Transcript
PSZ 19:16 (Pind. 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA υ
BORANG PENGESAHAN STATUS TESIS JUDUL:
COMPARISON BETWEEN BS 5950: PART 1: 2000 & EUROCODE 3 FOR THE DESIGN OF MULTI-STOREY BRACED STEEL FRAME
SESI PENGAJIAN:
Saya
2006 / 2007
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. 2. 3. 4.
Tesis adalah hakmilik Universiti Teknologi Malaysia. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian sahaja. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi pengajian tinggi. **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
Nama Penyelia
SABAH. Tarikh
CATATAN:
: 01 NOVEMBER 2006
Tarikh:
: 01 NOVEMBER 2006
*
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).
“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
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
I
PAGE
xv
INTRODUCTION
1.1
Introduction
1
1.2
Background of Project
3
1.3
Objectives
4
1.4 1.5
Scope of Project Report Layout
4 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
2.1.4 2.2
8 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
Loading
11
Design of Steel Beam According to BS 5950 2.3.1 Cross-sectional Classification
11 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
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
Bearing Capacity of Web
16
2.3.5.1 Unstiffened Web
16
2.3.5.2 Stiffened Web
17
Deflection
17
2.3.4
2.3.5
2.3.6 2.4
8
Actions of EC3
BS 5950
2.2.4 2.3
2.1.3.3 Serviceability Limit State
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
2.4.4
2.4.5 2.5
2.4.3.1 Low Shear Moment Capacity
20
2.4.3.2 High Shear Moment Capacity
20
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
Deflection
23
Design of Steel Column According to BS 5950 2.5.1
2.5.2
23
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
Column Subject to Combined Moment and
25
Compression Force
2.6
2.5.2.1 Cross-section Capacity
25
2.5.2.2 Member Buckling Resistance
26
Design of Steel Column According to EC3
26
2.6.1
Column Subject to Compression Force 2.6.1.1 Buckling Length, l
26 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
Column Subject to Combined Moment and
29
2.6.2
Compression Force
2.7
III
2.6.2.1 Cross-section Capacity
29
2.6.2.2 Member Buckling Resistance
30
Conclusion 2.7.1
Structural Beam
31
2.7.2
Structural Column
32
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
3.4.1
Structural Layout
38
3.4.2
Specifications
39
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
3.10
Structural Beam Design
46
3.9.1
BS 5950
47
3.9.2
EC 3
51
Structural Column Design
57
3.10.1 BS 5950 3.10.2 EC 3
57 61
RESULTS & DISCUSSIONS
4.1
V
38
3.5
3.9
IV
Structural Layout & Specifications
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
CONCLUSIONS
5.1
Structural Capacity
81
5.1.1
81
Structural Beam
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
4.12
(Revised) 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
Shear resistance
Pv
Mpl.y.Rd 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
- 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
Elastic modulus
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.
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 usingMicrosoft 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 srcinal 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.
11 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 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:
2.3.1
(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
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.
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.
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, F v. 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
13
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 M c = pySeff for class 3 semi-compact sections; and
Mc = pyZeff 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 Zeff is the effective section modulus.
14 2.3.3.2 High Shear Moment Capacity
This situation occurs when the maximum shear force F v 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
15 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
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 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
17
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; 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.
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.
18 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) (iii)
Shear capacity Moment capacity (Low shear or High shear)
(iv)
Bearing capacity of web
(v)
2.4.1
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/tf) for flange and depth-tothickness (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.
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/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 crosssection, the inequality should be satisfied: Vsd ≤ Vpl.Rd
where Vpl.Rd = Av (fy / √3) / γMO
Av is the shear area. f y 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. k γ is the buckling factor for shear, and ε = [235/fy]0,5
20
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 M c.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
21 force. For cross-sections with equal flanges, bending about the major axis, it is obtained as follows:
MV.Rd = (Wpl – ρAv2/4tw) 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, R y.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
22
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 by:
Ra.Sd = 0.5tw2(Efyw)0,5 [(tf / tw)0,5 + 3(tw / tf)(ss / d)] / γM1
where ss is the length of stiff bearing, and s s / d < 0,2. For member subject to bending moments, the following criteria should be satisfied:
Fsd ≤ Ra.Rd Msd ≤ Mc.Rd and Fsd / Ra.Rd + Msd / Mc.Rd ≤ 1,5
2.4.4.3 Buckling Resistance, Rb.Rd
The design buckling resistance Rb.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 beff = [h2 + ss2]0,5.
Rb.Rd = (χ βA fy A) / γM1
23 where βA = 1 and buckling curve c is used at Table 5.5.1 and Table 5.5.2.
2.4.5
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 EC3.
2.5
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.
2.5.1
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)
Effective length
(ii)
Slenderness
(iii)
Compression resistance
24 2.5.1.1 Effective Length,LE
The effective length LE 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 Mr 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.
2.5.1.2 Slenderness, λ
The slenderness λ of a compression member is generally taken as its effective length LE 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 = LE / r
2.5.1.3 Compression Resistance, Pc
According to Clause 4.7.4, the compression resistance Pc of a member is given by:
Pc = Ag pc (for class 1 plastic, class 2 compact and class 3 semi-compact cross-sections)
25
Pc = Aeff pcs (for class 4 slender cross-section)
where Aeff is the effective cross-sectional area; Ag is the gross cross-sectional area; pc the compressive strength obtained from Table 23 and Table 24; and pcs is the value of pc from Table 23 and Table 24 for a reduced slenderness of λ(Aeff/Ag)0.5, in which λ is based on the radius of gyration r of the gross cross-section.
2.5.2
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.
2.5.2.1 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 Ag p y
+
Mx M cx
+
My M cy
≤1
where Fc is the axial compression; Ag is the gross cross-sectional area; py is the design steel strength; Mx is the moment about major axis; M cx is the moment capacity about major axis; My is the moment about minor axis; and Mcy is the moment capacity about minor axis.
26 2.5.2.2 Member Buckling Resistance
In simple construction, the following stability check needs to be satisfied:
F Pc
+
Mx M bs
+
My py Z y
≤ 1. 0
where F is the axial force in column; Pc 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 Zy 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 5950.
2.6.1
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)
Buckling length
(ii)
Slenderness
(iii) (iv)
Compression resistance Buckling resistance
27
2.6.1.1 Buckling Length,l
The buckling length l of a compression member is dependant on the restraint condition at both ends. Clause 5.5.1.5 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 EC3.
2.6.1.2 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 250.
2.6.1.3 Compression Resistance, Nc.Rd
According to Clause 5.4.4, the compression resistance Nc.Rd of a member is given by:
Nc.Rd = A fy / γM0 (for class 1 plastic, class 2 compact and class 3 semi-compact crosssections)
28
Nc.Rd = Aeff fy / γM1 (for class 4 slender cross-section)
The design value of the compressive force NSd at each cross-section shall satisfy the following condition:
NSd ≤ Nc.Rd
2.6.1.4 Buckling Resistance, Nb.Rd
For compression members, Clause 5.5.1.1 states that the design buckling resistance of a compression member should be taken as:
Nc.Rd = χ βA A fy / γM1
where βA = 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 NSd at each cross-section shall satisfy the following condition:
NSd ≤ Nb.Rd
29 2.6.2
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.
2.6.2.1 Cross-section Capacity
Generally, cross-section capacity depends on the types of cross-section and applied moment. Clause 5.4.8.1 states that, for bi-axial bending the following approximate criterion may be used:
α
⎡ M y.Sd ⎤ ⎡ M z .Sd ⎤ β ⎢ ⎥ +⎢ ⎥ ≤1 ⎢⎣ M Ny. Rd ⎥⎦ ⎣ M Nz. Rd ⎦
for Class 1 and 2 cross-sections
M y .Sd N Sd M z .Sd + + ≤1 N pl . Rd M pl . y . Rd M pl . z . Rd
for a conservative approximation
where, for I and H sections, α = 2; β = 5n but β ≥ 1, in which n = Nsd / Npl.Rd.
M y .Sd N Sd M z .Sd + + ≤1 Af yd Wel . y f yd Wel . z f yd
for Class 3 cross-sections
M + N Sd e Ny M z .Sd + N Sd e Nz N Sd + y .Sd + ≤1 Aeff f yd Weff . y f yd Weff . z f yd
for Class 4 cross-sections
where fyd = fy/γM1; Aeff is the effective area of the cross-section when subject to uniform compression; Weff is the effective section modulus of the cross-section when subject
30 only to moment about the relevant axis; and eN is the shift of the relevant centroidal axis when the cross-section is subject to uniform compression.
However, for high shear (VSd ≥ 0.5 Vpl.Rd), Clause 5.4.9 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)fy for the shear area, where ρ = (2VSd / Vpl.Rd – 1)2.
2.6.2.2 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 My.Sd must satisfy the following condition:
k M N Sd + y y.Sd ≤ 1,0 N b. y. Rd ηM c. y. Rd
where Nb.y.Rd is the design buckling resistance for major axis; M c.y.Rd is the design moment resistance for major-axis bending, ky is the conservative value and taken as 1,5; and η = γM0 / γM1 for Class 1, 2 or 3 cross-sections, but 1,0 for Class 4.
2.7
Conclusion
This section summarizes the general steps to be taken when designing a structural member in simple construction.
31 2.7.1
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 1.0 Cross-sectional Classification
Flange subject to compression
EC3
Flange subject to compression
9ε
Class 1 Plastic
10ε
10ε
Class 2 Compact
11ε
15ε
Class 3 Semi-compact
15ε
Web subject to bending
Web subject to bending
(Neutral axis at mid depth)
(Neutral axis at mid depth)
80ε
Class 1 Plastic
72ε
100ε
Class 2 Compact
83ε
120ε
Class 3 Semi-compact
124ε
ε = (275 / py)
ε = (235 / fy)0,5
0.5
2.0 Shear Capacity
Pv = 0.6pyAv
Vpl.Rd = fyAv / (√3 x γM0)
Av = Dt
γM0 = 1,05 Av from section table
3.0 Moment Capacity
Mc = pyS
Class 1, 2
Mc.Rd = Wplfy / γM0
Mc = pyZ
Class 3
Mc.Rd = Welfy / γM0
Mc = pyZeff
Class 4
Mc.Rd = Wefffy / γM1
γM0 = 1,05 γM1 = 1,05 4.0 Bearing Capacity
32 Pbw = (b1 + nk)tpyw
Smaller of Ry.Rd = (ss + sy) tw fyw / γM1 Ra.Rd = 0,5tw2(Efyw)0,5 [(tf/tw)0,5 + 3(tw/tf)(ss/d)]/γM1 Rb.Rd = χβAfyA / γM1 5.0 Shear Buckling Resistance
d/t ≤ 70ε
d/tw ≤ 69ε
Ratio
6.0 Deflection
L / 360
Limit (Beam carrying plaster or
L / 350
other brittle finish)
N/A
2.7.2
Limit (Total deflection)
L / 250
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
1.0 Cross-sectional Classification
Flange subject to compression
Flange subject to compression
9ε
Class 1 Plastic
10ε
10ε
Class 2 Compact
11ε
15ε
Class 3 Semi-compact
15ε
Web (Combined axial load and
Web (Combined axial load and
bending) 80ε / 1 + r 1
Class 1 Plastic
bending) 396ε / (13α – 1)
100ε / 1 + 1.5r1
Class 2 Compact
456ε / (13α – 1)
33 120ε / 1 + 2r2
Class 3 Semi-compact
42ε / (0,67 + 0,33ψ)
r1 = Fc / dtpyw, -1 < r1 ≤ 1
ψ = 2γM0σa / fy – 1
r2 = Fc / Agpyw
σa = NSd / A
ε = (275 / py)0.5
α = 0,5(1 + γM0σw / fy) σw = NSd / dtw ε = (235 / fy)0,5 2.0 Compression Resistance
Pc = Agpc
Class 1, 2, 3
Pc = Aeffpcs
Class 4
Nc.Rd = Afy / γM0
γM0 = 1,05 Nc.Rd = Aefffy / γM1
3.0 Moment Resistance
Mb = pbSx
Class 1, 2
Mc.Rd = Wplfy / γM0
Mb = pbZx
Class 3
Mc.Rd = Welfy / γM0
Mb = pbZx.eff
Class 4
Mc.Rd = Wefffy / γM1
γM0 = 1,05 γM1 = 1,05 4.0 Stability Check
My M F + x + ≤ 1. 0 Pc M bs p y Z y
k M N Sd + y y.Sd ≤ 1,0 N b. y. Rd ηM c. y .Rd
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.
35
3.2
Structural Analysis with Microsoft Excel Worksheets
The structural analysis of the building frame will be carried out by using Microsoft Excel worksheets. As the scope of this study is limited at simple construction,
the use of advanced structural analysis software is not needed.
Sections 3.4 to 3.8 discuss in detail all the specifications and necessary data for the analysis of the multi-storey braced frame. Different factors of safety with reference to BS 5950 and EC3 are defined respectively.
Simple construction allows the connection of beam-to-column to be pinned jointed. Therefore, only beam shear forces will be transferred to the structural column. End moments are zero. Calculation of bending moment, M and shear force, V are based on simply-supported condition, that is
M = wL2 / 8
V = wL / 2
where w is the uniform distributed load and L the beam span.
Please refer to Appendices A1 and A2 for the analysis worksheets created for the purpose of calculating shear force and bending moment values based on the requirements of different safety factors of both codes.
36 3.3
Beam and Column Design with Microsoft Excel Worksheets
The design of beam and column is calculated with Microsoft Excel software. The Microsoft Excel software is used for its features that allow continual and repeated
calculations using values calculated in every cell of the worksheet. Several trial and error calculations can be used to cut down on the calculation time needed as well as prevent calculation error.
Furthermore, Microsoft Excel worksheets will show the calculation steps in a clear and fair manner. The method of design using BS 5950 will be based on the work example drawn by Heywood (2003). Meanwhile, the method of design using EC3 will be based on the work example drawn by Narayanan et. al. (1995).
Please refer to Appendices B1 to C2 for the calculation worksheets created for the purpose of the design of structural beam and column of both design codes.
37
Determine Research Objective and Scope
Phase 1 Literature Review
Determination of building and frame dimension Specify loadings & other specifications Phase 2 Frame analysis using 2 Microsoft Excel (V=wL/2, M=wL /8)
Design worksheet development using Microsoft Excel
Beams and columns design Phase 3
Fail Checking (Shear, Moment, Combined) Pass
Comparison between BS 5950 and EC3
END
Figure 3.1: Schematic diagram of research methodology
38 3.4
Structural Layout & Specifications
3.4.1
Structural Layout
In order to make comparisons of the design of braced steel frame between BS 5950-1: 2000 and Eurocode 3, a parametric study for the design of multi-storey braced frames is carried out.
The number of storey of the frame is set at four (4). In plan view, the 4-storey frame consists of four (4) bays; in total, there will be three (3) numbers of 4-storey frames. 4th storey is roof while the rest will serve as normal floors. Each of the frame’s longitudinal length is 6m. Two (2) lengths of bay width will be used in the analysis – 6m and 9m respectively.
The storey height will be 5m from ground floor to first floor; whereas for other floors (1st to 2nd, 2nd to 3rd, 3rd to roof), the storey height will be 4m.
Please refer to Figure 3.2 and Figure 3.3 for the illustrations of building plan view and elevation view respectively. The intermediate frame will be used as the one to be analysed and designed.
6m
6m
6/9m
6/9m
Figure 3.2 : Floor plan view of the steel frame building.
39
4m
4m
4m
5m
Figure 3.3 : Elevation view of the intermediate steel frame.
3.4.2
Specifications
The designed steel frame structure is meant for office for general use. All the bays will be serving the same function. Meanwhile, flat roof system will be introduced to cater for some activities on roof top. All the roof bays will be used for general purposes.
The main steel frame will consist of solely universal beam (UB) and universal column (UC). As this is a simple construction, all the beam-to-column connections are assumed to be pinned. Web cleats will be used as the connection method to create pinned connection. Top flange of beams are effectively restraint against lateral torsional buckling. Meanwhile, all the column-to-column connections are to be rigid.
40 Precast concrete flooring system will be introduced to this project. The type of precast flooring system to be used will be solid precast floor panel. Therefore, all floors will be of one-way slab. Consequently, each bay will contribute half of the load intensity to the intermediate frame.
The steel frame is assumed to be laterally braced. Therefore, wind load (horizontal load) will not be considered in the design. Only gravitational loads will be considered in this project.
3.5
Loadings
Section 2.2.3 of Concise Eurocode 3 (C-EC3) states that the characteristic values of imposed floor load and imposed roof load must be obtained from Part 1 and Part 3 of BS 6399 respectively. Therefore, all the values of imposed loads of both BS 5950 and EC3 design will be based on BS 6399.
For imposed roof load, section 6.2 (Flat roofs) states that, for a flat roof with access available for cleaning, repair and other general purposes, a uniform load intensity of 1.5kN/m2 is appropriate. In this design, this value will be adopted. Meanwhile, Table 8 (Offices occupancy class) states that the intensity of distributed load of offices for general use will be 2.5kN/m2. This value will be used as this frame model is meant for a general office usage. Multiplying by 6m (3m apiece from either side of the bay) will result in 9kN/m and 15kN/m of load intensity on roof beam and floor beam respectively.
For precast floor selfweight, precast solid floor panel of 100mm thick was selected for flat roof. Meanwhile, 125mm think floor panel will be used for other floors. Weight of concrete is given by 24kN/m3. Multiplying the thickness of the slabs, the intensity of slab selfweight will be 2.4kN/m2 and 3.0kN/m2 respectively.
41
The finishes on the flat roof will be waterproofing membrane and decorative screed. For other floors, a selection of floor carpets and ceramic tiles will be used, depending on the interior designer’s intention. A general load intensity of 1.0kN/m 2 for finishes (superimposed dead load) on all floors will be assumed.
Combining the superimposed dead load with selfweight, the total dead load intensity for roof and floor slabs are 3.4kN/m 2 and 4kN/m2 respectively. Multiplying by 6m (3m apiece from either side of the bay) will result in kN/m and 24kN/m of load intensity on roof beam and floor beam respectively.
3.6
Factor of Safety
Section 2.4.1.2 “Buildings without cranes” of BS 5950 states that, in the design of buildings not subject to loads from cranes, the principal combination of loads that should be taken into account will be load combination 1 – Dead load and imposed gravity loads. Partial safety factors for loads, γf should be taken as 1.4 for dead load, and 1.6 for imposed load.
In EC3, permanent actions G include dead loads such as self-weight of structure, finishes and fittings. Meanwhile, variable actions Q include live loads such as imposed load. From Table 2.1, for normal design situations, partial safety factors, γF for dead load, γG is given by 1,35. Meanwhile, for imposed floor load, γQ is given by 1,5.
Partial safety factor for resistance of Class 1, 2 or 3 cross-section, γM0, is given by 1,05. Partial safety factor for resistance of Class 4 cross-section, γM1, is given by 1,05 as well. The factor γM0 is used where the failure mode is plasticity or yielding. The
42 factor γM1 is used where the failure mode is buckling – including local buckling, which governs the resistance of a Class 4 (slender) cross-section.
3.7
Categories
In this project, in order to justify the effect of design strength of a steel member on the strength of a steel member, two (2) types of steel grade will be used, namely S 275 (or Fe 430 as identified in EC3) and S 355 (or Fe 510 as identified in EC3).
In BS 5950, design strength py is decided by the thickness of the thickest element of the cross-section (for rolled sections). For steel grade S 275, py is 275N/mm2 for thickness less than or equal to 16mm and 265N/mm 2 for thickness larger but less than or equal to 40mm. For steel grade S 355, in the meantime, py is 355N/mm2 and 345N/mm2 respectively for the same limits of thickness.
3.1.2 “Material properties for hot rolled steel” (C-EC3) limits thickness of flange to less than or equal to 40mm for nominal yield strength fy of 275N/mm2 and larger but less than or equal to 100mm for fy of 255N/mm2. Meanwhile, for Fe 510, fy is 355N/mm2 and 335N/mm2 respectively for the same thickness limits.
3.8
Structural Analysis of Braced Frame
3.8.1
Load Combination
This section describes the structural analysis of the steel frame. According to BS 5950, the load combination will be 1.4 times total dead load plus 1.6 times total imposed
43 load (1.4DL + 1.6LL). For the roof, the resultant load combination, w, will be 48kN/m. For all other floors, the w will be 62.64kN/m.
According to EC3, the load combination will be 1.35 times total dead load plus 1.5 times total imposed load (1,35DL + 1,5LL). For the roof, the resultant load combination, w, will be 45.9kN/m. For all other floors, the w will be 59.76kN/m.
3.8.2
Shear Calculation
This steel frame is pinned jointed at all beam-to-column supports. For simple construction, the shear, V at end connections is given by V = wl/2, where w is the resultant load combination and l is the bay width.
Inputting the resultant load combinations into the formula, the resulting shear values of both bay widths and codes of design can be summarized in Table 3.1 below:
Table 3.1 Resulting shear values of structural beams (kN) BS 5950 Location
EC 3
Bay Width
Bay Width
6m
9m
6m
9m
Roof
144
216
137.7
206.55
Other Floors
187.92
281.88
179.28
268.92
From Table 4.1, there is a difference of approximately 4.5% between the analyses of both codes. This is solely due to the difference in partial safety factors. Clearly, BS 5950 results in higher value of shear.
The next table, Table 3.2 will present the accumulating axial loads acting on the structural columns of the steel frame. This is done by summating the resultant shear
44 force from beam of each floor. Internal columns will sustain axial load two times higher than external columns of same floor level as they are connected to two beams.
Table 3.2 Accumulating axial load on structural columns (kN) BS 5950 Floor
6m Int.
Roof – 3 rd
3
nd
2 st
rd
nd
–2
–1
st
1 - Ground
EC 3 9m
Ext.
Int.
6m Ext.
Int.
9m Ext.
Int.
Ext.
288
144
432
216
275.4
137.7
413.1
206.55
663.84
331.92
995.76
497.88
633.96
316 .98
950.94
475.47
1039.68
519.84
1559.52
779.76
992.52
496.26
1488.78
744.39
1415.52
707.76
2123.28
1061.64
1351.08
675.54
2026.62
1013.31
Int. = Internal column Ext. = External column
The accumulating axial loads based on the two codes vary approximately 4.5%, similar with the beam shear.
3.8.3
Moment Calculation
For simple construction, since all the beam-to-column connections are pinned jointed, structural beam moment, M, can be calculated by using the formula M=wl2/8, where w is the resultant load combination and l is the bay width.
Inputting the resultant load combinations into the formula, the resulting moment values of both bay widths and codes of design can be summarized in Table 3.3:
45 Table 3.3 Resulting moment values of structural beams (kNm)
Location
BS 5950
EC 3
Bay Width
Bay Width
6m
9m
6m
9m
Roof
216
486
206.55
464.74
Other Floors
281.88
634.23
268.92
605.07
From Table 3.3, there is a difference of approximately 4.4% to 4.6% between the analyses of both codes. This is solely due to the difference in partial safety factors. Clearly, BS 5950 results in higher value of moment. Regardless of the width of the bay, the higher the load combination of a floor, the higher the difference percentage will be.
For the moments of the structural columns, since this is simple construction, there will be no end moments being transferred from the structural beams. However, there will be a moment due to eccentricity of the resultant shear from the beams. In this project, the eccentricity of the resultant shear from the face of the structural column will be 100mm. Since this is only preliminary analysis as well, the depth of the column has not been decided yet. Therefore, in this case, initially, the depth (D for BS 5950 and h for EC 3) of a structural column is assumed to be 400mm.
Subsequently, the eccentricity moment, Me, can be determined from the following formula:
Me = V (e + D/2) = V (e + h/2)
where V is resultant shear of structural beam (kN), e is the eccentricity of resultant shear from the face of column (m), D or h is the depth of column section (m).
46 V for external column can be easily obtained from shear calculation. However, for internal column, V should be obtained by deducting the factored combination of floor dead (DL) and imposed load (LL) with unfactored floor dead load. For BS 5950, V can be expressed as V = (1.4DL + 1.6LL) – 1.0DL. For EC 3, V can be expressed as V = (1,35DL + 1,5LL) – 1.0DL.
Table 3.4 below summarizes the moment values due to eccentricity. The moments for floor columns will be evenly distributed as the ratio of EI 1/L1 and EI2/L2 is less than 1.5.
Table 3.4 Resulting moment due to eccentricity of structural columns (kNm) BS 5950 Floor
6m
EC 3 9m
6m
9m
Int.
Ext.
Int.
Ext.
Int.
Ext.
Int.
Ext.
Roof
21.6
21.6
32.4
32.4
20.66
20.66
30.98
30.98
Other Floors
63.08
56.38
94.6
84.56
57.88
53.78
86.84
80.68
These values of eccentricity moments will be useful for the estimation of initial size of a column member during structural design in later stage.
3.9
Structural Beam Design
Structural beam design deals with all the relevant checking necessary in the design of a selected structural beam. In simple construction, two major checks that need to be done is shear and moment resistance at ultimate limit state. Next, serviceability check in the form of deflection check will need to be done.
47 The sub-sections next will show one design example which is the floor beam of length 6m and of steel grade S 275 (Fe 430).
3.9.1
BS 5950
In simple construction, necessary checks for ultimate limit state will be shear buckling, shear capacity, moment capacity and web bearing capacity. The shear and moment value for this particular floor beam is 187.92kN and 281.88kNm.
From the section table for universal beam, the sections are rearranged in ascending form, first the mass (kg/m) and then the plastic modulus S x (cm3). The moment will then be divided by the design strength py to obtain an estimated minimum plastic modulus value necessary in the design.
Sx = M / py = 281.88 x 103 / 275 3
= 1025cm From the rearranged table, UB section 457x152x60 is chosen. This is selected to give a suitable moment capacity. The size will then be checked to ensure suitability in all other aspects.
From the section table, the properties of the UB chosen are as follows: Mass = 59.8kg/m; Depth, D = 454.6mm; Width, B = 152.9mm; Web thickness, t = 8.1mm; Flange thickness, T = 13.3mm; Depth between fillets, d = 407.6mm; Plastic modulus, S x = 1290cm3; Elastic modulus, Zx = 1120cm3; b/T = 6.99; d/t = 50.3.
ε = √(275/py) = √(275/275)
48 = 1.0
Sectional classification is based on Table 11 of BS 5950. Actual b/T = 5.75, which is smaller than 9 ε = 9.0. This is the limit for Class 1 plastic section. Therefore, flange is Class 1 plastic section. Meanwhile, actual d/t = 50.3. For web of I-section, where neutral axis is at mid-depth, the limiting value for Class 1 plastic section is 80 ε = 80.0. Actual d/t did not exceed 80.0. Therefore, web is Class 1 plastic section. Since both flange and web are plastic, this section is Class 1 plastic section.
Next, clause 4.4.5 states that if the d/t ratio exceeds 70ε for a rolled section, shear buckling resistance should be checked. Since actually d/t < 70.0 in this design, therefore, shear buckling needs not be checked.
After clause 4.4.5 is checked, section 4.2.3 “Shear capacity” is checked. Shear capacity, Pv = 0.6pyAv, where Av = tD for a rolled I-section. Av = 8.1 x 454.6 = 3682.26mm 2 Pv = 0.6 x 275 x 3682.26 x 10 -3 = 607.57kN > Fv = 187.92kN Therefore, shear capacity is adequate. Next, section 4.2.5 “Moment capacity, Mc” is checked. 0.6Pv = 0.6 x 607.57 = 364.54kN > Fv
Therefore, it is low shear. For class 1 plastic cross-section, M c = pySx. Mc = 275 x 1290 x 10 -3
49 = 354.75kNm To avoid irreversible deformation under serviceability loads, M c should be limited to 1.2pyZx. 1.2pyZx = 1.2 x 275 x 1120 x 10 -3 = 369.6kNm > Mc, therefore, OK. M = 281.88kNm from analysis < Mc = 354.75kNm Therefore, moment capacity is adequate.
To prevent crushing of the web due to forces applied through a flange, section 4.5.2 “Bearing capacity of web” is checked. If F v exceeds Pbw, bearing capacity of web, bearing stiffener should be provided. Pbw = (b1 + nk)tpyw
r = 10.2mm b1 = t + 1.6r + 2T (Figure 13) = 8.1 + 1.6 x 10.2 + 2 x 13.3 = 51.02mm k=T+r = 13.3 + 10.2 = 23.5mm At support, n = 2 + 0.6be/k, be = 0, n = 2 b1 + nk = 98.02mm Pbw = 98.02 x 8.1 x 275 x 10 -3 = 218.34kN > Fv = 187.92kN
50
Therefore, the bearing capacity at support is adequate.
After necessary ultimate limit state checks have been done, the serviceability limit state check (Section 2.5) should be conducted. This is done in the form of deflection check. Generally, the serviceability load should be taken as the unfactored specified value. Therefore, only unfactored imposed load shall be used to calculate the deflection. w = 15kN/m for floors.
L = 6.0m E = 205kN/mm2 I = 25500cm4 The formula for calculating exact deflection, δ, is given by
δ = 5wL4 / 384EI = 5 x 15 x 64 x 105 / 384 x 205 x 25500 = 4.84mm
Table 8 (Suggested limits for calculated deflections) suggests that for “beams carrying plaster or other brittle finish), the vertical deflection limit should be L/360. In this case,
δlim = 6000 / 360 = 16.67mm >δ Therefore, the deflection is satisfactory. The section is adequate. This calculation is repeated for different sections to determine the suitable section which has the minimal mass per length. However, it should also satisfy all the required criteria in the ultimate limit state check.
51
This section satisfied all the required criteria in both ultimate and serviceability limit state check. Therefore, it is adequate to be used.
3.9.2
EC 3
In simple construction, necessary checks for ultimate limit state will be shear buckling, shear capacity, moment capacity, lateral torsional buckling, resistance of web to crushing, crippling and buckling. The shear and moment value for this particular floor beam is 179.28kN and 268.92kNm.
From the section table for universal beam, the sections are rearranged in ascending form, first the mass (kg/m) and then the plastic modulus W pl.y (cm3). The moment will then be divided by the design strength py to obtain an estimated minimum plastic modulus value necessary in the design.
Wpl.y = M / py = 268.92 x 103 / 275 = 977.9cm3
From the rearranged table, UB section 406x178x54 is chosen. This is selected to give a suitable moment capacity. The size will then be checked to ensure suitability in all other aspects.
From the section table, the properties of the UB chosen are as follows: Mass = 54kg/m; Depth, h = 402,6mm; Width, b = 177,6mm; Web thickness, tw = 7,6mm; Flange thickness, tf = 10,9mm; Depth between fillets, d = 360,4mm; Plastic modulus, Wpl.y = 1051cm3; Elastic modulus, W el.y = 927cm3; Shear area, Av = 32,9cm2; Area of
52 section, A = 68,6cm2; Second moment of area, I y = 18670cm4; iLT = 4,36cm; aLT = 131cm; c/tf = 8,15; d/tw = 47,4.
Before checks are done for ultimate limit states, section classification is a must. Based on Table 3.1, tf = 10,9mm. tf ≤ 40mm. For S275 (Fe 430), yield strength, fy = 275N/mm2 and ultimate tensile strength, fu = 430N/mm2. These values must be adopted as characteristic values in calculations. From Table 5.6(a), for “outstand element of compression flange, flange subject to compression only”, limiting c/tf ratio (c is half of b) is 9,2 for Class 1 elements. For “web subject to bending, neutral axis at mid depth”, limiting d/tw ratio is 66,6 for Class 1 elements. Actual c/tf = 8,15 ≤ 9,2. Flange is Class 1 element. Actual d/tw = 47,4 ≤ 66,6. Web is Class 1 element. Therefore, UB section 406x178x54 is Class 1 section.
Next, section 5.5.1 “Shear resistance of cross-section” of beam is checked. The design value of shear force, VSd from analysis at each cross-section should not exceed the design plastic shear resistance Vpl.Rd, that is Vpl.Rd = Av(fy / √3) / γM0. VSd = 179,28kN
γM0 = 1,05 Vpl.Rd = (32,9 x 100 x 275) / ( √3 x 1,05) = 497,48kN > 179,28kN Therefore, shear resistance is sufficient. 0,5Vpl.Rd = 0,5 x 497,48 = 298,49kN > VSd = 179,28kN
53
Therefore, low shear.
For low shear, section 5.5.2 “Moment resistance of cross-section with low shear” the design value of moment MSd must not exceed the design moment resistance of the cross-section Mc.Rd = Wpl.y fy / γM0 for Class 1 or Class 2 cross-section.
MSd = 268,92kNm Mc.Rd = 1051 x 275 x 10-3 / 1,05 = 275,26kNm > MSd Therefore, the moment capacity is sufficient.
The beam is fully restrained, not susceptible to lateral torsional buckling. Therefore, section 5.5.5 “Lateral-torsional buckling” needs not be checked.
Section 5.5.6 “Shear buckling” requires that webs must have transverse stiffeners at the supports if d/t w is greater than 63,8 and 56,1 for steel grade Fe 430 and Fe 510 respectively. Actual d/tw = 47,4 < 63,8. Therefore, shear buckling check is not required.
Section 5.6 “Resistance of webs to transverse forces” requires transverse stiffeners to be provided in any case that the design value VSd applied through a flange to a web exceeds the smallest of the following – Crushing resistance, R y.Rd, crippling resistance, Ra.Rd and buckling resistance, Rb.Rd.
For crushing resistance, Ry.Rd = (ss + sy) twfyw / γM1 where at support, sy = tf(bf/tw)0,5[fyf/fyw]0,5 [1 – (γM0 σf.Ed/fyf)2]0,5
54
At support, bending moment is zero.
σf.Ed = 0. γM0 = 1,05, ss = 50mm at support.
2
fyf = 275N/mm . sy = 10,9 (177,6 / 7.6)0,5 = 52.69mm Ry.Rd = (50 + 52,69) x 7,6 x 275 x 10 -3 / 1,05 = 204,4kN
For crippling resistance, Ra.Rd = 0,5tw2 (Efyw)0,5 [(tf/tw)0,5 + 3(tw/tf) (ss/d)] / γM1 ss/d = 50 / 360,4 = 0,14 ≤ 0,2. OK
γM1 = 1,05 E = 210kN/mm2 Ra.Rd = 0,5 x 7,62 (210000 x 275)0,5 [(10,9/7,6)0,5 + 3(7,6/10,9)(0,14)] / 1,05 = 307,8kN
For buckling resistance, Rb.Rd = βA fc A / γM1 A = beff x tw beff = 0,5[h2 + ss2]0,5 + a + ss/2 = 0,5 [402,62 + 502]0,5 + 0 + 50/2 = 227,8mm beff should be less than [h 2 + ss2]0,5 = 405,7mm. OK. A = 227,8 x 7,6 2
= 1731,28mm
55
βA = 1 γM1 = 1,05 For ends restrained against rotation and relative lateral movement (Table 5.29),
λ = 2,5 d/t = 2,5 x 360,4 / 7.6 = 118,6 From Table 5.13 (rolled I-section), buckling about y-y axis, curve (a) is used.
λ√βA = 118,6 λ√βA = 118, fc = 121N/mm2 λ√βA = 120, fc = 117N/mm2 By interpolation, fc = 119,8N/mm2 Rb.Rd = 1 x 119,8 x 1731,28 x 10 -3 / 1,05 = 197,5kN Ra.Rd = 307,8kN Ry.Rd = 204,4kN Minimum of the 3 values are 197,5kN, which is larger than V Sd = 179,28kN. Therefore, the web of the section can resist transverse forces. OK.
After necessary ultimate limit state checks have been done, the serviceability limit state check (Section 4.2) should be conducted. This is done in the form of deflection check. Generally, the serviceability load should be taken as the unfactored specified value. From Figure 4.1, deflection should take into account deflection due to both permanent loads and imposed loads.
δmax = δ1 + δ2 – δ0 (hogging δ0 = 0 at unloaded state) w1 = 27.6kN/m for floors. (Permanent load)
56
w2 = 15kN/m for floors. (Imposed load)
L = 6.0m E = 210kN/mm2 Iy = 18670cm4 The formula for calculating exact deflection, δ, is given by
δ = 5wL4 / 384EI δ1 = 5 x 27,6 x 64 x 105 / 384 x 210 x 18670 = 11,88mm
δ2 = 5 x 15 x 64 x 105 / 384 x 210 x 18670 = 6,46mm
Table 4.1 (Recommended limiting values for vertical deflections) suggests that for “floors and roofs supporting plaster or other brittle finish or non-flexible partitions”, the vertical deflection limit should be L/350 for
δ2 and L/250 for δmax. In this case,
δlim. 2 = 6000 / 350 = 17,14mm > δ2
δlim. max = 6000 / 250 = 24mm > δ1 + δ2 = 18,34mm Therefore, the deflection is satisfactory. The section is adequate. This calculation is repeated for different sections to determine the suitable section which has the minimal mass per length. However, it should also satisfy all the required criteria in the ultimate limit state check.
57 This section satisfied all the required criteria in both ultimate and serviceability limit state check. Therefore, it is adequate to be used.
3.10
Structural Column Design
Structural column design deals with all the relevant checking necessary in the design of a selected structural beam. In simple construction, apart from section classification, two major checks that need to be done is compression and combined axial and bending at ultimate limit state.
The sub-sections next will show one design example which is the internal column “ground floor to 1 st floor” (length 5m) of the steel frame with bay width 6m and of steel grade S 275 (Fe 430).
3.10.1 BS 5950
In simple construction, apart from section classification, necessary checks for ultimate limit state will be compression resistance and combined axial force and moment. The axial force and eccentricity moment value for this particular internal column are 1415.52kN and 63.08kNm respectively.
From the section table for universal column, the sections are rearranged in ascending form, first the mass (kg/m) and then the plastic modulus S x (cm3). The moment will then be divided by the design strength py to obtain an estimated minimum plastic modulus value necessary in the design.
Sx = M / py
58 = 63.08 x 103 / 275 = 229.4cm3
From the rearranged table, UC section 203x203x60 is chosen. This is selected to give a suitable moment capacity. The size will then be checked to ensure suitability in all other aspects.
From the section table, the properties of the UC chosen are as follows: Mass = 60kg/m; Depth, D = 209.6mm; Width, B = 205.2mm; Web thickness, t = 9.3mm; Flange thickness, T = 14.2mm; Depth between fillets, d = 160.8mm; Plastic modulus, S x = 652cm3; Elastic modulus, Zx = 581.1cm3; Radius of gyration, rx = 8.96cm, ry = 5.19cm; Gross area, Ag = 75.8cm2; b/T = 7.23 (b = 0.5B); d/t = 17.3.
T < 16mm, therefore, py = 275N/mm2
ε = √(275/py) = √(275/275) = 1.0
Sectional classification is based on Table 11 of BS 5950. Actual b/T = 7.23, which is smaller than 9 ε = 9.0. This is the limit for Class 1 plastic section (Outstand element of compression flange). Therefore, flange is Class 1 plastic section. Meanwhile, actual d/t = 17.3. For web of I-section under axial compression and bending, the limiting value for Class 1 plastic section is 80 ε / 1 + r1, where r1 is given by r1 = Fc / dtpy. r1 = 1415.52 x 103 / 160.8 x 9.3 x 275 = 3.44 but -1 < r1 ≤ 1, therefore, r1 = 1 Limiting d/t value = 80 x 1 / 1 + 1 = 40
59 > Actual d/t = 17.3 Therefore, the web is Class 1 plastic section. Since both flange and web are plastic, this section is Class 1 plastic section.
Next, based on section 4.7.2 “Slenderness” and section 4.7.3 “Effective lengths”, and from Table 22 (Restrained in direction at one end), the effective length, L E = 0.85L = 0.85 x 5000 = 4250mm.
λx = LEx / rx = 4250 / 8.96 x 10 = 47.4
Next, based on section 4.7.4 “Compression resistance”, for class 1 plastic section, compression resistance, Pc = Agpc. pc is the compressive strength determined from Table 24. For buckling about x-x axis, T < 40mm, strut curve (b) is used.
λx = 46, pc = 242N/mm2 λx = 48, pc = 239N/mm2 From interpolation,
λx = 47.4, pc = 239.9N/mm2 Pc = Agpc = 75.8 x 100 x 239.9 x 10 -3 = 1818.44kN > Fc = 1415.52kN Therefore, compressive resistance is adequate.
60 Next, for columns in simple construction, the beam reaction, R, is assumed to be acting 100mm from the face of the column. From frame analysis, M i = 63.08kNm. The moment is distributed between the column lengths above and below 1st floor, in proportion to the bending stiffness of each length. For EI / L1st-2nd : EI / Lground-1st < 1.5, the moment will be equally divided. Therefore, M = 31.54kNm.
Section 4.7.7 “Columns in simple structures”, when only nominal moments are applied, the column should satisfy the relationship (Fc / Pc) + (Mx / Mbs) + (My / pyZy) ≤ 1 My = 0, therefore, My / pyZy = 0 Equivalent slenderness λLT of column is given by
λLT = 0.5L / ry = 0.5 x 5000 / 5.19 x 10 = 48.17 From Table 16 (Bending strength pb for rolled sections),
λLT = 45, pb = 250N/mm2 λLT = 50, pb = 233N/mm2 From interpolation,
λLT = 48.17, pb = 260.78N/mm2 Mb = pbSx -3
= 260.78 x 652 x 10 = 170.03kNm
61 (Fc / Pc) + (Mx / Mbs) = 1415.52 / 1818.44 + 31.54 / 170.03 = 0.96 < 1.0 Therefore, the combined resistance against axial force and eccentricity moment is adequate. This section satisfied all the required criteria in ultimate limit state check. Therefore, it is adequate to be used.
3.10.2 EC 3
In simple construction, apart from section classification, necessary checks for ultimate limit state will be cross-section resistance (in the form of moment resistance) and in-plane failure about major axis (which is a combination of axial force and eccentricity moment). The axial force and eccentricity moment value for this particular internal column are 1351,08kN and 57,88kNm respectively.
From the section table for universal column, the sections are rearranged in ascending form, first the mass (kg/m) and then the plastic modulus W pl.y (cm3). The moment will then be divided by the design strength fy to obtain an estimated minimum plastic modulus value necessary in the design.
Wpl.y = MSd / fy = 57,88 x 103 / 275 = 210,5cm3
From the rearranged table, UC section 254x254x73 is chosen. This is selected to give a suitable moment capacity. The size will then be checked to ensure suitability in all other aspects.
62 From the section table, the properties of the UC chosen are as follows: Mass = 73kg/m; Depth, h = 254mm; Width, b = 254mm; Web thickness, t w = 8,6mm; Flange thickness, tf = 14,2mm; Depth between fillets, d = 200,2mm; Plastic modulus, Wpl.y = 3
3
990cm ; Elastic modulus, Wel.y = 895cm ; Radius of gyration, iy = 11,1cm, iz = 6,46cm; Area of section, A = 92,9cm2; Shear area, Av = 25,6cm2; Second moment of area, Iy = 11370cm4; iLT = 6,86cm; aLT = 98,5cm; c/tf = 8,94 (c = 0,5b); d/tw = 23,3.
2
2
tf = 14,2mm < 40mm, therefore, fy = 275N/mm , fu = 430N/mm
Sectional classification is based on Table 5.6(a) of C-EC3 for Class 1 elements. Actual c/tf = 8,94. From this table, for outstand element of compression flange (flange subject to compression only), the limiting values of c/t f for Class 1 and 2 are 9,2 and 10,2 respectively. Actual c/tf = 8,94 < 9,2. Therefore, flange is Class 1 element. For web subject to bending and compression, the classification depends on the mean web stress, σw. For symmetric I-section of Class 1 or 2,
σw = NSd / dtw = 1351,08 x 103 / 200,2 x 8,6 = 784,73N/mm2 Table 5.8 gives the limiting values of stress
σw for Class 1 and 2 cross-sections.
From Table 5.8, with d/tw = 23,3, the web is Class 1. Since both flange and web are plastic, this section is Class 1 section.
Next, section 5.6 “Axially loaded members with moments” will be checked. Beforehand, from, section 5.5.1,
63
Vpl.Rd = Av(fy / √3) / γM0 = (25,6 x 102 x 275) x 10-3 / (√3 x 1,05) = 387,1kN Maximum applied shear load (at top of column) is Vmax.Sd = My.Sd / L = 57,88 x 103 / 5000 = 11,58kN 0,5Vpl.Rd > Vmax.Sd Therefore, the section is subject to a low shear. From Table 5.27, n = NSd / Npl.Rd Reduced design plastic moment, allowing for axial force, MN.Rd is such that n < 0,1 : MNy.Rd = Mpl.y.Rd n ≥ 0,1 : MNy.Rd = 1,11 Mpl.y.Rd (1 – n) Npl.Rd = A fy / γM0 = 92,9 x 102 x 275 x 10-3 / 1,05 = 2433,1kN n = 1351,08 / 2433,1 = 0,555 ≥ 0,1 Therefore, MNy.Rd = 1,11 Mpl.y.Rd (1 – n) Mpl.y.Rd = Wpl.y fy / γM0 = 990 x 10-3 x 275 / 1,05 = 259,3kNm MNy.Rd = 1,11 x 259,3 x (1 – 0,555)
64 = 128,1kNm > MSd = 28,94kNm Therefore, the moment resistance is sufficient.
Lastly, section 5.6.3.2 “Axial compression and major axis bending” states that all members subject to axial compression N Sd and major axis moment M y.Sd must satisfy the expression (NSd / Nb.y.Rd) + (kyMy.Sd / ηMc.y.Rd) ≤ 1,0 Ly = 0,85L = 0,85 x 5000 = 4250mm Slenderness ratio
λy = Ly / iy = 4250 / 11,1 x 10 = 38,3 Based on Table 5.13 “Selection of buckling curve for f c”, for buckling about y-y axis, buckling curve (b) is used.
βA = 1 λy√βA = 38,3 tf ≤ 40mm
λy√βA = 38, fc = 250N/mm2 λy√βA = 40, fc = 248N/mm2 From interpolation,
λy√βA = 38,3, fc = 249,7N/mm2
65 Nb.y.Rd = βA fc A / γM1, γM1 = 1,05 = 1 x 249,7 x 92,9 x 10 2 x 10-3 / 1,05 = 2209,3kN ky = interaction factor about yy axis = 1,5 (Conservative value)
η = γM0 / γM1 =1 (NSd / Nb.y.Rd) + (kyMy.Sd / ηMc.y.Rd) = (1351,08 / 2209,3) + (1,5 x 28,94 / 1 x 128,1) = 0,95 < 1,0 Therefore, the resistance against in-plane failure against major axis is sufficient. This section 254x254x73 UC satisfied all the required criteria in ultimate limit state check. Therefore, it is adequate to be used.
CHAPTER IV
RESULTS & DISCUSSIONS
The results of the structural design of the braced steel frame (beam and column) are tabulated and compiled in the next sections. The results are arranged accordingly, namely structural capacity, deflection, and weight of steel.
4.1
Structural Capacity
Structural capacity deals with shear and moment resistance of a particular section chosen. Here, structural capacity is sub-divided into beam and column.
4.1.1
Structural Beam
UB sections ranging from 305x102x25 to 533x210x122 are being tabulated in ascending form. Shear capacity and moment capacity of each section are being calculated separately, based on steel grade S275 and S355. The results are shown in Table 4.1 for shear capacity and Table 5.2 for moment capacity. The results based on BS 5950 and EC3 calculation are compiled together to show the difference between each other.
67 Table 4.1 Shear capacity of structural beam UB SECTION
S275 Difference
BS 5950
EC 3
(kN)
(kN)
(kN)
305x102x25 305x102x28 305x102x33
291.98 305.61 340.53
284.28 303.93 334.18
7.7 1.68 6.35
305x127x37 305x127x42 305x127x48
356.6 405.5 461.84
358.37 399.2 447.58
305x165x40 305x165x46 305x165x54
300.37 338.95 404.61
356x127x33 356x127x39
% Diff.
S355 Difference
BS 5950
EC 3
(kN)
(kN)
(kN)
% Diff.
2.64 0.55 1.86
376.92 394.52 439.59
366.97 392.35 431.39
9.95 2.17 8.2
2.64 0.55 1.87
-1.77 6.3 14.26
-0.5 1.55 3.09
460.34 523.47 596.19
462.62 515.33 577.79
-2.28 8.14 18.4
-0.5 1.56 3.09
308.47 341.74 393.15
-8.1 -2.79 11.46
-2.7 -0.82 2.83
387.75 437.55 522.31
398.21 441.15 507.52
-10.46 -3.6 14.79
-2.7 -0.82 2.83
345.51 384.85
343.25 382.56
2.26 2.29
0.65 0.6
446.02 496.81
443.1 493.85
2.92 2.96
0.65 0.6
356x171x45 356x171x51 356x171x57 356x171x67
405.87 433.46 478.47 545.65
400.71 429.44 471.78 541.33
5.16 4.02 6.69 4.32
1.27 0.93 1.4 0.79
523.94 559.55 617.66 704.38
517.28 554.37 609.02 698.81
6.66 5.18 8.64 5.57
1.27 0.93 1.4 0.79
406x140x39 406x140x46
420.29 452.39
409.78 456.66
10.51 -4.27
2.5 -0.94
542.55 583.99
528.99 589.5
13.56 -5.51
2.5 -0.94
406x178x54 406x178x60 406x178x67 406x178x74
511.5 529.74 594.45 623.53
497.48 517.14 583.67 644.16
14.02 12.6 10.78 -20.63
2.74 2.38 1.81 -3.31
660.3 683.85 767.38 811.77
642.21 667.58 753.47 831.55
18.09 16.27 13.91 -19.78
2.74 2.38 1.81 -2.44
457x152x52 457x152x60 457x152x67 457x152x74 457x152x82
564.05 607.57 680.13 705.2 777.65
551.92 588.21 668.35 730.35 793.86
12.13 19.36 11.78 -25.15 -16.21
2.15 3.19 1.73 -3.57 -2.08
728.14 784.32 877.99 918.09 1012.42
712.48 759.33 862.78 942.81 1024.8
15.66 24.99 15.21 -24.72 -12.38
2.15 3.19 1.73 -2.69 -1.22
457x191x67 457x191x74 457x191x82 457x191x89 457x191x98
635.89 678.65 724.09 773.65 846.85
619.96 666.84 727.32 783.27 845.27
15.93 11.81 -3.23 -9.62 1.58
2.51 1.74 -0.45 -1.24 0.19
820.88 876.07 942.68 1007.2 1102.5
800.32 860.83 938.91 1011.13 1091.16
20.56 15.24 3.77 -3.93 11.34
2.5 1.74 0.4 -0.39 1.03
533x210x82
854.26
819.56
34.7
4.06
1102.77
1057.98
44.79
4.06
533x210x92
888.41
878.53
9.88
1.11
1146.86
1134.11
12.75
1.11
533x210x101
925.06
943.56
-18.5
-2
1204.32
1218.04
-13.72
-1.14
68 533x210x109
995.05
1007.06
-12.01
-1.21
1295.45
1300.03
-4.58
-0.35
533x210x122
1099.51
1115.94
-16.43
-1.49
1431.44
1440.57
-9.13
-0.64
The difference is based on deduction of shear capacity of EC3 from BS 5950. For steel grade S275, the difference percentage ranges from -3.57% to 4.06%. For steel grade S355, meanwhile, the difference percentage ranges from -2.69% to 4.06%. Negative value indicates that the shear capacity calculated from EC3 is higher than that from BS 5950.
There are a few explanations to the variations. The shear capacity of a structural beam is given by Pv = 0.6 py Av
… (BS 5950)
Av = Dt Vpl.Rd = (Av x fy) / (γM0 x √3)
… (EC3)
Av is obtained from section table. This value, however, varies with Av = Dt as suggested by BS 5950. Most of the values given are lesser than Dt value. Also, 1 / (γM0 x √3) ≈ 0.55, which is approximately 8.3% less than 0.6 as suggested by BS 5950. Therefore, these facts explain the reason why shear capacity of most of the sections designed by EC3 is lower than the one designed by BS 5950.
Table 4.2 Moment capacity of structural beam UB SECTION BS 5950 (kNm)
EC 3 (kNm)
305x102x25
94.05
88
305x102x28 305x102x33
110.83 132.28
305x127x37 305x127x42
148.23 168.85
S275 Difference (kNm)
S355 Difference (kNm)
% Diff.
BS 5950 (kNm)
EC 3 (kNm)
% Diff.
6.05
6.43
121.41
113.6
7.81
6.43
106.86 125.98
3.97 6.3
3.58 4.76
143.07 170.76
137.94 162.62
5.13 8.14
3.59 4.77
141.43 160.29
6.8 8.56
4.59 5.07
191.35 217.97
182.57 206.91
8.78 11.06
4.59 5.07
69 305x127x48
195.53
184.9
10.63
5.44
252.41
238.7
13.71
5.43
305x165x40 305x165x46 305x165x54
171.33 198 232.65
163.95 189.1 220.79
7.38 8.9 11.86
4.31 4.49 5.1
221.17 255.6 300.33
211.65 244.1 285.01
9.52 11.5 15.32
4.3 4.5 5.1
356x127x33 356x127x39
149.33 181.23
141.17 171.29
8.16 9.94
5.46 5.48
192.77 233.95
182.33 221.11
10.44 12.84
5.42 5.49
356x171x45 356x171x51
213.13 246.4
202.45 234.4
10.68 12
5.01 4.87
275.13 318.08
261.35 302.6
13.78 15.48
5.01 4.87
356x171x57 356x171x67
277.75 332.75
264.26 317.69
13.49 15.06
4.86 4.53
358.55 429.55
341.14 410.11
17.41 19.44
4.86 4.53
406x140x39 406x140x46
199.1 244.2
188.05 232.83
11.05 11.37
5.55 4.66
257.02 315.24
242.75 300.57
14.27 14.67
5.55 4.65
406x178x54 406x178x60 406x178x67 406x178x74
291.5 330 371.25 397.5
275.26 312.98 352.52 395.21
16.24 17.02 18.73 2.29
5.57 5.16 5.05 0.58
376.3 426 479.25 517.5
355.34 404.02 455.08 510.19
20.96 21.98 24.17 7.31
5.57 5.16 5.04 1.41
457x152x52 457x152x60 457x152x67 457x152x74 457x152x82
302.5 354.75 398.75 431.95 479.65
287.05 336.02 377.67 425.33 471.95
15.45 18.73 21.08 6.62 7.7
5.11 5.28 5.29 1.53 1.61
390.5 457.95 514.75 562.35 624.45
370.55 433.78 487.53 549.07 609.25
19.95 24.17 27.22 13.28 15.2
5.11 5.28 5.29 2.36 2.43
457x191x67 457x191x74 457x191x82 457x191x89 457x191x98
404.25 453.75 484.95 532.65 590.95
385.52 434.5 479.81 529.05 585.1
18.73 19.25 5.14 3.6 5.85
4.63 4.24 1.06 0.68 0.99
521.85 585.75 631.35 693.45 769.35
497.68 560.9 619.39 682.95 755.3
24.17 24.85 11.96 10.5 14.05
4.63 4.24 1.89 1.51 1.83
533x210x82 533x210x92 533x210x101 533x210x109 533x210x122
566.5 654.5 691.65 749.95 848
539 619.67 685.93 740.4 838.88
27.5 34.83 5.72 9.55 9.12
4.85 5.32 0.83 1.27 1.08
731.3 844.9 900.45 976.35 1104
695.8 799.93 885.47 955.8 1082.92
35.5 44.97 14.98 20.55 21.08
4.85 5.32 1.66 2.1 1.91
The difference is based on deduction of moment capacity of EC3 from BS 5950. For steel grade S275, the difference percentage ranges from 0.58% to 6.03%. For steel grade S355, meanwhile, the difference percentage ranges from 1.41% to 6.43%. Positive value indicates that the moment capacity calculated from EC3 is lower than that from BS 5950.
70
There are a few explanations to the variations. The moment capacity of a structural beam is given by Mc = py Sx Mc.Rd = Wpl.y fy / γM0
… (BS 5950) … (EC3)
From EC3 equation, 1 / γM0 ≈ 0.95. This is approximately 5% less than 1.0 as suggested by BS 5950. Besides that, there are some variations between plastic modulus specified by BS 5950 section table and EC3 section table. For example, for a UB section 3
406x178x54, plastic modulus based on BS 5950 (S x) and EC3 (Wpl.y) are 1060cm and 1051cm3 respectively. There is a variation of approximately 0.85%. Therefore, these facts explain the reason why moment capacity of most of the sections designed by EC3 is lower than the one designed by BS 5950.
4.1.2
Structural Column
In determining the structural capacity of a column, sectional classification tables – Table 11 and Table 5.3.1 of BS 5950 and EC3 respectively, are revised. For a column web subject to bending and compression, BS 5950 only provides a clearer guideline to the classification of Class 3 semi-compact section. Meanwhile, EC3 provides better guidelines to classify a section web, whether it is Class 1, Class 2 or Class 3 element.
A study is conducted to determine independently compression and bending moment capacity of structural column with actual length of 5m. Table 4.3 shows the result and percentage difference of compression resistance while Table 4.4 shows the result and percentage difference of moment resistance.
71 Table 4.3 Compression resistance and percentage difference UC SECTION BS 5950 (kN)
EC 3 (kN)
152x152x37
1027.63
956.1
203x203x46 203x203x52 203x203x60 203x203x71 203x203x86
1403.56 1588.95 1818.44 2199.15 2667.72
254x254x73 254x254x89 254x254x107 254x254x132 254x254x167 305x305x97 305x305x118 305x305x137 305x305x158 305x305x198 305x305x240 305x305x283
S275 Difference (kN)
S355 Difference (kN)
% Diff.
BS 5950 (kN)
EC 3 (kN)
% Diff.
71.53
6.96
1259.66
1142
117.66
9.34
1323.8 1500 1721.2 2067.3 2508.5
79.76 88.95 97.24 131.85 159.22
5.68 5.6 5.35 6 5.97
1773.41 2007.94 2298.26 2780.37 3373.46
1631 1849.7 2128 2566.8 3117.7
142.41 158.24 170.26 213.57 255.76
8.03 7.88 7.41 7.68 7.58
2341.45 2878.73 3454.34 4291.41 5419.6
2209.3 2715.9 3269.7 4057.6 5117.3
132.15 162.83 184.64 233.81 302.3
5.64 5.66 5.35 5.45 5.58
2982.65 3668.29 4402.89 5474.39 6918.72
2772.8 3411.3 4107.4 5099 6432.7
209.85 256.99 295.49 375.39 486.02
7.04 7.01 6.71 6.86 7.02
3205.31 3901.39 4553.57 5256.95 6612.78 8028.11 9489.33
3025.8 3695.7 4292 4965.7 6242.4 7572.7 8958.9
179.51 205.69 261.57 291.25 370.38 455.41 530.43
5.6 5.27 5.74 5.54 5.6 5.67 5.59
4097.01 4987.14 5821.16 6720.88 8455.58 10267.55 12138.99
3825.9 4677.1 5435.4 6294.2 7924.8 9626.4 11403.1
271.11 310.04 385.76 426.68 530.78 641.15 735.89
6.62 6.22 6.63 6.35 6.28 6.24 6.06
Table 4.4 Moment resistance and percentage difference UC SECTION BS 5950 (kNm)
EC 3 (kNm)
152x152x37
69.47
80.9
203x203x46 203x203x52 203x203x60 203x203x71 203x203x86
129.03 146.73 167.96 205.13 249.38
254x254x73 254x254x89 254x254x107
277.94 344.27 413.51
S275 Difference (kNm)
S355 Difference (kNm)
% Diff.
BS 5950 (kNm)
EC 3 (kNm)
% Diff.
-11.43
-16.45
73.69
104.5
-30.81
-41.81
130.2 148.5 171.3 209.8 256.4
-1.17 -1.77 -3.34 -4.67 -7.02
-0.91 -1.21 -1.99 -2.28 -2.81
160.33 182.21 208.5 254.35 309.08
168 191.7 221.1 270.8 331
-7.67 -9.49 -12.6 -16.45 -21.92
-4.78 -5.21 -6.04 -6.47 -7.09
259.3 320.8 388.7
18.64 23.47 24.81
6.71 6.82 6
348.82 431.88 518.18
334.7 414.2 501.7
14.12 17.68 16.48
4.05 4.09 3.18
72 254x254x132 254x254x167
521.91 669.51
490.3 633.3
31.61 36.21
6.06 5.41
653.96 838.26
632.9 817.5
21.06 20.76
3.22 2.48
305x305x97 305x305x118 305x305x137 305x305x158 305x305x198 305x305x240 305x305x283
438.6 538.83 633.77 738.82 946.51 1168.56 1403.39
416.2 511.2 600.5 700.6 900.4 1111.3 1287.4
22.4 27.63 33.27 38.22 46.11 57.26 115.99
5.11 5.13 5.25 5.17 4.87 4.9 8.26
575.44 705.68 828.47 964.08 1231.05 1515.42 1815.14
537.2 660 775.3 904.4 1162.4 1434.5 1676
38.24 45.68 53.17 59.68 68.65 80.92 139.14
6.65 6.47 6.42 6.19 5.58 5.34 7.67
Shear capacity designed by BS 5950 is overall higher than EC3 design by the range of 5.27 – 6.96% and 6.22 – 9.34% for steel grade S275 (Fe 430) and S355 (Fe 510) respectively. This is mainly due to the partial safety factor
γM1 of 1,05 imposed by EC3
in the design. Also, the compression strength f c determined from Table 5.14(a) of EC3 is less than the compression strength pc determined from Table 24 of BS 5950.
Meanwhile, as the size of section increases, the difference percentage changes from -16.45% to 8.26% for S275 (Fe 460) and -41.81% to 7.67% for S355 (Fe 510). This means that smaller sizes designed by EC3 have higher moment capacity than BS 5950 design. From the moment capacity formula of BS 5950,
Mb = pbSx
pb depends on equivalent slenderness λLT, which is also dependant on the member length. The bigger the member size, the higher the radius of gyration, ry is. Therefore, pb increases with the increase in member size.
However, moment capacity based on EC3 design,
Mpl.y.Rd = Wpl.y fy / γM0
73 The moment capacity is not dependant on equivalent slenderness. Therefore, when member sizes increase, eventually, the moment capacity based on EC3 is overtaken by BS 5950 design.
4.2
Deflection
Table 4.5 shows the deflection values due to floor imposed load. In BS 5950, this is symbolized as δ while for EC3, this is symbolized as
δ2.
Table 4.5 Deflection of floor beams due to imposed load UB SECTION
L = 6.0m
L = 9.0m
BS 5950
EC 3
Difference
% Diff.
BS 5950
EC 3
Difference
% Diff.
305x102x25 305x102x28 305x102x33 305x127x37
(δ, mm) 27.56 22.99 19 17.22
(δ2, mm) 27.62 22.16 18.54 16.83
(mm) -0.06 0.83 0.46 0.39
-0.22 3.61 2.42 2.26
(δ, mm) 139.53 116.41 96.17 87.18
(δ2, mm) 139.83 112.19 93.86 85.2
(mm) -0.3 4.22 2.31 1.98
-0.22 3.63 2.4 2.27
305x127x42 305x127x48
15.06 12.89
14.77 12.68
0.29 0.21
1.93 1.63
76.23 65.25
74.79 64.19
1.44 1.06
1.89 1.62
305x165x40 305x165x46 305x165x54
14.53 12.47 10.55
14.1 12.13 10.31
0.43 0.34 0.24
2.96 2.73 2.27
73.54 63.14 53.43
71.36 61.42 52.2
2.18 1.72 1.23
2.96 2.72 2.3
356x127x33 356x127x39
14.97 12.11
14.71 11.93
0.26 0.18
1.74 1.49
75.77 61.28
74.49 60.42
1.28 0.86
1.69 1.4
356x171x45 356x171x51 356x171x57 356x171x67
10.2 8.76 7.72 6.33
9.98 8.51 7.51 6.17
0.22 0.25 0.21 0.16
2.16 2.85 2.72 2.53
51.66 44.33 39.07 32.06
50.51 43.09 38 31.23
1.15 1.24 1.07 0.83
2.23 2.8 2.74 2.59
406x140x39 406x140x46
9.88 7.86
9.71 7.69
0.17 0.17
1.72 2.16
50.01 39.81
49.17 38.94
0.84 0.87
1.68 2.19
406x178x54 406x178x60 406x178x67 406x178x74
6.6 5.72 5.08 4.52
6.46 5.6 4.95 4.39
0.14 0.12 0.13 0.13
2.12 2.1 2.56 2.88
33.43 28.94 25.72 22.9
32.68 28.33 25.08 22.25
0.75 0.61 0.64 0.65
2.24 2.11 2.49 2.84
74
457x152x52 457x152x60 457x152x67 457x152x74 457x152x82
5.77 4.84 4.27 3.78 3.37
5.64 4.74 4.21 3.71 3.33
0.13 0.1 0.06 0.07 0.04
2.25 2.07 1.41 1.85 1.19
29.21 24.51 21.63 19.12 17.08
28.55 23.98 21.34 18.79 16.83
0.66 0.53 0.29 0.33 0.25
2.26 2.16 1.34 1.73 1.46
457x191x67 457x191x74 457x191x82 457x191x89
4.2 3.71 3.33 3.01
4.1 3.61 3.25 2.93
0.1 0.1 0.08 0.08
2.38 2.7 2.4 2.66
21.26 18.77 16.85 15.25
20.75 18.25 16.45 14.83
0.51 0.52 0.4 0.42
2.4 2.77 2.37 2.75
457x191x98
2.7
2.63
0.07
2.59
13.68
13.33
0.35
2.56
533x210x82 533x210x92 533x210x101 533x210x109 533x210x122
2.6 2.24 2.01 1.85 1.62
2.54 2.18 1.96 1.8 1.58
0.06 0.06 0.05 0.05 0.04
2.31 2.68 2.49 2.7 2.47
13.16 11.32 10.16 9.36 8.22
12.84 11.03 9.9 9.13 8.01
0.32 0.29 0.26 0.23 0.21
2.43 2.56 2.56 2.46 2.55
From Table 4.5 above, for a floor beam of 6m long, subject to 15kN/m of unfactored imposed floor load, the difference percentage ranges from -0.22% to 3.61%. Meanwhile, for a floor beam of 9m long, the difference percentage ranges from -0.22% to 3.63%. This is basically same as the range of beam length 6m. It also indicates that deflection value calculated from BS 5950 is normally higher than that from EC3.
The first explanation for this difference is the modulus of elasticity value, E. Section 3.1.3 “Other properties” of BS 5950 states that E = 205kN/mm2. Meanwhile, section 3.1.4 “Design values of material coefficients” of C-EC3 states that E = 210kN/mm2. Apart from that, there is also slight difference between second moment of area in both codes. For example, for a section 356x171x57, I x = 16000cm4 from BS 5950 section table. Meanwhile, Iy = 16060cm4 from EC3 section table.
The minor differences had created differences between the deflection values. However, the major difference between the deflection designs of these two codes is the total deflection, δmax, as required by EC3. Different from BS 5950, EC3 requires deflection due to permanent dead load to be included in the final design.
75
4.3
Economy of Design
After all the roof beams, floor beams, external columns and internal columns have been designed for the most optimum size, the results of the design (size of structural members) are tabulated in Table 4.6 and Table 4.7 for BS 5950 and EC3 design respectively. To compare the economy of the design, the weight of steel will be used as a gauge.
Table 4.6 Weight of steel frame designed by BS 5950 Model
Frame
No
Type
Section Designation Universal Beams
Universal Columns
Total Steel Weight
Floor
Roof
457x152x60
406x140x46
External
Internal
(tonne)
S275
1
2 Bay 4 Storey
To 2nd 2nd - 4th
(6m span)
2
2 Bay
203x203x46
203x203x60
152x152x30
203x203x46
203x203x52
203x203x86
203x203x46
203x203x52
152x152x37
203x203x52
152x152x23
152x152x37
203x203x46
203x203x71
152x152x37
203x203x46
4.744
Storey Storey
533x210x92
533x210x82
4 Storey
To 2nd
9.122
Storey 2nd - 4th
(9m span)
Storey
S355
3
2 Bay
406x140x46
406x140x39
4 Storey
To 2nd 2nd - 4th
(6m span) 4
2 Bay 4 Storey
Storey 533x210x82
457x191x67
To 2nd Storey 2nd - 4th
(9m span)
3.750
Storey
Storey
7.889
76 Table 4.7 Weight of steel frame designed by EC3 Model
Frame
No
Type
Section Designation Universal Beams
Universal Columns
Total Steel Weight
Floor
Roof
406x178x54
406x140x46
External
Internal
203x203x52
254x254x73
152x152x37
203x203x46
203x203x71
254x254x107
203x203x46
203x203x71
203x203x46
203x203x71
152x152x30
203x203x46
203x203x60
254x254x89
203x203x46
203x203x60
(tonne)
S275
5
2 Bay 4 Storey
To 2nd 2nd - 4th
(6m span) 6
2 Bay
4.821
Storey Storey 533x210x92
533x210x82
4 Storey
To 2nd
9.645
Storey 2nd - 4th
(9m span)
Storey
S355
7
2 Bay
406x178x54
356x171x45
4 Storey
To 2nd 2nd - 4th
(6m span) 8
2 Bay
4.571
Storey Storey 533x210x92
533x210x82
4 Storey
To 2nd
9.313
Storey 2nd - 4th
(9m span)
Storey
Summary of the total steel weight for the multi-storey braced steel frame design is tabulated in Table 4.8. The saving percentage, meanwhile, is tabulated in Table 4.9.
Table 4.8 Total steel weight for the multi-storey braced frame design Types of Frame
2Bay 4Storey
Bay Width
Steel
(m)
Grade
BS 5950
EC3
S275
4.744
4.821
3.750
4.571
S275
9.122
9.645
(Fe 430) S355
7.889
9.313
6
Total Steel Weight (ton)
(Fe 430) S355 (Fe 510) 2Bay 4Storey
9
(Fe 510)
77
Table 4.9
Percentage difference of steel weight (ton) between BS 5950 design and
EC3 design Frame
2Bay 4Storey
Bay
Steel
Total Steel Weight (ton)
Width (m)
Grade
BS 5950
EC3
%
6
S275
4.744
4.821
1.60
3.750
4.571
17.96
9.122
9.645
5.42
7.889
9.313
15.29
(Fe 430) S355 (Fe 510) 2Bay 4Storey
9
S275 (Fe 430) S355 (Fe 510)
As shown in Table 4.9, all frame types, beam spans and steel grade designed by using BS 5950 offer weight savings as compared with EC3. The percentage of saving offered by BS 5950 design ranges from 1.60% to 17.96%, depending on the steel grade. The percentage savings for braced steel frame with 9m span is higher than that one with 6m span. This is because deeper, larger hot-rolled section is required to provide adequate moment capacity and also stiffness against deflection.
Regardless of bay width, the percentage savings by using BS 5950 are higher than EC3 for S355 steel grade with respect to S275 steel grade. This is because overall deflection was considered in EC3 design. Meanwhile, unaffected by the effect of imposed load deflection, BS 5950 design allowed lighter section. This resulted in higher percentage difference.
Further check on the effect of deflection was done. This time, the connections of beam-to-column were assumed to be “partial strength connection”. Semi-continuous
78 frame is achieved in this condition. For uniformly distributed loading, the deflection value is given as:
δ = βwL4 / 384EI For a span with connections having a partial strength less than 45%, the deflection coefficient, β is treated as β = 3.5. This is different from pinned joint in simple construction, where zero “support” stiffness corresponds to a value of
β = 5.0,
which was used in the beam design.
Please refer to Appendix D for a redesign work after the
β value had been revised
and the section redesigned to withstand bending moment from analysis process. The renewed beam sections are tabulated in Table 4.10 shown. Columns remained the same as there was no change in the value of eccentricity moment and axial force.
Table 4.10 Weight of steel frame designed by EC3 (Semi-continuous) Model
Frame
No
Type
Section Designation (Semi-continous) Universal Beams
Universal Columns
Total Steel Weight
Floor
Roof
457x178x52
406x140x46
External
Internal
203x203x52
254x254x73
152x152x37
203x203x46
203x203x71
254x254x107
203x203x46
203x203x71
203x203x46
203x203x71
152x152x30
203x203x46
203x203x60
254x254x89
203x203x46
203x203x60
(tonne)
S275
5
2 Bay 4 Storey
To 2nd 2nd - 4th
(6m span) 6
2 Bay
4.749
Storey Storey 533x210x92
533x210x82
4 Storey
To 2nd
9.645
Storey 2nd - 4th
(9m span)
Storey
S355
7
2 Bay
406x140x46
356x127x39
4 Storey
To 2nd 2nd - 4th
(6m span) 8
2 Bay 4 Storey
Storey 533x210x82
457x151x67
To 2nd Storey 2nd - 4th
(9m span)
4.211
Storey
Storey
8.503
79
Summary of the total revised steel weight for the multi-storey braced steel frame design is tabulated in Table 4.11. The saving percentage, meanwhile, is tabulated in Table 4.12.
Table 4.11 Total steel weight for the multi-storey braced frame design (Revised) Types of Frame
Bay Width
Steel
Total Steel Weight (ton)
(m)
Grade
BS 5950
6
S275
4.744
4.749
3.750
4.211
9.122
9.645
7.889
8.503
EC3 (Semi-Cont)
2Bay 4Storey
(Fe 430) S355 (Fe 510) 2Bay 4Storey
9
S275 (Fe 430) S355 (Fe 510)
Table 4.12
Percentage difference of steel weight (ton) between BS 5950 design and
EC3 design (Revised) Frame
2Bay 4Storey
Bay
Steel
Width (m)
Grade
BS 5950
Total Steel Weight (ton) EC3 (Semi-Cont)
%
6
S275
4.744
4.749
0.11
3.750
4.211
10.95
S275
9.122
9.645
5.42
(Fe 430) S355
7.889
8.503
7.22
(Fe 430) S355 (Fe 510) 2Bay 4Storey
9
(Fe 510)
80
From Table 4.12, it can be seen that there is an obvious reduction of steel weight required for the braced steel frame, if it is built semi-continuously. Even though EC3 design still consumed higher steel weight, the percentage of difference had been significantly reduced to the range of 0.11% to 10.95%. The effect of dead load on the deflection of beam had been gradually reduced. The greater difference for steel grade S355 indicated that deflection still plays a deciding role in EC3 design. However, as the connection stiffness becomes higher, the gap reduces.
The ability of partial strength connection had enabled moment at mid span to be partially transferred to the supports (Figure 4.1(b)). Therefore, the sagging moment at mid span became less than that of simple construction (Figure 4.1(c)).
Eventually, if rigid connection is introduced, with deflection coefficient set as β = 1.0, the effect of deflection on the design will be eliminated. The moment capacity will be the deciding factor. Please refer to Figure 4.1(a) for the illustration of rigid connection.
MR wL2/8
wL2/8
MR wL2/8
(a)
(b) 2
Design moment, MD = wL /8 – MR
Figure 4.1
Bending moment of beam for: (a) rigid construction; (b) semi-rigid
construction; (c) simple construction.
(c)
CHAPTER V
CONCLUSIONS
This chapter presents the summary for the study on the comparison between BS 5950 and EC3 for the design of multi-storey braced frame. In review to the research objectives, a summary on the results of the objectives is categorically discussed. Suggestions of further research work are also included in this chapter.
5.1
Structural Capacity
5.1.1
Structural Beam
For the shear capacity of a structural beam, calculation based on EC3 had reduced a member’s shear capacity of up to 4.06% with regard to BS 5950 due to the variance between constant values of the shear capacity formula specified by both codes. Apart from that, the difference between the approaches to obtain shear area, Av value also caused the difference. The application of different steel grade did not contribute greater percentage of difference between the shear capacities calculated by both codes.
Meanwhile, for the moment capacity of structural beam, calculation based on EC3 had effectively reduced a member’s shear capacity of up to 6.43%. This is mainly due to the application of partial safety factor, γM0 of 1,05 in the moment capacity
82 calculation required by EC3, as compared to the partial safety factor, γM of 1.0 as suggested by BS 5950.
With the inclusion of partial safety factor, it is obvious that EC3 stresses on the safety of a structural beam. The design of structural beam proposed by EC3 is concluded to be safer than that by BS 5950.
5.1.2
Structural Column
In simple construction, only moments due to eccentricity will be transferred to structural column. In comparison, axial compression is much more critical. Therefore, only compressive resistance comparison of structural column was made.
A reduction in the range of 5.27% to 9.24% of column compressive resistance was achieved when designing by EC3, compared with BS 5950. This comparison is based on a structural column of 5.0m long. This is due to the implication of partial safety factor, γ
of 1,05 as required by EC3 design. Meanwhile, there is also a deviation in
M0
between the compressive strength, fc and pc respectively, of both codes. From interpolation, it was found that for a same value of λ, fc is smaller than pc.
The steel frame is assumed to be laterally braced. Therefore, wind load (horizontal load) will not be considered in the design. Only gravitational loads will be considered in this project.
5.2
Deflection Values
When subject to an unfactored imposed load, a structural beam will be subject to deflection. For the same value of unfactored imposed load, EC3 design created majority
83 lower deflection values with respect to BS 5950 design. The difference ranges from 0.22% to 3.63%. The main reason for the deviation is the difference in the specification of modulus of elasticity, E. BS 5950 specifies 205kN/mm2 while EC3 specifies 210kN/mm2. Higher E means the elasticity of a member is higher, thus can sustain higher load without deforming too much.
However, serviceability limit states check governs the design of EC3 as permanent loads have to be considered in deflection check. Section 4.2.1 of EC3 provided proof to this.
Therefore, taking into account deflection due to permanent loads, the total deflection was greater. Cross-section with higher second moment of area value, I will have to be chosen, compared with the section chosen for BS 5950 design.
5.3
Economy
Economy aspect in this study focused on the minimum steel weight that is needed in the construction of the braced steel frame. The total steel weight of structural beams and columns was accumulated for comparison.
In this study, it was found that EC3 design produced braced steel frames that require higher steel weight than the ones designed with BS 5950. For a 2-bay, 4-storey, 6m bay width steel frame, the consumption of steel for S275 (Fe 430) and S355 (Fe 510) is 4.744 tons and 3.750 tons for BS 5950 design; and 4.821 tons and 4.571 tons for EC3 design. For a 2-bay, 4-storey, 9m bay width steel frame, the consumption of steel for S275 (Fe 430) and S355 (Fe 510) is 9.122 tons and 7.889 tons for BS 5950 design; and 9.645 tons and 9.313 tons for EC3 design.
84 The percentages of differences are as follow:
(i)
2-bay, 4-storey, 6m bay width, S275 (Fe 430): 1.60%
(ii)
2-bay, 4-storey, 6m bay width, S355 (Fe 510): 17.96%
(iii)
2-bay, 4-storey, 9m bay width, S275 (Fe 430): 5.42%
(iv)
2-bay, 4-storey, 9m bay width, S355 (Fe 510): 15.29%
Further study was extended for the application of partial strength connection for beam-to-column connections in EC3 design. The reduction in deflection coefficient from 5.0 to 3.5 had successfully reduced the percentage of difference between the steel weights designed by both codes. The percentages of differences are as follow:
5.4
(i)
2-bay, 4-storey, 6m bay width, S275 (Fe 430): 0.11%
(ii)
2-bay, 4-storey, 6m bay width, S355 (Fe 510): 10.95%
(iii)
2-bay, 4-storey, 9m bay width, S275 (Fe 430): 5.42%
(iv)
2-bay, 4-storey, 9m bay width, S355 (Fe 510): 7.22%
Recommendation for Future Studies
For future studies, it is suggested that an unbraced steel frame design is conducted to study the behavior, structural design and economic aspect based on both of the design codes.
However, since the results of the third objective contradicted with the background of the study (claim by Steel Construction Institute), it is recommended that further studies to be conducted to focus on the economy aspect of EC3 with respect to BS 5950. This study showed that steel weight did not contribute to cost saving of EC3 design.
85
REFERENCES
Charles King (2005). “Steel Design Can be Simple Using EC3.” New Steel Construction, Vol 13 No 4, 24-27.
Steel Construction Institute (SCI) (2005). “EN 1993 Eurocode 3 – Steel.” Eurocodenews, November 2005, Issue 3, 4.
Taylor J.C. (2001). “EN1993 Eurocode 3: Design of Steel Structures.” ICE Journal, Paper 2658, 29-32.
British Standards Institution (2001). “British Standard – Structural Use of Steelwork in Building: Part 1: Code of Practice for Design – Rolled and Welded Sections.” London: British Standards Institution.
European Committee for Standardization (1992). “Eurocode 3: Design of Steel Structures: Part 1.1 General Rules and Rules for Buildings.” London: European Committee for Standardization.
Heywood M. D. & Lim J B (2003). “Steelwork design guide to BS 5950-1:2000 Volume 2: Worked examples.” Berkshire: Steel Construction Institute.
Narayanan R
et. al.
(1995). “Introduction to Concise Eurocode 3 (C-EC3) – with
Worked Examples.” Berkshire: Steel Construction Institute.
86
APPENDIX A1
87
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J o bT i t l e :
Braced Steel Frame Design (BS 5950-1 : 2000)
8 13 1 0
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Frame Analysis
Clien t :
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1 .0
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Checked by
DR. MAHMOOD
DATA No. of Bay No. of Storey Frame Longitudinal Length Bay Width, l Storey Height
=
=
2
= = = =
4 6 6 5 4
m m m (First Floor) m (Other Floors)
LOADING Roof Dead Load, DL LiveLoad,LL
= =
4 1.5
kN/m @ 2 kN/m @
Floors Dead Load, DL LiveLoad,LL
= =
4.6 2.5
kN/m @ 2 kN/m @
= =
1.4 1.6
LOAD FACTORS Dead Load, DL LiveLoad,LL
FACTORED LOAD w = 1.4DL + 1.6LL Roof w = 1.4 x 24 + 1.6 x 9 = 48 kN/m Floors w = 1.4 x 27.6 + 1.6 x 15 = 62.64 kN/m
2
24 9
kN/m kN/m
2
27.6 15
kN/m kN/m
88
Job No:
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Frame Analysis
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FRAME LAYOUT
2.1
Selected Intermediate Frame
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6m
6m
6m
2.2
6m
Precast Slab Panel Load Transfer to Intermediate Frame
89
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Frame Analysis
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Cut Section of Intermediate Frame
4m
[4]
4m [3]
4m [2]
[1]
5m
6m 3 .0
6m
LOAD LAYOUT 48 kN/m
48 kN/m
62.64k N/m
62.64k N/m
62.64k N/m
62.64k N/m
62.64k N/m
62.64k N/m
90
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Frame Analysis
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LOAD CALCULATION Frame bracing Laterally braced, horizontal load is not taken into account Beam restraint Top flange effectively restrained against lateral torsional buckling
4.1 Beam 2
M= wl / 8 V= wl / 2
Moment, Shear, Roof beams,
V = 48 x 6 / 2 = 144
kN
M = 48 x 6^2 / 8 = 216 kNm Floor beams, V = 62.64 x 6 / 2 = 187.92 kN M = 62.64 x 6^2 / 8 = 281.88 kNm 4.2 Column Shear Column
Shear (kN) Internal External
[4] [3] [2]
288 663.84 1039.68
144 331.92 519.84
[1]
1415.52
707.76
Moment External column will be subjected to eccentricity moment, contributed by beam shear. Eccentricity= 100 mm fromfaceofcolumn. Universal columnof depth 200 mm Internal column - Moments from left and right will cancel out each other.
91
Job No:
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5
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8 13 1 0
Su b j ec t :
Frame Analysis
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ANALYSIS SUMM ARY Moment (kNm)
216
216
281.88
281.88
281.88
281.88
281.88
281.88
Shear (kN) (144)
(144)
144
(187.92)
288
(187.92)
144
[1]
331.92
(187.92)
663.84
(187.92)
331.92
[2]
519.84
(187.92)
1039.68
(187.92)
519.84
[3]
[4] 707.76
1415.52
707.76
92
Job No:
1001
6
Page
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J o bT i t l e :
Braced Steel Frame Design (BS 5950-1 : 2000)
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Frame Analysis
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Column moment due to eccentricity (kNm) 21.6
21.6
21.6
[1] 21.6
28.19
21.6
31.54
28.19
21.6
28.19
28.19
31.54
31.54
28.19
28.19
28.19
28.19
31.54
31.54
28.19
28.19
[2]
[3]
[4] 28.19
31.54
28.19
Moments are calculated from (1.4DL+1.6LL) - 1.0DL Most critical condition
93
APPENDIX A2
94
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8 13 1 0
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Frame Analysis
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Checked by
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DATA No. of Bay No. of Storey Frame Longitudinal Length Bay Width, l Storey Height
=
=
2
= = = =
4 6 6 5 4
m m m (First Floor) m (Other Floors)
LOADING Roof Dead Load, DL LiveLoad,LL
= =
4 1.5
kN/m @ 2 kN/m @
Floors Dead Load, DL LiveLoad,LL
= =
4.6 2.5
kN/m @ 2 kN/m @
LOAD FACTORS Dead Load, DL = LiveLoad,LL =
1.35 1.5
FACTORED LOAD w = 1.35DL + 1.5LL Roof w = 1.35 x 24 + 1.5 x 9 = 45.9 kN/m Floors w = 1.35 x 27.6 + 1.5 x 15 = 59.76 kN/m
2
24 9
kN/m kN/m
2
27.6 15
kN/m kN/m
95
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Frame Analysis
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FRAME LAYOUT
2.1
Selected Intermediate Frame
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6m
6m
6m
2.2
6m
Precast Slab Panel Load Transfer to Intermediate Frame
96
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Cut Section of Intermediate Frame
4m
[4]
4m [3]
4m [2]
[1]
3 .0
5m
6m
6m
45.9k N/m
45.9k N/m
59.76k N/m
59.76k N/m
59.76k N/m
59.76k N/m
59.76k N/m
59.76k N/m
LOAD LAYOUT
97
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LOAD CALCULATION Frame bracing Laterally braced, horizontal load is not taken into account Beam restraint Top flange effectively restrained against lateral torsional buckling
4.1 Beam 2
M= wl / 8 V= wl / 2
Moment, Shear, Roof beams,
V = 45.9 x 6 / 2 = 137.7 kN M = 45.9 x 6^2 / 8 = 206.55 kNm Floor beams, V = 59.76 x 6 / 2 = 179.28 kN M = 59.76 x 6^2 / 8 = 268.92 kNm 4.2 Column Shear Column
Shear (kN) Internal External
[4] [3] [2]
275.4 633.96 992.52
137.7 316.98 496.26
[1]
1351.08
675.54
Moment External column will be subjected to eccentricity moment, contributed by beam shear. Eccentricity= 100 mm fromfaceofcolumn. Universal columnof depth 200 mm Internal column - Moments from left and right will cancel out each other.
98
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5 .0
ANALYSIS SUMM ARY
5.1
Moment (kNm)
5.2
206.55
206.55
268.92
268.92
268.92
268.92
268.92
268.92
Made by
CCH
Checked by
DR. MAHMOOD
Shear (kN) (137.7)
(137.7)
137.7
(179.28)
275.4
(179.28)
137.7
[1]
316.98
(179.28)
633.96
(179.28)
316.98
[2]
496.26
(179.28)
992.52
(179.28)
496.26
[3]
[4] 675.54
1351.08
675.54
99
Job No:
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U TM
J obTi t l e :
813 10
S ubj ect :
Braced Steel Frame Design (Eurocode 3) Frame Analysis
C l i en t:
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Made by Checked by
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CCH DR. MAHMOOD
Column moment due to eccentricity (kNm) 20.66
19.71
20.66
20.66
26.89
19.71
28.94
26.89
20.66
26.89
26.89
28.94
28.94
26.89
26.89
26.89
26.89
28.94
28.94
26.89
26.89
26.89
28.94
26.89
Moments are calculated from (1.35DL+1.5LL) - 1.0DL Most critical condition
100
APPENDIX B1
101
1003
Job No:
1
Page
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Grade =
CCH
Checked by
DR. MAHMOOD
S275
Section
Mass (kg/m)
Sx 3 (cm )
Section
Mass (kg/m)
Sx 3 (cm )
178x102x19 254x102x22 203x102x23 305x102x25 203x133x25 254x102x25 305x102x28 254x102x28 203x133x30 254x146x31 305x102x33 356x127x33 254x146x37 305x127x37 406x140x39 356x127x39 305x165x40 305x127x42 254x146x43 356x171x45 406x140x46 305x165x46 305x127x48 356x171x51 457x152x52 305x165x54 406x178x54
19 22 23.1 24.8 25.1 25.2 28.2 28.3 30 31.1 32.8 33.1 37 37 39 39.1 40.3 41.9 43 45 46 46.1 48.1 51 52.3 54 54.1
171 259 234 342 258 306 403 353 314 393 481 543 483 539 724 659 623 614 566 775 888 720 711 896 1100 846 1060
356x171x57 457x152x60 406x178x60 356x171x67 406x178x67 457x191x67 457x152x67 406x178x74 457x152x74 457x191x74 457x191x82 457x152x82 533x210x82 457x191x89 533x210x92 457x191x98 533x210x101 610x229x101 533x210x109 610x229x113 533x210x122 610x229x125 610x229x140 610x305x149 610x305x179 610x305x238
57 59.8 60.1 67.1 67.1 67.1 67.2 74.2 74.2 74.3 82 82.1 82.2 89.3 92.1 98.3 101 101.2 109 113 122 125.1 139.9 149.2 179 238.1
1010 1290 1200 1210 1350 1470 1450 1500 1630 1650 1830 1810 2060 2010 2380 2230 2610 2880 2830 3280 3200 3680 4140 4590 5550 7490
M = 281.88 kNm Sx = M / f y = 281.88 x 10^3 / 275 3 = 1025 cm
Try
Made by
457x152x60
UB
102
1003
Job No:
2
Page
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
1 .0
DATA
1.1
Trial Section
Made by
CCH
Checked by
DR. MAHMOOD
Initial trial section is selected to give a suitable moment capacity. The size is then checked to ensure suitability in all other aspects. Sectionchosen 1.2
=
457x152x60
Section Properties Mass Depth Width Web thickness Flangethickness Depthbetweenfillets Plastic modulus
2 .0
UB
Elastic modulus
= 59.8k g/m =D 454.6m m =B 152.9m m =t 8.1 mm T= 13.3 mm d= 407.6 mm cm Sx = 1290 cm Zx = 1120
Local buckling ratios: Flange Web
b/T = =d/t
5.75 50.3
SECTION CLASSIFICATION Gradeofsteel =T 13.3
= mm
Therefore, py =
S275 < 275
16mm
N/mm
ε = √ (275/py) = SQRT(275/275) = 1 Outstand element of compression flange, Limiting b/T Actual b/T
=
=
5.75
9 ε
<
=
9
9
Flangeis plastic Class 1
Section is symmetrical, subject to pure bending, neutral axis at mid-depth, Limiting d/t = 80 ε = 80 Actual d/t = 50.3 < 80 Web is plastic Class 1 Section is : Class 1 plastic section
103
1003
Job No:
3
Page
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
3 .0
Made by
CCH
Checked by
DR. MAHMOOD
SHEAR B UCKLING If d/t ratio exceeds 70 ε for rolled section, shear buckling resistance should be checked. d/t = 50.3 < 70 ε = 70 Therefore, shear buckling needs not be checked
4 .0
SHEAR CAPACIT Y Fv =
187.92
kN
Pv = 0.6pyAv py =
275
N/mm
Av = tD = 8.1 x 454.6 2 = 3682.26 mm Pv = 0.6 x 275 x 3682.26 x 0.001 F=v
607.57 <
kN Pv
Therefore, the shear capacity is adequate
5 .0
M OM ENT CAPACIT Y M=
281.88
kNm
0.6Pv = 0.6 x 607.57 = 364.542 kN Fv 0.6Pv < Therefore, it is low shear Mc = pySx = 275 x 1290 x 0.001 = 354.75 kNm 1.2pyZ = 1.2 x 275 x 1120 x 0.001 = 369.6 kNm Mc
<
1.2pyZ
OK
M
<
Mc
Moment capacity is adequate
104
1003
Job No:
4
Page
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
6 .0
WEB BEARING & BUCKLING
6.1
Bearing Capacity Pbw = (b1 + nk) tpyw r=
10.2
Made by
CCH
Checked by
DR. MAHMOOD
(Unstiffened web)
mm
b1 = t + 1.6r + 2T = 8.1 + 1.6 x 10.2 + 2 x 13.3 = 51.02 mm k= T+r = 13.3 + 10.2 = 23.5 mm At the end of a member (support), but n ≤ 5
n = 2 + 0.6be/k = 2 b1 + nk
= =
51.02 + 2 x 23.5 98.02 mm
Pbw
= =
98.02 x 8.1 x 275 x 0.001 218.34 kN
Fv
=
Fv
<
187.92
kN
Pbw
Bearing capacity at support is ADEQUATE
be =
0
105
1003
Job No:
5
Page
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
7.0
Made by
CCH
Checked by
DR. MAHMOOD
SERVICEABILITY D EFLECTION C HECK Unfactored imposed loads: =w
9 =
E= I=
kN/m kN/m
15
kN/mm
205 25500
cm
for roofs forfloors 2
4
4
5wL 384EI = 5 x 15 x 6^4 x 10^5 384 x 205 x 25500 = 4.84 mm
δ=
Beam condition Carrying plaster or other brittle finish Deflection limit = Span / 360 = 6 x 1000 / 360 = 16.67 mm 4.84mm
<
The deflection is satisfactory!
16.67mm
=L
6
m
106
APPENDIX B2
107
1004
Job No:
1
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Grade =
CCH
Checked by
DR. MAHMOOD
S275
Section
Wpl.y
Mass (kg/m)
(cm )
178x102x19 254x102x22 203x102x23 203x133x25 254x102x25 305x102x25 254x102x28 305x102x28 203x133x30 254x146x31 305x102x33 356x127x33
19 22 23 25 25 25 28 28 30 31 33 33
171 260 232 259 307 336 354 408 313 395 481 539
254x146x37 305x127x37 356x127x39 406x140x39 305x165x40 305x127x42 254x146x43 356x171x45 305x165x46 406x140x46 305x127x48 356x171x51 457x152x52 305x165x54 406x178x54
37 37 39 39 40 42 43 45 46 46 48 51 52 54 54
485 540 654 718 626 612 568 773 722 889 706 895 1096 843 1051
M = 268.92 W pl.y = M / f y
kNm
406x178x54
Section
UB
Wpl.y
Mass (kg/m)
(cm )
356x171x57 406x178x60 457x152x60 356x171x67 406x178x67 457x152x67 457x191x67 406x178x74 457x152x74 457x191x74 457x152x82 457x191x82
57 60 60 67 67 67 67 74 74 74 82 82
1009 1195 1283 1213 1346 1442 1472 1509 1624 1659 1802 1832
533x210x82 457x191x89 533x210x92 457x191x98 533x210x101 610x229x101 533x210x109 610x229x113 533x210x122 610x229x125 610x229x140 610x305x149 610x305x179 610x305x238
82 89 92 98 101 101 109 113 122 125 140 149 179 238
2058 2020 2366 2234 2619 2887 2827 3287 3203 3673 4139 4575 5515 7462
3
= 268.92 x 10^3 / 275 3 = 977.9 cm
Try
Made by
3
108
1004
Job No:
2
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
1 .0
DATA
1.1
Trial Section
=
Made by
CCH
Checked by
DR. MAHMOOD
L
6
Initial trial section is selected to give a suitable moment capacity. The size is then checked to ensure suitability in all other aspects.
Sectionchosen 1.2
=
406x178x54
Section Properties Mass Depth Width Web thickness
= 54 =h 402.6m =b 177.6m tw = 7.6
kg/m m m mm
Flange thickness Depthbetweenfillets Plastic modulus
tf = 10.9 mm d= 360.4 mm cm W pl.y = 1051
Elastic modulus Shear area,
W el.y = Av =
Areaofsection, Second moment of area,
2 .0
UB
A=
927 32.9
68.6 Iy = 18670
= mm
cm cm
iLT =
4.36
cm
aLT =
131
cm
c/tf =
8.15
d/tw =
47.4
SECTION CLASSIFICATION Gradeofsteel =t 10.9
cm cm
S275 <=
Therefore, fy =
275
N/mm
fu =
430
N/mm
(Fe430) 40mm
2
m
109
1004
Job No:
3
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
Classification of Trial Section (a) Outstand element of compression flange, flange subject to compression only : c/tf = 8.15 <= 9.2 Flange is Class 1 element
Class 1 limit : c/tf =
9.2
(b) Web, subject to be nding (neutral axis at mid dep th) : d/tw = 47.4 > 46.7 Web is Class 2 element
Class 1 limit : d/tw =
46.7
406x178x54 UB is a Class 2 section
3 .0
SHEAR RESIST ANCE VSd =
V pl.Rd
=
179.28
⎛ ⎜⎜ γ MO ⎝ Av
kN
⎞ ⎟⎟ 3⎠
fy
= 32.9x100 275 1.05 √3 = 497.48 kN VSd
4 .0
<
γMO =
1.05
x0.001
Vpl.Rd
Sufficient shear resistance
M OM ENT RESISTANCE MSd =
268.92
kNm
0.5Vpl.Rd = 0.5 x 497.48 = 298.49 kN VSd
<
0.5Vpl.Rd
Therefore, it is low shear Mc.Rd = W pl.y fy / γMO = 1051 x 275 x 0.001 / 1.05 = 275.26 kNm MSd Mc.Rd <
Moment capacity is adequate
110
1004
Job No:
4
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
5.0
Made by
CCH
Checked by
DR. MAHMOOD
LATERAL TO RSIONAL BU CKLING (L TB) Beam is fully restrained, not susceptible to LTB
6 .0
SHEAR B UCKLING For steel grade S275 (Fe 430), shear buckling must be checked if d/tw d/tw =
>
63.8
47.4
<
63.8
Shear buckling check is NOT required
7.0
7.1
RESISTANCE OF WEB TO TRANSVERSE FORCES Stiff bearing at support, s s =
50
mm
Stiff bearing at midspan, ss =
75
mm
Crushing Resistance Design crushing resistance, tw fyw Ry.Rd = (ss + sy)
γM1
At support,
sy
⎛b = t f ⎜⎜ f ⎝ tw
0.5
⎛ ⎞ ⎟⎟ × ⎜ ⎜ ⎠ ⎝
⎡ ⎛γ σ ⎞ ⎟ × ⎢1 − ⎜ MO f Ed ⎟ f yw ⎠ ⎢ ⎜⎝ f yf ⎣ 0.5
f yf
.
σf.Ed = Longitudinal stress in flange (My / I) =
0
γMO =
1.05
fyf =
275
sy =
52.69
⎞ ⎟ ⎟ ⎠
2
⎤ ⎥ ⎥ ⎦
0.5
at support (bending moment is zero) N/mm mm
Ry.Rd = (50 + 52.69) x 7.6 x 275 x 0.001 / 1.05 204.4 kN = VSd =
179.28
kN
<
Ry.Rd Sufficient crushing resistance
111
1004
Job No:
5
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
At midspan,
⎛ bf ⎞ ⎛ = 2t f ⎜⎝ t w ⎟⎠ × ⎜⎝ 0.5
sy
VSd =
⎞ ⎡ ⎛ γ MOσ f Ed ⎞ ⎤ ⎟⎠ ⎥ f yw ⎟⎠ × ⎢1 − ⎜⎝ f yf ⎣ ⎦ f yf
0.5
2
0.5
.
0 Crushing resistance is OK
7.2
Crippling Resistance Design crippling resistance At support,
⎡⎛ t f ⎞ ⎛t ⎞ s ⎤ 1 ⎢⎜⎜ ⎟⎟ + 3⎜⎜ w ⎟⎟⎛⎜ s ⎞⎟⎥ ⎢⎣⎝ t w ⎠ ⎝ t f ⎠⎝ d ⎠⎥⎦ γ M 0.5
Ra.Rd
= 0.5t w
ss/d ≤
2
(Ef )
0.5
yw
1
0.2
50 / 360.4 = γM1 =
0.14 1.05
E= Ra.Rd=
205
kN/mm
307.8
kN
VSd =
>
2
179.28
kN Sufficient crippling resistance
At mid span, MSd
≤
Mc.Rd 268.92 275.26 7.3
1.5
=
0.98
<=
1.5
OK
Buckling Resistance At support, h= =a
beff
=
402.6 mm 0 mm
1
[h 2
2
+ ss
]
2 0.5
+a+
ss 2
but
beff
≤ [h + s s 2
2
]
0.5
112
1004
Job No:
6
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
beff = 0.5 x SQRT(402.6^2 + 50^2) + 0 + 50 / 2 = 227.8 mm [h2 + ss2]0.5 =
<=
405.7
mm
Buckling resistance of web,
βAfcA
Rb.Rd =
γM1
βA =
1
γM1 =
1.05
A = beff x tw = 227.8 x 7.6 2 = 1731.28 mm Ends of web restrained against rotation and relative lateral movement.
λ = 2.5 d/t
l
= 0.75d
= 2.5 x 360.4 / 7.6 = 118.6 Rolled I-section, buckling about y-y axis, use curve a
λ √βA =
118.6
λ √βA
fc 121 117
118 120
fc = 121 - (118.6 - 118) x (121 - 117) / (120 - 118) =
119.8
N/mm
2
Rb.Rd = 1 x 119.8 x 1731.28 x 0.001 / 1.05 = 197.5k N >
VSd =
179.28
kN Sufficient buckling resistance
At mid span, VSd =
0
Sufficient buckling resistance at midspan
113
1004
Job No:
7
Page
U TM
Jo bTi t l e:
Braced Steel Frame Design (EC 3)
81 3 1 0
S u b je ct :
Beam Design (Floor Beams, L = 6.0m)
C l i e n t:
STC, UTM
SKUDAI, J O HO R
8.0
Made by
CCH
Checked by
DR. MAHMOOD
SERVICEABILITY LIMIT (DEFLECTION) Partial factor for dead load
γG =
1.0
Partial factor for imposed floor load
γ
1.0
Q
Dead
gd =
27.6
kN/m
Imposed
qd =
15
kN/m
=
δ2 = Variation of deflection due to variable loading δ1 = Variation of deflection due to permanent loading δ0 = Pre-camber of beam in unloaded state = 0 δmax = δ1 + δ2 - δ0 Iy =
18670
cm
E=
210
kN/mm
5(gd / qd) x L 384 EI
δ= δ1 = δ2 =
11.88
mm
6.46
mm
2
4
<
350 / = L
δmax = 11.88 + 6.46 =
18.34
mm
Recommended limiting vertical deflection for L 250
= =
δmax
6000 250 24m
<
24
Deflection limit is satisfactory.
m mm
δmax is
17.14
mm
OK
114
APPENDIX C1
115
1005
Job No:
Page
1
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Grade =
S275
Section
Mass (kg/m)
Sx 3 (cm )
152x152x23 152x152x30 152x152x37 203x203x46 203x203x52 203x203x60 203x203x71 254x254x73 203x203x86 254x254x89 305x305x97 254x254x107 305x305x118 356x368x129
23 30 37 46 52 60 71 73 86 89 97 107 118 129
184.3 247.1 310.1 497.4 568.1 652 802.4 988.6 978.8 1228 1589 1485 1953 2482
254x254x132 305x305x137 356x368x153 305x305x158 254x254x167 356x368x177 305x305x198 356x368x202 356x406x235 305x305x240 305x305x283 356x406x287 356x406x340 356x406x393 356x406x467 356x406x551 356x406x634
132 137 153 158 167 177 198 202 235 240 283 287 340 393 467 551 634
1875 2298 2964 2680 2417 3457 3436 3977 4689 4245 5101 5818 6994 8229 10009 12078 14247
M= 63.08 kNm Sx = M / fy = 63.08 x 10^3 / 275 3 cm = 229.4
Try
203x203x60
UC
Made by
CCH
Checked by
DR. MAHMOOD
116
1005
Job No:
Page
2
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
1 .0
CCH
Checked by
DR. MAHMOOD
DATA Fc =
1.1
Made by
1415.52 kN
=
L
5
m
Trial Section Initial trial section is selected to give a suitable moment capacity. The size is then checked to ensure suitability in all other aspects. Sectionchosen
1.2
=
203x203x60
Section Properties Mass Depth Width Web thickness Flangethickness Depthbetweenfillets Plastic modulus
= 60 kg/m =D 209.6m m =B 205.2m m =t 9.3 mm T= 14.2 mm d= 160.8 mm cm Sx = 652
Elastic modulus Radius of gyration,
Zx = rx =
581.1 8.96
cm cm
ry =
5.19
cm
Gross area,
Ag =
75.8
cm
Local buckling ratios: Flange Web
2 .0
UC
b/T = =d/t
7.23 17.3
SECTION CLASSIFICATION Gradeofsteel =T 14.2
= mm
Therefore, py =
S275 < < < 275
ε = √ (275/py) = SQRT(275/275) = 1
N/mm
16mm 40mm 63mm
2
117
UTM
J obTi tl e :
Page 1005 3 Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
Job No:
SKUDAI, J O HO R
Outstand element of compression flange, Limiting b/T = 9 ε Actual b/T = 7.23
Made by
CCH
Checked by
DR. MAHMOOD
= <
< <
9 9
10ε = 15ε =
10 15
Flangeisp lastic Class 1
Web of I- or H-section under axial compression and bending ("generally" case) r1 = Fc tpy -1 < r1 ≤ 1
= 1415.52 x 1000 / (160.8 x 9.3 x 275) = 3.44 r1 = 1 Actual d/t
=
Section is :
17.3 <
80ε +r1
=
40
<
100ε + . r1
=
40
Class 1 plastic section
3 .0
SLENDERNESS
3.1
Effective Length About the x-x axis, LEX = 0.85L
"Restrained in direction at one end"
= 0.85 x 5 x 1000 = 4250 mm λx = LEX / rx = 4250 / (8.96 x 10) = 47.4
4 .0
COMPRESSION RESISTANCE Fc =
1415.52 kN
Pc = pcAg py =
275
N/mm
Ag =
75.8
cm
Buckling about x-x axis
All ≥ 40ε
Web is plastic Class 1
118
1005
Job No:
Page
4
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
Use strut curve (b) x
=
47.4
λ
pc 242 239
46 48 Interpolation:
pcx = 242 - (47.4 - 46) / (48 - 46) x (242 - 239) N/mm = 239.9 c
= pc
g
= 239.9 x 75.8 x 100 x 0.001 = 1818.44 kN c
<
c
Therefore, the compressive resistance is adequate
5.0
NOMINAL M OM ENT D UE TO ECCENTRICITY For columns in simple construction, beam reaction, R is assumed to act 100mm off the face of the column. R From frame analysis sheets, Mi =
63.08
kNm
100 mm Moments are distributed between the column lengths above and below level 2, in proportion to the bending stiffness of each length. For EI/L1 : EI/L2 < 1.5, the moment will be equally divided. Therefore, M=
31.54
kNm
119
1005
Job No:
5
Page
UTM
J obTi tl e :
Braced Steel Frame Design (BS 5950-1 : 2000)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
6.0
Made by
CCH
Checked by
DR. MAHMOOD
COMBINED AXIAL FORCE AND MOMENT CHECK The column should satisfy the relationship
Fc
+
Pc
Mx M bs
+
My py Z y
≤1
λLT = 0.5 L/r y = (0.5 x 5 x 1000) / (5.19 x 10) = 48.17 py =
λLT
275
N/mm
2
pb 250 233
45 50
pb = 250 - (48.17 - 45) / (50 - 45) x (233 - 250) =
260.78
N/mm 2
Mb = pbSx = 260.78 x 652 x 0.001 = 170.03 kNm 1415.52 1818.44
+
31.54 170.03
=0
.96
<
1.00
The combined resistance against axial force and moment is adequate.
7 .0
CONCLUSION
4.0
Compression Resistance =
OK
6.0
Combined Axial Force and Moment Check =
OK
Use of the section is adequate Use:
203x203x60
UC
120
APPENDIX C2
121
1006
Job No:
Page
1
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
Grade =
S275
Section
Mass (kg/m)
Wpl.y 3 (cm )
152x152x23 152x152x30 152x152x37 203x203x46 203x203x52 203x203x60 203x203x71 254x254x73 203x203x86 254x254x89 305x305x97 254x254x107 305x305x118 356x368x129
23 30 37 46 52 60 71 73 86 89 97 107 118 129
184 248 309 497 567 654 801 990 979 1225 1589 1484 1952 2485
254x254x132 305x305x137 356x368x153 305x305x158 254x254x167 356x368x177 305x305x198 356x368x202 356x406x235 305x305x240 305x305x283 356x406x287 356x406x340 356x406x393 356x406x467 356x406x551 356x406x634
132 137 153 158 167 177 198 202 235 240 283 287 340 393 467 551 634
1872 2293 2970 2675 2418 3455 3438 3978 4691 4243 5101 5814 6997 8225 10010 12080 14240
M= 57.88 W pl.y = M / f y
kNm
= 57.88 x 10^3 / 275 3 cm = 210.5
Try
254x254x73
UC
Made by
CCH
Checked by
DR. MAHMOOD
122
1006
Job No:
Page
2
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
1 .0
CCH
Checked by
DR. MAHMOOD
DATA NSd =
1351.08 kN
Msd = 1.1
Made by
=
5
L
m
kNm
28.94
Trial Section Initial trial section is selected to give a suitable moment capacity. The size is then checked to ensure suitability in all other aspects. Sectionchosen
1.2
=
254x254x73
Section Properties Mass Depth Width Web thickness
= 73 kg/m = h 254 mm = b 254 mm tw = 8.6 mm tf = 14.2 mm d= 200.2 mm cm W pl.y = 990 cm W el.y = 895
Flange thickness Depthbetweenfillets Plastic modulus Elastic modulus Radius of gyration, Areaofsection, Second moment of area,
2 .0
UC
A=
iy =
11.1
cm
iz =
6.46
cm
92.9 Iy = 11370 iLT =
6.86
cm
aLT =
98.5
cm
c/tf =
8.94
d/tw =
23.3
SECTION CLASSIFICATION Gradeofsteel tf =
= 14.2
S275 mm
cm cm
<=
Therefore, fy =
275
N/mm
fu =
430
N/mm
(Fe430) 40mm
2
123
UTM
J obTi tl e :
Page 1006 Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
Job No:
3
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
Classification of Trial Section (a) Outstand element of compression flange, flange subject to compression only : c/tf = 8.94 <= 9.2 Flange is Class 1 element
Class 1 limit : c/tf =
9.2 Limit c/tf Class 2 = 10.2
(b) Web, subject to bending and compression : Classify web as subject to compression and bending d/tw = 23.3 <= 30.5 Web is Class 1 element
Class 1 limit : d/tw =
Class 3 = 13.9
30.5 Limit d/tw Class 2 = 35.1
Therefore, it is Class 1 section
3 .0
Class 3 = 38.8
CROSS-SECTION R ESISTANCE Sd
n= Npl.Rd =
γMO =
Npl.Rd y
γMO 1.05
Npl.Rd = 92.9 x 100 x 275 x 0.001 / 1.05 = 2433.1 kN n = 1351.08 / 2433.1 = 0.555 >=
0.1
n < 0.1
Mny.Rd = Mpl.y.Rd
n ≥ 0.1
Mny.Rd = 1.11 M pl.y.Rd(1-n) W pl.y fy
γMO Mpl.y.Rd = = 990 x 275 x 0.001 / 1.05 = 259.3 kNm
>
Mny.Rd =
128.1
kNm
MSd =
28.94
kNm Sufficient moment resistance
124
1006
Job No:
4
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Column Design (Internal Column, L = 5.0m)
C l i e nt:
STC, UTM
SKUDAI, J O HO R
4.0
Made by
CCH
Checked by
DR. MAHMOOD
IN-PLANE FAILURE ABOUT MAJOR AXIS Members subject to axial compression and major axis bending must satisfy
N Sd
+
N b . y . Rd
kyM ηM
≤ 1 .0
c . y . Rd
βA fc A
Nb.y.Rd = ly
y . Sd
γM1
= 0.85 L (Restrained about both axes) = 0.85 x 5 x 1000 = 4250 mm
Slenderness ratio
λy =
y
/ iy
= 4250 / (11.1 x 10) = 38.3 Buckling about y-y axis (Curve b) A
=
λy β A = tf
λ βA
1 38.3 <=
40mm
fc 250 248
38 40
fc = 250 - (38.3 - 38) x (40 - 38) / (250 - 248) N/mm = 249.7 Nb.y.Rd = 1 x 249.7 x 92.9 x 100 x 0.001 / 1.05 = 2209.3 kN y
=
1.5 Sd
(Conservative value) y
+
η
b.y.Rd
=
1351.08 2209.3
+
=
0.95
<
y.Sd c.y.Rd
1.5x28.94 128.1 x1
η = γMO γM1 =
1
1
Therefore, sufficient resistance against in-plane failure against major axis
125
1006
Job No:
5
Page
UTM
J ob Ti t l e:
Braced Steel Frame Design (EC 3)
81 3 1 0
S u bj ect :
Column Design (Internal Column, L = 5.0m)
Cl i en t :
STC, UTM
SKUDAI, J O H OR
5.0
CONCLUSION
3.0 4.0
Cross Section Resistance In-plane Failure About Major Axis Use of the section is adequate. Use:
254x254x73
UC
OK OK
Made by
CCH
Checked by
DR. MAHMOOD
126
APPENDIX D
127
1004
Job No:
1
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
Rev1
SKUDAI, J O HO R
Grade =
CCH
Checked by
DR. MAHMOOD
S275
Section
Wpl.y
Mass (kg/m)
(cm )
178x102x19 254x102x22 203x102x23 203x133x25 254x102x25 305x102x25 254x102x28 305x102x28 203x133x30 254x146x31 305x102x33 356x127x33
19 22 23 25 25 25 28 28 30 31 33 33
171 260 232 259 307 336 354 408 313 395 481 539
254x146x37 305x127x37 356x127x39 406x140x39 305x165x40 305x127x42 254x146x43 356x171x45 305x165x46 406x140x46 305x127x48 356x171x51 457x152x52 305x165x54 406x178x54
37 37 39 39 40 42 43 45 46 46 48 51 52 54 54
485 540 654 718 626 612 568 773 722 889 706 895 1096 843 1051
M = 268.92 W pl.y = M / f y
kNm
457x152x52
Section
UB
Wpl.y
Mass (kg/m)
(cm )
356x171x57 406x178x60 457x152x60 356x171x67 406x178x67 457x152x67 457x191x67 406x178x74 457x152x74 457x191x74 457x152x82 457x191x82
57 60 60 67 67 67 67 74 74 74 82 82
1009 1195 1283 1213 1346 1442 1472 1509 1624 1659 1802 1832
533x210x82 457x191x89 533x210x92 457x191x98 533x210x101 610x229x101 533x210x109 610x229x113 533x210x122 610x229x125 610x229x140 610x305x149 610x305x179 610x305x238
82 89 92 98 101 101 109 113 122 125 140 149 179 238
2058 2020 2366 2234 2619 2887 2827 3287 3203 3673 4139 4575 5515 7462
3
= 268.92 x 10^3 / 275 3 = 977.9 cm
Try
Made by
3
128
1004
Job No:
2
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
Rev1
SKUDAI, J O HO R
1 .0
DATA
1.1
Trial Section
=
Made by
CCH
Checked by
DR. MAHMOOD
L
6
Initial trial section is selected to give a suitable moment capacity. The size is then checked to ensure suitability in all other aspects.
Sectionchosen 1.2
=
457x152x52
Section Properties Mass Depth Width Web thickness
= 52 =h 449.8m =b 152.4m tw = 7.6
kg/m m m mm
Flange thickness Depthbetweenfillets Plastic modulus
tf = 10.9 mm d= 407.6 mm cm W pl.y = 1096
Elastic modulus Shear area,
W el.y = Av =
Areaofsection, Second moment of area,
2 .0
UB
A=
950 36.5
66.6 Iy = 21370
= mm
cm cm
iLT =
3.59
cm
aLT =
121
cm
c/tf =
6.99
d/tw =
53.6
SECTION CLASSIFICATION Gradeofsteel =t 10.9
cm cm
S275 <=
Therefore, fy =
275
N/mm
fu =
430
N/mm
(Fe430) 40mm
2
m
129
1004
Job No:
3
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
Rev1
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
Classification of Trial Section (a) Outstand element of compression flange, flange subject to compression only : c/tf = 6.99 <= 9.2 Flange is Class 1 element
Class 1 limit : c/tf =
9.2
(b) Web, subject to be nding (neutral axis at mid dep th) : d/tw = 53.6 > 46.7 Web is Class 2 element
Class 1 limit : d/tw =
46.7
457x152x52 UB is a Class 2 section
3 .0
SHEAR RESIST ANCE VSd =
V pl.Rd
=
179.28
⎛ ⎜⎜ γ MO ⎝ Av
kN
⎞ ⎟⎟ 3⎠
fy
= 36.5x100 275 1.05 √3 = 551.92 kN VSd
4 .0
<
γMO =
1.05
x0.001
Vpl.Rd
Sufficient shear resistance
M OM ENT RESISTANCE MSd =
268.92
kNm
0.5Vpl.Rd = 0.5 x 551.92 = 331.15 kN VSd
<
0.5Vpl.Rd
Therefore, it is low shear Mc.Rd = W pl.y fy / γMO = 1096 x 275 x 0.001 / 1.05 = 287.05 kNm MSd Mc.Rd <
Moment capacity is adequate
130
1004
Job No:
4
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
Rev1
SKUDAI, J O HO R
5.0
Made by
CCH
Checked by
DR. MAHMOOD
LATERAL TO RSIONAL BU CKLING (L TB) Beam is fully restrained, not susceptible to LTB
6 .0
SHEAR B UCKLING For steel grade S275 (Fe 430), shear buckling must be checked if d/tw d/tw =
>
63.8
53.6
<
63.8
Shear buckling check is NOT required
7.0
7.1
RESISTANCE OF WEB TO TRANSVERSE FORCES Stiff bearing at support, s s =
50
mm
Stiff bearing at midspan, ss =
75
mm
Crushing Resistance Design crushing resistance, tw fyw Ry.Rd = (ss + sy)
γM1
At support,
sy
⎛b = t f ⎜⎜ f ⎝ tw
0.5
⎛ ⎞ ⎟⎟ × ⎜ ⎜ ⎠ ⎝
⎡ ⎛γ σ ⎞ ⎟ × ⎢1 − ⎜ MO f Ed ⎟ f yw ⎠ ⎢ ⎜⎝ f yf ⎣ 0.5
f yf
.
σf.Ed = Longitudinal stress in flange (My / I) =
0
γMO =
1.05
fyf =
275
sy =
48.81
⎞ ⎟ ⎟ ⎠
2
⎤ ⎥ ⎥ ⎦
0.5
at support (bending moment is zero) N/mm mm
Ry.Rd = (50 + 48.81) x 7.6 x 275 x 0.001 / 1.05 = 196.68 kN VSd =
179.28
kN
<
Ry.Rd Sufficient crushing resistance
131
1004
Job No:
5
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
Rev1
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
At midspan,
⎛ bf ⎞ ⎛ = 2t f ⎜⎝ t w ⎟⎠ × ⎜⎝ 0.5
sy
VSd =
⎞ ⎡ ⎛ γ MOσ f Ed ⎞ ⎤ ⎟⎠ ⎥ f yw ⎟⎠ × ⎢1 − ⎜⎝ f yf ⎣ ⎦ f yf
0.5
2
0.5
.
0 Crushing resistance is OK
7.2
Crippling Resistance Design crippling resistance At support,
⎡⎛ t f ⎞ ⎛t ⎞ s ⎤ 1 ⎢⎜⎜ ⎟⎟ + 3⎜⎜ w ⎟⎟⎛⎜ s ⎞⎟⎥ ⎢⎣⎝ t w ⎠ ⎝ t f ⎠⎝ d ⎠⎥⎦ γ M 0.5
Ra.Rd
= 0.5t w
ss/d ≤
2
(Ef )
0.5
yw
1
0.2
50 / 407.6 = γM1 =
0.12 1.05
E=
kN/mm
205
Ra.Rd =
299.16
kN
VSd =
>
2
179.28
kN Sufficient crippling resistance
At mid span, MSd
≤
Mc.Rd 268.92 287.05 7.3
1.5
=
0.94
<=
1.5
OK
Buckling Resistance At support, h= =a
beff
=
449.8 mm 0 mm
1
[h 2
2
+ ss
]
2 0.5
+a+
ss 2
but
beff
≤ [h + s s 2
2
]
0.5
132
1004
Job No:
6
Page
UTM
J obTi tl e :
Braced Steel Frame Design (EC 3)
813 1 0
S ubj e c t:
Beam Design (Floor Beams, L = 6.0m)
C l i e nt:
STC, UTM
Rev1
SKUDAI, J O HO R
Made by
CCH
Checked by
DR. MAHMOOD
beff = 0.5 x SQRT(449.8^2 + 50^2) + 0 + 50 / 2 = 251.3 mm [h2 + ss2]0.5 =
<=
452.6
mm
Buckling resistance of web,
βAfcA
Rb.Rd =
γM1
βA =
1
γM1 =
1.05
A = beff x tw = 251.3 x 7.6 2 = 1909.88 mm Ends of web restrained against rotation and relative lateral movement.
λ = 2.5 d/t
l
= 0.75d
= 2.5 x 407.6 / 7.6 = 134.1 Rolled I-section, buckling about y-y axis, use curve a
λ √βA =
134.1
λ √βA
fc 103 98
130 135
fc = 103 - (134.1 - 130) x (103 - 98) / (135 - 130) =
98.9
N/mm
2
Rb.Rd = 1 x 98.9 x 1909.88 x 0.001 / 1.05 = 179.9k N >
VSd =
179.28
kN Sufficient buckling resistance
At mid span, VSd =
0
Sufficient buckling resistance at midspan
133
1004
Job No:
7
Page
U TM
Jo bTi t l e:
Braced Steel Frame Design (EC 3)
81 3 1 0
S u b je ct :
Beam Design (Floor Beams, L = 6.0m)
C l i e n t:
STC, UTM
Rev1
SKUDAI, J O HO R
8.0
Made by
CCH
Checked by
DR. MAHMOOD
SERVICEABILITY LIMIT (DEFLECTION) Partial factor for dead load
γG =
1.0
Partial factor for imposed floor load
γ
1.0
Q
Dead
gd =
27.6
kN/m
Imposed
qd =
15
kN/m
=
δ2 = Variation of deflection due to variable loading δ1 = Variation of deflection due to permanent loading δ0 = Pre-camber of beam in unloaded state = 0 δmax = δ1 + δ2 - δ0 Iy =
21370
cm
E=
210
kN/mm
3.5(gd / qd) x L 384 EI
δ= δ1 = δ2 =
7.26
mm
3.95
mm
2
4
<
350 / = L
δmax = 7.26 + 3.95 =
11.21
mm
Recommended limiting vertical deflection for δmax is L 250
= =
δmax
6000 250 24m
<
24
Deflection limit is satisfactory.
m mm
17.14
mm
OK
