EUROPEAN CONVENTION FOR CONSTRUCTIONAL STEELWORK CONVENTION EUROPEENNE DE LA CONSTRUCTION METALLIQUE E U R O P A I S C H E K O N V E N T I O N F U R S T A H L B A U
ECCS - Technical Committee 11 Composite Structures
Composite Beams and Columns to Eurocode 4
FIRST EDITION
1993 No 72
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the Copyright owner :
ECCS General Secretariat CECM Avenue des Ombrages, 32136 bte 20 EKS 8-1200 BRUSSEL (Belgium)
Tel. 382-762 04 29 Fax 382-762 09 35
ECCS assumes no liability with respect to the use for any application of the material and information contained in this publication.
FOREWORD
The Eurocodes are being prepared to harmonize design procedures between countries which are members of CEN (European Committee for Standardization) and have been published initially as ENV documents (European pre-standards - prospective European Standards for provisional application). The Eurocode for composite construction (referred to in this publication as EC4) is:
ENV 1994-1-1: Eurocode 4 Design of composite steel and concrete structures Part 1.1 : General rules and rules for buildings
The national authorities of the member states have issued National Application Documents (NAD) to make the Eurocodes operative whilst they have ENV-status.
This publication "Composite Beams and Columns to Eurocode 4" has been prepared by the ECCS-Technical Committee 11 to provide simplified guidance on composite beams and columns in supplement to EC4 and to facilitate the use of EC4 for the design of composite buildings during the ENV-period.
"Composite Beams and Columns to Eurocode 4" contains those rules from EC4 that are likely to be needed for daily practical design work. It is a self-standing document and contains additional information as simplified guidance, design tables and examples. References to EC4 are given in [ 1. Any other text, tables or figures not quoted from EC4 are deemed to satisfy the rules specified in EC4. In case of doubt, when rules are missing (e.g. for the design of composite slabs, etc.) or when more detailed rules are required, EC4 should be consulted in conjunction with the National Application Document for the country in which the building project is situated.
The working group of ECCS-TC 1 1, responsible for this publication is: are:
The other members of ECCS-TC 1 1
Anderson, D. Beguin, P. Bode, H. Brekelmans, J . Falke, J. Janss, J . Lawson, R. M. Mutignani, F.
United Kingdom France Germany (Chairman of TC11) Netherlands Germany Belgium United Kingdom Italy
Arda, T.S. Aribert, J.M. Axhag, F. Bossart, R . Cederwall, K. Lebet, J.P. Leskela, M. Schleich, J.B. Stark, J.W.B.
Turkey France Sweden Switzerland Sweden Switzerland Finland Luxembourg Netherlands
Tschemmernegg, F. Austria
Particular thanks are given to those organisations who supported the work. Besides ECCS itself and its members, specific contributions were made by:
Bauberatung Stahl, Germany Bundesvereinigung der Priifingenieure fur Baustatik, Germany The Department of Trade and Industry UK British Steel (Sections, Plates & Commercial Steels) UK
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The text was prepared for publication by the Steel Construction Institute, UK.
This publication presents useful information and worked examples on the design of composite beams and columns to Eurocode 4 Design of composite steel and concrete structures (ENV 1994-1-1). The information is given in the form of a concise guide on the relevant aspects of Eurocode 4 that affect the design of composite beams and columns normally encountered in general building construction.
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Each section of the publication reviews the design principles, gives design formulae and makes cross-reference to the clauses of Eurocode 4. Information on the design of composite slabs is also given, although the publication concentrates on the influence of the slab on the design of the composite beam.
Pesign aids are also presented to assist in selecting the size of steel beams to be used in certain applications. Worked examples cover the design of composite beams with full and partial shear connection, continuous beams, and composite columns.
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COMPOSITE BEAMS AND COLUMNS TO EUROCODE 4
CONTENTS
Page
SUMMARY NOTATION
PART 1: DESIGN GUIDE
1. INTRODUCTION
1.1 Scope of Publication 1.2 Cross-referencing 1.3 Partial Safety Factors
2. INITIAL DESIGN
I 3. ACTIONS AND COMBINATION RULES FOR DESIGN
3.1 Fundamental Requirements 3.2 Definitions and Classifications 3.3 Design Requirements
3.3.1 General 3.3.2 Ultimate limit state 3.3.3 Serviceability limit state
3.4 Design of Steel Beams
4. MATERIALS AND CONSTRUCTION
4.1 Description of Forms of Construction
4.1.1 Types of columns 4.1.2 Types of beams 4.1.3 Types of slabs 4.1.4 Types of Shear connectors 4.1.5 Types of erection 4.1.6 Types of connection
4.2 Properties of Materials
4.2.1 Concrete 4.2.2 Reinforcing steel 4.2.3 Structural steel
2 7
9
9 10 10
11
14
14 14 15
15 15 16
17
18
18
18 18 19 19 20 20
22
22 23 23
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4.2.4 Profiled steel decking for composite slabs
Partial Safety Factors for Resistance and Material Properties 4.3
5 . COMPOSITE OR CONCRETE SLABS
5.1 5.2
5.3
5.4
5.5
Introduction Initial Slab Design
5.2.1 Proportions of composite slabs 5.2.2 Construction condition 5.2.3 Composite action 5.2.4 Deflections
Influence of Decking on the Design of Composite Beams
5.3.1 Ribs transverse to beams 5.3.2 Ribs parallel to beam
Detailing Rules for Shear Connectors Welded Through Profiled Steel Decking
5.4.1 Welding and spacing of studs 5.4.2 Additional requirements for steel decking
Minimum Transverse Reinforcement
6. ULTIMATE LIMIT STATE: COMPOSITE BEAMS
6.1 Basis of Design of Composite Beams
6.1.1 General 6.1.2 Verification of composite beams 6.1.3 Effective width of the concrete flange 6.1.4 Classification of cross-sections 6.1.5 Distribution of internal forces and moments in continuous
beams
6.2 Resistance of Cross Sections
6.2.1 General 6.2.2 Positive moment resistance 6.2.3 Negative moment resistance 6.2.4 Vertical shear 6.2.5 Momen t-shear interaction
24
24
25
25 26
26 27 27 28
28
29 29
30
30 31
31
33
33
33 33 34 35
40
42
42 42 44 45 45
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6.3
6.4
6.5
Shear Connection
6.3.1 General 6.3.2 Resistance of shear connectors 6.3.3 Spacing of shear connectors 6.3.4 Longitudinal shear force 6.3.5 Transverse reinforcement
Partially Encased Beams
Lateral Torsional Buckling of Continuous Beams
7. SERVICEABILITY LIMIT STATE: COMPOSITE BEAMS
7.1 General Criteria
7.2 Calculation of Deflections
7.2.1 Second moment of area 7.2.2 Modular ratio 7.2.3 Influence of partial shear connection 7.2.4 Shrinkage-induced deflections 7.2.5 Continuous beams
7.3 Vibration Checks
7.4 Crack Control
8. ULTIMATE LIMIT STATE: COMPOSITE COLUMNS
8.1
8.2
8.3
Introduction
Design Method
8.2.1 General 8.2.2 Design assumptions 8.2.3 Local buckling 8.2.4 Shear between the steel and concrete components
Simplified Method of Design of Composite Columns
8.3.1 Resistance of cross-sections to axial load 8.3.2 Resistance of members to axial load 8.3.3 Resistance of cross-sections to combined compression
8.3.4 Analysis for moments applied to columns 8.3.5 Resistance of members to combined compression and
and uniaxial bending
uniaxial bending
46
46 46 48 49 53
56
57
59
59
59
59 61 63 63 64
65
65
67
67
68
68 68 68 69
70
70 71
74 76
76
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~
9.
10.
11.
12.
8.3.6 Limits of applicability of the simplified design method
FIRE RESISTANCE
CONSTRUCTION AND WORKMANSHIP
10.1 General 10.2 Sequence of Construction 10.3 Stability 10.4 10.5 Loads during Construction 10.6
Accuracy during Construction and Quality Control
Stud Connectors Welded through Profiled Decking
REFERENCES
DESIGN TABLES AND GRAPHS FOR COMPOSITE BEAMS
12.1 Moment Resistance of Composite Beam Relative to Steel Beam
12.2
12.3
Second Moment of Area of Composite Beam Relative to Steel Beam
Design Tables for Composite Beams Subject to Uniform Loading
ANNEX 1 DESIGN FORMULAE FOR COMPOSITE COLUMNS
PART 2: WORKED EXAMPLES
1. Simply Supported Composite Beam with Solid Slab and Full Shear Connection
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78
80
82
82 82 82 82 83 83
85
86
87
88
89
94
97
2. Simply Supported Composite Beam with Composite Slab and Partial Shear Connection
3. Continuous Composite Beam with Solid Slab
4. Composite Column with End Moments
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NOTATION
Notation is not presented in detail here and reference should be made to Eurocode 4 Part 1.1. However, the use of the following common symbols and subscripts is given to help understanding of this publication.
Symbols:
A
d E
beff
fck
* fY F G h I L M N Q t V W YF Y x
X E
cross-sectional area effective width of slab diameter of shear connector; depth of web considered in shear area modulus of elasticity of steel characteristic compressive (cylinder) strength of concrete yield strength of steel force in element of cross-section; load (action) permanent loads (actions) depth of element second moment of area length or span moment (with subscripts as below) axial force variable loads (actions) thickness of element of cross-section shear force plastic section modulus partial safety factor for loads partial safety factor for materials (with subscripts as below) slenderness d ( f y /235) reduction factor on axial resistance due to imperfection
Subscripts to symbols:
a
k P
PP R S Rd Sd
C
S
W
structural steel concrete characteristic value profiled steel decking (sheeting) reinforcement plastic resistance (in bending, shear or compression) resistance (of member) internal force or moment design value of resistance design value of internal force or moment web of steel section
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Member axes:
X
Y major axis bending 2 minor axis bending
along the axis of the member
Terminology:
This publication adopts the terminology used in Eurocode 4 Part 1.1. However, there are some important terms which may be defined to assist in understanding this document. These are:
Hogging moment
Sagging moment
Moment resistance
Stud connector
Decking
Transverse reinforcement
Negative moment causing compression in the bottom flange of the beam.
Positive moment causing tension in the bottom flange of the beam.
Resistance of the steel or composite cross-section to bending actions.
A particular form of shear connector comprising a steel bar and flat head that is welded automatically to the beam.
Profiled steel sheet which may be embossed for composite action with the concrete slab.
Reinforcement placed in the slab transversely (across) the steel beam.
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1.
1.1
INTRODUCTION
Eurocode 4 Part 1.1 deals with the design of composite steel and concrete structures. The publication Composite beams and columns to Eurocode 4 presents simplified guidance in accordance with the main Eurocode, but concentrates on the common forms of structure that are encountered in building construction.
Although the publication retains the principles and application rules of the Eurocode, it is not written in a code format because of the need to offer further explanation on the design principles. It is intended that each section is read as a design guide with cross-reference to the relevant clauses in EC4 (or EC3 or EC2, as appropriate). Because of this less formal presentation it is possible to introduce additional information and design aids in the form of tables and graphs.
Part 1 of the document covers the design methods for composite beams and composite columns. Also given are some design tables for composite beams using standard steel sections.
Part 2 presents a number of fully worked examples for simply supported and continuous composite beams, and composite columns.
Scope of Publication
A decision was made to limit the scope of the publication to the information that 90% of designers will need 90% of the time. In this sense, simply supported or continuous beams in braced construction are most typical of modern buildings. Similarly, composite beams are increasingly associated with composite slabs, rather than solid slabs. Composite columns are also increasingly popular.
In summary, the document covers the following aspects in detail:
Composite beams with composite or solid slabs Braced frames (non-sway) Simply supported (simple) connections Continuous beams (or with connections equivalent to the moment resistance of the beam) Welded stud shear connectors Full or partial shear connection Class 1 or 2 sections (class 3 webs are permitted for continuous beams) Composite columns (encased I sections or concrete filled sections) under axial load Composite columns with moments using simplified interactions Partially encased sections
The document makes only general reference (and does not include detailed information) on:
Global analysis of composite frames Design of connections Behaviour of composite slabs Cracking in concrete Other forms of shear connector Use of precast concrete slabs Lightweight concrete Lateral-torsional buckling Fire resistance aspects General analysis of composite columns
Specifically excluded is the use of:
Non-uniform cross-sections Class 3 or 4 sections Sway frames Partial strength connections
1.2 Cross-referencing
This publication is to be read as a self standing document and cross-refers to other sections within the text. To aid cross-referencing to Eurocode 4 (EC4) or other Eurocodes, the source clauses in these Eurocodes are presented in brackets at the start of each section, or adjacent to the relevant part of the text. All references to Eurocodes or EN standards or other important publications are listed in full at the back of the publication.
1.3 Partial safety factors
National authorities are able to select partial safety factors on loads and materials which are given as boxed values in the Eurocodes. Because this document is intended to be read throughout Europe the recommended boxed values have been used in the text, Worked Examples and Design Tables.
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Further information on partial safety factors is given in Sections 3 and 4.3.
INITIAL DESIGN
Composite beams comprise I or H section steel beams attached to a solid or composite floor slab by use of shear connectors. Composite slabs comprise profiled steel decking which supports the self weight of the wet concrete during construction and acts as reinforcement to the slab during in-service conditions.
Composite beams behave as a series of T beams in which the concrete is in compression when subject to positive moment and the steel is mainly in tension. The beams may be designed as simply-supported, or as continuous over a number of supports. The relative economy of simple or continuous construction depends on the benefits of reduced section size and depth in relation to the increased complexity of the design and the connections in continuous construction.
Composite beams may be designed to be unpropped for reasons of speed of construction. Propped construction may be appropriate where it is necessary to control deflections of the steel beam during construction. The sizing of the composite beam is independent of the form of construction provided the steel beam is able to support the loads developed during concreting.
The following recommendations are made for initial sizing of composite beams. It is important to recognise the difference between secondary beams which directly support the decking and composite slab and primary beams which support the secondary beams as point loads. Primary beams usually receive greater loads than secondary beams and therefore are usually designed to span a shorter distance for the same beam size. Alternatively, long span primary beams, such as composite trusses, can be designed efficiently with short span secondary beams. These cases are illustrated in Figure 2.1.
General features:
Slab depth - typically 120mm to 180mm depending on fire resistance, structural and other requirements
Slab span - 2.5m to 3.5m unpropped 3.5m to 5.5m propped subject to maximum span: depth ratio of 35 for a slab with continuity at one end (see Section 5 for further guidance).
Grid sizes - primary and secondary beams can be designed for approximately the same depth when grid dimensions are in proportion of 1 : lV2 respectively
Beam design
The following beam proportions should give acceptable deflections when the section size is determined for moment resistance.
a) Simply supported
Secondary beam
Primary beam
b) Continuous
Secondary beam
Primary beam
Steel grade -
Concrete grade -
Shear connectors -
- span: depth ratio of 18 to 20 (depth = total beam and slab depth)
- span: depth ratio of 15 to 18
- span: depth ratio of 22 to 25 (end bays)
- span: depth ratio of 18 to 22
higher grade steel (Fe 510) usually leads to smaller beam sizes than lower grade steel (Fe 360 or Fe 430)
C 25/30 for composite beams.
19mm diameter welded stud connectors are placed typically at 150mm spacing. These studs can be welded through the steel decking up to 1.25mm thick.
22mm diameter welded stud connectors where through- deck welding is not used.
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L i
T L column
span of slab
primary beam
-
&----8-12m--&
span of slab -primary beam
Figure 2.1 Framing plans for medium and long span beams
I 12 -18m L- :
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P4
3. ACTIONS AND COMBINATION RULES FOR DESIGN
3.1 Fundamental Requirements [2.1]
A structure shall be designed and constructed in such a way that:
0 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
0 with appropriate degrees of reliability, it will sustain all actions and influences likely to occur during execution (ie. construction period) and subsequent use, and have adequate durability in relation to maintenance costs.
A structure shall also be designed in such a way that it will not be damaged by events like explosions, or impact or consequences of human error to an extent disproportionate to the original cause.
3.2 Definitions and Classifications [2.2]
Limit States
Limit states are states beyond which the structure no longer satisfies the design performance requirements. Limit states are classified into:
a ultimate limit states 0 serviceability limit states.
Ultimate limit states are those associated with collapse, or with other forms of structural failure which may endanger the safety of people.
Serviceability limit states correspond to states beyond which specified in-service criteria are no longer met by the structure.
Actions
Definitions and principal classification*)'
An action (F) is:
0 a force (load) applied to the structure (direct action), or
0 an imposed deformation (indirect action); for example, temperature effects or differential settlement.
*)l Fuller definitions of the classification of actions will be found in the Eurocode for Actions.
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Actions are classified as:
0 permanent actions (G), eg. self-weight of structures, fittings, and fixed equipment.
0 variable actions (Q), eg. imposed loads, wind loads or snow loads.
e accidental actions (A), eg. explosions or impact from vehicles.
Characteristic values of actions F, are specified
a in the Eurocode for Actions or other relevant loading codes, or
0 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.
The design value F, of an action is expressed in general terms as:
where yF = partial safety factor for actions Fk = characteristic value of the action
3.3 Design Requirements [2.3]
3.3.1 General
It shalI be verified that no relevant limit state is exceeded. All relevant design situations and load cases shall be considered, including those at the construction phase. Possible deviations from the assumed directions or positions of actions shall be considered.
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.
3.3.2 Ultimate limit state
Verification conditions
When considering a limit state of failure of a section, member or connection (fatigue excluded), i t shall be verified that:
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r
where s d 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, associating all structural properties with the respective design values.
Combination of actions
For each load case, design values for the effects of actions shall be determined from combination rules involving design values of actions, as identified by Table 3.1. The most unfavourable combinations are considered at each critical location of the structure, for example, at the points of maximum negative or positive moment. In Table 3.1 a combination factor of 0.9 is taken into account. Eurocodes permit the use of other combination factors, if reliable load data are is available.
Load combinations to be considered:
* If the dead load G counteracts the variable action Q:
** If a variable load Q counteracts the dominant loading:
Yo = 0
permanent actions, eg. self weight
variable actions, eg. imposed loads on floors, snow loads, wind loads
the variable action which causes the largest effect at a given location
partial safety factor for permanent actions
partial safety factor for variable actions
Table 3.1 Combinations of actions for the ultimate limit state
3.3.3 Serviceability Limit State
For each load case, design values for the effects of actions shall be determined from combination rules involving design values of actions as identified by Table 3.2.
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Load combinations to be considered:
. Gk + Qk.max
I 2.
Parameters defined in Table 3.1.
Table 3.2 Combinations of actions for the serviceabilitv limit state
3.4 Design of Steel Beams
The steel beam is to be designed in accordance with Eurocode 3. The loads to be considered shall include the self weight of the beam and slab and an additional load taking account of the construction operation. Although no information is given in EC4 on these additional construction loads to be used in the design of the steel beams, it is consistent with the design of slabs to assume a construction load of 0.75 kN/m in the design of the beams.
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4.
4.1
4.1.1
4.1.2
MATERIALS AND CONSTRUCTION
Description of Forms of Construction
Types of column
Composite columns may be of the form shown in Figure 4.1. There are two main types; concrete encased (totally or partially), and concrete-filled columns.
Figure 4.1 Types of column
Types of beam
Composite beams may be of the form shown in Figure 4.2. Beams are usually of IPE or HE section (or UB or UC section). Partial encasement of the steel section provides increased fire resistance and resistance to buckling.
Figure 4.2 Types of beam
Shear connectors between the slab and beam provide the necessary longitudinal shear transfer for composite action. The shear connection of the steel beam to a concrete slab can either be by full or partial shear connection. This action is considered in Section 6.
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4.1.3 Types of slab
Slabs are either:
h 23d generally 7-d-L h 14d ductile
e concrete slabs: Prefabricated, or cast in situ, or e composite slabs: Profiled steel decking and concrete (see Section 5).
Slabs are generally continuous but are often designed as a series of simply supported elements spanning between the beams.
h
Figure 4.3 Types of composite and concrete slabs
4.1.4 Types of shear connector
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4.1.5
4.1.6
Types of erection
Beams and/or profiled steel sheets may be either propped or unpropped during concreting of the slab. The most economic method of construction is generally to avoid the use of temporary propping. Propping is needed where the steel beam is not able to support the weight of a thick concrete slab during construction, or where deflection of the steel beam would otherwise be unacceptable.
Types of connection
There are many types of connection. Some examples are given in Figure 4.6 for beam-to-column and beam-to-beam connections. In design to EC4, the two forms of connection generally envisaged are (i) nominally pinned or (ii) rigid and full strength. No application rules are given for partial strength connections, as defined in EC4 [4.10 5.31.
1 anti-crack reinforcement
secondary beam-
reinforcement 1
a. Examples of nominally pinned connections both in the construction and corn posit e stages
Figure 4.6 Examples of connections in composite frames
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reinforcement
1 I L e x t e n d e d end b. Example of rigid and full strength connection
tensile reinforcement
plate
c. Example of connections that are pinned in the construction stage and partial strength in the composite stage
Figure 4.6 (Continued) Examples of connections in composite frames
In Figures 4.6(b) and (c), the connections may be considered to be rigid, but may or may not develop the full strength of the composite section. In the case of Figure 4.6(c) the connection is pinned in the construction stage, but is made moment resisting by the slab reinforcement and fitting pieces which transfer the necessary tension and compression forces.
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4.2
Strength Class of Concrete
fck (compressive strength)
f,,, (tensile strength)
4.2.1
C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60
20 25 30 35 40 45 50
2.2 2.6 2.9 3.2 3.5 3.8 4.1
Properties of Materials
The material properties given in this Section are those required for design purposes.
Concrete [3.1 J
Normal and lightweight concrete may be used. In this Section, data for normal weight concrete are given. For lightweight, concrete see EC4 [3.1.4.1(3)].
Strength Class C
E,,, (kN/mm2)
C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60
29 30.5 32 33.5 35 36 37
The strength class (ie. C20) refers to cylinder strength of concrete, fck. The cube strength is given as the second figure (ie. /25).
Shrinkage (long-term free shrinkage strain ecs) for normal weight concrete:
in dry environment (filled members excluded) 325 x 10-6
in other environments and for filled members 200 x 10-6
The secant modulus of elasticity for short term loading is given in Table 4.2 below.
Table 4.2 Secant modulus of elasticity for concrete Ecm for short-term loading
Modular ratio, n = EJE,, using E, as in Table 4.4.
For long term (permanent) loads, the modulus of elasticity for concrete is reduced due to creep and is taken as Ec,,/3, leading to an increase in n by a factor of 3. In most cases of imposed loading the representative value of modulus of elasticity is taken as Ec,/2 [3.1.4.2(4)].
Although not generally required for general design:
10 x 10-6 / "C - - Coefficient of linear thermal expansion, aT
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4.2.2 Reinforcing steel [3.2]
Refer to EN 10 080, which is the product standard for reinforcement.
Types of Steel
e according to ductility characteristics: high (class H) or normal (class N)
0 according to surface characteristics: plain smooth or ribbed bars
Steel grades
B 500: characteristic yield strength fsk = 500N/mm2
The modulus of elasticity of reinforcing steel is taken as for structural steel.
4.2.3 Structural steel [3.3]
Nominal values of material strength are as given below. The nominal values may be adapted as characteristic values in calculations.
Nominal steel grade
Fe 360 Fe 430 Fe 510
Thickness t mm*)
t 5 40mm 40mm < t 5 lOOmm
fy f" fy f U 235 360 215 340 275 430 255 410 355 5 10 335 490
- - yield strength fr fU - - ultimate tensile strength
Table 4.3 Nominal values of strength of structural steels to EN 10 025 (in N/mm')
No values of material strength are given for high-strength steel. For this steel, clause 3.2.1(2) of EC3 is applicable.
- - 2 1 m [N/rnrn2] - - 81000 [N/mm2]
modulus of elasticity Ell shear modulus Ga coefficient of linear thermal expansion density P
10 x 10-6 [/"Cl - - 7850 [kg/m31 - -
(YT
Table 4.4 Design values of other properties of steel
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4.2.4 Profiled steel decking for composite slabs
Profiled Steel Decking
Composite slabs are dealt with in this publication only as far as they affect the design of the composite beam. Reference should be made to EC4 for further information on the design of composite slabs, with EN 10 147 as the product standard for steel sheeting .
Shear COMectOrS (studs, angles,
friction grip bolts) and Longitudinal Shear in Slabs
4.3 Partial Safety Factors for Resistance and Material Properties [2.3.3.2]
1.10
1 .oo
In general, resistance is determined by using design values of strength of the different materials or components as given in the individual chapters of EC4 or in this publication. Recommended values for fundamental and accidental combinations are given in Table 4.5. These values may be modified by the various National Authorities and are given as boxed values in EC4.
1.25
1 .oo
Combination
Fundamental
Accidental
Structural Steel
Y O
1.10
1 .oo
Concrete
Yc
1 S O
1.30
Steel Reinforcement
Ys
1.15
1 .oo
5 YW Yvs
Table 4.5 Partial safety factors for resistance and material properties
Values for bolts, rivets, pins, welds, and slip resistance of bolted connections are as given in EC3 clause 6.1.1(2).
Where the member resistance is influenced by the buckling of the structural steel section, a specific safety factor YRd = [ l . 101 is recommended [2.2.3.2(2)], [4.6.3], [4.8.3.2].
When the design value Rd is determined by tests, refer to Eurocode 4.
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5. COMPOSITE OR CONCRETE SLABS
5.1 Introduction
This section reviews the different forms of concrete slab that may be used in conjunction with composite beams, and the factors that influence the design of the beams. The detailed design of composite slabs, which is covered in chapter 7 of EC4, is not treated here.
Three types of concrete slab are often used in combination with composite beams. These three types are listed as follows:
0 Solid slab: This is a slab with no internal voids or rib openings, normally cast-in place using traditional wooden formwork.
* Composite slab: This is a slab which is cast-in-place using decking (cold- formed profiled steel sheeting) as permanent formwork to the concrete slab. When ribs of the decking have a re-entrant shape and/or are provided with embossments that can transmit longitudinal forces between the decking arid the concrete, the resulting slab acts as a composite slab in the direction of the decking ribs.
0 Precast concrete slab: This is a slab consisting of prefabricated concrete units and cast-in-place concrete. There are two forms that may be used: Thin precast concrete plate elements of approximately 50mm thickness are used as a formwork for solid slabs or alternatively, deep precast concrete elements are used for longer spans with a thin layer of cast-in-place concrete as a wearing surface. Deep precast concrete units often have hollow cores which serve to reduce their dead weight. The units may be designed to act compositely with the steel beams, but this aspect is outside the scope of this document.
No further information is given on solid or pre-cast concrete slabs in this section.
In the design of composite slabs the following aspects have to be considered:
* The cross-sectional geometry of the slab: In some cases the full cross- sectional area of the slab cannot be used for composite beam calculations. A reduced or effective cross-sectional area must be calculated. Formulae for determining effective slab widths are given in Section 6.1.3.
0 The influence of the slab on the shear connection between the slab and the beam: Stud behaviour and maximum strength may be modified due to the shape of the ribs in the slab (see Section 6.3.2.2). The correct placement of studs relative to ribs is of great importance.
e The quantity and placement of transverse reinforcement: Transverse reinforcement is used to ensure that longitudinal shear failure or splitting of the concrete does not occur before failure of the composite beam itself.
Page 25
r
Figure 5.1 Typical coniposite slab with re-entrant deck profile
5.2 Initial Slab Design
5.2.1 Proportions of composite slab
A typical composite slab is shown in Figure 5.1. In general such slabs consist of: decking (cold formed profiled steel sheeting), concrete and light mesh reinforcement. There are many types of decking currently marketed in Europe. These can be, however, broadly classified into two groups:
0 Re-entrant rib geometries. An example of such a profile is shown in Figure 5. I . Note that embossments are often placed on the the top flange of the deck.
0 Open or trapezoidal rib geometries. An example of such a profile is shown in Figure 5.2. Note that embossments are often placed on the webs of the deck.
Slab depths range from 100 to 200mm; 120 to 180mm being the most common depending on the fire resistance requirements.
Decking rib geometries may vary considerably in form, width and depth. Typical rib heights, h,, are between 40mm and 85mm. Centre-line distances between ribs generally vary between 150mm and 300mm. Embossment shapes and sheet overlaps also vary between decking manufacturers.
Page 26
generally vary between 150mm and 300mm. Embossment shapes and sheet overlaps also vary between decking manufacturers.
In general, the sheet steel is hot-dipped galvanised with 0.02mm of zinc coating on each side. The base material is cold-formed steel with thicknesses between 0.75mm and 1.5mm. The yield strength of the steel is in the range of 220 to 350N/mm2.
Deeper decks permit longer spans to be concreted without the need for propping. Ribs deeper than 85mm, however, are not treated in this document. For such ribs composite action with the steel beam may be significantly reduced, thus requiring special attention.
5.2.2 Construction condition
Normally, decking is first used as a construction platform. This means that it supports construction operatives, their tools and other material commonly found on construction sites. Good construction practice requires that the decking sheets be attached to each other and to all permanent supports using screws or shot-fired nails.
Next, the decking is used as formwork so that it supports the weight of the wet concrete, reinforcement and the concreting gang. The maximum span length of the decking without propping can be calculated according to the rules given in Part 1.3 of EC3. Characteristic loads for the construction phase are 1.5 kN/m2 on any 3 metres by 3 metres area and 0.75 kN/m2 on the remaining area, in addition to the self weight of the slab.
Typically, decking with a steel thickness of 1.2mm, and a rib height of 60mm, can span between 3m and 3.5m without propping.
50
Figure 5.2 Typical composite slab using a trapezoidal deck profile, showing the main geometrical parameters
5.2.3 Composite action
After the concrete has hardened, composite action is achieved by the combination of chemical bond and mechanical interlock between the steel decking and the concrete. The chemical bond is unreliable and is not taken into account in design. Composite slab design is generally based on information provided by the decking manufacturer,
Page 27
in the form of allowable imposed load tables. These values are determined from test results and their interpretation as required in EC4 clause 10.3. In most catalogues the resistance to imposed load is given as a function of decking type and steel sheet thickness, slab thickness, span length and the number of temporary supports. Generally, these resistances are well in excess of the applied loads, indicating that composite action is satisfactory or that the design is controlled by other limitations. However, care should be taken to read the catalogue for any limitations or restrictions due to dynamic loads, and concentrated point and line loads.
Maximum Span: Depth ratios
Normal weight concrete Light weight concrete
5.2.4 Deflections [7.6.2.2]
End span Internal span Single span
35 38 32 30 33 27
Deflection calculations in reinforced concrete are notoriously inaccurate, and therefore some approximations are justified to obtain an estimate for the deflections of a composite slab. The stiffness of a composite slab may be calculated from the cracked section properties of a reinforced concrete slab, by treating the cross-sectional area of decking as an equivalent reinforcing bar.
However, if the maximum ratio of span length to slab depth is within the limits of Table 5.1 no deflection check is needed. The end span should be considered as the general case for design. In this case it is assumed that minimum anti-crack reinforcement exists at the supports. Experience shows that imposed load deflections do not exceed span/350 when using the span to depth ratios shown in Table 5.1. More refined deflection calculations will lead to greater span to depth ratios than those given in Table 5.1.
5.3
Table 5.1: Maximum span to depth ratios of composite slabs
Influence of Decking on the Design of Composite Beams
Profiled steel change decking performs a number of important roles, and influences the design of the composite beam in a number of ways. It:
0
0
0
may provide lateral restraint to the steel beams during construction;
causes a possible reduction in the design resistance of the shear connectors;
acts as transverse reinforcement leading to a reduction in the amount of bar reinforcement needed.
These factors are addressed more fully in Section 6.
The orientation of the sheeting is important. Decking ribs may be oriented in two ways with respect to the composite beam:
Page 28
Decking ribs transverse to the steel beam, as shown in Figure 5.3. The decking may be discontinuous (Figure 5.3a), or continuous (Figure 5.3b) over the top flange of the beam.
e Decking ribs parallel to the steel beam, as shown in Figure 5.4.
The shear connectors may be welded through the decking, or placed in holes formed in the troughs of the decking. In the latter case the shear connectors can also be welded to the steel beam off-site. When the through welding procedure is used on site, studs may not be welded through more than one sheet and overlapping of sheets is not permitted.
5.3.1 Ribs transverse to the beam
The concrete slab in the direction of the beam is not a homogeneous (solid) slab. This has important consequences for the design of the composite beam, as only the depth of concrete over the ribs acts in compression. Additionally, there is often a significant influence on the resistance of the shear connectors due to the shape of the deck profile.
Figure 5.3
5.3.2 Ribs parallel to the beam
Decking ribs transverse to the beam
In the construction phase, decking with this orientation is not considered effective in resisting lateral torsional buckling of the steel beam.
In this case, the complete cross-section of the slab may be used in calculating the moment resistance of the beam. The orientation of the ribs also implies that there will be little reduction in the resistance of the studs due to the ribs in the concrete slab.
Page 29
Figure 5.4 Decking ribs parallel to the beam
5.4 Detailing Rules for Shear Connectors Welded Through Profiled Steel Decking [6.4.3.1]
5.4.1 Welding and spacing of studs
When the decking is continuous and transverse to the beam (Figure 5.3a), the correct placement of studs in relation to the decking rib is of great importance. The most important rules for welded headed studs are repeated here: Welded headed studs are normally between 19mm and 22mm in diameter. Stud diameters up to 19mm are generally used for through deck welding only. For welded studs the upper flange of the steel beam should be clean, dry and unpainted. For satisfactory welding, the deck thickness should not exceed 1.25mm if galvanized, or 1 S m m if ungalvanized. In all cases, welding trials shall be performed. The following limitations should also be observed:
0 The flange thickness of the supporting beams should not be less than 0.4 times the diameter of the studs, unless the studs are located directly over the web.
0 After welding, the top of the stud should extend at least 2 times diameter of the stud above the top of the decking ribs and should have a concrete cover of at least 20mm.
0 The minimum distance between the edge of the stud and the edge of the steel flange is 20mm.
0 The transverse spacing between studs should not be less than 4 times the diameter of the stud.
0 The longitudinal spacing between studs should not be less than 5 times the stud diameter and not greater than six times the overall slab depth nor 800mm [ 6.4.3(3)].
Page 30
5.4.2 Additional requirements for steel decking
Studs must be properly placed in decking ribs. A summary of these rules are shown in Figure 5 . 5 , and listed below:
e Studs are usually attached in every decking rib, in alternate ribs, or in some cases, in pairs in every rib. If more studs are needed than are given by a standard pattern these additional studs should be positioned in equal numbers near the two ends of the span.
e Some modem decks have a central stiffener in the rib which means that it is impossible to attach the stud centrally. In such cases it is recommended that studs are attached to the side of each stiffener closest to the end of the beam shown as the favourable side in Figure 5.5. This means that a change in location at midspan is needed.
e Alternatively, studs can be staggered so that they are attached on each side of the stiffener in adjacent ribs.
0 At discontinuities in the decking, studs should be attached in such a way that both edges of the decking at the discontinuity are properly anchored. If the decking is considered to act as transverse reinforcement this may mean placing studs in a zigzag pattern along the beam, as shown in Figure 5.5.
The minimum distance of the centre of the stud to the edge of the decking is defined in EC4 7.6.1.4(3) as 2.2 times the stud diameter.
Similar rules may be established for other forms of shear connectors such as shot- fired cold-formed angles.
5.5 Minimum Transverse Reinforcement
Transverse reinforcement must be provided in the slab to ensure that longitudinal shearing failure or splitting does not occur before the failure of the composite beam itself (see Section 6.3.5).
The decking is not allowed to participate as transverse reinforcement unless there is an effective means of transferring tension into the slab, such as by through-deck welding of the shear connectors. Where the decking is continuous, the decking is effective in transferring tension and can act as transverse reinforcement. This is not necessarily the case if the ribs are parallel to the beam because of overlaps in the sheeting.
Minimum amounts of transverse reinforcement are required. The reinforcement should be distributed uniformly. The minimum amount is 0.002 times the concrete section above the ribs.
Page 31
I
unfavourable side favourable side
- 2
2 2 0 2
i beam
- ,
2.2d beam =butt joint
stiffener end of s p a n 1
shear connector r
O I I-
t stiffener
,-shear connector
Page 32
Figure 5.5 Detailing of shear connectors in decks with a central stiffener
6. ULTIMATE LIMIT STATE OF COMPOSITE BEAMS
6.1 Basis of Design of Composite Beams
6.1.1 General [4.1]
The following clauses outline the design rules for composite beams. The treatment is largely restricted to Class 1 and Class 2 sections which are capable of developing their plastic moment of resistance without local buckling problems. Partially encased beams are also included. The majority of composite beams encountered in practice are thereby covered.
Composite structures and members should be so proportioned as to satisfy the basic design requirements for the ultimate limit state using the appropriate partial safety factors and load combinations.
Continuous composite beams may be analysed in all cases by elastic global analysis, and Class 1 beams by plastic hinge analysis.
transverse reinforcement -headed studs -
partially encasedA L steel sections: either rolled or welded Figure 6.1 Typical cross-sections of composite beams
Figure 6.1 shows typical cross-sections. Other combinations between steel sections and slabs are also used, but are not covered in this document.
6.1.2 Verification of composite beams [4.1.2]
Composite beams shall be checked for:
0 resistance of critical cross sections [4.4]
e resistance to longitudinal shear [6]
0 resistance to lateral-torsional buckling [4.6] in the case of continuous span beams or cantilevers (see Section 6.5)
0 resistance to shear buckling [4.4.4] and web crippling [4.7].
Page 33 1
The possible critical sections to be checked, are summarised below:
II ! I! rn! rn! I -
I
Figure 6.2 Critical sections for design calculation and related action effects
Critical cross-sections:
1-1 bending resistance 11-11 vertical shear resistance 111-111 bending moment - vertical shear interaction
Regions :
IV-IV
K L I } transverse reinforcement VI1
longitudinal shear resistance of the shear connectors longitudinal shear resistance of the slab and
lateral torsional buckling of bottom flange.
Critical cross-sections are for example the sections I, I1 and I11 shown in Figure 6.2, and also sections subjected to heavy concentrated loads or reactions.
In case of single span beams, subject to uniform load, no bending moment - vertical shear interaction has to be considered.
6.1.3 Effective width of the concrete flange [4.2.2]
The effective width be, for elastic global - analvsis may be assumed to be constant over the whole of each span. It may be taken as the value at midspan (beam supported at both ends), or as the value at the support (cantilever).
The effective breadth for verification of cross-sections should be taken as the midspan value (for sections in positive bending), or as the value at the support (for sections in negative bending).
Page 34
Figure 6.3 Effective width of concrete slab, be,
/ / ,'/ / .'/ ,// // /'/ / /'/ ,'/ / // /'/ ,'/ /'/ /'/ ' / / / /
The effective width on each side of the steel web should be taken as PO /8, but not greater than half the distance to the next adjacent beam web (see Figure 6.3). The length PO is:
0 equal to the span of simply supported beams
0 the approximate distance between points of zero bending moment in case of continuous composite beams (see Figure 6.4).
Figure 6.4 Length 4, for continuous beams
6.1.4 Classification of cross-sections [4.3]
6.1.4.1 General
Composite beams are classified into 4 Classes depending on the local buckling behaviour of the steel flange and/or the steel web in compression.
Page 35
~
The classification system of cross-sections of composite beams is as follows:
Class 1 (plastic) cross-sections are those which can form a plastic hinge with sufficient rotation capacity for plastic hinge analysis.
Class 2 (compact) cross-sections are those which can develop their plastic moment resistance, but have limited rotation capacity.
0 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.
e Class 4 cross-sections are those in which it is necessary to make explicit allowances for the effects of local buckling when determining the moment resistance or compression resistance of the section.
Class 3 and 4 cross-sections are not further considered in this document.
A cross-section is classified according to the least favourable class of its steel elements in compression, according to the following Tables 6.1 to 6.4. Steel webs and flanges in compression are classified according to their width to thickness ratios and stress distributions. The positions of the plastic neutral axes of composite sections should be calculated for the effective cross-section using design values of strengths of materials.
Cross-sections under positive bending, where the plastic neutral axis lies in the concrete or in the steel flange, belong to Class 1 independent of the width to thickness ratios of the web and the flanges.
Under certain circumstances the classification can be upgraded (refer to Section 6.4 and to EC4).
6.1.4.2 Flanges
I Flanges in compression I rolled I welded I
I I I
1 1 10E I 1 0 E I 9E I 9 E
I Steel I E I Fe 360
Fe 430
I Fe 510 I 0.81 I
Table 6.1 Maximum width-to-thickness ratios, c/t, for steel outstand flanges in compression
Page 36
The following observations may be made concerning rolled sections:
0 The steel compression flange, if properly attached to the concrete flange, may be assumed to be of Class 1.
All IPE, HEB and HEM sections belong to Class 1 (with regard to their flanges).
To classify steel flanges of HEA sections, see Table 6.2, which is based on the requirements of Table 6.1.
Other restrictions are given in EC4 [6.4.1 SI.
0
0
HEA Sections
160 180 200
240 260 280
300 320 340
360 400 450
Fe 360 Fe 430 Fe 510
1 1 2 1 2 3 1 2 3
1 2 3 2 3 3 2 3 3
2 3 3 1 2 3 1 1 3
1 1 2 1 1 1 1 1 1
Table 6.2 Classification of HEA Sections (based on flange proportions)
0 HEA sections deeper than 450 mm belong to Class 1.
0 HEA sections of Class 3 belong to Class 2, if they are partially encased (see Section 6.4)
6.1.4.3 Webs
Webs: (internal elements perpendicular to axis of bending)
Stress distribution
Class
1
2
Web subject to bending 01 = 0.5
d/t I 72 E
~ ~
d/t I 83 E
Web subject to compression
Q = 1.0
B d/t I 33 E
dlt I 38 E
Table 6.3 Maximum width-to-thickness ratios for steel webs
Web subject to bending and compression
0 I O1 I 1.0
when 01 > 0.5: d/t I 396 ~l(1301 - 1)
when 01 I 0.5: d/t I 36 E/CY
when 01 > 0.5: d/t I 456 d(1301 - 1)
when 01 S 0.5: d/t I 41.5 /a
Webs of all IPE and HE sections subject to bending, or bending and compression with a neutral axis characterized by Q I 0.5, belong to Class 1.
In case of single span beams under positive bending, local instability of the steel web is not critical for any IPE or HE profiles.
If the steel web is stressed fully in compression, Tables 6.4 a - d can be used for the classification based on the requirements in Table 6.3.
A Class 3 web that is encased in concrete in accordance with Section 6.4 [4.3.1 (6) to (9)] may be assumed to be in Class 2 [4.3.3.1(2)].
An uncased Class 3 web may be represented by an effective depth of web equivalent to a Class 2 web. The cross-section may then be analysed plastically and the section treated as Class 2 [4.3.3.1(3)], provided that the compression flange is Class 1 or 2.
Page 38
Tables 6.4 Classification of steel webs fully in compression (a = l), based on Table 6.3
IPE Sections
140 1 60 180
200 220 240
270 300 330
360
Fe 360
2
~ ~
Fe 430
3
~ ~~
Fe 510
4
Sections smaller than IPE 140 are in Class 1
HEA Sections ~
340 360 400
450 500 550
a00
Fe 360 Fe 430 ~
Fe 510
Sections smaller than HE 340A are in Class 1
Sections smaller than HE 450B are in Class 1
HEM Sections
1 1 1
2 3
600 650 700
800 900
1 1 2
3 4
Fe 360
1 2
Fe 430 I Fe 510
Sections smaller than HE 600M are in Class 1
6.1.5 Distribution of internal forces and moments in continuous beams [4.5]
6.1.5.1 General
Bending moments in composite beams at ultimate limit state (ULS) may be determined by elastic or rigid-plastic global analysis, using factored loads. The design bending moments shall not exceed the resistance of the composite beam. The verification shall be done at critical cross-sections (see section 6.1.2).
6.1 S .2 Plastic global analysis [4.5.2]
Plastic global analysis (or plastic hinge analysis) may be used for all continuous beams, provided that the following requirements are met [4.5.2.2(2)] [4.2.1(3)]:
e the steel cross-section is symmetrical about the plane of its web, e lateral torsional buckling does not occur, e the steel compression flange at a plastic hinge location is laterally restrained, e sufficient rotation capacity is available.
Rotation capacity is sufficient when the following requirements are met:
e the effective cross-sections at plastic hinge locations are in Class 1 and, elsewhere, all others are in Class 1 or 2
adjacent spans do not differ in length by more than 50% of the shorter span: e 0.66 I Lk/Lk+l 5 1.5
e end spans do not exceed 115% of the length of the adjacent span: Le I 1.15 L;
e the reinforcement in concrete sections under tension fulfils the requirements of high ductility (see Section 4.2.2 or EC2)
In case of heavy concentrated loads, refer to EC4 [4.5.2.2(2)(d)].
Class 2 sections are only permitted where no rotation capacity is required.
Page 40
6.1.5.3 Elastic global analysis [4.5.3]
Elastic global analysis is based on a linear stress-strain relationship [4.5.3.1].
No account need be taken of bending moments due to shrinkage.
Loss of stiffness, due to cracking of concrete in negative moment regions and yielding of steel, influences the distribution of bending moments in continuous composite beams.
Two methods of elastic global analysis are permitted by EC4 at the ultimate limit state to determine the bending moment distribution:
e uncracked section method, based on midspan effective width ignoring any , longitudinal reinforcement (method 1);
0 cracked section analysis, based on a section in the region of the internal support comprising the steel member together with the effectively anchored reinforcement located within the effective width at the support (method 2).
Method 1 Method 2
uncracked cracked
Figure 6.5 Definition of uncracked and cracked sections for elastic global analysis
Method 2 is more suitable for computer analysis. However, this method may be also used at the serviceability limit state to accurately determine the moments in cases of crack control in the slab. This method assumes that, for a length of 15% of the span on each side of the support, the section properties are those of the cracked section under negative moments (see Figure 6.5). I2 is the cracked second moment of area which is less than the uncracked value, I,. Refer to Section 7.2 for the calculation of these properties.
The elastic bending moments for a continuous composite beam of uniform depth within each span may be modified by reducing maximum negative moments by amounts not exceeding the percentage of Table 6.5. The resulting positive bending moments are then found by static equilibrium.
Page 41
Class of cross-section in negative moment region 1 2
For uncracked elastic analysis - method 1 40 30 For cracked elastic analysis - method 2 25 15
Table 6.5 Limits to redistribution of negative moments at supports, in terms of the maximum percentage of the initial bending moment to be reduced
6.2 Resistance of Cross-Sections
6.2.1 General
The design bending resistance may be determined by plastic theory, but only where the effective composite section is in Class 1 or Class 2.
6.2.2 Positive moment resistance [4.4.1.2(2)]
The following assumptions shall be made in the calculation of MR, = Mpl,Rd (see Figures 6.6 to 6.8). In all cases Msd I Mpf,Rd for adequate design.
The effective areas of longitudinal reinforcement in tension and in compression are stressed to their design yield strength f& /ys in tension or compression. Alternatively, reinforcement in compression in a concrete slab may be neglected. Profiled steel decking in compression shall be neglected.
The presence of profiled steel decking, when running transverse to the main span, reduces the area of concrete that may resist compression forces. Hence, the maximum possible depth of concrete in compression is h,, which is the depth of concrete flange above upper flange of profiled decking of depth, $.
The calculation method for MpI,Rd depends on the location of the plastic neutral axis. Three cases to be considered for doubly symmetric sections are as follows:
Case 1
hc
Neutral axis in the concrete flange 0,SS fck IT
Figure 6.6 Neutral axis in the concrete-flange: plastic stress distribution
F a = A, . f,, /ya Z C
= Fa /(b,ff . 0.85 fck /yc ) I h,
Mp,,Rd = Fa (ha/2 + h, h, - Z, /2) Case 2 Neutral axis in the steel flange
1 b e f f l
h, 'a2 U
Figure 6.7 Neutral axis in the steel flange: plastic stress distribution
F C = h, be, . 0.85 fck /yc For the neutral axis to lie in the flange: Fa > F, > F, where F, = d t,,, . fy /ya
Taking moments about the top flange, it follows that the moment resistance is:
M,,,,,, 2: Fa ha /2 + F, (2h, + h, )/2 Case 3 Neutral axis in the web
Figure 6.8 Neutral axis in the web: plastic stress distribution
For the neutral axis to lie in the web: F, < F, Hence, the depth of web in compression: zcw = 0.5 ha - Fc/(2 t,,, fy/ya)
Neutral axis depth: Z C = h, 3- h, + z,,
Page 43
where Mapl,Rd is the plastic moment resistance of the steel section alone.
6.2.3 Negative moment resistance
The composite cross-section consists of the steel section together with the effectively anchored reinforcement located within the effective breadth of the concrete flange at the support (see Figures 6.9 and 6.10). The reinforcement is located at height, a, above the top flange of the steel beam.
In the calculation of Mpl ,Rd two cases have to be considered:
Case 4 Neutral axis in steel flange for negative bending
!+ Fs
Figure 6.9 Neutral axis in the steel flange: plastic stress distribution (high degree of reinforcement)
For the neutral axis to lie in the top flange: Fa > F, > F,
Case 5 Neutral axis in steel web for negative bending
1 beff -7 P7 - - - - - 2qf$/la
I I I
Figure 6.10 Neutral axis in the web: plastic stress distribution
For the neutral axis to lie in web: F, < F,
Page 44
Depth of web in tension:
Neutral axis depth: ZC
ZCW = ha/2 - F, /(2t,,, . fy /ya )
= hc + h, + zc,
Mp],Rd = Mapl,Rd + F, (ha/2 + a) - F,2 /(4 t,,, fy /Ya ) 6.2.4 Vertical shear [4.4.2.2(2)]
The contribution of the concrete slab to the resistance to vertical shear is normally neglected. Therefore, the shear force resisted by the structural steel section should satisfy:
'Sd vpl,Rd
where V,],Rd is the plastic shear resistance given by:
vpj,Rd = (fy h/3)/ra
The shear area A, may be taken as follows (see EC3, 5.4.6):
Rolled I, H and C sections loaded parallel to the web, A, = 1,04 ha t,,, Built-up I sections, A, = d t,,,
In addition, the shear buckling resistance of a steel web shall be checked in the following cases [4.4.2.2(3)]:
e for a vertically unstiffened and uncased web, where d / t , > 69 E; .(for all IPE and HE profiles, d/t,,, < 69 E)
for an unstiffened web encased in concrete in accordance with Section 6.4, where d/t, > 124 E ;
e
If necessary, the shear buckling resistance can be calculated with the rules given in EC4 r4.4.41.
6.2.5 Moment-shear interaction [4.4.3]
Where the vertical shear V S d exceeds half the plastic shear resistance, Vp1,,d, allowance shall be made for its effect on the resistance moment at the same cross section. The plastic resistance moment should then be calculated using a reduced design yield strength fy,rd for the shear area A,, according to:
Page 45
Figure 6.11 Normal stress distribution for M-V interaction in negative bending
The following interaction criterion, based on Figure 6.1 1, should be satisfied:
where: M R d is the design moment resistance as given in Sections 6.2.2 and 6.2.3.
Mf,Rd is the design plastic moment resistance of the cross-section consisting of the flanges only.
6.3 Shear Connection [6]
6.3.1 General
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 at the ultimate limit state, ignoring the effect of natural bond between the materials.
Ductile connectors are those with sufficient deformation capacity to justify the assumption of ideal plastic behaviour of the shear connection in the structure.
Headed studs may be considered as ductile i f
height after welding, h 2 4d
16 mm 5 d 5 22 mm
and N/N, 2 the minimum degree of shear connection (see Figure 6.14).
6.3.2 Resistance of shear connectors [6.3.2.1]
6.3.2.1 Solid slabs
Diameter d [mml
22 19 16
The design shear resistance of a welded headed stud (as shown in Figure 4.5) with a normal weld collar should be determined from the smaller of
Equation (1) f,, = Equation (2) (01 = 1.0)
450 500 C 25/30 C 30/37 C 35/45 C 40/50 C 45/55
109.4 121.6 98.1 110.0 121.6 (132.9) (142.9) 81.6 90.7 73.1 82.1 90.7 (99.1) (106.6) 57.9 64.3 51.9 58.2 64.3 (70.3) (75.6)
P,, = 0.8 f,, (7rd2/4)lyv or
Equation (1)
P,, = 0.29 a d 2 /E,,)/?, Equation (2)
whichever is smaller,
~
where d and h are the diameter and height of the stud respectively (see Figure 4.5)
f U is the specified ultimate tensile strength of the material of the stud but not greater than 500 N/mm2. The commonly specified strength is 450 N/mm2.
fck is the characteristic cylinder strength of the concrete at the age considered;
Em is the mean value of the secant modulus of the concrete in accordance with Table 4.2;
Q = 0.2 [(h/d) + 11 Q = 1 for h/d > 4,
for 3 I h/d I 4;
The partial safety factor yv is given as 1.25 in Table 4.5. The resulting design resistances of stud connectors obtained from equations (1) and (2) are presented in Table 6.6 below.
Table 6.6 Design resistance PRd [kNl of stud connectors with h/d > 4
The value in brackets denote values which exceed those given by Equation (1); the lower value should therefore be used in design.
6.3.2.2 Influence of shape of profiled steel decking [6.3.3]
Where profiled steel decking with ribs parallel to the supporting beam is used, the studs are located within a region of concrete that has the shape of a haunch. The design shear resistance should be taken as their resistance in a solid slab, multiplied by the reduction factor k,, given by the following expression:
kp = 0.6 . b, /h, . [(h/% - l)] 5 1.0 where h I hp + 75
Figure 6.12 Beams with steel decking ribs parallel to the beam
Where studs of diameter not exceeding 20 mm are placed in ribs transverse to the supporting beam with a height h, not exceeding 85 mm and a width bo not less than h,, the design shear resistance should be taken as their resistance in a solid slab (calculated as given above except that fu should not be taken as greater than 450 Nlmm) multiplied by the reduction factor given by the following expression:
where N, is the number of stud connectors in one rib at a beam intersection, not to exceed 2 in computations.
For studs welded through the steel decking, k, should not be taken greater than 1.0 when N, = 1, and not greater than 0.8 when N, 1 2.
6.3.3 Spacing of shear connectors [6.1.3] [6.4]
Stud connectors may be spaced uniformly over a length L,, between adjacent critical cross-sections (see Section 6.1.2) provided that:
8 all critical sections in the span considered are in Class 1 or Class 2
8 N/N, satisfies the limits for partial shear connection given in Section 6.3.4.2, when L is replaced by L,.,, and
8 the plastic resistance moment of the composite section does not exceed 2.5 times the plastic resistance moment of the steel member alone.
Detailing rules for placement of studs are given in Section 5.4.
6.3.4 Longitudinal shear force
6.3.4.1 Full shear connection r6.2.1.13
a. Single span beams [6.2.1.1(1)]
For full shear connection, the total design longitudinal shear V, to be resisted by shear connectors between the point of maximum positive bending moment and the end support should be:
V, = F,, where FCf = A, f bya or F,f = o*8zfck hc /Yc
whichever is the smaller.
b. Continuous span beams [6.2.1.1(2)]
For full shear connection, the total design longitudinal shear V, to be resisted by shear connectors between the point of maximum positive bending moment and an intermediate support shall be calculated according to Figure 6.13 as follows:
V, = F,, + (A, fsk )/ys where A, is the effective area of longitudinal slab reinforcement.
This calculation is illustrated in Figure 6.13 for a particular case of the positions of the plastic neutral axes in negative and positive bending.
Figure 6.13(a) Moments in continuous beam
Page 49
(b) Internal force distribution
Figure 6.13 Calculation of the longitudinal shear force in continuous beam
The number of shear connectors for full shear connection shall be at least equal to the design longitudinal shear force V,, divided by the design resistance of a connector, PRd. Therefore, the number of shear connectors in the zone under consideration is:
PRd takes into account the influence of the shape of the profiled sheeting, as given in Section 6.3.2.2.
6.3.4.2 Partial shear connection with ductile shear connectors [6.2.1.2]
Partial shear connection may be used if all cross-sections are in Class 1 or 2.
Ideal plastic behaviour of the shear connectors may be assumed if a minimum degree of shear connection is provided (see Figure 6.14, where L is the beam span (metres)).
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9 y / / 0 '0 / ' I I / 1
I I I I '-&I I I I I
I I I I I I I
I I I I - Liml 0 5 10 15 20 25 Figure 6.14 Minimum degree of shear connection
The minimum degree of shear connection is defined by the following equations:
(a) N/Nf I 0.4 + 0.03 L where 3At 2 Ab (b) (c) N/N, 1 0.04 L where A, = A, (see further restrictions)
N/Nf 2 0.25 4- 0.03 L where A, = Ab
where A, = top flange area and A,, = bottom flange area
In all cases, N/Nf 2 0.4, where
N Nf
= number of shear connectors = number of shear connectors for full shear connection.
Equation (c) (line c in Figure 6.14) may be used when the following conditions are satisfied:
e
e
e
e
e
a single, centrally placed 19 mm diameter stud per trough, with a height after welding of not less than 76 mm rolled I or H sections has equal flanges the concrete slab is composite with sheeting that spans perpendicular to the beams and is continuous across it. deck profile with b, /h, 2 2 and h, 5 60 mm linear interaction method is used (see following)
The general method for other cases is line b in Figure 6.14.
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The moment resistance of a composite beam designed for partial shear connection may be determined by either of the following methods:
1. 2. Linear interaction method.
Stress block (or equilibrium) method
In Method 1 the force transferred to the concrete is determined by the longitudinal resistance of the shear connectors. Equilibrium equations can be established explicitly, in a similar manner to Section 6.2.2. The relationship is defined by the curve ABC in Figure 6.15.
Method 2 is more conservative, but is often preferred because it is a simple method of determining the moment resistance, knowing the moment resistances of the steel beam and the composite section for full shear connection. The relationship is defined by the line AC in Figure 6.15. Because it is a more conservative treatment of partial shear connection, the linear interaction method may be used with a less severe restriction on the minimum degree of shear connection.
I .o P--Fcf
-d % M pl,Rd - - - -
equilibrium method
linear interaction
f -a? B / / method
M p l , Rd I N or -
I .O Fcf Nf - F C
Figure 6.15 Relation between F, and MSd for partial shear connection
The force transferred by the shear connectors, Fc, in the linear interaction method is:
MSd - Mapl,Rd Fcf - - - Mapl,Rd Mpl,Rd
FC
where Mapl,Rd is the design moment resistance of the structural steel section. Fc, is the longitudinal shear force required for full shear connection, and Msd I Mpl,Rd, as determined for full shear connection.
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The design longitudinal shear force, V, can be determined from Figure 6.13 with FCf replaced by the force transferred by the shear connectors, F,.
I f F, is determined for a known distribution of shear connectors, then the maximum value of the reduced moment resistance may be calculated using the same linear interaction equation. This reduced moment resistance, MRd, should be not less than Msd, which is the applied moment.
Figure 6.16 Reduced bending moment resistance of cross-sections
A good approximation to the equilibrium method can be obtained by considering the moment-axial force interaction for an I section, as illustrated in Figure 6.16. It follows that:
where F, = force transferred by shear connectors = C PRd and N S Nf
Fa = axial resistance of steel section = A, fy /ya
The interaction between moment and shear is covered in Section 6.2.5.
6.3.5 Transverse reinforcement
6.3.5.1 Longitudinal shear in the slab [6.6.1]
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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. VSd should be determined in accordance with Section 6.3.4 and be consistent with the design of the shear connectors at the ultimate limit state.
Potential failure surfaces are shown in Figure 6.17. Top and bottom reinforcement in the slab may be considered to be effective. Where steel decking is continuous over the beam, or is effectively anchored by shear connectors, it may also be considered to act as transverse reinforcement. Failure surface a-a controls in these cases. Failure surface b-b is not considered critical in EC4 in cases where steel decking is used.
In determining VSd, account may be taken of the variation of longitudinal shear across the width of the concrete flange. Longitudinal shear is considered to be transferred uniformly by the shear connectors.
Figure 6.17 Typical potential surfaces of shear failure (examples)
6.3.5.2 Design resistance to longitudinal shear [6.6.2(1) to (5)]
The design resistance of the concrete flange (shear planes a-a illustrated in Figure 6.17) 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, provided it is continuous across the top flange of the steel beam or if it is welded to the steel beam by stud shear connectors.
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:
whichever is smaller, where
7Rd is the basic shear strength to be taken as 0.25 fctk0.05 /yc, (see Table 6.7)
Concrete 1 c 1 c 1 c 1 c strength 20125 25/30 30/37 35/45
rRd 0.25 0.30 0.33 0.37
Table 6.7 Basic shear strength 7Rd (in N / I I U ~ ~ )
rl = 1 for normal-weight concrete,
4050 45/55 50/60 *J rl = 0.3 + 0.7 (p/24) for lightweight-aggregate concrete of unit weight p in
w/m3,
A,, is the mean cross-sectional area per unit length of beam of the concrete shear surface under consideration,
A, is the sum of the cross-sectional areas of transverse reinforcement (assumed to the perpendicular to the beam) per unit length of beam crossing the shear surface under consideration (Figure 6.17) including any reinforcement provided for bending of the slab,
Vpd is the contribution of the steel decking, if applicable, as given in 6.3.5.3.
For a ribbed slab the area of concrete shear surface A,, 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 A,, but for parallel ribs it should not be included in A,,. These cases are illustrated in Figure 6.17.
Transverse reinforcement considered to resist longitudinal shear shall be anchored so as to develop its yield strength in accordance with EC2. At edge beams, anchorage may be provided by means of U-bars looped around the shear connectors.
6.3.5.3 Contribution o,f profiled steel decking as transverse reinforcement [6.6.3(1) to (2)]
Where the profiled steel sheets are continuous across the top flange of the steel beam, the contribution of the decking with ribs transverse to the beam may be taken as:
- fYP 'pd -
YPP
where Vpd is per unit length of the beam for each intersection of the shear surface by the sheeting,
A, is the cross-sectional area of the profiled steel decking per unit length of the beam, and
fyp is its yield strength, given in N/mm2.
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Where the decking 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 decking, the contribution of the decking should be taken as:
- 'pb,Rd *P fYP - but I - - Yap VPd S
where Ppb,Rd is the design resistance of a headed stud against tearing through the steel sheet [7.6.1.4]) and
s is the spacing centre-to-centre of the studs along the beam.
6.4 Partially Encased Beams
A typical partially encased composite beam is shown in Figure 6.18. The partial encasement provides fire protection to the steel beam.
Figure 6.18 Cross-section of partially encased beam
Reauiremen ts:
Concrete encasement the webs of composite beams shall be [4.3.1(6) to (S)]:
0 reinforced by longitudinal bars and stirrups, and/or welded mesh [4.3.1(7)]
0 mechanically connected to the web by stud connectors, welded bars, or bars through holes
0 capable of preventing buckling of the web and of any part of the compression flange towards the web.
Influence of encasement:
0 Substantial increase in fire resistance is possible (reference should be made to EC4 Part 1.2);
* A web in Class 3 may be represented by an effective web of the same cross- section in Class 2 [4.3.3.1(2)];
Web encasement may be assumed to contribute to resistance against local buckling [4.3.2,4.3.3], shear buckling [4.4.2.2] and lateral-torsional buckling [4.6.2]. However, the shear buckling resistance for an unstiffened and encased web shall be verified (by testing), if d/t, > 124 E [4.4.2.2(3)];
e No application rules are given for the contribution of concrete encasement of a steel web to resistance in bending and vertical shear.
Where the depth h of a partially encased steel member does not exceed the limit given in Section 6.5 [4.6.2(m)] by more than 200 mm [4.6.2], verification of lateral torsional buckling is not necessary provided the conditions in EC4, [4.6.2 (a) to (k)] are satisfied, (see Section 6.5).
6.5 Lateral-Torsional Buckling of Continuous Beams [4.6]
The concrete slab may usually be assumed to prevent the upper flange of the steel section (connected to the concrete part) from moving laterally.
In negative moment regions of continuous composite beams the lower flange is subject to compression. The tendency of the lower flange to buckle laterally is restrained by the distortional stiffness of the cross-section (inverted U-frame action).
Web encasement in accordance with Section 6.4 [4.3.1] may be assumed to contribute to resistance to lateral-torsional buckling [4.6.2], see Table 6.8.
No direct calculation for the lateral stability of a composite beam is necessary when the following conditions are satisfied:
adjacent spans do not differ in length by more than 20% of the shorter span or where there is a cantilever, its length does not exceed 15% of the adjacent span.
the loading on each span is uniformly distributed and the design permanent load exceeds 40% of the total load.
the shear connection in the steel-concrete interface satisfies the requirements of Sections 5.4 and 6.3.
e the slab proportions are typical of those in general building design (see Section 5.2).
ha I maximum depth of steel member is as given in Table 6.8.
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l t b - t I t b -
Profile
IPE HEA
Fe 360 Fe 430 Fe 510 Fe 360 Fe 430 Fe 510
600 550 400 800 750 600 800 700 650 1o00 900 850
All HEB sections satisfy the requirements for lateral torsional buckling.
The data in Table 6.8 for IPE sections is also applicable for UB and other equivalent rolled sections, provided the depth/width of the steel section does not exceed 2.75.
In other cases a check for lateral torsional buckling according to EC4 [4.6] and [Annex B] is required. If necessary, additional discrete lateral restraints may be provided to the compression flange, for example, by bracing or transverse members.
For edge beams, fully anchored top reinforcement is required in the slab [4.6.2(h)].
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7.
7.1
7.2
7.2.1
SERVICEABILITY LIMIT STATES [ 5 ] , [2.3.4]
General Criteria
The serviceability requirements for composite beams concern the control of deflections, cracking of concrete and, in some cases, vibration response. Deflections are important in order to prevent cracking or deformation of the partitions and cladding, or to avoid noticeable deviations of floors or ceilings. Floor vibrations may be important in long span applications, but these calculations are outside the scope of the Code (see Section 7.3).
Loads to be used at the serviceability limit state are presented in Section 3.3.3 [2.3.4]. Normally unfactored loads are used.
In order to calculate serviceability effects, account should be taken of any non-linear effects due to cracking, steel yielding etc. Most designers base assessments at the serviceability limit state on elastic behaviour (with certain modifications for creep and cracking etc). To avoid consideration of post-elastic effects, limits are often placed on the stresses existing in beams at the serviceability limit state.
- No stress limitations are made in Eurocode 4 because:
0 post-elastic effects in the mid span region are likely to be small and have little influence on deflections;
0 the influence of the connections on the deflection of simply supported beams has been neglected;
0 account is taken of plasticity in the support region of continuous beams.
Deflection limits are not specified in EC4. Reference is made to Eurocode 3 (see Tables 7.1 and 7.2) for limits on deflections due to permanent and variable loads.
Calciilat ion of deflect ions [5.2.2(2) J
Second moment of area
Deflections are calculated knowing the second moment of area of the composite section based on elastic properties (see Figure 7.1). Under positive moment the concrete may be assumed to be uncracked, and the second moment of area of the composite section (expressed as a transformed steel section) is:
I
state 0
6,,, = sagging in the final state relative to the straight line joining the supports.
6, = pre-camber (hogging) of the beam in the unloaded state (state 0)
6, = dueto G (variation of the deflection of the beam due to the permanent loads) (state 1)
6, = due to Q (variation of the deflection of the beam due to the variable loading) (state 2)
Table 7.1 Vertical deflections to be considered
Conditions
roofs generally
roofs frequently carrying personnel other than for maintenance
floors generally
floors and roofs supporting brittle finish or non-flexible partitions
floors supporting columns (unless the deflection has been included in the global analysis for the ultimate limit state)
* where a,,,, can impair the appearance of the building For cantilever: L = twice cantilever span
Limits
~ m l l x * 1/200
1/250
1/250
1/250
1/400
1/250
62
1/250
1/300
1/300
1/350
1/500
Table 7.2 Recommended limiting values for vertical deflections
where:
n is the ratio of the elastic moduli of steel to concrete (see Section 7.2.2) taking into account creep
r is the ratio of the cross-sectional area of the steel section, A,, relative to the area of the concrete section (beff hc).
I, is the second moment of area of the steel section
Note: other terms are as defined previously. The effective slab width, be, is the same as used at the ultimate limit state see Section 6.1.3 [5.2.2(3)].
The ratio Ic!Ia therefore defines the improvement in the stiffness of the composite section relative to the steel section. This ratio is presented in Section 11.2 for all IPE and HE sections (up to 600mm deep) for typical slab depth. Typically, Ic/Ia is in the range of 2.5 to 4.0, indicating that one of the main benefits of composite action is in reduction of deflections.
It is not usually necessary to calculate the cracked second moment of area under positive moment as the elastic neutral axis will normally lie in the steel beam, or near the base of the slab. Where it is necessary to know the cracked second moment of area under negative moment, a simple formula may be derived from Figure 7.2. Assuming that the reinforcement is placed at mid-height of the slab above the sheeting, this formula is:
A, (hc+2h, + ha)? + a - - 4 (1 +rs) 4,
where:
r, is the ratio of the cross-sectional area of reinforcement, A,, within the effectivebreadth of the slab to the cross-sectional area of the beam, A,.
This formula may be used in establishing the moments in elastic global analysis (method 2 in Section 6.1.5.3), or in crack control calculations (see Section 7.4).
7.2.2 Modular ratio r3.1.4.21
The values of elastic modulus of concrete under short term loads are given in Table 4.2. The elastic modulus under long term loads is affected by creep, which causes a reduction in the stiffness of the concrete. The modular ratio, n, is the ratio of the elastic modulus of steel to the time-dependent elastic modulus of concrete (see Section 4.2.1). Typically, the modular ratio for normal weight concrete is 6.5 for short term (variable) loading.
The elastic modulus of concrete for long term (permanent) loads is taken as one-third of the short term value, leading to a modulus ratio of approximately 20 for long term (permanent) loading in an internal environment.
-be- Er
- I,
filed steel shee - -
-
CROSS-SECTION
I- Ea
strain stress
ELASTIC STRESSES
Figure 7.1: Elastic analysis of composite beam under positive moment
I
/
OS t - - 7 ES
\ - - - - - I I \
t \ Ze
--
Ea o a
strain stress
Figure 7.2: Elastic analysis of composite beam under negative moment
I , L
- I - T -1-1
Figure 7.2: Elastic analysis of
--
- -
Ea
strain
---I OS
t - - 7 \ \ \ Ze
o a
stress
composite beam under negative moment
Page 62
For building of normal usage, surveys have shown that the proportions of variable and permanent imposed loads rarely exceed 3: 1. Although separate deflection calculations may be needed for the variable and permanent deflections, a representative modular ratio is usually appropr
