Design Guide for SHS Concreter Fillied COLUMN

8/13/2019 Design Guide for SHS Concreter Fillied COLUMN

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C o rus Tub es

Structural & Conveyance Business

Design guide for SHS concrete filled columns


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Design Guide for Concrete Filled

Columns

Original text by :-

S J HicksBEng, PhD (Cantab.)

G M Newman BSc(Eng), CEng, MIStructE, MIFireE

Additional text by :-

M Edwards BSc (Lond)A Orton BA (Cantab), CEng, MICE, MIStructE

A


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Publication2002 Corus Tubes

Care has been taken to ensure that the contents of this publication are accurate, but Corus UK Limited and its subsidiarycompanies do not accept responsibility for errors or for information which is found to be misleading. Suggestions for ordescriptions of the end use or application of products or methods of working are for information only and Corus UK Limitedand its subsidiaries accept no liability in respect thereof. Before using products supplied or manufactured by Corus UK Limited

customers should satisfy themselves of their suitability.

Main text2002 The Steel Construction Institute

Apart from any fair dealing for the purposes of research or private study or criticism or review, as permitted under theCopyright Designs and Patents Act, 1988, this publication may not be reproduced, stored or transmitted, in any form or by anymeans, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordancewith the terms of the licences issued by the UK Copyright Licensing Agency, or in accordance with the terms of licences issuedby the appropriate Reproduction Rights Organisation outside the UK.

Enquiries concerning reproduction outside the terms stated here should be sent to the publishers, The Steel ConstructionInstitute, at the address given on the title page.

Although care has been taken to ensure, to the best of our knowledge, that all data and information contained herein areaccurate to the extent that they relate to either matters of fact or accepted practice or matters of opinion at the time ofpublication, The Steel Construction Institute, the authors and the reviewers assume no responsibility for any errors in ormisinterpretations of such data and/or information or any loss or damage arising from or related to their use.


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FOREWORD

This publication was collated and edited at Corus Tubes, Corby from original contributions byDr Stephen Hicks and Mr Gerald Newman of SCI and supplementary text from Mr MikeEdwards and Mr Andrew Orton of Corus. It brings together the latest available information onthe design and construction of buildings using concrete filled structural hollow sections andsupersedes other publications by Corus and SCI.

The Steel Construction Institute develops and promotes the effective use of steel in construction.It is an independent, membership based organisation.

SCI's research and development activities cover many aspects of steel construction includingmulti-storey construction, industrial buildings, light steel framing systems and modularconstruction, development of design guidance on the use of stainless steel, fire engineering,

bridge and civil engineering, offshore engineering, environmental studies, value engineering,and development of structural analysis systems and information technology.

Membership is open to all organisations and individuals that are concerned with the use of steelin construction. Members include designers, contractors, suppliers, fabricators, academics andgovernment departments in the United Kingdom, elsewhere in Europe and in countries aroundthe world. The SCI is financed by subscriptions from its members, revenue from researchcontracts and consultancy services, publication sales and course fees.

The benefits of corporate membership include access to an independent specialist advisoryservice and free issue of SCI publications as soon as they are produced. A MembershipInformation Pack is available on request from the Membership Manager.

The Steel Construction Institute, Silwood Park, Ascot, Berkshire, SL5 7QN.Telephone: +44 (0) 1344 623345Fax: +44 (0) 1344 622944Email: [email protected]

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World Wide Web site: http://www.steel-sci.org


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Contents

Page No.

FOREWORD iiiSUMMARY vi

1 INTRODUCTION 11.2 Applications of concrete filled columns 4

2 NORMAL DESIGN 92.1 General 92.2 Material properties 92.3 Partial safety factors 112.4 Basis of design method 112.5 Restrictions on the simplified design method 132.6 Properties of cross-section 132.7 Column buckling resistance 172.8 Analysis of bending moments due to second-order effects 202.9 Combined compression and bending 212.10 Longitudinal and transverse shear 312.11 Load introduction 32

3 FIRE DESIGN 363.1 General 363.2 Protected columns 383.3 Unprotected columns 393.4 Partial safety factors 403.5 Properties of the cross-section 413.6 Column buckling resistance 423.7 Combined compression and bending 433.8 Material properties 45

4 FABRICATION AND CONNECTIONS 474.1 General 474.2 Column Splices and Flange plate connections 474.3 Beam-to-column connections 494.4 Shearhead connections to slabs 524.5 Base plate connections 53

5 PRACTICAL CONSIDERATIONS 545.1 Concrete Filling 54

6 SOFTWARE 58

7 REFERENCES 60


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SUMMARY

A concrete filled structural hollow section provides architects and engineers with a robust andinherently fire resistance column. This publication contains design information for thesecolumns for both the normal and fire conditions. The information is based on Eurocode 4. Alsoincluded are case studies illustrating the use of concrete filled columns and practical guidanceon concrete filling and connection design.

Design software, ConcFill 2, is described which will analyse sections for the normal and fireconditions.


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1 INTRODUCTION

Structural Hollow Sections (SHS) are the most efficient of all structural steel sections inresisting compression. Their availability in the high yield material Celsius 355 gives them ahigh strength to weight ratio and produces slender attractive lines that make them a naturalchoice for building structures. In addition, SHS can achieve a constant external dimension forall weights of a given size, which enables them to achieve standardisation of architectural andstructural details throughout the full height of the building.

Celsius is the brand name for Corus Tubes hot-finished structural hollow sections, Celsius 355being produced to the European Standard, EN 10210 S355J2H. Celsius sections are producedby the electric weld process and the J2 denotation signifies that they have a Charpy impactminimum average energy value of 27J at 20oC, making them suitable both for internal andexternal applications. Celsius sections are produced to the technical delivery requirements of

EN 10210-1:1994[1]

with dimensions and tolerances to EN 10210-2:1997[2]

. However, forCelsius sections, there is an improved corner profile of 2Tmaximum.

By filling hollow sections with concrete a composite section is produced (see Figure 1.1), whichwill increase the sections room temperature load carrying capacity, whilst retaining all theadvantageous features of the basic unfilled section. Alternatively, for the same original loadcapacity, it permits smaller composite sections to be used. The reduction in section size alsogives advantages in subsequent construction processes, including a reduced surface area forpainting or fire protection. In the fire condition the presence of the concrete filling acts as a heatsink.

Concrete or grout filled hollow sections can be divided into those that are externally protectedagainst fire by fire-rated boards, lightweight sprayed protection or intumescent coatings, and

those that have no such protection. A further division can be made, by differentiating betweenthose that are filled with plain concrete mixes and those that contain steel reinforcement withinthe mix.

Figure 1.1 Concrete filled square hollow section


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Externally protected composite sections are designed compositely at room temperature andexternal fire protection is applied to achieve the required fire rating of the column. Thecomposite action is maintained in the fire limit state, the external protection serving to limit therise in steel temperature such that the column capacity is always in excess of the fire limit statedesign load over the required fire resistance period. In general, externally protected sections willnot need to contain reinforcement in the mix in order to achieve the desired fire rating -reinforcement is usually added to such columns so to enhance axial capacity while minimising ormaintaining column SHS size. Reductions in the thickness of the external protection arepossible because of the heat sink effect, which effectively reduces the section factor of thecolumn; these reductions have been shown to be substantial in the case of filled hollow sectionswith intumescent coatings. In cases where smaller columns are used, particularly if speed ofconstruction is an issue, consideration should be given to sizing the SHS such as to use a plainfill with external protection, so that reinforcement can be dispensed with. Note that because ofthe tensile capacity of the steel in the composite column, in almost all cases, grout may be usedinterchangeably with concrete as the filling material.

Filled hollow sections that are not externally protected against fire are designed using theconcrete core alone to meet the fire limit state load requirements but the capacity of thecomposite section is checked for the room temperature design case. In general, such sectionswill need to contain reinforcement in the mix in order to minimise column dimensions and tosustain the required fire limit state design loads for such practical fire resistance periods of 60minutes or more.

Cost comparisons

Cost comparisons have shown that to establish the cost competitiveness of a column it isnecessary to take into account both the cost of the supplied and erected steel section togetherwith the cost of its fire protection. Such comparisons have shown that hollow sections can offer

a competitive first choice solution to structural columns in multi-storey construction.

Construction

Concrete or grout filling of structural hollow sections requires no special equipment and thefilling operation may be integrated into other concreting operations. The enhancement in theoverall efficiency obtained by filling a steel structural hollow section with concrete allows thedesigner a wider choice of sections. Filled hollow section columns combine the advantages ofeconomy in the use of materials with the construction advantages of the use of steelwork.Columns, whether externally fire-protected or not, will usually arrive to site as fully finishedelements with make-ups only at column splice joints, if any. Concrete filling of the hollowsection columns can take place on or off site. If filling takes place on site, then the steel column

and its connections are designed to carry all construction loads so that the operation of filling thecolumns can be taken off the critical path. In larger buildings, the best economy is obtained byplanning for the simultaneous working of different trades at different levels or plan positions.The hollow section columns may be filled from the top with a self-compacting or other type ofmix; alternatively, they can be filled from the bottom, through a gate-valve, with a pumpableconcrete or grout mix. Grout is often used as an alternative to concrete and this has substantialadvantages at the construction stage, such as easier filling and pumping and the avoidance ofunfilled voids.


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Advantages of composite hollow sections

In the initial construction period

The steel section dispenses with the need for formwork. Concrete placement and compaction inmany cases are unhindered by internal reinforcement.

Erection schedule is not dependent on concrete curing time.

During finishing

The concrete filling is protected against mechanical damage. Additional external fire protectionis not always necessary Slender columns reduce the application time and cost of appliedfinishes.

Completed building

Greater useable floor area.

Higher visibility.

Reduced maintenance.

Aesthetically pleasing.

Figure 1.2 Detail at the facade line of a plain filled concrete tubular column structurethat uses an intumescent coating as external fire protection

(Wellcome Trust Headquarters, London; structural engineer WSP Group)


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Many of these advantages were recognised early in the history of the use of iron and steel

hollow sections in construction, indeed the first known Patent relating to the concrete filling ofcircular hollow sections dates from 1898. The wider use of the composite concrete hollowsection did not really begin until the mid 20th Century following the results of structuralinvestigation and the availability of a comprehensive range of structural hollow sections.

A number of institutes in Britain and overseas have now undertaken considerable research intothe structural and fire resistance performance of concrete hollow sections aimed at developingsuitable design procedures for this form of construction. The results of this recent research arenow incorporated into prEN 1994-1-1: 2002 (EC4-1-1), the European code for compositeconstruction[18].

The material included in this manual makes the design of structural hollow section columns

filled with concrete simple and rapid when standard sections are used in conjunction withconcrete of common grades.

1.2 Applications of concrete filled columns

1.2.1 FLEET PLACE HOUSE, LONDON

The site of Fleet Place, off Holborn Viaduct in the City of London was comprehensivelyredeveloped at the same time as the adjacent Thameslink station. This eight-storey high officeblock on the site was built using concrete filled external CHS columns on each longitudinal faceof the building and has clear spans on the inside. So that they could be supported off existingpilecaps, the CHS columns were kinked at first floor level, except at the entrance leading to theThameslink station behind the building, where the columns were kinked at second and third

floor levels.

Figure 1.3 Tubular column with reinforced concrete infill without external fire protection

(Cheung Kong Center, Hong Kong; structural engineer Ove Arup & Partners)


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Technical details

Construction details

The columns have a constant external diameter of 323.9 mm but, within this serial size, varyfrom 323.9 30 CHS at the first floor, 323.9 16 CHS between second and fifth floors and323.9 12.5 CHS between sixth and seven floors. The CHS column material was Celsius hot-finished hollow section to EN10210 grade S355J2H.

The fire rating for internal elements was generally two hours but the requirement for theexternal columns was only 35 minutes in view of their position outside the cladding line. Nofire protection was given to the columns, a 45 minute rating being achieved by concrete fillingalone. The concrete infill used was to Grade 40 or Grade 60 depending on the vertical load.

Project data

Client: Heron Property Corporation

Architect: Skidmore, Owings & Merrill

Structural Engineer: Waterman Partnership

1.2.2 MONTEVETRO APARTMENT BLOCK, LONDON

Steel composite tubular columns have been used on the facade of this high specificationapartment block, which looks out across the River Thames. The composite columns were

chosen because of their small plan area and their slender shape which minimised the obstructionto the views out from the apartments.

Figure 1.4 Fleet Place House, London


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Technical details


CHS columns are used and, in the typical case, are only 244.5 mm in diameter. Within this serialsize the columns vary from 244.5 16 CHS to 244.5 20 CHS; for the most heavily loadedareas, the columns were increased to a maximum size of 355.6 16 CHS.

The steel CHS columns are used to support concrete flat slab floors. At the highest point theapartment block has twenty storeys and there are heavy axial loads in the columns in theseareas. The CHS column material was Celsius hot-finished hollow section to EN10210 gradeS355J2H.

The fire rating required for the columns varied between one and two hours and was achieved bythe combined effect of the concrete infill and an intumescent coating. No reinforcement wasused inside the CHS columns.

Project data

Client: Taylor Woodrow Capital Developments

Architect: Richard Rogers Partnership

Structural Engineer: Waterman Partnership

Figure 1.5 Montevetro Apartment Block, London


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1.2.3 PECKHAM LIBRARY, LONDON

This library building is of striking appearance. It is supported at the front by concrete-filledCHS columns, angled to form an irregular facade and enclosing a covered space, which is anextension of a new public square. There are 7 supporting columns, 18 metres long, which are

angled out of the vertical, the columns supporting steel tubular trusses at the fourth floor and asteel roof above. At ground floor level, the columns have a height of 18 metres, giving a heightto width ratio of 37. The angling of the columns helps to provide additional stiffness againstlateral loads and limits the development of bending moment in the columns.

Technical details


At ground floor level, the column line consists of a 323.9 20 CHS column at each end with323.9 16 CHS columns in-between. At first floor level, these section sizes reduce to 323.9 6.3 CHS members. All columns were designed without external protection, utilising an infilledconcrete core within the tubes to satisfy the requirement for a one-hour fire rating. The concreteinfill is reinforced with 8 T12 longitudinal bars with T6 links at 175 centres. The columns were

fabricated as full-height elements and were supplied in Celsius hot-finished hollow section toEN10210 grade S355J2H.

Project data

Client: London Borough of Southwark

Architect: Alsop Architects

Structural Engineer: Adams, Kara, Taylor

1.2.4 QUEENSBERRY HOUSE, LONDON

The steel columns used to support the floors of this six-storey office and commercial buildingsare CHS tubular columns. The columns use a tube-in-tube system in which one CHS section isplaced inside a larger one with all the voids grouted after erection of the floor structure.

Figure 1.6 Peckham Library, London


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Technical details


There is an atrium in the middle of the building, which is 6 metres wide, with 12 metre clearspans each side of the atrium in the transverse direction. In a typical case the column consists ofa 457 10 CHS outer tube and a 323.9 6.3 CHS inner tube and supports two floor beams oneach side. All columns were delivered to site in two three-storey lengths and were joined bymeans of an in situconcrete joint in the inner tube and by bolting and welding on the outer tube.After erection, the columns only needed to be made good at the joint and given a final finishcoat of paint.

No external fire protection was necessary, the internal column and grout infill having sufficientload capacity by itself in the fire limit state. At room temperatures, the full section capacity ofthe tube-in-tube column is utilised. The CHS column material was Celsius hot-finished hollow

section to EN10210 grade S355J2H.Project data

Client: General Accident and Capital & City

Architect: RHWL

Structural Engineer: Buro Happold

Figure 1.7 Queensberry House, London


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2 NORMAL DESIGN

2.1 GeneralIn general, a composite column must be designed for the ultimate limit state. For structuraladequacy, the internal forces and moments resulting from the most unfavourable loadcombination should not exceed the design resistances of the composite cross-sections. Whilelocal buckling of the steel sections may be eliminated, the reduction in the compressionresistance of the composite column due to overall buckling should be allowed for, together withthe effects of residual stresses and initial imperfections. Moreover, the second order effects inslender columns, as well as the effect of creep and shrinkage of concrete under long-termloading, must be considered if they are significant. The reduction of flexural stiffness due tocracking of the concrete in the tension area should also be considered. These are provided foreither explicitly, or empirically, in prEN 1994-1-1: 1994[18](EC4-1-1).

2.2 Material properties

2.2.1 Hot rolled structural steel

Nominal values of the yield stress yf , and the ultimate tensile stress uf , for structural steel are

presented in Table 2.1 below.

Table 2.1 Mechanical properties of Celsius Sections

Nominal thickness of element t(mm)

t40 mm 40 mm


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Section 2.6.2, provision is given within EC4-1-1[18]to reduce the secant modulus of elasticity,depending on the proportion of permanent load acting on the column.

The density of structural concrete is assumed to be 2400 kg/m for plain, unreinforced, concreteand 2500 kg/m for reinforced concrete.

Table 2.2 Characteristic compressive strength fck(cylinders), mean tensile strengthfctmand secant modulus of elasticity Ecmfor structural concrete

Strength class ofconcrete

C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

fck(N/mm) 20 25 30 35 40 45 50

fctm(N/mm) 2.2 2.6 2.9 3.2 3.5 3.8 4.1

Ecm(N/mm) 29000 30500 32000 33500 35000 36000 37000

2.2.3 Steel reinforcement bars

In the UK, steel bars for the reinforcement of concrete should conform to BS 4449:1997 [19]. DDENV 10080: 1996[20], which is currently at the draft for development stage, will eventuallyreplace this British Standard. However, the 1997 edition of BS 4449 has been revisedconsiderably compared to its earlier versions, to bring it into line with the requirements of EC2-1-1[16]. The properties most frequently required in design calculations are referred to in Clause3.2 of EC2-1-1; types of reinforcement steel are classified as follows:

High (class H) or normal (class N), according to ductility characteristics.

Plain smooth or, ribbed bars, according to surface characteristics.

Steel grades that should be used in construction are given in Table 2.3.

Table 2.3 Characteristic yield strength fsk, ductility requirements and modulus ofelasticity Esof reinforcing steel

Reinforcingsteel standard

BS 4449: 1997[19]

DD ENV 10080: 1996[20]

Name 460A (class N) 460B (class H) B500A (class N) B500B (class H)

fsk(N/mm) 460 500

Total elongationat maximumforce (%)

2.5 5.0 2.5 5.0

Elongation atfracture (%)

12 14 - -

Es(N/mm) 210000 210000

According to EC4-1-1

As can be seen from Table 2.3, apart from the obvious difference in the characteristic yieldstrength skf , between reinforcing steels complying with BS 4449:1997

[19]and DD ENV 10080:1996[20], BS 4449 also specifies a minimum elongation at fracture: thereby guaranteeing thelength of the plastic deformation plateau. Furthermore, in the 1997 edition of BS 4449, theminimum elongation at fracture of 14%, for 460B steel, is higher than the 12% requirement forthis yield strength, given in earlier versions of this code of practice. A graphical representationof the difference in the elongation requirements for these two standards is shown in the stress-strain curve in Figure 2.1.


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It should be noted, however, that although the ductility of reinforcing bars has a significanteffect on the behaviour of continuous composite beams[21], this property is of little significancewith respect to the design of composite columns at ambient temperature. Concrete filled hollowsections may be used without any reinforcement, except for reasons of fire resistance (seeSection 3).

2.3 Partial safety factors

National authorities are free to select appropriate values for partial safety factors for loads andmaterials, and substitute them for boxed values in the Eurocodes. The boxed values and theUK National Application Document (NAD) values are:

Loads: EC4-1-1boxed values UK NAD

Imposed (variable) load, Q 1.50 1.50

Dead (permanent) load, G 1.35 1.35

Materials:

Steel, a 1.10 1.05

Concrete,c 1.50 1.50

Reinforcement, s 1.15 1.15

2.4 Basis of design methodIn EC4-1-1, isolated columns are defined as compression members that are integral parts of abraced or non-sway frame but which are considered to be isolated for design purposes.

Definitions of non-sway structures are given in EC2-1-1[16]as follows:

Structures or structural elements, with or without bracing elements, for which the influenceof displacements of the connections upon the design moments and forces may be neglected,are classified as non-sway. Otherwise, they are classified as sway.

Minimum elongation

at fracture

Total elongation at

maximum force uk

Stress

Strain

Minimum elongation

at fracture

Total elongation at

maximum force uk

Stress

Strain

Figure 2.1 Elongation limits for steel reinforcement bars


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Braced building structures, where substantial shear walls or core structures provide thebracing, may be assumed to be non-sway.

Frames may be classified as non-sway if the first order displacements of the connections donot increase the effects of actions calculated without considering these displacements by

more than 10%. In general, it is sufficient to consider only the relevant bending momentsdue to these second-order effects.

A similar definition of a non-sway frame in DD ENV 1993-1-1: 1992[28](EC3-1-1) is also givenfor reference:

A frame may be classified as non-sway if its response to in-plane horizontal forces issufficiently stiff for it to be acceptably accurate to neglect any additional internal forces ormoments arising from horizontal displacements of its nodes.

Two methods of design for isolated composite columns in braced or, non-sway frames are given

within EC4-1-1:

2.4.1 General design method

This comprehensive method is used for composite columns with non-symmetrical or non-uniform cross-section over the column length. It is also used for composite columns of doublysymmetrical, and uniform cross-section over the column height, when the limits of applicabilityfor the simplified design method are not satisfied (see Section 2.5). In these circumstances,some of the important design issues which should be considered using the general method, areas follows:

geometrical and material non-linearity;

second order effects (on slender columns);

creep and shrinkage of the concrete under long-term loading;

contribution of the tensile strength of the concrete between cracks;

imperfections for the calculation of internal forces and moments about both axes;

distribution of internal forces and moments between the steel section and the concrete bymeans of a clearly defined load path;

transfer of longitudinal shear stress at the interface between the steel section and theconcrete under large transverse shear; and

chemical bond and friction together with mechanical shear connection if necessary.

In order to allow for these design considerations, it is necessary to use sophisticated computersoftware, which operate with both geometrical and material non-linearity. In general, the designeffort is considerable. Thus, this method is not preferred for use in practical design, and isoutside the scope of this publication.

2.4.2 Simplified design method

This method is used for composite columns of doubly symmetrical and uniform cross-sectionover the column height. It is based on certain assumptions relating to the geometricalconfigurations of the composite cross-sections. Moreover, it also adopts the European bucklingcurves for steel columns as the basis of column buckling design. The limits of applicability ofthis method given in EC4-1-1 are also listed in Section 2.5; when the limits are not satisfied, theabove general design method should be used.


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It should be noted that this method is formulated in such a way that only hand calculation isrequired in practical design. The simplified design method is presented in detail within thispublication. The calculation procedure is in six parts, as follows:

(i) Check that the limits of the simplified design method are satisfied.

(ii) Calculate the properties of the cross-section.

(iii) Calculate the buckling resistance of the column.

(iv) Check whether second-order effects should be considered

(v) Calculate the effect of interaction between axial load and bending.

(vi) Calculate the longitudinal and transverse shear.

2.5 Restrictions on the simplified design method

The application of the simplified design method is subject to various restrictions, as follows:

(a) The column is doubly-symmetrical and is of uniform cross-section over the height of thecolumn.

(b) The steel contribution ratio must satisfy the following conditions:

9.02.0

If is less than 0.2, the column may be designed according to EC2-1-1 [16]. If is largerthan 0.9, the concrete is ignored in the calculations, and the column is designed as a baresteel section.

(c) The maximum non-dimensional slenderness ratio of the composite column is limitedto 2.0.

(d) The maximum amount of longitudinal reinforcement that can be considered in theanalysis is 6% of the concrete area. However, if design for fire resistance is not needed,according to prEN 1994-1-1: 2001[17], no minimum amount of reinforcement is normallynecessary within a filled SHS column; in other words:

0% c

s

A

A6.0%.

2.6 Properties of cross-section2.6.1 Squash (plastic) resistance, Npl,Rd

The plastic resistance, to compression, of a composite cross-section represents the maximumload that can be applied to a short composite column. It is important to recognize that concretefilled circular hollow sections exhibit enhanced resistance due to the triaxial containmenteffects. Concrete filled rectangular sections (RHS) do not achieve such enhancement.

Local buckling of steel hollow sections

Before the plastic resistance of the concrete filled hollow section is calculated, it should beinsured that local buckling of the steel does not occur. To prevent premature local buckling, thewidth to thickness ratio of the steel section in compression must satisfy the following limits:

For concrete filled rectangular hollow sections (RHS) 52t

h


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For concrete filled circular hollow sections (CHS) 290t

d

where:

t is the wall thickness of the steel hollow section in mm.

h is the larger outer dimension of the rectangular hollow section in mm.

d is the outer diameter of the circular hollow section in mm.

y

235

f=

yf is the yield strength of the steel section in N/mm.

Local buckling in some rectangular hollow sections with large h/t ratios may be critical. Nospecific design recommendation is given within EC4-1-1, and design using sections whichexceed the local buckling limits should be verified by tests.

Concrete filled rectangular hollow sections (RHS)

The plastic resistance of a concrete filled rectangular hollow section (i.e., the so-called squashload) is given by the sum of the resistances of the components as follows:

c

ckc

s

sks

a

yaRdpl,

fAfAfAN ++=

where:

aA is the area of the steel section.

sA is the area of the reinforcement.

cA is the area of the concrete.

yf is the yield strength of the steel section.

skf is the characteristic yield strength of the steel reinforcement bars.

kcf is the characteristic compressive strength (cylinder) of the concrete.

For ease of expression,a

y

f,

s

sk

fand

c

ck

fare presented as design strengths of the respective

materials in the remainder of Section 2 as: ydf , sdf and cdf respectively. As a result of this

simplification, the above equation for the plastic resistance of the composite column, can berewritten in the following compact form:

cdcsdsydaRdpl, fAfAfAN ++=

Concrete filled circular hollow sections (CHS)

For composite columns with concrete filled circular hollow sections, the increased resistance ofconcrete due to the confining effect of the circular hollow section may be included. Thisrestraint to transverse strain in a three dimensional confinement results in increased concrete


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If the eccentricity e exceeds the value d/10, or if the non-dimensional slenderness ratio exceeds the value 0.5, then 010 = and 0.120 = . Table 2.4 gives the basic values 10 and

20 for different values of .

Table 2.4 Basic values of 10and 20to allow for the effect of triaxial confinement inconcrete filled circular hollow sections

Non-dimensional

slenderness ratio 0 0.1 0.2 0.3 0.4 0.5

10 4.90 3.22 1.88 0.88 0.22 0

20 0.75 0.80 0.85 0.90 0.95 1.00

2.6.2 Effective flexural stiffness

Short-term loading

The effective flexural stiffness of the composite column ( )eEI is obtained from adding the upthe flexural stiffnesses of the individual components of the cross-section:

( ) ccmssaae 6.0 IEIEIEEI ++=

where:

aI , sI and cI are the second moment of area, about the appropriate axis of bending, for the

steel section, the reinforcement and the concrete (assumed uncracked)respectively.

aE and sE are the elastic moduli for the structural steel and the reinforcement respectively.

ccm6.0 IE is the effective stiffness of the concrete component (the 0.6 factor is anempirical multiplier, which has been determined from a calibration exercise, togive good agreement with test results).

cmE is the secant modulus of elasticity for structural concrete; see Table 2.2.

Long-term loadingFor composite columns under long-term loading, the creep and shrinkage of concrete will causea reduction in the effective elastic stiffness of the composite column, thereby reducing thebuckling resistance. However, this effect is only significant for slender columns; as a simplerule, the effect of long-term loading should be considered if the buckling length to depth ratio ofa composite column exceeds 15.

If the eccentricity of loading (see Section 2.6.1) is more than twice the cross-section dimension,the effect on the applied bending moment distribution caused by increased deflections, due tocreep and shrinkage of the concrete, will be very small. Consequently, it may be neglected andno provision for long-term loading is necessary. Moreover, no provision is necessary if the non-

dimensional slenderness of the composite column is less than the limiting values givenwithin Table 2.5 below.


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Table 2.5 Limiting values of for long-term loading

Frame typeBraced non-sway frame

Sway frames and/orunbraced frames

Concrete filled hollow sections ( )18.0

( )15.0

The steel contribution factor , given in Table 2.5 above, is defined as follows:

Rdpl,

yda

N

fA=

If the eccentricity of loading is less than twice the cross-section dimension and the non-dimensional slenderness of the composite column is less than the limiting values givenwithin Table 2.5, the effect of creep and shrinkage of concrete should be allowed for byreducing the effective elastic modulus of the concrete to the value:

=

Sd

SdG,cdc

5.01

N

NEE

where:

SdN is the design applied load.

SdG,N is the part of the design load permanently acting on the column.

Table 2.5 also allows the effect of long-term loading to be ignored for concrete filled hollow

sections with 0.2 , provided that is greater than 0.6 for braced (or non-sway) columns,and 0.75 for unbraced (and/or sway) columns.

2.7 Column buckling resistance

The plastic resistance to compression of a composite cross-section Rdpl,N represents themaximum load that can be applied to a short column. However, for slender columns, with lowelastic critical load, overall buckling considerations may be more significant.

In Figure 2.2(b), the buckling resistance of a column is expressed as a proportion of the plasticresistance to compression NPl,R , thereby non-dimensionialising the vertical axis compared toFigure 2.2(a). The horizontal axis may be non-dimensionalised similarly by use of the Eulerbuckling load crN as is also shown in Figure 2.2(b).

By incorporating the effects of both residual stresses and geometric imperfections, the Europeanbuckling curves may be drawn on this basis as shown in Figure 2.2(c). These curves form the

basis of column buckling design for both steel and composite columns.


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The buckling resistance is calculated from the plastic resistance and the Euler (elastic) criticalload using the EC3-1-1[28]buckling curve a (N.B. at the fire limit state, curve c is used due toits close agreement with the results from fire tests; see Section 0). The Euler buckling load isgiven by:

( )2

e2

crl

EIN

=

where:

( )eEI is the effective elastic flexural stiffness of the composite column (see Section 2.6.2).

l is the buckling length of the column.

EC4-1-1 suggests that the buckling length l of an isolated non-sway composite column mayconservatively be taken as equal to its system length L. Alternatively, the buckling length maybe determined using Annex E of EC3-1-1.

The non-dimensional slenderness ratio is given by:

cr

Rpl,

N

N=

ab

c1.00

2.01.000

0.2

=pl,R

cr

=Rd

pl,Rd

N

N

N

N

(c)

l/r Slenderness

pl

cr

N

N

(a)

=pl

pl

cr

NN

N

N(b)

N

Figure 2.2 (a) Idealised column buckling curve, (b) Non-dimensionalised columnbuckling curve, (c) European buckling curves according to EC3-1-1


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where:

Rpl,N is the plastic resistance of the composite cross-section to compression, according to

Section 2.6.1, with 0.1csa === .

The resistance of a composite column in axial compression (buckling load) is obtained from:

Rdpl,Rd .NN =

where:

is the reduction coefficient for buckling obtained from curve a of EC3-1-1, and is

dependant on the non-dimensional slenderness ratio .

The reduction factor may be determined from:

[ ] 5.0221

+= but 0.1

where:

( )[ ]22.015.0 ++=

is an imperfection parameter depending on the buckling curve considered.

Relevent Buckling Curves and Imperfection Factors

According to prEN 1994-1-1, circular or rectangular hollow section columns filled with plainconcrete or containing up to 3% reinforcement can be designed using buckling curve a with animperfection factor, , = 0.21. However, concrete filled sections containing between 3% to 4%reinforcement must be designed using buckling curve b with an imperfection factor, , = 0.34(see Figure 2.3 (a) and (b) below).

In addition, concrete filled circular hollow section columns as shown in Figure 2.3(c) containingan additional open Section used as primary steel can also be designed as a composite sectionusing buckling curve b with an imperfection factor, , = 0.34.

Figure 2.3 Typical column cross-sections


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Although not explicitly stated, Clause 4.8.3.2 of EC4-1-1, while defining the partial safetyfactors implies that isolated non-sway composite columns need not bechecked for buckling, ifany of the following conditions is satisfied:

(i) the axial force in the column is less than cr1.0 N ; or(ii) the non-dimensional slenderness ratio is less than 0.2.

2.8 Analysis of bending moments due to second-ordereffects

Under the action of the design axial load SdN on a column with an initial imperfection 0e , as

shown in Figure 2.4, there will be a maximum internal moment of 0SdeN . It is important to note

that this second order moment, or imperfection moment, does not need to be consideredseparately, as its effect on the buckling resistance of the composite column is already accountedfor in the European buckling curves as shown in Figure 2.2(c).

However, in addition to axial forces, a composite column may be also subject to end momentsas a consequence of transverse loads acting on it or, because the composite column is a part of aframe. The moments and displacements obtained initially are referred to as first order values.For slender columns, the first order displacements may be significant and additional, orsecond order, bending moments may be induced under the actions of the applied loads. As asimple rule, the second order effects should be considered if the buckling length to depth ratioof a composite column exceeds 15.

The second order effects on bending moments for isolated non-sway columns should beconsidered if both of the following conditions are satisfied:

1) 1.0cr

Sd >N

N

where:

SdN is the design applied load.

crN is the Euler buckling load.

2) ( )r> 22.0

where:

is the non-dimensional slenderness ratio

r is the ratio of the smaller to the larger end moment (see Figure 2.5). If there isany transverse loading, rshould be taken as 1.0.

NSd NSd

eo

Figure 2.4 Initially imperfect column under axial compression


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The second order effects in an isolated non-sway column may be allowed for by modifying themaximum first-order bending moment max,SdM , with a correction factor k, which is defined as

follows:

0. 11

cr,eff

Sd

=

N

Nk

where:

SdN is the design applied load

cr,effN is the elastic critical load of the composite column based on the system length,L, anda reduced design value of effective stiffness (EI)e,II

where:

(EI)e,II = 0.9(EaIa+EsIs+ 0.5EcmIc)

is the equivalent moment factor.

For columns with transverse loading within the column length, the value for should be takenas 1.0. For pure end moments, can be determined as follows:

r44.066.0 += but 44.0

2.9 Combined compression and bendingThe design for a composite column subjected to combined compression and bending is carriedout in stages as follows:

The composite column is isolated from the framework, and the end moments, which resultfrom the analysis of the system as a whole, are taken to act on the column underconsideration. Internal moments, and forces within the column length, are determined fromthe structural consideration of end moments, axial and transverse loads.

For each axis of symmetry, the buckling resistance to compression should be checked withthe relevant non-dimensional slenderness of the composite column.

In the presence of applied moment about one particular axis e.g., the y-y axis, the momentresistance of the composite cross-section should be checked with the relevant non-

dimensional slenderness of the composite column i.e., y , instead of z , although z may

be larger, and thus more critical, than y .

For slender columns (see Table 2.5 and Section 2.8), both the effect of long-term loadingand the second-order effects are included.

SdSd

-1 r +1 rMM

Figure 2.5 Ratio r of the end moments


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It should be noted that, by adopting the EC4-1-1[18]simplified method, imperfections within thecolumn length need not be considered as they are taken account of in the relevant bucklingcurve when determining the buckling resistance of the column (see Section 2.7).

2.9.1 Combined compression and uni-axial bendingIn EC4-1-1[18], the resistance of a composite column subjected to combined compression andbending is determined from an interaction curve. For a bare steel section, the interaction curve ischaracterised by a continuous reduction of the moment resistance with a corresponding increasein axial load.

However, as shown from the interaction curve in Figure 2.6: a short composite column mayexhibit an increase in moment resistance under axial load. The reason for this increase is that,under some favourable conditions, the compressive axial load prevents concrete cracking, andtherefore makes the cross-section of a short composite column more effective in resistingmoments.

An interaction curve between compressive axial load and moment can be obtained for a shortcomposite column by considering several possible positions of the neutral axis within the cross-section, and determining the internal forces and moments from the resulting plastic stressblocks. For the simplified method given within EC4-1-1, sufficient accuracy in estimating theeffects of combined compression and bending may be found by constructing the interaction

curve, shown in Figure 2.7, from 4 or 5 points.

1.0

1.0

0

Rd

MN

Rd

pl,Rd

N

N

M

Mpl,Rd

Figure 2.6 Interaction curve for a composite column subjected to compression anduni-axial bending


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For composite columns, which are doubly symmetrical and of a uniform cross-section over theirheight, the following approach given in EC4-1-1[18], and the UK NAD, may be adopted.

Figure 2.8 shows the plastic stress distributions within the cross-section of a concrete filled RHSat point A, B, C, D and E of the interaction curve given in Figure 2.7. The significance of eachof these points are as follows:

Point A indicates the plastic resistance of the cross-section to compression, in the absenceof an applied bending moment:

0ARdpl,A

==

MNN

Point B corresponds to the plastic moment resistance of the cross-section, in the absence ofan applied axial load:

Rdpl,B

B 0

MM

N

=

=

At point C, the axial compression and moment resistance of the composite column aregiven as:

Rdpl,C

cdcRdc,Rdpm,C )(or

MM

fANNN

===

N

AE

C

D

B

M

pl,Rd

pm,Rd

pm,Rd

N

N

N

pl,Rd max,RdM M

Figure 2.7 Interaction curve with linear approximation


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The expressions may be obtained by combining the stress distributions of the cross-sectionat points B and C; the compression area of the concrete at point B is equal to the tensionarea of the concrete at point C. The moment resistance at point C is equal to that at point B,since the stress resultants from the additionally compressed parts cancel one another out inthe central region of the cross-section. However, these additionally compressed regionscreate an internal axial force, which is equal to the plastic resistance to compression of theconcrete alone i.e., Rdpm,N or Rdc,N .

At point D, the plastic neutral axis coincides with the centroid of the cross-section, and theresulting axial force is half of the value at point C, i.e.:

Rdmax,D

Rdpm,D 2/

MM

NN

=

=

Point Acd yd sd

pl.Rd

cd yd sd

cd yd sd

cd yd sd

cd yd sd

Point B

n

++

B

Point C

n

+ +

C

C

+

Point D

Point E

+

D

E

E

E

f f f

f f f

f f f

f f f

f f f

h

h

No moment

N

M = M

zero axial forcepl,.Rd

pl,Rd

c,Rd

M = M

N = N

2

max,Rd

c,Rd

M

N

n

h

M = M

NDN =

h /2

h/4 (N.B., the moment resistance Mmax,Rd, at point D, is not allowed in the UK NAD)

Figure 2.8 Stress distributions for the points on the interaction curve for concrete filledhollow sections, according to EC4-1-1[18]


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Generally, point D is less than point C in design.

Point E is mid-way between A and C, and is often required for highly non-linear interactioncurves, in order to achieve a better a better approximation. For concrete filled structuralhollow sections, the use of point E will yield a more economical design; however, muchmore calculation effort is required. Thus, to retain simplicity, point E tends not to be used.

According to the UK NAD, the additional moment resistance of the composite cross-section(indicated by point D within Figure 2.7), should not be taken account of in design. Therefore, inthe UK, an interaction curve consisting of A-C-B or A-E-C-B may only be considered.

The plastic moment resistance of a concrete filled hollow section may be evaluated as follows:

)()(5.0)( psnpssdcnppccdpanpaydRdpl, WWfWWfWWfM ++=

where:

ydf , sdf , cdf area

y

f,

s

sk

fand

c

ck

frespectively

paW , pcW , psW are the plastic section moduli for the steel section, the concrete of the

composite cross-section (assumed to be uncracked) and thereinforcement respectively.

panW , pcnW , psnW are the plastic section moduli of the corresponding components within

the region of n2h from the centre-line of the composite cross-section.

The values of the relevant parameters in the above equation for concrete filled hollow sectionsare:

Rectangular hollow sections

( )( )( ) ps

232

pc 24

3

2

4

22Wrt

hrr

thtbW

=

where: ris the internal radius of the corners to the hollow section

Circular hollow sections

( ) ps3

pc 62 WtdW =

In general, for both types of section:

( )( )cdydcd

cdsdsncdcn 242

2

fftbf

ffAfAh

+

=

where: snA is the area of reinforcing bars within the region of n2h from the centreline of thecomposite cross-section.

For rectangular hollow sections, it can be explicitly stated that:

Wpan= 2t.hn2


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( ) psn2

npcn 2 WhtbW =

Similar simple explicit equations cannot be written for circular sections. However, the aboveequations can be conservatively applied to circular sections with a high accuracy by substituting

diameter d for breadth b

For the calculation of the resistances at the additional point E, RdE,N and RdE,M (see above),

the neutral axis is located between nh and the border of the section, so that

hhh 25.05.0 nE += . Using rectangular hollow sections, the axial resistance of the column forthis case is:

( ) ( ) ) ( ) Rdpm,cdsdsEcdydnEcdnERdE, 222 NffAffhhtfhhbN +++=

where sEA is the sum of the areas of reinforcement lying in the additional compression region

between Eh and nh .

The magnitude of RdE,M is calculated from the above equations but with Eh substituted for nh

in the values of panW and pcnW .

Again, the above equations can be applied to circular sections by substituting diameter d forbreadth b but may become highly over-conservative. In such circumstances it may be preferableto simply apply a linear interpolation between points A and C

The principal for checking the composite cross-section under combined compression and uni-axial bending, in accordance with EC4-1-1[18], is illustrated graphically in Figure 2.9. Firstly, the

resistance of the composite column under axial load is determined in the absence of bending,which is given by Rdpl,N (see Section 2.7). The moment resistance of the composite column

should then be checked with the relevant non-dimensional slenderness, which is in the sameplane of the applied moment. As mentioned earlier, the initial imperfections of columns havebeen incorporated within the appropriate buckling curve, and no additional consideration ofgeometrical imperfections is necessary in the evaluation of bending moments within the columnheight.

Consider the interaction curves for combined compression and uni-axial bending shown inFigure 2.9. Under an applied force SdN equal to Rdpl,N , the horizontal coordinate Rdpl,kM

represents the second order moment due to imperfections within the column, otherwise known

as the imperfection moment. It is important to recognise that the moment resistance of thecolumn has been fully utilised in the presence of the imperfection moment; the column,therefore, cannot resist any additional applied moment. Moreover, the influence of theimperfections decreases when the axial load ratio is less than , and it is assumed to varylinearly between n and . For an axial load ratio less than n , the effect of imperfections isneglected.

It is important to note that the value n accounts for the fact that the influence of theimperfections and that of the bending moment do not always act together unfavourably. Forcolumns with only end moments, n may be determined as follows:

( )4

1n

r=


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where ris the ratio of the small to the large end moment (see Figure 2.5).

If transverse loads occur within the column height, then rmust be taken as unity and n is thus

equal to zero (i.e., it coincides with the origin of the interaction curve shown in Figure 2.9).

With a design axial load ofSd

N , the design axial load ratiod

is defined as follows:

Rdpl,Sdd /NN=

By reading off the horizontal distance from the interaction curve (see Figure 2.9), the momentresistance ratio may be obtained, and the moment resistance of the composite column undercombined compression and uni-axial bending may be evaluated. Details of the UK NADmethod for calculating , and its limitations, are discussed below.

EC4-1-1[18]considers that the design is adequate when the following condition is satisfied:

Rdpl,Sd 9.0 MM

where:

SdM is the design bending moment, which may be factored to allow for second-order effects,

if necessary (see Section 2.8).

is the moment resistance ratio obtained from the interaction curve.

Rdpl,M is the plastic moment resistance of the composite cross section.

The interaction curve shown in Figure 2.9 has been determined without considering the strainlimitations within the concrete. Hence the moments, including second-order effects (ifnecessary), are calculated using the effective elastic flexural stiffness ( )eEI , and taking into

Rd Rd

n

d

1.0

dk

Rd

(a) (b)

d

1.0

Rd

n

dk0 0

Cross-sectioninteraction curve A

C

B

pm

1.0 1.0

N

N

N

N

M

M

M

M

pl,Rd pl,Rd

pl,Rd pl,Rd

Figure 2.9 Interaction curve for compression and uni-axial bending using (a) the EC4-1-1 method; and (b) the simplified method in the UK NAD


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account the entire concrete area of the cross-section (i.e., the concrete is uncracked).Consequently, in order to allow for these simplifications, the 0.9 constant, shown in the aboveequation, is applied to the moment resistance.

For concrete filled hollow sections, the interaction curve of A-E-C-B (shown in Figure 2.7) maybe preferred to A-C-B (shown in Figure 2.9(b)), as it will give a more economical design:especially for columns with high axial load and low end moments (although much morecalculation effort is required). For a better approximation, the position of point E may be chosento be closer to point A rather than being mid-way between points A and C. For furtherinformation, refer to EC4-1-1[18].

Requirements of the UK National Application Document (NAD)

The following additional requirements are specified in the UK NAD:

For columns under combined compression and bending, the ratio n should bedetermined[24,25]as follows:

(i) Concrete filled rectangular hollow sections

Providing the non-dimensional slenderness does not excess 1.0, the ratio pmd

may be determined from the equation shown above. For values of in the range of 1.0 to2.0, 0n = .

(ii) Concrete filled circular or square hollow sections

The ratio n may be determined from the equation shown above, with no limits place on

the non-dimensional slenderness . The design moment resistance, in combined compression and uni-axial bending, of a

composite column should not exceed the design plastic moment resistance Rdpl,M ,

irrespective of the applied loadN(i.e., point D on the interaction curve shown in Figure 2.7is not allowed).

Combined compression and uni-axial bending to the UK National ApplicationDocument

In order to comply with the UK NAD, the moment resistance ratio , for a composite columnunder combined compression and uni-axial bending should be evaluated as follows:

( )( )( )( )npm

nd

1

1

= when pmd

( )( )( )( )npm

nd

1

11

= when pmd <

where:

pm is the axial resistance ratio due to the concrete, Rdpl,Rdpm, /NN

d is the axial resistance ratio, Rdpl,Sd /NN


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is the reduction factor due to column buckling (see Section 2.7).

For concrete filled rectangular hollow sections

n ( )41 r= for 0.1


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After the evaluation of the moment resistance ratios y and z for both axes, as described in

the previous section, the interaction of the moments must also be checked using the linear curveshown in Figure 2.10 (c). This linear interaction curve is cut off at y9.0 and z9.0 . The

design moments, Sdy,M and Sdz,M , related to the respective plastic moment resistances, must

lie within the moment interaction curve.

EC4-1-1[18]considers the check is adequate when all the following conditions are satisfied:

9.0Rdy,pl,y

Sdy, M

M

9.0Rdz,pl,z

Sdz, M

M

and 0.1Rdz,pl,z

Sdz,

Rdy,pl,y

Sdy, +M

M

M

M

As it is only necessary to consider the effect of geometric imperfections in the critical plane ofthe column buckling, the moment resistance ratio in the other plane may be evaluated withoutthe consideration of imperfections, which is presented as follows:

1.0

d

n

k d1.0

z

a 1.0

d

1.0

Rd Rd

b

z

Rd Rd

(a) Plane expected to fail, withconsideration of imperfections

(b) Plane without considerationof imperfections

(c) Moment interaction curvefor bi-axial bending

c

y

y

0.9

y

y0.9

z

y

N

N

N

N

M

M

M

M

M

M

M

M

pl,Rd pl,Rd

pl,Rd pl,Rd

pl,y,Rd

y,Rd

z,Rd

pl,z,Rd

Figure 2.10 Verification for combined compression and bi-axial bending


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=

2

Rdpl,a,

a,Sdww,d 1

21

V

Vtt

where:

a,SdV is the design shear force to be resisted by the cross-section

Rdpl,a,V is the plastic resistance of the steel cross-section in shear =3

ydv

fA

vA is the shear area of the steel section.

For rectangular hollow sections of uniform thickness:

Load parallel to depth, h, )/(v hbAhA +=

Load parallel to breadth, b, )/(v hbAbA +=

For circular hollow sections and tubes of uniform thickness, = /2v AA

However, no reduction in the web thickness is necessary when:

Rdpl,a,a,Sd 5.0 VV <

Using the effective wall thickness of the web w,dt of the steel hollow section, the momentresistance of the composite cross-section may be evaluated using the same set of expressionsgiven within 2.9.1: without any modification.

For simplicity, the division of the shear force between the hollow section and the concrete maybe neglected, and the design shear force is assumed to be resisted by the steel section alone.

2.11 Load introductionWhere a load is applied to a composite column, it must be ensured that the load is distributed

between the individual components of the cross-section in proportion to their design resistanceswithin a specified introduction length. For composite columns using SHS, this may be achievedas follows:

(i) No shear connection needs to be provided for load introduction through a cap plate, at thetop of a column, if the full interface between the concrete section and endplate ispermanently in compression: after due consideration of the effects of creep and shrinkage.Otherwise, the load introduction has to be verified according to (v). For concrete filledcircular hollow sections, the effect caused by the confinement may be taken into account

for load introduction according to Section 2.6.1, but using the values 10 and 20 for =

0.

(ii) If the cross-section of a cap-plate is only partially loaded (see Figure 2.12), loads may bedistributed with a ratio of 1:2.5, over the thickness of the end plate. The concrete stressesshould be limited then in the area of the effective load introduction area for concrete filledhollow sections according to Figure 2.12, Figure 2.13 and (vi) below.


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(iii) In absence of a more accurate method, when loads are introduced at an intermediateposition of an SHS length, the introduction length should be assumed not to exceed 2.5d,

where d is the minimum transverse dimension in the case of concrete filled rectangularhollow sections or the outside diameter of the column for circular hollow sections.

(iv) Shear connectors should be provided in the load introduction area, and in areas with changeof cross-section, if a design shear strength at the interface between the steel and concreteexceeds the values given in Section 2.10 viz.: 0.40 N/mm for RHS; and 0.55 N/mm forCHS. The shear forces should be determined from the change of sectional forces of thesteel or reinforced concrete section within the introduction length, where the sectionalforces should be determined by plastic theory. If the loads are introduced only into theconcrete cross section, the values resulting from an elastic analysis considering creep andshrinkage should be taken into account. At a beam connection position, it is necessary tocheck that:

For an RHS column: sSd AV /)1( < 0.40 N/mm with dbAs 5.2=

For a CHS column: sSd AV /)1( < 0.55 N/mm with 4/5.22dAs =

where:

SdV is the design shear load to be transferred to the column by a beam connection.

is the steel contribution ratio.

sA is the usable shear area/connection at the concrete interface.

b is the breadth of RHS face at a shear connector.

d is the minimum dimension of an RHS or diameter of a CHS.

If load introduction would give rise to excessive interface shear stresses, then additionalshear stud connectors, or a through gusset plate (Figure 2.13), should be provided in theload introduction area, to enable the additional load to be introduced into the concrete core.

(v) Shear studs may be designed using the usual method given in EC4-1-1[18], based on thefollowing assessment, namely that the design shear strength of a stud should be determined

as the lower of:

F

Steel

Concrete1:1

1:2.5 1:2.5

1:1

Figure 2.12 Load dispersion through a locally loaded cap plate


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( ) vuRd dfP = /4/8.0 2

or

( ) vcmckRd EfdP = /29.0 2

with ( )[ ]1/2.0 = dh for 3 h/d4

0.1= for h/d> 4

where:

uf is the specified ultimate strength of the shear stud material (but not greater that 500N/mm)

ckf is the characteristic cylinder strength of the concrete.

cmE is the secant modulus of the concrete as given in Table 2.2.

d is the diameter of the shank of shear stud.

h is the length of the shear stud within the concrete core

v is a partial safety factor of 1.25.

(vi) When a concrete filled circular or rectangular square hollow section is only partially loadedby plate stiffeners at a cap column divider plate position (column section type A-A inFigure 2.13), or from a gusset plate through the profile at an intermediate column lengthposition (section type B-B in Figure 2.13), the local design resistance strength of concrete

N Sd

eg

ts

tc

c,Rd

A A

Section A - A Section B - B

B B

c,Rd

SdM

N Sd

fyd

te

e

A1

cst + 5t

Figure 2.13 Load introduction into a concrete core through a gusset plate


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Rdc, under the gusset plate or stiffener, resulting from the sectional forces of the concrete

section, should be determined by:

l

cdc

l

c

ck

yclcddRc, 1

A

fA

A

A

f

f

t

af

+=

where:

fcd

andfck are the design strength of the steel and the characteristic strength of the concrete

respectively.

t is the wall thickness of the steel tube.

a is the diameter of the tube or the width of the rectangular section.

Ac is the cross-sectional area of the concrete.

Al is the loaded area under the gusset plate according to Figure 2.13.

cL is 4.9 for circular steel tubes; and 3.5 for rectangular sections.

The ratio Ac /A

l in the equation above should not exceed 20. Welds between the gusset

plate and the steel hollow sections should be designed according to Section 3 of prEN1993-1-8: 2002[29].

(vii) For concrete filled circular hollow sections, longitudinal reinforcement may be fully takeninto account when assessing cross-sectional design parameters, even where thereinforcement is not welded to the end plates or in direct contact with the endplates,provided that the gap e

gbetween the reinforcement and the end plate does not exceed 30

mm (see also column section type A-A in Figure 2.13).

Alternatively, proprietary nailed connectors can used to effect the required shear transfercapacity. These must be shot fired through the tube wall from the outside in a defined patternbefore concrete filling. Typically, they can have a design shear capacity of 12 kN/connector andare placed at a spacing of 50 mm between connectors[34].For further informationsee the cited

reference.


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3 FIRE DESIGN

3.1 GeneralThe presence of load bearing concrete within a hollow steel column has a beneficial effect onthe fire resistance of the steel section. Columns may be fire protected in the conventional wayusing externally applied protection but, in many cases, significant periods of fire resistance canbe obtained without the need for external protection. Guidance on both methods of achievingfire resistance is given in this section; however, the emphasis is on the use of unprotectedsections. Nevertheless, in most practical cases, applying external protection has the practicaladvantage of removing the need to use reinforcment bars to obtain longer periods of fireresistance.

Note that in any particular case, reducing the applied loads will increase the fire resistance of acolumn.

Extensive experimental and theoretical investigations on the fire performance of concrete filledcolumns, without applied protection, have been carried out in Europe and the UK with thesupport of: the European Coal and Steel Community (ECSC); the International Committee forthe Development and Study of Tubular Structures (CIDECT); and various nationalgovernments. These studies have led to the development of the design rules that are nowincluded in the design codes of many countries in addition to DD ENV 1994-1-2: 2000[3](EC4-1-2) and BS5950-8: 1990[22].

The design guidance presented in this publication is based on the Eurocode methodology ratherthan BS5950-8. SCI and Corus are of the opinion that the Eurocode methods are more

advanced than BS5950-8 and are therefore preferred.Software to design concrete filled hollow sections for both normal conditions and fire has beenwritten by SCI and is available on a Corus CD for general use. The software only coversunprotected sections. Details of the software are given in Section 6.

3.1.1 Behaviour in fire

Under ambient conditions the steel and concrete material in a concrete filled hollow sectionmove together, and hence longitudinal steel and concrete strains are equal. Accordingly, thestress in each material is proportional to the ratio of the elastic moduli of the two materials.

On heating, the steel will try to expand more rapidly than the concrete, and will therefore begin

to resist a greater proportion of the applied load. However, at the same time, the steel yieldstress and modulus of elasticity will begin to reduce and, eventually, the steel will begin to shedload into the concrete.

Heat from the steel shell will be transferred to the outer layers of the concrete core, causing theirtemperature to rise. However, concrete is not a good conductor of heat, and the rate of heat flowthrough the core will be slow.

As the temperature of the outer layers increases, the concrete strength itself will begin to fall asthe heat degrades the concrete. The degradation includes the driving off of water, which ispresent both as free moisture and from the hydrated constituents of the mix. This produces amarked plateau in the concretes temperature-time profile as a considerable amount of heat is

absorbed in converting this moisture to steam.


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It is imperative that venting is provided in the steel shell to allow any steam to escape. BS5950-8 and EC4-1-2 recommend that the sections should contain one vent hole, with aminimum diameter of 20 mm, at the top and bottom of each storey (see Section 4.1.1). Thelongitudinal spacing of these holes should never exceed 5 m. Care must also be taken to ensurethat these vent holes are positioned such that they are not within the depth of the floorconstruction.

The steel shell contains the concrete and prevents direct flame impingement, both preventingprogressive spalling and reducing the rate of degradation of the core.

Failure of the column will occur when the combined strength of the steel and concrete hasreduced to the level of the applied load.

Parameters affecting fire performance

The most significant design parameters affecting the performance of concrete filled columns infire are detailed below.

Material strength

From solely a fire resistance perspective, the most efficient column is obtained by using a highstrength concrete with a thin-walled grade S275 steel section. This gives the most advantageousratio of concrete load capacity to overall column strength.

Column size

As the external size of a column increases, the cross-sectional area of the concrete core willincrease at a faster rate than that of the steel. Accordingly, the core of a larger sized column willsupport a greater proportion of the total load than a smaller one.

External protection (if applied)Externally applied protection will reduce the rate of heating and will therefore increase the fireresistance. The use of external protection will normally eliminate the need to reinforce theconcrete core.

Applied load

The lower the level of the applied load, the lower the stresses produced, and the longer theperiod of fire stability of the column.

Effective length

For short columns (i.e., columns with effective lengths up to approximately 12 times the column

width), failure will occur when the combined strength of the materials reduces to a level that isless than the applied load (i.e., a crushing failure). As the column length increases, failure willbecome progressively more related to instability considerations. EC4-1-2 allows a reduction inthe effective length of columns in fire (see Section 3.6.1 for further details).

Bending moments and eccentricity

When the flexural stiffness of the steel shell is lost, the bending resistance of the column issignificantly reduced, because of the relatively low value of the elastic modulus for concrete andits poor flexural strength compared to steel.

The effect of accidental eccentricity and out-of-straightness in a column subjected to nominalaxial loads is not significant for short columns. However, this can be a significant factor for

slender columns in fire.


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The presence of moments in the column produced by either end moments or an eccentricallyapplied end load (cleat loading) also has a significant effect on the fire stability.

Reinforcement

The presence of reinforcement in the concrete will improve the flexural and axial properties ofthe core and so improve the fire resistance, particularly where buckling stability and/or bendingmoments are major factors.

The Eurocodes use the parameter axis distance and not concrete cover to describe the positionof the reinforcement within the concrete core. Axis distance is measured from the centre of thebar to the inside of the steel tube, as shown in Figure 3.1.

3.2 Protected columnsConcrete-filled structural hollow section columns with a design capacity based on the roomtemperature properties of the full cross-section may be protected against fire with externally

applied insulating materials. The presence of the concrete core will substantially add to the heatsink of the column and so markedly reduced the effective Section Factor of the compositecolumn. The Section Factor VAm / is the ratio of the exposed perimeter to the area of steel andis commonly used in assessing the required thickness of fire protection.

The thickness of fire protection material required for a concrete-filled structural hollow sectioncolumn may be determined as follows:

1. Determine the resistance of the fully composite column according to EC4-1-1.

2. Calculate the utilization factor in fire, defined as:

C20atResistance

statelimitfireatLoad=

3. Using the utilization factor, assess the critical temperature for the section using thedesign procedures for a simple steel section according to ENV 1993-1-2: 1995[27](EC3-1-2).

4. The effect of the heat sink, from the presence of the concrete core, is to increase theSection Factor of the steel section. As a result, the effective Section Factor may becalculated based on an increased wall thickness of the steel section as follows[31, 32]:

cesse ttt +=

Axisdistance

Axisdistance

Figure 3.1 Illustration of axis distance for CHS and SHS sections


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with ice bt 15.0= for Tbi 12<

Ttce 8.1= for Tbi 12

where:ts is the wall thickness (mm).

tce is the effective increase in wall thickness due to the concrete core (mm).bi is the minimum dimension of the concrete core (mm).T is the fire resistance time (mins).

5. Calculate the effective Section Factor.

se

m

tV

A

onbasedSHSofArea

SHSofareaSurface=

6. The thickness of fire protection material required can then be obtained in theconventional manner.

The above method for determining the thickness of externally applied fire protection may beused for any passive insulating materials. The same approach may also be adopted forintumescent coatings, provided that suitable test evidence is available.

3.3 Unprotected columns

The method proposed in this section directly follows the principles of Eurocode 4. EC4-1-2gives general design methods for composite columns and, in Annex G, specific rules forconcrete filled hollow sections. Following a calibration exercise, SCI and Corus concluded thata combination of the two methods was the best approach, which is fully in line with theprinciples of this Eurocode.

For the combined buckling resistance and bending check, SCI and Corus have adopted a moreconservative approach than that recommended by EC4-1-2. This approach takes into accountthe slenderness of the column; a factor presently ignored in the Eurocode.

Tables to allow an estimate of the column size to achieve the required fire resistance are givenin Section 6.

The Eurocode states, in general principles, that the buckling resistance of a column may becomputed by using buckling curve c. The squash resistance and Euler buckling resistances arecalculated by integrating across the cross section taking into account the temperaturedistribution and corresponding material properties.

Thus, the buckling resistance is given by:

Rdpl,fi,Rdfi, NN =


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where:

is the reduction coefficient for buckling obtained from curve c of Section 5.5.1, of

EC3-1-1 and is dependant on the non-dimensional slenderness ratio .

Rdpl,fi,N is the design value of the plastic resistance to axial compression in the fire situation.

The calculation is carried out in five stages, as follows:

1. Carry out a thermal analysis to establish the temperature distribution throughout thecross-section.

2. Calculate the properties of the cross-section.3. Calculate the buckling resistance of the column.4. Calculate the bending resistance of the column.5. Calculate the effect of interaction between axial load and bending.

DD ENV 1991-2-2: 1996[26] (EC1-2-2) gives an equation for determining the heat transfer,which includes two partial factors. These are applied to the radiation and convection terms.They are included to allow heating rates in different furnaces to be modelled.

Rate of heat input (W/m) = ( ) ( ) ( )4s4

grrsgc 273273 +++

where:

s is the steel temperature (C)

g is the gas temperature (C)r is the effective emmissivity

is the Stefan Boltzmann constant (5.67 10-8W/m K4)

Values for the other parameters are given in EC1-2-2, as follows:

is the convection coefficient = 25 W/m2K

c is the partial factor for convection (a boxed value) = 1.0

r is the partial factor for radiation (a boxed value) = 1.0

is the orientation (view) factor = 1.0

The UK NAD to EC1-2-2 specifies 0.45 for r . From a consideration of test data, SCI andCorus consider this value to be too low[4]for calculating the heat input to concrete filled hollowsections. It is therefore recommended that a value of 1.0 for r is more appropriate for concretefilled hollow sections.

3.4 Partial safety factorsDuring 2002 the UK National Application Document (NAD) for EC4-1-2 is expected to bepublished. This will specify the partial safety factors and combination factors that should beused in the UK. The relevant factors that are due to be given in the NAD are:


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Partial material factors:

Steel, M,fi,a 1.0

Concrete, M,fi,c 1.1

Reinforcement, sM,fi, 1.0

Combination factors, 1,1 , for imposed floor loading:

Storage 0.9Escape stairs and lobbies 0.9Plant 1.0All other areas 0.7

The NAD will also give more conservative values than the Eurocode for the effective length ofcolumns in fire (see Section 3.6.1).

3.5 Properties of the cross-sectionIt is generally not feasible to carry out design calculations by hand and use of the ConcFillsoftware is advised (see Section 6). The first step is to divide the cross-section into a number ofelements, as part of a finite difference thermal analysis. The structural section properties arethen calculated by summing the properties of all the elements, with due account being paid tothe effect of the temperature on each element.

3.5.1 Squash (plastic) resistance, Nfi,pl,Rd

The squash resistance of the composite column is calculated from the following summation:

++= m M,fi,cc,c,

k sM,fi,

max,s,s,

j M,fi,a

max,a,a,Rdpl,fi,

fAfAfA

N

where:

a,A is the area of an element of the steel section.

s,A is the area of an element of the reinforcement.

c,A is the area of an element of the concrete.

max,a,f is the strength of the steel section element at temperature (see Section 3.8.1).

max,s,f is the strength of a steel reinforcement bar at temperature (see Section 3.8.2).

c,f is the strength of the concrete element at temperature (see Section 3.8.3).

ifi,M, is the partial material safety factor for the element.

3.5.2 Effective flexural stiffness

The effective flexural stiffness of the composite column ( ) efffi,EI can be determined from:

( ) ,, c,m c,s,k s,a,j ,a,efffi, IEIEIEEI ++=

where:


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a,I , s,I and c,I are the second moment of area of each element.

,a,E , ,s,E and ,c,E are the tangent moduli of the stress-strain relationship for the material

of each element at its temperature and stress .

3.6 Column buckling resistance

3.6.1 Effective length of composite columns in fire

The effective (buckling) length of composite columns in fire can be determined from Clause4.3.6 of EC4-1-2, which is shown schematically in Figure 3.2. For columns within anintermediate storey of a building, the buckling length of the column is 0.5 times the systemlength. For columns on the top storey, the buckling length should be taken as 0.7 times thesystem length.

In the draft UK NAD for EC4-1-2 the factors of 0.5 and 0.7 have been conservatively increasedto 0.7 and 0.85 respectively.

3.6.2 Buckling resistance

The buckling resistance is calculated from the squash resistance and the Euler (elastic) criticalload using the EC3-1-1 buckling curve c. The Euler buckling load is given by:

where:

l is the buckling length of the column in fire

The non-dimensional slenderness ratio is given by:

crfi,

Rdpl,fi,

N

N

=

L

L

L

Shear wall or other bracing system

L

0.7L

0.85L

Figure 3.2 Effective length of columns in fire conditions (N.B., the values of 0.7 and0.85 are taken from the draft UK NAD)

2( )2

ef ffi, crfi,

=

l

EI


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The resistance of a composite column in axial compression (buckling load) is obtained from:

Rdpl,fi,Rdfi, NN =

where: is the reduction coefficient for buckling obtained from curve c of Section 5.5.1, of

EC3-1-1 and is dependant on the non-dimensional slenderness ratio .

The reduction factor may be determined from:

[ ] 5.0221

+= but 0.1

where:

( ) 22.015.0 ++=

is an imperfection parameter depending on the buckling curve considered. Forbuckling curve c the imperfection factor, , is 0.49.

3.7 Combined compression and bendingThe design method can be applied to columns in multi-storey steel frames. These columns

should carry predominately axial loads. It is recommended that the ratio of applied moment tomoment capacity should not exceed 0.67.

The calculation of the plastic bending resistance is broadly similar to the calculation of thesquash load and flexural stiffness. Two steps have to be carried out.

Find the plastic neutral axis such that:

=++ 0cfi,M,c,c,

sfi,M,

max,s,s,

afi,M,

max,a,a, fAfAfA

where the stresses are considered as positive in tension or negative in compression.

Calculate the plastic moment resistance:

++= yfA

yfA

yfA

Mcfi,M,

c,c,

sfi,M,

max,s,s,

afi,M,

max,a,a,Rdfi,

whereyrepresents the distance from the centroid of each element to the plastic neutral axis.

The interaction of axial compression and bending is checked using the expression below. Thisis a more conservative approach than that given in the Eurocode.

0.1Rdfi,

fyy

Rdfi,

fxx

Rdfi,

f ++=M

Mk

M

Mk

N

NR


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where:

fN is the applied load.

fxM is the maximum applied moment about the major axis.

fyM is the maximum applied moment about the minor axis.xk , yk are modification factors based on slenderness (see Section 3.7

Documents

Design Guide for SHS Concreter Fillied COLUMN