COMPARISON BETWEEN BS 5950: PART 1: 2000 & EUROCODE 3 FOR THE DESIGN OF MULTI-STOREY BRACED STEEL FRAME CHAN CHEE HAN

Transcription

1 i COMPARISON BETWEEN BS 5950: PART 1: 2000 & EUROCODE 3 FOR THE DESIGN OF MULTI-STOREY BRACED STEEL FRAME CHAN CHEE HAN A project report submitted as partial fulfillment of the requirements for the award of the degree of Master of Engineering (Civil Structure) Faculty of Civil Engineering Universiti Teknologi Malaysia NOVEMBER, 2006

2 To my beloved parents and siblings iii

3 iv ACKNOWLEDGEMENT First of all, I would like to express my appreciation to my thesis supervisor, PM. Dr. Ir. Mahmood Md. Tahir of the Faculty of Civil Engineering, Universiti Teknologi Malaysia, for his generous advice, patience and guidance during the duration of my study. I would also like to express my thankful appreciation to Dr. Mahmood s research students, Mr. Shek and Mr. Tan for their helpful guidance in the process of completing this study. Finally, I am most thankful to my parents and family for their support and encouragement given to me unconditionally in completing this task. Without the contribution of all those mentioned above, this work would not have been possible.

4 v ABSTRACT Reference to standard code is essential in the structural design of steel structures. The contents of the standard code generally cover comprehensive details of a design. These details include the basis and concept of design, specifications to be followed, design methods, safety factors, loading values and etc. The Steel Construction Institute (SCI) claimed that a steel structural design by using Eurocode 3 is 6 8% more cost-saving than using BS 5950: Part 1: This study intends to testify the claim. This paper presents comparisons of findings on a series of two-bay, four-storey braced steel frames with spans of 6m and 9m and with steel grade S275 (Fe 460) and S355 (Fe 510) by designed using BS 5950: Part 1: 2000 and Eurocode 3. Design worksheets are created for the design of structural beam and column. The design method by Eurocode 3 has reduced beam shear capacity by up to 4.06% and moment capacity by up to 6.43%. Meanwhile, structural column designed by Eurocode 3 has compression capacity of between 5.27% and 9.34% less than BS 5950: Part 1:2000 design. Eurocode 3 also reduced the deflection value due to unfactored imposed load of up to 3.63% in comparison with BS 5950: Part 1: However, serviceability limit states check governs the design of Eurocode 3 as permanent loads have to be considered in deflection check. Therefore, Eurocode 3 produced braced steel frames which consume 1.60% to 17.96% more steel weight than the ones designed with BS 5950: Part 1: However, with the application of partial strength connections, the percentage of difference had been reduced to the range of 0.11% to 10.95%.

5 vi ABSTRAK Dalam rekabentuk struktur keluli, rujukan kepada kod piawai adalah penting. Kandungan dalam kod piawai secara amnya mengandungi butiran rekabentuk yang komprehensif. Butiran-butiran ini mengandungi asas dan konsep rekabentuk, spesifikasi yang perlu diikuti, cara rekabentuk, factor keselamatan, nilai beban, dan sebagainya. Institut Pembinaan Keluli (SCI) berpendapat bahawa rekabentuk struktur keluli menggunakan Eurocode 3 adalah 6 8% lebih menjimatkan daripada menggunakan BS 5950: Part 1: Kajian ini bertujuan menguji pendapat ini. Kertas ini menunjukkan perbandingan keputusan kajian ke atas satu siri kerangka besi terembat 2 bay, 4 tingkat yang terdiri daripada rentang rasuk 6m dan 9m serta gred keluli S275 (Fe 430) dan S355 (Fe 510). Kertas kerja komputer ditulis untuk merekabentuk rasuk dan tiang keluli. Rekebentuk menggunakan Eurocode 3 telah mengurangkan keupayaan ricih rasuk sehingga 4.06% dan keupayaan momen rasuk sebanyak 6.43%. Selain itu, tiang keluli yang direkebentuk oleh Eurocode 3 mempunyai keupayaan mampatan 5.27% 9.34% kurang daripada rekabentuk menggunakan BS 5950: Part 1: Eurocode 3 juga mengurangkan nilai pesongan yang disebabkan oleh beban kenaan tanpa faktor sehingga 3.63% berbanding BS 5950: Part 1: Namun begitu, didapati bahawa keadaan had kebolehkhidmatan mengawal rekabentuk Eurocode 3 disebabkan beban mati tanpa faktor yang perlu diambilkira dalam pemeriksaan pesongan. Justeru, Eurocode 3 menghasilkan kerangka keluli dirembat yang menggunakan berat besi 1.60% 17.96% lebih banyak daripada kerangka yang direkabentuk oleh BS 5950: Part 1: Namun begitu, penggunaan sambungan kekuatan separa telah berjaya mengurangkan lingkungan berat besi kepada 0.11% 10.95%.

6 vii TABLE OF CONTENTS CHAPTER TITLE PAGE THESIS TITLE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF APPENDICES LISTOF NOTATIONS i ii iii iv v vi vii xii xiii xiv xv I INTRODUCTION 1.1 Introduction Background of Project Objectives Scope of Project Report Layout 5

7 viii II LITERATURE REVIEW 2.1 Eurocode 3 (EC3) Background of Eurocode 3 (EC3) Scope of Eurocode 3: Part 1.1 (EC3) Design Concept of EC Application Rules of EC Ultimate Limit State Serviceability Limit State Actions of EC BS Background of BS Scope of BS Design Concept of BS Ultimate Limit States Serviceability Loading Design of Steel Beam According to BS Cross-sectional Classification Shear Capacity, P v Moment Capacity, M c Low Shear Moment Capacity High Shear Moment Capacity Moment Capacity of Web against Shear Buckling Web not Susceptible to Shear Buckling Web Susceptible to Shear Buckling Bearing Capacity of Web Unstiffened Web Stiffened Web Deflection Design of Steel Beam According to EC Cross-sectional Classification Shear Capacity, V pl.rd Moment Capacity, M c.rd 20

8 ix Low Shear Moment Capacity High Shear Moment Capacity Resistance of Web to Transverse Forces Crushing Resistance, R y.rd Crippling Resistance, R a.rd Buckling Resistance, R b.rd Deflection Design of Steel Column According to BS Column Subject to Compression Force Effective Length, L E Slenderness, λ Compression Resistance, P c Column Subject to Combined Moment and 25 Compression Force Cross-section Capacity Member Buckling Resistance Design of Steel Column According to EC Column Subject to Compression Force Buckling Length, l Slenderness, λ Compression Resistance, N c.rd Buckling Resistance, N b.rd Column Subject to Combined Moment and 29 Compression Force Cross-section Capacity Member Buckling Resistance Conclusion Structural Beam Structural Column 32 III METHODOLOGY 3.1 Introduction 34

9 x 3.2 Structural Analysis with Microsoft Excel Worksheets Beam and Column Design with Microsoft Excel 36 Worksheets 3.4 Structural Layout & Specifications Structural Layout Specifications Loadings Factor of Safety Categories Structural Analysis of Braced Frame Load Combination Shear Calculation Moment Calculation Structural Beam Design BS EC Structural Column Design BS EC 3 61 IV RESULTS & DISCUSSIONS 4.1 Structural Capacity Structural Beam Structural Column Deflection Economy of Design 75 V CONCLUSIONS 5.1 Structural Capacity Structural Beam 81

10 xi Structural Column Deflection Values Economy Recommendation for Future Studies 84 REFERENCES 85 APPENDIX A1 86 APPENDIX A2 93 APPENDIX B1 100 APPENDIX B2 106 APPENDIX C1 114 APPENDIX C2 120 APPENDIX D 126

11 xii LIST OF TABLES TABLE NO. TITLE PAGE 2.1 Criteria to be considered in structural beam design Criteria to be considered in structural column design Resulting shear values of structural beams (kn) Accumulating axial load on structural columns (kn) Resulting moment values of structural beams (knm) Resulting moment due to eccentricity of structural columns (knm) Shear capacity of structural beam Moment capacity of structural beam Compression resistance and percentage difference Moment resistance and percentage difference Deflection of floor beams due to imposed load Weight of steel frame designed by BS Weight of steel frame designed by EC Total steel weight for the multi-storey braced frame design Percentage difference of steel weight (ton) between BS design and EC3 design 4.10 Weight of steel frame designed by EC3 (Semi-continuous) Total steel weight of the multi-storey braced frame design 79 (Revised) 4.12 Percentage difference of steel weight (ton) between BS design and EC3 design (Revised)

12 xiii LIST OF FIGURES FIGURE NO. TITLE PAGE 3.1 Schematic diagram of research methodology Floor plan view of the steel frame building Elevation view of the intermediate steel frame (a) Bending moment of beam for rigid construction (b) Bending moment of beam for semi-rigid construction (c) Bending moment of beam for simple construction 80

13 xiv LIST OF APPENDICES APPENDIX TITLE PAGE A1 Frame Analysis Based on BS A2 Frame Analysis Based on EC3 93 B1 Structural Beam Design Based on BS B2 Structural Beam Design Based on EC3 106 C1 Structural Column Design Based on BS C2 Structural Column Design Based on EC3 120 D Structural Beam Design Based on EC3 (Revised) 126

14 xv LIST OF NOTATIONS BS 5950: PART 1: 2000 EUROCODE 3 Axial load F N Sd Shear force F v V Sd Bending moment M M Sd Partial safety factor γ γ M0 Radius of gyration γ M1 - Major axis r x i y - Minor axis r y i z Depth between fillets d d Compressive strength p c f c Flexural strength p b f b Design strength p y f y Slenderness λ λ Web crippling resistance P crip R a.rd Web buckling resistance P w R b.rd Web crushing resistance - R y.rd Buckling moment resistance M bx M b.y.rd Moment resistance at major axis M cx M c.y.rd M pl.y.rd Shear resistance P v V pl.y.rd Depth D h Section area A g A Effective section area A eff A eff Shear area A v A v

15 xvi Plastic modulus - Major axis S x W pl.y - Minor axis S y W pl.z Elastic modulus - Major axis Z x W el.y - Minor axis Z y W el.z Flange b/t c/t f Web d/t d/t w Width of section B b Effective length L E l Flange thickness T t f Web thickness t t w

16 CHAPTER I INTRODUCTION 1.1 Introduction Structural design is a process of selecting the material type and conducting indepth calculation of a structure to fulfill its construction requirements. The main purpose of structural design is to produce a safe, economic and functional building. Structural design should also be an integration of art and science. It is a process of converting an architectural perspective into a practical and reasonable entity at construction site. In the structural design of steel structures, reference to standard code is essential. A standard code serves as a reference document with important guidance. The contents of the standard code generally cover comprehensive details of a design. These details include the basis and concept of design, specifications to be followed, design methods, safety factors, loading values and etc. In present days, many countries have published their own standard codes. These codes were a product of constant research and development, and past experiences of experts at respective fields. Meanwhile, countries or nations that do not publish their own standard codes will adopt a set of readily available code as the national reference. Several factors govern the type of code to be adopted, namely suitability of application of the code set in a country with respect to its culture, climate and national preferences; as well as the trading volume and diplomatic ties between these countries.

17 2 Like most of the other structural Eurocodes, Eurocode 3 has developed in stages. The earliest documents seeking to harmonize design rules between European countries were the various recommendations published by the European Convention for Constructional Steelwork, ECCS. From these, the initial draft Eurocode 3, published by the European Commission, were developed. This was followed by the various parts of a pre-standard code, ENV1993 (ENV stands for EuroNorm Vornorm) issued by Comité Européen de Normalisation (CEN) the European standardisation committee. These preliminary standards of ENV will be revised, amended in the light of any comments arising out of its use before being reissued as the EuroNorm standards (EN). As with other Europeans standards, Eurocodes will be used in public procurement specifications and to assess products for CE (Conformité Européen) mark. The establishment of Eurocode 3 will provide a common understanding regarding the structural steel design between owners, operators and users, designers, contractors and manufacturers of construction products among the European member countries. It is believed that Eurocode 3 is more comprehensive and better developed compared to national codes. Standardization of design code for structural steel in Malaysia is primarily based on the practice in Britain. Therefore, the move to withdraw BS 5950 and replace with Eurocode 3 will be taking place in the country as soon as all the preparation has completed. Codes of practice provide detailed guidance and recommendations on design of structural elements. Buckling resistance and shear resistance are two major elements of structural steel design. Therefore, provision for these topics is covered in certain sections of the codes. The study on Eurocode 3 in this project will focus on the subject of moment and shear design.

18 3 1.2 Background of Project The arrival of Eurocode 3 calls for reconsideration of the approach to design. Design can be complex, for those who pursue economy of material, but it can be simplified for those pursuing speed and clarity. Many designers feel depressed when new codes are introduced (Charles, 2005). There are new formulae and new complications to master, even though there seems to be no benefit to the designer for the majority of his regular workload. The increasing complexity of codes arises due to several reasons; namely earlier design over-estimated strength in a few particular circumstances, causing safety issues; earlier design practice under-estimated strength in various circumstances affecting economy; and new forms of structure evolve and codes are expanded to include them. However, simple design is possible if a scope of application is defined to avoid the circumstances and the forms of construction in which strength is over-estimated by simple procedures. Besides, this can be achieved if the designer is not too greedy in the pursuit of the least steel weight from the strength calculations. Finally, simple design is possible if the code requirements are presented in an easy-to-use format, such as the tables of buckling stresses in existing BS codes. The Steel Construction Institute (SCI), in its publication of eurocodesnews magazine has claimed that a steel structural design by using Eurocode 3 is 6 8% more cost-saving than using BS Lacking analytical and calculative proof, this project is intended to testify the claim.

19 4 1.3 Objectives The objectives of this project are: 1) To compare the difference in the concept of the design using BS 5950: Part 1: 2000 and Eurocode 3. 2) To study on the effect of changing the steel grade from S275 to S355 in Eurocode 3. 3) To compare the economy aspect between the designs of both BS 5950: Part 1: 2000 and Eurocode Scope of Project The project focuses mainly on the moment and shear design on structural steel members of a series four-storey, 2 bay braced frames. This structure is intended to serve as an office building. All the beam-column connections are to be assumed simple. The standard code used here will be Eurocode 3, hereafter referred to as EC3. A study on the basis and design concept of EC3 will be carried out. Comparison to other steel structural design code is made. The comparison will be made between the EC3 with BS 5950: Part 1: 2000, hereafter referred to as BS The multi-storey steel frame will be first analyzed by using Microsoft Excel worksheets to obtain the shear and moment values. Next, design spreadsheets will be created to calculate and design the structural members.

20 5 1.5 Report Layout The report will be divided into five main chapters. Chapter I presents an introduction to the study. Chapter II presents the literature review that discusses the design procedures and recommendations for steel frame design of the codes EC3 and BS Chapter III will be a summary of research methodology. Results and discussions are presented in Chapter IV. Meanwhile, conclusions and recommendations are presented in Chapter V.

21 CHAPTER II LITERATURE REVIEW 2.1 Eurocode 3 (EC3) Background of Eurocode 3 (EC3) European Code, or better known as Eurocode, was initiated by the Commission of European Communities as a standard structural design guide. It was intended to smooth the trading activities among the European countries. Eurocode is separated by the use of different construction materials. Eurocode 1 covers loading situations; Eurocode covers concrete construction; Eurocode 3 covers steel construction; while Eurocode 4 covers for composite construction Scope of Eurocode 3: Part 1.1 (EC3) EC3, Design of Steel Structures: Part 1.1 General rules and rules for buildings covers the general rules for designing all types of structural steel. It also covers specific rules for building structures. EC3 stresses the need for durability, serviceability and resistance of a structure. It also covers other construction aspects only if they are necessary for design. Principles and application rules are also clearly stated. Principles should be typed in Roman wordings. Application rules must be written in italic style. The use of local application rules are allowed only if they have similar principles as EC3

22 7 and their resistance, durability and serviceability design does not differ too much. EC3 stresses the need for durability, serviceability and resistance of structure (Taylor, 2001). It also covers other construction aspects only if they are necessary for design Design Concept of EC3 All designs are based on limit state design. EC3 covers two limit states, which are ultimate limit state and serviceability limit state. Partial safety factor is applied to loadings and design for durability. Safety factor values are recommended in EC3. Every European country using EC3 has different loading and material standard to accommodate safety limit that is set by respective countries Application Rules of EC3 A structure should be designed and constructed in such a way that: with acceptable probability, it will remain fit for the use for which it is required, having due regard to its intended life and its cost; and with appropriate degrees of reliability, it will sustain all actions and other influences likely to occur during execution and use and have adequate durability in relation to maintenance costs. It should also be designed in such a way that it will not be damaged by events like explosions, impact or consequences of human errors, to an extent disproportionate to the original cause. Potential damage should be limited or avoided by appropriate choice of one or more of the following criteria: Avoiding, eliminating or reducing the hazards which the structure is to sustain; selecting a structural form which has low sensitivity to the hazards considered; selecting a structural form and design that can survive adequately the accidental removal of an individual element; and tying the structure together.

23 Ultimate Limit State Ultimate limit states are those associated with collapse, or with other forms of structural failure which may endanger the safety of people. Partial or whole of structure will suffer from failure. This failure may be caused by excessive deformation, rupture, or loss of stability of the structure or any part of it, including supports and foundations, and loss of equilibrium of the structure or any part of it, considered as a rigid body Serviceability Limit State Serviceability limit states correspond to states beyond which specified service criteria are no longer met. It may require certain consideration, including: deformations or deflections which adversely affect the appearance or effective use of the structure (including the proper functioning of machines or services) or cause damage to finishes or non-structural elements; and vibration, which causes discomfort to people, damage to the building or its contents, or which limits its functional effectiveness Actions of EC3 An action (F) is a force (load) applied to the structure in direct action, or an imposed deformation in indirect action; for example, temperature effects or settlement. Actions are classified by variation in time and by their spatial variation. In time variation classification, actions can be grouped into permanent actions (G), e.g. self-weight of structures, fittings, ancillaries and fixed equipment; variable actions (Q), e.g. imposed loads, wind loads or snow loads; and accidental loads (A), e.g. explosions or impact from vehicles. Meanwhile, in spatial variation classification, actions are defined as fixed actions, e.g. self-weight; and free actions, which result in different arrangements of actions, e.g. movable imposed loads, wind loads, snow loads.

24 9 2.2 BS Background of BS 5950 BS 5950 was prepared to supersede BS 5950: Part 1: 1990, which was withdrawn. Several clauses were technically updated for topics such as sway stability, avoidance of disproportionate collapse, local buckling, lateral-torsional buckling, shear resistance, members subject to combined axial force and bending moment, etc. Changes were due to structural safety, but offsetting potential reductions in economy was also one of the reasons. BS 5950 comprises of nine parts. Part 1 covers the code of practice for design of rolled and welded sections; Part 2 and 7 deal with specification for materials, fabrication and erected for rolled, welded sections and cold formed sections, sheeting respectively; Part 3 and Part 4 focus mainly on composite design and construction; Part 5 concerns design of cold formed thin gauge sections; Part 6 covers design for light gauge profiled steel sheeting; Part 8 comprises of code of practice for fire resistance design; and Part 9 covers the code of practice for stressed skin design Scope of BS 5950 Part 1 of BS 5950 provides recommendations for the design of structural steelwork using hot rolled steel sections, flats, plates, hot finished structural hollow sections and cold formed structural hollow sections. They are being used in buildings and allied structures not specifically covered by other standards.

25 Design Concept of BS 5950 There are several methods of design, namely simple design, continuous design, semi-continuous design, and experimental verification. The fundamental of the methods are different joints for different methods. Meanwhile, in the design for limiting states, BS 5950 covers two types of states ultimate limit states and serviceability limit states Ultimate Limit States Several elements are considered in ultimate limit states. They are: strength, inclusive of general yielding, rupture, buckling and mechanism formation; stability against overturning and sway sensitivity; fracture due to fatigue; and brittle fracture. Generally, in checking, the specified loads should be multiplied by the relevant partial factors γ f given in Table 2. The load carrying capacity of each member should be such that the factored loads will not cause failure Serviceability Limit States There are several elements to be considered in serviceability limit states Deflection, vibration, wind induced oscillation, and durability. Generally, serviceability loads should be taken as the unfactored specified values. In the case of combined imposed load and wind load, only 80% of the full specified values need to be considered when checking for serviceability. In the case of combined horizontal crane loads and wind load, only the greater effect needs to be considered when checking for serviceability.

26 Loading BS 5950 had identified and classified several loads that act on the structure. There are dead, imposed and wind loading; overhead traveling cranes; earth and groundwater loading. All relevant loads should be separately considered and combined realistically as to compromise the most critical effects on the elements and the structure as a whole. Loading conditions during erection should be given particular attention. Where necessary, the settlement of supports should be taken into account as well. 2.3 Design of Steel Beam According to BS 5950 The design of simply supported steel beam covers all the elements stated below. Sectional size chosen should satisfy the criteria as stated below: (i) (ii) (iii) (iv) (v) (vi) Cross-sectional classification Shear capacity Moment capacity (Low shear or High shear) Moment Capacity of Web against Shear Buckling Bearing capacity of web Deflection Cross-sectional Classification Cross-sections should be classified to determine whether local buckling influences their capacity, without calculating their local buckling resistance. The classification of each element of a cross-section subject to compression (due to a bending moment or an axial force) should be based on its width-to-thickness ratio. The elements of a cross-section are generally of constant thickness.

27 12 Generally, the complete cross-section should be classified according to the highest (least favourable) class of its compression elements. Alternatively, a crosssection may be classified with its compression flange and its web in different classes. Class 1 is known as plastic section. It is cross-section with plastic hinge rotation capacity. Class 1 section is used for plastic design as the plastic hinge rotation capacity enables moment redistribution within the structure. Class 2 is known as compact section. It enables plastic moment to take place. However, local buckling will bar any rotation at constant moment. Class 3 is known as semi-compact section. When this section is applied, the stress at the extreme compression fiber can reach design strength. However, the plastic moment capacity cannot be reached. Class 4 is known as slender section. Sections that do not meet the limits for class 3 semi-compact sections should be classified as class 4 slender. Cross-sections at this category should be given explicit allowance for the effects of local buckling Shear Capacity, P v The web of a section will sustain the shear in a structure. Shear capacity is normally checked at section part that sustains the maximum shear force, F v. Clause of BS 5950 states the shear force F v should not be greater than the shear capacity P v, given by: P v = 0.6p y A v

28 13 in which A v is the shear area. BS 5950 provides various formulas for different type of sections. p y is the design strength of steel and it depends on the thickness of the web Moment Capacity, M c At sectional parts that suffer from maximum moment, moment capacity of the section needs to be verified. There are two situations to be verified in the checking of moment capacity low shear moment capacity and high shear moment capacity Low Shear Moment Capacity This situation occurs when the maximum shear force F v does not exceed 60% of the shear capacity P v. Clause of BS 5950 states that: M c = p y S for class 1 plastic or class 2 compact cross-sections; M c = p y Z or alternatively M c = p y S eff for class 3 semi-compact sections; and M c = p y Z eff for class 4 slender cross-sections where S is the plastic modulus; S eff is the effective plastic modulus; Z is the section modulus; and Z eff is the effective section modulus.

29 High Shear Moment Capacity This situation occurs when the maximum shear force F v exceeds 60% of the shear capacity P v. Clause of BS 5950 states that: M c = p y (S ρs v ) < 1.2p y Z for class 1 plastic or class 2 compact cross-sections; M c = p y (Z ρs v /1.5) or alternatively M c = p y (S eff ρs v ) for class 3 semi-compact sections; and M c = p y (Z eff ρs v /1.5) for class 4 slender cross-sections in which S v is obtained from the following: - For sections with unequal flanges: S v = S S f, in which S f is the plastic modulus of the effective section excluding the shear area A v. - Otherwise: S v is the plastic modulus of the shear area A v. and ρ is given by ρ = [2(F v /P v ) 1] 2

30 Moment Capacity of Web against Shear Buckling Web not Susceptible to Shear Buckling Clause of BS 5950 states that, if the web depth-to-thickness d/t 62ε, it should be assumed not to be susceptible to shear buckling and the moment capacity of the cross-section should be determined using Web Susceptible to Shear Buckling Clause states that, if the web depth-to-thickness ratio d/t > 70ε for a rolled section, or 62ε for a welded section, it should be assumed to be susceptible to shear buckling. The moment capacity of the cross-section should be determined taking account of the interaction of shear and moment using the following methods: a) Low shear Provided that the applied shear F v 0.6V w, where V w is the simple shear buckling resistance, V w = dtq w where d = depth of the web; q w = shear buckling strength of the web; obtained from Table 21 BS 5950 t = web thickness b) High shear flanges only method If the applied shear F v > 0.6V w, but the web is designed for shear only, provided that the flanges are not class 4 slender, a conservative value M f for

31 16 the moment capacity may be obtained by assuming that the moment is resisted by the flanges alone, with each flange subject to a uniform stress not exceeding p yf, where p yf is the design strength of the compression flange. c) High shear General method If the applied shear F v > 0.6V w, provided that the applied moment does not exceed the low-shear moment capacity given in a), the web should be designed using Annex H.3 for the applied shear combined with any additional moment beyond the flanges-only moment capacity M f given by b) Bearing Capacity of Web Unstiffened Web Clause states that bearing stiffeners should be provided where the local compressive force F x applied through a flange by loads or reactions exceeds the bearing capacity P bw of the unstiffened web at the web-to-flange connection. It is given by: P bw = (b 1 + nk)tp yw in which, - except at the end of a member: n = 5 - at the end of a member: n = b e /k but n 5 and k is obtained as follows: - for a rolled I- or H-section: k = T + r - for a welded I- or H-section: k = T

32 17 where b 1 is the stiff bearing length; b e is the distance to the nearer end of the member from the end of the stiff bearing; p yw is the design strength of the web; r is the root radius; T is the flange thickness; and t is the web thickness Stiffened Web Bearing stiffeners should be designed for the applied force F x minus the bearing capacity P bw of the unstiffened web. The capacity P s of the stiffener should be obtained from: P s = A s.net p y in which A s.net is the net cross-sectional area of the stiffener, allowing for cope holes for welding. If the web and the stiffener have different design strengths, the smaller value should be used to calculate both the web capacity P bw and the stiffener capacity P s Deflection Deflection checking should be conducted to ensure that the actual deflection of the structure does not exceed the limit as allowed in the standard. Actual deflection is a deflection caused by unfactored live load. Suggested limits for calculated deflections are given in Table 8 of BS 5950.

33 Design of Steel Beam According to EC3 The design of simply supported steel beam covers all the elements stated below. Sectional size chosen should satisfy the criteria as stated below: (i) (ii) (iii) (iv) (v) Cross-sectional classification Shear capacity Moment capacity (Low shear or High shear) Bearing capacity of web a) Crushing resistance b) Crippling resistance c) Buckling resistance Deflection Cross-sectional Classification A beam section should firstly be classified to determine whether the chosen section will possibly suffer from initial local buckling. When the flange of the beam is relatively too thin, the beam will buckle during pre-mature stage. To avoid this, Clause 5.3 of EC3 provided limits on the outstand-to-thickness (c/t f ) for flange and depth-tothickness (d/t w ) in Table Beam sections are classified into 4 classes. Class 1 is known as plastic section. It is applicable for plastic design. This limit allows the formation of a plastic hinge with the rotation capacity required for plastic analysis. Class 2 is also known as compact section. This section can develop plastic moment resistance. However, plastic hinge is disallowed because local buckling will occur first. It has limited rotation capacity. It can also achieve rectangular stress block.

34 19 Class 3 is also known as semi-compact section. The stress block will be of triangle shape. Calculated stress in the extreme compression fibre of the steel member can reach its yield strength, but local buckling is liable to prevent development of the plastic moment resistance. Class 4 is known as slender section. Pre-mature buckling will occur before yield strength is achieved. The member will fail before it reaches design stress. It is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance. Apart from that, the ratios of c/t f and d/t w will be the highest among all four classes Shear Capacity, V pl.rd The web of a section will sustain shear from the structure. Shear capacity will normally be checked at section that takes the maximum shear force, V sd. At each crosssection, the inequality should be satisfied: V sd V pl.rd where V pl.rd = A v (f y / 3) / γ MO A v is the shear area. f y is the steel yield strength and γ MO is partial safety factor as stated in Clause Shear buckling resistance should be verified when for an unstiffened web, the ratio of d/t w > 69ε or d/t w > 30ε k γ for a stiffened web. k γ is the buckling factor for shear, and ε = [235/f y ] 0,5

35 Moment Capacity, M c.rd Moment capacity should be verified at sections sustaining maximum moment. There are two situations to verify when checking moment capacity that is, low shear moment capacity and high shear moment capacity Low Shear Moment Capacity When maximum shear force, V sd is equal or less than the design resistance V pl.rd, the design moment resistance of a cross-section M c.rd may be determined as follows: Class 1 or 2 cross-sections: M c.rd = W pl f y / γ MO Class 3 cross-sections: M c.rd = W el f y / γ MO Class 4 cross-sections: M c.rd = W eff f y / γ M1 where W pl and W el the plastic modulus and elastic modulus respectively. For class 4 cross-sections, W eff is the elastic modulus at effective shear area, as stated in Clause γ MO and γ M1 are partial safety factors High Shear Moment Capacity Clause states that, when maximum shear force, V sd exceeds 50% of the design resistance V pl.rd, the design moment resistance of a cross-section should be reduced to M V.Rd, the reduced design plastic resistance moment allowing for the shear

36 21 force. For cross-sections with equal flanges, bending about the major axis, it is obtained as follows: M V.Rd = (W pl ρa v 2 /4t w ) f y / γ MO but M V.Rd M c.rd where ρ = (2V sd / V pl.rd 1) Resistance of Web to Transverse Forces The resistance of an unstiffened web to transverse forces applied through a flange, is governed by one of the three modes of failure Crushing of the web close to the flange, accompanied by plastic deformation of the flange; crippling of the web in the form of localized buckling and crushing of the web close to the flange, accompanied by plastic deformation of the flange; and buckling of the web over most of the depth of the member. However, if shear force acts directly at web without acting through flange in the first place, this checking is unnecessary. This checking is intended to prevent the web from buckling under excessive compressive force Crushing Resistance, R y.rd Situation becomes critical when a point load is applied to the web. Thus, checking should be done at section subject to maximum shear force. Clause provides that the design crushing resistance, R y.rd of the web of an I, H or U section should be obtained from: R y.rd = (s s + s γ ) t w f γw / γ M1 in which s γ is given by s γ = 2t f (b f / t w ) 0,5 (f yf / f yw ) 0,5 [1 (σ f.ed / f yf ) 2 ] 0,5

37 22 but b f should not be taken as more than 25t f. σ f.ed is the longitudinal stress in the flange. f yf and f yw are yield strength of steel at flange and web respectively Crippling Resistance, R a.rd by: The design crippling resistance R a.rd of the web of an I, H or U section is given R a.sd = 0.5t w 2 (Ef yw ) 0,5 [(t f / t w ) 0,5 + 3(t w / t f )(s s / d)] / γ M1 where s s is the length of stiff bearing, and s s / d < 0,2. For member subject to bending moments, the following criteria should be satisfied: F sd R a.rd M sd M c.rd and F sd / R a.rd + M sd / M c.rd 1, Buckling Resistance, R b.rd The design buckling resistance R b.rd of the web of an I, H or U section should be obtained by considering the web as a virtual compression member with an effective b eff, obtained from b eff = [h 2 + s s 2 ] 0,5. R b.rd = (χ β A f y A) / γ M1

38 23 where β A = 1 and buckling curve c is used at Table and Table Deflection Deflection checking should be conducted to ensure that the actual deflection of the structure does not exceed the limit as allowed in the standard. Actual deflection is a deflection caused by unfactored live load. Suggested limits for calculated deflections are given in Table 4.1 of EC Design of Steel Column According to BS 5950 The design of structural steel column is relatively easier than the design of structural steel beam. Column is a compressive member and it generally supports compressive point loads. Therefore, checking is normally conducted for capacity of steel column to compression only. This, however, applies only to non-moment sustaining column Column Subject to Compression Force Cross-sectional classification of structural steel column is identical as of the classification of structural steel beam. For a structural steel column subject to compression load only, the following criteria should be checked: (i) (ii) (iii) Effective length Slenderness Compression resistance

39 Effective Length, L E The effective length L E of a compression member is determined from the segment length L centre-to-centre of restraints or intersections with restraining members in the relevant plane. Depending on the conditions of restraint in the relevant plate, column members that carry more than 90% of their reduced plastic moment capacity M r in the presence of axial force is assumed to be incapable of providing directional restraint. For continuous columns in multi-storey buildings of simple design, in accordance of Table 22, depending on the conditions of restraint in the relevant plane, directional restraint is based on connection stiffness and member stiffness Slenderness, λ The slenderness λ of a compression member is generally taken as its effective length L E divided by its radius of gyration r about the relevant axis. This concept is not applicable for battened struts, angle, channel, T-section struts, and back-to-back struts. λ = L E / r Compression Resistance, P c by: According to Clause 4.7.4, the compression resistance P c of a member is given P c = A g p c (for class 1 plastic, class 2 compact and class 3 semi-compact cross-sections)

40 25 P c = A eff p cs (for class 4 slender cross-section) where A eff is the effective cross-sectional area; A g is the gross cross-sectional area; p c the compressive strength obtained from Table 23 and Table 24; and p cs is the value of p c from Table 23 and Table 24 for a reduced slenderness of λ(a eff /A g ) 0.5, in which λ is based on the radius of gyration r of the gross cross-section Column Subject to Combined Moment and Compression Force For a column subject to combined moment and compression force, the crosssection capacity and the member buckling resistance need to be checked Cross-section Capacity Generally, for class 1 plastic, class 2 compact and class 3 semi-compact cross sections, the checking of cross-section capacity is as follows: Fc A p g y M + M x cx M + M y cy 1 where F c is the axial compression; A g is the gross cross-sectional area; p y is the design steel strength; M x is the moment about major axis; M cx is the moment capacity about major axis; M y is the moment about minor axis; and M cy is the moment capacity about minor axis.

41 Member Buckling Resistance In simple construction, the following stability check needs to be satisfied: F P c M + M x bs + p M y y Z y 1.0 where F is the axial force in column; P c the compression resistance of column; M x the maximum end moment on x-axis; M b the buckling resistance moment; p y the steel design strength; and Z y the elastic modulus. 2.6 Design of Steel Column According to EC3 The design of steel column according to EC3 is quite similar to the design of steel column according to BS Column Subject to Compression Force Cross-sectional classification of structural steel column is identical as of the classification of structural steel beam. For a structural steel column subject to compression load only, the following criteria should be checked: (i) (ii) (iii) (iv) Buckling length Slenderness Compression resistance Buckling resistance

42 Buckling Length, l The buckling length l of a compression member is dependant on the restraint condition at both ends. Clause states that, provided that both ends of a column are effectively held in position laterally, the buckling length l may be conservatively be taken as equal to its system length L. Alternatively, the buckling length l may be determined using informative of Annex E provided in EC Slenderness, λ The slenderness λ of a compression member is generally taken as its buckling length l divided by its radius of gyration i about the relevant axis, determined using the properties of the gross cross-section. λ = l / i For column resisting loads other than wind loads, the value of λ should not exceed 180, whereas for column resisting self-weight and wind loads only, the value of λ should not exceed Compression Resistance, N c.rd given by: According to Clause 5.4.4, the compression resistance N c.rd of a member is N c.rd = A f y / γ M0 (for class 1 plastic, class 2 compact and class 3 semi-compact crosssections)

43 28 N c.rd = A eff f y / γ M1 (for class 4 slender cross-section) The design value of the compressive force N Sd at each cross-section shall satisfy the following condition: N Sd N c.rd Buckling Resistance, N b.rd For compression members, Clause states that the design buckling resistance of a compression member should be taken as: N c.rd = χ β A A f y / γ M1 where β A = 1 for Class 1, 2 or 3 cross-sections; and A eff / A for Class 4 cross-sections. χ is the reduction factor for the relevant buckling mode. For hot rolled steel members with the types of cross-section commonly used for compression members, the relevant buckling mode is generally flexural buckling. The design value of the compressive force N Sd at each cross-section shall satisfy the following condition: N Sd N b.rd

44 Column Subject to Combined Moment and Compression Force For a column subject to combined moment and compression force, the crosssection capacity and the member buckling resistance need to be checked Cross-section Capacity Generally, cross-section capacity depends on the types of cross-section and applied moment. Clause states that, for bi-axial bending the following approximate criterion may be used: M M y. Sd Ny. Rd α M + M z. Sd Nz. Rd β 1 for Class 1 and 2 cross-sections N N Sd pl. Rd M + M y. Sd pl. y. Rd M + M z. Sd pl. z. Rd 1 for a conservative approximation where, for I and H sections, α = 2; β = 5n but β 1, in which n = N sd / N pl.rd. N Af Sd yd M + W el. y y. Sd f yd M + W el. z z. Sd f yd 1 for Class 3 cross-sections N Sd A f eff yd M + W y. Sd + N eff. y f Sd yd e Ny M + + N W f z. Sd eff. z Sd yd e Nz 1 for Class 4 cross-sections where f yd = f y /γ M1 ; A eff is the effective area of the cross-section when subject to uniform compression; W eff is the effective section modulus of the cross-section when subject

45 30 only to moment about the relevant axis; and e N is the shift of the relevant centroidal axis when the cross-section is subject to uniform compression. However, for high shear (V Sd 0.5 V pl.rd ), Clause states that the design resistance of the cross-section to combinations of moment and axial force should be calculated using a reduced yield strength of (1 ρ)f y for the shear area, where ρ = (2V Sd / V pl.rd 1) Member Buckling Resistance A column, subject to buckling moment, may buckle about major axis or minor axis or both. All members subject to axial compression N Sd and major axis moment M y.sd must satisfy the following condition: N N Sd b. y. Rd k ym + ηm y. Sd c. y. Rd 1,0 where N b.y.rd is the design buckling resistance for major axis; M c.y.rd is the design moment resistance for major-axis bending, k y is the conservative value and taken as 1,5; and η = γ M0 / γ M1 for Class 1, 2 or 3 cross-sections, but 1,0 for Class Conclusion This section summarizes the general steps to be taken when designing a structural member in simple construction.

46 Structural Beam Table 2.1 shown compares the criteria to be considered when designing a structural beam. Table 2.1 : Criteria to be considered in structural beam design BS 5950 CRITERIA EC3 Flange subject to compression 9ε 10ε 15ε Web subject to bending (Neutral axis at mid depth) 80ε 100ε 120ε ε = (275 / p y ) Cross-sectional Classification Class 1 Plastic Class 2 Compact Class 3 Semi-compact Class 1 Plastic Class 2 Compact Class 3 Semi-compact Flange subject to compression 10ε 11ε 15ε Web subject to bending (Neutral axis at mid depth) 72ε 83ε 124ε ε = (235 / f y ) 0,5 P v = 0.6p y A v A v = Dt 2.0 Shear Capacity V pl.rd = f y A v / ( 3 x γ M0 ) γ M0 = 1,05 A v from section table M c = p y S M c = p y Z M c = p y Z eff 3.0 Moment Capacity Class 1, 2 Class 3 Class 4 M c.rd = W pl f y / γ M0 M c.rd = W el f y / γ M0 M c.rd = W eff f y / γ M1 γ M0 = 1,05 γ M1 = 1, Bearing Capacity

47 32 P bw = (b 1 + nk)tp yw Smaller of R y.rd = (s s + s y ) t w f yw / γ M1 R a.rd = 0,5t 2 w (Ef yw ) 0,5 [(t f /t w ) 0,5 + 3(t w /t f )(s s /d)]/γ M1 R b.rd = χβ A f y A / γ M1 d/t 70ε 5.0 Shear Buckling Resistance Ratio d/t w 69ε L / Deflection Limit (Beam carrying plaster or other brittle finish) L / 350 N/A Limit (Total deflection) L / Structural Column Table 2.2 shown compares the criteria to be considered when designing a structural beam. Table 2.2 : Criteria to be considered in structural column design BS 5950 CRITERIA EC3 Flange subject to compression 9ε 10ε 15ε Web (Combined axial load and bending) 80ε / 1 + r 1 100ε / r Cross-sectional Classification Class 1 Plastic Class 2 Compact Class 3 Semi-compact Class 1 Plastic Class 2 Compact Flange subject to compression 10ε 11ε 15ε Web (Combined axial load and bending) 396ε / (13α 1) 456ε / (13α 1)

48 33 120ε / 1 + 2r 2 r 1 = F c / dtp yw, -1 < r 1 1 r 2 = F c / A g p yw ε = (275 / p y ) 0.5 Class 3 Semi-compact 42ε / (0,67 + 0,33ψ) ψ = 2γ M0 σ a / f y 1 σ a = N Sd / A α = 0,5(1 + γ M0 σ w / f y ) σ w = N Sd / dt w ε = (235 / f y ) 0,5 P c = A g p c P c = A eff p cs 2.0 Compression Resistance Class 1, 2, 3 Class 4 N c.rd = Af y / γ M0 γ M0 = 1,05 N c.rd = A eff f y / γ M1 M b = p b S x M b = p b Z x M b = p b Z x.eff 3.0 Moment Resistance Class 1, 2 Class 3 Class 4 M c.rd = W pl f y / γ M0 M c.rd = W el f y / γ M0 M c.rd = W eff f y / γ M1 γ M0 = 1,05 γ M1 = 1, Stability Check F P c M + M x bs + p M y y Z y 1.0 N N Sd b. y. Rd k ym + ηm y. Sd c. y. Rd 1,0

49 CHAPTER III METHODOLOGY 3.1 Introduction As EC3 will eventually replace BS 5950 as the new code of practice, it is necessary to study and understand the concept of design methods in EC3 and compare the results with the results of BS 5950 design. The first step is to study and understand the cross-section classification for steel members as given in EC, analyzing the tables provided and the purpose of each clause stated in the code. At the same time, an understanding on the cross-section classification for BS 5950 is also carried out. Analysis, design and comparison works will follow subsequently. Beams and columns are designed for the maximum moment and shear force obtained from computer software analysis. Checking on several elements, such as shear capacity, moment capacity, bearing capacity, buckling capacity and deflection is carried out. Next, analysis on the difference between the results using two codes is done. Eventually, comparison of the results will lead to recognizing the difference in design approach for each code. Please refer to Figure 3.1 for the flowchart of the methodology of this study.