Eurocode-4-1-1-1994-EN
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Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Eurocode 4: Design of composite steel and concrete structures — Part 1.1: General rules and rules for buildings — (together with United Kingdom National Application Document)
UDC 624.92.016:624.07
DD ENV 1994-1-1:1994
DD ENV 1994-1-1:1994
Cooperating organizations
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
The European Committee for Standardization (CEN), under whose supervision this European Prestandard was prepared, comprises the national standards organizations of the following countries: Austria Belgium Denmark Finland France Germany Greece Iceland Ireland Italy Luxembourg Netherlands Norway Portugal Spain Sweden Switzerland United Kingdom
This Draft for Development, having been prepared under the direction of the Technical Sector Board for Building and Civil Engineering (B/-), was published under the authority of the Standards Board and comes into effect on 15 May 1994 © BSI 05-2000 The following BSI reference relates to the work on this Draft for Development: Committee reference B/525/4 ISBN 0 580 22797 9
Oesterreichisches Normungsinstitut Institut belge de normalisation Dansk Standardiseringsraad Suomen Standardisoimisliito, r.y. Association française de normalisation Deutsches Institut für Normung e.V. Hellenic Organization for Standardization Technological Institute of Iceland National Standards Authority of Ireland Ente Nazionale Italiano di Unificazione Inspection du Travail et des Mines Nederlands Normalisatie-instituut Norges Standardiseringsforbund Instituto Portuguès da Qualidade Asociación Española de Normalización y Certificación Standardiseringskommissionen i Sverige Association suisse de normalisation British Standards Institution
Amendments issued since publication Amd. No.
Date
Comments
DD ENV 1994-1-1:1994
Contents
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Cooperating organizations National foreword Text of National Application Document Foreword Text of ENV 1994-1-1 National annex NA (informative) Committees responsible
© BSI 05-2000
Page Inside front cover ii iii 2 9 Inside back cover
i
DD ENV 1994-1-1:1994
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
National foreword This publication comprises the English language version of ENV 1994-1-1:1992 Eurocode 4: Design of composite steel and concrete structures — Part 1.1: General rules and rules for buildings, as published by the European Committee for Standardization (CEN), plus the National Application Document to be used with the ENV in the design of buildings to be constructed in the United Kingdom. ENV 1994-1-1:1992 results from a programme of work sponsored by the European Commission to make available a common set of rules for the design of building and civil engineering works. An ENV is made available for provisional application, but does not have the status of a European Standard. The aim is to use the experience gained to modify the ENV so that it can be adopted as a European Standard. The values for certain parameters in the ENV Eurocodes may be set by CEN members so as to meet the requirements of national regulations. These parameters are designated by P in the ENV. During the ENV period of validity, reference should be made to the supporting documents listed in the National Application Document (NAD). The purpose of the NAD is to provide essential information, particularly in relation to safety, to enable the ENV to be used for buildings constructed in the UK. The NAD takes precedence over corresponding provisions in the ENV. The Building Regulations 1991, Approved Document A 1992, (published December 1991) draws designers’ attention to the potential use of ENV Eurocodes as an alternative approach to Building Regulation compliance. ENV 1994-1-1:1992 has been thoroughly examined over a period of several years and is considered to offer such an alternative approach, when used in conjunction with the NAD. Compliance with ENV 1994-1-1:1992 and the NAD does not in itself confer immunity from legal obligations. Users of this document are invited to comment on its technical content, ease of use and any ambiguities or anomalies. These comments will be taken into account when preparing the UK national response to CEN on the question of whether the ENV can be converted to an EN. Comments should be sent in writing to BSI, 2 Park Street, London W1A 2BS, quoting the document reference, the relevant clause and, where possible, a proposed revision, within 2 years of the issue of this document.
Summary of pages This document comprises a front cover, an inside front cover, pages i to xxii, the ENV title page, pages 2 to 134, an inside back cover and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. ii
© BSI 05-2000
DD ENV 1994-1-1:1994
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
National Application Document for use in the UK with ENV 1994-1-1:1992
© BSI 05-2000
iii
DD ENV 1994-1-1:1994
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Contents of National Application Document Introduction 1 Scope 2 References 3 Partial safety factors, combination factors and other values 4 Loading codes 5 Reference standards 6 Additional recommendations Annex A (normative) General requirements for structural integrity Annex B (normative) Application rules for composite columns in simple framing Table 1 — Partial safety factors (¾ factors) Table 2 — Combination factors (Ó factors) for persistent and transient design situations Table 3 — Combination factors for accidental design situations Table 4 — Boxed values Table 5 — References in EC4 to other codes and standards List of references
iv
Page v v v v viii ix xiii xvi xvii v vii vii viii ix xx
© BSI 05-2000
DD ENV 1994-1-1:1994
Introduction This National Application Document (NAD) has been prepared under the direction of the Civil Engineering and Technical Sector Board for Buildings and Civil Engineering. It has been developed from: a) a textual examination of ENV 1994-1-1:1992; b) calibration against UK practice, supporting standards and test data; c) trial calculations.
1 Scope This NAD provides information required to enable ENV 1994-1-1:1992 (EC4-1.1) to be used for the design of buildings to be constructed in the UK.
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
2 References 2.1 Normative references This National Application Document incorporates, by reference, provisions from specific editions of other publications. These normative references are cited at the appropriate points in the text and the publications are listed on page xx. Subsequent amendments to, or revisions of, any of these publications apply to this National Application Document only when incorporated in it by updating or revision. 2.2 Informative references This National Application Document refers to other publications that provide information or guidance. Editions of these publications current at the time of issue of this standard are listed on page xx, but reference should be made to the latest editions.
3 Partial safety factors, combination factors and other values a) The values for partial safety factors (¾) should be those given in Table 1 of this NAD. b) The values for combination factors (Ó) should be those given in Table 2 and Table 3 of this NAD. c) The values for the boxed factors should be those given in Table 4 of this NAD. Table 1 — Partial safety factors (¾ factors) Reference in EC4-1.1
Definition
Symbol
Condition
Value Boxed EC4
UK
2.3.2.2 1)
Partial safety factor for accidental actions
¾A
Accidental
1.00
1.05
2.3.2.2 3)
Partial safety factor for permanent actions in accidental design situations
¾GA
Favourable
1.00
0.90
¾GA
Unfavourable
1.00
1.05
Partial safety factors for permanent actions
¾G.inf
Favourable
1.00
1.00
¾G.sup
Unfavourable
1.35
1.35
Partial safety factors for variable actions
¾Q.inf
Favourable
0.00
0.00
¾Q.sup
Unfavourable
1.50
1.50
¾Q.sup
2 or more combined
1.50
1.50
¾G.inf
Favourable part
1.10
1.10
¾G.sup
Unfavourable part
1.35
1.35
¾G.inf
Favourable and unfavourable parts
1.00
1.00
2.3.3.1 1) 2.3.3.1 1)
2.3.3.1 3)
© BSI 05-2000
Partial safety factors for permanent actions
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DD ENV 1994-1-1:1994
Table 1 — Partial safety factors (¾ factors) Reference in EC4-1.1
2.3.3.2 1)
2.3.3.2 1)
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
2.3.3.2 1)
2.3.3.2 1)
Definition
Symbol
Condition
Value Boxed EC4
UK
Partial safety factors for structural steel
¾a
Fundamental
1.10
1.05
¾a
Accidental (except earthquakes)
1.00
1.05
Partial safety factors for concrete
¾c
Fundamental
1.50
1.50
¾c
Accidental (except earthquakes)
1.30
1.30
Partial safety factors for steel ¾s reinforcement ¾s
Fundamental
1.15
1.15
Accidental (except earthquakes)
1.00
1.00
Partial safety factors for profiled steel sheeting
¾ap
Fundamental
1.10
1.05
¾ap
Accidental (except earthquakes)
1.00
1.05
2.3.3.2 2)
Partial safety factors for ¾M elastic mechanical properties
General
1.00
1.00
2.3.3.2 2)
Partial safety factors for non-mechanical coefficients
¾M
General
1.00
1.00
4.1.1 5)
Partial safety factors for the buckling resistance of structural steel
¾Rd
Accidental combinations
1.00
1.05
4.4.1.4 3)
Partial safety factors for steel ¾Rd
Resistance of Class 4 cross sections
1.10
1.05
4.6.3 1)
Partial safety factors for steel ¾Rd
Resistance of Class 1 or 2 cross 1.10 sections
1.05
Resistance of Class 3 cross sections
1.10
1.05
For a column length with
1.10
1.05
Æ k 0.2 or Nsd/Ncr k 0.1 otherwise
1.10
1.05
1.35
1.35
¾Rd 4.8.3.2 1)
Partial safety factors for steel ¾Ma ¾Ma
4.8.3.5 1)
Partial safety factors for the elastic flexural stiffness of concrete
¾c
6.3.2.1
Partial safety factors for shear studs
¾v
Ultimate limit state
1.25
1.25
6.3.7
Partial safety factors for angle connectors in solid slabs
¾v
Ultimate limit state
1.25
1.25
6.5.2.1 1)
Partial safety factors for friction grip bolts
¾v
1.25
1.35
7.6.1.3 2)
Partial safety factors for slabs with mechanical or frictional interlock
¾vs
For use in equation 7.6
1.25
1.25
10.2.5 1)
Partial safety factor for shear ¾v connectors
Test evaluation
1.25
1.25
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© BSI 05-2000
DD ENV 1994-1-1:1994
Table 1 — Partial safety factors (¾ factors) Reference in EC4-1.1
Definition
Symbol
Value
Condition
Boxed EC4
UK
E.2 5)
Partial safety factor for shear ¾v connection
Shear strength
1.25
1.25
E.4 4)
Partial safety factor for shear ¾v connection
End anchorage
1.25
1.25
Table 2 — Combination factors (Ó factors) for persistent and transient design situations Variable actiona
Ó0
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Imposed floor loads Dwellings
0.4
0.2
Office and stores
0.7
0.6
0.3
Parking
0.7
0.7
0.6
0.7
0.2
0
0.7
0.2
0
0.7
0.6
0.3
b
Vertical
Crane loadsc
Ó2
0.5
Wind loads Imposed roof loads
Ó1
Horizontal 0.9 (Vertical and Horizontal) a For
the purposes of EC4-1.1 these four categories of variable action should be treated as separate and independent variable actions. b Local drifting of snow on roofs should be treated as an accidental action [see 6.1.1 c)]. c The most onerous of the three specified alternatives should be treated as a single variable action.
Table 3 — Combination factors for accidental design situations Variable action
Imposed floor loads
Ó1 or Ó2 for use in A.3 and A.4
Dwellings
0.35a
Offices
0.35a
Stores
1.0
Parking
0.35a
Wind loadsb
0.35
Imposed roof loads
0.35
Crane loadsc
Vertical
1.00
Horizontal
0.00
a
Where the variable action is of a persistent or quasi-permanent nature, the Ó factor should be taken as 1.0. b The full value obtained from CP 3 Chapter V-2 should be multiplied by 0.35 c The values given in this table assume that the crane is stationary. The vertical load to which the combination factor is applied is the static load value.
© BSI 05-2000
vii
DD ENV 1994-1-1:1994
Table 4 — Boxed values Reference in EC4-1.1
3.1.3 2)
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
3.1.3 2)
Definition
Symbol
Condition
Value Boxed EC4
UK
Long-term free shrinkage ¼cs strain from setting of the concrete: dry environments ¼ cs
Normal-weight concrete
325 × 10
Light-weight concrete
500 × 10–6
500 × 10–6
Long-term free shrinkage strain from setting of the concrete: other environments and in filled members
¼cs
Normal-weight concrete
200 × 10–6
200 × 10–6
¼cs
Light-weight concrete
300 × 10–6
300 × 10–6
20 %
30 %
3 N/mm2
3 N/mm2
–6
325 × 10–6
4.8.3.13 6)
% reduction in the partial safety factor for the favourable component Nsd
5.3.2 2)
Minimum tensile strength of concrete
10.2.5 1)
Reduction for the characteristic resistance PRk
10 %
10 %
10.2.5 4)
Reduction for the characteristic slip capacity
10 %
10 %
10.3.1.5 5)
Reduction for the characteristic values m and k
10 %
10 %
10.3.2.5
Design resistance of composite slab
a)
0.75
0.75
b)
0.5
0.5
c)
0.75
0.75
fcte
E.2 4)
Reduction for the characteristic shear strength
10 %
10 %
E.4 3)
Reduction for the characteristic resistance of the end anchorage
10 %
10 %
E.5 4)
Lower limit on bending resistance
10 %
10 %
4 Loading codes The loading codes to be used are: BS 648:1964 BS 6399: BS 6399-1:1984 BS 6399-3:1988 CP3: CP3:Chapter V: CP3:Chapter V-2:1972 BS 5950: BS 5950-3: BS 5950-3.1:1990
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Schedule of weights of building materials Design loading for buildings Code of practice for dead and imposed loads Code of practice for imposed roof loads Code of basic data for the design of buildings Loading Wind loads Structural use of steelwork in building Design in composite construction Code of practice for design of simple and continuous composite beams Clause 2.2 Loading © BSI 05-2000
DD ENV 1994-1-1:1994
BS 5950-4:1993
Code of practice for design of composite slabs with profiled steel sheeting Clause 2.2 Loading Code of practice for falsework Section 4 Loads applied to falsework
BS 5975:1982
In using the above documents with EC4-1.1 the following modifications should be noted: a) The imposed floor loads of a building should be treated as one variable action to which the reduction factors given in BS 6399-1:1984 are applicable. b) The characteristic wind loading should be taken as 90 % of the value obtained from CP3:Chapter V-2:1972.
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5 Reference standards The supporting standards to be used, including materials specifications and standards for construction are listed in Table 5. Table 5 — References in EC4-1.1 to other codes and standards Reference in Document EC4-1.1 referred to 1.1.1 3) Eurocode 2
1.1.1 3)
Eurocode 3
1.1.1 4)
Eurocode 8
1.1.1 5)
Eurocode 1
1.1.2 5)
Eurocode 2
Eurocode 3
1.1.3 2)
Eurocode 4
1.4.1 1)
ISO 8930
1.4.1 2)
ISO 6707-1
1.5 1)
ISO 1000
© BSI 05-2000
Document title or subject area Design of concrete structures Part 1. General rules and rules for buildings Part 1A Plain or lightly-reinforced concrete structures Part 1B Precast concrete structures Part 1C The use of lightweight aggregate concrete Part 1D The use of unbonded and external prestressing tendons Part 10. Fire resistance of concrete structures Design of steel structures Part 1.1 General rules and rules for buildings Part 1.2 Fire resistance
Status ENV 1992-1-1
Draft Draft
DD ENV 1992-1-1 (See note 1) BS 8110-1, and section 8 of BS 8110-2:1985 BS 8110-1 Section 5 of BS 8110-2:1985
No draft
Section 8 of BS 8110-1:1985
Draft
BS 8110-1 and section 4 of BS 8110-2:1985
ENV 1993-1-1
DD ENV 1993-1-1 (See note 1) Section 7 of BS 5950-4:1993 BS 5950-8 BS 5950-4, BS 5950-6 (See note 6) and BS 5950-7 —
Draft
Draft
Part 1.3 Cold formed thin gauge Draft members and sheeting Design of structures for earthquake In preparation resistance Basis of design and actions on structures In preparation
Design of concrete structures Part 1 General rules and rules for buildings Design of steel structures Part 1.1 General rules and rules for buildings Design of composite steel and concrete structures Part 1.2 Fire resistance General principles on reliability of structures — List of equivalent terms Building and civil engineering — Vocabulary — Part 1: General terms SI units and recommendations for the use of their multiples and of certain other units
UK document
BS 6399-1 and BS 6399-3 CP3: Chapter V-2 2.2 of BS 5950-3.1:1990 2.2 of BS 5950-4:1993 Section 4 of BS 5975:1982
ENV 1992-1-1
DD ENV 1992-1-1
ENV 1993-1-1
DD ENV 1993-1-1
Draft
Section 7 of BS 5950-4:1993 BS 5950-8 BS 8110-1 Section 4 of BS 8110-2:1985 Published 1987 — Published 1989 — Published 1981 —
ix
DD ENV 1994-1-1:1994
Table 5 — References in EC4-1.1 to other codes and standards Reference in EC4-1.1
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
2.2.1.1 4)
2.2.1.1 4)
Document referred to Eurocode 2
Eurocode 3
Chapter 2 [except 2.3.1 3)]
Eurocode 1
2.2.2.2 1)
“other relevant loading codes”
Document title or subject area
Status
UK document
Design of concrete structures Part 1 General rules and rules for buildings
ENV 1992-1-1
DD ENV 1992-1-1 (See note 1)
Part 1A Plain or lightly-reinforced concrete structures
Draft
3.8.1.4 and 3.9.4 of BS 8110-1:1985
Part 1B Precast concrete structures
Draft
Section 5 of BS 8110-1:1985
Part 1C The use of lightweight aggregate concrete
Draft
Section 5 of BS 8110-2:1985
Part 1D The use of unbonded and external prestressing tendons
No draft
Section 4 of BS 8110-1:1985
Part 10 Fire resistance of concrete structures
Draft
3.3.6 of BS 8110-1:1985 Section 4 of BS 8110-2:1985
Part 1.1 General rules and rules for buildings
ENV 1993-1-1
DD ENV 1993-1-1 (See note 1)
Part 1.2 Fire resistance
Draft
Section 7 of BS 5950-4:1993 BS 5950-8
Part 1.3 Cold formed thin gauge members and sheeting
Draft
BS 5950-4, BS 5950-5 and BS 5950-6 (See note 6)
Basis of design and actions on structures
In preparation
BS 6399-1 and BS 6399-3
Design of steel structures
CP3:Chapter V-2 2.2 of BS 5950-3.1:1990 2.2 and 5.3 of BS 5950-4:1993 (See note 2) Section 4 of BS 5975:1982 DD ENV 1994-1-1
2.3.1 3) ENV note
Eurocode 1
3.1.2 2) ENV note
Basis of design and actions on structures
In preparation
DD ENV 1994-1-1
Variation in time of fc and fct
—
7.2 of BS 8110-2:1985 3.1.2.3 of DD ENV 1992-1-1:1992
3.2
EN 10080
Steel for the reinforcement of concrete
Draft
See below
3.2.3 2)
“national documents”
Reinforcing steel not covered by EN 10080
—
BS 4449 BS 4482 BS 4483
3.3 3.4
EN 10025
Hot rolled products of non-alloy structural steels — Technical delivery conditions
Published 1990
BS EN 10025
3.3.5
Ref. Standard 2 of EC3
Dimensions of sections and plates
ENV 1993-1-1
Table 7 of NAD of DD ENV 1993-1-1:1992
3.4
EN 10113
Hot rolled products in weldable fine grain structural steels
1992
BS EN 10113
3.4
prEN 10147
Continuous hot-dip zinc coated non-alloy structural steel sheet and strip: technical delivery conditions
Draft
BS 2989
3.4
ISO 4997
Cold reduced steel sheet of structural quality
1978
—
3.4.1 3) ENV note
“European Technical Approvals or National Documents”
Tolerances on embossments for profiled None steel sheeting
—
x
© BSI 05-2000
DD ENV 1994-1-1:1994
Table 5 — References in EC4-1.1 to other codes and standards
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Reference in EC4-1.1
Document referred to
Document title or subject area
Status
UK document
3.4.5
ISO 4998
Continuous hot-dip zinc coated carbon steel sheet of structural quality
1977
—
3.5.2 5) ENV note 3.5.2 6)
“European Standards or European Technical Approvals”
Testing of shear connector material
None
3.4 of BS 5950-3.1:1990
Part 1.2 Fire resistance
Draft
BS 5950-8
4.3.1 10)
Eurocode 4
4.6.2 k)
Euronorm 19-57 IPE joists — Parallel flanged joists
4.6.2 k)
Euronorm 53-62 Broad flanged beams with parallel sides Published 1962 —
4.8.2.2 12)
“appropriate parts of Eurocode 2”
4.8.2.5 1)
Eurocode 4
Published 1957 —
Design of concrete structures Part 1 General rules and rules for buildings
ENV 1992-1-1
DD ENV 1992-1-1 (See note 3)
Part 1B Precast concrete structures
Draft
BS 8110-1 (See note 3)
Part 1.2 Fire resistance
Draft
BS 5950-8 BS 8110-1 Section 4 of BS 8110-2:1985
4.8.3.3 1)
4.9.4.1 1)
“appropriate part of Eurocode 2”
“relevant Eurocode”
Design of concrete structures Part 1 General rules and rules for buildings
ENV 1992-1-1
DD ENV 1992-1-1 (See note 3)
Part 1B Precast concrete structures
Draft
BS 8110-1 (See note 3)
Eurocode 2 Design of concrete structures Various
(See note 4)
Eurocode 3 Design of steel structures
Various
(See note 5)
Eurocode 5 Design of timber structures
In preparation
BS 5268
Eurocode 6 Design of masonry structures In preparation
BS 5628
6.1.1 9)
“European Standards or European Technical Approvals or national documents”
Methods of interconnection, other than None the shear connectors covered in chapter 6
BS 5400-5 BS 5950-3.1
6.3.2.1 ENV note
“Reference Standards”
Minimum dimensions for normal weld collar
In the absence of a European and a UK standard DIN 32500-3 and DIN 8563-10 may be used
Work not started
Specifications for welding for stud shear connectors
Appendix A of BS 5950-3.1:1990
7.1.1 1)
“another Eurocode”
Eurocode 8 Design of structures for earthquake resistance
In preparation
—
7.1.1 3)
Eurocode 3
Part 1.3 Cold formed thin gauge members and sheeting
Draft
BS 5950-9 (See note 6)
7.2.3 1) 7.4.1 2) 7.5.1 7.5.2 1)
Eurocode 3
Part 1.3 Cold formed thin gauge members and sheeting
Draft
BS 5950-4
7.3.2.1 1)
Eurocode 1
Basis of design and actions on structures In preparation
© BSI 05-2000
2.2 of BS 5950-4:1993
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DD ENV 1994-1-1:1994
Table 5 — References in EC4-1.1 to other codes and standards
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Reference in EC4-1.1
Document referred to
Document title or subject area
Status
UK document
7.4.1 2)
Eurocode 3
Part 1.3 Cold formed thin gauge members and sheeting
Draft
A.2.3 of BS 5950-3.1:1990
8.1 2)
“relevant chapters of Eurocode 2”
Eurocode 2 Design of concrete structures
Various
BS 8110-1 (See note 3)
8.3 2)
“appropriate part of Eurocode 2”
8.2 2) ENV note
Eurocode 1
Basis of design and actions on structures
In preparation
Section 4 of BS 5975:1982
8.4
Eurocode 2
Part 1B Precast concrete structures
Draft
Section 5 of BS 8110-1:1985
9.1 4) ENV note
“Reference Standards or other Documents”
Responsibility or other requirements to — the contractor
9.4.3.1 1)
“appropriate standards”
Welding tests
—
A.3 of BS 5950-3.1:1990
9.4.4.1 2)
Eurocode 3
Part 1.3 Cold formed thin gauge members and sheeting
Draft
4.8 of BS 5950-4:1993 Section 6 of BS 5950-6 (See note 6)
10.2.5 2)
Eurocode 3
Part 1.1: Annex Z
Draft
5.3.2.4 of BS 5400-5:1979
A.2.1
DP 9690
Classification of environmental conditions for concrete structures
In preparation
DD ENV 1992-1-1
ENV 206
Concrete — Performance, production, placing and compliance criteria
Expected before EC4
EN 10080
Steel for the reinforcement of concrete
Draft
BS 4449 BS 4482 BS 4483
ISO 3898
Bases for design of structures — Notations — General symbols
1987
—
ISO 8930
General principles on reliability of structures — List of equivalent terms
1987
—
Contractor’s obligations stated in contract documents, particularly drawings, specification, bill of quantities and standard forms of contract (e.g. ICE Conditions of contract, JCT Standard form of building contract, General conditions of government contract for building and civil engineering works). BS 5975
A.4
NOTE 1 Clause 1.1.1 of Eurocode 4-1.1 is not specific to this Part only, and the reference in 1.1.1 3) to Eurocodes 2 and 3 is a general one. The Parts of these Eurocodes already published or currently in preparation are listed. For those Parts in preparation, Table 5 lists the equivalent UK documents relevant to execution of a building or civil engineering works. NOTE 2 UK documents relevant to Parts 2 of Eurocodes 2 and 3 are not the subject of this NAD. NOTE 3 Part 1.1 of Eurocode 2 and the associated NAD do not deal with considerations special to precast concrete elements. Reference should be made to BS 8110. NOTE 4 For Parts of Eurocode 2 and the equivalent UK documents, see entries in Table 5 for EC4 reference 2.2.1.1 4). NOTE 5 For Parts of Eurocode 3 and the equivalent UK documents, see entries in Table 5 for EC4 reference 2.2.1.1 4). NOTE 6 To be published.
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© BSI 05-2000
DD ENV 1994-1-1:1994
6 Additional recommendations 6.1 Guidance on EC4-1.1 NOTE
6.1.1 to 6.1.7 should be followed when designing in accordance with EC4-1.1.
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6.1.1 Chapter 2. Basis of Design a) Clause 2.1 2) Structural integrity. Design rules to provide structural integrity by limiting the effects of accidental damage are given in Annex A. b) Clause 2.2.1.2 2) Strength and stability should be checked for the construction stage where the steel beam acts non-compositely to support the permanent load of formwork and the imposed load of fresh concrete plus construction loads or temporary storage loads. c) Clause 2.3.2.2 Accidental design situation. When designing for the accidental situation in Table 2.1 of EC4-1.1 the values of Ó1, Ó2 and Ak should be determined from Annex A and Table 3 of this NAD. The accidental load Ak (34 kN/m2 see A.4) should be multiplied by a ¾A factor of 1.05. The ¾GA factor should be taken as 1.05, except where the dead load is considered as consisting of unfavourable and favourable parts, in which case the favourable part should be multiplied by a ¾GA factor of 0.9 and the unfavourable part should be multiplied by a ¾GA factor of 1.05. 6.1.2 Chapter 3. Materials a) Clause 3.2 Pending the issue of prEN 10080 as an EN, reference should be made to BS 4449:1988 (bars) and BS 4483:1985 (welded fabric) for the material properties of reinforcing steels. The differences between the British Standards and the draft European Standard are summarized in 6.3 a) of the NAD to DD ENV 1992-1-1:1992 (EC2-1). b) Clause 3.3 For material properties of structural steels to be used in design calculations for composite steel and concrete structures reference should be made to clauses 5 and 6 of the NAD to DD ENV 1993-1-1:1992 (EC3-1.1). c) Clause 3.4 For additional guidance on the material properties of profiled steel sheeting for composite slabs reference should be made to the NAD to EC3-1.31). d) Clause 3.5.2 6) The material properties of shear connectors should be in accordance with the recommendations in 3.4 of BS 5950-3.1:1990. 6.1.3 Chapter 4. Ultimate limit state a) Clause 4.6.3 4) When calculating the elastic critical moment Mcr, from Annex F of EC3-1.1 the additional recommendations give in 6.1.3 e) of the NAD to DD ENV 1993-1-1:1992 (EC3-1.1) apply. b) Clause 4.7.1 Diagonal, tension and torsional stiffeners should be designed using the method given in 6.1.3 g) of the NAD to DD ENV 1993-1-1:1992 (EC3-1.1). c) Clause 4.8.2.5 2) When determining the cover to reinforcement the additional recommendations given in 6.4 a) and b) of the NAD to DD ENV 1992-1-1:1992 (EC2-1) apply. d) Clause 4.8.3.6 Where no guidance on the buckling length is given in DD ENV 1993-1.1 (EC3-1.1) the nominal effective lengths for a strut given in 4.7.2 of BS 5950-1:1990 should be used. 1) In
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When calculating the elastic critical load, Ncr, a buckling length, l, of less than 0.7 times the system length, L, may be used for a member only where it can be demonstrated that the stiffness of the connecting members and of the connections to be used would justify such a value. In all other cases the buckling length, l, should not be taken as less than 0.7 times the system length. e) Clause 4.8.3.9 For members subject to combined compression and bending the ratio ·n should be determined as follows. 1) Encased steel sections (including web filled sections) and rectangular filled sections Provided that the non-dimensional slenderness, Æ, does not exceed 1.0, the ratio #n may be determined from the recommendations given in 4.8.3.13 4) of EC4-1.1. For values of Æ in the range 1.0 to 2.0, ·n should be taken as zero. 2) Concrete filled circular and square sections For concrete filled circular and square sections the ratio ·n may be determined from the recommendations given in 4.8.3.13 4) of EC4-1.1. f) Clause 4.8.3.1 3) c) The term “relative slenderness” in the heading of 4.8.3.7 has the same meaning as “non-dimensional slenderness”. g) Clause 4.8.3.11 The design moment resistance in combined compression and uniaxial bending should not exceed the design plastic moment, Mpl.Rd, irrespective of the normal force N. h) Clause 4.8.3.13 The additional recommendations given in 6.2.3 g) of this NAD supplement the recommendations given in paragraph 6) and supersede those given in paragraph 7) of 4.8.3.13 of EC4-1.1 i) Clause 4.9.2.2 The recommendations given in Annex B of this NAD may be used for the design of columns in simple framing. As an alternative to the recommendations given in Annex B, cased columns may be designed using the method given in 6.3.2 of this NAD. 6.1.4 Chapter 6. Shear connection in beams for buildings a) Clause 6.3.2.1 The design shear resistance, PRd, of shear connectors in lightweight concrete with a dry density exceeding 1 750 kg/m3 should be taken as 90 % of the value of the design shear resistance calculated for normal weight concrete with the same characteristic strength. b) Clause 6.4.1.2 When calculating the cover required for shear connectors, the specified cover for reinforcement should be in accordance with Table 6 of the NAD to 1992-1-1:1992 (EC2-1). c) Clause 6.5.2.1 1) The design pre-loading force, Fp.Cd, used in design calculations should be determined in accordance with the recommendations given in 6.1.4 d) of the NAD to 1993-1-1:1992. d) Clause 6.5.2.1 2) If after final tightening, the bolt or nut of a high strength friction grip bolt assembly installed in accordance with the recommendations given in BS 4604 is slackened off for any reason the bolt, nut and washer (washers) should be discarded and not re-used. 6.1.5 Chapter 7. Composite slabs with profiled steel sheeting for buildings a) Clause 7.3.2.1 The recommendations on construction loads given in 2.2.3 of BS 5950-4:1993 supersede paragraphs 2) and 3) of 7.3.2.1 in EC4-1.1. b) Clause 7.3.2.1 4) When the central deflection, ¸, of the profiled steel sheeting during construction exceeds either 1/250 or 20 mm the additional weight of concrete due to the deflection of the sheeting should be taken into account in the self-weight of the concrete slab and in the design of the supporting structure.
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c) Clause 7.4.1 As an alternative to elastic analysis, profiled steel sheeting may be analysed in accordance with the recommendations given in EC3-1.32). d) Clause 7.4.1 2) Profiled steel sheeting spanning onto a steel beam may be assumed to provide restraint to the beam flanges to which it is connected and should be fixed using either: — shot fired fixings; — self tapping screws; — welding (including stud shear connectors welded through the sheeting); or — bolting. The spacing of fasteners should not be greater than 500 mm at the ends of sheets, nor greater than 1 000 mm where the sheet is continuous. The design of the fixings should be in accordance with BS 5950-62). The stiffness of other types of shuttering or formwork is generally not sufficient to provide the necessary lateral restraint, unless specifically designed to do so. 6.1.6 Annex C. Simplified calculation method for resistance of doubly symmetric composite cross sections in combined compression and bending a) Clauses C.1 and C.4 The design moment of resistance in combined compression and uniaxial bending should not exceed the design plastic resistance, Mpl.Rd, irrespective of the normal force N. 6.1.7 Annex D. Design of composite columns with mono-symmetrical cross sections — simplified method a) Clause D.4 The design moment of resistance in combined compression and uniaxial bending should not exceed in magnitude the appropriate design plastic resistance moment Mpl.y–.Rd or Mpl.y+.Rd, irrespective of the normal force N. 6.2 Recommendations on subjects not covered in EC4-1.1 6.2.1 Fire Resistance Pending the issue of ENV 1994-1-2 (EC4-1.2), BS 5950-8:1990 should be used. 6.2.2 Cased Sections As an alternative to the rules given in Annex B of this NAD, cased columns and beams may be designed using the method given in 6.2.3 of the NAD to DD ENV 1993-1-1:1992 (EC3-1.1). 6.2.3 Vibration Where it is necessary to control vibration, the recommendations given in 6.4 of BS 5950-3.1:1990 should be used.
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Annex A (normative) General recommendations for structural integrity A.1 Introduction All structures should follow the principles given in 2.1 of EC4-1.1. This annex gives application rules which satisfy the principle of structural integrity given in 2.1 2) of EC4-1.1. These application rules apply to buildings. For the purposes of this provision, it may be assumed that substantial permanent deformation of members and their connections is acceptable. A.2 Tying forces A.2.1 Recommendations for all buildings Every building should be effectively tied together at each principal floor and roof level. All columns should be effectively restrained in two directions approximately at right angles at each principal floor or roof which they support. This anchorage may be provided by either beams or tie members. Where possible these should be arranged in continuous lines as close as practicable to the columns and to each edge. At re-entrant corners the peripheral tie should be anchored into the framework. Ties may be either steel members or steel reinforcement embedded in concrete or masonry provided that they are properly anchored to the framework. Steel members and reinforcement provided for other purposes may be utilized as ties. When checked as ties other loading may be ignored. Beams designed to carry the floor or roof loading will generally be suitable provided that their end connections are capable of resisting tension. All ties and their end connections should be of a standard of robustness commensurate with the structure of which they form a part and should have a design tension resistance of not less than 75 kN at floors or 40 kN at roof level. Ties are not required at a roof level where steelwork supports cladding weighing not more than 0.7 kN/m2 and carries roof loads only. Where a building is provided with expansion joints, each section between expansion joints should be treated as a separate building for the purpose of this clause. A.2.2 Additional recommendations for tall multi-storey buildings Local or national regulations may stipulate that tall multi-storey buildings be designed to localize accidental damage. Composite steel-concrete framed buildings which satisfy the recommendations of A.2.1 may be assumed to meet this requirement provided that the five additional conditions given below are met. A tall multi-storey building which is required to be designed to localize accidental damage but which does not satisfy these five additional conditions should be checked as recommended in A.3. a) Bracing. The bracing or shear walls should be so distributed throughout the building that no substantial portion of the structural framework is solely reliant on a single plane of bracing in each direction. b) Tying. The ties referred to in A.2.1 should be arranged in continuous lines wherever practicable throughout each floor and roof level in two directions approximately at right angles. These and their connections should be checked for the following design tensile forces, which need not be considered as additive to other forces. 1) Generally: 0.5wf st La for any internal ties and 0.25wf st La for edge ties but not less than 75 kN for floors or 40 kN at roof level, where wf is the total factored dead and imposed load per unit area of floor or roof; st is the mean transverse spacing of the ties; La is the greatest distance, in the direction of the tie under consideration, between the centres of adjacent lines of supporting columns, frames or walls.
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2) At the periphery: ties anchoring columns at the periphery of a floor or roof should be checked for the greater of: — the force given in item b) 1) and — 1 % of the design vertical load in the column at that level. c) Columns. All column splices should be capable of resisting a design tensile force of not less than two-thirds of the design vertical load applied to the column from the floor level next below the splice. Where the framework is not of continuous construction in at least one direction, the columns should be carried through at each beam-to-column connection. d) Integrity. Any beam which carries a column should be checked, together with the members which support it, for localization of damage as recommended in A.3. e) Floor units. Where precast concrete or other heavy floor or roof units are used they should be effectively anchored in the direction of their span either to each other over a support or directly to their supports as recommended in BS 8110. A.3 Localization of damage At the accidental limit state, where required by A.2, the effect of the removal of any single column, or beam carrying a column should be assessed for each storey of a building in turn. Where the removal of one of these members would result in collapse of any area greater than 70 m2 or 15 % of the area of the storey, that member should be designed as a key element as recommended in A.4. In this check the appropriate value of Ó of the ordinary wind load and of the ordinary imposed load should be considered together with the dead load, except that in the case of buildings used predominantly for storage, or where the imposed load is of a persistent nature, the full imposed load should be used. The combination factors, Ó1 and Ó2, for accidental design situations are given in Table 3. The ¾GA factor should be taken as 1.05, except that where the dead load is considered as consisting of unfavourable and favourable parts, the favourable part should be multiplied by a ¾GA factor of 0.9 and the unfavourable part should be multiplied by a ¾GA factor of 1.05. A.4 Design of key elements Key elements or members are single structural elements which support a floor or roof area of more than 70 m2 or 15 % of the area of the storey. Any other member or other structural component which provides lateral restraint vital to the stability of a key element should itself also be designed as a key element for the same accidental loading. Where it is required by A.3 to design a member as a key element, the accidental loading, Ak, should be chosen having particular regard to the importance of the key element and the consequences of failure and should not be less than 34 kN/m2. The accidental load, Ak should be multiplied by a ¾A factor of 1.05. Accidental loads should be applied to members from appropriate directions together with the reactions from other building components attached to the member which are subject to the same loading but limited to the ultimate resistance of these components or their connections. When designing for the accidental situation the member should be designed for the accidental load in combination with the dead and imposed loads [see 2.3.2.2 2) of EC4-1.1]. The combination factors for use with these loads are given in Table 3.
Annex B (normative) Application rules for composite columns in simple framing B.1 General The application rules in B.2 to B.5 apply to columns in structures of simple framing, and are intended to be used in conjunction with the method given in 4.8.3 of EC4-1.1. B.2 Pattern loading Pattern loading need not normally be considered in simple framing. However, unbalanced loading due to variations in span or specified loading should be taken into account. B.3 Buckling length of column The buckling length of a composite column should be taken as the system length. When the nominal moments obtained as described in B.5 are the only applied moments, the moment ratio, r, should be taken as 1.0 giving a moment factor ¶ of 1.1 in 4.8.3.10 4) of EC4-1.1 and a ratio ·n of 0 in 4.8.3.13 4) of EC4-1.1. © BSI 05-2000
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B.4 Eccentricities Beam end reactions should be taken as acting at a distance from the face of the composite section equal to 100 mm, or at the centre of the length of stiff bearing, whichever gives the great eccentricity. B.5 Unbalanced loading Where composite columns are subject to unbalanced loading, they should be designed for the resulting moment. In multi-storey buildings where the columns are effectively continuous at each floor level, the net moment at one level should be divided between the column lengths above and below that level in proportion to the values of (EI/L), for each length. The value of EI for a composite column should be determined according to 4.9.6.2 of EC4-1.1. The moments due to the eccentricities given in B.4 should be assumed to have no effect at the levels above and below the level at which they are applied. B.6 Connections Connections are to be designed as non-composite in accordance with the rules given in clause 6 of DD ENV 1993-1-1:1992 (EC3-1.1), ignoring any reinforcement which may be provided for the control of cracking. The connections should satisfy the requirements of 6.4.2.1 and 6.4.3.1 of DD ENV 1993-1-1:1992 (EC3-1.1) for nominally pinned connections.
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List of references (see clause 2) Normative references BSI publications
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BRITISH STANDARDS INSTITUTION, London
BS 648:1964, Schedule of weights of building materials. BS 4604, Specification for the use of high strength friction grip bolts in structural steelwork. BS 4604, Metric series. BS 4604-1:1970, General grade. BS 4604-2:1970, Higher grade (parallel shank). BS 5950, Structural use of steelwork in building. BS 5950-3, Design of composite construction. BS 5950-3.1:1990, Code of practice for design of simple and continuous composite beams. BS 5950-4:1993, Code of practice for design of composite slabs with profiled steel sheeting. BS 5950-6, Code of practice for design of light gauge sheeting, decking and cladding3). BS 5950-8:1990, Code of practice for fire resistant design. BS 5975:1982, Code of practice for falsework. BS 6399, Design loading for buildings. BS 6399-1:1984, Code of practice for dead and imposed loads. BS 6399-3:1988, Code of practice for imposed roof loads. BS 8110, Structural use of concrete. BS 8110-1:1985, Code of practice for design and construction. BS 8110-2:1985, Code of practice for special circumstances. CP3, Code of basic data for the design of buildings. CP3:Chapter V, Loading. CP3:Chapter V-2:1972, Wind loads. DD ENV 1992, Eurocode 2: Design of concrete structures. DD ENV 1992-1-1:1992, General rules and rules for buildings (together with United Kingdom National Application Document). DD ENV 1993, Eurocode 3: Design of steel structures. DD ENV 1993-1-1:1992, General rules and rules for buildings (together with United Kingdom National Application Document).
Informative references BSI publications BRITISH STANDARDS INSTITUTION, London
BS 2989:1992, Specification for continuously hot-dip zinc coated and iron-zinc alloy coated steel flat products: tolerances on dimensions and shape. BS 4449:1988, Specification for carbon steel bars for the reinforcement of concrete. BS 4482:1985, Specification for cold reduced steel wire for the reinforcement of concrete. BS 4483:1985, Specification of steel fabric for the reinforcement of concrete. BS 5268, Structural use of timber. BS 5400, Steel, concrete and composite bridges. 3)
In preparation
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BS 5400-5:1979, Code of practice for design of composite bridges. BS 5628, Code of practice for use of masonry. BS 5950, Structural use of steelwork in building. BS 5950-5:1987, Code of practice for design of cold formed sections. BS 5950-7:1992, Specification for materials and workmanship: cold formed sections. BS EN 10025:1993, Hot rolled products of non-alloy structural steels — Technical delivery conditions. BS EN 10113, Hot-rolled products in weldable fine grain structural steels. BS EN 10113-1:1993, General delivery conditions. BS EN 10113-2:1993, Delivery conditions for normalized/normalized rolled steels. BS EN 10113-3:1993, Delivery conditions for thermomechanical rolled steels.
ISO publications International Organization for Standardization, (ISO), Geneva (All publications are available from BSI Sales) ISO 1000:1981, SI units and recommendations for the use of their multiples and of certain other units. ISO 3898:1987, Bases for design of structures — Notations — General symbols. ISO 4997:1991, Cold-reduced steel sheet of structural quality. ISO 4998:1991, Continuous hot-drip zinc-coated carbon steel sheet of structural quality. ISO 6707-1:1989, Building and civil engineering — Vocabulary — Part 1: General terms. ISO 8930:1987, General principles on reliability for structures — List of equivalent terms.
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EUROPEAN PRESTANDARD
ENV 1994-1-1:1992
PRÉNORME EUROPÉENNE October 1992
EUROPÄISCHE VORNORM UDC 624.92.016:624.07
Descriptors: Buildings, concrete structures, steel construction, building codes, design, dimensions
English version
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Design of composite steel and concrete structures — Part 1-1: General rules and rules for buildings
Conception et dimensionnement des structures mixtes acier-béton — Partie 1-1: Règles générales et règles pour les bâtiments
Entwurf von Verbundbauwerken aus Stahl und Beton — Teil 1-1: Allgemeine Regeln und Regeln für Hochbauten
This European Prestandard was approved by CEN on 1992-10-23 as a prospective standard for provisional application. The period of validity of this ENV is limited initially to three years. After two years the members of CEN will be requested to submit their comments, particularly on the question whether the ENV can be converted into a European Standard (EN). CEN members are required to announce the existance of this ENV in the same way as for an EN and to make the ENV available promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in parallel to the ENV) until the final decision about the possible conversion of the ENV into an EN is reached. CEN members are the national standards bodies of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
CEN European Committee for Standardization Comité Européen de Normalisation Europäisches Komitee für Normung Central Secretariat: rue de Stassart 36, B-1050 Brussels © 1992 Copyright reserved to CEN members
Ref. No. ENV 1994-1-1:1992 E
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Foreword to Eurocode 4: Part 1.1 0.1 Objectives of the Eurocodes 1) The structural Eurocodes comprise a group of standards for the structural and geotechnical design of buildings and civil engineering works. 2) They are intended to serve as reference documents for the following purposes: a) As a means to prove compliance of building and civil engineering works with the essential requirements of the Construction Products Directive (CPD). b) As a framework for drawing up harmonized technical specifications for construction products. 3) They cover execution and control only to the extent that is necessary to indicate the quality of the construction products, and the standard of the workmanship, needed to comply with the assumptions of the design rules. 4) Until the necessary set of harmonized technical specifications for products and for methods of testing their performance is available, some of the Structural Eurocodes cover some of these aspects in informative annexes. 0.2 Background to the Eurocode programme 1) The Commission of the European Communities (CEC) initiated the work of establishing a set of harmonized technical rules for the design of building and civil engineering works which would initially serve as an alternative to the different rules in force in the various Member States and would ultimately replace them. These technical rules became known as the “Structural Eurocodes”. 2) In 1990, after consulting their respective Member States, the CEC transferred work of further development, issue and updates of the Structural Eurocodes to CEN, and the EFTA Secretariat agreed to support the CEN work. 3) CEN Technical Committee CEN/TC 250 is responsible for all Structural Eurocodes. 0.3 Eurocode programme 1) Work is in hand on the following Structural Eurocodes, each generally consisting of a number of parts: EN 1991, Eurocode 1: Basis of design and actions on structures. EN 1992, Eurocode 2: Design of concrete structures. EN 1993, Eurocode 3: Design of steel structures. EN 1994, Eurocode 4: Design of composite steel and concrete structures. EN 1995, Eurocode 5: Design of timber structures.
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EN 1996, Eurocode 6: Design of masonry structures. EN 1997, Eurocode 7: Geotechnical design. EN 1998, Eurocode 8: Design of structures for earthquake resistance. In addition the following may be added to the programme: EN 1999, Eurocode 9: Design of aluminium structures. 2) Separate sub-committees have been formed by CEN/TC 250 for the various Eurocodes listed above. 3) This part of the Structural Eurocode for Design of Composite Steel and Concrete Structures is being issued by CEN as a European Prestandard (ENV) with an initial life of three years. 4) This Prestandard is intended for experimental practical application in the design of the building and civil engineering works covered by the scope as given in 1.1.2, and for the submission of comments. 5) After approximately two years CEN members will be invited to submit formal comments to be taken into account in determining future action. 6) Meanwhile, feedback and comments on this Prestandard should be sent to the Secretariat of sub-committee CEN/TC 250/SC 4 at the following address: National Standards Authority of Ireland, Glasnevin, Dublin 9, Ireland or to your national standards organization. 0.4 National Application Documents 1) In view of the responsibilities of authorities in member countries for the safety, health and other matters covered by the essential requirements of the CPD, certain safety elements in this ENV have been assigned indicative values which are identified by . The authorities in each member country are expected to assign definitive values to these safety elements. 2) Many of the harmonized supporting standards, including the Eurocodes giving values for actions to be taken into account and measures required for fire protection, will not be available by the time this Prestandard is issued. It is therefore anticipated that a National Application Document (NAD) giving definitive values for safety elements, referencing compatible supporting standards and providing national guidance on the application of this Prestandard, will be issued by each member country or its Standard Organization. 3) It is intended that this Prestandard is used in conjunction with the NAD valid in the country where the building or civil engineering works are located.
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0.5 Matters specific to this Prestandard 0.5.1 Cross-references to other Eurocodes 1) It is stated in 1.1.2 5) that “Part 1.1 of Eurocode 4 shall in all cases be used in conjunction with Parts 1.1 of Eurocodes 2 and 3”. To assist users, many cross-references to Eurocode 2 and 3 are given, in the general form “clause ... of EC2” (or EC3). In this Prestandard: — EC2 means ENV 1992-1-1 Eurocode 2: Part 1.1; revised final draft, 31 October 1990; — EC3 means ENV 1993-1-1 Eurocode 3: Part 1.1; edited draft, issue 5, November 1990, corrected July 1991. [Drafting note: These definitions of EC2 and EC3 are subject to revision by CEN, to enable reference to be made to the published ENV versions of EC2 and EC3.] It should not be assumed that cross-references are given to all relevant clauses of EC2 and EC3. 2) Repetitions from EC2 and EC3 are limited to material that is frequently needed for reference; for example, Table 3.1 on properties of concrete. 3) There are general references to Eurocode 1, but no references to specific clauses. In a few clauses (e.g., 7.3.2.1) application rules for actions are given. These apply only until the relevant Part of Eurocode 1 is available. 0.5.2 The treatment of *M for structural steel The use in this Prestandard of partial safety factors for concrete and reinforcement is as in EC2. For structural steel, clause 0.5.5 of EC3 is relevant. It was not possible to reproduce the method of EC3, where factors *M0 or *M1 are applied to resistances of cross-sections or members, because most of the *M factors given in this Prestandard are applied to strengths of materials (clause 2.2.3.2). The symbols *M0 and *M1 are therefore replaced in Eurocode 4: Part 1.1 by different symbols, *a and *Rd respectively. The method of drafting makes possible the assignment by a national authority of definitive values such that *a s *Rd. In this respect, it is consistent with the use of factors *M0 and *M1 in EC3. 0.5.3 Notes in this Prestandard Two types of note are used: — [Note: ...]. These notes should appear also in the EN version of Eurocode 4: Part 1.1. — [ENV Note: ...]. These notes relate to other Eurocodes and Reference Standards as they are in mid-1991. They will not appear in this form in the EN version of Eurocode 4: Part 1.1.
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Contents Foreword 0.1 Objectives of the Eurocodes 0.2 Background to the Eurocode programme 0.3 Eurocode programme 0.4 National Application Documents 0.5 Matters specific to this Prestandard 0.5.1 Cross-references to other Eurocodes 0.5.2 The treatment of *M for structural steel 0.5.3 Notes in this Prestandard 1 Introduction 1.1 Scope 1.1.1 Scope of Eurocode 4 1.1.2 Scope of Part 1.1 of Eurocode 4 1.1.3 Further Parts of Eurocode 4 1.2 Distinction between principles and application rules 1.3 Assumptions 1.4 Definitions 1.4.1 Terms common to all Eurocodes 1.4.2 Special terms used in this Part 1.1 of Eurocode 4 1.5 S.I. Units 1.6 Symbols used in part 1.1 of Eurocode 4 1.6.1 Latin upper case letters 1.6.2 Greek upper case letters 1.6.3 Latin lower case letters 1.6.4 Greek lower case letters 1.6.5 Subscripts 1.6.6 Use of subscripts in Part 1.1 of Eurocode 4 1.6.7 Conventions for member axes 2 Basis of design 2.1 Fundamental requirements 2.2 Definitions and classifications 2.2.1 Limit states and design situations 2.2.2 Actions 2.2.3 Material properties 2.2.4 Geometrical data 2.2.5 Load arrangements and load cases 2.3 Design requirements 2.3.1 General 2.3.2 Ultimate limit states
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2.3.4 2.4 3 3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.5 3.5.1 3.5.2 4 4.1 4.1.1 4.1.2 4.1.3 4.2
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Partial safety factors for ultimate limit states Serviceability limit states Durability Materials Concrete General Concrete strength classes Shrinkage of concrete Deformability of concrete — elastic theory Deformability of concrete — other theories Thermal expansion Reinforcing steel General Types of steels Steel grades Modulus of longitudinal deformation Stress-strain diagram Thermal expansion Structural steel General and scope Yield strength Design values of other material coefficients Stress-strain relationship Dimensions, mass and tolerances Profiled steel sheeting for composite slabs General and scope Yield strength Nominal values of other material coefficients Stress-strain relationship Coating Connecting devices General Shear connectors Ultimate limit states Basis General Beams Composite columns, frames and connections Properties of cross-sections of beams
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4.2.1 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.5 4.5.1 4.5.2 4.5.3 4.6 4.6.1 4.6.2 4.6.3 4.7 4.7.1 4.7.2 4.8 4.8.1 4.8.2 4.8.3 4.9 4.9.1 4.9.2 4.9.3 4.9.4 4.9.5 4.9.6 4.9.7 4.10 4.10.1
Effective section Effective width of concrete flange for beams in buildings Flexural stiffness Classification of cross-sections of beams General Classification of steel flanges in compression Classification of steel webs Resistances of cross-sections of beams Bending moment Vertical shear Bending and vertical shear Shear buckling resistance Interaction between bending and shear buckling Internal force and moments in continuous beams General Plastic analysis Elastic analysis Lateral torsional buckling of composite beams for buildings General Check without direct calculation Buckling resistance moment Web crippling General Effective web in Class 2 Composite columns Scope General method of design Simplified method of design Internal forces and moments in frames for buildings General Design assumptions Allowance for imperfections Sway resistance Methods of global analysis Elastic global analysis Rigid-plastic global analysis Composite connections in braced frames for buildings General
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4.10.2 4.10.3
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4.10.4 4.10.5 5 5.1 5.2 5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.3.3 5.3.4
5.3.5 6 6.1 6.1.1 6.1.2 6.1.3 6.2 6.2.1
6.2.2
6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6 6.3.7 6.4 6.4.1 6.4.2
Classification of connections Connections made with bolts, rivets or pins Splices in composite members Beam-to-column connections Serviceability limit states General Deformations General Calculation of maximum deflections of beams Cracking of concrete in beams General Minimum reinforcement Analysis of the structure for the control of cracking Control of cracking due to direct loading, without calculation of crack widths Control of cracking by calculation of crack widths Shear connection in beams for buildings General Basis of design Deformation capacity of shear connectors Spacing of shear connectors Longitudinal shear force Beams in which plastic theory is used for resistance of cross sections Beams in which elastic theory is used for resistances of one or more cross sections Design resistance of shear connectors General Stud connectors in solid slabs Headed studs used with profiled steel sheeting Block connectors in solid slabs Anchors and hoops in solid slabs Block connectors with anchors or hoops in solid slabs Angle connectors in solid slabs Detailing of the shear connection General recommendations Stud connectors
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Page 6.4.3 6.4.4 6.4.5 6.4.6 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.6 6.6.1 6.6.2 6.6.3 6.6.4
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6.6.5 7 7.1 7.1.1 7.1.2 7.2 7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.2 7.3.3 7.4 7.4.1 7.4.2 7.5 7.5.1 7.5.2 7.6 7.6.1 7.6.2 8 8.1
Headed studs used with profiled steel sheeting Block connectors Anchors and hoops Angle connectors Friction grip bolts General Ultimate limit state Serviceability limit state Detailing of friction grip bolts Transverse reinforcement Longitudinal shear in the slab Design resistance to longitudinal shear Contribution of profiled steel sheeting Minimum transverse reinforcement Longitudinal splitting Composite slabs with profiled steel sheeting for buildings General Scope Definitions Detailing provisions Slab thickness and reinforcement Aggregate Bearing requirements Actions and action effects Design situations Actions Load combinations and load cases Analysis for internal forces and moments Profiled steel sheeting as shuttering Composite slab Verification of profiled steel sheeting as shuttering Ultimate limit state Serviceability limit state Verification of composite slabs Ultimate limit state Serviceability limit state Floors with precast concrete slabs for buildings General
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8.2 8.3 8.4
Actions Partial safety factors for materials Design, analysis, and detailing of the floor system 8.4.1 Support arrangements 8.4.2 Joints between precast elements 8.4.3 Interfaces 8.5 Joint between steel beams and concrete slab 8.5.1 Bedding and tolerances 8.5.2 Corrosion 8.5.3 Shear connection and transverse reinforcement 8.6 Concrete floor designed for horizontal loading 9 Execution 9.1 General 9.2 Sequence of construction 9.3 Stability 9.4 Accuracy during construction and quality control 9.4.1 Static deflection during and after concreting 9.4.2 Compaction of concrete 9.4.3 Shear connection in beams and columns 9.4.4 Composite slabs with profiled steel sheeting 10 Design assisted by testing 10.1 General 10.2 Tests on shear connectors 10.2.1 General 10.2.2 Testing arrangement 10.2.3 Preparation of specimens 10.2.4 Testing procedure 10.2.5 Test evaluation 10.3 Testing of composite floor slabs 10.3.1 Parametric tests 10.3.2 Specific tests Annex A (normative) Reference documents A.1 Scope A.2 Standards on materials and products associated with Part 1.1 of Eurocode 4 A.2.1 Standards mentioned in EC2 A.2.2 Standards mentioned in EC3 A.2.3 Other standards mentioned in EC4
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A.3 Reference documents for execution A.4 General standards Annex B (normative) Lateral-torsional buckling B.1 Methods based on a continuous inverted-U frame model B.1.1 Simplified method for calculation of slenderness ratio B.1.2 Elastic critical moment B.1.3 Double symmetrical steel sections B.1.4 Mono-symmetrical steel sections Annex C (normative) Simplified calculation method for resistance of doubly symmetric composite cross sections in combined compression and bending C.1 Scope and assumptions C.2 Compressive resistances C.3 Position of neutral axis C.4 Bending resistances C.5 Interaction with transverse shear C.6 Neutral axes and plastic section moduli of some cross sections C.6.1 General C.6.2 Major axis bending of encased I-sections C.6.3 Minor axis bending of encased I-sections C.6.4 Concrete filled circular and rectangular hollow sections Annex D (normative) Design of composite columns with mono-symmetrical cross-sections — simplified method D.1 General D.2 Scope D.3 Design for axial compression D.4 Design for compression and uniaxial bending D.5 Long-term behaviour of concrete Annex E (normative) Partial shear connection method for composite slabs E.1 Scope E.2 Determination of Eu.Rd E.3 Verification of the longitudinal shear resistance E.4 Verification of composite slabs with end anchorage
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E.5
Verification of composite slabs with additional reinforcement Annex F (informative) Checklists of the information required in test reports F.1 Push tests F.1.1 Scope F.1.2 Test specimens F.1.3 Testing F.1.4 Results F.2 Testing of composite slabs F.2.1 Scope F.2.2 Test specimens F.2.3 Testing F.2.4 Results Figure 3.1 — Design stress-strain diagram for reinforcement Figure 3.2 — Bilinear stress-strain relationship Figure 3.3 — Idealisation for computer calculations Figure 4.1 — Typical cross-sections of composite beams Figure 4.2 — Effective section of rib of composite slab Figure 4.3 — Equivalent spans, for effective width of concrete flange Figure 4.4 — Use of an effective web in Class 2 for a section in hogging bending with a web in Class 3 Figure 4.5 — Plastic stress distributions for a composite beam with profiled steel sheeting and full shear connection, where the plastic neutral axis is within the steel section Figure 4.6 — Resistance in bending and vertical shear in absence of shear buckling Figure 4.7 — Distribution of shear connectors Figure 4.8 — Lateral-torsional buckling Figure 4.9 — Typical cross sections of composite columns, with notation Figure 4.10 — Effective perimeter c of a reinforcing bar Figure 4.11 — Stud connectors in composite column Figure 4.12 — Interaction curve for compression and uniaxial bending
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Figure 4.13 — Stress distributions corresponding to the interaction curve (Figure 4.12) Figure 4.14 — Deign procedure for compression and uniaxial bending Figure 4.15 — Typical values for ·n Figure 4.16 — Design for compression and biaxial bending Figure 5.1 — Reduction factor for the bending moment at supports Figure 6.1 — Relation between Fc and MSd Figure 6.2 — Relations between Fc and MSd Figure 6.3 — Beam with profiled steel sheeting parallel to the beam Figure 6.4 — Block connectors Figure 6.5 — Definition of Af2 Figure 6.6 — Example of anchor and hoop Figure 6.7 — Example of combination of block connector with anchor and hoop Figure 6.8 — Angle connector Figure 6.9 — Dimensions of haunches Figure 6.10 — Hoop connector Figure 6.11 — Example for shear connections with friction-grip bolts Figure 6.12 — Typical potential surfaces of shear failure Figure 6.13 — Potential shear surfaces in a slab with profiled steel sheeting Figure 7.1 — Typical forms of interlock in composite slabs Figure 7.2 — Sheet and slab dimensions Figure 7.3 — Minimum bearing lengths Figure 7.4 — Loads on profiled sheeting Figure 7.5 — Distribution of concentrated load Figure 7.6 — Illustration of possible critical sections Figure 7.7 — Stress distribution for sagging bending if the neutral axis is above the steel sheet Figure 7.8 — Stress distribution for sagging bending if neutral axis is in the steel sheet Figure 7.9 — Shear span Figure 7.10 — Equivalent simple span for determination of the longitudinal shear resistance of a composite slab Figure 7.11 — Critical perimeter for punching shear
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Page Figure 7.12 — Slip behaviour in external spans Figure 8.1 — Joints between precast floor elements Figure 10.1 — Possible failure modes of the push specimens Figure 10.2 — Test specimen for standard push test Figure 10.3 — Test specimen for specific push test Figure 10.4 — Determination of slip capacity $u Figure 10.5 — Illustration of possible failure modes Figure 10.6 — Test set-up Figure 10.7 — Evaluation of test results Figure 10.8 — Test details Figure B.1 — Lateral-torsional buckling Figure C.1 — Polygonal interaction curve Figure C.2 — Composite cross section symmetrical about two axes Figure C.3 — Encased I-sections with notation Figure C.5 — Concrete filled circular and rectangular hollow sections with notation Figure D.1 — Axes of a mono-symmetrical cross section Figure D.2 — Example for the two interaction curves for a mono-symmetrical cross section related to the same bending resistance Mp=.y+.Rd Figure E.1 — Determination of the degree of shear connection from Mtest Figure E.2 — Design partial interaction diagram Figure E.3 — Verification procedure Figure E.4 — Design partial interaction diagram for a slab with end anchorage Figure E.5 — Contribution of additional longitudinal reinforcement Table 1.1 — List of Equivalent Terms in various Languages Table 2.1 — Design values of actions for use in the combination of actions Table 2.2 — Partial safety factors for actions on building structures for persistent and transient design situations Table 2.3 — Partial safety factors for resistances & material properties 8
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Table 3.1 — Concrete strength classes, characteristic compressive strength fck (cylinders) and characteristic tensile strength fct of the concrete (in N/mm2) Table 3.2 — Values of the secant modulus of elasticity Ecm (in kN/mm2) Table 3.3 — Nominal values of yield strength fy and ultimate tensile strength fu for structural steel to EN 10025 Table 3.4 — Yield strength of basic material fyb Table 4.1 — Maximum width-to-thickness ratios for steel outstand flanges in compression Table 4.2 — Maximum width-to-thickness ratios for steel webs Table 4.3 — Limits to redistribution of hogging moments, per cent of the initial value of the bending moment to be reduced Table 4.4 — Maximum depth h (mm) of uncased steel member for which clause 4.6.2 is applicable Table 4.5 — Values of )10 and )20 when e = 0 Table 4.6 — Limiting values of Æ for clause 4.8.3.5 2) Table 4.7 — Factors " for the determination of moments according to second order theory Table 4.8 — Design assumptions Table 5.1 — Maximum steel stress for minimum reinforcement, high bond bars Table 5.2 — Maximum bar spacing for high bond bars Table B.1 — Values of factor C4 for spans with transverse loading Table B.2 — Values of factor C4 for spans without transverse loading Table B.3 — Values of factor C4 at end supports, for spans with a cantilever extension
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1 Introduction 1.1 Scope
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1.1.1 Scope of Eurocode 4 1) Eurocode 4 applies to the design of composite structures and members for buildings and civil engineering works. The composite structures and members are made of structural steel and reinforced or prestressed concrete connected together to resist loads. Eurocode 4 is subdivided into various separate parts, see 1.1.2 and 1.1.3. 2) This Eurocode is only concerned with the requirements for resistance, serviceability and durability of structures. Other requirements, e.g. concerning thermal or sound insulation, are not considered. 3) Execution4) is covered in Chapter 9, and by reference to Eurocodes 2 and 3, to the extent that it is necessary to indicate the quality of the construction materials and products which should be used and the standard of workmanship on site needed to comply with the assumptions of the design rules. Generally, the rules related to execution and workmanship are to be considered as minimum requirements which may have to be further developed for particular types of buildings or civil engineering works4) and methods of construction4). [ENV Note: See also the Foreword; in the present document, execution is not covered in Chapter 9 to the extent stated above.] 4) Eurocode 4 does not cover the special requirements of seismic design. Provisions related to such requirements are provided in Eurocode 8 “Design of structures for earthquake resistance”5) which complements or adapts the rules of Eurocode 4 specifically for this purpose. 5) Numerical values of the actions on buildings and civil engineering works to be taken into account in the design are not given in Eurocode 4. They are given in Eurocode 1 “Basis of design and actions on structures”5) applicable to the various types of construction4). 1.1.2 Scope of Part 1.1 of Eurocode 4 1) Part 1.1 of Eurocode 4 gives a general basis for the design of composite structures and members for buildings and civil engineering works. 2) In addition, Part 1.1 gives for composite slabs, beams, columns and frames detailed rules which are mainly applicable to ordinary buildings. The applicability of these rules may be limited, for practical reasons or due to simplifications; their use and any limits of applicability are explained in the text where necessary. 3) The following subjects are dealt with in Part 1.1: — — — — — — — — — — — — —
Chapter 1: Chapter 2: Chapter 3: Chapter 4: Chapter 5: Chapter 6: Chapter 7: Chapter 8: Chapter 9: Chapter 10: Annex A: Annex B: Annex C:
— Annex D: — Annex E: — Annex F:
Introduction Basis of Deign Materials Ultimate limit states Serviceability limit states Shear connection in beams for buildings Composite slabs with profiled steel sheeting for buildings Floors with precast concrete slabs for buildings Execution Deign assisted by testing Reference documents Lateral-torsional buckling Resistance of doubly symmetric composite cross sections in combined compression and bending Composite columns with mono-symmetrical cross section Partial shear connection method for composite slabs Checklists of the information required in test reports
4) For the meaning of this term, 5) At present at the draft stage.
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(Normative) (Normative) (Normative) (Normative) (Normative) (Informative)
see 1.4.1 2)
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4) Chapter 1 and Chapter 2 are common to all Eurocodes, with the exception of some additional clauses which are required for composite construction. 5) Part 1.1 of Eurocode 4 shall in all cases be used in conjunction with Parts 1.1 of Eurocodes 2 and 3. 6) This Part 1.1 does not cover: — resistance to fire nor, more generally, resistance at non-climatic temperatures — resistance to highly repeated actions liable to result in fatigue — resistance to dynamic actions that are not quasi-static — particular aspects of special types of civil engineering works (such as bridges, crane girders, masts, towers, offshore platforms, nuclear containment vessels); see 1.1.3 2) — particular aspects of special types of buildings (such as industrial buildings as far as fatigue would need to be considered) — prestressed structures — members the structural steel component of which has cross-sections with no axis of symmetry parallel to the plane of its web — members the structural concrete component of which is made of no-fines concrete, or of aerated concrete or of concrete including heavy aggregate, or has less reinforcement than the minimum values given in clause 5.4 of EC2, or contains expanding or non-shrinkage admixtures — composite plates consisting of a flat steel plate connected with a concrete slab — sway frames — some types of shear connectors (see Chapter 6) — semi-continuous frames such that rigid-plastic global analysis cannot be used [see 1.4.2 1), and in EC3 clause 5.2.2.4 and Table 5.2.1] — base plates beneath composite columns — particular aspects of composite piles for foundations — particular aspects of members with haunched or tapered steel components — particular aspects of box girders — particular aspects of totally or partially encased beams (see however 4.3.3.1 and Annex B) — and more generally particular aspects mentioned as not covered in the following chapters (relating for example to the form of cross-sections). 7) The implicit inclusion of a type of building or a form of structure [as defined in 1.4.1 2)] does not imply that all details of its design are coveted conclusively. 1.1.3 Further Parts of Eurocode 4 1) This Part 1.1 of Eurocode 4 will be supplemented by further Parts which will complement or adapt it for particular aspect of special types of buildings and civil engineering works, special methods of construction and certain other aspects of design which are of general practical importance. 2) Further Parts of Eurocode 4 which, at present, are being prepared or are planned are the following: Part 1.2 Fire resistance; Part 2 Bridges.
1.2 Distinction between principles and application rules 1) Depending on the character of the individual clauses, distinction is made in this Eurocode between Principles and Application Rules. 2) The Principles comprise: — general statements and definitions for which there is no alternative, as well as — requirements and analytical models for which no alternative is permitted unless specifically stated. 3) The Principles are printed in roman type. 4) The Application Rules are generally recognised rules which follow the Principles and satisfy their requirements.
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5) It is permissible to use alternative design rules different from the Application Rules given in the Eurocode, provided that it is shown that the alternative rules accord with the relevant Principles and are at least equivalent with regard to the resistance, serviceability and durability achieved by the structure if designed using the present Eurocode. 6) The Application Rules are printed in italics. This is an Application Rule. [Note: Tables and figures have the same status as the paragraphs to which they relate.]
1.3 Assumptions
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1) The assumptions given in clauses 1.3 1) of EC2 and EC3, which are identical, are applicable. 2) The design procedures are valid only when the requirements for execution workmanship given in Chapter 9 are also complied with. 3) Numerical values identified by are given as indications. Other values may be specified by Member States.
1.4 Definitions 1.4.1 Terms common to all Structural Eurocodes 1) Unless otherwise stated in the following, the terminology used in International Standard ISO 8930 applies. 2) The following terms are used in common for all Structural Eurocodes with the following meanings. — Construction Works: Everything that is constructed or results from construction operations6). This term covers both building and civil engineering works. It refers to the complete construction comprising both structural and non-structural elements. — Execution: The activity of creating a building or civil engineering works. The term covers work on site; it may also signify the fabrication of components off site and their subsequent erection on site7) — Structure: Organized combination of connected parts designed to provide some measure of rigidity8). This term refers to load carrying parts. — Type of building or civil engineering works: Type of “construction works” designating its intended purpose, e.g. dwelling house, industrial building, road bridge9). — Form of structure: Structural type designating the arrangement of structural elements, e.g. beam, triangulated structure, arch, suspension bridge. — Construction material: A material used in construction work, e.g. concrete, steel, timber, masonry. — Type of construction: Indication of principal structural material, e.g. reinforced concrete construction, steel construction, timber construction, masonry construction, composite construction. — Method of construction: Manner in which the construction will be carried out, e.g. cast in place, prefabricated, cantilevered. — Structural system: The load bearing elements of a building or civil engineering works and the way in which these elements are assumed to function, for the purpose of modelling. 3) The equivalent terms in various languages are given in Table 1.1. 1.4.2 Special terms used in this Part 1.1 of Eurocode 4 1) The following terms are used in Part 1.1 of Eurocode 4 with the following meanings: — Frame: A structure or portion of a structure, comprising an assembly of directly connected structural members, designed to act together to resist load. This term covers both plane frames and three-dimensional frames.
6) This definition accords with International Standard ISO 6707-1. 7) (for the English version only): In English “construction” may be used
instead of “execution” in certain combinations of words where there is no ambiguity (e.g. “during construction”). 8) International Standard ISO 6707-1 gives the same definition but adds “or a construction works having such an arrangement”. In the Structural Eurocodes this addition is not used, in order to facilitate unambiguous translations. 9) (for the English version only): “Type of construction works” is not used in English.
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Table 1.1 — List of Equivalent Terms in various Languages ENGLISH
FRANCAIS
Construction Works
Construction
Bauwerk
DEUTSCH
Costruzione
ITALIANO
Bouwwerk
NEDERLANDS
Obras
ESPANOL
Execution
Execution
(Bau-) Ausfuhrung
Esecuzione
Uitvoering
Ejecucion
Structure
Structure
Tragwerk
Struttura
Draagconstructie
Estructura
Nature de Type of Building or civil construction engineering works
Art des Bauwerks
Tipo di construzione
Type bouwwerk Tipe de obra
Form of structure
Type de structure
Art des Tragwerks
Tipo di struttura
Type draagconstructie
Tipologia estructural
Construction material
Materiau de construction
Baustoff; Werkstoff (Stahlbau)
Materiale da construzione
Constructie materiaal
Material de construccion
Type of construction
Mode de construction
Bauweise
Sistema construttivo
Bouwwijze
Tipo de construccion
Method of construction
Procede d’execution
Bauverfahren
Procedimento esecutivo
Bouwmethode
Procedimiento constrctivo
Structural system
Systeme structural
Tragsystem
Sistema strutturale
Constructief systeem
Sistema estructural
— Sub-frame: A frame which forms part of a larger frame, but is treated as an isolated frame in a structural analysis. — Type of framing: Terms used to distinguish between frames which are either. — continuous, in which only both equilibrium and the structural properties of the members need be considered in the global analysis; — semi-continuous, in which also the structural properties of the connections need explicit consideration in the global analysis; or — simple, in which only equilibrium need be considered in the global analysis. — For sway frames and non-sway frames see 4.9.4.2 and EC3 clause 5.2.5.2. — For braced frames and non-braced frames see 4.9.4.3 and EC3 clause 5.2.5.3. — Composite frame: In Part 1.1 of EC4, a composite frame is a framed structure for a building or similar construction works, in which some or all of the beams and columns are composite members and most of the remaining members are structural steel members. The use of reinforced or prestressed concrete or masonry members in bracing systems (as defined in EC3) is not excluded. — Composite member: A structural member with components of concrete and of structural or cold-formed steel, interconnected by shear connection so as to limit the longitudinal slip between concrete and steel and the separation of one component from the other. — Propped structure or member: A structure or member the steel elements of which are supported until the concrete elements are able to resist stresses. — Unpropped structure or member: A structure or member in which the weight of concrete elements is applied to steel elements. — Shear connection: An interconnection between the concrete and steel components of a composite member that has sufficient strength and stiffness to enable the two components to be designed as parts of a single structural member. Except as provided in 4.8.2.7 and 7.1.2.2 shear connection means mechanical shear connection that does not rely on bond or adhesion at interfaces between steel and concrete. — Full and partial shear connection are defined in 4.1.2 6). 12
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— Composite connection: A connection between a composite member and any other member in which reinforcement is intended to contribute to the resistance of the connection. — Rigid composite connection: A composite connection such that its deformation has no significant influence on the distribution of internal forces and moments in the structure, nor on its overall deformation (see 4.10.2.). — Composite column: A composite member subjected mainly to compression and bending. Only columns with cross-sections of the types defined in 4.8.1 are treated in this Eurocode. — Composite beam: A composite member subjected mainly to bending. Only those in which the structural steel section is symmetrical about its minor axis are treated in this Eurocode. — Continuous composite beam: A beam with three or more supports, in which the steel section is either continuous over internal supports or is jointed by full-strength and rigid connections, with connections between the beam and each support such that it can be assumed that the support does not transfer significant bending moment to the beam. At the internal supports the beam may have either effective reinforcement or only nominal reinforcement. — Composite slab: A bi-dimensional horizontal composite member subjected mainly to bending, in which profiled steel sheets: — are used as permanent shuttering capable of supporting wet concrete, reinforcement and site loads, and — subsequently combine structurally with the hardened concrete and act as part or all of the tensile reinforcement in the finished slab. — Global analysis: The determination of a consistent set of internal force and moments in a structure which are in equilibrium with a particular defined set of actions on the structure, and are based on the properties of the materials. [ENV Note: The terminology of the various types of analyses has not yet been fully harmonised between EC2, EC3 and EC4.]
1.5 S.I Units 1) S.I. Units shall be used in accordance with ISO 1000. 2) For calculations, the following units are recommended: — forces and loads — unit mass — unit weight — stresses and strengths — moments (bending .....)
: kN, kN/m, kN/m2 : kg/m3 : kN/m3 : N/mm2 (= MN/m2 or MPa) : kNm.
1.6 Symbols used in part 1.1 of Eurocode 4 1) Only the main symbols are defined in this chapter. Symbols which are used only in small parts of this Eurocode are defined where they appear. [Note: The following lists of symbols include the principal combinations of symbols and subscripts used in this Eurocode. The lists do not include symbols used in one place only, nor those symbols used in EC2 and EC3 but not directly in EC4.] 1.6.1 Latin upper case letters A C E F G I K L
Accidental action; Area Fixed value; Factor Effect of actions; Modulus of elasticity Action; Force Permanent action; shear modulus Second moment of area Stiffness factor (I/L) Length; Span; System length
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M MRd MSd N PR Q R S V W X
Moment in general; Bending moment Design value of the resisting bending moment Design value of the applied internal bending moment Axial force; Number of shear connectors Shear resistance of a shear connector Variable action Resistance Internal forces and moments (with subscripts d or k) Shear force Section modulus Value of a property of a material
1.6.2 Greek upper case letters %
Difference in ...........(precedes main symbol)
1.6.3 Latin lower case letters a b c d e f fck fsk fu fy fyp h i k l
Distance; Geometrical data Width; Breadth Distance; Outstand; Thickness of concrete cover Diameter; Depth Eccentricity Strength (of a material) Characteristic compressive strength of concrete Characteristic tensile yield strength of reinforcement Specified ultimate tensile strength of the material of a stud, a bolt, a rivet... Nominal tensile yield strength of structural steel Characteristic (nominal) tensile yield strength of profiled steel sheeting Height Radius of gyration Coefficient; Factor (or = or L) Length; Span; Buckling length. [Note: l can be replaced by L or by = (handwritten) for certain lengths or to avoid confusion with 1 (numeral).] m Factor for composite slabs n Modular ratio r Radius s Spacing; Distance t Thickness v Shear force per unit length w Crack width xx, yy, zz Rectangular axes
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1.6.4 Greek lower case letters ! " * $ & ) F 2 4 5 @ B E : · ?
Angle; Ratio; Coefficient of linear thermal expansion; Factor Angle; Ratio; Factor Partial safety factor (always with appropriate subscript: e.g., F, G, Q, A, M, Ma, a, ap, c, s, v, Rd) Steel contribution ratio; Deflection Strain; Coefficient Coefficient Angle; Slope (or 2 if non-dimensional) Slenderness ratio Coefficient of friction; Moment ratio Poisson’s ratio Unit mass; Reinforcement ratio Normal stress Shear stress Diameter of a reinforcing bar Reduction factor (for buckling) Factors defining representative values of variable actions; Stress ratio
1.6.5 Subscripts A a b c cr cs d dst eff e e= f G h i inf k l LT M m max N nom p p= Q R r
Accidental Structural steel Buckling; Bolt; Beam; Bottom Compression; Concrete; Composite cross section (or crit) Critical Concrete shrinkage Deign Destabilizin Effective Effective (with further subscript) Elastic Flange; Full; Front Permanent (referring to actions) Haunch Index (replacing a numeral) Inferior; Lower Characteristic (or =) Longitudinal Lateral — torsional Material Allowing for bending moment; Mean Maximum Allowing for axial force Nominal (possibly supplementing a) Profiled steel sheeting Plastic Variable (referring to actions) Resistance Reduced
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S s stb sup t ten u v w x y z 0,1,2,
Internal fore; Internal moment Reinforcing steel Stabilizing Superior; Upper Tension; Tensile; Transversal; Top Tension Ultimate Vertical; Related to shear connection Web Axis along member Major axis of cross-section; Yield Minor axis of cross-section etc.... Particular values
1.6.6 Use of subscripts in part 1.1 of Eurocode 4 Reference should be made to clause 1.6.6 of Eurocode 3. 1.6.7 Conventions for member axes Reference should be made, if relevant, to clause 1.6.7 of Eurocode 3.
2 Basis of design 2.1 Fundamental requirements 1) A structure shall 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. 2) A structure shall also be designed in such a way that it will not be damaged by events like explosions, impact or consequences of human errors, to an extent disproportionate to the original cause. 3) The potential damage should be limited or avoided by appropriate choice of one or more of the following: — 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 — tying the structure together. 4) The above requirements shall be met by the choice of suitable materials, by appropriate design and detailing and by specifying control procedures for production, construction and use as relevant for the particular project.
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2.2 Definitions and classifications 2.2.1 Limit states and design situations
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2.2.1.1 Limit states 1) Limit states are states beyond which the structure no longer satisfies the design performance requirements. Limit states are classified into: — ultimate limit states — serviceability limit states. 2) Ultimate limit states are those associated with collapse, or with other forms of structural failure which may endanger the safety of people. 3) States prior to structural collapse which, for simplicity, are considered in place of the collapse itself are also classified and treated as ultimate limit states, e.g. the bending resistance of a member having cross-sections in Class 3. 4) Ultimate limit states which may require consideration include: — loss of equilibrium of the structure or any part of it, considered as a rigid body — failure by excessive deformation, rupture, or loss of stability of the structure or any part of it, including shear connection (i.e. the connection between the concrete and the steel parts), supports and foundations. Limit states may also concern only concrete or steel parts of the structure (e.g. the steel part during an erection phase), for which reference should be made to Eurocode 2 and Eurocode 3 respectively. 5) Serviceability limit states corresponds to states beyond which specified service criteria are no longer met. 6) Serviceability limit states which may require consideration include: — 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 — vibration which causes discomfort to people, damage to the building or its contents, or which limits its functional effectiveness — cracking of the concrete which is likely to affect appearance, durability or water-tightness adversely — damage to concrete because of excessive compression, which is likely to lead to loss of durability — slip at the steel-concrete interface when it becomes large enough to invalidate design checks for other serviceability limit states in which the effects of slip are neglected. 2.2.1.2 Design situations 1) Design situations are classified as: — persistent situations corresponding to normal conditions of use of the structure — transient situations, for example during construction or repair — accidental situations. 2) For composite structures attention is drawn to the necessity of identifying and considering, when relevant, several transient design situations corresponding to the successive phases of the building process. For example, it may be necessary not only to consider the situation of the steel beam supporting the fresh concrete, but even to distinguish several situations corresponding to successive phases of pouring the concrete. 2.2.2 Actions [Note: fuller definitions of the classification of actions will be found in Eurocode 1.] 2.2.2.1 Definitions and principal classification 1) An action (F) is: — a force (load) applied to the structure (direct action), or — an imposed deformation (indirect action), e.g. temperature effects, settlement or shrinkage.
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2) Actions are classified: i) by their variation in time: — permanent actions (G), e.g. self-weight of structures, fittings, ancilliaries and fixed equipment — variable actions (Q), e.g. imposed loads, wind loads or snow loads — accidental actions (A), e.g. explosions or impact from vehicles ii) by their spatial variation: — fixed actions, e.g. self-weight [but see 2.3.2.3 2) for structures very sensitive to variations in self-weight] — free actions, which result in different arrangements of actions, e.g. movable imposed loads, wind loads, snow loads. 3) Supplementary classifications relating to the response of the structure are given in the relevant clauses. 4) For composite structures, a classification of the effects of actions is adopted in calculations, as follows: — shrinkage of concrete and non-uniform changes of temperature result in internal forces in cross sections, and curvatures and longitudinal strains in members. The effects that occur in isostatic structures, and also in hyperstatic structures when compatibility of the deformations is not considered, are classified as primary (isostatic) effects. For these effects, the associated actions have to be considered as direct or indirect [see 1) above], according to their nature — the primary effects of shrinkage and temperature are associated in hyperstatic structures with additional action-effects, such that the total effects are compatible. These additional effects are classified as secondary (hyperstatic) effects. For these effects the associated actions, which are usually forces at external supports, are to be considered as imposed deformations (indirect actions). This classification has consequences either in 2.3.3.1 4) hereafter if the global analysis is linear, or in the global analysis itself in the other cases. 2.2.2.2 Characteristic value of actions 1) Characteristic values Fk are specified: — in Eurocode 1 or other relevant loading codes, or — by the client, or the designer in consultation with the client, provided that the minimum provisions specified in the relevant loading codes or by the competent authority are observed. 2) For permanent actions where the coefficient of variation is large (e.g. for some earth pressures) or where the actions are likely to vary during the life of the structure (e.g. for some superimposed permanent loads), two characteristic values are distinguished, an upper (Gk, sup) and a lower (Gk, inf). Elsewhere a single characteristic value [Gk) is sufficient. 3) The self-weight of the structure may, in most cases, be calculated on the basis of the nominal dimensions and mean unit masses. 4) Because of the continuous and monotonic variation in time of shrinkage, in most cases two values should be considered for this action, associated respectively with two extreme points of the design life, represented by the symbolic expressions t = 0 and t = Z. In particular cases only the intermediate range should be investigated. 5) For variable actions the characteristic value (Qk) corresponds to either: — the upper value with an intended probability of not being exceeded, or the lower value with an intended probability of not being reached, during some reference period, having regard to the intended life of the structure or the assumed duration of the design situation, or — the specified value, e.g. an intended limit for use. 6) For accidental actions the characteristic value Ak (when relevant) generally corresponds to a specified value. 2.2.2.3 Representative values of variable actions [Note: fuller definitions of representative values will be found in Eurocode 1.] 1) The main representative value is the characteristic value Qk.
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2) Other representative values are related to the characteristic value Qk by means of a factor ?i. These values are defined as: — combination value: — frequent value: — quasi-permanent value:
?0Qk (see 2.3.2.2 and 2.3.4) ?1Qk (see 2.3.2.2 and 2.3.4) ?2Qk (see 2.3.2.2 and 2.3.4)
3) Supplementary representative values are used for fatigue verification and dynamic analysis. 4) The factors ?0, ?1 and ?2 are specified: — in Eurocode 1 or other relevant loading codes, or — by the client, or the designer in consultation with the client, provided that the minimum provisions specified in the relevant loading codes or by the competent authority are observed.
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2.2.2.4 Design values of actions 1) The design value Fd of an action is expressed in general terms as: Fd = *FFk
(2.1)
where *F is the partial safety factor for the action considered — taking account of, for example, the possibility of unfavourable deviations of the actions, the possibility of inaccurate modelling of the actions, uncertainties in the assessment of effects of actions and uncertainties, in the assessment of the limit state considered. 2) Specific examples of the use of *F are: Gd = *GGk Qd = *QQk or *Q?iQk Ad = *AAk (if Ad is not directly specified) 3) The upper and lower design values of permanent actions are expressed as follows: — where only a single characteristic value Gk is used [see 2.2.2.2 2)] then: Gd,sup = *G,sup Gk Gd,inf = *G,inf Gk — where upper and lower characteristic values of permanent actions are used [see 2.2.2.2 2)] then: Gd,sup = *G,sup Gk,sup Gd,inf = *G,inf Gk,inf where
Gk,inf Gk,sup *G,inf *G,sup
is the lower characteristic value of the permanent action is the upper characteristic value of the permanent action is the lower value of the partial safety factor for the permanent action is the upper value of the partial safety factor for the permanent action.
2.2.2.5 Design values of the effects of actions 1) The effects of actions (E) are response (for example, internal forces and moments, stresses, strains) of the structure to the actions. Design values of the effects of actions (Ed) are determined from the design values of the actions, geometrical data and material properties when relevant, in accordance with 2.3.1 4), as: Ed = E(Fd, ad, ...) where ad is defined in 2.2.4.
(2.2)
2.2.3 Material properties 2.2.3.1 Characteristic values 1) A material property is represented by a characteristic value Xk which in general corresponds to a fractile in the assumed statistical distribution of the particular property of the material, specified by relevant standards and tested under specified conditions. Certain properties of some components (e.g., resistance of a shear connector PRk) are treated as material properties.
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2) For some material properties a nominal value is used as the characteristic value; this is the case for most of the material properties relating to the steel parts of composite structures. 3) For other material properties the characteristic values are for some verifications substituted or supplemented by mean or nominal values, which correspond to the most likely values throughout the structure for which a minimum characteristic value has been specified; this is the case for concrete properties and for physical coefficients. 4) A material property may have two characteristic values, the upper value and the lower value. In most case only the lower values of strengths need to be considered. However the upper values shall be taken into account where overstrength effect may produce a significant reduction in safety; this is for example the case for the tensile strength of concrete in the calculation of the effects of indirect actions. 2.2.3.2 Design values
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1) The design value Xd of a material property represented by its lower characteristic value is defined as: Xd = Xk,inf/*M where *M is the partial safety factor for the material property [see 2.3.3.2 1)]. However, the design value PRd of the resistance of a shear connector is defined in a similar way, as PRd = PRk/*v where *v is a unified value applicable for any mode of failure of the shear connection. 2) For composite structures, the design values of the material strengths and geometrical data, when relevant, shall be used to determine the design resistances of members or cross-sections, according to the individual chapters, as: Rd = R(Xd, ad ...)
(2.3)
in most cases. Where the resistance is influenced by the buckling of the structural steel, other formulations are used, including a specific safety factor *Rd [see 4.1.1 5)]. 3) The design value Rd may be determined form tests. In this case Rd is defined according to formula (2.3) or as: Rd = R(Xk, ak . . .)/*M
(2.3bis)
where *M is a partial factor for the resistance [see 2.3.3.2 9)]. 2.2.4 Geometrical data 1) Geometrical data are generally represented by their nominal values: ad = anom
(2.4)
2) In some cases the geometrical design values are defined by: ad = anom + %a
(2.5)
where %a is the additive partial safety margin for the geometrical datum. The values of %a are given in the appropriate clauses. [ENV Note: %a covers mainly imperfections but also, in some cases, deviations due to neglected parasitic tic phenomena, e.g. thermal differences.] 3) Imperfections to be adopted in the global analysis of the structure are treated in 4.8.2.3 and 4.9.3. 2.2.5 Load arrangements and load cases [Note: detailed rules on load arrangements and load cases are given in Eurocode 1. 1) A load arrangement identifies the position, magnitude and direction of a free action. 2) A load case identifies compatible load arrangements, sets of deformations and imperfections considered for a particular verification. 3) For the relevant combinations of actions, sufficient load cases shall be considered to enable the critical design conditions to be established. 4) Simplified load cases may be used, if based on a reasonable interpretation of the structural response.
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5) For continuous beams and slabs in buildings without cantilevers subjected to dominantly uniformly distributed loads, it will generally be sufficient to consider only the following load arrangements: a) alternate spans carrying the design variable and permanent loads (*Q Qk + *G Gk), other spans carrying only the design permanent load *G Gk, b) any two adjacent spans carrying the design variable and permanent loads (*Q Qk + *G Gk), all other spans carrying only the design permanent load *G Gk. [ENV Note: 4) and 5) possibly to be transferred to Eurocode 1.]
2.3 Design requirements
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2.3.1 General 1) It shall be verified that no relevant limit state is exceeded. 2) All relevant design situations and load cases shall be considered. 3) Possible deviations from the assumed directions or positions of actions shall be considered. [ENV Note: it is assumed that guidance will be found in relevant chapters of the Eurocode 1.] 4) Calculations shall be performed using appropriate design models (supplemented, if necessary, by tests) involving all relevant variables. The models shall be sufficiently precise to predict the structural behaviour, commensurate with the standard of workmanship likely to be achieved, and with the reliability of the information on which the design is based. 2.3.2 Ultimate limit states 2.3.2.1 Verification conditions 1) When considering a limit state of static equilibrium or of gross displacements or deformations of the structure, it shall be verified that: Ed,dst k Ed,stb
(2.6)
where Ed,dst and Ed,stb are the design effects of destabilizing actions and stabilizing actions, respectively. 2) When considering a limit state of rupture or excessive deformation of a section, member or connection (fatigue excluded) it shall be verified that: Sd k Rd
(2.7)
where Sd is the design value of an internal force or moment (or of a respective vector of several internal forces or moments) and Rd is the corresponding design resistance, as defined in 2.2.3.2 2) or 3). 3) When considering a limit state of transformation of the structure into a mechanism, it shall be verified that a mechanism does not occur unless actions exceed their design values, taking account of the respective design values of all structural properties. 4) When considering a limit state of stability induced by second-order effects, it shall be verified that instability does not occur unless actions exceed their design values, taking account of the respective design values of all structural properties. In addition, sections shall be verified according to 2) above. [Note: Equation (2.8) of EC3 is not considered in this Part of EC4.] 2.3.2.2 Combinations of actions 1) For each load case, design values Ed for the effects of actions shall be determined from combination rules involving design values of actions as identified by Table 2.1 Table 2.1 — Design values of actions for use in the combination of actions Design situation
Permanent actions Gd
Variable actions Qd Leading variable action
Accompanying variable actions
Persistent and Transient
*GGk
*QQk
?0*QQk
Accidental (if not specified differently elsewhere)
*GAGk
?1Qk
?2Qk
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Accidental actions Ad
*AAk (if Ad is not specified directly)
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2) The design values of Table 2.1 shall be combined using the following rules (given in symbolic form): — Persistent and transient design situations for verifications other than those relating to fatigue (fundamental combinations): (2.9) — Accidental design situations (if not specified differently elsewhere): (2.10)
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where: Gk,j = characteristic values of the permanent actions Qk,l = characteristic value of one of the variable actions Qk,i = characteristic values of the other variable actions Ad = design value (specified value) of the accidental action *G,j = partial safety factor for the permanent action Gk,j *GAj = as *G,j, but for accidental design situations *Q,i = partial safety factor for the variable action Qk,i and ?0, ?1, ?2 are factors defined in 2.2.2.3. 3) Combinations for accidental design situations either involve an explicit accidental action A or refer to a situation after an accidental event (A = 0). Unless specified otherwise, *GA = may be used. 4) In expressions (2.9) and (2.10), indirect actions shall be introduced where relevant. 5) Simplified combinations for building structures are given in 2.3.3.1. [Note: detailed rules on combinations of actions are given in Eurocode 1.] 2.3.2.3 Design values of permanent actions 1) In the various combinations defined above, those permanent actions that increase the effect of the variable actions (i.e. produce unfavourable effects) shall be represented by their upper design values and those that decrease the effect of the variable actions (i.e. produce favorable effects) by their lower design values [see 2.2.2.4 3)]. 2) Where the results of a verification may be very sensitive to variations of the magnitude of the same permanent action from place to place in the structure, this action shall be treated as consisting of separate unfavourable and favourable parts. This applies in particular to the verification of static equilibrium. 3) Where a single permanent action is treated as consisting of separate unfavourable and favourable parts, allowance may be made for the relationship between these parts by adopting special design values [see 2.3.3.1 3) for building structures]. 4) Except for the cases mentioned in 2), the whole of each permanent action should be represented throughout the structure by either its lower or its upper design value, whichever gives the more unfavourable effect. 5) For continuous beams and frames, the same design value of the self-weight of the structure [evaluated as in 2.2.2.2 3)] may be applied to all spans, except for cases involving the static equilibrium of cantilevers (see clause 2.3.2.4 of EC3). 2.3.2.4 Verification of static equilibrium Clause 2.3.2.4 of EC3 is applicable.
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2.3.3 Partial safety factors for ultimate limit states 2.3.3.1 Partial safety factors for actions on building structures 1) For the persistent and transient design situations the partial safety factors given in Table 2.2 shall be used. Table 2.2 — Partial safety factors for actions on building structures for persistent and transient design situations Permanent actions (*G)
Variable actions (*Q) Leading variable action
Accompanying variable actions
—b
—b
Favourable effect
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*F,inf
1.0a
Unfavourable effect *F,sup
1.35a
1.5
1.5
a See b
also paragraph 3) See Eurocode 1; in normal cases for building structures *Q,inf = 0
2) For accidental design situations to which equation (2.10) applies, the partial safety factors for the variable actions are taken as equal to 1.0. For permanent actions see 2.3.2.2 3). 3) Where, according to 2.3.2.3 2), a single permanent action needs to be considered as consisting of unfavourable and favourable parts, the favourable part may, as an alternative, be multiplied by *G,inf = 1.1 and the unfavourable part by: *G,sup = 1.35 provided that by applying *G,inf = both to the favourable part and the unfavourable part does not give a more unfavourable effect. 4) For imposed deformations [see 2.2.2.1 1) and 4)], where non-linear methods of analysis are used, the factors for variable actions given above apply. For a linear calculation, the factor for unfavourable effects shall be reduced by 20 %. 5) For vectorial (i.e. multi-component) effects in columns, if a component of the effect is favourable, reference sum be made to 4.8.3.13 6). 6) For building structures, as a simplification, the expression (2.9) may be replaced by whichever the following combinations gives the larger value: considering only the most unfavourable variable action: (2.11) considering all unfavourable variable actions (2.12)
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2.3.3.2 Partial safety factors for resistances and material properties 1) Except in certain cases mentioned in 2.2.3.2 2) and 3) the factors *M are applied to lower characteristic or nominal strengths of materials [following 2.2.3.2 1)], and are as given in Table 2.3. Table 2.3 — Partial safety factors for resistances & material properties Structural steel
Concrete
Steel reinforcement
Profiled steel sheeting
*a
*c
*s
*ap
Combination
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(= *M0 in EC3)
Fundamental
1.10
1.5
1.15
1.10
Accidental (except earthquakes)
1.0
1.3
1.0
1.0
2) The values in Table 2.3 are assumed to take account of, inter alia, differences between the strength of test specimens of the structural materials and their strength in situ. They are applicable to some elastic mechanical properties, but only in cases specified in the relevant clauses; in other cases they should be substituted by *M = 1.0. For physical non-mechanical coefficients (e.g. density, thermal expansion), *M shall be taken as equal to 1.0. 3) Higher or lower values of *c may be used if these are justified by adequate quality assurance procedures [see 1.3 2)]. 4) Values of *M for shear connection are given as *v in 6.3.2.1 for studs, 6.3.7 for angle connectors and 6.5.2.1 for friction grip bolts. [ENV Note: *v is not yet defined for other types]. 5) Values of *M for bolts, rivets, pins, welds, and slip resistance of bolted joints are as given in clause 6.1.1 2) of EC3. 6) Values of *M for longitudinal shear in composite slabs are given in 7.6.1. 7) For steel members in composite structures, values of *M for fundamental combinations are as given in the relevant clauses of Chapter 5 of Part 1.1 of Eurocode 3, or in Part 1.3 of Eurocode 3. 8) For reinforced concrete members in composite structures, values of *M are as given in clause 2.3.3.2 of EC2 [i.e. as given in 1) to 3) above]. 9) Where structural properties are determined by testing, reference shall be made to Chapter 10 and Annex F. 2.3.4 Serviceability limit states 1) It shall be verified that: Ed k Cd or Ed k Rd
(2.13)
where: Cd Ed
is a nominal value or a function of certain design properties of materials related to the deign effect of actions considered, and is the design value of the effect of actions, determined on the basis of one of the combinations defined below.
The required combination is identified in the particular clause of chapter 5 for each serviceability verification.
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2) Three combinations of actions for serviceability limit states are defined by the following expressions: Rare combination: (2.14) Frequent combination: (2.15) Quasi-permanent combination:
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(2.16) where the notation is defined in 2.3.2.2 2). Imposed deformations should be considered when relevant. 3) Where simplified compliance rules are given in the relevant clauses dealing with serviceability limit states, detailed calculations using combinations of actions are not required. 4) Where the design considers compliance of serviceability limit states by detailed calculations, simplified expressions may be used for building structures. 5) For building structures, as a simplification, expression (2.14) for the rare combination may be replaced by whichever of the following combinations gives the larger value: — considering only the most unfavourable variable action: (2.17) — considering all unfavourable variable actions: (2.18) These two expressions may also be used as a substitute for expression (2.15) for the frequent combination. 6) Values of *M shall be taken as 1.0, except where stated otherwise in particular clauses.
2.4 Durability 1) To ensure an adequately durable structure, the following inter-related factors shall be considered: — the use of the structure — the required performance criteria — the expected environmental conditions — the composition, properties and performance of the materials — the shape of members and the structural detailing — the quality of workmanship and level of control — the particular protective measures — the likely maintenance during the intended life. 2) The internal and external environmental conditions shall be estimated at the design stage to asses their significance in relation to durability and to enable adequate provisions to be made for protection of the materials. 3) Section 4.1 of EC2 is applicable to composite structures. [ENV Note: clause subject to development for the steel parts.]
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3 Materials 3.1 Concrete 3.1.1 General 1) The properties most frequently required for design calculations are summarised hereafter. For lightweight concretes they are given as functions of their oven-dry unit mass, @, which is in kg/m3 in the formulae in this Chapter. 2) Concrete strength classes higher than C50/60 should not be used unless their use is appropriately justified. No Application Rules are given for this case.
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3.1.2 Concrete strength classes This Eurocode is based on the characteristic cylinder strength, fck, measured at age 28 days in accordance with clause 3.1.2.2 of EC2. The strength fck shall be at least equal to 20 N/mm2 (MPa). 2) The design should be based on a strength class of concrete which corresponds to a specified value of fck. Table 3.1 gives for the different strength classes the characteristic strength fck and the corresponding values of the associated cube strength (e.g. the classification of concrete C 20/25 refers to cylinder/cube strengths) and, for normal-weight concrete, of the mean tensile strength fctm and characteristic tensile strengths fctk 0.05 and fctk 0.95. The columns of this Table associated with fck equal to 12 and 16 are intended only to provide information on the properties of concretes of higher class, being less than 28 days old. Table 3.1 — Concrete strength classes, characteristic compressive strength fck (cylinders) and characteristic tensile strength fct of the concrete (in N/mm2) Strength Class of Concrete
C20/25
C25/30
C30/37
C35/45
C40/50
C45/55
C50/60
fck
12
16
20
25
30
35
40
45
50
fctm
1.6
1.9
2.2
2.6
2.9
3.2
3.5
3.8
4.1
fctk 0.05
1.1
1.3
1.5
1.8
2.0
2.2
2.5
2.7
2.9
fctk 0.95
2.0
2.5
2.9
3.3
3.8
4.2
4.6
4.9
5.3
[ENV Note: Pending a rule applicable to both EC2 and EC4, on the variation in time of fc and fct, guidance may be found in existing national codes or standards.] 3) For lightweight concretes, tensile strengths can be obtained by multiplying the values obtained from the Table by the factor ) = 0.30 + 0.70 (@/2400). 3.1.3 Shrinkage of concrete 1) Where accurate control of the profile during execution is essential, or where shrinkage is expected to take exceptional values because of the composition of concrete or because of its environment (e.g. very frequently wet concrete), or when shrinkage has to be assessed at intermediate times, reference should be made to clause 3.1.2.5.5 and Appendix I of EC2. 2) In the most common cases generally and unless differently specified or justified for the particular project, the total long-term free shrinkage strain from setting of the concrete, &cs, may be given the following values as an acceptable approximation: — in dry environments (whether outside or within buildings, concrete-filled members excluded) 325
× 10–6 for normal-weight concrete
500
× 10–6 for lightweight concrete
— in other environments and in filled members 200
× 10–6 for normal-weight concrete
300
× 10–6 for lightweight concrete.
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3.1.4 Deformability of concrete — elastic theory 3.1.4.1 Secant modulus of elasticity for short-term loading 1) Nominal values of the mean secant modulus Ecm for short-term loading for normal-weight concrete of a given strength class or of characteristic compressive strength fck are given in Table 3.2. Table 3.2 — Values of the secant modulus of elasticity Ecm (in kN/mm2) Strength Class C (or fck) Ecm
(12) 26
(16) 27.5
C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 29
30.5
32
33.5
35
36
37
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2) For an age t less than 28 days, Ecm should be obtained from Table 3.2 taking into account the actual compressive strength at age t. 3) For lightweight concretes, secant moduli can be obtained by multiplying the values obtained from the Table by (@/2400)2. 3.1.4.2 Modular ratios [ENV Note: Possibly to be revised for lightweight concrete when the corresponding clause of Eurocode 2 have been drafted]. 1) The deformation of the concrete due to creep shall be taken into account. 2) If it is specified for the particular project that the rules for application given below are not accepted, the nominal values given in clauses 3.1.2.5.5 of EC2 should be adopted. 3) For the design of buildings, global analyses of sway frames excepted, it is accurate enough to take account of creep by replacing in analyses concrete areas Ac by effective equivalent steel areas equal to Ac/n, where n is the nominal modular ratio, defined by n = Ea/E½c, where Ea is the elastic modulus of structural steel, given in 3.3.3 below, and E½c is an “effective” modulus of concrete, taking in the various cases the values given below. 4) If specified for the particular project and in any case for buildings mainly intended for storage, two nominal values E½c should be used: one equal to Ecm for short term effects, the other equal to Ecm/3 for long term effects. In other cases E½c may be taken equal to Ecm/2, Ecm having the value defined in 3.1.4.1. 3.1.4.3 Poisson’s ratio If needed for design purposes, the nominal value of Poisson’s ratio for elastic strains should be assumed to be 0.2. It may be assumed to be zero when concrete in tension is assumed to be cracked. 3.1.5 Deformability of concrete — other theories 1) If a rigid-plastic theory, as defined in Chapter 4, is used, a “stress-block” starting from the neutral axis is assumed; the value of the design stress is defined in the corresponding clauses of Chapter 4 and Annex C, Annex D, and Annex E. [Note: In Sections 4.4 and 4.8 of EC4, for verifications relating to ultimate limit states a degree of plastification similar to that admitted in EC3 may be considered. This is the reason why in these cases the stress block is defined differently from EC2.] 2) If an elastic-plastic theory is used, whether for global analysis or for cross-section analysis or for both, reference should be made to clause 4.2.1.3.3 of EC2. 3.1.6 Thermal expansion The nominal value of the coefficient of linear thermal expansion !T should be taken as 10 × 10–6/°C for normal-weight concrete. [ENV Note: subject to the final version of Part 1C of EC2, the value 7 × 10–4 is suggested for lightweight concrete.]
3.2 Reinforcing steel 3.2.1 General The properties most frequently required for design calculations and summarised hereafter. If relevant, reference shall be made to Section 3.2 of EC2. [ENV Note: Section 3.2 may have to be revised after completion of EN 10080 and subsequent European standards].
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3.2.2 Types of steels
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1) The steels covered by EC4 shall be distinguished as follows: — according to surface characteristics: a) plain smooth bars or wires (including welded mesh) and b) ribbed bars or wires (including welded mesh), resulting in high bond action (as specified in EN 10080). ENV Note: clause 3.2.5.1 of EC2 characterizes high bond bars as having a rib factor, denoted fR, not less than in EN 10080, which is in preparation and whose Table 5 in clause 5.7.2 give values ranging from 0.036 (for d = 4 mm) to 0.056 (for d U 11 mm) — according to ductility characteristics: high or normal, as defined in 3.2.4.2 2) of EC2. ENV Note: clauses 3.2.1 6) and 3.2.4.2 of EC2 define &uk as the characteristic value of the elongation at maximum load, to be specified in “relevant standards”.][ — according to weldability, clauses 3.2.5.2 and 4.2.2.4.2 of EC2 are applicable. 3.2.3 Steel grades 1) A grade denotes the value of the specified characteristic yield strength fsk in N/mm2 (MPa). 2) Standardized grades are defined in EN 10080 (in preparation) or in national documents for material not covered by EN 10080. In addition to fsk, the following shall be defined: tensile strength ft, minimum ratio ft/fsk, elongation at maximum load &u, all of them as characteristic values; and also the projected rib factor fR. 3.2.4 Modulus of longitudinal deformation For the design of composite structures, the nominal value of the modus of longitudinal deformation Es may for simplicity be taken as equal to the value specified in EC3 for structural steel, i.e. 210 kN/mm2 (GPa). 3.2.5 Stress-strain diagram For design of composite structures, the stress-strain diagram may for simplicity consist of two branches: — a first branch, starting from the origin with a slope equal to Es, up to fsk (or fsk/*s according to the corresponding clauses of Chapter 4); and — a second branch which is horizontal or, for practical use of computers, is assumed to have a very small slope such as 10–4 Es and in this last case is limited to the strain .
Figure 3.1 — Design stress-strain diagram for reinforcement 3.2.6 Thermal expansion The nominal value of the coefficient of linear thermal expansion !T may for simplicity be taken as 10 × 10–4/°C.
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3.3 Structural steel 3.3.1 General and scope 1) This Part 1.1 of Eurocode 4 covers the design of composite structures fabricated from steel material conforming to Chapter 3 of EC3. No application rules are given for the use of high-strength steel to Annex D of EC3. For this steel, clause 3.2.1 2) of EC3 is applicable. 2) Section 3.2 of EC3 is applicable to composite structures. 3) The properties most frequently required for design calculations are summarized hereafter.
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
3.3.2 Yield strength 1) The nominal values of the yield strength fy and the ultimate tensile strength fu for hot rolled steel/members are given in Table 3.3 for steel grades Fe 360, Fe 430 and Fe 510, in accordance with EN 10025. Table 3.3 — Nominal values of yield strength fy and ultimate tensile strength fu for structural steel to EN 10025 Thickness t mma Nominal steel grade
t k 40 mm fy(N/mm ) 2
40 mm < t k 100 mm
fu(N/mm ) 2
fy(N/mm2)
fu(N/mm2)
Fe 360
235
360
215
340
Fe 430
275
430
255
410
Fe 510
355
510
335
490
at
is the nominal thickness of the element
2) The nominal values in Table 3.3 may be adopted as characteristic values in calculations. 3) As an alternative, the nominal values specified in EN 10025 for a larger range of thicknesses may be used. 3.3.3 Design values of other material coefficients 1) The material coefficients to be adopted in calculations for the steels covered by this Eurocode shall be taken as follows: — modulus of elasticity — shear modulus — Poisson’s ratio — unit mass
Ea = 210 000 N/mm2 Ga = E/2(1 + 5a) 5a = 0.3 @a = 7 850 kg/m3
2) For simplification in design calculations for composite structures, the value of the coefficient of linear thermal expansion !T may be taken as 10 × 10–4 per °C, which is the value given in EC2 for reinforcing steel and normal weight concrete. 3.3.4 Stress-strain relationship 1) In accordance with clause 5.2.1.4 of EC3, for design calculations the relation between stress and strain of structural steel may be idealised as elastic-perfectly plastic, as shown in Figure 3.2. 2) To avoid possible computational difficulties when using a computer the alternative bilinear stress-strain relationship indicated in Figure 3.3 may be used.
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Figure 3.2 — Bilinear stress-strain relationship
Figure 3.3 — Idealisation for computer calculations 3.3.5 Dimensions, mass and tolerances The dimensions and mass per unit length of all rolled steel sections, plates and structural hollow sections, and their dimensional and mass tolerances, shall conform with Reference Standard 2 of EC3.
3.4 Profiled steel sheeting for composite slabs 3.4.1 General and scope 1) This Part 1 of Eurocode 4 covers the design of composite slabs with profiled steel sheets manufactured from mild steel in accordance with EN 10025, high strength steel in accordance with prEN 10113, cold reduced steel sheet in accordance with ISO 4997:1978 or galvanised steel sheet in accordance with prEN 10147. [ENV Note: Reference to ISO-standards to be replaced by reference to EN-standards, if available] 2) It is recommended that the bare metal thickness should not be less than 0.75 mm except where the steel sheeting is used only as permanent shuttering. The use of thinner sheets is not precluded, provided that adequate theoretical evidence and test data are available. 3) Part 1.3 of Eurocode 3 is applicable to steel sheeting used for composite slabs. [ENV Note Reference standards should be prepared for profiled steel sheeting, including tolerances on embossments [see also 10.3.1.3 2)]. In their absence, reference should be made to European Technical Approvals or national documents. 3.4.2 Yield strength 1) The nominal values of the yield strength of the basic martial fyb are given in Table 3.4, for the steel grades given in the standards referred to in 3.4.1. 2) The nominal values of fyb in Table 3.4 may be adopted as characteristic values fyp in calculations.
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Table 3.4 — Yield strength of basic material fyb Standard
EN 10025
prEN 10113-2
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
prEN 10113-3
ISO 4997
prEN 10147
fyb
Grade
(N/mm2)
Fe 360
235
Fe 430
275
Fe 510
355
Fe E 275 N
275
Fe E 355 N
355
Fe E 460 N
460
Fe E 275 TM
275
Fe E 355 TM
355
Fe E 420 TM
420
Fe E 460 TM
460
CR 220
220
CR 250
250
CR 320
320
Fe E 220 G
220
Fe E 250 G
250
Fe E 280 G
280
Fe E 320 G
320
Fe E 350 G
350
3.4.3 Nominal values of other material coefficients The material coefficients given in 3.3.3 for hot rolled structural steel are applicable to profiled steel sheets. 3.4.4 Stress-strain relationship The idealisations of the relation between stress and strain given in 3.3.4 for hot rolled structural steel are applicable to profiled steel sheet. 3.4.5 Coating 1) The exposed surfaces of the steel sheeting shall be adequately protected to resist the particular atmospheric conditions. 2) A zinc coating of specified, should be in accordance with ISO standard, “Continuous hot-dip coated carbon steel sheet of structural quality, ISO 4998:1977”, or with relevant standards in force. 3) A zinc coating of total mass 275 g/m2 (including both sides) is normally sufficient for internal floors in a non-aggressive environment, but the specification may be varied depending on service conditions. 4) Coating other than by galvanizing should not be used unless sufficient testing has demonstrated that the sheeting satisfies the requirements of this Eurocode.
3.5 Connecting devices 3.5.1 General 1) Connecting devices shall be suitable for their specified use. 2) For connecting devices other than shear connectors, Section 3.3 of EC3 is applicable. 3.5.2 Shear connectors 1) The resistance of a connector is the maximum load in the direction considered (in most cases parallel to the interface between concrete flange and steel beam) that can be carried by the connector before failure. The resistance of a connector may be different for reversal in the direction of thrust. Due account shall be taken of this.
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2) The characteristic resistance PRk shall be the specified resistance below which not more than 5 % of results of tests on samples of a homogeneous population may be expected to fall. When a guaranteed minimum resistance is specified this may be considered as the characteristic resistance. 3) The design resistance PRd shall be the characteristic resistance divided by the appropriate partial safety factor *v. For the determination of the design resistance by testing, refer to Chapter 10. 4) The material of the connector shall be of a quality which takes into account its required, performance and the methods of fixing to the structural steelwork. Where fixing is by means of welding, the quality of material shall take account of the welding technique to be used. Where anchors or hoops act as shear connectors, special care shall be taken that the material is of an appropriate weldable quality. 5) The specified mechanical properties of the connector material shall comply with the following requirements: — the ratio of the specified ultimate tensile strength fu to the specified minimum yield strength fy is not less than 1.2; — the elongation at failure on a gauge length of 5.65ÆAo (where A, is the original cross section area) is not less than 12 %. For studs, these material properties relate to the finished product. [ENV Note: Testing of shear connector material is under consideration. Final proposals will be given after consultation with stud manufacturers.] 6) Depending on the type of shear connector, reference should be made to European Standards or European Technical Approvals or, in their absence, to national documents. 7) The head of stud connectors should have a diameter of not less than 1.5d and a depth of not less than 0.4d, Where d is the shank diameter of the stud.
4 Ultimate limit states 4.1 Basis 4.1.1 General 1) The scope of this chapter is composite beams, columns, frames and connections, except that design of shear connection in beams and in-plane shear in a concrete flange are treated in Chapter 6. Beams with concrete-encased steel webs are included. Beams with fully-encased steel sections are excluded. Composite slabs are treated in Chapter 7 and use of precast concrete slabs in Chapter 8. 2) Composite structures and members shall be so proportioned that the basic design requirements for the ultimate limit state given in Chapter 2 are satisfied. The relevant design requirements given in Chapters 2 of EC2 and EC3 shall also be satisfied. 3) For building structures, the requirements of clause 2.3.2.4 of EC3 concerning static equilibrium shall be satisfied. 4) In analyses of composite structures, members, and cross-sections, appropriate accost shall be taken of the properties of concrete and reinforcing steel as defined in EC2, and of the properties of steel as defined in EC3. Account shall be taken of loss of resistance or ductility associated with buckling of steel, and with cracking, crushing, or spalling of concrete. 5) The partial safety factors *M and *Rd are defined in 2.2.3.2. Values of *M for ultimate limit states are given in 2.3.3.2. For certain resistances where buckling of steel is relevant, *a for structural steel is replaced by *Rd. Its value for fundamental combinations is given in relevant clauses in this Chapter. For accidental combinations, *Rd = . 6) No consideration of temperature effects in verifications for ultimate limit states is normally necessary for composite structures for buildings. 7) The effects of shrinkage of concrete may be neglected in verifications for ultimate limit states for composite structures for buildings, except in global analyses with members having cross-sections in Class 4 ( 4.3 and 4.5.3.3). 8) The effects of creep of concrete on both global and local analyses may be allowed for in composite members and frames in building structures by the use of modular ratios. For slender columns, 4.8.3.6 2) is relevant.
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9) For composite members in building structures, a fatigue check is not normally required, except for: — members supporting lifting applies or rolling loads — members supporting vibrating machinery — members subject to wind-induced oscillations — members subject to crowd-induced oscillations.
Figure 4.1 — Typical cross-sections of composite beams 4.1.2 Beams 1) Composite beams are defined in 1.4.2. Typical types of cross-section are shown in Figure 4.1 and Figure 4.8. 2) No application rules are given for the contribution of concrete encasement of a steel web to resistance in bending or vertical shear. However, web encasement in accordance with 4.3.1 may be assumed to contribute to resistance to local buckling (4.3.2, 4.3.3) or lateral-torsional buckling (4.6.2). 3) Composite beams shall be checked for: — resistance of critical cross-sections (4.4) — resistance to lateral-torsional buckling (4.6) — resistance to shear buckling (4.4.4) and web crippling (4.7) — resistance to longitudinal shear (Chapter 6). 4) Critical cross-sections include: — sections of maximum bending moment — supports — sections subjected to heavy concentrated loads or reactions — places where a sudden change of cross-section occurs, (other than a change due to cracking of concrete). 5) For checking resistance to longitudinal shear, a critical length consists of a length of the interface between structural steel and concrete bounded by two critical cross sections. For this purpose critical cross sections also include: — free ends of cantilevers and — in tapering members, sections so chosen that the ratio of the greater to the lesser second moment of area for any pair of adjacent sections does not exceed two. 6) The concepts “full shear connection” and “partial shear connection” are applicable only to beams in which plastic theory is used for calculating bending resistances of critical cross sections. A span of a beam, or a cantilever, has full shear connection when increase in the number of shear connectors would not increase the design bending resistance of the member. Otherwise, the shear connection is partial. Limits to the use of partial shear connection are given in 6.1.2. 4.1.3 Composite columns, frames, and connections These subjects are treated in sections 4.8 to 4.10, respectively. Sections 4.2 to 4.7 (Beams) and 4.8 (Columns) apply both to isolated members and to members in composite frames.
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Figure 4.2 — Effective section of rib of composite slab
4.2 Properties of cross-sections of beams 4.2.1 Effective section 1) Allowance shall be made for the flexibility of a concrete flange in in-plane (shear lag) either by means of rigorous analysis, or by using an effective width of flange in accordance with 4.2.2. 2) The effective section of an effective width of composite slab with its ribs running at an angle F to the beam should be taken as the full area of the concrete above the top of the ribs plus cos2 F times the area of the concrete within the depth of the ribs (Figure 4.2). Where F > 60°, cos2 F should be taken as zero. 3) Where rigid-plastic global analysis or plastic analysis of cross sections is used, only reinforcement of high ductility, as defined in clause 3.2.4.2 of EC2, should be included in the effective section. Welded mesh should not be included unless it has been shown to have sufficient ductility, when built into a concrete slab, to ensure that it will not fracture. 4) Profiled steel sheeting should not be included in the effective section of a beam unless the ribs run parallel to the beam and the detail design ensures continuity of strength across joints in the sheeting and appropriate resistance in longitudinal shear. 5) For classification and analysis of cross-sections, a web in Class 3 may be represented by an effective web in Class 2, in accordance with 4.3.3. 6) The effective cross-section properties of structural steel compression elements in Class 4, as defined in 4.3.1, shall be based on effective widths in accordance with clause 5.3.5 of EC3.
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Figure 4.3 — Equivalent spans, for effective width of concrete flange 4.2.2 Effective width of concrete flange for beams in buildings 4.2.2.1 Effective width for global analysis 1) A constant effective width may be assumed over the whole of each span. This value may be taken as the value at midspan, for a span supported at both ends, or the value at the support, for a cantilever. 2) The total effective width beff of concrete flange associated with each steel web should be taken as the sum of effective widths be of the portion of the flange on each side of the centreline of the steel web (Figure 4.3). The effective width of each portion should be taken as be = =o/8 but not greater than b. 3) The actual width b of each portion should be taken as half the distance from the web to the adjacent web, measured at mid-depth of the concrete flange, except that at a free edge the actual width is the distance from the web to the free edge. 4) The length =o is the approximate distance between points of zero bending moment. For simply-supported beams it is equal to the span. For typical continuous beams, =o may be assumed to be as shown in Figure 4.3, in which values at supports are shown above the beam, and midspan values below the beam. 4.2.2.2 Effective width for verification of cross-sections 1) For sections in sagging bending, the appropriate midspan value given by 4.2.2.1 should be used. 2) For sections in hogging bending, the value at the relevant support given by 4.2.2.1 should be used. 4.2.3 Flexural stiffness 1) The elastic section properties of a composite cross-section should be expressed as those of an equivalent steel cross-section by dividing the contribution of the concrete component by a modular ratio n, as given in 3.1.4.2. 2) The uncracked and cracked flexural stiffnesses of a composite cross section are defined as EaI1 and EaI2, respectively, where: Ea I1 I2
is the modulus of elasticity for structural steel, is the second moment of area of the effective equivalent steel section calculated assuming that concrete in tension is uncracked, and is the second moment of area of the effective equivalent steel section calculated neglecting concrete in tension but including reinforcement.
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4.3 Classification of cross-sections of beams
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4.3.1 General 1) The classification system defined in clauses 5.3.2 1) to 6) of EC3 applies to cross-sections of composite beams. The definitions of the four classes are as follows: — Class 1 cross sections are those which can form a plastic hinge with the rotation capacity required for plastic analysis. — Class 2 cross-sections are those which can develop their plastic moment resistance, but have limited rotation capacity. — Class 3 cross-sections are those in which the 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 cross-sections are those in which it is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance. 2) A cross-section is classified according to the least favourable class of its steel elements in compression. The class of a composite section normally depends on the sign of the bending moment at that section. 3) The performance of a steel compression element in Class 2, 3, or 4 can be improved by attaching it to a reinforced concrete element. The restrained steel element may be placed in a higher class, provided that the relevant improvement has been established. 4) Where relevant application rules are given, a steel compression element may be represented by an effective element in a higher class. 5) Positions of plastic neutral axes of composite sections shall be calculated using design values of strengths of materials. 6) For a web to be treated as “encased” in Table 4.1, the concrete that encases it shall be reinforced, mechanically connected to the steel section, and capable of preventing buckling of the web and of any part of the compression flange towards the web. 7) The concrete that encases a web should extend over the full width of both steel flanges. It should be reinforced by longitudinal bars and stirrups, and/or welded mesh. 8) The concrete between the flanges may be fixed to the web by welding the stirrups to the web or by means of bars (: U 6 mm) through holes and/or studs with a diameter greater than 10 mm welded to the web. 9) The longitudinal spacing of the studs on each side of the web or of the bars through holes should not exceed 400 mm. The distance between the inner face of each flange and the nearest row of fixings to the web should not exceed 200 mm. For steel profiles with a maximum depth of more than 400 mm and two or more rows of fixings, a staggered arrangement of the studs and/or bars through holes may be used; 10) For fire design, reference should be made to EC4-1.2. 4.3.2 Classification of steel flanges in compression 1) A steel compression flange that is restrained from buckling by effective attachment to a concrete flange by shear connectors in accordance with 6.4.1.5 may be assumed to be in Class 1. 2) The classification of other steel flanges in compression in composite beams shall be in accordance with Table 4.1, for outstand flanges, and Table 5.3.1 (sheet 2) of EC3, for internal flange elements.
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Figure 4.4 — Use of an effective web in Class 2 for a section in hogging bending with a web in Class 3 4.3.3 Classification of steel webs 4.3.3.1 Sections where the compression flange is in Class 1 or 2 1) The class of the web shall be determined from Table 4.2. The plastic stress distribution for the effective composite section shall be used; except at the boundary between Classes 3 and 4, where the elastic stress distribution shall be used, as in 4.3.3.2. 2) A web in Class 3 that is encased in concrete in accordance with 4.3.1 6) to 9) may be represented by an effective web of the same cross-section in Class 2. 3) An uncased web in Class 3 may be represented by an effective web in Class 2, by assuming that the depth of web that resists compression is limited to 20t& adjacent to the compression flange, and 20t& adjacent to the new plastic neutral axis, as shown in Figure 4.4 for hogging bending. [Note. The method of paragraph 3) is intended to reduce discontinuities in design methods. Otherwise, the classification of webs is over-sensitive to small changes in the area of longitudinal reinforcements or in the effective width of the slab. The value 20t& a conservative approximation, which gives a small discontinuity at the Class 2-3 boundary]. Table 4.1 — Maximum width-to-thickness ratios for steel outstand flanges in compression
Rolled Class
Welded
Type
Encased web
Web not encased
Web encased
Stress distribution (compression positive) 1 2 3
Rolled Welded Rolled Welded Rolled Welded fy (M/mm2) &
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c/t u 10& c/t u 9& c/t u 11& c/t u 10& c/t u 15& c/t u 14&
235 1.0
275 0.92
c/t u 10& c/t u 9& c/t u 15& c/t u 14& c/t u 21& c/t u 20&
355 0.81 37
ENV 1994-1-1:1992
Table 4.2 — Maximum width-to-thickness ratios for steel webs Webs: (Internal elements perpendicular to axis of bending)
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Class
Web subject to bending
Web subject to compression
Web subject to bending and compression
Stress distribution (compression positive) when ! > 0.5: 1
d/t k 72&
d/t k 33&
d/t k 396&/(13! – 1)
when ! < 0.5:
d/t k 36&/! when ! > 0.5: 2
d/t k 83&
d/t k 38&
d/t k 456&/(13! – 1)
when ! < 0.5:
d/t k 41,5&/!
Stress distribution (compression positive) 3
d/t k 124&
d/t k 42&
when ? > – 1: d/t k 42&/(0.67 + 0.33?) when ? k – 1:
38
fy
235
275
355
&
1
0.92
0.81
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4.3.3.2 Sections where the compression flange is in Class 3 or 4 1) The class of the web shall be determined from Table 4.2, using the elastic neutral axis. 2) In beams for buildings, the position of the elastic neutral axis should be determined for the effective concrete flange, neglecting concrete in tension, and the gross cross-section of the steel web. The modular ratio for concrete in compression should be as used in the global analysis for long-term effects. 3) [Note. For a cross-section in hogging bending, and where unpropped construction is used, the depth of web in compression in the completed beam depends on the load case, and may be slightly less than that given by this simplified method. In buildings it is essential (for simplicity) that classification of sections is independent of the arrangement of variable loads on the spans of a continuous beam.]
4.4 Resistances of cross-sections of beams 4.4.1 Bending moment
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4.4.1.1 Basis 1) Section 4.4 is applicable to composite sections where the structural steel component has an axis of symmetry in the plane of the web, and to bending in this plane. 2) The design bending resistance may be determined by plastic theory only where the effective composite section is in Class 1 or Class 2. 3) Elastic analysis may be applied to cross-sections of any class. 4) The following assumptions shall be made: — the tensile strength of concrete is neglected; — plane cross-sections of the structural steel and reinforced concrete parts of a composite member each remain plane. 5) No account need be taken of the effects of longitudinal slip in composite members with full shear connection. Plane cross-sections of these members should be assumed to remain plane. 6) Fastener holes in steel elements shall be considered, following clause 5.4.5.3 of EC3. 7) Small holes in steel through which reinforcing bars pass should be treated as holes for fasteners. 4.4.1.2 Plastic resistance moment of a section with full shear connection 1) Full shear connection is defined in 4.1.2 6). 2) The following assumptions shall be made in the calculation of Mp=.Rd: a) there is full interaction between structural steel, reinforcement, and concrete; b) effective area of the structural steel member is stressed to its design yield strength fy/*a in tension or compression; c) the effective areas of longitudinal reinforcement in tension and in compression are stressed to their design yield strengths fsk/*s in tension or compression. Alternatively, reinforcement in compression in a concrete slab may be neglected. d) profiled steel sheeting in compression shall be neglected. 3) Any profiled steel sheeting in tension included within the effective area, following 4.2.1 4), should be assumed to be stressed to its design yield strength fy/*ap. 4) It shall be assumed that the effective area of concrete in compression resists a stress of 0.85 fck/*c, constant over the whole depth between the plastic neutral axis and the most compressed fibre of the concrete. 5) Typical plastic stress distributions are shown in Figure 4.5.
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4.4.1.3 Plastic resistance moment of a section with partial shear connection
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1) Partial shear connection in accordance with 6.2.1 may be used in composite beams for buildings for the compressive force in the concrete slab.
(a) sagging bending (b) hogging bending Figure 4.5 — Plastic stress distributions for a composite beam with profiled steel sheeting and full shear connection, where the plastic neutral axis is within the steel section 2) The plastic moment of resistance of the beam should be calculated in accordance with 4.4.1.2, except that a reduced value of the compressive force in the concrete, Fc, determined from 6.2.1, should be used in place of the force given by 4.4.1.2 4). The location of the plastic neutral axis in the slab is determined by the new force Fc. There is a second plastic neutral axis within the steel section, which should be used for the classification of the web. 4.4.1.4 Elastic resistance to bending 1) Stresses shall be calculated by elastic theory, using an effective cross section in accordance with 4.2.1 and 4.2.2.2. 2) Account shall be taken of creep of concrete in compression, in accordance with 3.1.4.2. 3) In the calculation of Me=.Rd, the limiting bending stresses shall be taken as: — 0.85 fck/*c in concrete in compression; — fy/*a in structural steel in tension, or in compression in a cross-section in Class 1, 2, or 3; — fy/*Rd in structural steel in compression in an effective cross-section in Class 4, where *Rd = ; — fsk/*s in reinforcement in tension or compression. Alternatively, reinforcement in compression in a concrete slab may be neglected. 4) Where unpropped construction is used, stresses due to actions on the structural steelwork alone shall be added to stresses due to actions on the composite member. 5) Where unpropped construction is used, the elastic resistance to bending, Me=.Rd, for a particular cross-section and a loading that causes bending moments Ma in the steel member and Mc in the composite member, shall be calculated as follows. Let r be the highest of the ratios of total bending stress [4), above] to limiting stress [3), above]. Then, Me=.Rd = (Ma + Mc)/r. 4.4.2 Vertical shear 4.4.2.1 Scope Clauses 4.4.2 to 4.4.5 apply to composite beams with a rolled or welded structural steel section with a solid web, without longitudinal stiffeners. The web may have transverse stiffeners. In welded sections, the steel flanges are assumed to be plates of rectangular cross-section.
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4.4.2.2 Deign methods 1) The resistance to vertical shear shall be taken as the resistance of the structural steel section in accordance with clause 5.4.6 of EC3, unless the value of a contribution from the reinforced concrete part of the beam has been established. 2) The shear force resisted by the structural steel section shall satisfy: VSd k Vp=.Rd where Vp=.Rd is the design plastic shear resistance given by:
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where
Av is the shear area of the structural steel member, given in clause 5.4.6 of EC3.
3) In addition, the shear buckling resistance of a steel web shall be verified as specified in 4.4.4 where: — for an unstiffened and uncased web, d/tw > 69&; — for an unstiffened web encased in accordance with 4.3.1, d/tw > 124&; — for a stiffened and uncased web,
— for a stiffened and encased web, d/tw exceeds both of the two preceding limits; where
d
is the depth of the web as defined in Figure 1.1 of EC3 for rolled sections and Figure 5.6.1 of EC3 for welded sections,
tw
is the thickness of the web,
kE
is the buckling factor for shear given in clause 5.6.3 of EC3,
& = Æ (235/fy), with fy in N/mm2 units. 4.4.3 Bending and vertical shear 1) Where the vertical shear VSd exceeds half the plastic shear resistance Vp=.Rd given by 4.4.2, allowance shall be made for its effect on the resistance moment. 2) Except where 4.4.2.2 3) is applicable, the following interaction criterion should be satisfied: MSd k Mf.Rd + (MRd – Mf.Rd)[1 – (2VSd/Vp=.Rd – 1)2] where MSd and VSd are the design values, Vp=.Rd
is given by 4.4.2.2 2),
MRd is the design bending resistance given by 4.4.1, Mf.Rd is the design plastic bending resistance of a cross section consisting of the flanges only, with effective sections as used in the calculation of MRd. 3) The interaction is illustrated in Figure 4.6.
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Figure 4.6 — Resistance in bending and vertical shear in absence of shear buckling 4.4.4 Shear buckling resistance 1) The Principles of paragraphs 5.6.1 2) and 3) of EC3 are applicable. 2) For composite beams, steel webs that shall be verified for shear buckling resistance are defined in 4.4.2.2 3). 3) Webs shall be provided with transverse stiffeners at supports where: — for uncased webs, d/tw > 69& — for webs encased in accordance with 4.3.2, d/tw > 124&, The symbols are as defined in 4.4.2.2 3). 4) No contribution from web encasement to the shear resistance of a web with d/tw > 124& shall be assumed, unless verified by testing. 5) No account shall be taken of a contribution from the concrete slab to the anchorage of a web tension field in a flange, unless the shear connection is designed for the relevant vertical force. 6) For unstiffened webs and for webs with transverse stiffeners only, the methods given in clauses 5.6.2 to 5.6.6 of EC3 are applicable, with *M1 for structural steel taken as the value given in clause 5.1.1 of EC3. References to flanges in these clauses are to structural steel flanges only. 7) For simply-supported beams without intermediate stiffeners, with full shear connection, and subjected to uniformly-distributed loading, the method of clause 5.6.3 of EC3 as modified by paragraphs a) to d) below may alternatively be used. a) The simple post-critical shear strength Eba should be determined as follows: — for — for — for where fyw Æw
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is the nominal yield strength of the steel web and is the web slenderness (not exceeding 4.0) defined in clause 5.6.3 of EC3.
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b) The number N of shear connectors in each half span should be sufficient to provide full shear connection as defined in 4.1.2 6). Where VSd > Vcr, the N connectors should not be distributed in accordance with 6.1.3, but as shown in Figure 4.7,
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where
Vcr = dtwEcr, Ùcr is as defined in clause 5.6.3 of EC3, d and tw are defined in 4.4.2.2 3), N2 = N(1 – Vcr/VSd)2, N1 = N – N2, and beff is the effective flange width, defined in 4.2.2.1.
c) The steel end post should be designed for a uniform axial compressive force equal to the maximum design shear force VSd for the cross-section, considering stability both in and out of the plane of the web. d) The welds connecting the web to the end post and to a length 1.5 beff of the steel top flange should be designed for a shear force (fyw/ 3 ) tw per unit length of web.
Figure 4.7 — Distribution of shear connectors 4.4.5 Interaction between bending and shear buckling Clause 5.6.7 of EC3 is applicable, with the following modifications, to composite beams in which the design axial force Nsd = 0. a) The word “flange” refers to both steel and composite flanges. b) Where the method of 4.4.4 7) is applicable, Vba.Rd may be taken as the design shear buckling resistance given by that method. c) The symbol Mp=.Rd in clauses 5.6.7.2 3) and 5.6.7.3 5) of EC3 should be replaced by MRd, which is the design bending resistance of the composite section given by 4.4.1. d) Where the tension field method is used, clause 5.6.7.3 3) of EC3 may, be assumed to be applicable to a composite section in which the steel member has equal flanges.
4.5 Internal forces and moments in continuous beams 4.5.1 General 1) Section 4.5 is applicable to continuous beams as defined in 1.4.2. Where bending moment is applied to a beam through a connection to a supporting column, the global analysis should be in accordance with 4.9. 2) Plastic global analysis may be used for continuous beams in buildings where the requirements of 4.5.2 are satisfied. 3) Elastic global analysis may be used for all continuous beams. For beams in buildings, bending moments found by elastic analysis may be redistributed in accordance with 4.5.3.4. 4) The effects of slip and uplift may be neglected at interfaces between steel and concrete at which shear connection is provided in accordance with Chapter 6.
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4.5.2 Plastic analysis 4.5.2.1 General 1) Plastic global analysis may be carried out using either rigid-plastic or elastic-plastic methods. 2) The following methods of elastic-plastic analysis may be used: — elastic/perfectly-plastic — elasto-plastic. 3) Elastic-plastic methods of analysis shall satisfy the principles of 4.1.1. Elasto-plastic methods of analysis shall take account of the load/slip behaviour of the shear connection. No application rules are given for these methods.
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4.5.2.2 Requirements for rigid-plastic analysis 1) At each plastic hinge location: a) the cross-section of the structural steel component shall be symmetrical about the plane of its web; b) the rotation capacity shall be sufficient to enable the required hinge rotation to develop; c) the proportions and restraints of steel components shall be such that lateral-torsional buckling does not occur; d) lateral restraint shall be provided. 2) For composite beams in buildings, requirements b) and d) may be assumed to be satisfied when: a) all effective cross sections at plastic hinge locations are in Class 1; and all other effective cross sections are in Class 1 or Class 2, excluding effective webs to 4.3.3.1 3); b) adjacent spans do not differ in length by more than 50 % of the shorter span; c) end spans do not exceed 115 % of the length of the adjacent span; d) in any span in which more than half of the total design load is concentrated within a length of one-fifth of the span, then at any hinge location where the concrete slab is in compression, not more than 15 % of the overall depth of the member should be in compression; e) the steel compression flange at a plastic hinge location is laterally restrained. Condition d) does not apply where it can be shown that the hinge will be the last to form in that span. 4.5.3 Elastic analysis 4.5.3.1 General 1) Elastic global analysis shall be based on the assumption that the stress-strain relationships for the materials are linear, whatever the stress level. The tensile strength of concrete may be neglected. 2) For beams in buildings, flexural stiffnesses may be taken as the “uncracked” values EaI1 throughout the length of a beam. Alternatively, flexural stiffnesses may be taken as the “cracked” values EaI2 over 15 % of the span on each side of each internal support, and as the values EaI1 elsewhere. These methods are defined as “uncracked” and “cracked” elastic analysis, respectively. The stiffnesses EaI1 and EaI2 are defined in 4.2.3 2). 4.5.3.2 Sequence of construction Where unpropped construction is used for structures with composite beams that have cross-sections in Class 3 or Class 4, appropriate global analyses shall be made for the separate effects of permanent actions applied to the steel member and actions applied to the composite member. 4.5.3.3 Effects of shrinkage of concrete in beams for buildings Account shall be taken at cross-sections in Class 4 of the bering moments due to restraint from supports of the deformations caused by shrinkage of the concrete slab.
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4.5.3.4 Redistribution of moments in beams for buildings 1) The design bending moment distribution given by an elastic analysis may be redistributed in a way that satisfies equilibrium, and takes account of the effects of cracking of concrete, inelastic behaviour of materials, and local buckling of structural steelwork. 2) a) The elastic bending moments for a continuous composite beam of uniform depth within each span may be modified: — by reducing maximum hogging moments by amounts not exceeding the percentages given in Table 4.3; or — in beams with all cross-sections in Classes 1 or 2 only, by increasing maximum hogging moments by amounts not exceeding 10 %, for “uncracked” elastic analysis, or 20 %, for “cracked” elastic analysis b) For each load case, the internal forces and moments after redistribution should be in equilibrium with the loads. c) For composite cross sections in Class 3 or 4, the figures in Table 4.3 relate to bending moments assume in design to be applied to the composite meaner. Moments applied to the steel member should not be redistributed. Table 4.3 — Limits to redistribution of hogging moments, per cent of the initial value of the bending moment to be reduced Class of cross section in hogging moment region
1
2
3
4
For “uncracked” elastic analysis
40
30
20
10
For “cracked” elastic analysis
25
15
10
0
4.6 Lateral-torsional buckling of composite beams for buildings 4.6.1 General 1) A steel flange that is attached to a concrete or composite slab by shear connection in accordance with Chapter 6 may be assumed to be laterally stable, provided that the overall width of the slab is not less than the depth of the steel member. 2) All other steel flanges in compression shall be checked for lateral stability. 3) In checks for lateral stability of beams built unpropped, the bending moment at any cross section shall be taken as the sum of the moment applied to the composite member and the moment applied to its structural steel component. 4.6.2 Check without direct calculation A continuous beam or a beam in a frame that is composite throughout its length may be designed without additional lateral bracing when the following conditions are satisfied. a) Adjacent spans do not differ in length by more than 20 % of the shorter span. Where there is a cantilever, its length does not exceed 15 % of that of the adjacent span. b) The loading on each span is uniformly distributed, and the design permanent load exceeds 40 % of the total design load. c) The top flange of the steel member is attached to a reinforced concrete or composite slab by shear connectors in accordance with Chapter 6. d) The longitudinal spacing of studs or rows of studs, s, is such that for uncased beams s/b k 0.02 d2 h/tw3 where
d is the diameter of the studs, and b, h, and tw are as shown in Figure 4.8.
For steel members partly encased in concrete in accordance with 4.3.2, the spacing should not exceed 50 % of the maximum spacing for the uncased beam. e) The longitudinal spacing of connectors other than studs is such that the resistance of the connection to transverse bending is not less than that required when studs are used.
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Figure 4.8 — Lateral-torsional buckling f) The same slab is also attached to another supporting member approximately parallel to the composite beam considered, to form an inverted-U frame of breadth a (Figure 4.8). g) If the slab is composite, it spans between the two supporting members of the inverted-U frame considered. h) Where the slab is simply-supported at the composite beam considered, fully anchored top reinforcement extends over the length AB shown in Figure 4.8. The area of this reinforcement should be such that the resistance of the slab to hogging transverse bending, per unit length of beam, is not less than fytw3/4*a, where the notation is as in d) above. i) At each support of the steel member, its bottom flange is laterally restrained and its web is stiffened. Elsewhere, the web is unstiffened. j) The bending stiffness of the solid or composite slab is such that Ecm Ic2 U 0.35 Eatw2 a/h. where EcmIc2 is the mean of the flexural stiffnesses per unit width of slab at midspan and above the steel beam considered, neglecting concrete in tension, and including transformed areas of reinforcement and any profiled sheeting that contributes to the resistance Mc.Rd in accordance with 7.6.1.2; Ecm is as defined in 3.1.4.1; Ea is as defined in 3.3.3; and tw, a, and h are as shown in Figure 4.8. k) The steel member is an IPE section to Euronorm 19–57 or an HE section to Euronorm 53–62 or another hot-rolled section of similar shape with Aw/Aa k 0.45, the same depth h, and
where Aw = hstw, as in Table 4.1 and Table 4.2, Aa is the area of the structural steel section, and hs, tw, tf and b are as shown in Figure 4.8. l) If the steel member is not partly encased, its depth h is in accordance with Table 4.4. m) If the steel member is partly encased in concrete in accordance with 4.3.1, its depth h does not exceed the limit given in Table 4.4 by more than 200 mm.
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Table 4.4 — Maximum depth h (mm) of uncased steel member for which clause 4.6.2 is applicable Nominal steel grade
Steel member
IPE or similar HE or similar
Fe 360
Fe 430
Fe 510
k 600
k 550
k 400
k 800
k 700
k 650
4.6.3 Buckling resistance moment 1) The design buckling resistance moment of a laterally unrestrained beam shall be taken as Mb.Rd = #LTMp=.Rd(*a/*Rd)
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for a Class 1 or Class 2 cross-section, with *Rd = Mb.Rd = #LTMe=.Rd(*a/*Rd) for a Class 3 cross-section, with *Rd = Mb.Rd = #LTMe=.Rd
,
and
for a Class 4 cross-section, where #LT Mp=.Rd
is the reduction factor for lateral-torsional buckling, is the plastic resistance moment given by 4.4.1.2 or 4.4.1.3,
Mc=.Rd
is the elastic resistance to bending given by 4.4.1.4.
2) Values of #LT for the appropriate slenderness ÆLT may be obtained from Table 5.5.2 in EC3, with Æ = Æ LT and # = #LT, using: column a for rolled sections column c for welded beams. or may be determined from but ·LT k 1. where
and
!LT = 0.21 for rolled sections !LT = 0.49 for welded beams.
3) The value of Æ LT may be determined from for a Class 1 or Class 2 cross-section. for a Class 3 or Class 4 cross-section. where Mp=
is the value of Mp=.Rd when the *M factors *a, *c, and *s are taken as 1.0.
Mp=
is the value of Me=.Rd when the *M factors *a, *c, and *s are taken as 1.0.
Mcr
is the elastic critical moment for lateral-torsional buckling.
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4) A simplified method for the calculation of Æ LT and information for the calculation of Mcr are given in Annex B, based on the continuous U-frame model. Where a beam does not comply with the conditions of Annex B, the value of Mcr shall be determined from specialist literature, or by numerical analysis, or (conservatively) by determining Mcr from Annex F of EC3, for the steel member alone. 5) When the slenderness Æ LT k 0.4, no allowance for lateral-torsional buckling is necessary.
4.7 Web crippling 4.7.1 General 1) The principles of Section 5.7 of EC3 are applicable to non-composite steel flanges of composite beams, and to the adjacent part of the web. 2) The application rules of section 5.7 of EC3 are applicable to non-composite steel flanges of composite beams, and to the adjacent part of the web.
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4.7.2 Effective web in Class 2 At an internal support of a beam designed using an effective web in Class 2 [in accordance with 4.3.3.1 3)], transverse stiffening should be provided unless it can be shown that the unstiffened web has sufficient resistance to web crippling.
4.8 Composite columns 4.8.1 Scope 1) Composite columns are defined in 1.4.2. The steel section and the uncracked concrete section usually have the same centroid. Typical types of cross-section are shown in Figure 4.9: — concrete encased sections (steel section completely covered by concrete — Figure 4.9a), — concrete filled sections (concrete completely covered by steel — Figure 4.9d)–Figure 4.9f), — partially encased sections (steel section partially covered by concrete — Figure 4.9b) and Figure 4.9c).
Figure 4.9 — Typical cross sections of composite columns, with notation 48
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2) This clause 4.8 applies to isolated non-sway columns. These may be: — compression members which are integral parts of a non-sway frame but which are considered to be isolated for design purposes, or — isolated compression members that satisfy the classification “non-sway” as given in clause 4.3.5.3.3 of EC2 or clause 5.2.5.2 of EC3, as appropriate. Isolated columns are illustrated in Figure 4.26 of EC2. 3) Two methods of design are given: — a general method in 4.8.2 including columns with non-symmetrical or non-uniform cross section over the column length, — a simplified method in 4.8.3 for columns of double symmetrical and uniform cross section over the column length using the European Strut Curves of EC3. Application rules for columns of mono-symmetrical section are given in Annex D. 4.8.2 General methods of design 4.8.2.1 General A composite column of any cross-section, loaded by normal forces and bending moments, shall be checked for: — resistance of member (4.8.2.2 to 4.8.2.3) — resistance to local buckling (4.8.2.4) — introduction of loadings (4.8.2.6) — resistance to shear (4.8.2.7 to 4.8.2.8). 4.8.2.2 Design procedures 1) Design for structural stability shall take account of second order effects including imperfections and shall ensure that, for the most unfavourable combinations of actions at the ultimate limit state, instability does not occur, and that the resistance of individual cross-sections subjected to bending and longitudinal force is not exceeded. 2) The partial safety factors *M are as given in 2.3.3.2 1) and 4.1.1 5), except that *c for concrete may be reduced where 12) below applies. 3) Second order effects shall be considered in any direction in which failure may occur, if they affect the structural stability significantly. 4) In accordance with clause 4.3.5.1 5) of EC2, the influence of second order effects should be considered if the increase above the first order bending moments, due to deflections within the column length, exceeds 10 %. In this check, creep effects should be treated according to 9) and 10). (Note. This check should be made by second-order elastic analysis of the column length, with its ends assumed to be pinned and subjected to the internal forces and moments determined by the global analysis, and with transverse loading, if any.) 5) Plane sections shall be assumed to remain plane. Full composite action up to failure shall be assumed between the steel and concrete components of the member. 6) The following stress-strain relationships should be used in the (non-linear) analysis: — for concrete as given in 3.1.5, — for reinforcing steel as given in 3.2.5, and — for structural steel as given in 3.3.4. 7) Where second-order deformations are being calculated, the stress-strain diagram for concrete given in clause 4.2.1.3.3 of EC2 should be used with fcd and Ecd taken as fcd = fck/*c Ecd = Ecm/*c For the safety factor *c, clauses A.3.1 3) and A.3.1 6) of EC2 apply. (Note. This paragraph does not apply to calculation of resistances of cross-sections.) 8) Shrinkage and creep effects shall be considered if they are likely to reduce the structural stability significantly.
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9) For simplification, creep effects may be ignored if the increase in the first order bending moments due to creep deformations and longitudinal force resulting from permanent load does not exceed 10 %. 10) According to clause A.3.4 9) of EC2, creep deformations of slender compression members in non-sway frames for buildings with monolithic connections to slabs or beams at their two ends may normally be disregarded. 11) The contribution of the tensile strength of the concrete between cracks (tension stiffening) may be taken into account. 12) Partial safety factors for materials within precast concrete elements shall be in accordance with the appropriate Parts of Eurocode 2.
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4.8.2.3 Imperfections 1) Imperfections within the column length shall be taken into account for the calculation of the internal forces and moments. 2) The equivalent initial bow imperfections should be related to the following buckling curves given in clause 5.5.1 of EC3: — for concrete — filled hollow sections, the appropriate curve from clause 5.5.1 of EC3. — curve b for fully or partly concrete-encased I-sections with bending about the strong axis of the steel section. — curve c for fully or partly concrete-encased I-sections with bending about the weak axis of the steel section — curve d for other concrete-encased steel sections. 4.8.2.4 Local buckling of steel members 1) The influence of local buckling of steel members on the resistance of the column shall be considered in design. 2) The effects of local buckling of steel members in composite columns may be neglected for steel sections fully encased to 4.8.2.5 and for other types of composite columns, provided that: — for circular hollow steel sections, d/t k 90&2 — for rectangular hollow steel sections, h/t k 52& — for partly-encased I-sections, b/tf k 44& where, as shown in Figure 4.9 d is the external diameter of a circular hollow steel section, h is the greater overall dimension of the section parallel to a principal axis, t is the thickness of the wall of a concrete-filled hollow section, tf and b are the thickness and overall breadth of the flange of a steel I-section or a similar section, and fy is the yield strength of the steel in N/mm2 units. 3) If the values in 2) are exceeded, the effect of local buckling should be taken into account by an appropriate experimentally confirmed method. 4.8.2.5 Cover and reinforcement 1) For fully-encased steel sections at least a minimum reinforced concrete cover shall be provided to ensure: — the safe transmission of bond forces — the protection of the steel against corrosion — that spalling will not occur — an adequate fire resistance, in accordance with EC4-1.2. 2) The concrete cover to a flange of a fully-encased steel section should be not less than 40 mm, nor less than one-sixth of the breadth b of the flange. The cover to reinforcement should be in accordance with clause 4.1.3.3 of EC2. 3) The longitudinal reinforcement in concrete-encased columns which is allowed for in the resistance of the cross-section should be not less than 0.3 % of the cross-section of the concrete. 50
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4) The transverse reinforcement in concrete-encased columns should be designed according to clause 5.4.1.2.2 of EC2. 5) For the spacing of the reinforcement clause 5.2 of EC2 applies. 6) The clear distance between longitudinal reinforcing bars and the structural steel section may be smaller than required by 5), even zero. In this case, for bond the effective perimeter, c, of the reinforcing bar should be taken as half or one quarter of its perimeter as shown in Figure 4.10 at (a) and (b) respectively.
Figure 4.10 — Effective perimeter c of a reinforcing bar 7) Welded mesh reinforcement may be used as links in concrete-encased columns, but should not contribute to or supply the longitudinal reinforcement. 8) In concrete-filled hollow sections normally no longitudinal reinforcement is necessary. 4.8.2.6 Shear between the steel and concrete components 1) Provision shall be made for internal forces and moments applied from members connected to the ends of a column length to be distributed between the steel and concrete components of the column, considering the shear resistance at the interface between steel and concrete according to 4.8.2.7. 2) A clearly defined load path shall be provided that does not involve an amount of slip at this interface, that would invalidate the assumptions made in design. 3) The introduction length for the shear force should not be assumed to exceed twice the relevant traverse dimension. 4) In an I-section with concrete only between the flanges the concrete should be gripped by stirrups and a clearly defined load transmission path between concrete and steel web should be identified (i.e., stirrups should pass through the web or be welded to the web, or should interlock with shear connectors.) 5) Where composite columns are subjected to significant transverse shear as for example by local horizontal loads, provision shall be made for the transfer of the corresponding longitudinal shear stress at the interface between steel and concrete. 6) In absence of a more accurate method, elastic analysis of the uncracked composite section, considering the sequence of construction, should be used to estimate longitudinal shear stress due to transverse shear between the steel and concrete. 7) Calculated resultant shear stresses at the interface between steel and concrete should nowhere be excessive according to 4.8.2.7.
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4.8.2.7 Resistance to shear 1) The shear resistance shall be provided by bond stresses and friction at the interface or by mechanical shear connection, such that no significant slip occurs. 2) The design shear strength due to bond and friction should be taken as: — — — —
for completely concrete encased sections for concrete filled hollow sections for flanges in partially encased sections for webs in partially encased sections
0.6 N/mm2 0.4 N/mm2 0.2 N/mm2 zero.
3) Alternatively it may be shown by tests that full interaction can be relied upon until failure of the member.
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4.8.2.8 Stud connectors attached to the web of a composite column 1) Where stud connectors are attached to the web of a concrete-encased steel I-section (Figure 4.11) or a similar section, the lateral expansion of the concrete against which they bear is prevented by the adjacent steel flanges. The resulting frictional forces provide resistance in longitudinal shear additional to that given by 6.3.2. 2) This additional resistance may be assumed to be 4PRd/2 on each flange, for each row of studs, as shown in Figure 4.11, where PRd is the design resistance of one stud, defined in 6.3.2, and 4 is the relevant coefficient of friction given in 6.5.2. 3) In absence of better information from tests these values should only be allowed when the clear distance between the flanges as shown in Figure 4.11 does not exceed — 300 mm using one stud per row — 400 mm using two studs per row — 600 mm using three or more studs.
Figure 4.11 — Stud connectors in composite column 4.8.3 Simplified method of design 4.8.3.1 Scope 1) The method given in 4.8.3, if applied, should be used as a whole in accordance with 4.8.1 2). If individual clauses are used as part of another method, the applicability needs to be checked. 2) As this method takes account of imperfections within the column length, allowance need not again be made for these, but all other provisions of 4.8.2 apply when the method of 4.8.3 is used, except 4.8.2.2 4) and 4.8.2.2 9).
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3) The scope of this simplified method is limited as follows: a) The column is of double-symmetrical and uniform cross section over the column length. (Note. The centres of area of the steel section and the uncracked concrete section therefore coincide. This point is defined as the centroid of the section even when the bending moment is sufficient to cause cracking of concrete. Certain mono-symmetric sections are treated in Annex D.) b) The steel contribution ratio $ as defined in 4.8.3.4 should lie between 0.2 and 0.9. The steel members may be rolled or welded.
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c) The non-dimensional slenderness Æ defined in 4.8.3.7 should not exceed 2.0. d) For fully-encased steel sections, limits to the thickness of concrete cover that may be used in the calculations are: — in the y-direction, 40 mm k cy k 0.4b, — in the z-direction, 40 mm k cz k 0.3h, where the notation is as shown in Figure 4.9. Greater cover can be used but should be ignored in calculation. e) The cross-sectional area of longitudinal reinforcement that may be used in the calculations should not exceed 4 % of the area of the concrete. f) If the longitudinal reinforcement is neglected in calculations for the resistance of the column, and if the ambient exposure is according to EC2 Table 4.1 line 1 for buildings, the following reinforcement may be assumed to be adequate: — longitudinal bars of minimum diameter 8 mm at a maximum spacing of 250 mm, — links with minimum diameter of 6 mm and a maximum spacing of 200 mm, — for welded mesh reinforcement the minimum diameters may be reduced to 4 mm. 4) Typical cross sections and relevant notation are shown in Figure 4.9. 5) Note. It may be found convenient to verify the design of a composite column in the following sequence. a) Check the limitations of scope given in 4.8.3.1 3). b) Check for local buckling (4.8.2.4). c) Check cover and reinforcement (4.8.2.5). d) Calculate Ncr and Æ (4.8.3.7) and determine *Ma from 4.8.3.2. e) Decide whether second-order analysis for bending moments is required by 4.8.3.10. f) Verify the resistance of the column following 4.8.3.3, 4.8.3.8, 4.8.3.9, and 4.8.3.11 to 4.8.3.14. g) Verify the load introduction and longitudinal shear according to 4.8.2.6 to 4.8.2.8. 4.8.3.2 Partial safety factors *Ma, *a, and *Rd 1) In clause 4.8.3 the partial safety factor *M for structural steel is written as *Ma. In accordance with 4.1.1 5) it has one of two values, as follows. a) For a column length with Æ k 0.2 or NSd/Ncr k 0.1, *Ma = *a = where Nsd
, is the design axial load, and
Æ and Ncr
are in accordance with 4.8.3.7.
b) Otherwise, *Ma = *Rd =
,
2) Exceptions to 1) above are given in particular clauses.
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4.8.3.3 Resistance of cross sections to axial loads 1) The plastic resistance to compression Npl.Rd of a composite cross-section should be calculated by adding the plastic resistances of its components: Npl.Rd = Aafy/*Ma + Ac(0.85fck/*c) + Asfsk/*s, where Aa, Ac and As are the cross-sectional areas of the structural steel, the concrete, and the reinforcement, respectively,
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fy, fck and fsk are their characteristic strengths in accordance with EC3 or EC2, and *Ma, *c, and *s are partial safety factors at the ultimate limit states. For precast elements, *c and *s are given in the appropriate Part of Eurocode 2. 2) The plastic resistance of concrete-filled hollow sections Npl.Rd may be calculated with 0.85fck being replaced by fck. 3) For concrete-filled tubes of circular cross section, account may be taken of the increase in strength of concrete caused by confinement provided that — the relative slenderness Æ given by 4.8.3.7 does not exceed 0.5, and — the greatest design bending moment calculated by first-order theory, Mmax.Sd, does not exceed NSd d/10, where d is the external diameter of the column. 4) The plastic resistance to compression may then be calculated from Npl.Rd = Aa)2fy/*Ma + Ac(fck/*c) [1 + )1 (t/d)(fy/fck)] + Asfsk/*s where t is the wall thickness of the steel tube, )1 and )2 are coefficients defined below, and the other symbols are defined above. 5) The eccentricity of loading e is defined as Mmax.Sd/NSd. The values of )10 and )20 when e = 0 are given in Table 4.5, or may be taken as follows: (but U 0) (but k 1.0). Table 4.5 — Values of )10 and )20 when e = 0 0
0.1
0.2
0.3
0.4
U 0.5
)10
4.90
3.22
1.88
0.88
0.22
0.00
)20
0.75
0.80
0.85
0.90
0.95
1.00
Æ
6) The values of )1 and )2 for 0 < e k d/10 are as follows: )1 =)10 (1 – 10e/d) )2 = )20 + (1 – )20) (10e/d). For e > d/10, )1 = 0 and )2 = 1.0. 4.8.3.4 Steel contribution ratio The steel contribution ratio is defined as $ = (Aafy/*a)/Npl.Rd, where Np=.Rd is calculated with *Ma = *a.
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4.8.3.5 Effective elastic flexural stiffness of cross sections 1) For short-term loading the effective elastic flexural stiffness of a cross section of a composite column, (EI)e, should be calculated from
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(EI)e = EaIa + 0.8 EcdIc + EsIs where Ia, Ic and Is are the second moments of area for the considered bending plane of the structural steel, the concrete (assumed to be uncracked), and the reinforcement, respectively; Ea and Es are the elastic moduli for the structural steel and the reinforcement; 0.8EcdIc is the effective stiffness of the concrete part; Ecd = Ecm/*c; Ecm is the secant modulus of concrete according to 3.1.4.1; *c = is the safety factor for the stiffness according to clauses A.3.1 and A.3.4 of EC2. 2) More accurate account should be taken to the influence of long-term loading on the effective elastic flexural stiffness where — the relative slenderness Æ in the plane of bending being considered exceeds the limit given in Table 4.6 and — e/d < 2, where e is the eccentricity of loading as defined in 4.8.3.3 5), d is the overall depth of the cross section in the plane of bending considered, $ is as defined in 4.8.3.4, and Æ is as defined in 4.8.3.7. For comparison with the limits given in Table 4.6, Æ may be calculated without considering the influence of long-term loading on flexural stiffness. Under these conditions, the effective elastic modulus of the concrete should be reduced to the value Ec = Ecd (1 – 0.5NG.Sd/NSd) where NSd is the design axial load for the column length, and NG.Sd is the part of this load that is permanent. Table 4.6 — Limiting values of Æ for clause 4.8.3.5 2) Braced non-sway frames
Sway frames and/or unbraced frames
Concrete-encased sections
0.8
0.5
Concrete-filled tubes
0.8/(1 – $)
0.5/(1 – $)
4.8.3.6 Buckling lengths of a column 1) The buckling length = of an isolated non-sway composite column may conservatively be taken as equal to its system length, L. 2) Alternatively, = may be determined using Annex E of EC3 and the following rules: — flexural stiffness of adjacent members attached by rigid connections should be those used in the frame analysis according to 4.9.6.2; — Table E.2 of EC3 may be assumed to apply when the beams are composite, or of steel or reinforced concrete, and also where concrete slabs without beams are used. 3) Where the beams are composite, clause E.2 8) of EC3 is replaced by the following rule. Where, in the global analysis for the same load case, the elastic hogging moment in a composite beam is reduced by more than 20 % for “uncracked” analysis or more than 10 % for “cracked” analysis, the relevant beam stiffness Kb should be taken as zero. 4) Except where relevant rules are given in EC2 or EC3, paragraphs 1) to 3) above may be used for reinforced concrete and steel columns in non-sway composite frames.
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4.8.3.7 Relative slenderness 1) The elastic critical load for the column length, Ncr, shall be calculated from Ncr = ;2(EI)e/=2 where (EI)e is given in 4.8.3.5, and = is the buckling length in accordance with 4.8.3.6. 2) The non-dimensional slenderness for the plane of bending considered is given by
where Npl.R is the value of Npl.Rd according to 4.8.3.3 when the *M factors *Ma, *c, and *s are taken as 1.0. 4.8.3.8 Resistance of members in axial compression
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1) The member has sufficient resistance if for both axes NSd k ·Npl.Rd where
Npl.Rd is the resistance in accordance with 4.8.3.3 and · is the reduction coefficient for the relevant buckling mode given in clause 5.5.1 of EC3 in terms of the relevant slenderness Æ and the relevant buckling curve. 2) Appropriate buckling curves are: — curve a for concrete-filled hollow sections, — curve b for fully or partly concrete-encased I-sections with bending about the strong axis of the steel section, — curve c for fully or partly concrete encased I-sections with bending about the weak axis of the steel section. 4.8.3.9 Combined compression and bending 1) For each of the axes of symmetry a separate check is necessary with the relevant slenderness, bending moments and resistance in bending. 2) For compression and uniaxial bending this check should be done according to 4.8.3.10 to 4.8.3.13 for the bending plane and according to 4.8.3.8 for the non-bending plane. 3) For compression and biaxial bending the check is given in 4.8.3.14. 4.8.3.10 Analysis for bending moments 1) Bending moments at the ends of the member should be determined assuming that the axial force acts through the centroid as defined in the Note to 4.8.3.1 3) a). 2) Columns generally shall be checked for second order effects. 3) Isolated non-sway columns need not be checked for second order effects if: — NSd/Ncr k 0.1 where Ncr is defined in 4.8.3.7 1); or
— for columns with end moments, the relative slenderness do not exceed where r is the ratio of the end moments according to Table 4.7. If there is any transverse loading, r should be taken as 1.0.
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Table 4.7 — Factors " for the determination of moments according to second order theory line
moment distribution
moment factors "
first order bending moments from lateral loads in isolated non-sway column
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1
comment
MSd is the maximum bending moment within the column length due to lateral forces ignoring second order effects " = 1.0
end moments in a non-sway frame 2
MSd and rMSd are the end moments from a frame analysis according to 4.9 " = 0.66 + 0.44r but " U 0.44
3) When checking second order effects, flexural stiffness should be calculated in accordance with 4.8.3.5. 4) For simplification, second order effects in an isolated non-sway column may be allowed for by increasing the greatest first-order design bending moment MSd by a correction factor k given by k = "/[1 – (NSd/Ncr)] U 1.0 where Ncr is the critical load for the relevant axis according to 4.8.3.7 1) with the effective length = taken as the column length, and " is an equivalent moment factor given in Table 4.7. In absence of more accurate calculation the value of " should not be taken less than 1.0 for combined action of end moments and moments from lateral load. 4.8.3.11 Resistance of cross sections in combined compression and uniaxial bending 1) Points on the interaction curve of Figure 4.12, showing resistance in combined compression and uniaxial bending, may be calculated assuming rectangular stress blocks as shown in Figure 4.13, and taking account of the design shear force VSd according to 4.8.3.12. 2) Figure 4.13 shows stress distributions corresponding to the points A to D of the interaction curve (Figure 4.12), for a typical concrete-encased I-section with bending about the strong axis of the steel section. 3) For concrete filled hollow sections the plastic resistances may be calculated with 0.85fck being replaced by fck. 4) As a simplification, the curve maybe replaced by a polygonal diagram (dashed line in Figure 4.12). More information for the calculations for points A to D is given in Annex C. 5) An additional point E should be determined approximately midway between point A and point C of Figure 4.12 if the resistance of the column to axial compression (·Npl.Rd) is greater than Npm.Rd, where Npm.Rd is the plastic resistance of the concrete section alone. This is not necessary for I-profiles with bending about the strong axis of the steel section. 4.8.3.12 Influence of shear forces The design transverse shear force VSd may be assumed to act on the structural steel section alone, or may be shared between the steel and the concrete. The influence on the bending resistance of the shear force assumed to be resisted by the steel should be considered according to 4.4.3 1) and 2).
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Figure 4.12 — Interaction curve for compression and uniaxial bending
Figure 4.13 — Stress distributions corresponding to the interaction curve (Figure 4.12)
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4.8.3.13 Resistance of members in combined compression and uniaxial bending
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1) The design procedure is given in step-by step form, with reference to Figure 4.14.
Figure 4.14 — Design procedure for compression and uniaxial bending 2) The resistance of the member in axial compression is ·Npl.Rd, calculated in accordance with 4.8.3.8, where · accounts for the influence of imperfections and slenderness. The corresponding value for bending of the cross section 4k is determined from ·, as shown in Figure 4.14. 3) Let ·d = NSd/Np=.Rd where NSd is the design axial force, and let the corresponding bending resistance of the cross section be given by 4d. 4) Where the variation of bending moment along the column length is approximately linear, the ratio ·n may be calculated from ·n = · (1 – r)/4, but ·n k ·d,
where r is the ratio of the lesser to the greater end moment as shown in Figure 4.15. Otherwise, ·n should be taken as zero.
Figure 4.15 — Typical values for ·n 5) The length 4 in Figure 4.14 is calculated from 4 = 4d – 4k (·d – ·n)/(· – ·n). 6) Where NSd < Npm.Rd (Figure 4.12), the increase of the bending resistance due to the normal force may be overestimated if the acting normal force N and the bending moment M are independent. This should be accounted for by reducing the partial safety factor for the favourable component NSd by [see clause 2.3.3.1 7) of EC2]. 7) The value of 4 should not be taken as greater than 1.0, unless the bending moment MSd is due solely to the action of the eccentricity of the force NSd, e.g., in an isolated column without transverse loads acting between the column ends.
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8) The member has sufficient resistance if MSd k 0.94Mpl.Rd, where MSd Mpl.Rd
is the maximum design bending moment within the column length, calculated in accordance with 4.8.3.10 including second order effects if necessary; and is the bending moment calculated using the stress distribution shown in Figure 4.13 (B), with *Ma in accordance with 4.8.3.11 3).
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4.8.3.14 Combined compression and biaxial bending 1) Due to the different slendernesses, bending moments, and resistances of bending for the two axes, in most cases a check for the biaxial behaviour is necessary. 2) Imperfections should be considered only in the plane in which failure is expected to occur [e.g. z-axis in Figure 4.16(a)]. For the other plane of bending no imperfection needs to be considered for that plane [e.g. y-axis in Figure 4.16(b)]. If it is not evident which plane is the more critical, checks should be made for both planes. 3) The following design method should be used for a design axial force NSd combined with design bending moment My.Sd and Mz.Sd. 4) The values of 4 for the two axes of bending, 4y and 4z, are found in accordance with 4.8.3.13. 5) The member is strong enough if My.Sd k 0.9 4yMpl.y.Rd, Mz.Sd k 0.9 4zMpl.z.Rd, and My.Sd/4yMpl.y.Rd + Mz.Sd/4zMpl.z.Rd k 1.0. with Mpl.y.Rd and Mpl.z.Rd according to 4.8.3.11, referring to the relevant axis. An example is given in Figure 4.16(c).
(a) Plane expected to fail with consideration of imperfections (b) Plane without consideration of imperfections (c) Interaction diagram for bending resistance
Figure 4.16 — Design for compression and biaxial bending
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4.9 Internal forces and moments in frames for buildings
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4.9.1 General 1) Section 4.9 is applicable to composite frames as defined in 1.4.2 1). It is assumed that most of the structural members and connections are either composite or of structural steel. Where the structural behaviour of the frame is essentially that of a reinforced or prestressed concrete structure, with only a few composite members, global analysis shall be generally in accordance with section 2.5 of EC2. 2) The definitions and classifications of methods of global analysis, types of framing, and types of connections are similar to those used in Section 5.2 of EC3, which is applicable to structural steel members in composite frames. The classification of frames, as braced or unbraced and sway or non-sway, is consistent with that given in clause 5.2.5 of EC3. 3) The scope of this Section excludes sway frames, as defined in 4.9.4.2. (Note. These may be treated later in an Annex). 4) The general principles for plastic analysis given in 4.5.2.1 are applicable, but no application rules are given for elastic-plastic methods of analysis. 5) No application rules are given for global analysis of unbraced non-sway frames, as defined in 4.9.4. (Note. These may be given later in an Annex). 6) No application rules are given for global analysis of frames with semi-rigid connections. These connections are defined in 4.10.5.2 and, for steel connections, in clause 6.4.2.3 of EC3. 7) [Note. It may be found convenient to verify the design of a composite braced frame in the following sequence. a) Define the imperfections of the frame (4.9.3) and represent them by equivalent horizontal forces at nodes. b) Ensure that no steel connection is “semi-rigid”, using 4.10.5 and clause 6.9.6 of EC3. c) For members of reinforced or prestressed concrete, ensure the ductility requirements of clause 2.5.3 of EC2 are met. d) Check that the frame is braced (4.9.4.3). e) Check that the bracing substructure is non-sway (4.9.4). f) Decide whether the requirements for rigid-plastic global analysis (4.9.7) are satisfied. g) Carry out global analyses (4.9.5 to 4.9.7) for relevant load combinations and arrangements and hence find design internal forces and moments at each end of each member. h) Verify the composite beams (4.2 to 4.4), columns (4.8), and connections (4.10). i) Verify beams, columns, and connections of structural steel (to EC3) and of concrete (to EC2). j) Reference is made to the effective length (buckling length) of reinforced concrete and steel columns in 4.8.3.6 4). k) For reinforced concrete columns, clauses 4.3.5.5.3 and 4.3.5.6 of EC2 (“isolated columns”) are applicable.] 4.9.2 Design assumptions 4.9.2.1 Basis 1) The assumptions made in the global analysis shall be consistent with the anticipated behaviour of the connections. 2) The assumptions made in the design of the members shall be consistent with the method used for global analysis and with the anticipated behaviour of the connections. 3) Composite connections are classified in 4.10. For steel beam-to-column connections, Section 6.9 of EC3 is applicable. 4) Table 4.8 shows the types of connections for use with each type of framing, depending on the method of global analysis used. 5) Nominally pinned connections may be used in continuous construction at points where continuity is not required, provided that the connection is designed as non-composite in accordance with Chapter 6 of EC3, ignoring any reinforcement which may be provided for the control of cracking.
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Table 4.8 — Design assumptions Type of framing (Terminology)
Method of global analysis
Simple
Statically determinate
Types of connections
— Nominally pinned, steel (6.4.2.1 and 6.4.3.1 of EC3)
Continuous
Elastic
— Rigid, steel (6.4.2.2 of EC3) — Nominally pinned (6.4.2.1 of EC3) — Rigid, composite (4.10.5.2)
Rigid-plastic
— Full-strength, steel (6.4.3.2 of EC3) — Nominally pinned (6.4.3.1 of EC3)
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— Full-strength, composite 4.10.5.3) Semi-continuous
Rigid-plastic
As for continuous framing (above) and: — partial-strength, steel (6.4.3.3 of EC3) — partial-strength, composite (4.10.5.3)
4.9.2.2 Simple framing In simple framing, the connections between the members may be assumed not to develop moments. In the global analysis, members may be assumed to be effectively pin connected. 4.9.2.3 Continuous framing Both elastic and rigid-plastic analyses should be based on the assumption of full continuity, except where nominally pinned connections are used. 4.9.2.4 Semi-continuous framing Rigid-plastic analysis should be based on the design moment resistances of connections which have been demonstrated to have sufficient rotation capacity; see clauses 6.4.3.3 and 6.9.5 of EC3. 4.9.2.5 Effects of deformations Internal forces and moments in non-sway frames may generally be determined using first-order theory, using the initial geometry of the structure. Alternatively, second-order theory may be used. 4.9.3 Allowance for imperfections 1) The principles of clause 5.2.4 of EC3 are applicable, with the following modification and additions. 2) Clause 5.2.4.2 4) of EC3 applies only to steel columns. For composite and reinforced concrete columns, the effects of imperfections within the member may be neglected in a global analysis for a frame within the scope of this Section. 3) For braced frames, the effects of frame imperfections shall be included in the global analysis of the bracing. 4) The application rules of clause 5.2.4 of EC3 are applicable. 4.9.4 Sway resistance 4.9.4.1 General 1) The principles of clause 5.2.5 of EC3 are applicable with the following modifications, to non-sway composite frames, whether braced or unbraced, in which most of the columns are composite or of structural steel. 2) Where a composite frame is classified as braced and the bracing system is not composite, that system shall be designed to the relevant Eurocode, and shall satisfy the requirements for resistance and stiffness given in clause 5.2.5.3 of EC3. 4.9.4.2 Classification as sway or non-sway 1) The criteria of clause 5.2.5 of EC3 shall be used to classify a composite frame as non-sway. Consideration shall be given to the effects of cracking and creep of concrete. 2) A braced frame shall be treated as a non-sway frame.
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4.9.4.3 Classification as braced or unbraced 1) The criteria of clause 5.2.5.3 of EC3 shall be used to classify a composite frame as braced. Consideration shall be given to the effects of cracking and creep of concrete. 2) A composite frame may be treated as braced if the bracing system reduces its horizontal displacements by at least 80 %, when account is taken in both analyses of the effects of cracking of concrete and, where necessary, of creep. 3) Where the analyses are based on uncracked cross-sections of composite beams, the limit of 80 % may also be used. 4) The application rules of clause 5.2.5.3 of EC3 are applicable to composite bracing systems.
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4.9.5 Methods of global analysis 1) The internal forces and moments in a statically determinate structure shall be obtained using statics. 2) The internal forces and moments in a statically indeterminate structure may generally be determined using either. — elastic global analysis in accordance with 4.9.6, or — plastic global analysis in accordance with 4.9.7. 3) Where the global analysis is carried out by applying the loads in a series of increments, it may be assumed to be sufficient, in the case of building structures, to adopt simultaneous proportional increases of all loads. 4.9.6 Elastic global analysis 4.9.6.1 General 1) Elastic global analysis shall be based on the assumption that the stress-strain relationships for the materials are linear, whatever the stress level. Concrete in tension may be included or neglected. When it is included, reinforcement in tension may be neglected. Reinforcement in compression may normally be neglected. 2) The effects of slip and uplift may be neglected at interfaces between steel and concrete at which shear connection is provided in accordance with Chapter 6. 3) The principles of 4.5.3.2 (sequence of construction) and 4.5.3.3 (shrinkage of concrete) are applicable. 4) Elastic global analysis should be used only where all connections are either rigid or nominally pinned. 4.9.6.2 Flexural stiffness 1) Creep effects shall be considered if they are likely to reduce the structural stability significantly. 2) For composite beams in braced frames, 4.5.3.1 2) is applicable. 3) Creep effects in columns may be ignored if the increase in the first order bending moments resulting from permanent loads and due to creep deformations and longitudinal force does not exceed 10 %. 4) For first order analysis, the elastic stiffness of a composite column should be taken as EaI1 where Ea is the modus of elasticity of structural steel and I1 is the “uncracked” second moment of area, defined in 4.2.3. 4.9.6.3 Redistribution of moments 1) The bending moment distribution given by an elastic global analysis may be redistributed in a way that satisfies equilibrium, and takes account of the effects of cracking of concrete, inelastic behaviour of materials, and all types of buckling. 2) Bending moments from a first-order elastic analysis may be redistributed: — in steel members in accordance with clause 5.2.1.3 3) of EC3; but for unpropped construction, subject to 4.5.3.4 2) c). — in concrete members subject mainly to flexure, in accordance with clause 2.5.3.4.2 of EC2; — in spans of composite beams in braced frames with rigid full-strength connections at their ends, or with one rigid full-strength connection and one nominally pinned connection, in accordance with 4.5.3.4 2); — but elastic moments may not be reduced in concrete or composite columns. Where beam-to-column connections are rigid and midspan moments are redistributed to supports, column end moments should be increased, according to the relative stiffness of the members. For columns, stiffness should be based on the length between centres of restraint.
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4.9.7 Rigid-plastic global analysis
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4.9.7.1 General 1) Rigid-plastic global analysis shall not be used unless: — the frame is non-sway in accordance with 4.9.4; — the frame, if unbraced in accordance with 4.9.4, is of two storeys or less; — all the members of the frame are steel or composite; — the cross-sections of steel members satisfy the principles of clauses 5.2.7 and 5.3.3 of EC3; — composite beams satisfy the principles of 4.5.2.2 1); — the steel material satisfies clause 3.2.2.2 of EC3. 2) Where rigid-plastic global analysis is used, the connections in the frame should be steel or composite and either: — have been shown to have sufficient rotation capacity, or — have a design moment resistance at least 1.2 times the design plastic moment resistance of the connected beam [4.10.5.3 2)]. 3) In rigid-plastic analysis, elastic deformations of the members, connections, and foundations are neglected and plastic deformations are assumed to be concentrated at plastic hinge locations. 4) In frames for buildings, it is not normally necessary to consider the effects of alternating plasticity. 4.9.7.2 Plastic hinges 1) At each plastic hinge location: a) the cross section of the structural steel member or component shall be symmetrical about a plane parallel to the plane of the web or webs; b) the proportions and restraints of steel components shall be such that lateral-torsional buckling does not occur; c) lateral restraint to the compression flange shall be provided at all hinge locations at which plastic rotation may occur under any load case; d) the rotation capacity shall be sufficient, when account is taken of any axial compression in the member, to enable the required hinge rotation to develop. 2) Where rotation requirements are not calculated, all members containing plastic hinges shall have effective cross-sections at plastic hinge locations that are in Class 1 in accordance with Section 4.3, or Section 5.3 of EC3, as appropriate. 3) For composite beams, all other effective cross-sections should be in Class 1 or Class 2. 4) For individual spans of composite beams that contain a sagging moment hinge that is not the last to form, 4.5.2.2 2) d) should be satisfied. 5) Design should ensure that plastic hinges do not occur in composite columns. 6) Where plastic hinges occur in steel columns, clauses 5.2.7 3) and 4) of EC3 should be satisfied. 7) Where the cross-section of a steel member varies along its length, clause 5.3.3 5) of EC3 is applicable. 8) Where restraint is required by 4.9.7.2 1) d), it should be located within a distance along the member from the calculated hinge location, that does not exceed half the depth of the steel component or member.
4.10 Composite connections in braced frames for buildings 4.10.1 General 1) Composite connections are defined in 1.4.2. Other connections in composite frames shall be designed in accordance with EC2 or EC3, as appropriate. 2) This Section 4.10 is intended for use with Chapter 6 of EC3. It supplements or modifies that chapter. 3) In this Section 4.10, the term “connection” refers to composite connections. 4) The internal forces and moments applied to connections for the ultimate limit state shall be determined by global analysis conforming with 4.9. 5) The resistance of a connection shall be determined on the basis of the resistances of the individual components. 64
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6) Connections may be designed by distributing the internal forces and moments in the best rational way, provided that the distribution is in accordance with clause 6.1.4 of EC3. In addition, the deformations implied by the distribution shall be within the deformation capacity of the reinforcement and any concrete assumed to resist compression. 7) Ease of fabrication and assembly shall be considered in the design of all joints and splices. Clause 6.3.3.5 of EC2 and clause 6.1.5 of EC3 are applicable. 4.10.2 Classification of connections Section 6.4 of EC3 is applicable, with the reference to Table 5.2.1 and clause 5.2.2 of EC3 replaced by reference to Table 4.8 and clause 4.9.2 of EC4. 4.10.3 Connections made with bolts, rivets or pins 4.10.3.1 General
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Section 6.5 of EC3 is applicable, with the modifications given below. 4.10.3.2 Distribution of forces between fasteners 1) Due account shall be taken of the forces in the reinforcement and concrete components of the connection, except as allowed in 4.9.2.1 5). 2) Figure 6.5.7 of EC3 is not applicable. 4.10.3.3 Pin connections No provision is made for the use of pin connections to clause 6.5.13 of EC3 as part of a composite connection. 4.10.4 Splices in composite members Section 6.8 of EC3 is applicable provided that due account is taken of the forces in the reinforcement and concrete when designing the splice between the structural steel components. 4.10.5 Beam-to-column connections 4.10.5.1 General Section 6.9 of EC3 is applicable to composite connections, with the modifications given below. 4.10.5.2 Classification by rotational stiffness 1) Clause 6.9.6.2 of EC3 is applicable, except that semi-rigid connections and unbraced frames are outside the scope of 4.10 of EC4. 2) For classification of a connection, the value taken for the flexural rigidity of the connected beam should be consistent with that taken for a section adjacent to the connection in global analysis of the frame. 4.10.5.3 Classification by moment resistance 1) Clause 6.9.6.3 of EC3 is applicable. 2) If the connected beam is a composite member, the plastic moment resistance Mpl.Rd should be that of the beam’s cross-section immediately adjacent to the connection, calculated in accordance with 4.4.1.2 or 4.4.1.3 of EC4. 4.10.5.4 Classification of moment-rotation characteristics 1) The classification boundary for braced frames given in Figure 6.9.8 of EC3 is applicable. 2) For composite beams, the plastic moment resistance and flexural rigidity are defined in 4.10.5.3 and 4.10.5.2 respectively. 4.10.5.5 Calculated properties 1) Clause 6.9.7 of EC3 is applicable provided that due account is taken of the forces in the reinforcement and in concrete components of the connection. 2) The criteria for the tension zone shall include yielding of the reinforcement of the connection. 3) The buckling resistance of the column web can be improved by encasement in reinforced concrete. Account may be taken of such improvement where it has been established by testing.
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4.10.5.6 Application rules The detailed rules given in Annex J of EC3 may be applied to components of composite connections, if appropriate.
5 Serviceability limit states (Note: Serviceability limit states for composite slabs with profiled steel sheeting are covered in Chapter 7, for floors with precast concrete slabs in Chapter 8, and for friction grip bolts in Section 6.5).
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5.1 General 1) This chapter covers the common serviceability limit states. These are: — deflection control, and — crack control. Other limit states (such as vibration) may be of importance in particular structures but these are not covered in this Part of Eurocode 4. 2) Calculation of stresses and deformations at the serviceability limit state shall take into account the effects of: — shear lag; — increased flexibility resulting from significant incomplete interaction, due to slip and/or uplift; — cracking and tension stiffening of concrete in hogging moment regions; — creep and shrinkage of concrete; — yielding of steel, if any, especially when unpropped construction is used; — yielding of reinforcement, if any, in hogging moment regions. These effects shall be established by test or analysis, where practicable. 3) In the absence of a more rigorous analysis, the effects of creep may be taken into account by using modular ratios, as given in 3.1.4.2, for the calculation of flexural stiffnesses.
5.2 Deformations 5.2.1 General 1) Deformations shall not adversely affect the use, efficiency, or appearance of the structure. Composite members shall be so proportioned that deflections of beams and sidesway of unbraced frames are within acceptable limits. Appropriate limits depend on the properties of any non-structural components, such as partitions in buildings, and on the intended use and occupancy of the structure. 2) In buildings it will normally be satisfactory to consider the deflections under the rare combination of loading. 3) For buildings the recommended limits for horizontal deflections at the tops of the columns are as given in clause 4.2.2 4) of EC3. 4) For floor and roof construction in buildings, the deflection limits given in clause 4.2.2 of EC3 are applicable. The sagging vertical deflection $max for unpropped beams should be determined for the underside of the beam, only where the deflection can impair the appearance of the building. In all other cases the reference level is the upperside of the composite beam. 5.2.2 Calculation of maximum deflections of beams 1) Deflections due to loading applied to the steel member alone shall be calculated in accordance with EC3. 2) Deflections due to loading applied to the composite member shall be calculated using elastic analysis with corrections for the effects given in 5.1 2). 3) The influence of shear lag on deflections can usually be ignored. For members where breadth b of the concrete flange exceeds one-eighth of the span, shear lag may be allowed for by using the effective area of concrete flange given in 4.2.2.1 when calculating stiffness. 4) The effects of incomplete interaction may be ignored in spans or cantilevers where one or more of the critical cross sections is in Class 3 or 4.
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5) The effects of incomplete interaction may be ignored in unpropped construction provided that: a) the design of the shear connection is in accordance with Chapter 6; b) either not less shear connectors are used than half the number for full shear connection, or the forces on the shear connectors do not exceed 0.7 PRk, as defined in 3.5.2; c) in case of a ribbed slab with ribs transverse to the beam, the height of the ribs does not exceed 80 mm. 6) If the conditions in 5) are not met, but N/Nf U 0.4, then in lieu of testing or accurate analysis, the increased deflection arising from incomplete interaction may be determined from: for propped construction:
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for unpropped construction:
where
$a $c N/Nf
is the deflection for the steel beam acting alone; is the deflection for the composite beam with complete interaction; is the degree of shear connection as given in 6.1.2.
7) The effect of cracking of concrete in hogging moment regions may be taken into account by adopting one of the following methods of analysis: a) The hogging bending moment at each internal support and the resulting top-fibre tensile stress in the concrete, Bct, are first calculated using the flexural stiffnesses EaI1. For each support at which Bct exceeds 0.15 fck, the stiffness should be reduced to the value EaI2 over 15 % of the length of the span on each side of the support. A new distribution of bending moments is then determined by re-analysing the beam. At every support where stiffnesses EaI2 are used for a particular loading, they should be used for all other loadings. Flexural stiffnesses EaI1 and EaI2 are defined in 4.2.3. b) For beams with critical sections in Classes 1, 2 or 3 the following method may be used. At every support where Bct exceeds 0.15 fck, the bending moment is multiplied by the reduction factor f1 given in Figure 5.1, and corresponding increases are made to the bending moments in adjacent spans. Curve A may be used when the loadings per unit length on all spans are equal and the lengths of all spans do not differ by more than 25 %. Otherwise the approximate lower bound value f1 = 0.6 (line B) should be used.
Figure 5.1 — Reduction factor for the bending moment at supports
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8) In unpropped beams in buildings, account may be taken of the influence of local yielding of structural steel over a support by multiplying the bending moment at the support, determined according to the methods given in this clause, with an additional reduction factor as follows: f2 = 0.5 if fy is reached before the concrete slab has hardened; f2 = 0.7 if fy is caused by the loading after concrete has hardened. 9) In statically-determinate beams in buildings, the effect of curvature due to shrinkage of concrete should be included when the ratio of span to overall depth of the beam exceeds 20 and the predicted free shrinkage strain of the concrete exceeds 400 × 10–6.
5.3 Cracking of concrete in beams
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5.3.1 General 1) Cracking shall be limited to a level that will not be expected to impair the proper functioning and durability of the structure or cause its appearance to be unacceptable. 2) Cracking is almost inevitable where reinforced concrete elements of composite beams are subject to tension resulting from either direct loading or restraint of imposed deformations. 3) Where cracks are avoided by measures such as the provision of joints that can accommodate the movement, the measures taken shall not impair the proper functioning of the structure or cause its appearance to be unacceptable. 4) Where the exposure is class 1, according to clause 4.1.2.2 of EC2, crack width has no influence on durability, and flexural cracks may be permitted to form without any attempt to control their width. In accordance with 1) above: — their appearance shall be acceptable, if they are visible, and — any finish to the surface of the concrete shall not be brittle. 5) Where a composite beam is subjected to hogging bending, and no attempt is made to control the width of cracks in the concrete of its top flange, the longitudinal reinforcement provided within the effective width of that flange should be not less than: — 0.4 % of the area of concrete, for propped construction, or — 0.2 % of the area of concrete, for unpropped construction. The reinforcement should extend over a length span/4 each side of an internal support, or length/2 for a cantilever. The effective width should be as given in 4.2.2.2. No account should be taken of any profiled steel sheeting. The maximum spacing of the bars should be in accordance with 7.2.1 3), for a composite slab, or with clause 5.4.3.2.1 of EC2, for a non-composite slab. 6) Appropriate limits to design crack widths, taking account of the proposed function and nature of the structure and the costs of limiting cracking, shall be determined. 7) Design crack-width limits should be agreed with the client. 8) Limitation of cracks to acceptable widths, and the avoidance of uncontrolled cracking between widely-spaced bars, are achieved by ensuring a) that, at all sections likely to be subjected to significant tension due to restraint of imposed deformations, whether or not the restraint is combined with direct loading, a minimum amount of bonded reinforcement is present, sufficient to ensure that the reinforcement will remain elastic when cracking first occurs, and b) that bar spacings and diameters are limited. 9) In the absence of specific requirements (e.g., watertightness), it may be assumed that for exposure classes 2 to 4, according to clause 4.1.2.2 of EC2, limitation of the design crack width to about 0.3 mm will generally be satisfactory for reinforced concrete elements of composite beams in buildings, in respect of appearance and durability. 10) Special measures to limit crack widths may be necessary for members subjected to exposure class 5 according to clause 4.1.2.2 of EC2. The choice of measures will depend on the nature of the aggressive chemical involved.
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11) Application rules are given in clauses 5.3.2 and 5.3.4 for design crack widths wk of 0.3 mm, for general use except where the exposure is class 5; and of 0.5 mm, which may be appropriate where the exposure is Class 1. It is assumed that the reinforcing bars have high-bond action, in accordance with 3.2.2 1). 12) [Note. It may be found convenient to consider cracking of concrete in a composite beam in a building as follows. a) Determine those regions where concrete may be subjected to longitudinal tension due to loading and/or to restraint of imposed deformation, and determine the area of reinforcement required for the ultimate limit states. b) Decide the exposure class, and the crack-width limit (if any). Use 5.3.1 5) if applicable. c) In regions where only minimum reinforcement is required, and crack widths are influenced more by imposed deformations than by loading, use 5.3.2. This gives the minimum area of tensile reinforcement and the maximum diameter for the reinforcing bars. d) In other regions, use 5.3.3 to determine internal forces and moments. Then use 5.3.4 if the crack-width limit is 0.3 mm or 0.5 mm. Otherwise, use 5.3.5. Clause 5.3.4 gives the maximum spacing for reinforcing bars. The required areas are known [paragraph a) above], so bar diameters can be calculated.] 5.3.2 Minimum reinforcement 1) In determining the minimum area of reinforcement required to ensure that the reinforcement remains elastic when cracking first occurs, account shall be taken of the different types of restraint distinguished in clause 4.4.2.2 of EC2, and of the stress distribution in the concrete just before it cracks. 2) Where crack widths are to be controlled in a concrete flange of a composite beam, (and unless more rigorous calculation shows a lesser area to be adequate), the cross-sectional area As of reinforcement within the effective area of the concrete flange within the tensile zone, Act, should satisfy As U kkcfcte Act/Bst where: fcte
is the effective tensile strength of the concrete at the time when cracks may first be expected to occur. Values of fcte may be obtained by taking as the class the strength at the time cracking is expected to occur, and using the value fctm given in Table 3.1. When the age of the concrete at cracking cannot be established with confidence as being less than 28 days, it is suggested that a minimum tensile strength of
Bst k kc
where hc zo
(5.1)
N/mm2 be adopted;
is the maximum stress permitted in the reinforcement immediately after cracking. It depends on the chosen bar size, as given in Table 5.1, and should not exceed the characteristic yield strength of the reinforcement; is defined in clause 4.4.2.2 3) of EC2, and should be taken as 0.8; is a coefficient that may conservatively be taken as 0.9. It takes account of self-equilibrating stresses and the stress distribution in the slab prior to cracking, and is more accurately given by
is the thickness of the concrete flange, excluding any haunch or ribs, and is the vertical distance between the centroids of the uncracked unreinforced concrete flange and the uncracked unreinforced composite section, calculated using the modular ratio for short term effects, Ea/Ecm.
At least half of the required minimum reinforcement should be placed between mid-depth of the slab and the face subjected to the greater tensile strain. 3) Minimum longitudinal reinforcement for the concrete encasement of the web of a steel I-section should be determined from eq.(5.1) with k = 0.8, kc = 0.4, and Bst = fsk.
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Table 5.1 — Maximum steel stress for minimum reinforcement, high bond bars Maximum bar size, mm
6
8
Design crack width
10
12
16
20
Maximum steel stress Bs or Bst, N/mm
25
32
2
wk = 0.3 mm
450
400
360
320
280
240
200
160
wk = 0.5 mm
500
500
500
450
380
340
300
260
4) For restraint cracking, but not for load-induced cracking, the maximum bar diameter may be modified to a value :s, where :s = :s* (fcte/2.5)
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where
:s* fcte
is the bar diameter that relates to stress Bst, in accordance with Table 5.1; is as defined in 5.3.2 2).
5.3.3 Analysis of the structure for the control of cracking 1) Internal forces and moments shall be determined by elastic global analysis. The Principles of 4.5.3 are applicable. 2) The quasi-permanent combination of actions, defined in 2.3.4 2), should normally be used. 3) The application rules of 4.5.3 are applicable, except that the limits to the redistribution of moments given in Table 4.3 are replaced by the following: — for “cracked” elastic analysis, zero for sections of any class; — for “uncracked” elastic analysis: — 15 % for hogging regions with cross-sections in class 1 or 2, — 10 % for other regions of hogging bending moment. 5.3.4 Control of cracking due to direct loading, without calculation of crack widths 1) This clause is applicable in regions where the quantity of tensile reinforcement required to provide resistance to bending at ultimate limit states exceeds the minimum reinforcement required by 5.3.2. 2) Tensile stresses in reinforcement should be determined by elastic analysis of cross sections. The effect of tension stiffening in a composite section increases the tensile stress that is relevant to control of cracking to a value Bs. This equation may be used for reinforcement in a concrete flange of a composite beam:
where: is the stress in the reinforcement closest to the relevant concrete surface, calculated neglecting concrete in tension and in accordance with 5.3.3 and 4.4.1.4 1), 2), and 4); Act is the effective area of the concrete flange within the tensile zone; As is the total area of all layers of longitudinal reinforcement within the effective area Act; fctm is the mean tensile strength of the concrete, from Table 3.1; ! is given by ! = AI/(Aa Ia) where A and I are area and second moment of area, respectively, of the composite section neglecting concrete in tension and profiled sheeting, if any; and Aa and Ia are the corresponding properties of the structural steel section. Bse
3) In beams for buildings, Bse may be calculated neglecting the effects of shrinkage of concrete, except as required by 4.5.3.3. 4) If the stress Bs is found to exceed the design yield strength for the reinforcement, fsk, the section should be re-designed. This is not necessary if the maximum calculated stress in the structural steel exceeds its yield strength fy, but Bs does not exceed fsk. 5) Where the steel stress Bs is within the range available in Table 5.2, the maximum spacing of the reinforcing bars should be determined from that table.
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Table 5.2 — Maximum bar spacing for high bond bars Steel stress Bs N/mm2
k 160
200
240
280
maximum bar spacing
wk = 0.3 mm
250
200
160
110
(mm)
wk = 0.5 mm
250
250
250
250
320
360
400
use Table 5.1 200
140
80
6) Where Table 5.2 is not applicable, the maximum diameter of the reinforcing bars should be determined from Table 5.1, for the relevant values of Bs and wk. 7) Control of cracking in the concrete encasement of the web of a steel I-section should be in accordance with this cause 5.3.4, with Bs taken as 0.5 fsk.
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5.3.5 Control of cracking by calculation of crack widths 1) The crack width to be compared with the design value wk shall be calculated in accordance with the Principles of clause 4.4.2.4 of EC2. 2) Tensile stresses in reinforcement should be calculated taking account of tension stiffening in cracked concrete. In the absence of a more accurate method, Bs may be calculated as given in 5.3.4.
6 Shear connection in beams for buildings 6.1 General 6.1.1 Basis of design 1) Shear connectors and transverse reinforcement shall be provided throughout the length of the beam to transmit the longitudinal shear force between the concrete slab and the steel beam for the ultimate limit state, ignoring the effect of natural bond between the two. 2) The number of connectors shall be at least equal to the design shear force, determined according to 6.2, divided by the design resistance of a connector, PRd, determined according to 6.3 or 6.5. 3) If all cross-sections are in Class 1 or Class 2, partial shear connection may be used, if the design ultimate loading is less than that which could be carried by the member if full shear confection were provided. The number of connectors shall then be determined by a partial connection theory taking into account the deformation capacity of the shear connectors. 4) Shear connectors shall be capable of providing resistance to uplift of the concrete slab. 5) To prevent uplift of the slab, shear connectors should be designed for a nominal tensile force, perpendicular to the plane of the steel flange, of at least 0.1 times the design shear resistance of the connectors. If necessary they should be supplemented by anchoring devices. 6) Headed stud shear connectors in accordance with 6.3.2 and 6.4.2 or 6.3.3 and 6.4.3 may be assumed to provide sufficient resistance to uplift, unless the shear connection is subjected to direct tension. 7) Longitudinal shear failure are splitting of the concrete slab due to concentrated forces applied by the connectors shall be prevented. 8) If the detailing of the shear connection is in accordance with 6.4 and the transverse reinforcement is in accordance with 6.6, it may be assumed that longitudinal shear failure and splitting is prevented. 9) Methods of interconnection, other than the shear connectors covered in this chapter, may be used to effect the transfer of longitudinal forces between a steel member and the slab, provided the adequacy with regard to behaviour and strength is demonstrated by tests and supported by a conceptual model. Depending on the type of shear connector, reference shall be made to European Standards or European Technical Approvals or, in their absence, to national documents. The design of the composite beam shall conform to be design of a similar member employing either studs or other shear connectors as included in this code, in so far as practicable 6.1.2 Deformation capacity of shear connectors 1) Ductile connectors are those with sufficient deformation capacity to justify the assumption of ideal plastic behaviour of the shear connection in the structure considered. 2) Headed studs with an overall length after welding not less than 4 times the diameter, and with a shank of diameter not less than 16 mm and not exceeding 22 mm, may be considered as ductile within the following limits for the degree of shear connection, which is defined by the ratio N/Nf. © BSI 05-2000
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For steel sections with equal flanges: Lk5
(6.1)
5 k L k 25
(6.2)
L U 25
(6.3)
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For steel sections having a bottom flange with an area not exceeding 3 times the area of the upper flange:
L k 20
L U 20
where
L Nf N
(6.4)
is the span in metres, is the number of shear connectors determined for the relevant length of beam in accordance with 6.2.1.1, and is the number of shear connectors provided within the same length of beam.
3) The following shear connectors may be considered as having the same deformation capacity as headed studs with the dimensions given in 2): a) friction grip bolts designed in accordance with 6.5; b) other connections having a characteristic slip capacity of not less than 6 mm at the characteristic resistance, determined from push tests in accordance with 10.2. 4) Headed stud connectors may be considered as ductile over a wider range of spans than given in 2) above where: a) the studs have an overall length after welding not less than 76 mm, and a shank of diameter not less than 19 mm and not exceeding 20 mm; b) the steel section is a rolled I or H with equal flanges; c) the concrete slab is composite with profiled steel sheeting that spans perpendicular to the beam and is continuous across it; d) there is one stud per rib of sheeting, placed centrally within the rib; e) for the sheeting, bo/hp U 2 and hp k 60 mm, where the notation is as in 6.3.3.1; f) the force Fc is calculated by the method of 6.2.1.2 3).
Where these conditions are satisfied, the ratio N/Nf should satisfy: L k 10 10 k L k 25
L U 25
(6.5)
where L, N, and Nf are as defined in 6.1.2 2). 72
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6.1.3 Spacing of shear connectors 1) The shear connectors shall be spaced along the beam so as to transmit longitudinal shear and to prevent separation between the concrete slab and the steel beam, considering an appropriate distribution of design longitudinal shear force. 2) In cantilevers and negative moment regions of continuous beams, the shear connectors shall be spaced to suit the curtailment of tension reinforcement, ignoring the anchorage length of curtailed bars. 3) Stud connectors in accordance with 6.3.2 and 6.3.3 may be spaced uniformly over a length Lcr between adjacent critical cross-sections as defined in 4.1.2 provided that: — all critical sections in the span considered are in Class 1 or Class 2, — N/Nf satisfies the limit given by 6.1.2, when L is replaced by Lcr, and — the plastic resistance moment of the composite section does not exceed 2.5 times the plastic resistance moment of the steel member alone. 4) If the plastic resistance moment exceeds 2.5 times the plastic resistance moment of the steel member alone, additional checks on the adequacy of the shear connection should be made at intermediate points approximately mid-way between adjacent critical cross-sections. 5) The required number of shear connectors may be distributed between a point of maximum sagging bending moment and an adjacent support or point of maximum hogging moment, in accordance with the longitudinal shear calculated by elastic theory for the loading considered. Where this is done, no additional checks on the adequacy of the shear connection are required, unless the method of 4.4.4 7) for shear buckling resistance of a web is used.
6.2 Longitudinal shear force 6.2.1 Beams in which plastic theory is used for resistance of cross sections 6.2.1.1 Full shear connection 1) For full shear connection, the total design longitudinal shear V= to be resisted by shear connectors spaced in accordance with 6.1.3 between the point of maximum sagging bending moment and a simple end support shall be: V= = Fcf
(6.6)
where
or whichever is the smaller, and Aa Ac Ase
is the area of structural steel, is the effective area of concrete, defined in 4.2.1 and 4.2.2, excluding any web encasement, is the area of any longitudinal reinforcement in compression that is included in the calculation of the bending resistance,
and these areas relate to the cross-section at the point of maximum sagging bending moment.
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2) For full shear connection, the total design longitudinal shear V= to be resisted by shear connectors spaced in accordance with 6.1.3 between the point of maximum sagging bending moment and an intermediate support or a restrained end support shall be (6.7) where
As is the effective area of longitudinal slab reinforcement Aap is the effective area of any profiled steel sheeting, used in accordance with 4.2.1 4),
and these areas relate to the cross section at the support, and Fcf is as defined in 1) above, and is taken as zero for a cantilever.
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6.2.1.2 Partial shear connection with ductile connectors 1) If the connectors are ductile as defined in 6.1.2, it may be assumed that sufficient slip can occur at the ultimate limit state for moments of resistance at critical sections to be calculated from plastic theory in accordance with 4.4.1.3. 2) In the absence of a more rigorous calculation the longitudinal shear V= may be taken as: V= = Fc
(6.8)
between the considered cross-section with a sagging bending moment and a simple end support; and (6.9) between the considered cross-section with a sagging bending moment and an intermediate support or a restrained end support; where Fc
is the compressive force in the concrete flange necessary to resist the design sagging bending moment MSd, calculated from plastic theory in accordance with 4.4.1.3, and the other symbols are as in 6.2.1.1.
The relation between Fc and MSd is qualitatively given by the curve ABC in Figure 6.1.
Figure 6.1 — Relation between Fc and MSd
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3) For the method given in 2) a conservative value for Fc may alternatively be determined by the straight line AC in Figure 6.1 (6.10) where Mapl.Rd and Mpl.Rd are the design plastic resistances to sagging bending of the structural steel section alone, and of the composite section with full shear connection, respectively.
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6.2.1.3 Partial shear connection with non-ductile connectors 1) If the shear connectors are not ductile as defined in 6.1.2 the longitudinal shear shall be determined from stress distributions at the critical cross-sections based on full continuity at the interface between steel and concrete. 2) The total design longitudinal shear V= may be determined with the simplified method given in 6.2.1.2 except that Fc is determined from:
where
Me=.Rd Ma.Sd Fe=
for MSd k Me=.Rd
(6.11)
for Me=.Rd k MSd < Mp=.Rd
(6.12)
is the moment that causes a tensile stress fy/*a in the extreme bottom fibre of the steel section; where unpropped construction is used 4.4.1.4 4) is applicable, is the sagging moment acting in the steel section due to actions on the structural steelwork alone before the composite action becomes effective, is the compressive force in the concrete slab at moment Me=:Rd.
a) Structures which are not fully supported during construction
b) Structures which are fully supported during construction
Figure 6.2 — Relations between Fc and MSd 6.2.2 Beams in which elastic theory is used for resistances of one or more cross sections If elastic theory is applied to cross sections in accordance with 4.4.1.4, the longitudinal shear per unit length shall be calculated by elastic theory from the vertical shear force added after the shear connection has become effective. The elastic properties of the cross section shall be those used in the calculation of the longitudinal stresses.
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6.3 Design resistance of shear connectors 6.3.1 General 1) Where the concrete slab is unhaunched, or the haunch satisfies 6.3.3.1 or 6.4.1.4, the design resistance of shear connectors embedded in normal-density or lightweight-aggregate concrete (density greater than 1 750 kg/m3) should be calculated from the equations given in this Section. 2) Where the concrete density or haunch dimensions do not satisfy the conditions in 1) above, or where other types of shear connectors are employed than covered in this Section, in the absence of a European Technical Approval the design resistance should be determined in accordance with 3.5.2 using the characteristic resistance determined from push tests in accordance with 10.2. (Note: All references to the length of the stud refer to the length after welding). 6.3.2 Stud connectors in solid slabs
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6.3.2.1 Headed studs — shear resistance The design shear resistance of an automatically welded headed stud with a normal weld collar, should be determined from PRd = 0.8 fu(;d2/4)/*É
(6.13)
or (6.14) whichever is smaller, where
d fu
is the diameter of the shank of the stud; is the specified ultimate tensile strength of the material of the stud but not greater than 500 N/mm2; fck is the characteristic cylinder strength of the concrete at the age considered; Ecm is the mean value of the secant modulus of the concrete in accordance with 3.1.4.1; ! = 0.2 [(h/d) + 1] for 3 k h/d k 4; != 1 for h/d > 4, and h is the overall height of the stud.
The partial safety factor *5 should be taken as for the ultimate limit state. These formulae may not be used for studs of diameter greater than 22 mm. [ENV Note: Minimum dimensions for a normal weld collar and specifications for welding should be given in Reference Standards for stud shear connectors to be prepared by CEN. DIN 32500-3 and DIN 8563-10 can be used as a basis. In the absence of a European Standard a normal weld collar should comply with the following requirements: — the weld should have a regular form and be fused to the shank of the stud. — the diameter should be not less than 1.25d, — the mean height should be not less than 0.20d and the minimum height not less than 0.15d.] 6.3.2.2 Influence of tension on shear resistance Where headed stud connectors are subjected to direct tensile force in addition to shear, the design tensile force per stud Ften should be calculated. If Ften k 0.1 PRd, where PRd is the design shear resistance defined in 6.3.2.1, the tensile force may be neglected. If Ften > 0.1 PRd, the connection is not within the scope of this Part 1.1 of Eurocode 4. 6.3.2.3 Studs without head — shear resistance Equations (6.13) and (6.14) may be used for studs without heads, provided uplift of the slab is prevented. The ties which resist uplift should be designed for the ultimate limit state in accordance with 6.1.1 5).
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6.3.3 Headed studs used with profiled steel sheeting 6.3.3.1 Sheeting with ribs parallel to the supporting beams
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
The studs are located within a region of concrete that has the shape of a haunch (Figure 6.3). Where the sheeting is continuous across the beam, the width of the haunch, bo, is equal to the width of the trough as given in Figure 7.2. Where the sheeting is not continuous, bo is defined in a similar way as given in Figure 6.3. The depth of the haunch should be taken as hp, the overall depth of the sheeting excluding embossments.
Figure 6.3 — Beam with profiled steel sheeting parallel to the beam The design shear resistance should be taken as their resistance in a solid slab (see 6.3.2.1) multiplied by the reduction factor k= given by the following expression: k= = 0.6 (bo/hp) [(h/hp) – 1] k 1.0
(6.15)
where h is the overall height of the stud, but not greater than hp + 75 mm. 6.3.3.2 Sheeting with ribs transverse to the supporting beams 1) Where studs of diameter not exceeding 20 mm are placed in ribs with a height hp not exceeding 85 mm and a width bo not less than hp, the design shear resistance should be taken as their resistance in a solid slab (calculated as given by 6.3.2.1, except that fu should not be taken as greater than 450 N/mm2) multiplied by the reduction factor kt given by the following expression: (6.16) where Nr is the number of stud connectors in one rib at a beam intersection, not to exceed 2 in computations, and other symbols are as defined in 6.3.3.1. For studs welded through the steel sheeting, kt should not be taken greater than 1.0 when Nr = 1 and not greater than 0.8 when Nr U 2. 2) For the other cases not within the scope of 1), the design resistance should be determined from tests in accordance with 10.2. 6.3.3.3 Biaxial loading of shear connectors Where the shear connectors are provided to produce composite action both for the beam and for the composite slab, the combination of forces acting on the stud should satisfy the following: (6.17)
where
F=
is the design longitudinal force caused by composite action in the beam, and
Ft
is the design transverse force caused by composite action in the slab (Chapter 7).
6.3.4 Block connectors in solid slabs 1) Connectors may be designed as block connectors if the front is not wedge shaped and is so stiff that it can reasonably be assumed that at failure the pressure on the concrete in front of the connector is uniformly distributed. © BSI 05-2000
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2) Bar, T–, [– and horseshoe connectors may be designed as block connectors if the detailing provisions in 6.4.4 are satisfied.
Figure 6.4 — Block connectors 3) The design resistance of a block connector should be determined from PRd = ½ Af1fck/*c where
Af1 ) Af2
*c
(6.18)
is the area of the front surface, as shown in Figure 6.4; is equal to but not greater than 2.5 for normal density concrete or 2.0 for lightweight aggregate concrete; is the area of the front surface of the connector enlarged at a slope of 1 : 5 to the rear surface of the adjacent connector (Figure 6.5). Only the parts of Af2 falling within the concrete section may be taken into account; is the partial safety factor for concrete in accordance with 2.3.3.2.
Figure 6.5 — Definition of Af2 4) In the design of the welds fastening the block connector to the steel beam the eccentricity of the force shall be taken into account. 5) The welds should be designed in accordance with Section 6.6 of EC3 for 1.2 PRd. 6) Ties to prevent uplift shall be designed in accordance with 6.1.1.
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6.3.5 Anchors and hoops in solid slabs
Figure 6.6 — Example of anchor and hoop
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1) The design resistance to longitudinal shear for each leg of anchors and hoops should be determined from (6.19) where As ! "
is the cross-sectional area of the anchor or the hoop, is the angle between the anchor bar or the hoop and the plane of the flange of the beam, is the angle in the horizontal plane between the anchor bar and the longitudinal axis of the beam for anchors set at a splay, fyd is the design strength of the material of the bar, to be taken as fy/*a or fsk/*s whichever is applicable, *a, *s are the partial safety factors for structural steel and reinforcement in accordance with 2.3.3.2.
6.3.6 Block connectors with anchors or hoops in solid slabs
Figure 6.7 — Example of combination of block connector with anchor and hoop 1) Block connectors may be assumed to share load with anchors or hoops, provided due account is taken of the differences of stiffness of the block connector and the anchors or the hoop. 2) In the absence of more accurate calculations or tests, the design resistance of the combination should be determined from one of the following expressions, whichever is applicable PRd comb = PRd block + 0.5 PRd anchors PRd comb = PRd block + 0.7 PRd hoop
(6.20) (6.21)
3) The welds fastening the block connector with anchors or hoop to the steel beam should be designed for 1.2 PRd for the block plus PRd for each anchor or the hoop.
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6.3.7 Angle connectors in solid slabs
Figure 6.8 — Angle connector 1) The design resistance of an angle connector welded to the steel beam as shown in Figure 6.8 should be determined from PRd = 10 bh3/4 fck2/3/*5 where PRd b h fck
(6.22)
is in Newtons is the length of the angle in mm, is the width of the upstanding leg of the angle in mm, is the characteristic strength of concrete in N/mm2.
The partial safety factor *5 should be taken as for the ultimate limit state. 2) In the design of the welds fastening the angle to the steel beam the eccentricity of the force should be akin as e = h/4. 3) The welds should be designed in accordance with Section 6.6 of EC3 for 1.2 PRd. 4) The reinforcement used to prevent uplift should be determined from: Aefsk/*s U 0.1 PRd (6.23) where Ae fsk *s
is the cross-sectional area of the bar, ;:2/4 is the characteristic yield strength of the reinforcement, the partial safety factor for reinforcement in accordance with 2.3.3.2.
6.4 Detailing of the shear connection 6.4.1 General recommendations 6.4.1.1 Resistance to separation The surface of a connector that resists separation forces (that is, the inside of a hoop or the underside of the head of a stud) shall extend not less than 30 mm clear above the bottom reinforcement.
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6.4.1.2 Cover and compaction of concrete 1) The detailing of shear connectors shall be such that concrete can be adequately compacted around the base of the connector. 2) If cover over the connector is required, it should be a) not less than 20 mm, or b) as specified by EC2 for reinforcement, less 5 mm, whichever is greater 3) If cover is not required the top of the connector may be flush with the upper surface of the concrete slab.
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
6.4.1.3 Local reinforcement in the slab 1) Where the shear connection is adjacent to a longitudinal edge of a concrete slab, transverse reinforcement provided in accordance with 6.6 shall be fully anchored in the concrete between the edge of the slab and the adjacent row of connectors (see 6.6.5). 2) At the end of a composite cantilever, sufficient local reinforcement shall be provided to transfer forces from the shear connectors to the longitudinal reinforcement. 6.4.1.4 Haunches other than formed by profiled steel sheeting 1) Where a concrete haunch is used between the steel girder and the soffit of the concrete slab, the sides of the haunch should lie outside a line drawn at 45° from the outside edge of the connector (Figure 6.9). 2) The concrete cover from the side of the haunch to the connector should be not less than 50 mm. 3) Transverse reinforcing bars sufficient to satisfy the requirements of 6.6 should be provided in the haunch at least 40 mm clear below the surface of the connector that resists uplift.
Figure 6.9 — Dimensions of haunches 6.4.1.5 Spacing of connectors 1) Where it is assumed in design that the stability of either the steel or the concrete member is ensured by the connection between the two, the spacing of the shear connectors shall be sufficiently close for this assumption to be valid. 2) Where a steel compression flange, that would otherwise be in a lower class, is assumed to be in Class 1 or Class 2 because of restraint from shear connectors, the centre-to-centre spacing of the shear connectors in the direction of compression should not exceed the following limits: — where the slab is in contact over the full length (e.g. solid slab)
— where the slab is not in contact over the full length (e.g. slab with ribs transverse to the beam)
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The clear distance from the edge of a compression flange to the nearest line of shear connectors should not exceed
where t fy
is the thickness of the flange, and is the nominal yield strength of the flange in N/mm2 units.
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
3) The maximum longitudinal centre-to-centre spacing of shear connectors should not exceed 6 times the total slab thickness nor 800 mm. 4) Alternatively, connectors may be placed in groups, with the spacing of groups greater than that specified for individual connectors, provided that consideration is given in design to the non-uniform flow of longitudinal shear, to the greater possibility of slip and vertical separation between the slab and the steel member, and to buckling of the steel flange. 6.4.1.6 Dimensions of the steel flange 1) The thickness of the steel plate or flange to which a connector is welded shall be sufficient to allow proper welding and proper transfer of load from the connector to the plate without local failure or excessive deformation. [For studs see 6.4.2 4).] 2) The distance between the edge of a connector and the edge of the flange of the beam to which it is welded should be not less than 20 mm (Figure 6.9). 6.4.2 Stud connectors 1) The overall height of a stud should be not less than 3d, where d is the diameter of the shank. 2) A stud connector should have a head in accordance with 3.5.2 7) or be provided with ties to resist separation forces in accordance with 6.1.1. 3) The spacing of studs in the direction of the shear force should be not less than 5d; the spacing in the direction transverse to the shear force should be not less than 2.5d in solid slabs and 4d in other cases. 4) Except when the studs are located directly over the web, the diameter of a welded stud should not exceed 2.5 times the thickness of that part to which it is welded, unless test information is provided to establish the resistance of the stud as shear connector. 6.4.3 Headed studs used with profiled steel sheeting 6.4.3.1 General 1) Studs may be welded through the steel sheeting provided that it is shown by procedure trials that the quality can be consistently achieved. Otherwise, holes for placing studs shall be made through the sheets as necessary. 2) It is possible to weld through a profiled steel sheet overlapping an edge trim. The sheets should be in close contact and the total thickness of the sheeting should not exceed 1.25 mm if galvanised or 1.5 mm if not galvanised. The maximum thickness of galvanising should not exceed 30 microns on each sheet face. (Note. Welding through two galvanised profiled steel sheets is not recommended.) 3) After installation, the connectors should extend not less than 2d above the top of the steel deck, where d is the diameter of the shank. 4) The minimum width of the troughs that are to be filled with concrete should be not less than 50 mm. 6.4.3.2 Sheeting with ribs transverse to the supporting beam 1) The profiled steel sheeting should be anchored in each trough to each steel beam designed for composite action. Such anchorage may be provided by stud connectors, a combination of stud connectors and arc spot (puddle) welds, or other devices specified by the designer. 2) When the sheeting is such that studs cannot be placed centrally within a trough, they should be placed in accordance with 9.4.3.1 4).
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6.4.4 Block connectors 1) The height of a bar connector should not exceed 4 times the thickness. 2) A T-connector should be a hot rolled section or part of it with a flange width not exceeding 10 times the flange thickness. The height of a T-connector should not exceed 10 times the flange thickness nor 150 mm. 3) A [-connector should be a hot rolled section with a web width not exceeding 25 times the web thickness. The height of a [-connector should not exceed 15 times the web thickness nor 150 mm. 4) The height of a horseshoe should not exceed 20 times the web thickness nor 150 mm.
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
6.4.5 Anchors and hoops 1) The anchorage length and the concrete cover shall be in accordance with clause 5.2.3 of EC2. 2) A hoop may be assumed to be sufficiently anchored when the following conditions are met: r W 7.5 Î, = W 4r, and concrete cover W 3 Î, where the symbols are as shown in Figure 6.10.
Figure 6.10 — Hoop connector 3) The anchors and hoops designed for longitudinal shear should point in the direction of thrust. Where thrust can occur in both directions, connectors pointing in both directions should be provided. 6.4.6 Angle connectors 1) The height h of the upstanding leg of an angle connector should not exceed 10 times the thickness nor 150 mm. 2) The length b of an angle connector should not exceed 300 mm unless the resistance is determined by testing in accordance with Chapter 10.
6.5 Friction grip bolts 6.5.1 General 1) High strength friction grip bolts may be used to provide a shear connection between a steel member and a precast concrete slab forming a composite beam. An example is shown in Figure 6.11. 2) Unless otherwise stated clauses 6.5.3, 6.5.8 and 7.5.6 of EC3 on slip-resistant connections apply.
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Figure 6.11 — Example for shear connections with friction-grip bolts 6.5.2 Ultimate limit state 6.5.2.1 Design friction resistance 1) The design friction resistance per bolt should be taken as PRd = 4Fpr.Cd/*v
(6.24)
where Fpr.Cd 4
is the preloading force in the bolt, based on Fp.Cd given by clause 6.5.8.2 of EC3, reduced to take account of the effects of creep and shrinkage of the concrete; is the coefficient of friction, which may be taken as 0.50 for steel flanges not less than 10 mm thick and 0.55 for steel flanges not less than 15 mm thick, blasted with shot or grit, with loose rust removed and no pitting;
*É
is the partial safety factor, to be taken as
.
2) The reduction in the preloading force in the bolt due to creep and shrinkage of the concrete should either be determined by long-term tests, or should be assumed to be not less than 40 % of Fp.Cd. The loss of the preloading force can be reduced by re-tightening after an interval of time. 3) For other friction surfaces, the value of 4 should be determined by suitable testing in accordance with the appropriate standard in force. 6.5.2.2 Deign resistance of a bolt in shear and bearing Where the shear resistance is assumed to be developed by the resistance of the bolts alone in shear and bearing, the maximum design longitudinal shear per bolt should not exceed the design shear resistance of a bolt, determined in accordance with clause 6.5.5 of EC3, nor the bearing resistance, which may be taken equal to PRd determined with equation (6.14) in this code. 6.5.2.3 Combined resistance Where the shear resistance is assumed to be developed by a combination of friction and shear, the combined shear resistance should be established by suitable testing. 6.5.2.4 Effects of slip The effects of slip may be neglected for verifications at the ultimate limit state in beams with cross-sections in Class 1 and 2 and holes with a clearance not exceeding 3 mm. 6.5.3 Serviceability limit state 1) Slip shall be limited to a level such that the Principles of Chapter 5 are fulfilled. 2) The slip may be ignored, if the longitudinal design shear per bolt does not exceed the longitudinal shear resistance per bolt PRd developed by friction alone, as given by equation (6.24) but with *É = 1.0.
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6.5.4 Detailing of friction grip bolts 1) The design of the connection shall ensure that the bearing stress between the steel beam and the concrete flange is not excessive. 2) The washer under the head of each bolt shall be of sufficient stiffness to ensure that the bearing stress on the concrete is not excessive. 3) Adequate reinforcement, in spiral or other form, should be provided to ensure that the load is transferred from the bolt to the interface without local splitting or crushing of the concrete, unless tests show it to be unnecessary. The rules for local load introduction given in clause 2.5.3.7.4 of Eurocode 2 apply.
6.6 Transverse reinforcement
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6.6.1 Longitudinal shear in the slab 1) Transverse reinforcement in the slab shall be designed for the ultimate limit state so that premature longitudinal shear failure or longitudinal splitting is prevented. 2) The design longitudinal shear per unit length for any potential surface of longitudinal shear failure within the slab vSd shall not exceed the design resistance to longitudinal shear vRd of the shear surface considered.
Figure 6.12 — Typical potential surfaces of shear failure The length of the shear surface b-b shown in Figure 6.12 should be taken as equal to 2h plus the head diameter for a single row of stud shear connectors or staggered stud connectors, or as equal to 2h + st plus the head diameter for stud shear connectors arranged in pairs, where h is the height of the studs and st is the transverse spacing centre-to-centre of the studs. 3) Where profiled steel sheeting is used transverse to the beam it is not necessary to consider shear surfaces of type b-b, provided that the design resistances of the studs are determined using the appropriate reduction factor kt as given in 6.3.3.2. 4) The design longitudinal shear per unit length of beam in a shear surface vSd shall be determined in accordance with 6.2 and be consistent with the design of the shear connectors for the ultimate limit state. 5) In determining ÉSd account may be taken of the variation of longitudinal shear across the width of the concrete flange. © BSI 05-2000
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6.6.2 Design resistance to longitudinal shear 1) The design resistance of the concrete flange (shear planes a-a illustrated in Figure 6.12) shall be determined in accordance with the principles in clause 4.3.2.5 of EC2. Profiled steel sheeting with ribs transverse to the steel beam may be assumed to contribute to resistance to longitudinal shear, if it is continuous across the top flange of the steel beam or if it is welded to the steel beam by stud shear connectors. 2) In the absence of a more accurate calculation the design resistance of any surface of potential shear failure in the flange or a haunch should be determined from: ÉRd = 2.5 AcÉ) ERd + Ae fsk/*s + Épd
(6.25)
or
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
(6.26) whichever is smaller, where ERd fck fsk ) = ) = AcÉ Ae
Épd
is the basic shear strength to be taken as 0.25 fctk 0.05/*c, is the characteristic cylinder strength of the concrete in N/mm2 units, is the characteristic yield strength of the reinforcement, 1 for normal-weight concrete, 0.3 + 0.7(@/24) for lightweight-aggregate concrete of unit weight @ in kN/m3, is the mean cross-sectional area per unit length of beam of the concrete shear surface under consideration, is the sum of the cross-sectional areas of transverse reinforcement (assumed to be perpendicular to the beam) per unit length of beam crossing the shear surface under consideration (Figure 6.12) including any reinforcement provided for bending of the slab, is the contribution of the steel sheeting, if applicable, as given in 6.6.3.
3) For a ribbed slab the area of concrete shear surface AcÉ should be determined taking into account of the effect of the ribs. Where the ribs run transverse to the span of the beam, the concrete within the depth of the ribs may be included in the value of AcÉ in equation (6.25); but for potential shear surfaces of type e-e in Figure 6.12, it should not be included in AcÉ in equation (6.26). 4) Transverse reinforcement taken into account for resistance to longitudinal shear shall be anchored so as to develop its yield strength in accordance with EC2. 5) Anchorage may be provided by means of U-bars looped around the shear connectors. 6.6.3 Contribution of profiled steel sheeting 1) Where the profiled steel sheets are continuous across the top flange of the steel beam, the contribution of profiled steel sheeting with ribs transverse to the beam should be taken as (6.27) where
86
Épd is per unit length of the beam for each intersection of the shear surface by the sheeting, Ap is the cross-sectional area of the profiled steel sheeting per unit length of the beam, and fyp is its yield strength, given in 3.4.2.
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2) Where the profiled steel sheeting with ribs transverse to the beam is discontinuous across the top flange of the steel beam, and stud shear connectors are welded to the steel beam directly through the profiled steel sheets, the contribution of the profiled steel sheeting should be taken as
where
Ppb.Rd
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
s
is the design bearing resistance of a headed stud welded through the sheet according to 7.6.1.4, and is the longitudinal spacing centre-to-centre of the studs.
Figure 6.13 — Potential shear surfaces in a slab with profiled steel sheeting 6.6.4 Minimum transverse reinforcement 6.6.4.1 Solid slabs The area of reinforcement in a solid slab should be not less than 0.002 times the concrete area being reinforced and should be uniformly distributed. 6.6.4.2 Ribbed slabs 1) Where the ribs are parallel to the beam span, the area of transverse reinforcement should be not less than 0.002 times the concrete cover slab area in the longitudinal direction and should be uniformly distributed. 2) Where the ribs are transverse to the beam span the area of transverse reinforcement should be not less than 0.002 times the concrete slab area in the longitudinal direction and should be uniformly distributed. Profiled steel sheets continuous across the top flange of the steel beam may be assumed to contribute to this requirement. 6.6.5 Longitudinal splitting To prevent longitudinal splitting of the concrete flange caused by the shear connectors, the following additional recommendations should be applied in all composite beams where the distance from the edge of the concrete flange to the centreline of the nearest row of shear connectors is less than 300 mm: a) Transverse reinforcement should be supplied by U-bars passing around the shear connectors. These U-bars should be located below the top of the shear connectors. b) Where headed studs are used as shear connectors, the distance from the edge of the concrete flange to the centre of the nearest studs should not be less than 6d, where d is the nominal diameter of the stud, and the U-bars should be not less than 0.5d in diameter. c) The U-bars should be placed as low as possible while still providing sufficient bottom cover. (Note: These conditions normally apply to edge beams but may also occur adjacent to large openings.)
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7 Composite slabs with profiled steel sheeting for buildings 7.1 General
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7.1.1 Scope 1) This Chapter deals with composite floor slabs spanning only in the direction of the ribs. It applies to designs for building structures where the imposed loads are predominantly static, including industrial buildings where floors may be subject to moving loads. For structures where the imposed load is largely repetitive or applied abruptly in such a manner as to produce dynamic effects, composite slabs are permitted, but special care shall be taken over the detailed design to ensure that the composite action does rot deteriorate in service. Slabs subject to seismic loading are not excluded, provided an appropriate design method for the seismic conditions is defined for the particular project or is given in another Eurocode. 2) In the sagging moment regions additional reinforcement, including any provided for fire resistance, may be taken into account for the resistance of composite slabs. Application rules for the calculation of the contribution of reinforcement to the resistance are only given for the partial connection method in Annex E. 3) Composite slabs may be used to provide lateral restraint to the steel beams and to act as a diaphragm to resist wind action, but no specific rules are given. The length/width ratio, effect of openings and the additional forces on the shear connectors shall be considered. For diaphragm action of the profiled steel sheeting while it is acting as formwork the rules given in Part 1.3 of Eurocode 3 apply. 4) The testing procedure recommended in 10.3.2 may be used to justify a composite slab which is outside the scope of Chapter 7. 7.1.2 Definitions 7.1.2.1 Composite slab A composite slab is one in which profiled steel sheets are used as permanent shuttering capable of supporting the wet concrete, reinforcement and construction loads. Subsequently, the profiled steel sheets combine structurally with the hardened concrete and act as part or all of the tensile reinforcement in the finished floor. 7.1.2.2 Composite behaviour Composite behaviour is that which occurs after a floor slab comprising profiled steel sheet, plus any additional reinforcement, and hardened concrete have combined to form a single structural element. The profiled steel sheet shall be capable of transmitting horizontal shear at the interface between the sheet and the concrete; pure bond between steel sheeting and concrete is not considered effective for composite action. Composite behaviour between profiled sheeting and concrete shall be ensured by one or more of the following means (see Figure 7.1): a) mechanical interlock provided by deformations in the profile (indentations or embossments); b) frictional interlock for profiles shaped in a re-entrant form; c) end anchorage provided by welded studs or another type of local connection between the concrete and the steel sheet, only in combination with a) or b); d) end anchorage by deformation of the ribs at the end of the sheeting, only in combination with b). Other means are not excluded but are not within the scope of this Eurocode.
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Figure 7.1 — Typical forms of interlock in composite slabs
7.2 Detailing provisions 7.2.1 Slab thickness and reinforcement 1) The overall depth of the composite slab h shall be not less than 80 mm. The thickness of concrete, hc, above the main flat surface of the top of the ribs of the sheeting shall be not less than 40 mm. 2) If the slab is acting compositely with the beam or is used as a diaphragm, the total depth shall be not less than 90 mm and hc shall be not less than 50 mm. 3) Where reinforcement is required to be placed within the depth hc of the concrete, the maximum spacing of the bars should be in accordance with clause 5.4.3.2.1 of EC2, based on the overall depth h of the composite slab, unless closer spacing is required for the control of cracking (Section 5.3). 7.2.2 Aggregate The nominal size of the aggregate depends on the smallest dimension in the structural element within which concrete is poured, and shall not exceed the least of: a) 0.40 hc (see Figure 7.2); b) bo/3, where bo is the mean width of the ribs (minimum width for re-entrant profiles) (see Figure 7.2); c) 31.5 mm (sieve C 31.5).
Figure 7.2 — Sheet and slab dimensions 7.2.3 Bearing requirements 1) Bearing at temporary supports of profiled steel sheeting as shuttering shall be checked in accordance with Part 1.3 of Eurocode 3. 2) Composite slabs bearing on steel or concrete should have a minimum bearing of 75 mm with a minimum end bearing of 50 mm for the profiled steel sheeting [see Figure 7.3(a) and Figure 7.3(c)]. 3) For composite slabs bearing on other materials these values should be increased to a minimum of 100 mm and 70 mm respectively [see Figure 7.3(b) and Figure 7.3(d)].
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4) For overlapping and continuous sheets bearing on steel or concrete, the minimum bearing should be 75 mm and for other materials 100 mm [see Figure 7.3(e) and Figure 7.3(f)]. 5) The minimum bearings given above may be reduced, if speckled in the project specifications and provided the design takes into account relevant factors such as tolerances, loading, span, height of support and provision of continuity reinforcement. When reduced bearings are used, precautions should be taken that fastening of the sheet can still be achieved without damage to the bearings, and that collapse cannot occur as a result of accidental displacement during erection.
Figure 7.3 — Minimum bearing lengths
7.3 Actions and action effects 7.3.1 Design situations All relevant design situations and limit states shall be considered in design so as to ensure an adequate degree of safety and serviceability. The following situations are considered in this code. i) Profiled steel sheeting as shuttering Verification is required for the behaviour of the profiled steel sheeting while it is acting as formwork for the wet concrete. Account shall be taken of the effect of props, if any. ii) Composite slab Verification is required for the floor slab after composite behaviour has commenced and any props have been removed. 7.3.2 Actions 7.3.2.1 Profiled steel sheet as shuttering 1) The following loads shall be taken into account in calculation for the steel deck as shuttering: — weight of concrete and steel deck; — construction loads including local heaping of concrete during construction; — storage load, if any; — “ponding” effect (increased depth of concrete due to deflection of the sheeting). [Note: Until sufficient information is given in Eurocode 1, the following rules apply.]
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2) The construction loads represent the weight of operatives and concreting plant and take into account any impact or vibration which may occur during construction. In any area of 3 m by 3 m (or the span length, if less), in addition to the weight of the concrete, the characteristic construction load and weight of surplus concrete should together be taken as 1.5 kN/m2. Over the remaining area a characteristic loading of 0.75 kN/m2 should be added to the weight of concrete. These loads should be placed to cause the maximum bending moment and/or shear.
Figure 7.4 — Loads on profiled sheeting 3) These minimum values are not necessarily sufficient for excessive impact or heaping of concrete, or pipeline or pumping loads. If appropriate, provision should be made in design for the additional loading. Without the concrete the sheet should be shown by test or calculation to be able to resist a characteristic load of 1 kN on a square area of side 300 mm, in the most unfavourable place, at any location except a rib adjacent to a free edge. 4) If the central deflection $ of the sheeting under its own weight plus that of the wet concrete, calculated for serviceability, is less than =/250 and less than 20 mm, the ponding effect may be ignored in the design of the steel sheeting. If either of these limits is exceeded, this effect should be allowed for; for example by assuming in design that the nominal thickness of the concrete is increased over the whole span by 0.7$. 7.3.2.2 Composite slab In design checks for the ultimate limit state it may be assumed that the whole of the loading acts on the composite slab, provided this assumption is also made in design for longitudinal shear. 7.3.3 Load combinations load cases 1) The loads shall be applied in whatever realistic combination is most unfavourable for the effect under consideration 2) The load arrangements given in 2.2.5 5) should be considered.
7.4 Analysis for internal forces and moments 7.4.1 Profiled steel sheeting as shuttering 1) Elastic analysis shall be used. Where sheeting is considered as continuous, flexural stiffness may be determined without consideration of the variation of stiffness due to parts of the cross-section in compression not being fully effective. 2) Where shuttering is assumed to provide lateral bracing, the appropriate rules in Part 1.3 of Eurocode 3 apply, it may be assumed that the effectiveness of the lateral restraint is not impaired when the shuttering carries wet concrete. 7.4.2 Composite slab 7.4.2.1 Analysis 1) The following methods of analysis may be used: a) linear analysis with or without redistribution; b) rigid-plastic global analysis based either on the kinematic method (upper bound) or on the static method (lower bound) provided that it is shown that sections where plastic rotations are required have sufficient rotation capacity;, c) elastic-plastic analysis taking into account the non-linear material properties. 2) The application of linear methods of analysis is suitable for the serviceability limit states as well as for the ultimate limit states. Plastic methods, with their high degree of simplification, shall only be used in the ultimate limit state.
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3) If the effects of cracking of concrete are neglected in the analysis, the bending moments at internal supports may optionally be reduced by up to 30 %, and corresponding increases made to the sagging bending moments in the adjacent spans. 4) A continuous slab may be designed as a series of simply supported spans. Nominal reinforcement in accordance with 7.6.2.1 should be provided over intermediate supports. 5) Plastic analysis without any direct check on rotation capacity may be used for the ultimate limit state if reinforcing steel of class H in accordance with clause 3.2.2 of EC2 is used and the span is less than 3.0 m. 7.4.2.2 Effective width for concentrated point and line loads
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
1) Where concentrated point or line loads parallel to the span of the slab are to be supported by the slab, they may be considered to be distributed over a width bm, measured immediately above the ribs of the sheeting, as shown in Figure 7.5 and given by: bm = bp + 2(hc + hf) where: bp is the width of the concentrated load, perpendicular to the span of the slab; hc is the thickness of the slab above the ribs of the profiled sheeting and hf is the thickness of the finishes, if any.
(7.1)
Figure 7.5 — Distribution of concentrated load 2) For concentrated line loads perpendicular to the span of the slab, the preceding formula for bm may be used, with bp taken as the length of the concentrated line load. 3) The width of the slab considered to be effective for global analysis and for resistance should not exceed the following: a) for bending and longitudinal shear: — for simple spans and exterior spans of continuous slabs bem = bm + 2Lp[1 – (Lp/L)] k slab width
(7.2)
— for interior spans of continuous slabs bem = bm + 1.33 Lp[1 – (Lp/L)] k slab width
(7.3)
b) for vertical shear: beÉ = bm + Lp [1 – (Lp/L)] k slab width where: Lp L
(7.4)
is the distance from the centre of the load to the nearest support; is the span length.
4) To ensure the distribution of line or point loads over the width considered to be effective, transverse reinforcement shall be placed on or above the sheeting. This transverse reinforcement shall be designed in accordance with Eurocode 2 for the transverse bending moments.
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5) If the characteristic imposed loads do not exceed the following values, a nominal transverse reinforcement may be used without calculation: — concentrated load: 7.5 kN — distributed load: 5.0 kN/m2. This nominal transverse reinforcement should have a cross-sectional area of not less than 0.2 % of the area of structural concrete above the ribs, and should extend over a width of not less than bem as calculated in this clause. Minimum anchorage lengths should be provided beyond this width in accordance with clause 5.2.3.4 of EC2. Reinforcement provided for other purposes may fulfil all or part of this rule. 6) In the absence of such reinforcement, effective widths for both shear and moment calculations are limited to bm.
7.5 Verification of profiled steel sheeting as shuttering Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
7.5.1 Ultimate limit state Verification of the profiled steel sheeting for the ultimate limit state shall be in accordance with Part 1.3 of Eurocode 3. Due consideration shall be given to the effect of embossments or indentations on the design resistances. 7.5.2 Serviceability limit state 1) Section properties shall be determined in accordance with Part 1.3 of Eurocode 3. 2) The deflection of the sheeting under its own weight plus the weight of wet concrete, but excluding the construction load, should not exceed L/180 or 20 mm where L is the effective span between supports (props being supports in this context). 3) These limits may be varied where: — greater detection will not impair the strength or efficiency of the floor; and — the additional weight of concrete due to ponding is taken into account in the design of the floor and supporting structure. 4) Where soffit deflection is considered important (e.g. for service requirements or aesthetics) it may be necessary to reduce these limits.
7.6 Verification of composite slabs 7.6.1 Ultimate limit state 7.6.1.1 Design criteria 1) The resistance of a composite slab shall be sufficient to withstand the design loads and to ensure that no ultimate limit state is reached, based on one of the following modes of failure (see Figure 7.6): — Critical section I. Flexure: bending resistance Mp.Rd. This section can be critical if there is complete shear connection at the interface between the sheet and the concrete (see 7.6.1.2). — Critical section II. Longitudinal shear: longitudinal shear resistance V=.Rd. The maximum load on the slab is determined by the resistance of the shear connection. The ultimate moment of resistance Mp.Rd at section I cannot be reached. This is defined as partial shear connection (see 7.6.1.3). — Critical section III. Vertical and punching shear: vertical shear resistance Vv.Rd. This section will be critical only in special cases, for example in deep slabs of short span with loads of relatively large magnitude (see 7.6.1.5).
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Figure 7.6 — Illustration of possible critical sections
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
7.6.1.2 Flexure 1) The bending resistance Mp.Rd of any cross section shall be determined by plastic theory in accordance with 4.4.1.2 but with the design yield strength of the steel member (sheeting) taken as fyp/*ap. In hogging bending the contribution of the steel sheeting shall only be taken into account when the sheet is continuous. 2) For the effective area of the steel sheeting the width of embossments and indentations in the sheet should be neglected, unless it is shown by tests that a larger area is effective. 3) The effect of local buckling of compressed parts of the sheeting should be taken into account by using effective widths not exceeding twice the values given in Table 4.2 for Class I steel webs. 4) The sagging bending resistance of a composite slab with the neutral axis above the sheeting may be calculated as follows: Mp.Rd = Ncf (dp – 0.5 x) where Ncf Ap dp x
b
(7.5a)
is Ap fyp/*ap; is the effective area of the steel sheet in tension according to paragraph 2); is the distance from the top of the slab to the centroid of the effective area of the steel sheet; is the depth of the stress block for the concrete, given by
is the width of the cross-section considered.
The stress distribution is given in Figure 7.7.
Figure 7.7 — Stress distribution for sagging bending if the neutral axis is above the steel sheet
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5) The sagging bending resistance of a composite slab with the neutral axis in the sheeting may be calculated from Figure 7.8 or for simplification as follows (concrete in the ribs neglected): Mp.Rd = Ncf z + Mpr
(7.5b)
where: Mpr
is the reduced plastic resistance moment of the sheeting, given by:
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
Ncf = hc b (0.85 fck/*c) and: Mpa ht e ep
is the design plastic resistance moment of the effective cross-section of the sheeting; is the total depth of the slab: is the distance from the centroid of the effective area of the steel sheet to its underside; is the distance of the plastic neutral axis of the effective area of the sheeting to its underside
and other symbols are as in 4) above.
p.n.a. plastic neutral axis c.a. centroidal axis Figure 7.8 — Stress distribution for sagging bending if neutral axis is in the steel sheet 7.6.1.3 Longitudinal shear for slabs without end anchorage 1) The provisions in this clause 7.6.1.3 apply to composite slabs with mechanical or frictional interlock [types a) and b) as defined in 7.1.2.2]. The design resistance of these slabs against longitudinal shear shall be determined by the empirical method (“m-k” method) as outlined in this clause or by the partial connection method as given in Annex E to this Eurocode.
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2) The maximum design vertical shear V for a width of slab b should not exceed the design shear resistance V=.Rd determined from the following semi-empirical relation: V=.Rd = bdp[(m Ap/bLs) + k)]/*És
(7.6)
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
where: b, dp and Ls are in mm; Ap is in mm2; m and k are in N/mm2; Ls is the shear span, defined below; m,k are design values for the empirical factors obtained from tests carried out in accordance with 10.3.1; *És is for use in equation (7.6) only and other symbols as defined in 7.6.1.2. 3) For design, Ls should be taken as: a) L/4 for a uniform load applied to the entire span length; b) the distance between the applied load and the nearest support for two equal and symmetrically placed loads; c) for other loading arrangements, including a combination of distributed and asymmetrical point loads, an assessment should be made based upon test results or by approximate calculations similar to the following. The L/4 shear span for a uniformly distributed load is obtained by equating the area under the shear force diagram for the uniformly distributed load to that due to a symmetrical two point load system, both loadings having the same value. Figure 7.9 shows these two cases.
Figure 7.9 — Shear span 4) Where the composite slab is designed as continuous, it is permitted to use an equivalent simple span between points of contraflexure for the determination of shear resistance. For end spans, however, the full exterior span length should be used in design.
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Figure 7.10 — Equivalent simple span for determination of the longitudinal shear resistance of a composite slab 7.6.1.4 Longitudinal shear for slabs with end anchorage 1) Unless contribution to longitudinal shear resistance by other shear devices is shown by testing, the end anchorage of type c), as defined in 7.1.2.2, shall be designed for the tensile force in the steel sheet at the ultimate limit state. 2) The design resistance against longitudinal shear of slabs with end anchorage of types c) and d), as defined in 7.1.2.2, may be determined by the partial connection methods as given in Annex E. 3) The design resistance of a headed stud welded through the steel sheet used for end anchorage should be taken as the smaller of the design shear resistance of the stud in accordance with 6.3.3.1 or the bearing resistance of the sheet determined with the following expression: Ppb.Rd = k:ddotfyp/*ap
(7.7)
where: k: = I + a/ddo k 4.0 and:
Ppb.Rd is the design bearing resistance of a headed stud welded through the sheet; ddo is the diameter of the weld collar which may be taken as 1.1 times the diameter of the shank of the stud; a is the distance from the centre of the stud to the end of the sheeting, to be not less than 2 ddo; and t is the thickness of the sheeting.
7.6.1.5 Vertical shear The vertical shear resistance VÉ.Rd of a composite slab over a width equal to the distance between centres of ribs, should be determined from: VÉ.Rd = bodpERd kÉ (1.2 + 40@)
(7.8)
where: bo is the mean width of the concrete ribs (minimum width for re-entrant sheeting); ERd is the basic shear strength to be taken as 0.25 fctk/*c; fctk is fctk 0.05 as given in 3.1.2 2) and 3.1.2 3); @ = Ap/bodp < 0.02; Ap is the effective area of the steel sheet in tension, according to 7.6.1.2 2), within the considered width bo; kÉ = (1.6 – dp) U 1 with dp expressed in m. 7.6.1.6 Punching shear The punching shear resistance Vp.Rd of a composite slab at a concentrated load should be determined from: Vp.Rd = CphcERdkÉ(1.2 + 40@)
(7.9)
where: Cp is the critical perimeter determined as shown in Figure 7.11; ERd and kÉ are as given in 7.6.1.5.
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Figure 7.11 — Critical perimeter for punching shear 7.6.2 Serviceability limit state 7.6.2.1 Cracking of concrete 1) The crack width in hogging moment regions of continuous slabs shall be checked in accordance with clause 4.4.2 of EC2. 2) Where continuous slabs are designed as simply-supported in accordance with 7.4.2.1 4), the cross-sectional area of the anti-crack reinforcement shall be not less than 0.2 % of the cross-sectional area of the concrete on top of the steel sheet for unpropped construction and 0.4 % of the cross-sectional area above the ribs for propped construction. 7.6.2.2 Deflection 1) The Principles and Application Rules of 5.2.1 apply. 2) Calculations of deflections may be omitted if both: — the span to depth ratio does not exceed the limits given in Table 4.14 of EC2, for lightly stressed concrete, in accordance with clause 4.4.3.2 of EC2, and — the condition of 7.6.2.2 9), for neglect of the effects of end slip, is satisfied. 3) The deflection of the sheeting due to its own weight and the weight of the wet concrete need not be included in this verification for the composite slab. 4) In practice two conditions of span arise for composite slabs. They are either: — an internal span, or — an external span. 5) For an internal span where the slab is composite, as defined in 7.1.2.2 a), b) or c), the deflection should be determined using the following approximations. a) The second moment of area should be taken as the average of the values for the cracked and uncracked section. b) For concrete of normal density, an average value of the modular ratio for both long and short term effects may be used, as given in 3.1.4.2.
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6) For external spans, end slip can have a significant effect on deflection. For non-ductile behaviour, initial end slip and failure may be coincident [Figure 7.12 a)], while for semi-ductile behaviour, end slip may also affect the deflection [see Figure 7.12 b)]. Results of tests carried out on composite slabs and approved by the relevant authority should be consulted to establish the serviceability behaviour for external spans. 7) Where test behaviour indicates initial slip at the desired service load level for the non-anchored slab, end anchorage should be used in external spans. 8) If the influence of the shear connection between the sheeting and the concrete is not known from experimental verification for a composite floor with end anchorage, the design should be simplified to an arch with a tensile bar. From that scheme the lengthening and shortening gives the deflection that should be taken into account. 9) Generally no account need be taken of end slip if the initial slip load in the tests (defined as the load causing an end slip of 0.5 mm) exceeds 12 times the desired service load. 10) Where end slip exceeding 0.5 mm occurs at a load below 1.2 times the design service load, then end anchors should be provided. Alternatively, deflections should be calculated including the effect of end slip (which should be carried out by consulting approved test information), or the design service load should be reduced so that initial end slip occurs at not less than 1.2 times the new service load.
a) Non — ductile behaviour
b) Semi — ductile behaviour
Figure 7.12 — Slip behaviour in external spans [see 7.6.2.2 6)]
8 Floors with precast concrete slabs for buildings 8.1 General 1) This Chapter deals with reinforced or prestressed precast concrete slabs or planks, used either as floors spanning between steel beams or as permanent formwork for insitu concrete. 2) The precast elements shall be designed in accordance with the relevant chapters of Eurocode 2 and also for composite action with the steel beams. [ENV Note: The following numbers of clauses of Eurocode 2 Part 1B Precast Concrete Elements and Structures are a part of the 13th Draft. These numbers may change in the final version of Eurocode 2 Part 1B and the contents of this Chapter may then have to be changed.]
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8.2 Actions 1) Attention shall be given to the local effects of heavy concentrated loads applied above or adjacent to joints between precast elements. 2) The following loads shall be taken into account in calculations for precast elements as permanent formwork: — weight of insitu concrete and precast elements; — construction loads, including local heaping of concrete during construction, and storage load, if any; — ponding effect (increased depth of insitu concrete due to deflection of the precast elements). [ENV Note: Until sufficient information is given in Eurocode 1, the rules given in the following paragraph are provided.] 3) Clauses 7.3.2.1 2) and 7.3.2.1 4) are applicable to precast elements acting as permanent formwork. The minimum loads given in 7.3.2.1 2) are not necessarily sufficient for excessive impact or heaping of concrete, or pipeline or pumping loads. If appropriate, provision should be made in design for the additional loading. 4) In the design of the composite member, reduced values for shrinkage and creep of the precast concrete may be used, by considering its age when composite action is first established.
8.3 Partial safety factors for materials 1) For the structural steel, any reinforcement that is embedded in insitu concrete, and the insitu concrete, the safety factors given in 2.3.3 and 2.3.4 shall be used. 2) Partial safety factors for materials within precast concrete elements shall be in accordance with the appropriate Parts of Eurocode 2.
8.4 Design, analysis, and detailing of the floor system 8.4.1 Support arrangements 1) The precast floor elements may be designed as simply supported or as continuous. The connections between elements at their supports should be designed and detailed accordingly. 2) The top reinforcement of continuous or cantilevering precast floors should be anchored in the precast elements or in a structural topping layer, in accordance with clause [2.5.3.5] of EC2 Part 1B. 8.4.2 Joints between precast elements 1) When the floor is considered as monolithic, joints between precast elements shall be designed for all internal forces and moments that are required to be transferred from one element to another. 2) Vertical shear force may be transferred between adjacent elements by the lapping of projecting reinforcement, or by other shear transferring connections, e.g. by shaping the joints as in Figure 8.1.
Figure 8.1 — Joints between precast floor elements 8.4.3 Interfaces Interfaces between insitu concrete and precast elements used as permanent formwork should be detailed and constructed in accordance with clause [2.5.3.8] of EC2 Part 1B, to enable the completed floor to be considered as monolithic in design.
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8.5 Joint between steel beams and concrete slab 8.5.1 Bedding and tolerances 1) Where a precast slab is supported on steel beams with or without bedding, the thickness of any bedding used and the vertical tolerances of the bearing surfaces shall be such that local stresses in the concrete slab are not excessive. 2) Particular care should be taken when friction-grip bolting according to 6.5 is used. 8.5.2 Corrosion 1) The protection of the steel top flange against corrosion throughtout the life of the structure shall be considered. 2) In buildings where corrosion will not be expected to impair the proper function of the structure or cause its appearance to be unacceptable, no protection of the top flange of the steel beam is required.
Licensed Copy: Sheffield University, University of Sheffield, 17 July 2003, Uncontrolled Copy, (c) BSI
8.5.3 Shear connection and transverse reinforcement 1) The shear connection and the transverse reinforcement shall be designed in accordance with 8.4.3 and the relevant clauses in Chapter 6. 2) If shear connectors welded to the steel beam project into recesses within slabs or joints between slabs, which are filled with concrete or mortar after erection, the detailing shall be such that the infill can be fully compacted. 3) In the absence of relevant experience, the minimum thickness of infill around each shear connector should be at least 25 mm. 4) If shear connectors are arranged in groups, sufficient reinforcement should be provided near each group to prevent premature local failure in either the precast or the insitu concrete. In the absence of relevant experience, the resistance of a proposed shear connection should be checked by tests in accordance with Chapter 10. 5) Where a joint between precast elements is parallel to and above the steel beam, continuous transverse reinforcement need not be provided for horizontal shear if the recommendations of 6.4.1.3 and 6.6 are followed for each of the two slabs independently.
8.6 Concrete floor designed for horizontal loading If a concrete floor is designed as a beam or a diaphragm for horizontal loading (for example, from wind), account shall be taken of any interaction between the resulting shear forces and those due to composite action, as these may add up in joints between the concrete elements. The resulting tensile forces may also require additional reinforcement in slabs or across joints.
9 Execution 9.1 General 1) This chapter specifies the minimum standards of workmanship required during execution to ensure that the design assumptions of this Eurocode are satisfied and hence that the intended level of safety can be attained. 2) This chapter gives specific recommendations related to the design of composite structures. In addition, the relevant clauses of appropriate Parts of Eurocode 2 and Eurocode 3 are applicable to composite structures. 3) This chapter is neither intended, nor extensive enough, for a contract document. 4) This chapter defines what is to be provided, irrespective of the persons, according to the national practice, who will have the responsibility for providing it. [ENV Note: It is assumed that all matters not related to design but to responsibility or other requirements to the contractor will be found in Reference Standards or other Documents].
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2) These shall include instructions for control measurements in the different phases construction, if appropriate. 3) The speed and sequence of concreting should be required to be such that partly matured concrete is not damaged as a result of limited composite action occurring from deformation of the steel beams under subsequent concreting operations.
9.3 Stability
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1) The stability of the steelwork shall be ensured during construction, particularly before the development of composite action. 2) It shall not be assumed that permanent or temporary formwork provides restraint to steel members susceptible to buckling unless it has been demonstrated that the formwork and its fixings are capable of transferring sufficient restraining forces from the supports to the steel member.
9.4 Accuracy during construction and quality control 9.4.1 Static deflection during and after concreting 1) Section 5.2 is applicable. 2) The shuttering and the supporting structure should be such that they can follow without deterioration the deflections of the steel beams that are assumed to occur during concreting. 3) When unpropped construction is used, measures should be taken to limit additional thickness of the floor slabs resulting from deflections of the steel beams, unless extra thickness of concrete be taken into account in the final design. 9.4.2 Compaction of concrete Special attention should be paid to the achievement of satisfactory compaction around shear connectors and in concrete-filled steel tubes. 9.4.3 Shear connection in beams and columns 9.4.3.1 Headed studs in structures for buildings 1) The proper duration of the welding period and the strength of the current shall be determined on the basis of trial weldings under site conditions, and tests in accordance with the appropriate standards in force. 2) The quality of the stud welding shall be checked by visual inspection. Special attention shall be given to the weld collar and the length of the stud. Any studs with defective welding shall be replaced. In addition, a number of studs specified and selected as specified in these documents shall be bent, until the head of each such stud is displaced laterally from its original position a distance of approximately one quarter of the height of the stud. The stud weld shall not show any signs of cracking. The satisfactory studs shall be left in the bent position. 3) Studs should not be welded to contaminated steel surfaces (e.g. water, moisture, grease etc.) [ENV Note: This clause may later be moved to a Reference Standard]. 4) Where the sheeting is such that studs cannot be placed centrally within a trough, they should be placed alternately on the two sides of the trough, throughout the length of the span. 9.4.3.2 Anchors, hoops, block connectors 1) The welding of anchors, hoops and block connectors shall be in accordance with the relevant clauses of EC3. 2) Anchors and hoops that shall be welded should comply with the conditions of weldability given in EC2. They may be either butt welded or bent and fillet welded. When fillet welding is used, the bend adjacent to the weld should be made in the red hot condition. 9.4.3.3 Friction grip bolts 1) The interface between the steel member and the concrete flange shall be free of paint or other applied finishes, oil, dirt, rust, loose mill scale, burrs and other defects which would prevent a uniform sealing between the two elements, or would interfere with the development of friction between them. 2) The method should be in accordance with the relevant clauses of Chapter 7 of EC3.
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9.4.3.4 Corrosion protection in the interface 1) Steel parts of composite beams in buildings in general need not be protected against corrosion unless particular corrosion action has to be taken into account. If the steel parts must be protected against corrosion by painting, the painting may also be applied in the interface and to the shear connectors. 2) Where protection from corrosion is required without the interface and shear connectors being fully painted, the protection should extend at least 30 mm into the interface. 9.4.3.5 Surface condition For composite columns without mechanical shear connection, the surface of the steel section in contact with the concrete filling or encasement should be unpainted and free from oil, grease and loose scale or rust. 9.4.4 Composite slabs with profiled steel sheeting
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9.4.4.1 Profiled steel sheet as shuttering — Fixing of sheets 1) The sheets shall be fixed: — during laying to keep them in position and to provide a safe working platform; — to ensure connection between adjacent sheets and between the sheets and supporting beams; — to transmit horizontal forces and shear, where necessary. 2) The spacing of the fasteners should be not greater than 500 mm at the ends of the sheets. At side laps, the sheets should be fastened to each other, as necessary, to control differential deflection. The design of the fixing should be in accordance with the relevant clauses of Part 1.3 of EC3. 9.4.4.2 Cleaning of shear prior to concreting All oil, dirt and deleterious matter shall be removed from the upper surface of the sheeting, but any greasiness remaining on the sheets from the forming process need not be removed. 9.4.4.3 Loads The values of the construction and storage loads assumed in design of the sheeting shall be clearly shown on the relevant site plans. Those responsible for controlling work on site shall not allow these loads to be exceeded. 9.4.4.4 Stud connectors welded through profiled sheeting Stud connectors may be welded through the sheet to the supporting beams under the following conditions: a) Clause 9.4.3.1 should be followed. b) Any paint on the steel beam near the weld should be removed. c) When the sheet is ungalvanised, the gross thickness should not exceed 1.5 mm and any corrosion should be minimal. d) The overall thickness of a galvanised sheet should not exceed 1.25 mm and galvanising should not exceed 30 microns on each face of the sheet. e) Wet conditions at the time of welding should be avoided. f) Before welding, the sheet should be in close contact with the steel. g) Stud connectors should not be welded through more than one thickness of sheet. [ENV Note: The above conditions are provisional until the relevant Reference Standard is available.] 9.4.4.5 End anchorages The fabrication of end anchorages by deformation of profiled sheeting on site shall comply with the conditions laid down in 7.1.2.2.
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10 Design assisted by testing
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10.1 General 1) Unless otherwise specified, Chapter 8 of EC3 applies. Reference is made to the guidelines for loading tests given in Annex Y of EC3. 2) In this Eurocode specific additional rules are given for: a) tests on shear connectors in 10.2 and b) testing of composite floor slabs in 10.3. 3) When design is based on experimental evidence, the properties of the materials and the dimensions of the test specimen shall not exceed the specified characteristic values. Where this is not possible, the design resistance determined from the tested structure or element shall be adjusted to take account of possible variations of the characteristic properties of the materials and of the dimensions. 4) If structural properties, to be determined by testing, are influenced by cracking of concrete, the evaluation shall account for the considerable variation in the tensile strength of concrete. In this case, the influence of shrinkage and temperature differences on cracking shall be considered. 5) If the actual structure is subjected to long term loading, the effects of creep of concrete and progressive slip at the interface shall be evaluated.
10.2 Tests on shear connectors 10.2.1 General 1) Where the design rules in Chapter 6 are not applicable, the design shall be based on tests, carried out in a way that provides information on the properties of the shear connection required for design in accordance with this Eurocode. 2) The variables to be investigated include the geometry and the mechanical properties of the concrete slab, the shear connectors and the reinforcement. 3) The resistance to loading, other than fatigue loading, may be determined by push tests in accordance with the requirements in this Section. 4) From these push tests, the failure load, the mode of failure and the load/deformation performance are obtained. 5) The mode of failure is likely to be one of the possible failure modes as given in Figure 10.1, or a combination of these. 6) For each specimen tested, the test report should normally contain the information as listed in Annex F.
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shearing of the connector just above the weld collar (can also occur in ribbed slabs)
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local concrete crushing around the foot of the shear connector (can also occur in ribbed slabs)
pull-out of a concrete cone
shearing off of the concrete rib
cracking off of the concrete rib or tension shear failure, occurring after very large deformations of the shear connector, due to plastic hinges.
Figure 10.1 — Possible failure modes of the push specimens 10.2.2 Testing arrangement 1) Where the shear connectors are used in T-beams with a concrete slab of uniform thickness, or with haunches complying with 6.4.1.4, standard push tests may be used. In other cases specific push tests should be used. 2) For standard push tests the dimensions of the test specimen, the steel section and the reinforcement should be as given in Figure 10.2. If after evaluation the reinforcement is less than that required according to Section 6.6, the test may be repeated with the required reinforcement. The recess in the concrete slabs is optional.
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Figure 10.2 — Test specimen for standard push test 3) Specific push tests should be carried out on test specimens generally as shown in Figure 10.3. The slabs and the reinforcement should be suitably dimensioned in comparison with the beams for which the test is designed. In particular: a) the length = of each slab should be related to the longitudinal spacing of the connectors in the composite structure; b) the width b of each slab should not exceed the effective width of the slab of the beam; c) the thickness h of each slab should not exceed the minimum thickness of the slab in the beam; d) where a haunch in the beam does not comply with 6.4.1.4, the slabs of the push specimen should have the same haunch and reinforcement as the beam; e) the recess in the concrete slabs, shown in Figure 10.3, is optional.
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Figure 10.3 — Test specimen for specific push test 10.2.3 Preparation of specimens 1) Each concrete slab should be cast in the horizontal position, as is done for composite beams in practice. 2) Bond at the interface between flanges of the steel beam and the concrete should be prevented by greasing the flange or by other suitable means. 3) The push specimens should be air-cured. 4) For each mix a minimum of four concrete specimens (cylinders or cubes) for the determination of the cylinder strength should be prepared at the time of casting the push specimens. The concrete strength fcm should be taken as the mean value. 5) The compressive strength of the concrete at the time of testing should be 70 % ± 10 % of the specified strength of the concrete of the beams for which the test is designed. This requirement can be met by using concrete of the specified grade, but testing earlier than 28 days after casting of the specimens. 6) The yield strength, the tensile strength and the maximum elongation of a representative sample of the shear connector material should be determined. 7) If profiled steel sheeting is used for the slabs, the tensile strength and the yield strength of the profiled steel sheet should be obtained from coupon tests on specimens cut from the sheets as used in the push tests. 10.2.4 Testing procedure 1) The load should first be applied in increments up to 40 % of the expected failure load and then cycled 25 times between 5 % and 40 % of the expected failure load. 2) Subsequent load increments should then be imposed such that failure does not occur in less than 15 minutes. 3) The longitudinal slip between each concrete slab and the steel section should be measured continuously during loading or at each load increment. The slip should be measured at least until the load has dropped to 20 % below the maximum load. 4) As close as possible to each group of connectors, the transverse separation between the steel section and each slab should be measured.
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10.2.5 Test evaluation 1) If three tests on nominally identical specimens are carried out and the deviation of any individual test result from the mean value obtained from all tests does not exceed 10 %, the design resistance may be determined as follows. The characteristic resistance PRk should be taken as the minimum failure load (divided by the number of connectors) reduced by The design resistance PRd should be calculated from: PRd = (fu/fut)(PRk/*É) k PRk/*É
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where
fu fut *É
is the minimum specified ultimate strength of the connector material, is the actual ultimate strength of the connector material in the test specimen, and should be taken as
2) If the deviation from the mean exceeds 10 %, at least three more tests of the same kind should be made. The test evaluation should then be carried out in accordance with Annex Z of EC3. 3) Where the connector is composed of two separate elements, one to resist longitudinal shear and the other to resist forces tending to separate the slab from the steel beam, the ties which resist separation shall be sufficiently stiff and strong so that separation in push tests, measured when the connectors are subjected to 80 per cent of their ultimate load, is less than half of the longitudinal movement of the slab relative to the beam. 4) The slip capacity of a specimen should be taken as the maximum slip measured at the characteristic load level, as shown in Figure 10.4. The characteristic slip capacity $uk should be taken as the minimum test value of $u reduced by or determined by statistical evaluation from all the test results. In the latter case, the characteristic slip capacity should be taken as the 5 % fractile with a confidence level of 75 %.
Figure 10.4 — Determination of slip capacity $u
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10.3 Testing of composite floor slabs 10.3.1 Parametric tests
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10.3.1.1 General 1) Parametric tests are a series of full-scale tests over a range of parameters performed to obtain data for the determination of the design resistance to longitudinal shear. 2) The variables to be investigated include the thickness and the type of steel sheeting, the steel grade, the coating of the steel sheet, the concrete slab thickness, the density and grade of concrete and the shear span length Ls. 3) To reduce the number of tests as required for a complete investigation, the results obtained from a test series may be used also for other values of variables as follows: — for thicknesses of the steel sheeting t larger than tested, — for slab thicknesses ht smaller than tested, — for concrete with specified strength fck not less than 0.8fcm, where fcm is the mean value of the concrete strength in the tests, — for steel sheeting having a yield strength fyp not less than 0.8fym, where fym is the mean value of the yield strength in the tests. 4) From these tests the failure load, the mode of failure and the load/deflection and load/slip performances are obtained. 5) The mode of failure will be one of the three described in 7.6.1.1. However, as the object is to determine the resistance to longitudinal shear, test results shall lie in the region I–II of Figure 10.5. Failure in longitudinal shear is indicated by relative movement (end slip) between the sheeting and the concrete at the ends of the test specimen, at a load lower than the flexural bending strength. The absence of end slip indicates complete shear connection and the failure is to be considered as flexural in this case. The length Ls is as defined in this Section 10.3; the other symbols are as in 7.6.1.2 and 7.6.1.3.
Figure 10.5 — Illustration of possible failure modes 6) The tests will provide either design values for the factors m and k or the design value Eu.Rd to be used in the partial connection method given in Annex E. 7) For each specimen tested, the test report should normally contain the information as listed in Annex F. 10.3.1.2 Testing arrangement 1) Tests shall be carried out on simply supported slabs. 2) The test set-up should be as shown in Figure 10.6 or equivalent.
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Figure 10.6 — Test set-up 3) Two equal concentrated line loads, placed symmetrically at L/4 and 3L/4 on the span, should be applied to the specimen. 4) The distance between the centre line of the supports and the end of the slab shall not exceed 100 mm. 5) The width of the bearing plates and the line loads shall not exceed 100 mm. 6) When the tests are used to determine m and k factors, for each variable to be investigated two groups of three tests (indicated in Figure 10.7 by regions A and B) or three groups of two tests should be performed. For specimens in region A, the shear span should be as long as possible while still providing failure in longitudinal shear. For specimens in region B, the shear span should be as short as possible while still providing failure in longitudinal shear, but not less than 3ht in length. 7) When the tests are used to determine Eu.Rd for the partial connection method (Annex E), for each type of steel sheet or coating not less than six tests should be carried out on specimens without additional reinforcement or end anchorage. The test specimens should be chosen so that the test information may be considered as representative for the whole range of degree of shear connection () k 1.0). The span and the slab thickness should be varied such that at least three tests have a value of ) between 0.7 and 1.0. When sufficient preknowledge from former tests is available to prove that the behaviour is ductile, the test series may be reduced to the three tests having a value of ) between 0.7 and 1.0. The influence of the sheet thickness may be determined by testing three additional specimens, for each thickness to be investigated, such that one test has a shear span length Ls equal to 3ht to check ductility, and the other two tests have a value of ) between 0.7 and 1.0. 8) When the partial connection method is used to determine the contribution of end anchorage, three additional tests should be carried out, one with Ls = 3ht and the other two such that ) has values between 0.7 and 1.0. 9) When the partial connection method is used to account for the contribution of reinforcement the validity of the method should be proved by three additional tests, one with Ls = 3ht and the other two such that ) has values between 0.7 and 1.0.
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10.3.1.3 Preparation of specimens
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1) The surface of the profiled steel sheet shall be in the “as-rolled” condition, no attempt being made to improve the bond by degreasing the surface. 2) The shape and embossment of the profiled sheet shall accurately represent the sheets to be used in practice. The measured spacing and depth of the embossments shall not deviate from the nominal values by more than 5 % and 10 % respectively. 3) Thin steel sheet crack inducers, extending to the full depth of the slab and coated with a debonding agent, should be placed across the full width of the test slab under the applied loads. Crack inducers are placed to better define the shear span length, Ls and to eliminate the tensile strength of concrete. 4) It is permitted to restrain exterior webs of the deck so that they act as they would act in wider slabs. 5) The width b of the test slabs should not be less than: — three times the overall depth; — 600 mm; and — the cover width of the profiled sheet. 6) Specimens shall be cast in the fully supported condition. This is the most unfavourable situation for the shear bond mode of failure. 7) Mesh reinforcement may be placed in the slab, for example to reinforce the slab during transportation, against shrinkage, etc. If placed it must be located such that it acts in compression under sagging moment. 8) The concrete for all specimens in a series to investigate one variable shall be of the same mix and cured under the same conditions. 9) For each group of slabs that will be tested within 48 hours, a minimum of four concrete specimens, for the determination of the cylinder or cube strength, shall be prepared at the time of casting the test slabs. The concrete strength fcm of each group shall be taken as the mean value, when the deviation from the mean value does not exceed 10 %. When the deviation of the compressive strength from the mean value exceeds 10 %, the concrete strength shall be taken as the maximum observed value. 10) The tensile strength and yield strength of the profiled steel sheet shall be obtained from coupon tests on specimens cut from each of the sheets used to form the test slabs. 10.3.1.4 Test loading procedure 1) The test loading procedure is intended to represent loading applied over a period of time. It is in two parts consisting of an initial test, where the slab is subjected to cyclic loading; this is followed by a subsequent test, where the slab is loaded to failure under an increasing load. 2) If two groups of three tests are used, one of the three tests in each group may be subjected to just the subsequent static test without cyclic loading in order to determine the level of the cyclic load for the other two. 3) Initial test: the slab shall be subjected to an imposed cyclic load, which varies between a lower value not greater than 0.5 Wq and an upper value not less than 1.5 Wq, where Wq is the anticipated value of the characteristic load which will act on the slab, excluding the weight of the composite slab. 4) The loading should be applied for 5 000 cycles in a time not less than 3 hours. 5) Subsequent test: on completion of the initial test, the slab shall be subjected to a static test where the imposed load is increased progressively, such that failure does not occur in less than 1 hour. The failure load Wt is the load imposed on the slab at failure plus the weight of the composite slab and spreader beams. 6) In the subsequent test the load may be applied either as force-controlled or deflection-controlled.
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10.3.1.5 Determination of design values for m and k
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1) From the load-deflection curve recorded in the subsequent test the behaviour is classified as brittle or ductile. The behaviour is classified as ductile if the failure load exceeds the load causing first recorded end slip by more than 10 %. If the maximum load is reached at a midspan deflection exceeding L/50, the failure load shall be taken as the load at the midspan deflection of L/50. Otherwise the behaviour is classified as brittle. 2) If the behaviour is ductile the representative experimental shear force Vt shall be taken as 0.5 times the value of the failure load Wt as defined in 10.3.1.4. If the behaviour is brittle this value shall be reduced, using a factor 0.8. 3) From the tests the design relationship (i.e. values of m and k) for longitudinal shear resistance shall be determined as shown in Figure 10.7.
NOTE
b, dp and Ls are in mm, Ap is in mm2, Vt is in N.
Figure 10.7 — Evaluation of test results 4) The design relationship shall be taken as the characteristic line determined with an appropriate statistical model. 5) If two groups of three tests are used and the deviation of any individual test result in a group from the mean of the group does not exceed 10 %, the design relationship may determined in accordance with Annex Z of EC3 or as follows: From each group the characteristic value is deemed to be the one obtained by taking the minimum value of the group reduced by . The design relationship is formed by the straight line through these characteristic values for groups A and B. 10.3.2 Specific tests 10.3.2.1 General 1) Specific tests are a series of full-scale tests on a representative element of a particular proposed floor assembly, as constructed on site, using actual loading or a close approximation to it. The purpose of such a test is to provide design information. 2) From these tests the failure load, the mode of failure and the load/deflection and load/slip performances are obtained. The mode of failure will be one of the three described in 7.6.1.1. 3) The results obtained shall be applied only to structures where the span, profiled steel sheeting and concrete thickness are as tested. 4) The information included in the report for each slab tested shall be in accordance with Annex F.
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10.3.2.2 Testing arrangement
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1) A minimum of three full-scale tests shall be carried out on a representative element of the proposed floor construction using actual loadings or, for uniformly distributed-loads, a close simulation of the loading as shown in Figure 10.8. For continuous spans, either multiple spans shall be tested or the support moments simulated on a single span.
Figure 10.8 — Test details 2) The distance between the centre line of an end support and the end of the slab shall not exceed half the least width of bearing to be used in practice. 3) The width of the bearing plates shall be less than the least width of bearing in practice. The width of the line loads shall not exceed 100 mm. 10.3.2.3 Specimen preparation 1) The provisions of 10.3.1.3 1) to 5) and 10.3.1.3 8) to 10) apply. 2) The crack inducers required according to 10.3.1.3 3) ensure that cracks form in the tensile zone of the slab. When four-point loading is used, the crack inducers should be positioned under the central loads, as shown in Figure 10.8. For non-uniform or asymmetrical loading arrangements, the crack inducers should be positioned at the points of maximum bending moment. 10.3.2.4 Test loading procedure The test procedure is intended to represent loading over a period of time. It is in two parts consisting of an initial test as described in 10.3.1.4 3) and 4), where the slab is subjected to cyclic loading; this is followed by a subsequent test, where the slab is loaded to failure under an increasing load. This subsequent test is as described in 10.3.1.4 5) and 6). 10.3.2.5 Determination of the design resistance The design resistance for the proposed slab shall be taken as corresponding to the lowest from the following: a) times the average imposed load plus the self weight of the composite slab at a deflection of 1/50 th of the span for those slabs which do not fail in the initial test; b) times the average value of the failure load Wt for those slabs which fail with sudden and excessive slip, where the failure load Wt is the load imposed on the slab at failure plus the weight of the composite slab; c) times the average value of the failure load Wt for those slabs which fail without sudden and excessive slip; and d) the upper value of the imposed load plus the self weight of the composite slab used in the initial test. [Note: The factors in a) to c) are considered to include both the calculation of the characteristic resistance and *M.]
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Annex A (normative) Reference documents A.1 Scope 1) This Annex gives a list of existing or anticipated documents which are recognized as usefully supplementing Part 1.1 of Eurocode 4. 2) This list should not be considered to be exhaustive, because many such documents in turn refer to further documents. [Note: For use of this annex, reference should also be made to the Foreword and to 1.1.2 3).] A.2 Standards on materials and products associated with Part 1.1 of Eurocode 4 The following standards, mentioned in Part 1.1 of Eurocode 2, Eurocode 3 or Eurocode 4 should be considered, at least partially, as defining Application Rules complementary to this Eurocode. A.2.1 Standards mentioned in EC2 — DP 9690 (in preparation) classifying physical and chemical environments in relation with the durability of concrete structures — ENV 206 (1989/02), Concrete — Performance, Production, Placing and Compliance Criteria — EN 10080 (in preparation) on reinforcing steels. A.2.2 Standards mentioned in EC3 Refer to Annex B of EC3: clauses B.2.1 to B.2.6. A.2.3 Other standards mentioned in EC4 No other standard is mentioned in Part 1.1 of Eurocode 4. [ENV Note: It is considered that non-standardized types of shear connectors should be defined by technical approvals issued by national or local relevant authorities or bodies, as far as they are not yet defined by European technical approvals.] A.3 Reference documents for execution Partial guidance may be found in the documents mentioned in Annex B of EC3, clauses B.2.7 and B.2.8. [ENV Note: It is considered that there should be European or International Standards for the aspects of execution particular for composite structures, for example for welding of shear connectors.] A.4 General standards 1) Part 1.1 of Eurocode 4 generally is in accordance with the two following standards: — ISO 3898 (2nd edition — 1987/12/15). Bases for design of structures — Notations — General symbols. — ISO 8930 (1st edition — 1987/0/0). General principles on reliability of structures — List of equivalent terms. 2) When symbols or terms supplementing those used in Part 1.1 of Eurocode 4 are necessary in designs, it is recommended for the sake of easy understanding that they should be chosen to avoid any discrepancy with these two standards. ISO 8930 should also be strictly followed for translating this Eurocode.
Annex B (normative) Lateral-torsional buckling This Annex is for use with clause 4.6.3. B.1 Methods based on a continuous inverted-U frame model B.1.1 Simplified method for calculation of slenderness ratio 1) For uncased beams that satisfy the conditions of B.1.2 1) and have a double symmetrical steel section, the slenderness ratio Æ LT for a Class 1 or Class 2 cross-section may conservatively be taken as
where fy is the yield strength of the structural steel, and the other symbols are defined in B.1.2 or Figure B.1.
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2) For a cross-section in Class 3 or Class 4, the value given in 1) should be multiplied by (Mel/Mp=)½, in accordance with 4.6.3 3).
Figure B.1 — Lateral-torsional buckling B.1.2 Elastic critical moment 1) This clause is applicable to a composite beam with continuity at one or both ends and a restrained top flange, that satisfies conditions c) and f) to j) of 4.6.2. The steel member should be a double symmetrical or mono-symmetrical rolled or welded I-section, uniform throughout the span considered. The shear connection should satisfy 6) and 7) below. 2) The model for this method is the continuous inverted-U frame. It does not rely on the provision of web stiffeners, except those required by 4.6.2 i). 3) No special provision need be made at internal supports to provide warping fixity or to prevent rotation on plan of the steel bottom flange. 4) The elastic critical hogging moment Mcr at an internal support may be taken as
where L
is the length of the beam between points at which the bottom flange of the steel member is laterally restrained,
C4
is a property of the distribution of bending moment within length L given in Table B.1 to Table B.3. Where the bending moments at the supports are unequal, C4 relates to the support with the larger hogging moment. The bending moment Mo in Table B.1 and Table B.3 is the mid-length moment on a simply supported span of length L.
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5) The properties of the effective cross-section in the hogging moment region are as follows:
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kc is a factor given in clause B.1.3 or B.1.4; Ea and G are respectively the modulus of elasticity and the shear modulus for steel, given in 3.3.3; A is the area of the equivalent composite section, as defined in 4.2.3 1), neglecting concrete in tension; Iy is the second moment of area for major-axis bending of the composite section of area A; Aa is the area of the structural steel section; Iay and Iaz are second moments of area of the structural steel section about its centre of area, C; ix2 = (Iay + Iaz)/Aa; Iafz is the second moment of area of the bottom flange about the minor axis of the steel member; Iat is the St. Venant torsion constant of the steel section; ks is a transverse stiffness per unit length of the beam, given by
k1
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is the flexural stiffness of the cracked concrete or composite slab in the direction transverse to the steel beam, which may be taken as k1 = 4EaI2/a for a slab continuous across the steel beam and k1 = 2EaI2/a for a simply supported or cantilever slab;
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Loading and support conditions
Bending moment diagram
C4 ? = 0.50 ? = 0.75 ? = 1.00 ? = 1.25 ? = 1.50 ? = 1.75 ? = 2.00 ? = 2.25 ? = 2.50
41.5
30.2
24.5
21.1
19.0
17.5
16.5
15.7
15.2
33.9
22.7
17.3
14.1
13.0
12.0
11.4
10.9
10.6
28.2
18.0
13.7
11.7
10.6
10.0
9.5
9.1
8.9
21.9
13.9
11.0
9.6
8.8
8.3
8.0
7.8
7.6
28.4
21.8
18.6
16.7
15.6
14.8
14.2
13.8
13.5
12.7
9.8
8.6
8.0
7.7
7.4
7.2
7.1
7.0
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Table B.1 — Values of factor C4 for spans with transverse loading
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Table B.2 — Values of factor C4 for spans without transverse loading Loading and support conditions
Bending moment diagram
C4 ? = 0.00
? = 0.25
? = 0.50
? = 0.75
? = 1.00
11.1
9.5
8.2
7.1
6.2
11.1
12.8
14.6
16.3
18.1
Table B.3 — Values of factor C4 at end supports, for spans with a cantilever extension
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Loading and support conditions
EaI2
k2
Bending moment diagram
Lc/L
C4 ? = 0.00
? = 0.50
? = 0.75
? = 1.00
0.25
47.6
33.8
26.6
22.1
0.50
12.5
11.0
10.2
9.3
0.75
9.2
8.8
8.6
8.4
1.00
7.9
7.8
7.7
7.6
is the “cracked” flexural stiffness per unit width of the concrete or composite slab, as defined in 4.2.3 2); and I2 should be taken as the lower of: — the value at midspan, for sagging bending, and — the value at an internal support, for hogging bending; is the flexural stiffness of the steel web, to be taken as
for an uncased beam and as
for a beam partly encased in concrete in accordance with 4.3.1 6) to 9); n is the modular ratio Ea/Ec; E’c is the effective modulus for concrete for long term effects, given in 3.1.4.2 3) or 4); 5a is Poisson’s ratio for steel; b is the breadth of the top flange of the steel member; hs is the distance between the shear centres of the flanges of the steel member; and other symbols are defined in Figure B.1.
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6) Except where specific account is taken of the influence of inverted-U frame action on the resistance of the shear connection, the longitudinal spacing of studs or rows of studs, s, should be such that
where
d fu
is the diameter of the studs, is the tensile strength of the studs, as defined in 6.3.2.1,
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·LT and Æ LT are as given in 4.6.3, ks is as defined in B.1.2 5), and b is as shown in Figure B.1. 7) The longitudinal spacing of connectors other than studs should be such that the resistance of the connection to transverse bending is not less than that required when studs are used. B.1.3 Double symmetrical steel sections Where the cross section of the steel member is symmetrical about both axes, the factor kc in B.1.2 is given by:
where zc
is the distance between the centre of area of the steel member and mid-depth of the slab,
and other symbols are defined in B.1.2. B.1.4 Mono-symmetrical steel sections Where the cross-section of the steel member has unequal flanges, the factor kc in B.1.2 is given by:
where
zf = hsIafz/Iaz
and may be taken as zj = 0.4hs (2 Iafz/Iaz – 1) when Iafz > 0.5 Iaz; zs
is the distance from the centroid of the steel section (C in Figure B.1) to its shear centre, positive when the shear centre and the compression flange are on the same side of the centroid;
and other symbols are defined in B.1.2 or B.1.3.
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Annex C (normative) Simplified calculation method for resistance of doubly symmetric composite cross sections in combined compression and bending
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C.1 Scope and assumptions 1) This method is applicable to design in accordance with 4.8 of columns with cross sections that are symmetrical about both principal axes and consist of any arrangement of structural steel, concrete, and reinforcing bars. Examples are shown in Figure 4.9. 2) The resistance of cross sections to any combination of axial force N and bending moment M about a principal axis is represented by a curve. This Annex gives methods for the calculation of the compressive resistances which define the five points A, B, C, D and E on the curve shown in Figure C.1. The interaction curve may be replaced by the polygonal diagram AECDB through these points. 3) Plastic analysis is used, with rectangular stress blocks for structural steel, reinforcement, and concrete in accordance with 4.8.3.3 and 4.8.3.11.
Figure C.1 — Polygonal interaction curve C.2 Compressive resistances 1) The plastic resistance Npl.Rd is given by 4.8.3.3. The resistance Npm.Rd is calculated as follows. 2) Figure C.2 represents a generalised cross section of structural steel and reinforcement (cross hatched), and of concrete, symmetrical about two axes through its centre of area G. For bending only (point B) the neutral axis is line BB which defines region (1) of the cross section, within which concrete is in compression. The line CC at the same distance hn on the other side of G is the neutral axis for point C in Figure C.1. This is because the areas of structural steel, concrete, and reinforcement in region (2) are all symmetrical about G, so that the changes of stress when the axis moves from BB to CC add up to the resistance Npm.Rd and the bending resistance is unchanged. Using subscripts 1 to 3 to indicate regions (1) to (3), Npm.Rd = Rc2 + 2|Ra2| where Rc2 and Ra2
(C.1)
is the resistance of the concrete in region 2), is the resistance of the steel in region 2).
3) In the notation of 4.8.3.3 Rc2 = Ac2(0.85 fck/*c) or Rc2 = Ac2fck/*c, respectively Ra2 = Aa2fy/*Ma + As2fsk/*s, when compressive forces and strengths of materials are taken as positive. 4) From symmetry, Ra1 =|Ra2| and Rc1 = Rc3
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(C.2)
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For neutral axis at BB, N = 0, so that Ra1 + Rc1 =|Ra2|+|Ra3|
(C.3)
From (C.2) and (C.3), |Ra2| = Rc1 = Rc3 Substituting in (C.1), Npm.Rd = Rc2 + Rc1 + Rc3 = Rc
(C.4)
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where Rc is the compressive resistance of the whole area of concrete, which is easily calculated.
Figure C.2 — Composite cross section symmetrical about two axes C.3 Position of neutral axis Equations for hn depend on the axis of bending, the type of cross section and the cross section properties. The equations are derived from equations C.1 and C.4, and are given for some cross sections in C.6. C.4 Bending resistances 1) The axial resistance at point D in Figure C.1 is half that at point C, so the neutral axis for point D is line DD in Figure C.2. 2) The bending resistance at point D is Mmax.Rd = Wpafyd + Wpsfsd + Wpcfcd/2
(C.5)
where Wpa, Wps and Wpc are the plastic section moduli for the structural steel, the reinforcement, and the concrete part of the section (for the calculation of Wpc the concrete is assumed to be uncracked), and fyd, fsd and fcd are the design strengths for the structural steel, the reinforcement and the concrete: fyd = fy/*Ma fsd = fsk/*s fcd = fck/*c for concrete filled sections and fcd = 0.85 fck/*c for other sections. 3) The bending resistance at point B is Mpl.Rd = Mmax.Rd – Mn.Rd
(C.6)
with Mn.Rd = Wpanfyd + Wpsnfsd + Wpcnfcd/2
(C.7)
where Wpan, Wpsn and Wpcn are the plastic section moduli for the structural steel, the reinforcement and the concrete parts of the section within region (2) of Figure C.2. 4) Equations for the plastic section moduli of some cross sections are given in C.6.
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C.5 Interaction with transverse shear If the shear force to be resisted by the structural steel is considered according to 4.8.3.12 the appropriate areas of steel should be assumed to resist shear alone. The method of this Annex can be applied using the remaining areas. C.6 Neutral axes and plastic section moduli of some cross sections C.6.1 General 1) The compressive resistance of the whole area of concrete is Npm.Rd = Ac fcd
(C.8)
2) The value of the plastic section modulus of the total reinforcement is given by
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(C.9)
where ei are the distances of the reinforcement bars of area Asi to the relevant middle line (y-axis or z-axis). 3) The equations for the position of the neutral axis hn are given for selected positions in the cross sections. The resulting value hn should lie within the limits of the assumed region. 4) An additional point E may be found by placing the neutral axis at a significant line between line CC and the border of the section [region (3) in Figure C.2] and determining the resulting normal force and bending moment. C.6.2 Major axis bending of encased I-sections
Figure C.3 — Encased I-sections with notation 1) The plastic section modulus of the structural steel may be taken from tables or be calculated from: (C.10) and (C.11)
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2) For the different positions of the neutral axes, hn and Wpan are given by: a) neutral axis in the web: hn k h/2 – tf (C.12) Wpan = twhn2
(C.13)
where Asn is the sum of the area of reinforcing bars within the region of depth 2hn; b) neutral axis in the flange: h/2 – tf < hn < h/2
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(C.14)
(C.15) c) neutral axis outside the steel section: h/2 k hn k hc/2
Wpan = Wpa.
(C.16)
(C.17)
3) The plastic modulus of the concrete in the region of depth 2hn then results from Wpcn = bchn2 – Wpan – Wpsn
(C.18)
with
(C.19)
where Asni are the areas of reinforcing bars within the region of depth 2hn and ezi are the distances from the middle line. C.6.3 Minor axis bending of encased I-sections 1) The notation is given in Figure C.3. 2) The plastic section modulus of the structural steel may be taken from tables or be calculated from: (C.20) and (C.21)
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3) For the different positions of the neutral axes, hn and Wpan are given by: a) neutral axis in the web: hn k tw/2 (C.22) Wpan = hhn2
(C.23)
b) neutral axis in the flanges: tw/2 < hn < b/2
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(C.24)
(C.25) c) neutral axis outside the steel section: b/2 k hn k bc/2 (C.26)
Wpan = Wpa.
(C.27)
4) The plastic modulus of the concrete in the region of depth 2hn then results from Wpcn = hchn2 – Wpan – Wpsn
(C.28)
with Wpsn according to equation (C.19) changing subscript z to y. 5) For the calculation of NE.Rd and ME.Rd, the resistances at the additional point E, the neutral axis should be located so that NE.Rd is close to the average of Npm.Rd and Np=.Rd. 6) For a neutral axis in the flanges (tw/2 < hE k b/2), the normal force NE results from: NE.Rd = hc(hE – hn)fcd + 2tf(hE – hn)(2fyd – fcd) + AsE(2fsd – fcd) + Npm.Rd (C.29) provided also that tw/2 < hn < b/2. AsE is the sum of the areas of reinforcement lying in the additionally compressed region between hE and hn. 7) For tw/2 < hE k b/2, the plastic section moduli are calculated by using equations C.25 and C.28, substituting hn by hE. Equation C.6 then leads to the moment ME.
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C.6.4 Concrete filled circular and rectangular hollow sections
Figure C.5 — Concrete filled circular and rectangular hollow sections with notation 1) The following equations are derived for rectangular hollow sections with bending about the y-axis of the section (see Figure C.5). For bending about the z-axis the dimensions h and b are to be exchanged as well as the subscripts z and y. The equations C.30 to C.35 may be used for circular hollow sections with good approximation by substituting h = b = d and r = d/2 – t. (C.30) with Wps according to equation (C.9). 2) Wpa may be taken from tables or be calculated from (C.31)
(C.32) Wpcn = (b – 2t)hn2 – Wpsn Wpan = bhn2 – Wpcn – Wpsn
(C.33) (C.34)
with Wpsn according to equation (C.19). 3) For the calculation of NE.Rd and ME.Rd, the resistances at the additional point E, the neutral axis is located half-way between hn and the border of the section, so that hE = hn/2 + h/4. 4) The normal force NE results from: NE.Rd = b(hE – hn)fcd + 2t(hE – hn)(2fyd – fcd) + AsE(2fsd – fcd) + Npm.Rd
(C.35)
where AsE is the sum of the areas of reinforcement lying in the additionally compressed region between hE and hn. 5) The plastic section moduli are calculated by using equations C.33 and C.34, substituting hn by hE. Equation C.6 then leads to the moment ME.Rd.
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Annex D (normative) Design of composite columns with mono-symmetrical cross sections — simplified method D.1 General For the design of composite columns with mono-symmetrical cross sections all rules of 4.8.3 should be observed, except those referring only to doubly symmetrical sections and/or biaxial bending. The following application rules should be observed additionally for the non-symmetrical plane of bending. D.2 Scope 1) The elastic centre of area of the uncracked composite cross section should be determined using the elastic stiffnesses with the secant modulus of elasticity for concrete according to 3.1.4.1. 2) The amount of non-symmetry, determined by the distance between the axis through the centre of area and the middle line of the cross section (Figure D.1), should not exceed h/10, where h is the overall depth of the section parallel to the axis of symmetry. D.3 Design for axial compression 1) A normal force acting through the elastic centre of area is assumed to create only axial compression. 2) The slenderness Æ according to 4.8.3.7 should be determined using elastic stiffnesses according to D.2 1). 3) For design according to 4.8.3, the relevant buckling curves in clause 5.5.1 of EC3 are: — curve b for concrete filled hollow sections, — curve c for concrete encased I-sections with bending about the strong axis of the section — curve d for all other sections. D.4 Design for compression and uniaxial bending 1) The M-N interaction curve for the cross section should be calculated according to the plastic centroidal axis. This axis is defined by the centre of the strength distributions under pure compression, i.e. it is the axis about which the bending moment of the internal forces is zero when the section resists a compressive force equal to Npl.Rd. 2) The distance from the plastic centroidal axis to the elastic centroidal axis (epl in Figure D.1) is given by
where
Ai Ei fi zi
are the relevant areas are the stiffness moduli for the areas according to D.2 are the design strengths of the materials for the areas, and are the distances to the reference axis for the calculation.
3) The design rule of 4.8.3.13 8) changes to |Msd|+ NSdep=|k 0.94Mp=.Rd
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Figure D.1 — Axes of a mono-symmetrical cross section 4) Special care should be taken when the bending moment changes its sign along the column length. Two interaction curves and two bending resistances Mp=.Rd then have to be determined, as shown in Figure D.2.
Figure D.2 — Example for the two interaction curves for a mono-symmetrical cross section related to the same bending resistance Mp=.y+.Rd D.5 Long-term behaviour of concrete 1) The influence of long-term loads should be taken into account if significant. 2) The influence may be allowed for by an additional eccentricity of the permanent normal force ecs = ee= – ee=,t where ee= ee=,t
is the elastic centroidal axis for short term loading calculated using stiffnesses according to D.2 with Ec according to 3.1.4.1, and is the elastic centroidal axis for long term loading calculated using stiffnesses according to D.2 with Ec = E½c according to 3.1.4.2.
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Annex E (normative) Partial shear connection method for composite slabs
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E.1 Scope 1) In this annex the partial shear connection method is given which is allowed in 7.6.1.3 1) as an alternative to the “m-k” method. 2) The partial shear connection method should be used only for composite slabs with a ductile behaviour as defined in 10.3.1.5 1). 3) The partial shear connection method may be used to account for contributions from end anchorage and additional reinforcement, provided that it is proved by the additional tests specified in 10.3.1.2 8) and 9) that the method is valid. E.2 Determination of Eu.Rd 1) The horizontal shear strength at the steel-concrete interface shall be determined by means of tests in accordance with 10.3.1. 2) The partial interaction diagram, as shown in Figure E.1, should be determined using the measured dimensions and strengths of the concrete and the steel sheet. For the concrete strength the mean value fcm of a group as specified in 10.3.1.3 9) may be used.
Figure E.1 — Determination of the degree of shear connection from Mtest Mp.Rm and Ncf should be determined according to 7.6.1.2 4) or 5) as appropriate, but using measured values of dimensions and strengths instead of design values. The relation between M and Nc may be calculated as follows: M = Ncz + Mpr where
and other symbols are as defined in 7.6.1.2, except that in the equation for Mpr, Ncf is replaced by Nc.
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3) From the maximum applied loads, the bending moment M at the cross-section under the point load due to the applied load, dead weight of the slab and spreader beams should be determined. The path A F B F C in Figure E.1 then gives a value ) for each test, and a value Eu from:
where Lo is the length of the overhang. 4) The characteristic shear strength Eu.Rk should be taken as minimum value obtained from all tests reduced by . 5) The design shear strength Eu.Rd is the characteristic strength Eu.Rk divided by *É = . E.3 Verification of the longitudinal shear resistance 1) For the verification, design values for the strengths of materials should be used. 2) With the design shear strength Eu.Rd determined according to E.2, the design partial interaction diagram should be determined (Figure E.2). In this diagram the bending resistance MRd of a cross-section at a distance Lx from the nearer support is plotted against Lx. The length Lsf is given by:
For Lx U Lsf the shear connection is full, so the bending resistance (flexural failure) is critical. For Lx < Lsf the shear connection is partial, so the longitudinal shear resistance is critical.
Figure E.2 — Design partial interaction diagram 3) At any cross-section the design bending moment MSd should not exceed the design resistance MRd. The verification procedure is illustrated in Figure E.3 for two slabs with different types of loading and span.
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Figure E.3 — Verification procedure E.4 Verification of composite slabs with end anchorage 1) The horizontal shear strength of an end anchorage may be determined by at least three additional tests as specified in 10.3.1.2 8). 2) For each test the value of ) should be determined as given in E.2. The resistance of the end anchorage follows from: V= = )Ncf – Eumb (Ls + Lo) where Eum is the mean value of Eu determined by the tests with the same sheeting but without end anchorage. 3) The characteristic resistance of the end anchorage should be taken as the minimum value obtained from all tests reduced by . 4) The design value V=d is the characteristic resistance V=k divided by *É = . 5) The verification should essentially follow the same procedure as given in E.3; but for the determination of the design partial interaction diagram, account may be taken of the contribution of the end anchorage by modification of Nc as follows: Nc = b Lx Eu.Rd + V=d The results in a shift of the basic diagram in the Lx – direction over a distance – V=d/b Eu.Rd, as illustrated in Figure E.4.
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Figure E.4 — Design partial interaction diagram for a slab with end anchorage E.5 Verification of composite slabs with additional reinforcement 1) If additional bottom reinforcement is taken into account the verification should essentially follow the same procedure as given in E.3 but the design partial interaction diagram should be modified by calculating MRd as follows (Figure E.5): MRd = Np z1 + Mpr + Nas z2 where
Np = b Lx Eu.Rd Nas = As fsk/*s z2 = ds – 0.5 x
As is the area of fully-anchored bottom reinforcement within width b, and other symbols are as in 7.6.1.2 5).
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2) The validity of the partial connection method for composite slabs with additional reinforcement should be proved by three additional tests as specified in 10.3.1.2 9). 3) For each test the theoretical maximum moment should be calculated as given in 1) above, with the following modifications: — use of measured dimensions and strengths; — Np = b (Ls + Lo) Eum where Eum is the mean value of Eu determined by the tests with the same sheeting but without additional reinforcement. 4) The partial connection method is deemed to be valid if no bending resistance obtained from the tests is more than lower than the theoretical value calculated according to 3) above.
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Annex F (informative) Checklists of the information required in test reports F.1 Push tests F.1.1 Scope In this section the information is listed which normally should be included in reports of push tests in accordance with Section 10.2. F.1.2 Test specimens 1) Specimen description (nominal): — shape and dimensions of the shear connection; — dimensional tolerances agreed by the manufacturer; — guaranteed or specified ultimate strength of the connection material. For specimens with ribbed slabs and profiled steel sheeting the following additional information is required: — shape and dimensions of the steel sheet; — dimensional tolerances agreed by the manufacturer; — guaranteed or specified ultimate strength of the sheeting material; — through deck welding or punching. 2) Specimen preparation: — surface condition of the steel flange; — position of concrete member during casting and curing; — curing time of specimen and of test cubes/cylinders. — curing procedure of specimen and of test cubes/cylinders. For specimens with ribbed slabs and profiled steel sheeting the following additional information is required: — surface condition of the steel sheet. 3) Specimen properties (measured): — geometrical properties of the concrete slabs (height), width and length; — mean geometrical properties of five shear connectors taken from the lot to be used (height, shank diameter and head diameter); — geometry of the weld collar if any; — position and dimensions of the reinforcement; — spacing and number of shear connectors; — details of the composition of the concrete mix (grading and type of aggregate, type of cement, water/cement ratio); — mechanical properties of the concrete (cylinder or cube compressive strength); — mechanical properties of the shear connectors (yield strength, tensile strength and maximum elongation at fracture); — mechanical properties of the reinforcement (yield strength and tensile strength).
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For specimens with ribbed slabs and profiled steel sheeting the following additional information is required: — geometrical properties of the steel sheet; — mechanical properties of the steel sheet. F.1.3 Testing 1) Testing arrangement: — description of the testing assembly and position of load; — description of the concrete base conditions. 2) Test loading procedure: — frequency, number of cycles and value of the dynamic loading; — loading increment. 3) Description of instrumentation: — applied load; — slip measurement; — measurement of transverse separation between the steel member and the slabs. F.1.4 Results 1) Load-slip curve with the characterization of: — ultimate load — ultimate deformation — load at first observable crack. 2) Transverse separation between the steel member and the slabs. 3) Additional information on test: — identification of the failure mode; — any significant event. F.2 Testing of composite slabs F.2.1 Scope In this section the information is listed which normally should be included in reports of tests on composite slabs in accordance with Section 10.3. F.2.2 Test specimens 1) Specimen description (nominal): — shape and cross-section geometry of the steel sheet; — dimensional tolerances agreed by the manufacturer; — guaranteed yield point (or specified yield point of the steel sheet). 2) Specimen preparation: — surface condition of the steel deck (steel surface coating and condition), — propping during casting and curing; — curing time concrete curing procedure. 3) Specimen properties (measured): — cross-section geometry of the profiled steel sheet, including the spacing and dimensions of the shear transfer devices (embossment or indentation); — position and dimensions of the mesh reinforcement; — geometrical dimensions of the composite slabs (height, width and length); — mechanical properties of the profiled steel sheet (tensile strength, yield strength, elongation); — details of the composition of the concrete mix (grading and type of aggregate, type of cement, water/cement ratio); — mechanical properties of the concrete at the date of testing: cylinder or cube strength and tensile strength.
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F.2.3 Testing 1) Testing arrangement: — description of the testing assembly; — position of loads; — width of the load application; — shear span; — span length; — crack inducers; — overhang. 2) Test loading procedure: — spreader beams weight; — steel deck dead load; — concrete dead load; — loading increment; — type of loading; — rate of loading; — cyclic loading variation; — number of cycles. 3) Description of instrumentation: — deflection at midspan; — applied load (including self weight, spreader beams, jacks, etc. if of influence to the composite action); — end slip (at both ends of specimen). F.2.4 Results 1) Load-deflection curve with the characterization of: — end slip at each load increment; — load at first observable crack, and at midspan deflection of L/50; — ultimate load (maximum load); — deflection at first slip; — deflection under maximum load; — maximum deflection (deflection at the end of the test). 2) Additional information on test: — any significant event; — identification of the mode of failure; — location of failure crack.
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National annex NA (informative) Committees responsible
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The preparation of the National Application Document for use in the UK with ENV 1994-1-1:1992 was entrusted by Technical Committee B/525, Building and civil engineering structures, to Subcommittee B/525/4, Composite construction, upon which the following bodies were represented: Association of Consulting Engineers British Industrial Fasteners Federation British Steel Industry Concrete Society Department of the Environment (Building Research Establishment) Department of the Environment (Construction Directorate) Department of the Environment (Specialist Services) Department of Transport Institution of Civil Engineers Society of Engineers Incorporated Steel Construction Institute
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