21 6,2 g 7,7 21,6 20 6,0 d 9,5 18,8 19 5,5 d 8,8 13,3 18 250x75x4.5 6,6 g 5,5 25,6 21 6,4 g 8,0 22,3 21 6,2 g 9,9 19,5 20 5,7 d 9,4 14,3 18 300x75x3.0 6,8 g 5,7 26,6 22 6,6 g 8,2 23,0 21 6,1 d 8,5 16,8 20 5,6 d 7,9 11,9 18 300x75x4.0 7,4 g 6,3 28,6 24 7,1 g 9,1 24,8 23 6,7 d 10,2 19,7 22 6,2 d 9,5 14,1 20 300x75x4.5 7,6 g 6,5 29,4 25 7,4 g 9,5 25,5 24 7,0 d 11,0 21,1 23 6,4 d 10,3 15,0 21 350x75x3.0 7,7 g 6,5 29,8 25 7,4 g 9,4 25,9 24 6,7 d 9,1 17,5 22 6,2 d 8,5 12,5 20 350x75x4.0 8,4 g 7,2 32,2 27 8,1 g 10,7 28,4 27 7,5 d 11,1 20,8 24 6,9 d 10,3 14,8 22 350x75x4.5 8,6 g 7,5 33,2 28 8,3 g 10,9 28,6 27 7,8 d 11,9 22,2 26 7,2 d 11,2 15,9 23 400x75x3.0 8,6 g 7,3 33,1 28 8,2 d 10,2 27,5 27 7,4 d 9,7 18,3 24 6,8 d 9,0 13,0 22 400x75x4.0 9,3 g 8,2 35,7 31 9,0 g 11,8 30,8 29 8,2 d 11,9 21,8 27 7,6 d 11,0 15,6 25 400x75x4.5 9,6 g 8,5 36,9 32 9,3 g 12,3 31,8 30 8,6 d 12,9 23,5 28 7,9 d 12,0 16,8 26 450x75x3.0 9,5 g 8,2 36,5 31 8,9 d 10,9 28,7 29 8,1 d 10,4 19,2 26 7,4 d 9,6 13,6 24 450x75x4.0 10,3 g 9,1 39,3 34 9,9 g 13,1 33,8 33 9,0 d 12,6 22,9 29 8,3 d 11,8 16,4 27 450x75x4.5 10,6 g 9,5 40,5 35 10,2 g 13,7 34,9 34 9,4 d 13,7 24,7 31 8,6 d 12,8 17,7 28 109 HEAVY COLD FORMED DOUBLE EXTENDED C SECTIONS BEAM DATA • Internal beam • Uniform load • Beam spacing 2.4 m • Steel strength S350 • Pin resistance 18 kN SLAB DATA • Slab depth 130 mm • Concrete strength C30/37 Beam is unpropped during construction Table A3.4 Design table for composite beam with double extended C, H-CFS. IMPOSED LOAD kN/m2 1.5 2.5 3.5 4.5 DESIGNATION LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N LE (m) δE (mm) δS (mm) N 200x75x100x4.0 5,5 g 4,5 21,7 18 5,3 g 6,5 18,8 17 5,1 g 8,1 16,5 17 4,8 d 7,7 12,1 15 200x75x100x5.0 5,9 g 4,9 22,9 19 5,7 g 7,1 20,0 18 5,5 g 8,8 17,5 18 5,2 d 9,0 13,8 17 200x75x100x6.0 6,2 g 5,2 24,1 20 6,0 g 7,5 20,9 19 5,8 g 9,3 18,3 19 5,5 d 10,1 15,4 18 250x75x100x4.0 6,5 g 5,5 25,5 21 6,3 g 8,0 22,1 21 6,0 d 9,1 17,9 19 5,5 d 8,5 12,7 18 250x75x100x5.0 7,0 g 6,0 27,0 23 6,7 g 8,6 23,4 22 6,5 g 10,6 20,4 21 6,0 d 9,9 14,7 19 250x75x100x6.0 7,4 g 6,4 28,3 24 7,1 g 9,2 24,6 23 6,9 g 11,3 21,4 22 6,4 d 11,3 16,4 21 300x75x100x4.0 7,5 g 6,5 29,1 25 7,3 g 9,4 25,1 24 6,8 d 10,0 18,9 22 6,2 d 9,3 13,5 20 300x75x100x5.0 8,1 g 7,0 31,0 26 7,8 g 10,1 26,6 25 7,4 d 11,7 21,8 24 6,8 d 10,9 15,6 22 300x75x100x6.0 8,5 g 7,5 32,6 28 8,2 g 10,8 28,0 27 7,9 g 13,3 24,4 26 7,3 d 12,4 17,6 24 400x75x100x4.0 9,5 g 8,4 36,4 31 9,1 g 12,1 31,3 30 8,3 d 11,6 21,2 27 7,6 d 10,8 15,1 25 400x75x100x5.0 10,2 g 9,1 38,7 33 9,8 g 13,1 33,2 32 9,1 d 13,7 24,5 30 8,3 d 12,8 17,6 27 400x75x100x6.0 10,7 g 9,8 40,8 35 10,3 g 14,0 34,9 34 9,8 d 15,7 27,7 32 9,0 d 14,7 19,9 29