Structural steel design
2.1 DESIGN THEORIES
2.1.1 Development of design:
The specific aim of structural design is, for a given framing arrangement, to determine the member sizes to support the structure’s loads. The historical basis of design was trial and error. Then with development of mathematics and science the design theories—elastic, plastic and limit state—were developed, which permit accurate and economic designs to be made. The design theories are discussed; design methods given in BS 5950: Part 1 are set out briefly. Reference is also made to Eurocode 3 (EC3). The complete codes should be consulted. 2.1.2 Design from experience Safe proportions for members such as depth/thickness, height/width, span/depth etc. were determined from experience and formulated into rules. In this way, structural forms and methods of construction such as beam-column, arch-barrel vault and domes in stone, masonry and timber were developed, as well as cable structures using natural fibres. Very remarkable structures from the ancient civilizations of Egypt, Greece, Rome and the cathedrals of the middle ages survive as a tribute to the ingenuity and prowess of architects using this design basis. The results of the trial-and-error method still survive in our building practices for brick houses. An experimental design method is still included in the steel code. 2.1.3 Elastic theory Elastic theory was the first theoretical design method to be developed. The behaviour of steel when loaded below the yield point is much closer to true elastic behaviour than that of other structural materials (Figure 2.1). All sections and the complete structure are assumed to obey Hooke’s law and recover to their original state on removal of load if not loaded past yield. Design to elastic theory was carried out in accordance with BS 449, The Use of Structural Steel in Building. For design the structure is loaded with the working loads, that is the maximum loads to which it will be subjected during its life. Statically determinate structures are analysed using simple theory of statics. For statically indeterminate structures, linear or first-order elastic theory is traditionally used for analysis. The various load cases can be combined by superposition to give the worst cases for design. In modern practice, second-order analysis taking account of deflections in the structure can be performed, for which computer programs and code methods are available. In addition, analysis can be performed to determine the load factor which will cause elastic instability where the influence of axial load on bending stiffness is considered. Dynamic analyses can also be carried out. Elastic analysis continues to form the main means of structural analysis. In design to elastic theory, sections are sized to ensure permissible stresses are not exceeded at any point in the structure. Stresses are reduced where instability due to buckling such as in slender compression members, unsupported compression flanges of slender beams, deep webs etc. can occur. Deflections under working loads can be calculated as part of the analysis and checked against code limits. The loading, deflection and elastic bending moment diagram and elastic stress distribution for a fixed base portal are shown in Figure 2.2(a). The permissible stresses are obtained by dividing the yield stress or elastic critical buckling stress where stability is a problem by a factor of safety. The one factor of safety takes account variations in strengths of materials, inaccuracies in fabrication, possible overloads etc. to ensure a safe design. 2.1.4 Plastic theory Plastic theory was the next major development in design. This resulted from work at Cambridge University by the late Lord Baker, Professors Horne, Heyman etc. The design theory is outlined. When a steel specimen is loaded beyond the elastic limit the stress remains constant while the strain increases, as shown in Figure 2.1(b). For a beam section subjected to increasing moment this behaviour results in the formation of a plastic hinge where a section rotates at the plastic moment capacity. Plastic analysis is based on determining the least load that causes the structure to collapse. Collapse occurs when sufficient plastic hinges have formed to convert the structure to a mechanism. The safe load is the collapse load divided by a load factor. In design the structure is loaded with the collapse or factored loads, obtained by multiplying the working loads by the load factor, and analysed plastically. Methods of rigid plastic analysis have been developed for single-storey and multistorey frames where all deformation is assumed to occur in the hinges. Portals are designed almost exclusively using plastic design. Software is also available to carry out elastic-plastic analysis where the frame first acts elastically and, as the load increases, hinges form successively until the frame is converted to a mechanism. More accurate analyses take the frame deflections into account. These secondary effects are only of importance in some slender sway frames. The plastic design methods for multistorey rigid non-sway and sway frames are given in BS 5950. The loading, collapse mechanism and plastic bending moment diagram for a fixed-base portal are shown in Figure 2.2(b). Sections are designed using plastic theory and the stress distributions for sections subjected to bending only and bending and axial load are also shown in the figure. Sections require checking to ensure that local buckling does not occur before a hinge can form. Bracing is required at the hinge and adjacent to it to prevent overall buckling. Fig. 2.1 Stress-strain diagrams: (a) structural steels—BS 5950 and EC3; (b) plastic design. 18
STRUCTURAL STEEL DESIGN
2.1.5 Limit state theory and design codes Limit state theory was developed by the Comitée Européen Du Béton for design of structural concrete and has now been widely accepted as the best design method for all materials. It includes principles from the elastic and plastic theories and incorporates other relevant factors to give as realistic a basis for design as possible. The following concepts are central to limit state theory. 1. Account is taken in design of all separate conditions that could cause failure or make the structure unfit for its intended use. These are the various limit states and are listed in the next section. 2. The design is based on the actual behaviour of materials in structures and performance of real structures established by tests and long-term observations. Good practice embodied in clauses in codes and specifications must be followed in order that some limit states cannot be reached. 3. The overall intention is that design is to be based on statistical methods and probability theory. It is recognized that no design can be made completely safe; only a low probability that the structure will not reach a limit state can be achieved. However, full probabilistic design is not possible at present and the basis is mainly deterministic. Fig. 2.2 Loading, deflection, bending and stress distributions: (a) elastic analysis; (b) plastic analysis. DESIGN THEORIES 19 4. Separate partial factors of safety for loads and materials are specified. This permits a better assessment to be made of uncertainties in loading, variations in material strengths and the effects of initial imperfections and errors in fabrication and erection. Most importantly, the factors give a reserve of strength against failure. The limit state codes for design of structural steel now in use are BS 5950: Part 1 (1990) and Eurocode 3 (1993). All design examples in the book are to BS 5950. Eurocode 3 is not discussed. However, references are made in some cases. In limit state philosophy, the steel codes are Level 1 safety codes. This means that safety or reliability is provided on a structural element basis by specifying partial factors of safety for loads and materials. All relevant separate limit states must be checked. Level 2 is partly based on probabilistic concepts and gives a greater reliability than a Level 1 design code. A Level 3 code would entail a fully probabilistic design for the complete structure. 2.2 LIMIT STATES AND DESIGN BASIS BS 5950 states in Clause 1.01 that: The aim of structural design is to provide with due regard to economy a structure capable of fulfilling its intended function and sustaining the design loads for its intended life. In Clause 2.1.1 the code states: Structures should be designed by considering the limit states at which they become unfit for their intended use by applying appropriate factors for the ultimate limit state and serviceability limit state. The limit states specified for structural steel work on BS 5950 are in two categories: Table 2.1 Limit states specified in BS 5950 Ultimate Serviceability 1. Strength including yielding rupture, buckling and transformation into a mechanism 5. Deflection 2. Stability against overtwining and sway 6. Vibration, e.g. wind-induced oscillation 3. Fracture due to fatigue 7. Repairable damage due to fatigue 4. Brittle fracture 8. Corrosion and durability • ultimate limit states which govern strength and cause failure if exceeded; • serviceability limit states which cause the structure to become unfit for use but stopping short of failure. The separate limit states given in Table 1 of BS 5950 are shown in Table 2.1. 2.3 LOADS, ACTIONS AND PARTIAL SAFETY FACTORS The main purpose of the building structure is to carry loads over or round specified spaces and deliver them to the ground. All relevant loads and realistic load combinations have to be considered in design. 2.3.1 Loads BS 5950 classifies working loads into the following traditional types. 1. Dead loads due to the weight of the building materials. Accurate assessment is essential. 2. Imposed loads due to people, furniture, materials stored, snow, erection and maintenance loads. Refer to BS 6399. 3. Wind loads. These depend on the location, the building size and height, openings in walls etc. Wind causes external and internal pressures and suctions on building surfaces and the phenomenon of periodic vortex shedding can cause vibration of structures. Wind loads are estimated from maximum wind speeds that can be expected in a 50-year period. They are to be estimated in accordance with CP3: Chapter V, Part 2. A new wind load code BS 6399: Part 2 is under preparation. 20 STRUCTURAL STEEL DESIGN 4. Dynamic loads are generally caused by cranes. The separate loads are vertical impact and horizontal transverse and longitudinal surge. Wheel loads are rolling loads and must be placed in position to give the maximum moments and shears. Dynamic loads for light and moderate cranes are given in BS 6399: Part 1. Table 2.2 BS 5950 design loads for the ultimate limit state Load combination Design loada Dead load 1.4 GK Dead load restraining overturning 1.0 GK Dead and imposed load 1.4 GK+1.6 QK Dead, imposed and wind load 1.2 (GK+QK+WK) aGK=dead load; QK=imposed load; WK=wind load. Seismic loads, though very important in many areas, do not have to be considered in the UK. The most important effect is to give rise to horizontal inertia loads for which the building must be designed to resist or deform to dissipate them. Vibrations are set up, and if resonance occurs, amplitudes greatly increase and failure results. Damping devices can be introduced into the stanchions to reduce oscillation. Seismic loads are not discussed in the book. 2.3.2 Load factors/partial safety factors and design loads Load factors for the ultimate limit state for various loads and load combinations are given in Table 2 of BS 5950. Part of the code table is shown in Table 2.2. In limit state design, Design loads=characteristic or working loads FK ×partial factor of safety γ 2.4 STRUCTURAL STEELS—PARTIAL SAFETY FACTORS FOR MATERIALS Some of the design strengths, py , of structural steels used in the book, taken from Table 6m in BS 5950, are shown in Table 2.3. Design strength is given by Table 2.3 BS 5950 design strength pY Grade Thickness (mm) pY (N/mm) 43 ≤16 275 ≤40 265 50 ≤16 355 ≤40 345 In BS 5950, the partial safety factor for materials γm=1.0. In Eurocode 3 the partial safety factors for resistance are given in Section 5.1.1. The value for member design is normally 1.1. 2.5 DESIGN METHODS FROM CODES—ULTIMATE LIMIT STATE 2.5.1 Design methods from BS 5950 The design of steel structures may be made to any of the following methods set out in Clause 2.1.2 of BS 5950: • simple design; DESIGN THEORIES 21 • rigid design; • semirigid design; • experimental verification. The clause states that: the details of members and connections should be such as to realize the assumptions made in design without adversely affecting other parts of the structure. (a) Simple design The connections are assumed not to develop moments that adversely affect the member or structure. The structure is analysed, assuming that it is statically determinate with pinned joints. In a multistorey beam-column frame, bracing or shear walls acting with floor slabs are necessary to provide stability and resistance to horizontal loading. (b) Rigid design The connections are assumed to be capable of developing actions arising from a fully rigid analysis, that is, the rotation is the same for the ends of all members meeting at a joint. The analysis of rigid structures may be made using either elastic or plastic methods. In Section 5 of the code, methods are given to classify rigid frames into non-sway, i.e. braced or stiff rigid construction and sway, i.e. flexible structures. The non-sway frame can be analysed using first-order linear elastic methods including subframe analysis. For sway frames, second-order elastic analysis or methods given in the code (extended simple design or the amplified sway method) must be used. Methods of plastic analysis for non-sway and sway frames are also given. (c) Semirigid design The code states that in this method some degree of joint stiffness short of that necessary to develop full continuity at joints is assumed. The relative stiffnesses of some common bolted joints are shown in the behaviour curves in Figure 2.3. Economies Fig. 2.3 Beam-column joint behaviour curves. 22 STRUCTURAL STEEL DESIGN in design can be achieved if partial fixity is taken into account. The difficulty with the method lies in designing a joint to give a predetermined stiffness and strength. The code further states that the moment and rotation capacity of the joint should be based on experimental evidence which may permit some limited plasticity. However, the ultimate tensile capacity of the fastener is not to be the failure criterion. Computer software where the semirigid joint is modelled by an elastic spring is available to carry out the analyses. The spring constant is taken from the initial linear part of the behaviour curve. Plastic analysis based on joint strength can also be used. The code also gives an empirical design method. This permits an allowance to be made in simple beam-column structures for the inter-restraint of connections by an end moment not exceeding 10% of the free moment. Various conditions that have to be met are set out in the clause. Two of the conditions are as follows. • The frame is to be braced in both directions. • The beam-to-column connections are to be designed to transmit the appropriate restraint moment in addition to the moment from eccentricity of the end reactions, assuming that the beams are simply supported. (d) Experimental verification The code states that where the design of a structure or element by the above methods is not practicable, the strength, stability and stiffness may be confirmed by loading tests as set out in Section 7 of the code. 2.5.2 Analysis of structures—Eurocode 3 The methods of calculating forces and moments in structures given in Eurocode 3, Section 5.2 are set out briefly. 1. Statically determinate structures—use statics. 2. Statically indeterminate structures—elastic global analysis may be used in all cases. Plastic global analysis may be used where specific requirements are met. 3. Elastic analysis—linear behaviour may be assumed for first- and second-order analysis where sections are designed to plastic theory. Elastic moments may be redistributed. 4. Effects of deformation—elastic first-order analyses is permitted for braced and non-sway frames. Second-order theory taking account of deformation can be used in all cases. 5. Plastic analysis—either rigid plastic or elastic-plastic methods can be used. Assumptions and stress-strain relationships are set out. Lateral restraints are required at hinge locations. 2.5.3 Member and joint design Provisions for member design from BS 5950 and are set out briefly. 1. Classification of cross-sections—in both codes, member cross-sections are classified into plastic, compact, semicompact and slender. Only the plastic cross-section can be used in plastic analysis ((d) below). 2. Tension members—design is based on the net section. The area of unconnected angle legs is reduced. 3. Compression members: • Short members—design is based on the squash resistance; • Slender members—design is based on the flexural buckling resistance. 4. Beams—bending resistances for various cross-section types are: • plastic and compact—design for plastic resistance; • semicompact—design for elastic resistance; • slender—buckling must be considered; • biaxial bending—use an interaction expression. • bending with unrestrained compression flange—design for lateral torsional buckling. DESIGN THEORIES 23 Shear resistance and shear buckling of slender webs to be checked. Tension field method of design is given in both codes. Combined bending and shear must be checked in beams where shear force is high. Webs checks—check web crushing and buckling in both codes. A flange-induced buckling check is given in Eurocode No. 3. 5. Members with combined tension and moment—checks cover single axis and biaxial bending. • interaction expression for use with all cross-sections; • more exact expression for use with plastic and compact cross-sections where the moment resistance is reduced for axial load. 6. Members with combined compression and moment—checks cover single axis and biaxial bending: • local capacity check—interaction expression for use with all cross-sections; more exact expression for use with plastic and compact cross-sections where the moment resistance is reduced for axial load; • overall buckling check—simplified and more exact interaction checks are given which take account of flexural and lateral torsional buckling. 7. Members subjected to bending shear and axial force—design methods are given for members subjected to combined actions. 8. Connections—procedures are given for design of joints made with ordinary bolts, friction grip bolts, pins and welds. 2.6 STABILITY LIMIT STATE Design for the ultimate limit state of stability is of the utmost importance. Horizontal loading is due to wind, dynamic and seismic loads and can cause overturning and failure in a sway mode. Frame imperfections give rise to sway from vertical loads. BS 5950 states that the designer should consider stability against overturning and sway stability in design. 1. Stability against overturning—to ensure stability against overturning, the worst combination of factored loads should not cause the structure or any part to overturn or lift off its seating. Checks are required during construction. 2. Sway stability—the structure must be adequately stiff against sway. The structure is to be designed for the applied horizontal loads and in addition a separate check is to be made for notional horizontal loads. The notional loads take account of imperfections such as lack of verticality. The loads applied horizontally at roof and floor level are taken as the greater of: • 1% of the factored dead loads; • 0.5% of the factored dead plus imposed load. Provisions governing their application are given. 2.7 DESIGN FOR ACCIDENTAL DAMAGE 2.7.1 Progressive collapse and robustness In 1968, a gas explosion near the top of a 22-storey precast concrete building blew out side panels, causing building units from above to fall onto the floor of the incident. This overloaded units below and led to collapse of the entire corner of the building. A new mode of failure termed ‘progressive collapse’ was identified where the effects from a local failure spread and the final damage is completely out of proportion to the initial cause. New provisions were included in the Building Regulations at that time to ensure that all buildings of five stories and over in height were of sufficiently robust construction to resist progressive collapse as a result of misuse or accident. 24 STRUCTURAL STEEL DESIGN 2.7.2 Building Regulations 1991 In Part A, Structure of the Building Regulations, Section 5, A3/A4 deals with disproportionate collapse. The Regulations state that all buildings must be so constructed as to reduce the sensitivity to disproportionate collapse due to an accident. The main provisions are summarized as follows. 1. If effective ties complying with the code are provided, no other action is needed (Section 2.7.3(a)). 2. If ties are not provided, then a check is to be made to see if loadbearing members can be removed one at a time without causing more than a specified amount of damage. 3. If in (2), it is not possible in any instance to limit the damage, the member concerned is to be designed as a ‘protected’ or ‘key’ member. It must be capable of withstanding 34 kN/m2 from any direction. 4. Further provisions limit damage caused by roof collapse. The Building Regulations should be consulted. 2.7.3 BS 5950 Requirements for structural integrity Clause 2.4.5 of BS 5950 ensures that design of steel structures complies with the Building Regulations. The main provisions are summarized. The complete clause should be studied. (a) All buildings Every frame must be effectively tied at roof and floors and columns must be restrained in two directions at these levels. Beam or slab reinforcement may act as ties, which must be capable of resisting a force of 75 kN at floor level and 40 kN at roof level. (b) Certain multistorey buildings To ensure accidental damage is localized the following recommendations should be met. • Sway resistance—no substantial part of a building should rely solely on a single plane of bracing in each direction. • Tying—ties are to be arranged in continuous lines in two directions at each floor and roof. Design forces for ties are specified. Ties anchoring columns at the periphery should be capable of resisting 1% of the vertical load at that level. • Columns—column splices should be capable of resisting a tensile force of two-thirds of the factored vertical load. • Integrity—any beam carrying a column should be checked for localization of damage ((c) below). • Floor units should be effectively anchored to their supports. (c) Localization of damage The code states that a building should be checked to see if any single column or beam carrying a column could be removed without causing collapse of more than a limited portion of the building. If the failure would exceed the specified limit the element should be designed as a key element. In the design check the loads to be taken are normally dead load plus one-third wind load plus one-third imposed load; the load factor is 1.05. The extent of damage is to be limited. (d) Key element A key element is to be designed for the loads specified in (c) above plus the load from accidental causes of 34 kN/m2 acting in any direction
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