PSZ 19:16 (Pind. 1/97) UNIVERSITI TEKNOLOGI MALAYSIA BORANG PENGESAHAN STATUS TESIS COMPARISON BETWEEN BS 5950: PART 1: 2000 & EUROCODE 3 FOR JUDUL: THE DESIGN OF MULTI-STOREY BRACED STEEL FRAME SESI PENGAJIAN: 2006 / 2007 Saya CHAN CHEE HAN (HURUF BESAR) mengaku membenarkan tesis (PSM / Sarjana/ Doktor Falsafah )* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut: 1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi pengajian tinggi. 4. **Sila tandakan ( ) SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam (AKTA RAHSIA RASMI 1972) TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/ badan di mana penyelidikan dijalankan) TIDAK TERHAD Disahkan oleh (TANDATANGAN PENULIS) (TANDATANGAN PENYELIA) Alamat Tetap: PETI SURAT 61162, 91021 TAWAU, PM DR. IR. MAHMOOD MD. TAHIR SABAH. Nama Penyelia : 01 NOVEMBER 2006 : 01 NOVEMBER 2006 Tarikh Tarikh: CATATAN: * Potong yang tidak berkenaan. ** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/ organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD. υ Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau Laporan Projek Sarjana Muda (PSM). υ
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PSZ 19:16 (Pind. 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS COMPARISON BETWEEN BS 5950: PART 1: 2000 & EUROCODE 3 FOR JUDUL: THE DESIGN OF MULTI-STOREY BRACED STEEL FRAME
SESI PENGAJIAN: 2006 / 2007
Saya CHAN CHEE HAN (HURUF BESAR)
mengaku membenarkan tesis (PSM/ Sarjana/ Doktor Falsafah)* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:
1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk
tujuan pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara
SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam (AKTA RAHSIA RASMI 1972)
TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/ badan di mana penyelidikan dijalankan)
TIDAK TERHAD
Disahkan oleh
(TANDATANGAN PENULIS) (TANDATANGAN PENYELIA)
Alamat Tetap:
PETI SURAT 61162,
91021 TAWAU, PM DR. IR. MAHMOOD MD. TAHIR SABAH.
Nama Penyelia
: 01 NOVEMBER 2006 : 01 NOVEMBER 2006
Tarikh
Tarikh:
CATATAN: *
Potong yang tidak berkenaan.
** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/ organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.
υ
Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau Laporan Projek Sarjana Muda (PSM).
υ
“I hereby declare that I have read this project report and in
my opinion this project report is sufficient in terms of scope and
quality for the award of the degree of Master of Engineering
(Civil – Structure).”
Signature :
Name of Supervisor : P.M. Dr. Ir. Mahmood Md. Tahir
Date : 01 NOVEMBER 2006
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
ii
I declare that this project report entitled “Comparison Between BS 5950: Part 1:
2000 & Eurocode 3 for The Design of Multi-Storey Braced Steel Frame” is the result
of my own research except as cited in the references. The report has not been
accepted for any degree and is not concurrently submitted in candidature of any other
degree.
Signature :
Name : Chan Chee Han
Date : 01 NOVEMBER 2006
iii
To my beloved parents and siblings
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.
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: 2000. 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: 2000.
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: 2000. However, with the application of
partial strength connections, the percentage of difference had been reduced to the
range of 0.11% to 10.95%.
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: 2000. 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: 2000. Eurocode 3 juga mengurangkan nilai pesongan
yang disebabkan oleh beban kenaan tanpa faktor sehingga 3.63% berbanding BS
5950: Part 1: 2000. 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: 2000. Namun
begitu, penggunaan sambungan kekuatan separa telah berjaya mengurangkan
lingkungan berat besi kepada 0.11% – 10.95%.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
THESIS TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xii
LIST OF FIGURES xiii
LIST OF APPENDICES xiv
LISTOF NOTATIONS xv
I INTRODUCTION
1.1 Introduction 1
1.2 Background of Project 3
1.3 Objectives 4
1.4 Scope of Project 4
1.5 Report Layout 5
viii
II LITERATURE REVIEW
2.1 Eurocode 3 (EC3) 6
2.1.1 Background of Eurocode 3 (EC3) 6
2.1.2 Scope of Eurocode 3: Part 1.1 (EC3) 6
2.1.3 Design Concept of EC3 7
2.1.3.1 Application Rules of EC3 7
2.1.3.2 Ultimate Limit State 8
2.1.3.3 Serviceability Limit State 8
2.1.4 Actions of EC3 8
2.2 BS 5950 9
2.2.1 Background of BS 5950 9
2.2.2 Scope of BS 5950 9
2.2.3 Design Concept of BS 5950 10
2.2.3.1 Ultimate Limit States 10
2.2.3.2 Serviceability 10
2.2.4 Loading 11
2.3 Design of Steel Beam According to BS 5950 11
2.3.1 Cross-sectional Classification 11
2.3.2 Shear Capacity, Pv 12
2.3.3 Moment Capacity, Mc 13
2.3.3.1 Low Shear Moment Capacity 13
2.3.3.2 High Shear Moment Capacity 14
2.3.4 Moment Capacity of Web against Shear Buckling 15
2.3.4.1 Web not Susceptible to Shear Buckling 15
2.3.4.2 Web Susceptible to Shear Buckling 15
2.3.5 Bearing Capacity of Web 16
2.3.5.1 Unstiffened Web 16
2.3.5.2 Stiffened Web 17
2.3.6 Deflection 17
2.4 Design of Steel Beam According to EC3 18
2.4.1 Cross-sectional Classification 18
2.4.2 Shear Capacity, Vpl.Rd 19
2.4.3 Moment Capacity, Mc.Rd 20
ix
2.4.3.1 Low Shear Moment Capacity 20
2.4.3.2 High Shear Moment Capacity 20
2.4.4 Resistance of Web to Transverse Forces 21
2.4.4.1 Crushing Resistance, Ry.Rd 21
2.4.4.2 Crippling Resistance, Ra.Rd 22
2.4.4.3 Buckling Resistance, Rb.Rd 22
2.4.5 Deflection 23
2.5 Design of Steel Column According to BS 5950 23
2.5.1 Column Subject to Compression Force 23
2.5.1.1 Effective Length, LE 24
2.5.1.2 Slenderness, λ 24
2.5.1.3 Compression Resistance, Pc 24
2.5.2 Column Subject to Combined Moment and 25
Compression Force
2.5.2.1 Cross-section Capacity 25
2.5.2.2 Member Buckling Resistance 26
2.6 Design of Steel Column According to EC3 26
2.6.1 Column Subject to Compression Force 26
2.6.1.1 Buckling Length, l 27
2.6.1.2 Slenderness, λ 27
2.6.1.3 Compression Resistance, Nc.Rd 27
2.6.1.4 Buckling Resistance, Nb.Rd 28
2.6.2 Column Subject to Combined Moment and 29
Compression Force
2.6.2.1 Cross-section Capacity 29
2.6.2.2 Member Buckling Resistance 30
2.7 Conclusion
2.7.1 Structural Beam 31
2.7.2 Structural Column 32
III METHODOLOGY
3.1 Introduction 34
x
3.2 Structural Analysis with Microsoft Excel Worksheets 35
3.3 Beam and Column Design with Microsoft Excel 36
Worksheets
3.4 Structural Layout & Specifications 38
3.4.1 Structural Layout 38
3.4.2 Specifications 39
3.5 Loadings 40
3.6 Factor of Safety 41
3.7 Categories 42
3.8 Structural Analysis of Braced Frame 42
3.8.1 Load Combination 42
3.8.2 Shear Calculation 43
3.8.3 Moment Calculation 44
3.9 Structural Beam Design 46
3.9.1 BS 5950 47
3.9.2 EC 3 51
3.10 Structural Column Design 57
3.10.1 BS 5950 57
3.10.2 EC 3 61
IV RESULTS & DISCUSSIONS
4.1 Structural Capacity 66
4.1.1 Structural Beam 66
4.1.2 Structural Column 70
4.2 Deflection 73
4.3 Economy of Design 75
V CONCLUSIONS
5.1 Structural Capacity 81
5.1.1 Structural Beam 81
xi
5.1.2 Structural Column 82
5.2 Deflection Values 82
5.3 Economy 83
5.4 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
xii
LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 Criteria to be considered in structural beam design 31
2.2 Criteria to be considered in structural column design 32
3.1 Resulting shear values of structural beams (kN) 43
3.2 Accumulating axial load on structural columns (kN) 44
3.3 Resulting moment values of structural beams (kNm) 45
3.4 Resulting moment due to eccentricity of structural columns (kNm) 46
4.1 Shear capacity of structural beam 67
4.2 Moment capacity of structural beam 68
4.3 Compression resistance and percentage difference 71
4.4 Moment resistance and percentage difference 71
4.5 Deflection of floor beams due to imposed load 73
4.6 Weight of steel frame designed by BS 5950 75
4.7 Weight of steel frame designed by EC3 76
4.8 Total steel weight for the multi-storey braced frame design 76
4.9 Percentage difference of steel weight (ton) between BS 5950 77
design and EC3 design
4.10 Weight of steel frame designed by EC3 (Semi-continuous) 78
4.11 Total steel weight of the multi-storey braced frame design 79
(Revised)
4.12 Percentage difference of steel weight (ton) between BS 5950 79
design and EC3 design (Revised)
xiii
LIST OF FIGURES
FIGURE NO. TITLE PAGE
3.1 Schematic diagram of research methodology 37
3.2 Floor plan view of the steel frame building 38
3.3 Elevation view of the intermediate steel frame 39
4.1(a) Bending moment of beam for rigid construction 80
4.1(b) Bending moment of beam for semi-rigid construction 80
4.1(c) Bending moment of beam for simple construction 80
xiv
LIST OF APPENDICES
APPENDIX TITLE PAGE
A1 Frame Analysis Based on BS 5950 86
A2 Frame Analysis Based on EC3 93
B1 Structural Beam Design Based on BS 5950 100
B2 Structural Beam Design Based on EC3 106
C1 Structural Column Design Based on BS 5950 114
C2 Structural Column Design Based on EC3 120
D Structural Beam Design Based on EC3 (Revised) 126
xv
LIST OF NOTATIONS
BS 5950: PART 1: 2000 EUROCODE 3
Axial load F NSd
Shear force Fv VSd
Bending moment M MSd
Partial safety factor γ γM0
γM1
Radius of gyration
- Major axis rx iy
- Minor axis ry iz
Depth between fillets d d
Compressive strength pc fc
Flexural strength pb fb
Design strength py fy
Slenderness λ λ
Web crippling resistance Pcrip Ra.Rd
Web buckling resistance Pw Rb.Rd
Web crushing resistance - Ry.Rd
Buckling moment resistance Mbx Mb.y.Rd
Moment resistance at major axis Mcx Mc.y.Rd
Mpl.y.Rd
Shear resistance Pv Vpl.y.Rd
Depth D h
Section area Ag A
Effective section area Aeff Aeff
Shear area Av Av
xvi
Plastic modulus
- Major axis Sx Wpl.y
- Minor axis Sy Wpl.z
Elastic modulus
- Major axis Zx Wel.y
- Minor axis Zy Wel.z
Flange b/T c/tf
Web d/t d/tw
Width of section B b
Effective length LE l
Flange thickness T tf
Web thickness t tw
CHAPTER I
INTRODUCTION
1.1 Introduction
Structural design is a process of selecting the material type and conducting in-
depth 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.
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.
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 5950. Lacking analytical and calculative proof, this project is
intended to testify the claim.
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 3.
1.4 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 5950.
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.
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 5950. 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.
CHAPTER II
LITERATURE REVIEW
2.1 Eurocode 3 (EC3)
2.1.1 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.
2.1.2 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
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.
2.1.3 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.
2.1.3.1 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.
8
2.1.3.2 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.
2.1.3.3 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.
2.1.4 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.
9
2.2 BS 5950
2.2.1 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.
2.2.2 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.
10
2.2.3 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.
2.2.3.1 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 γf given in Table 2. The load carrying capacity of each member should be such
that the factored loads will not cause failure.
2.2.3.2 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.
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2.2.4 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 ground-
water 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) Cross-sectional classification
(ii) Shear capacity
(iii) Moment capacity (Low shear or High shear)
(iv) Moment Capacity of Web against Shear Buckling
(v) Bearing capacity of web
(vi) Deflection
2.3.1 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.
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Generally, the complete cross-section should be classified according to the
highest (least favourable) class of its compression elements. Alternatively, a cross-
section 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.
2.3.2 Shear Capacity, Pv
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, Fv. Clause 4.2.3
of BS 5950 states the shear force Fv should not be greater than the shear capacity Pv,
given by:
Pv = 0.6pyAv
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in which Av is the shear area. BS 5950 provides various formulas for different type of
sections. py is the design strength of steel and it depends on the thickness of the web.
2.3.3 Moment Capacity, Mc
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.
2.3.3.1 Low Shear Moment Capacity
This situation occurs when the maximum shear force Fv does not exceed 60% of
the shear capacity Pv. Clause 4.2.5.2 of BS 5950 states that:
Mc = pyS for class 1 plastic or class 2 compact cross-sections;
Mc = pyZ or alternatively Mc = pySeff for class 3 semi-compact sections; and
Mc = pyZeff for class 4 slender cross-sections
where S is the plastic modulus; Seff is the effective plastic modulus; Z is the section
modulus; and Zeff is the effective section modulus.
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2.3.3.2 High Shear Moment Capacity
This situation occurs when the maximum shear force Fv exceeds 60% of the
shear capacity Pv. Clause 4.2.5.3 of BS 5950 states that:
Mc = py(S – ρSv) < 1.2pyZ for class 1 plastic or class 2 compact cross-sections;
Mc = py(Z – ρSv/1.5) or alternatively Mc = py(Seff – ρSv) for class 3 semi-compact
sections; and
Mc = py(Zeff – ρSv/1.5) for class 4 slender cross-sections
in which Sv is obtained from the following:
- For sections with unequal flanges:
Sv = S – Sf, in which Sf is the plastic modulus of the effective section excluding the
shear area Av.
- Otherwise:
Sv is the plastic modulus of the shear area Av.
and ρ is given by ρ = [2(Fv/Pv) – 1]2
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2.3.4 Moment Capacity of Web against Shear Buckling
2.3.4.1 Web not Susceptible to Shear Buckling
Clause 4.4.4.1 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 2.3.3.
2.3.4.2 Web Susceptible to Shear Buckling
Clause 4.4.4.2 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 Fv ≤ 0.6Vw, where Vw is the simple shear
buckling resistance,
Vw = dtqw
where
d = depth of the web;
qw = 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 Fv > 0.6Vw, but the web is designed for shear only,
provided that the flanges are not class 4 slender, a conservative value Mf for
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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 pyf, where pyf is the design strength of the compression flange.
c) High shear – General method
If the applied shear Fv > 0.6Vw, 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 Mf given by
b).
2.3.5 Bearing Capacity of Web
2.3.5.1 Unstiffened Web
Clause 4.5.2.1 states that bearing stiffeners should be provided where the local
compressive force Fx applied through a flange by loads or reactions exceeds the bearing
capacity Pbw of the unstiffened web at the web-to-flange connection. It is given by:
Pbw = (b1 + nk)tpyw
in which, - except at the end of a member: n = 5
- at the end of a member: n = 2 + 0.6be/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
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where b1 is the stiff bearing length; be is the distance to the nearer end of the member
from the end of the stiff bearing; pyw is the design strength of the web; r is the root
radius; T is the flange thickness; and t is the web thickness.
2.3.5.2 Stiffened Web
Bearing stiffeners should be designed for the applied force Fx minus the bearing
capacity Pbw of the unstiffened web. The capacity Ps of the stiffener should be obtained
from:
Ps = As.netpy
in which As.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 Pbw and the stiffener capacity Ps.
2.3.6 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.
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2.4 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) Cross-sectional classification
(ii) Shear capacity
(iii) Moment capacity (Low shear or High shear)
(iv) Bearing capacity of web
a) Crushing resistance
b) Crippling resistance
c) Buckling resistance
(v) Deflection
2.4.1 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/tf) for flange and depth-to-
thickness (d/tw) in Table 5.3.1. 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.
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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/tf and d/tw
will be the highest among all four classes.
2.4.2 Shear Capacity, Vpl.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, Vsd. At each cross-
section, the inequality should be satisfied:
Vsd ≤ Vpl.Rd
where Vpl.Rd = Av (fy / √3) / γMO
Av is the shear area. fy is the steel yield strength and γMO is partial safety factor
as stated in Clause 5.1.1.
Shear buckling resistance should be verified when for an unstiffened web, the
ratio of d/tw > 69ε or d/tw > 30ε √kγ for a stiffened web. kγ is the buckling factor for
shear, and ε = [235/fy]0,5
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2.4.3 Moment Capacity, Mc.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.
2.4.3.1 Low Shear Moment Capacity
When maximum shear force, Vsd is equal or less than the design resistance Vpl.Rd,
the design moment resistance of a cross-section Mc.Rd may be determined as follows:
Class 1 or 2 cross-sections: Mc.Rd = Wpl fy / γMO
Class 3 cross-sections: Mc.Rd = Wel fy / γMO
Class 4 cross-sections: Mc.Rd = Weff fy / γM1
where Wpl and Wel the plastic modulus and elastic modulus respectively. For class 4
cross-sections, Weff is the elastic modulus at effective shear area, as stated in Clause
5.3.5. γMO and γM1 are partial safety factors.
2.4.3.2 High Shear Moment Capacity
Clause 5.4.7 states that, when maximum shear force, Vsd exceeds 50% of the
design resistance Vpl.Rd, the design moment resistance of a cross-section should be
reduced to MV.Rd, the reduced design plastic resistance moment allowing for the shear
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force. For cross-sections with equal flanges, bending about the major axis, it is obtained
as follows:
MV.Rd = (Wpl – ρAv
2/4tw) fy / γMO but MV.Rd ≤ Mc.Rd
where ρ = (2Vsd / Vpl.Rd – 1)2
2.4.4 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.
2.4.4.1 Crushing Resistance, Ry.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 5.7.3
provides that the design crushing resistance, Ry.Rd of the web of an I, H or U section
should be obtained from:
Ry.Rd = (ss + sγ) tw fγw / γM1
in which sγ is given by sγ = 2tf (bf / tw)0,5 (fyf / fyw)0,5 [1 – (σf.Ed / fyf)2]0,5
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but bf should not be taken as more than 25tf. σf.Ed is the longitudinal stress in the flange.
fyf and fyw are yield strength of steel at flange and web respectively.
2.4.4.2 Crippling Resistance, Ra.Rd
The design crippling resistance Ra.Rd of the web of an I, H or U section is given
External column will be subjected to eccentricity moment, contributed by beam shear.Eccentricity = 100 mm from face of column.Universal column of depth 200 mmInternal column - Moments from left and right will cancel out each other.
External column will be subjected to eccentricity moment, contributed by beam shear.Eccentricity = 100 mm from face of column.Universal column of depth 200 mmInternal column - Moments from left and right will cancel out each other.
Initial trial section is selected to give a suitable moment capacity.The size is then checked to ensure suitability in all other aspects.
Section chosen = 457x152x60 UB
1.2 Section Properties
Mass = 59.8 kg/mDepth D = 454.6 mmWidth B = 152.9 mmWeb thickness t = 8.1 mmFlange thickness T = 13.3 mmDepth between fillets d = 407.6 mmPlastic modulus Sx = 1290 cm3
Elastic modulus Zx = 1120 cm3
Local buckling ratios:Flange b/T = 5.75Web d/t = 50.3
2.0 SECTION CLASSIFICATION
Grade of steel = S275T = 13.3 mm < 16mm
Therefore, py = 275 N/mm2
ε = √ (275/py)= SQRT(275/275)= 1
Outstand element of compression flange,Limiting b/T = 9ε = 9 Flange is plasticActual b/T = 5.75 < 9 Class 1
Section is symmetrical, subject to pure bending, neutral axis at mid-depth,Limiting d/t = 80ε = 80Actual d/t = 50.3 < 80 Web is plastic
Initial trial section is selected to give a suitable moment capacity.The size is then checked to ensure suitability in all other aspects.
Section chosen = 203x203x60 UC
1.2 Section Properties
Mass = 60 kg/mDepth D = 209.6 mmWidth B = 205.2 mmWeb thickness t = 9.3 mmFlange thickness T = 14.2 mmDepth between fillets d = 160.8 mmPlastic modulus Sx = 652 cm3
Elastic modulus Zx = 581.1 cm3
Radius of gyration, rx = 8.96 cmry = 5.19 cm
Gross area, Ag = 75.8 cm2
Local buckling ratios:Flange b/T = 7.23Web d/t = 17.3