RESEARCH SAMPLE PAPERS

 

ABSTRACT

This paper presents a numerical procedure which is called the Vector form intrinsic finite element method. It is used to analyze the nonlinear behavior of structural collapse under seismic excitation.  Nonlinear  dynamic analysis was  performed due  to the large  amount of  literature  supporting it  as the  superior method  of analysis  as  compared to nonlinear  static  analysis .  The accuracy  of  the  multistory  frame  model  was  also  confirmed through comparison of  its response under  blast loading with  that of  an existing study in  the literature, and the results were in good agreement . The whole progressive collapse processes   of the framed structures in various conditions are also simulated. The numerical procedures in Vector form intrinsic finite element method provided for new concept to deal a large deformation and rotation from continuous state to discontinuous state. The geometry nonlinear and nonlinear materials have been considered. The damage indexes of the element are adopted to decide failure criteria of element joints. In order to simulate the progressive collapse behavior of the structures, the compression between of the numerical simulation Vector form intrinsic finite element method and shake table experiments demonstrate the accuracy of the Vector form intrinsic finite element  method.

The information presents applications of proposed collapse methodology to the development of collapse fragility curves and the evaluation of the mean annual frequency of collapse. The previous of the problems; we can analyze and short out of the problems related to the collapse. Because, mainly part of the collapse.  

KEYWORDS

 Vector form intrinsic finite element method, Progressive collapse, Damage index,  Collapse analysis, Discontinuous displacement, Collision/Impact, Geometric nonlinearity.

 

 

 

1. INTRODUCTION

         To prevent the immeasurable losses of human lives and social properties due to earthquakes and terrorist attacks, resistance evaluation and retrofitting of civil infrastructures have become an important issue of many countries in the world. Great attention has been focused on a type of failure known as “progressive collapse” since the Ronan Point apartment collapse in London in 1986 (Griffiths et al., 1986). In recent years, however, terrorist attacks have also become evident as seen in the Alfred P. Murrah Building in Oklahoma City in 1995 and the World Trade Center in New York, 2001 which did not withstand the fires from terrorist attacks that have eventually induced progressive collapse of the building. The 27 May 2006 earthquake has hit the provinces of Yogyakarta and Central Java in Indonesia which lead to RC and brick building’s collapse. Besides experimental and theoretical studies, numerical simulation is another way to assist engineers to understand the nonlinear dynamic failure behavior of structure under an earthquake excitation. Recently, the V-fife method has been proposed by Ting, et al. (2004a, 2004b) and Wang and Ting (2004). This method applies a unique approach to compute the effects of rigid motion, allowing the simulation of extremely large deformation of elastic motion structures. The V-fife method will be explained in greater detail later in this paper. It redefines a set of deformation coordinates on the element in each time step. Therefore, it removes each element’s rigid body rotations and displacements. The V-fife method adopts a convicted material frame and the explicit time integration method for solving the equations of motion. This method has been successfully applied to the nonlinear motion analysis of the 2D elastic frame (Wu et al., 2006), the dynamic stability analysis of the space truss structure (Wang et al., 2006), and the elastic-plastic analysis of a space truss structure (Wang et al. 2005). The key objective of this study is to construct the V-fife method for the analysis of RC frame subjected to extremely large deformation having inelastic material properties. In this paper, analysis of collapse structures included multiple frame elements motion for large deformation and rotation from continuous states to discontinuous state. The comparison between numerical simulation of V-5 method and shake table experiments demonstrates the accuracy of V-5 method. Based on the survey around the heavily damaged area, three key problems in collapse analysis of structures were identified as description of discontinuous displacements, collision/impact between structural elements and adjacent buildings, and geometric nonlinearity of structures.  Some research work trying to solve the solutions is also introduced.

 2. VECTOR FORM INTRINSIC FINITE ELEMENT METHOD

            In this study, the V-5 method is extended in order to analyze elastic-plastic systems containing multiple deformable bodies with the following characteristics:

 (1) Interact with each other.

 (2) Discontinuous.

 (3) undergo large deformations and arbitrary rigid body motions.

                 Since the conventional finite element method (FEM) is an energy-based method, it does not require the balance of forces within each element. Since these unbalanced residual forces will do some work under virtual rigid body motion it will cause inaccuracy and un-convergence of the computed results. In order to solve these problems, the V-5 method has been proposed.

There are vector form intrinsic finite element method includes four main procedures:

(1) Construct the equation of motion using Newton’s Law at the mass points.

 (2) Update the material frame.

 (3) Compute the fictitious reversed rotations.

 (4) Determine the deformation coordinates.

            These aforementioned computation procedures have some points in common with the concept of the modern FEM. However, the key concept of the V-5 is that V-5 maintains the intrinsic nature of the original FEM. The V-5 method makes use of the strong form of equilibrium at each element. All the forces are balanced within each element. These forces are obtained from the principle of virtual work. The associated nodal displacements satisfy the compatibility condition.

3. FINITE ELEMENT ANALYSIS MODELING OF CONCRETE FRAMES

           Finite element analysis software program was used to model a three-story reinforced Concrete frame building. To simulate blast loading condition, a time history air pressure wave was applied to the frame. Nonlinear dynamic time history response of the frame model was validated with that of an existing study in the literature (Jayashree et al. 2013) and they were in good agreement.

3.1 GEOMETRY AND MATERIAL PROPERTIES OF THE FRAME STRUCTURES

             The simulated frame consisted of two bays in A  one  bay in B, and three story elevations in C Directions of the global coordinate system.   All bays  were equally spaced  at 8 m in  x and  y directions.  The floor to floor height of each story was equal to 3 m .  Base rectangular model with x y and z coordinates b) plan view of rectangle c) plan view of the square model d) plan view of the L-shaped.

The beams were assumed to be 45 x 25 cm reinforced concrete sections. All story columns were 300*300 mm  RC sections with eight longitudinal bars (29 mm).  The hoop reinforcement bars Were  assumed to be 12 mm with 15 cm longitudinal spacing and concrete cover of 40mm.                   The floors diaphragm were treated  as thin  shell sections  with  two layers  of the  reinforcement.  The thickness of the slab was 100mm with 1 mm of concrete cover. The concrete compressive strength and modulus of elasticity were 25 MPa and 23,158 MPa, respectively. The bars were made of grade  60,  with  the  yield  strength  of  414  MPa  and   modulus  of  elasticity  of  2x10^5  MPa, respectively.

3.2. LOADING AND BOUNDARY CONDITIONS

            Consideration of the structures joints, moment connections while all columns of  the ground were modeled as fixed supports.  Additionally, the end length offset option in SAP2000 was used to connect the beams and columns properly. All floor systems were assumed to work as diaphragms.

 

3.3. ANALYSIS PROCEDURE

         The blast load was applied to the validated reinforced concrete frame by performing nonlinear time history analysis.  P-M2-M3 and M3 plastic hinges were applied to both ends of columns and  both ends of the beams, respectively. P-M2-M3 plastic hinges have a moment rotation curve which is used to describe a combination of axial and bending behavior of column elements (SAP2000 2014). ‘Automatic plastic hinges’ option in SAP2000 software program was used for this purpose. All plastic hinge definitions are based on tables 6-7 and 6-8 of FEMA 356 (FEMA 2000. A 5 percent constant damping ratio was assumed. The analysis was performed for 2 seconds with 250.

3.4. NON-LINEAR SOLUTION AND FAILURE CRITERION

           Iteration method was used to predict the required load value to form the first plastic hinges as they exceeded the collapse prevention condition.  Based on the GSA, for the nonlinear dynamic analysis, the moment and rotation values should not exceed the collapse prevention condition. The magnitude of blast load was changed by increasing or decreasing the load scale-factor. Based on the choice of referring co-ordinates, methods regarding geometric formulation of deformable bodies may be categorized there are two types: Lagrangian Formulation and Eulerian Formulation. In 1979 Argyris and Doltsinis employed the current unstressed configuration to deal with large deformation and inelastic problems, where are iteration needed since the current configuration remains unknown. In structural analysis the geometric nonlinearity related with large deformation are usually avoided by assuming concentrated plasticity of materials. Thus a general only large displacement/large rotation with small deformation are considered in structural analysis.

3.4.1 LARGE DESPLACEMENT ROTATION

          The consideration of the geometric non-linearity frame structure P and Delta effects of the structures. The introducing a geometric stiffness matrix, the coupling between bending moment and axial force can be taken into account in terms of the effective stiffness. These methods, however, can be not suitable for collapse analysis of framed structures. For example, the variation of axial forces cannot be considered appropriately in dynamic analysis.

3.4.2 FAILURES DUE TO THE BUCKLING

      The well-known three-hinged buckling problem can also be solved using the current unstressed configuration. Referring to the current unstressed configuration might be a good choice considering buckling failure in a consistent manner with other geometric nonlinearity.

4. DISCONTINUOUS DISPLACEMENT

         An intact structure under extreme conditions usually will subject to various failures such as cracking, yielding and even fracture. As far as the distribution of displacement and deformation is concerned, it may be termed as having discontinuous displacement. A typical example is the failure of a beam-column member in the formation of a plastic hinge – the slope along the member has some discontinuities, which has been widely studied over the past decades.

 

4.1 DISCONTINUOUS DISPLACEMENT IN BEAM-COLUMN MEMBERS

         These displacement discontinuities are most common in damage investigation as shown in Fig.1 and Fig.2, where some failures with discontinuities in slope (for example, Fig.1) can be successfully described by plastic hinge model. There are plenty of literatures on using plastic hinges in collapse analysis and seismic assessment such as

 

                                   Fig-1                                                                             fig-2

 

4.2 DISCONTINUOUS DISPLACEMENT OF SLAB/WALL ELEMENTS

 

         It is well known that most of the casualties are caused by collapses in strong earthquakes. In fact it might more appropriate to say that most of the casualties resulted from collapse of floor slabs and walls. Such, show as figures.

 

 

Unfortunately such kind of behavior of slab/wall under extreme conditions cannot be simulated appropriately using available models. The application of DEM and its extended form is also prohibited by similar problems in dealing with beam-column members as described in Section 2. In current design codes, the roles that slab/wall plays in the whole structural system carrying external loads is usually simplified in modeling. 

In the multi-storey frame structure buildings are damages from earthquake generally initiates at position of structural weaknesses. The openings present in slabs are often providing discontinuities in distribution of loads. But when these openings are provided at suitable position the of structure to damage can be avoided. Structural engineers have developed confidence in the design of buildings. In the present work openings are enclosed by shear walls at placed different positions.

5. DESIGNING CONCEPT OF FRAME STRUCTURES

There are works process of the designing of the structures. Because first of all the designing 

DESIGN THEORIES OF STEEL STRUCTURE

 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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                Steel structures—structural engineering

 1.1 NEED FOR AND USE OF STRUCTURES: Structures are one of mankind’s basic needs next to food and clothing, and are a hallmark of civilization. Man’s structural endeavours to protect himself from the elements and from his own kind, to bridge streams, to enhance a ruling class and for religious purposes go back to the dawn of mankind. Fundamentally, structures are needed for the following purposes: • to enclose space for environmental control; • to support people, equipment, materials etc. at required locations in space; • to contain and retain materials; • to span land gaps for transport of people, equipment etc. The prime purpose of structures is to carry loads and transfer them to the ground. Structures may be classified according to use and need. A general classification is: • residential—houses, apartments, hotels; • commercial—offices, banks, department stores, shopping centres; • institutional—schools, universities, hospitals, gaols; • exhibition—churches, theatres, museums, art galleries, leisure centres, sports stadia, etc.; • industrial—factories, warehouses, power stations, steelworks, aircraft hangers etc. Other important engineering structures are: • bridges—truss, girder, arch, cable suspended, suspension; • towers—water towers, pylons, lighting towers etc.; • special structures—offshore structures, carparks, radio telescopes, mine headframes etc. Each of the structures listed above can be constructed using a variety of materials, structural forms or systems. Materials are discussed first and then a general classification of structures is set out, followed by one of steel structures. Though the subject is steel structures, steel is not used in isolation from other materials. All steel structures must rest on concrete foundations and concrete shear walls are commonly used to stabilize multistorey buildings.

 1.2 STRUCTURAL MATERIALS—

TYPES AND USES From earliest times, naturally occurring materials such as timber, stone and fibres were used structurally. Then followed brickmaking, rope-making, glass and metalwork. From these early beginnings the modern materials manufacturing industries developed. The principal modern building materials are masonry, concrete (mass, reinforced and prestressed), structural steel in rolled and fabricated sections and timber. All materials listed have particular advantages in given situations, and construction of a particular building type can be in various materials, e.g. a multistorey building can be loadbearing masonry, concrete shear wall or frame or steel frame. One duty of the designer is to find the best solution which takes account of all requirements — economic, aesthetic and utilitarian. The principal uses, types of construction and advantages of the main structural materials are as follows. • Masonry—loadbearing walls or columns in compression and walls taking in-plane or transverse loads. Construction is very durable, fire resistant and aesthetically pleasing. Building height is moderate, say to 20 storeys. • Concrete—framed or shear wall construction in reinforced concrete is very durable and fire resistant and is used for the tallest buildings. Concrete, reinforced or prestressed, is used for floor construction in all buildings, and concrete foundations are required for all buildings. • Structural steel—loadbearing frames in buildings, where the main advantages are strength and speed of erection. Steel requires protection from corrosion and fire. Claddins and division walls of other materials and concrete foundations are required. Steel is used in conjunction with concrete in composite and combined frame and shear wall construction. Structural steels are alloys of iron, with carefully controlled amounts of carbon and various other metals such as manganese, chromium, aluminium, vanadium, molybdenum, neobium and copper. The carbon content is less than 0.25%, manganese less than 1.5% and the other elements are in trace amounts. The alloying elements control grain size and hence steel properties, giving high strengths, increased ductility and Table 1.1 Strengths of steels used in structures Steel type and use Yield stress (N/mm2 ) Grade 43—structural shapes 275 Grade 50—structural shapes 355 Quenched and self-tempering 500 Quenched tempered-plates 690 Alloy bars—tension members 1030 High carbon hard-drawn wire for cables 1700 fracture toughness. The inclusion of copper gives the corrosion resistant steel Cor-ten. High-carbon steel is used to manufacture hard drawn wires for cables and tendons. The production processes such as cooling rates, quenching and tempering, rolling and forming also have an important effect on the micro structure, giving small grain size which improves steel properties. The modern steels have much improved weldability. Sound full-strength welds free from defects in the thickest sections can be guaranteed. A comparison of the steels used in various forms in structures is given in Table 1.1. The properties of hot-rolled structural steels are given Chapter 2 (Table 2.3). Structural steels are hot-rolled into shapes such as universal beams and columns. The maximum size of universal column in the UK is 356×406 UC, 634 kg/m, with 77 mm-thick flanges. Trade-ARBED in Luxembourg roll a section 360×401 WTM, 1299 kg/m, with 140 mm-thick flanges. The heavy rolled columns are useful in high-rise buildings where large loads must be carried. Heavy built-up H, I and box sections made from plates and lattice members are needed for columns, transfer girders, crane and bridge girders, etc. At the other end of the scale, light weight cold-rolled purdins are used for roofing industrial buildings. Finally, wire, rope and high-strength alloy steel bars are required for cable-suspended and cable-girder roofs and suspended floors in multistorey buildings.

 1.3 TYPES OF STRUCTURES 1.3.1 General types of structures The structural engineer adopts a classification for structures based on the way the structure resists loads, as follows. 1. Gravity masonry structures—loadbearing walls resist loads transmitted to them by floor slabs. Stability depends on gravity loads. 2. Framed structures—a steel or concrete skeleton collects loads from plate elements and delivers them to the foundations. 3. Shell structures—a curved surface covers space and carries loads. 4. Tension structures—cables span between anchor structures carrying membranes. 5. Pneumatic structures—a membrane sealed to the ground is supported by internal air pressure. 2 STEEL STRUCTURES—STRUCTURAL ENGINEERING Examples of the above structures are shown in Figure 1.1 1.3.2 Steel structures Steel-framed structures .may be further classified into the following types: 1. single-storey, single- or multibay structures which may be of truss or stanchion frames or rigid frame of solid or lattice members; 2. multistorey, single- or multibay structures of braced or rigid frame construction—many spectacular systems have been developed; 3. space structures (space decks, domes, towers etc.)—space decks and domes (except the Schwedler dome) are redundant structures, while towers may be statically determinate space structures; 4. tension structures and cable-supported roof structures; Fig. 1.1 General types of structures. TYPES OF STRUCTURES 3 5. stressed skin structures, where the cladding stabilizes the structure. As noted above, combinations with concrete are structurally important in many buildings. Illustrations of some of the types of framed steel structures are shown in Figure 1.2. Braced and rigid frame and truss roof and space deck construction are shown in the figure for comparison. Only framed structures are dealt with in the book. Shell types, e.g. tanks, tension structures and stressed skin structures are not considered. For the framed structures the main elements are the beam, column, tie and lattice member. Beams and columns can be rolled or built-up I, H or box. Detailed designs including idealization, load estimation, analysis and section design are given for selected structures.

 1.4 FOUNDATIONS Foundations transfer the loads from the building structure to the ground. Building loads can be vertical or horizontal and cause overturning and the foundation must resist bearing and uplift loads. The correct choice and design of foundations is essential in steel design to ensure that assumptions made for frame design are achieved in practice. If movement of a foundation should occur and has not been allowed for in design, it can lead to structural failure and damage to finishes in a building. The type of foundation to be used depends on the ground conditions and the type of structure adopted The main types of foundations are set out and discussed briefly, as follows. 1. Direct bearing on rock or soil. The size must be sufficient to ensure that the safe bearing pressure is not exceeded. The amount of overall settlement may need to be limited in some cases, and for separate bases differential settlement can be important. A classification is as follows: • pad or spread footing used under individual columns; • special footings such as combined, balanced or tied bases and special shaped bases; • strip footings used under walls or a row of columns; • raft or mat foundations where a large slab in flat or rubbed construction supports the complete building; • basement or cellular raft foundations; this type may be in one or more storeys and form an underground extension to the building that often serves as a carpark. 2. Piled foundations, where piles either carry loads through soft soil to bear on rock below or by friction between piles and earth. Types of piles used vary from precast driven piles and cast-in-place piles to large deep cylinder piles. All of the above types of foundations can be supported on piles where the foundation forms the pile cap. Foundations are invariably constructed in concrete. Design is covered in specialist books. Some types of foundations for steelframed buildings are shown in Figure 1.3. Where appropriate, comments on foundation design are given in worked examples.

 1.5 STRUCTURAL ENGINEERING

 1.5.1 Scope of structural engineering Structural engineering covers the conception, planning, design, drawings and construction for all structures. Professional engineers from a number of disciplines are involved and work as a team on any given project under the overall control of the architect for a building structure. On engineering structures such as bridges or powerstations, an engineer is in charge. Lest it is thought that the structural engineer’s work is mechanical or routine in nature, it is useful to consider his/her position in building construction where the parties involved are: • the client (or owning organization), who has a need for a given building and will finance the project; • the architect, who produces proposals in the form of building plans and models (or a computer simulation) to meet the client’s requirements, who controls the project and who engages consultants to bring the proposals into being; • consultants (structural, mechanical, electrical, heating and ventilating etc.), who carry out the detail design, prepare working drawings and tender documents and supervise construction; 

4 STEEL STRUCTURES—STRUCTURAL ENGINEERING • contractors, who carry out fabrication and erection of the structural framework, floors, walls, finishes and installation of equipment and services. The structural engineer works as a member of a team and to operate successfully requires flair, sound knowledge and judgement, experience and the ability to exercise great care. His or her role may be summarized as planning, design preparation of drawings and tender documents and supervision of construction. He/she makes decisions about materials, structural form and design methods to be used. He/she recommends acceptance of tenders, inspects, supervises and approves fabrication and construction. He/she has an overall responsibility for safety and must ensure that the consequences of failure due to accidental causes are limited in extent. The designer’s work, which is covered partially in this book, is one part of the structural engineer’s work. 1.5.2 Structural designer’s work The aim of the structural designer is to produce the design and drawings for a safe and economical structure that fulfils its intended purpose. The steps in the design process are as follows