Composite Beams & Columns to Eurocode 4

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

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

Page 1

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.

~

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.

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 Page 3

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

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 Page 5

~

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

~ ~

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

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

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.

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

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.

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.

L i

T L column span

of

slab primary beam

-

& -8 -1 2 m -&

span of slab -primary beam

Figure 2.1 Framing plans for medium and long span beams

I

12 -18m

L-

:

Page 13

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.

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), it shall be verified that:

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.

Load combinations to be considered:

’.

G k + 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.

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.

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

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

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.

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

-

-

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

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].

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.

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.

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.

5 0

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:

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.

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)].

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

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

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].}

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

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

9 E

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

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.

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

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)].

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.

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

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,,

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 M p l , R d 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

P

7

- - - - -

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,