OneSteel Composite Structures Design Booklet Db3.1

Design of Composite Slabsfor Strength

Design Booklet DB3.1

OneSteel Market MillsComposite Structures Design Manual

February 2001


DB3.1–ii Composite Slabs Edition 2.0 - February 2001Design of Composite Slabs for Strength

Published by

OneSteel Manufacturing Pty LimitedABN 42 004 651 325

Produced by the

Centre for Construction Technology & ResearchUniversity of Western Sydney

Contributors

Dr. Mark Patrick *Centre for Construction Technology & Research

Dr. Chong Chee Goh *Mr. David Proe *

Mr. Rodney Wilkie ** Formerly BHP Melbourne Research Laboratories

Reviewed by

Prof. Russell BridgeCentre for Construction Technology & Research

Mr. Rennie DarmaninScott Wilson Irwin Johnston Pty Ltd

Endorsed by

BHP Building ProductsStramit Industries

Woodroffe Industries Pty Ltd

Edition 1.0 - May 1998Edition 2.0 - February 2001

DisclaimerWhile every effort has been made and all reasonable care taken toensure the accuracy of the material contained herein, thecontributors, editors and publishers of this booklet shall not be heldliable or responsible in any way whatsoever, and expressly disclaimany liability or responsibility for any loss or damage, cost orexpenses, howsoever incurred by any person whether the user ofthe booklet or otherwise including without limitation, loss or damage,costs or expenses incurred as a result of or in connection with thereliance, whether whole or partial by any person as a foresaid uponany part of the contents of this booklet. Should expert assistance berequired, the services of a competent person should be sought.


Edition 2.0 - February 2001 Composite Slabs DB3.1–iiiDesign of Composite Slabs for Strength

ForewordOneSteel is a leading manufacturer of steel long products in Australia after its spin-off from BHP PtyLtd on the 1st November 2000. It manufactures a wide range of steel products, including structural,rail, rod, bar, wire, pipe and tube products and markets welded beams.

OneSteel is committed to providing to design engineers, technical information and design tools toassist with the use, design and specification of its products. This design booklet “Design ofComposite Slabs for Strength” was one of the first two design booklets of the Composite StructuresDesign Manual, which is now being completed and maintained by OneSteel.

The initial development work required to produce the design booklets was carried out at BHPMelbourne Research Laboratories before its closure in May 1998. OneSteel Market Mills is fundingthe University of Western Sydney’s Centre for Construction Technology and Research in continuingthe research and development work to publish this and future booklets.

The Composite Structures Design Manual refers specifically to the range of long productsthat are manufactured by OneSteel and plate products that continue to be manufactured byBHP. It is strongly recommended that OneSteel sections and reinforcement and BHP plateproducts are specified for construction when any of the design models in the design bookletsare used, as the models and design formulae including product tolerances, mechanicalproperties and chemical composition have been validated by detailed structural testing usingonly OneSteel and BHP products.

To ensure that the Designer’s intent is met, it is recommended that a note to this effect beincluded in the design documentation.


DB3.1–iv Composite Slabs Edition 2.0 - February 2001Design of Composite Slabs for Strength

ContentsPreface ........................................................................................................ v

1. SCOPE AND GENERAL

1.1 Scope ................................................................................................ 11.2 General.............................................................................................. 1

2. TERMINOLOGY............................................................................................... 33. DESIGN CONCEPTS

3.1 Shear Connection.............................................................................. 53.2 Slab in Bending ................................................................................. 73.3 Vertical Shear .................................................................................... 103.4 Sheeting Support Conditions............................................................. 103.5 Curtailment of Positive Tensile Reinforcement ................................. 113.6 Preventing Sudden Collapse ............................................................. 123.7 Effects of Propping ............................................................................ 13

4. DESIGN MODELS

4.1 General.............................................................................................. 144.2 Positive Moment Capacity................................................................. 144.3 Positive Vertical Shear Capacity ....................................................... 174.4 Negative Moment Regions ................................................................ 184.5 Effective Span ................................................................................... 18

5. DESIGN APPROACH

5.1 General.............................................................................................. 205.2 Definition of Design Situation ............................................................ 205.3 Identification of Potentially Critical Cross-Sections ........................... 205.4 Calculation of Design Action Effects ................................................. 225.5 Design of Negative-Moment Regions................................................ 235.6 Design of Positive-Moment Regions ................................................. 26

6. DESIGN RULES6.1 Design Objectives ............................................................................. 286.2 Limit State Requirements for Strength .............................................. 286.3 Application ......................................................................................... 286.4 Design Loads..................................................................................... 296.5 Methods of Structural Analysis .......................................................... 306.6 Moment Redistribution ...................................................................... 306.7 Negative-Moment Regions................................................................ 306.8 Positive-Moment Regions ................................................................. 31

7. WORKED EXAMPLES

7.1 General.............................................................................................. 337.2 Definition of Design Situation ............................................................ 337.3 Identification of Potentially Critical Cross-Sections ........................... 347.4 Design of Negative-Moment Regions................................................ 357.5 Design of Positive-Moment Regions ................................................. 37

8. REFERENCES ................................................................................................ 43APPENDICES

A Referenced Australian Standards ..................................................... 44B Notation ............................................................................................. 45C Strength Design Information for Proprietary

Profiled Steel Sheeting Products....................................................... 48D Design Positive Moment Capacity Tables for

Proprietary Profiled Steel Sheeting Products .................................... 50E Design Positive Vertical Shear Capacity Tables for

Proprietary Profiled Steel Sheeting Products .................................... 55


Edition 2.0 - February 2001 Composite Slabs DB3.1–vDesign of Composite Slabs for Strength

PrefaceThis design booklet forms part of a suite of booklets covering the design of simply-supported andcontinuous composite beams, composite slabs, composite columns, steel and compositeconnections and related topics. The booklets are part of the OneSteel Market Mills’ CompositeStructures Design Manual which has been produced to foster composite steel-frame buildingconstruction in Australia to ensure cost-competitive building solutions for specifiers, builders anddevelopers.

Composite slabs have a long history of use in Australia dating back to the mid-1960’s when JohnLysaght (Australia) was promoting Bondek as a “new release composite slab structural floordecking”. Local bond stress was calculated using the SAA Code for Concrete Buildings AS CA2-1963 and was not to exceed 40 psi (0.27 MPa). It was understood at the time that bond between thegalvanised sheeting and the concrete was achieved by virtue of chemical adhesion of the cementpaste to the zinc coating. The maximum span that could be used in practice was determined fromuniformly-loaded slab tests, with the aim of ensuring that sufficient safety remained against bondfailure, noting that load-carrying capacity, and therefore the bond stress at failure, reduced as spanincreased.

Considerable research into the behaviour of composite slabs has been performed at BHP MelbourneResearch Laboratories in subsequent years. New types of profiled steel sheeting have beendeveloped which no longer depend on adhesion bond for their anchorage. Mechanical and frictionalresistance have now been identified as the major contributors to the bond developed by theseproducts, similar to deformed reinforcing bars. Estimates of these resistances can be derived from anewly-developed Australian test called the Slip-Block Test, for which an Australian Standard isbeing prepared. Alternatively, slab tests can be used to estimate the strength of the mechanicalresistance. This research has allowed this design booklet covering the design of composite slabs forstrength to be written. A unified approach is presented, whereby, for the first time in Australia, all themajor types of profiled steel sheeting currently produced in this country can be designed by the samemethods.

A method of design for bending strength is presented. The method is based on partial shearconnection strength theory, and is very similar to that used to design simply-supported compositebeams for bending strength (see Design Booklet DB1.1). Data about the shear connectionperformance of proprietary sheeting products must be obtained from either slab tests or the Slip-Block Test. The mechanical resistance must at least by assumption be ductile.

A method of design for vertical shear is also presented.

For products which develop ductile mechanical resistance of sufficient magnitude, use of the designrules contained in this booklet can lead to very significant improvements in economy compared withthe designs obtained currently. Owing to the high tensile capacity of the sheeting in positive-momentregions, a major saving can result by allowing moment redistribution from negative to positivemoment regions in continuous composite slabs, leading to a significant reduction in the amount oftop-face reinforcing steel.

The design rules presented in this booklet are being used as a basis for one of the strength designmethods in a new Australian Standard on composite slabs currently being prepared, noting that amethod will also be provided for products with either weak or non-ductile mechanical resistance. Theslabs may be either simply-supported or continuous, while the loading must be essentially static innature and uniformly-distributed. Partial shear connection strength theory can be used to designslabs with line loads perpendicular to the span, and this feature is used in the method of design forvertical shear. The rules are presented entirely in limit state format, and the design principles onwhich they are based are in harmony with the latest European design provisions. Design for otherlimit states such as serviceability (e.g. deflection and cracking), durability and fire resistance will becovered in later design booklets.

Edition 1.0 was published by BHP in May 1998. Edition 2.0 contains changes as a result of the moveto 500 MPa reinforcing steels, some minor corrections to the first edition, and is published byOneSteel.


Edition 2.0 - February 2001 Composite Slabs DB3.1–1Design of Composite Slabs for Strength

1. SCOPE AND GENERAL1.1 ScopeThe design for strength of composite slabs incorporating profiled steel sheeting that can developductile mechanical resistance with the concrete is covered in this booklet. The type of constructionenvisaged is shown in Fig. 1.1.

For profiled steel sheeting that can develop ductile longitudinal slip resistance of sufficientmagnitude, the sheeting can provide a very efficient design solution by performing multiple functions.Prior to placing the concrete, the sheeting acts as a platform for construction activities (ConstructionStages 1 and 2 in AS 2327.1, Simply Supported Beams). It then acts as formwork for the wetconcrete (Construction Stage 3), and must also support the concrete immediately after it has set(Construction Stage 4). After the concrete has hardened sufficiently and composite action is attained(Construction Stages 5 and 6, and the in-service condition), the sheeting acts as effective bottom-face tensile reinforcement in the direction of the sheeting ribs, with the composite slab being treatedin design as a member spanning in one direction.

The composite slab may be supported on steel beams, masonry walls or similar narrow supports.These permanent types of supports should extend across the full width of the slab, and the ends ofthe sheets should pass onto them. Live loads are assumed to be predominantly static in nature,uniformly-distributed and applied to the top surface of the slab.The design rules given in Section 6 of this booklet are deemed to be appropriate design informationwhich satisfies all the requirements of Clause 3.1.3.2 of AS 2327.1 (see Appendix A for referencedAustralian Standards).

Negative tensilereinforcement for flexure andcrack control

Transverse reinforcementfor shrinkage and temperature control,and to control longitudinal splitting at ultimate load

Profiled steel sheeting

Steel beam

Masonry wall, lintel,or steel perimeter beam

One-way slabspanning direction

Uniformly-distributed load (UDL)

Positive tensilereinforcement for flexure

Longitudinal shear reinforcementin vicinity of shear connectors

In-situ concrete

Shear connector

Figure 1.1 Typical Composite Slab Construction

Reference should be made to Section 4 of AS 2327.1 concerning loads and other actions that mustbe considered when designing a composite slab during Construction Stages 5 and 6 and the in-service condition.

The notation used in this booklet is described in Appendix B.

Information relating to Australian proprietary sheeting products is contained in Appendices C, D andE of this booklet.

1.2 GeneralA composite slab comprises profiled steel sheeting, OneSteel reinforcement in the form of eitherwelded-bar mesh or deformed bars, and cast in-situ concrete, as shown in Fig. 1.1. It is commonpractice in Australia to construct continuous composite slabs with negative tensile reinforcementprovided over supports for flexure and crack control. Positive tensile reinforcement may be provided


DB3.1–2 Composite Slabs Edition 2.0 - February 2001Design of Composite Slabs for Strength

to add flexural strength to the slab under room-temperature or fire conditions. Transversereinforcement must be provided for shrinkage and temperature control, while longitudinal shearreinforcement is also required in the vicinity of shear connectors attached to the steel beams.

The coating, design properties and cleanliness of the profiled steel sheeting must satisfyClause 2.1.5 of AS 2327.1. The design properties of the reinforcement and concrete are specified inSection 6 of AS 3600, Concrete Structures.

For profiled steel sheeting used in simply-supported composite beam construction, its geometrymust comply with Clause 1.2.4 of AS 2327.1 (see Fig. 1.2). The requirement in Fig. 1.2 for aminimum cover slab thickness of 65 mm determines the minimum value of overall slab thickness,Dc , that may be used with any particular proprietary profiled steel sheeting product (see AppendixC).

It is a requirement of AS 2327.1 that the area of the voids formed by the steel ribs in the concrete isnot greater than 20 percent of the area of the concrete within the depth of the steel ribs, i.e. the steelribs must be relatively small. A major reason for this restriction was to avoid the problems associatedwith designing the shear connection when a profile with wide steel ribs is used, noting that compositeslabs used in accordance with AS 2327.1 are close to being solid concrete slabs.

Several aspects of composite slab design can be significantly affected by a large reduction inconcrete due to the presence of profiled steel sheeting with wide steel ribs. These are:

(a) the moment capacity of support regions in negative bending, whereby the compressivecapacity of the concrete may be significantly diminished; and

(b) the vertical shear capacity of both positive and negative moment regions.

Although item (a) can be handled in a straightforward manner by calculation, this is not considered tobe the case for item (b). It will be explained herein that a method of design for vertical shear hasbeen developed from testing. The tests were all performed on composite slabs that were effectivelysolid concrete slabs.It follows that, similar to the situation with simply-supported composite beams designed inaccordance with AS 2327.1, the design rules contained in this design booklet must be restricted intheir application to composite slabs incorporating profiled steel sheeting with geometry that satisfiesFig. 1.2.

Dc

sr

hr ≤ 80

(Dc-hr) ≥=65 hr/2

bcr ≥=150bsrbb ≤ 20

Steel ribLongitudinal stiffeners

hs ≤ 10

(a) Steel rib

(b) Longitudinal stiffeners

Longitudinal stiffeners

Figure 1.2 Profiled Steel Sheeting Geometry Restrictions

Consideration should also be given to the minimum top cover to shear connectors given in Table 8.5of AS 2327.1. Other issues which might affect the minimum value of slab thickness, Dc , such asthermal insulation in fire, durability and serviceability will be dealt with in other booklets.



2. TERMINOLOGYComposite slabA cast in-situ concrete slab that incorporates profiled steel sheeting as permanent soffit formwork.

Complete shear connectionWhere the moment capacity at a cross-section is not limited by the strength of the shear connectionbetween the sheeting and the concrete.

Construction StagesThe following Construction Stages defined in AS 2327.1 (see Clause 4.2 and Appendix F) arerelevant to the design of a composite slab:

Stage 1: Period between when the steelwork is erected, and the formwork is placed and, ifappropriate, fixed to the steel beams.

Stage 2: Period between the end of Construction Stage 1 and immediately prior to thecommencement of casting the slab concrete.

Stage 3: Period between commencement of casting the slab concrete and its initial set under theprevailing site conditions.

Stage 4: Period after initial set of the concrete until its compressive strength fcj' reaches 15 MPa,

which corresponds to the development of composite action. No additional loads shouldbe placed on the concrete to ensure that the shear connection is not damaged during thissensitive period, which may require back-propping of beams and/or slabs.

Stage 5: Period until the concrete compressive strength fcj' reaches fc

' (i.e.15 ≤ <f fcj c' ' ). Removal

of slab formwork/falsework or props to the steel beams or slabs may occur during thisstage. With composite action initially developed, the strength of the beam may beassessed using appropriate values for the compressive strength of the concrete (seeClause 6.4.2 of AS 2327.1) and the design shear capacity of the shear connectors.

Stage 6: The remaining period of construction until the structure goes into service. The designstrength of the composite beams has been reached. The in-service loads are yet to beapplied, but appropriate construction loads should be considered.

In-service condition: The structure is occupied.

Conventional reinforcementSteel reinforcement other than the sheeting, which can take the form of deformed bars (OneSteel’s500PLUS® Rebar or BAMTEC®) or welded mesh (OneSteel’s OneMesh500™).

Cover slabThe part of the slab above the plane passing through the tops of the sheeting ribs.

Critical cross-sectionA cross-section at which the ratio of either the design bending moment, M * , to the design momentcapacity, φMuo , or the design vertical shear force, V * , to the design vertical shear capacity, φVuc ,is a maximum.

Degree of shear connection, ββββThe ratio of the resultant tensile force in the sheeting at a cross-section, Tsh , at the strength limitstate, to the resultant tensile force in the sheeting for the same cross-section with complete shearconnection, Tcsc .



Effective slab depth, dThe distance from the centroid of the tensile reinforcing steel (including sheeting and conventionalreinforcement) to the compressive face of the slab.

Frictional resistanceThe component of longitudinal slip resistance which develops at supports where sheeting passesover, and is affected by a change in the magnitude of the support reaction.

Longitudinal slipThe slip that occurs in the direction of the steel ribs at the interface between the concrete and theprofiled steel sheeting.

Longitudinal slip resistanceThe property of a profiled steel sheeting product to resist longitudinal slip by a combination ofmechanical and frictional resistance.

Mechanical resistanceThe component of longitudinal slip resistance which develops along the member between thesheeting and concrete, and is unaffected by a change in the magnitude of the support reaction.

Negative-moment region (hogging bending)Region in which tension occurs at the top of the slab under the loading relevant to the aspect ofdesign under consideration.

Partial shear connectionWhere the moment capacity at a cross-section is limited by the strength of the shear connectionbetween the sheeting and the concrete.

Positive-moment region (sagging bending)Region in which tension occurs at the bottom of the slab under the loading relevant to the aspect ofdesign under consideration.

Potentially critical cross-sectionA cross-section that is likely to be critical.

Shear connectionThe interconnection between the profiled steel sheeting and concrete of a composite slab whichenables the two components to act together as a single structural member to resist longitudinal slip.

Shear spanDistance from a critical cross-section in the positive moment region to the nearer end of the span.

Steel proportion, pThe cross-sectional area of conventional reinforcement in tension, Ast , divided by the width of slabbeing considered, b , and the effective slab depth, d , i.e. p A bd= st / ( ) .



3. DESIGN CONCEPTS3.1 Shear ConnectionThe shear connection of a composite slab is the interconnection between the sheeting and concretewhich resists longitudinal slip, and is represented by the values of the shear connection parametersHr and µ . Design values for these shear connection parameters corresponding to a proprietaryprofiled steel sheeting product must be determined from tests. The mechanical resistance Hr canbe estimated from full-scale slab tests [1], or alternatively from a small-scale test called the Slip-BlockTM Test [2, 3]. The Slip-Block Test, developed in Australia and being prepared as an AustralianStandard, has received international recognition [4, 5, 6]. Estimates of the coefficient of friction µcan be obtained from Slip-Block Test data, and can be used to give better estimates of Hr obtainedfrom slab tests [6, 12].

Longitudinal SlipLongitudinal slip initially occurs between the steel sheeting and the concrete in regions of positivebending wherever the concrete is cracked. Cracking might occur due to a combination of flexure andrestraint due to shrinkage. Adhesion or chemical bond is broken in the region of cracks immediatelythey form, and is never regained. The case of a simply-supported composite slab which is at thepoint of failure in bending is illustrated in Fig. 3.1. Slip has extended the full length of the shear spanresulting in end slip. Adhesion bond is lost over the entire shear span. Correspondingly, the crack atthe critical cross-section can become quite large as loading continues, if this cross-section exhibitspartial shear connection. The amount of end slip which occurs depends on a number of factors, viz.:the magnitude of the applied load; the magnitude of the longitudinal slip resistance developedbetween the sheeting and the concrete; and, the geometry of the slab. End slip under service loadsshould be avoided since this can reduce the flexural stiffness of a slab significantly, which will beconsidered in a future booklet covering design for deflection.

CEnd slip

UDL

Profiled steel sheetingSupportreaction

Slip occurs along full length of shear span. Widecrack may develop at critical cross-section

Tsh

Figure 3.1 Longitudinal Slip in a Simply-Supported Composite Slab in Flexure

Mechanical Resistance Along MemberUnder positive bending, the sheeting in the soffit of a simply-supported composite slab develops aresultant tensile force, Tsh . Bending of the sheeting also normally occurs due to curvature of theslab. The magnitude of the tensile force is increased if the concrete is cracked. At the strength limitstate, the tensile force Tsh developed at a critical cross-section is assumed to be resisted in part bymechanical resistance. This mechanical resistance, Hr , is assumed to develop uniformly with slipover the entire length of the shear span and across the full width of the slab, and is expressed as aforce per unit plan area of sheeting with units of kPa. (Frictional resistance may also develop at theslab supports, which also contributes to resisting Tsh - see below.) The resultant tensile force in thesheeting therefore develops at a uniform rate along the length of the slab due to mechanicalresistance. The maximum or limiting value of Tsh (equal to Tcsc ) is reached when either the tensilecapacity of the sheeting or the compressive capacity of the concrete is attained. This is illustrated inFig. 3.2(a).

The variation of mechanical resistance, Hr , once slip is initiated, as measured in the Slip-Block Test,is shown diagrammatically in Fig. 3.2(b). As in a slab, adhesion bond must be broken to initiate slip,which causes the block to jump about half a milli-metre, depending on various parameters, whichexplains why the initial portion of the curve in Fig. 3.2(b) is shown dashed. Readings are not normally



taken at slips above 10 mm, since experience shows that slabs usually attain their maximumstrength at slips much less than this amount. The magnitude of Hr depends on the profile geometryincluding the influence of such features as embossments, and may also depend on the sheetingthickness, tbm , and the compressive strength of the concrete. While the variation of Hr with slip isshown to be reasonably constant in Fig. 3.2(b), i.e. the mechanical resistance is ductile, this is notalways so, in which case one of a number of procedures can be adopted to calculate arepresentative value of Hr for design.

C

Tsh

UDL

Profiled steel sheetingx

Tsh = Tcsc

Tsh = Hrx

(a) Development of tensile force in sheetingthrough mechanical resistance

Mechanical resistance Hr

Mec

hani

cal r

esis

tanc

e, H

r (k

Pa)

Slip, s (mm)0.5 10.0(b) Variation of mechanical

resistance with slip

Figure 3.2 Mechanical Resistance Developed along the Sheeting

Frictional Resistance At SupportsFor sheeting which is continuous over a support, frictional resistance develops at the interfacebetween the sheeting and the concrete due to the clamping effect of the support reaction (see Fig.3.3(a)) [2, 3, 7]. It is because of this effect that the strength of a composite slab can increase as loadis applied to it and has lead to the concept of a limiting moment capacity [2].

C

Tsh

UDL

(a) Development of tensile force in sheetingthrough frictional resistance

Coe

ffici

ent o

f fric

tion,

µµ µµ

Slip, s (mm) 10.0

(b) Variation of coefficient of friction with slip

Frictional resistance, µR*

Sheeting continuesover support

Reaction atsupport, R*

Profiled steelsheeting

0.5

Figure 3.3 Frictional Resistance at Support

The frictional resistance is proportional to the magnitude of the support reaction acting through thepans of the sheeting, R * , and the coefficient of friction, µ . The variation of the coefficient of friction,µ , with slip, as measured in the Slip-Block Test, is shown diagrammatically in Fig. 3.3(b).

Ductile Shear ConnectionThe method of design for bending strength described in this booklet is based on the assumption thatthe shear connection between the sheeting and the concrete is ductile, i.e. both the mechanicalresistance, Hr , and the coefficient of friction, µ , are assumed to be constant in magnitude,irrespective of the amount of slip. Typical Slip-Block Test results and the idealised ductile behaviourare shown in Fig. 3.4.



Mec

hani

cal r

esis

tanc

e, H

r (kP

a)

Mechanical resistanceCoefficient of friction

0.5 10.0

(a) Actual

Coe

ffici

ent o

f fric

tion,

µµ µµ

Mec

hani

cal r

esis

tanc

e, H

r (kP

a)

Mechanical resistanceCoefficient of friction

0.5 10.0

(b) Assumed behaviour

Coe

ffici

ent o

f fric

tion,

µµ µµ

Slip, s (mm) Slip, s (mm)

Figure 3.4 Shear Connection Behaviour of Profiled Steel Sheeting

3.2 Slab in BendingThe strength model for the positive-moment region of a composite slab in bending will be discussedin this section with reference to the simply-supported slab shown in Fig. 3.5. Partial shear connectionstrength theory has been developed to calculate the ultimate strength of such a slab on the basisthat it will fail by either flexure or longitudinal slip. This theory can also be used to calculate thebending strength of positive-moment regions of continuous slabs.

Conventional reinforcement


UDL Slab

Figure 3.5 Simply-Supported Composite Slab

Slab End SegmentA free-body diagram of an end segment of the slab in Fig. 3.5 is shown in Fig. 3.6. It is assumed thatthe slab is subjected to a uniformly-distributed load, and that it has reached its ultimate strength andwill fail either by flexure or longitudinal slip. The end segment is bounded by the critical cross-sectionwhere the design bending moment, M * , equals the moment capacity of the cross-section, Muo , ineither complete or partial shear connection.

Conventional reinforcement


UDL

xR*

V* M*

Criticalcross-section

Figure 3.6 Free-body Diagram of Slab End Segment

Simple-Plastic Rectangular Stress Block TheoryThe positive moment capacity at any cross-section of a composite slab in either complete or partialshear connection can be calculated using simple-plastic rectangular stress block theory. This sametheory is used to calculate the positive moment capacity of simply-supported composite beams in AS



2327.1 (Appendix D). The moment capacity is obtained by solving equations of equilibrium, whileignoring strain compatibility over the depth of the cross-section. The presence of any conventionalreinforcement in the slab can be readily taken into account. The calculation principles assumed areas follows:

(a) the concrete has zero tensile strength;

(b) a uniform compressive stress of 0 85. 'fc develops in the concrete directly below the top surfaceof the slab;

(c) the elements of the sheeting (flanges, webs, pans) are stressed uniformly to their yield stress,fsy.sh , whether in tension or compression (whereby bending in the sheeting can develop);

(d) the conventional tensile reinforcement is stressed uniformly to its yield stress, fsy , whether intension or compression;

(e) the resultant tensile force in the sheeting, Tsh , is defined as the difference between the totaltensile force and total compressive force which develop in the elements of the sheeting, suchthat 0 ≤ ≤T Tsh y.sh , i.e. when Tsh = 0 the sheeting is in pure bending (non-composite), andwhen T Tsh y.sh= it is in pure tension (a complete shear connection case);

(f) the resultant tensile force in the sheeting, Tsh , cannot exceed the total longitudinal shear forcethat can be transferred by the shear connection between the sheeting and the concrete;

(g) the sum of the compressive forces in the concrete and any conventional reinforcement incompression equals the sum of the resultant tensile force in the sheeting and the force in anyconventional reinforcement in tension; and

(h) the effect of vertical shear on the distribution of longitudinal stresses in either the concrete orthe steel is ignored.

The end segment of a slab is shown in Fig. 3.7. Rectangular stress blocks are used to calculate themoment capacity of the internal end cross-section. For the case shown no compressivereinforcement is present.

Profiled steel sheetingR*

(b) Cross-section(a) Slab end segment

CTy.st

Tsh

fsy.sh

(c) Assumed stress distribution

0.85f'cConventional reinforcementV* M*

Muo+

2fsy.sh

C =Ty.st+Tsh

ysh

Figure 3.7 Representation of Slab End Segment and Rectangular Stress Block Theory

Moment Capacity at a Cross-SectionIn order to calculate the moment capacity at a cross-section, it is necessary to know the totallongitudinal shear force that can be transferred by the shear connection between the sheeting andthe concrete, i.e. the strength of the shear connection. As one moves in from the end of the sheeting,this strength increases due to increased anchorage of the sheeting in the concrete. The form of therelationship between positive moment capacity, Muo

+ , and the distance from the end of sheeting, x ,is shown in Fig. 3.8 for a slab with a small overhang. At the end of the slab, only the bare sheeting isassumed to contribute to the bending strength, i.e. M Muo u.sh

+ = . The moment capacity, Muo+ , then

rises progressively, and is assumed to take a step jump at the support due to friction. The momentcapacity continues to build up within the span moving closer towards the critical cross-section, andmay reach a peak corresponding to complete shear connection.



x (increasing)

UDL

R*

Critical cross-section

Muo

Mu.sh

(can be either completeor partial shear connection)

Step jump due to µR*

+

Muc

Figure 3.8 Moment Capacity of Slab Cross-Sections

Complete Shear ConnectionComplete shear connection corresponds to when flexural failure rather than longitudinal slip failurewould occur at a cross-section, i.e. the strength of the shear connection between the end of thesheeting and the cross-section concerned is not the limiting factor which determines the momentcapacity of the cross-section. In this case, the sheeting can be considered to be fully anchored. Thisis possible even though some slip must occur for the mechanical resistance to develop, which mightalso register at the end of the slab as end slip if adhesion bond is broken along the full length of theshear span.

When the distance x from an end of the sheeting is sufficiently large for the magnitude of Tsh toreach either the tensile capacity of the sheeting, i.e. T A fsh sh sy.sh= , or the maximum possiblecompressive force that can develop in the concrete above the sheeting ribs, i.e.T f D h bsh c c r= −0 85. ( )' , then it is assumed that no further increase in Tsh is possible, and the cross-section is considered to be in complete shear connection. The limiting value of resultant tensile forcein the sheeting under the condition of complete shear connection is termed, Tcsc .

Partial Shear ConnectionPartial shear connection exists at a cross-section when the cross-section moment capacity isdetermined by longitudinal slip failure rather than by flexural failure. Hence, the strength of the shearconnection between an end of the slab and the cross-section of concern limits its moment capacity.As a consequence of slip, the moment capacity of the cross-section is less than the theoreticalflexural capacity.

The region of a composite slab with partial shear connection, where anchorage of the sheeting is notfully developed, is analogous to regions in a reinforced-concrete member in the vicinity of where barsare terminated. Partial shear connection is accounted for when calculating positive moment capacity,Muo

+ , by limiting the resultant tensile force in the sheeting, Tsh , to that which corresponds to thestrength of the shear connection being reached.

Degree of Shear ConnectionThe degree of shear connection, β , at a cross-section is defined as the ratio of the resultant tensileforce in the sheeting, Tsh , to the tensile force in the sheeting at complete shear connection, Tcsc ,i.e.:

β = TT

sh

csc, 0 1≤ ≤β 3.2(1)

Cross-sections of a slab end segment with complete and partial shear connection are shown inFig. 3.9. The positive moment capacity, Muo

+ , of a composite slab cross-section is affected by thevalue of β , which increases with the distance x from the end of the sheeting.



Partialshear connection

β < 1.0

R*Complete

shear connectionβ = 1.0

x

Posi

tive

mom

ent c

apac

ity, M

uo

ββββ1.0

Completeshearconnection

Partialshearconnection

+

Partial Complete

UDL

Muc

Figure 3.9 Relationship between Positive Moment Capacity and Degree of Shear Connection

3.3 Vertical ShearExtensive testing has been conducted on simply-supported composite slabs subjected to aperpendicular line load placed at various distances from the support, with the minimum distancebeing 15. Dc [8]. All of the slabs incorporated a profiled steel sheeting product (Bondek II), thegeometry of which satisfied Fig. 1.2 and therefore AS 2327.1. Therefore, as explained in Section 1.2,all the slabs were effectively solid concrete slabs. The applied vertical shear force is highest whenthe distance from the support is the least. This testing showed that no slab failed in vertical shearbefore reaching the load corresponding to its moment capacity under partial shear connectionstrength theory. This result may be used to obtain a safe estimate of the nominal positive verticalshear capacity (Vuc

+ ) of a composite slab subjected to uniformly-distributed loading, since it showsthat a composite slab can at least withstand the vertical shear force applied when a line load isplaced at a distance of 15. Dc from the support and the applied moment equals the moment capacityof the loaded cross-section.

This method of calculating vertical shear capacity can account for the presence of positiveconventional tensile reinforcement acting in conjunction with the sheeting, since the momentcapacity calculation method described in Section 3.2 enables the contribution of this reinforcement tobe included. Such cases were included in the testing program, and the above conclusion was alsotrue for these test specimens.

This method can also be applied to the positive-moment regions of continuous slabs. For thispurpose, a hypothetical support can be placed at each point of contraflexure (under uniform loadingon all spans), and the portion of the slab between these supports can be treated as being simply-supported. At hypothetical support points, the end of the sheeting will extend past the support, andits contribution to the mechanical resistance can be included in the calculation of moment capacity.No frictional resistance should be assumed to exist at hypothetical supports (see Fig. 4.3).

The method is restricted to composite slabs incorporating profiled steel sheeting products with ageometry that satisfies Fig. 1.2. All three Australian products described in Appendix C are suitable.

No consideration is given herein to including shear reinforcement in composite slabs.

3.4 Sheeting Support ConditionsIt follows from Section 3.1 that the resultant tensile force in the sheeting, Tsh , at a cross-section isresisted by mechanical resistance developed along the length of the sheeting, and possibly frictionalresistance developed at the supports. The amount of frictional resistance developed is affected bythe way the sheeting is supported, which is explained as follows.

• If the sheeting is terminated at a support but does not extend over the full width of the support(see support B in Fig. 3.10), it is conservatively assumed in design that the frictional resistanceequals zero.



• If the sheeting is continuous over the full width of a support (see supports A and C in Fig. 3.10)then the frictional resistance equals µR* (i.e. µR*A and µR*C at supports A and C, respectively).

Figure 3.10 illustrates the sheeting support conditions for a typical continuous slab and thecalculation of the resultant tensile force Tsh at various potentially critical cross-sections (PCC’s),noting that at any of these cross-sections T T T Tsh sh.L sh.R csc= min.( , , ) . The terms Tsh.L and Tsh.R arethe maximum tensile forces that can develop in the sheeting to the Left and Right of the potentiallycritical cross-section. Examples of how to calculate these terms are given in Fig. 3.10. If the sheetingis continuous over the full width of support B, i.e. not at as shown in Fig. 3.10, it is theoreticallypossible that the concrete may not have sufficient compressive capacity to transmit the full tensileforce in the sheeting across the support. However, this situation is normally not critical and will beignored in design.

Negative tensile reinforcement


Positive tensile reinforcement

Sheeting terminateson supportR*A R*B R*C

A B C

x1 x3x2 x4

hr

At PCC-1Tsh.L = Hrx1+ µR*ATsh.R = Hrx2

At PCC-2Tsh.L = Hrx3Tsh.R = Hrx4+ µR*C

1 2

Figure 3.10 Sheeting Support Conditions and Terms for Calculation of Tsh

3.5 Curtailment of Positive Tensile ReinforcementClause 9.1.3.1 of AS 3600 has the following requirements.(i) The termination and anchorage of flexural reinforcement is based on a hypothetical bending

moment diagram formed by displacing the calculated positive moment envelope a distance Dcalong the slab from each side of the relevant cross-sections of maximum moment. This ruleaccounts for the influence of diagonal cracking which produces a free-body diagram similar tothat for a truss.

(ii) Certain proportions of the total positive moment reinforcement required at mid-span must beextended past the near face of the supports. The supports may be at a simply-supporteddiscontinuous end of a slab, or where the slab is continuous or flexurally restrained.

With respect to item (i):

• the calculation of the design moment capacity φMuo+ of a composite slab at cross-sections

sufficiently far away from supports is considered conservative enough to ignore this effect; and

• it is recommended when designing the conventional bottom-face reinforcement that thetermination locations of this reinforcement are extended by distance D Lc + sy.t .

With respect to item (ii), it is recommended that:

• the sheeting extends fully onto the support at a simply-supported discontinuous end of a slab(see supports A and C in Fig. 3.10);

• the sheeting extends to the centre of the support where a slab is continuous but the support isdesigned as simply-supported for strength; and

• the sheeting may extend partially onto the support where a slab is continuous and the supportis designed as continuous for strength (see support B in Fig. 3.10).



These latter three recommendations are intended to ensure that the composite slab has sufficientpositive moment capacity in the vicinity of the supports.

3.6 Preventing Sudden CollapseIt is desirable that when loaded to failure, concrete members do not collapse suddenly exhibitingbrittle failure [9]. As a general rule, unless it can be demonstrated that the onset of cracking at anycross-section will not lead to sudden collapse of the member, the nominal moment capacity, Muo , ateach cross-section should not be less than the minimum value given by,

( )Muo min = 12. 'Zfcf 3.6(1)where

Z = section modulus of the uncracked section, referred to the extreme fibre at whichflexural cracking occurs; and

fcf' = characteristic flexural tensile strength of concrete.

The nominal moment capacity, Muo , is calculated assuming a fully-cracked section. If the nominalmoment capacity is too small, Muo could be less than the moment required to cause first cracking ofthe concrete. If such a member was statically determinate, e.g. a simply-supported slab or acantilever, cracking would result in a sudden failure. To prevent such a failure, Muo must be greaterthan the cracking moment at the critical cross-section, and a minimum value ( )Muo min that is twenty

per cent higher than the moment required to produce an extreme fibre tensile stress of fcf' is

recommended. It is sufficiently accurate to calculate ( ) . .' 'M Zf bD fcuo min c2

cf= =12 0 2 , while from

Clause 6.1.1.2 of AS 3600 it follows that ( ) . 'M bD fuo min c2

c= 0 12 .

In the case of a simply-supported composite slab, it follows that Eq. 3.6(1) should be satisfied at thecritical cross-sections.

In the case of a continuous composite slab, the onset of cracking due to negative bending at aninterior support (where M Muo uo min

− −< ( ) ) will not result in sudden failure in an adjacent span, if the

positive moment capacity, Muo+ , at the critical cross-section within the span is sufficient to safely

carry the additional positive moments after redistribution. The requirement of Eq. 3.6(1) can bewaived at an internal support in this case. This is consistent with the common overseas practice ofdesigning continuous composite slabs as simply-supported at the strength limit state [1].

The design information given in this booklet will allow the designer to check that Eq. 3.6(1) issatisfied at a critical cross-section in the positive moment region of a simply-supported or continuouscomposite slab. In the context of this design booklet, the nominal moment capacity Muo

+ must be

determined using partial shear connection strength theory, and therefore Muo+ is determined

assuming a fully-cracked section. A critical parameter affecting the result of this assessment is thevalue of mechanical resistance, Hr , applicable to the profiled steel sheeting product being used.Other factors affecting the result are whether the span is simply-supported or an end or internalspan, the design loads, the sheeting support conditions, the slab span, L , and overall depth, Dc ,etc. A parametric investigation has been conducted, which shows that Eq. 3.6(1) is satisfied in thepositive moment regions of simply-supported or continuous slabs not containing any bottom-facereinforcement, provided all of the following conditions are met, viz.:

• mechanical resistance Hr ≥ 100 kPa;

• the slabs are uniformly loaded; and• the slabs are practically proportioned to meet normal deflection limits and have a span-to-

depth ratio L D/ c ≥ 15 .



The implications of this study are that:

• designers will not have to check that Eq. 3.6(1) is satisfied in positive-moment regions whendesigning uniformly-loaded composite slabs incorporating any of the proprietary profiled steelsheeting products described in Appendix C, provided that L D/ c ≥ 15 ; and

• it has been decided to limit use of the design rules in Section 6 to products with Hr ≥ 100 kPa.

3.7 Effects of ProppingIn unpropped construction, before the concrete hardens the profiled steel sheeting must support itsown weight, that of the concrete, reinforcing steel and any construction loads. The steel sheeting isthus stressed and deflected before the concrete is stressed under the action of service loads.Composite action is assumed to be developed between the sheeting and the concrete when theconcrete compressive strength, fcj

' , reaches 15 MPa (see Clause 4.2.3 of AS 2327.1).

In propped construction, the steel sheeting spans are chosen to avoid excessive deflection orponding and prevent collapse. The props may possibly be removed as soon as composite actiondevelops (i.e. fcj

' = 15 MPa), and the prop loads are then effectively transferred onto the compositeslab as line loads.

At ultimate load, the longitudinal stresses in the sheeting and the concrete redistribute themselvesinternally such that the positive moment capacity, Muo

+ , corresponding to either partial or completeshear connection, is the same whether the slab was constructed propped or unpropped. This isconsistent with the assumption that simple-plastic rectangular stress block theory (see Section 3.2)can be used to calculate the moment capacity of critical cross-sections for profiled steel sheetingproducts with ductile shear connection. Therefore, with this latter proviso applying, the sequence ofconstruction does not have to be considered during the strength design of a composite slab. Thus,line loads induced when the props are removed can be ignored, and all of the slab dead load can betreated as a uniformly-distributed load at the strength limit state.



4. DESIGN MODELS4.1 GeneralThe design models used to represent the physical behaviour of a simply-supported or continuouscomposite slab at the strength limit state are summarised in this section.

4.2 Positive Moment CapacityThe strength model for a simply-supported or continuous composite slab has been described inSection 3.2. In order to calculate the nominal positive moment capacity, Muo

+ , at each cross-section,the compact portion of the sheeting cross-section is assumed to be effective. In general, in positivemoment regions the sheeting will be under a combination of bending and tension. The magnitude ofthe resultant tensile force, Tsh , that can develop in the sheeting depends on the degree of shearconnection, β , at the particular cross-section of concern. Properly-anchored conventionallongitudinal tensile reinforcement can contribute to the positive moment capacity at a cross-section.More detailed aspects of the design approach [2, 3] are discussed below.

Compactness of SheetingCompactness of the sheeting is affected by the longitudinal stresses in the sheeting and theslenderness of the sheeting plate elements. The concrete can provide a very significant confiningeffect to the sheeting ribs, which is too conservative to ignore when assessing compactness. On theother hand, embossments can reduce the effectiveness of the steel to support longitudinalcompressive or tensile stresses, since in this regard they are in effect gross imperfections. Thiseffect can, however, normally be ignored in design.

It is not necessary to cover this subject in detail in this booklet, since, as will be mentioned inAppendix C, slab tests have shown that for all three Australian profiled steel sheeting productsaddressed therein, the sheeting cross-section may be assumed to be compact for the current rangeof base metal thicknesses. Therefore, the full cross-section is assumed effective. This statementonly applies to the composite state, and is certainly not the case when the sheeting acts as formworkprior to the concrete hardening.

Equilibrium Strength ModelThe equilibrium of longitudinal forces acting on the steel sheeting in the critical end region of asimply-supported slab is shown in Fig. 4.1 at the point the maximum bending moment is reached.The sheeting is assumed to pass over the support such that the entire support reaction R * istransmitted through the pans of the sheeting. The resultant tensile force in the sheeting, Tsh , isbalanced by the mechanical resistance force, H xr , and the frictional resistance force, µR * . SinceTsh cannot exceed Tcsc , it can be written that (per unit width of slab):

Tsh = min.( , )H x R Tr csc*+ µ 4.2(1)

x

µR*

M*

Support

Tsh

Hr

Muo

+

-

R*

Bending momentdiagram

+

Figure 4.1 Equilibrium Strength Model with Sheeting passing over Entire Support



Since the value of Tsh can be affected by the magnitude of the support reaction, R * , the nominal

positive moment capacity, Muo+ , of a cross-section can be affected by the distribution and magnitude

of the applied loads. This leads to the concept of a limiting moment capacity, which is useful forcalculating the maximum load-carrying capacity of a composite slab when its strength increases withload [2]. However, this is beyond the scope of this booklet which is intended for situations when thedesign loads are known.

A more accurate representation of a composite slab failing in longitudinal slip is to account fordiagonal cracking adjacent to the critical cross-section [2, 3, 11]. It is important to account for areduced shear span due to this effect, in cases when concentrated loads are placed near supports.In this case, the term x in Eq. 4.2(1) must be reduced. This issue was also discussed in Section 3.5.However, for the purposes of this design booklet, the application of which is limited to the design ofuniformly-loaded slabs, Eq. 4.2(1) is considered sufficiently accurate.

Magnitude of Force Transmitted across InterfaceIf the sheeting passes over the entire support, it can be assumed in design that the whole of thedesign support reaction R * is transmitted across the interface between the sheeting and theconcrete, and contributes to the frictional resistance that is developed. Therefore, the interfacialpressure is concentrated at the supports and equal to zero elsewhere. Testing and analysis haveconfirmed that this assumption is valid [7, 11].

When the sheeting passes onto only part of the support, the conservative approach is to assumethat no frictional resistance is developed.

Cross-sections with Complete Shear ConnectionThe resultant tensile force in the sheeting at a cross-section with complete shear connection, Tcsc ,can be calculated using rectangular stress block theory as discussed in Section 3.2. Alternatively, fora slab with conventional reinforcement of cross-sectional area, Ast

+ , in the bottom face, the followingequation can be shown to be conservative:

Tcsc = min. ( . ( ) , )'0 85f D h b T Tc c r y.st y.sh− − 4.2(2)where Ty.sh = A fsh sy.sh 4.2(3)

Ty.st = A fst sy+ 4.2(4)

Ignoring any frictional resistance, i.e. µR* = 0 , it follows from Eq. 4.2(1) that a distance measuredfrom an end of the sheeting, xcsc , which guarantees the attainment of complete shear connection,can be calculated as follows:

xcsc = TH b

y.sh

r4.2(5)

For cross-sections located further than distance xcsc from the nearer end of the sheeting, the

nominal positive moment capacity, Muo+ , can in all cases be calculated assuming complete shear

connection between the sheeting and the concrete. For situations where µR * is not zero, there willbe some cross-sections closer than this distance from the end of the sheeting which will also haveattained complete shear connection, which may in any case be confirmed by calculation.

Cross-sections with Partial Shear ConnectionCross-sections located closer than distance xcsc from the nearer end of the sheeting should bedesigned on the basis of partial shear connection. For these cross-sections, the resultant tensileforce in the sheeting, Tsh , can be obtained from Eqs 4.2(1) and 4.2(2). The distance x in Eq. 4.2(1)should be measured from whichever of the adjacent ends of the sheeting that gives the lesser valueof Tsh .

Moment Capacity of Cross-SectionsCalculations of nominal positive moment capacity have been performed for composite slabsincorporating a particular profiled steel sheeting product (Bondek II) and different amounts of



conventional reinforcement in the bottom face [10]. Three levels of cross-section analysis have beenused, with the first being the most rigorous and the third being the most simplified:

(a) moment-curvature analysis, in which the stress in the concrete is obtained from the CEB-FIPstress-strain curve and account is taken of strain compatibility over the depth of the cross-section [3];

(b) simple-plastic rectangular stress block theory as described in Section 3.2, in which the stressin the concrete is obtained from the Whitney rectangular stress block, strain compatibility isignored and conventional reinforcement is always assumed to be at its yield stress when it lieson the tensile side of the plastic neutral axis in the steel, and is ignored otherwise; and

(c) rectangular stress-block theory as above, except the sheeting is lumped at the height of itscentroid above the soffit, y sh , which varies with the degree of shear connection

Figure 4.2 shows typical curves of nominal positive moment capacity, Muo+ , versus resultant tensile

force in the sheeting, Tsh , for the three methods described above. Two slab situations areconsidered covering under-reinforced and over-reinforced cases.

Includingreinforcement

0 200 400 600 800

20

10

30

40

50

60

Excludingreinforcement

Slab 1

Tsh (kN/m) Tsh (kN/m)

Includingreinforcement

0 200 400 600 800

40

0

80

120

160

180

Excludingreinforcement

Slab 2

Slab tbm Dc f'c yst fsy

(mm) (mm) (MPa) (mm2/m) (mm) (MPa)

1.0 90 25 300 30 400

1.0 200 25 500 60 4002

1

Method

(c)

(b)

(a)

Muo

(kN

m/m

)

+

Muo

(kN

m/m

)

+

Ast+

(Mu.sh+Mu.st)

Mu.sh Mu.sh

(Mu.sh+Mu.st)

Figure 4.2 Comparison of Calculation Methods

It can be seen that these three approaches have been found to be in excellent agreement for thetypical range of parameters used in composite slabs, and the third method is therefore proposed fordesign purposes. The design equations are given in Section 5.6.

Over-Reinforced Cross-sectionsAn over-reinforced cross-section is defined as one at which the moment capacity is controlled by thecompressive strength of the concrete rather than the tensile strength of the reinforcing steel. Thissituation can occur in the positive moment region of shallow composite slabs, and is more likely tooccur in unpropped construction when the thickness of the steel sheeting is dictated by the formworkstage (Construction Stages 1 to 3 in AS 2327.1).In cases when ku > 0 4. , Clause 8.1.3 of AS 3600 requires compressive reinforcement to be placedin the member and a lower value of φ to be used when calculating φMuo .

However, the following issues need to be considered concerning the applicability of this clause to thedesign of over-reinforced cross-sections in the positive moment region of a normally-proportionedcomposite slab:

500

500

240400



• the design positive moment capacity, φMuo+ , of the critical cross-section will normally be well in

excess of the applied bending moment, M *+ , on account of the large tensile capacity of thesheeting;

• although the ductility of these cross-sections may be limited, this is unlikely to reduce the load-carrying capacity of the slab to any significant extent on account of their significant over-capacity; and

• in any case, partial shear connection will tend to reduce the degree to which cross-sections areover-reinforced as they move towards the sheeting ends.

In light of these significant differences compared with normal reinforced-concrete slabs, it isrecommended that the requirements of Clause 8.1.3 of AS 3600 concerning when ku > 0 4. are notapplicable to the design of the positive moment regions of over-reinforced composite slabs, viz.:(i) top-face compressive reinforcement is not required; and, (ii) φ = 0.8 irrespective of the value of

ku+ when calculating φMuo

+ .

4.3 Positive Vertical Shear CapacityThe design model representing when the positive vertical shear capacity of a composite slab isreached is shown in Fig. 4.3. As explained in Section 3.3, partial shear connection strength theory isused to calculate the nominal positive vertical shear capacity, Vuc

+ . The possibility of diagonalsplitting failure is not considered, despite being exhibited in tests on slabs with concentrated loads[8], because the design rules in Section 6 are restricted to the design of uniformly-loaded compositeslabs.

UDL

ShearForce

M*

V*

Dc

BendingMoment

P

1.5Dc

ShearForce

BendingMoment Moment

Nominal moment capacity curve, Muo

ACTU

ALH

YPO

THET

ICAL

Vuc+

+

M*

Figure 4.3 Vertical Shear Failure of a Positive Moment Region



4.4 Negative Moment RegionsIt is normal to design the negative moment regions of composite slabs as reinforced-concrete slabs,conservatively ignoring the presence of the profiled steel sheeting acting as compressivereinforcement, but possibly accounting for the loss in cross-sectional area of the concrete in thebottom face due to the sheeting rib voids (see Section 1.2). In the case of profiled steel sheetingproducts which satisfy the geometric restrictions in Fig. 1.2, the loss of concrete area is insignificantfor design purposes. Therefore, the negative moment regions of slabs incorporating any of the threeprofiled steel sheeting products listed in Appendix C (viz. Bondek II, Comform and Condeck HP) canbe treated as solid concrete slabs, both with respect to design for bending strength and verticalshear. The design rules of Section 9 of AS 3600 are therefore applicable.

4.5 Effective SpanFor the purpose of determining the effective span, Lef , of a composite slab, the support reaction R *may be assumed to act in one of the following positions, as deemed appropriate.

(a) When the composite slab is supported on steel beams, the end reactions should be assumedto be applied through the centre of the steel beams, and the effective span taken as thedistance between the centreline of adjacent beams (see Fig. 4.4(a)).

(b) When the composite slab is supported on masonry walls, the end reactions should beassumed to be at the lesser of Dc / 2 or bs / 2 in from the front face of the support, and theeffective span taken as the distance between the end reactions (see Fig. 4.4(b)).

(c) Where the sheeting ribs are not orientated perpendicular to the support lines, the slab shouldbe designed as a series of parallel one-way strips with individual spans taken along thecentreline of each strip. The number of strips should be selected such that the difference inlength of the two longitudinal sides of any strip does not exceed 10% (see Fig. 4.4(c)). Theeffective span of each strip should then be determined in accordance with item (a) or (b), asappropriate.



Dc

Lef

End reaction

(a) Composite slab supported on steel beams

Dc

bs

End reaction

(b) Composite slab supported on masonry walls

bs2

(bs<Dc)

bs

Dc2

(bs≥=Dc)

Lef

Supportline

Supportline

Lef4

Lef3 Lef1Lef2

≤=1.1, etc.

Strip 1

Strip 2

Strip 3

Strip 4

(c) Effective span where sheeting ribs are not orientated perpendicular to support lines

Lef2

Lef1

Sheeting ribs

UDL

UDL

Figure 4.4 Assumed Position of End Support Reactions and Determinationof Effective Span of a Composite Slab



5. DESIGN APPROACH5.1 GeneralThe purpose of this section is to explain the design approach adopted in this booklet. The actualdesign rules are presented in Section 6, and cover design for bending and vertical shear of simply-supported and continuous composite slabs. Restrictions applying to the application of the designrules are clearly stated in Section 6.3.

A flowchart summarising the normal procedure followed when designing for strength is given in Fig.5.1. The flowchart is explained in the remainder of this section. Design for bending and vertical shearare both addressed.

5.2 Definition of Design SituationThe framing layout and general design criteria must be known at the outset of design. Criteriaconcerning design for serviceability, durability and fire will normally have a significant influence onthe initial choice of the spans of the slab, L , and its overall depth, Dc , as will the design of thesheeting for the formwork stage. The formwork design also often governs the choice of the basemetal thickness, tbm , and a decision whether to use propped or unpropped construction is critical inthis regard. The concrete cover appropriate to the design exposure condition will determine themaximum height of the top-face reinforcement.

Depending on various factors such as the spans involved and the magnitude of the design loads, itmight be decided to design the slab as simply-supported for strength. This is possible because acomposite slab normally has a substantial intrinsic positive moment capacity. Reinforcement mightstill be required over the supports, however, in order to ensure continuity to limit deflections, and tocontrol cracking, which are design issues that will be covered in future booklets.

The ductility of the conventional reinforcement to be used, as defined for Class N and Class Lreinforcing steel in AS 4671, can also have an impact on the strength design. In this regard,Amendment Nos 1 and 2 of AS 3600 have placed restrictions on the use of Class L (Low ductility)reinforcement compared with Class N (Normal ductility) reinforcement (see Section 5.4).

5.3 Identification of Potentially Critical Cross-SectionsA potentially critical cross-section (PCC) is defined as a cross-section that may be a critical orgoverning cross-section with regard to the strength of the slab. This concept is useful for designpurposes, since identification of these cross-sections at the outset of design enables strength checksto be made at these cross-sections only. Design for both bending and shear strength, in positive andnegative moment regions, can be approached in this manner.

The following examples of potentially critical cross-sections are given for bending or shear:

(a) sections of maximum design positive or negative design bending moments, M *max ;

(b) sections of maximum design vertical shear force, V *max (but not closer than Dc to the face ofany support);

(c) sections in positive or negative bending where conventional reinforcement is effectivelyterminated, which should conservatively be assumed to occur at a distance equal to thetensile development length, Lsy.t , away from the physical end of the reinforcement; and

(d) for a slab with a uniformly-distributed load, additional potentially critical cross-sections shall betaken at one-third and two-thirds of the distance from the peak positive moment position/s tothe ends of the span or adjacent contraflexure points, as appropriate, depending on whetherthe support is simply-supported or continuous, measured from the peak positive momentposition/s (see Fig. 5.2).

Note: In many situations it will be immediately obvious which side of the maximum momentcross-section is more critical, avoiding having to check both.



Start StrengthDesign

Define designsituation

Identify all potentiallycritical cross-sections (i.e. PCC's)

Yes

Calculate design actioneffects M* and V* at each PCC

Simply-supported slab,or continuous slab designed as

simply-supportedfor strength ?

No

Section 6

Section 5.2

Section 5.3

Yes

No

Negative-moment region(Section 5.5)

Positive-moment region(Section 5.6)

Select larger of twoku values above-

Calculate ku for maximumamount of moment

redistribution

-

Detail negativereinforcement

Check V* ≤=φVuc

Initially ignore presence of anyconventional reinforcement, i.e. Ast= 0+

Obtain strength design information forproprietary profiled steel sheeting from

Appendix C (Hr, µ, tbm, Ash, ysh, Mu.sh, Κ)

Calculate xcsc

Calculate Tsh at each PCC:Tsh = Tcsc, if x ≥ xcsc, otherwise

Tsh = min.(Tsh.L, Tsh.R, Tcsc)

Calculate φMuo at each PCC(If Ast= 0 use Appendix D, linearly

interpolating with β1)

+

Check M* ≤=φMuo at each PCC+ +

Calculate φVuc at PCCfor shear, from Appendix E

+

Check V* ≤=φVuc at PCCfor shear

++

Detail conventional positivetensile reinforcement Ast, if any.+

Design for strengthis complete

Increase tbm or add positive tensilereinforcement

No

Yes

Section 5.4

Calculate R* at supports wheresheeting is continuous

Class Nreinforcement

Class L reinforcement or cantilever

Calculate ku for nomoment redistribution

-

Check ku for (Muo)min-

Calculate Astcorresponding to

ku value

-

-

-

Calculate β1 at each PCC:β1 = Tsh/Ty.sh

+ -

Section 5.4

-

Figure 5.1 Flowchart showing Normal Procedure for Strength Design



UDL

1 3 524 L1M*max

1/3 (L1) 1/3 (L1) 1/3 (L1) 1/3 (L1)

1 3 524L1 M*max

1/3 (L1) 1/3 (L1) 1/3 (L1) 1/3 (L1)

(c) Interior span

(a) Simple span

1 3 524L1

M*max

1/3 (L1) 1/3 (L1) 1/3 (L1) 1/3 (L1)

(b) End span

L1

UDL

UDL

+

+

+

Figure 5.2 Additional Potentially Critical Cross-Sections

It should be noted that cross-sections at which concentrated line loads are applied perpendicular tothe span at the strength limit state would be PCC’s. However, for reasons explained herein, thisloading case is beyond the scope of this design booklet. As mentioned in Section 3.7, line loads canarise when props supporting part of the slab dead load are removed during construction. Theseloads can be considered to act on a composite slab at the serviceability limit state during the in-service condition. However, at the strength limit state, internal redistribution of stresses occurs andthe dead load of the slab can be considered to be uniformly distributed irrespective of theconstruction sequence.

5.4 Calculation of Design Action Effects

GeneralA composite slab shall be considered to be either simply-supported or continuous, with each spanhaving an effective span, Lef , as defined in Section 4.5. The design bending moment, M * , anddesign shear force, V * , at each potentially critical cross-section should normally be calculated usinglinear elastic analysis. Reference should be made to Clause 7.6 of AS 3600 for this purpose. Thedesign support reactions R * are also required at locations where the sheeting is continuous. Thedesign loads should be calculated in accordance with Section 6.4 of this booklet.

Moment RedistributionBecause the steel sheeting typically has a large cross-sectional area and a high design yield stress,the resulting composite slab generally has substantial intrinsic positive moment capacity. For efficient



use of this capacity in continuous slabs, adoption of the maximum permissible amount ofredistribution of moments from negative-moment regions to positive-moment regions is desirable.

An alternative approach to designing for redistribution in accordance with Clause 7.6.8 of AS 3600 isto design a continuous slab as a series of simply-supported spans, corresponding to 100%redistribution. Steel ductility is not an issue when taking this design approach, since the contributionof any support reinforcement to the load-carrying capacity of the slab is ignored. Redistribution by anintermediate amount is allowed using plastic analysis in accordance with Clause 7.9 of AS 3600.However, a designer should confirm in this case that the PCC’s have sufficient rotation capacity for aplastic mechanism to form, noting that this normally necessitates Class N steel to be used over thesupports. The 100% redistribution case would be expected to produce large crack widths underservice loads, but this can be overcome by providing sufficient top-face reinforcement (i.e. reducingthe amount of redistribution), and will be discussed in a later booklet in this series.

Several matters should be clarified when applying Clause 7.6.8 of AS 3600, viz.:

• redistribution is normally only allowed if Class N (as opposed to Class L) reinforcement is usedover the supports;

• the elastic bending moment distribution before redistribution is determined assuminguncracked cross-sections; and

• the amount of redistribution is measured by the percentage of the moment beforeredistribution.

Design for moment redistribution is discussed further in the next section.

5.5 Design of Negative-Moment RegionsThis section has application to composite slabs considered continuous, which develop negativesupport moments at the strength limit state. Slabs with cantilevers must naturally be designed fornegative support moments. The right-hand branch of the lower part of the flowchart in Fig. 5.1 isapplicable to this discussion.It is assumed that if a span of a continuous slab does not require negative reinforcement forstrength, then it will be designed as simply-supported at the strength limit state, i.e. the left-handbranch of the flowchart in Fig. 5.1 will be taken, in which case Section 5.6 should be referred to.

Design Incorporating Moment RedistributionSimplified sets of equations are presented below to enable reinforcement quantities to be directlycalculated from design bending moment values. These equations are derived from rectangularstress block equations and equations for the redistribution limits in AS 3600 [10]. In accordance withAmendment Nos 1 and 2 of AS 3600, in the absence of more detailed calculation, Class Nconventional reinforcement must be used as negative moment reinforcement if redistribution isallowed.

It will be assumed that any moment redistribution is from negative- to positive-moment regions. Themoment redistribution parameter at a support, η , will be defined as follows:

M *− = ( )1− −η M *e 5.5(1)

where M *e− is the elastically-determined design negative bending moment and M *− is the design

negative bending moment after redistribution.Clause 7.6.8 of AS 3600 limits the maximum value of η which reduces with increasing values of theneutral axis parameter, ku

− . The parameter ku− is directly proportional to the tensile capacity of the

negative tensile reinforcement and is defined as:

ku− =

pf

fsy

c'0 85. γ

5.5(2)

where p =Abd

st−

−5.5(3)



and Ast− is the area of top-face reinforcement over the interior support, d − is the effective depth of

this reinforcement, and γ is the stress block parameter for concrete as defined in Clause 8.1.2.2 of

AS 3600. It can be noted from Eqs 5.5(2) and 5.5(3) that the value of ku− is calculated for a cross-

section designed using the redistributed bending moment.

According to Clause 7.6.8 of AS 3600, the amount of moment redistribution allowed at a supportdepends on the maximum value of ku at any peak moment region in the adjacent spans. Thesepeak moment regions include the peak positive moment locations in the two adjoining spans and thenegative moment location being considered. This rule is considered to be more restrictive thannecessary. It is anticipated that in any span of a composite slab designed with redistribution, thepositive moment hinge will always be the last to form, since all redistribution is from negativemoment regions to positive moment regions, and also, the design positive moment capacity, φMuo

+ ,is normally well in excess of the design positive moment, M *+ . Hence, the value of ku in positivemoment regions need not normally be considered, and the redistribution permitted at any supportcross-section becomes simply a function of the value of ku at that cross-section, i.e.:

η = 0 3 0 20 3 0 75 0 2 0 4. .. . .

for for . <

u

u u

kk k

−

− −≤

− ≤�5.5(4)

Mom

ent

redi

strib

utio

npa

ram

eter

, ηη ηη

0 0.10.05

0.10

0.15

0.20

0.25

0.30

0.35

0.2 0.3 0.4Neutral axis parameter, ku

-

Figure 5.3 Moment Redistribution Parameter

Based on the rectangular stress block approximation for a singly-reinforced concrete cross-sectionwith ku

− ≤ 0 4. , the nominal negative moment capacity, Muo− , is given by Eq. 5.5(5). The design

equation relating the design negative moment capacity, φMuo− , and the elastic negative design

moment, M *e− , is given as Eq. 5.5(6).

Muo− = 0 85 1 0 5 2. ( . ) ( )γ γk k f b du u c

'− − −− 5.5(5)

φMuo− = ( )1− −η M *e 5.5(6)

For design incorporating redistribution to the limit specified in Clause 7.6.8 of AS 3600 and for ku−

values not exceeding 0.4, the required minimum value of ku− (and hence the minimum quantity of

conventional top-face reinforcement) can be obtained by use of the following relationship:

ku− = ( )a a a1 1 2− −2 / γ 5.5(7)

where a1 = 1 for ku− ≤ 0 20. 5.5(8)

= 10 75

0 85−−.

. φγm

f*e

c' for 0 20 0 40. .< ≤−ku 5.5(9)

a2 =14

0 85.

.*

φm

fe−

c' 5.5(10)

and m *e− =

Mb d

*e−

−( )25.5(11)



where φ is the strength or capacity reduction factor as given in Table 2.3 of AS 3600 for bending

without axial tension or compression, and equals 0.8 for ku− ≤ 0 4. .

Design Not Incorporating Moment RedistributionFor design not incorporating redistribution and for ku

− values not exceeding 0.4, the required

minimum value of ku− can be obtained by use of the following relationship:

ku− = ( )a a a1 1 2− −2 / γ 5.5(12)

where a1 = 1 5.5(13)

a2 =2

0 85.*

φm

fe−

c' 5.5(14)

and m *e− =

Mb d

*e−

−( )25.5(15)

Either Class L (OneMesh500™) or Class N (500PLUS® Rebar or BAMTEC®) reinforcement may beused in this case, although it would normally be assumed that the possibility of moment redistribution(cantilevers excepted) would at least be investigated if Class N steel is going to be used (see Fig.5.1).

Minimum Strength RequirementThe issue of preventing sudden collapse was discussed in Section 3.6. In view of that discussion,and the concern in AS 3600 with the ductility of Class L steel reinforcement, it is recommended thatthe minimum strength requirement M Muo uo min

− −≥ ( ) should be satisfied in the following situations:

• the negative moment region is part of a cantilever; or

• Class L reinforcement is used to provide negative moment capacity.

Concern about using Class L reinforcement if M Muo uo min− −< ( ) arises because in this case only one

crack will form in each support region, and accordingly, the rotation capacity of these regions will berelatively limited.

It follows that the minimum strength requirement M Muo uo min− −≥ ( ) may be waived when the negative

moment region is not part of a cantilever provided Class N reinforcement is used (see Fig. 5.1).

In order to satisfy M Muo uo min− −≥ ( ) , it follows from Section 3.6 that ( ) . 'M bD fuo min c

2c

− = 0 12 , and

substituting this for ( )Muo min− in Eq. 5.5(5) gives:

ku− = 1 1 0 24

0 85 1 2− −

−

��

��

.

. ( / )/

f d Dc'

ct c

γ 5.5(16)

The larger of the values of ku− given by Eqs 5.5(12) and 5.5(16) should be used to calculate Ast

− .

Design for Vertical ShearThe design of negative-moment regions for vertical shear can be carried out in accordance withSection 9 of AS 3600. This follows from the discussion in Section 4.4 where it was explained that thecomposite slab negative-moment regions can be treated as solid reinforced-concrete sections forprofiled steel sheeting products conforming with Fig. 1.2.



5.6 Design of Positive-Moment Regions

Initial Parameter ValuesThe parameters which define the properties of the profiled steel sheeting must be known and can betaken from Appendix C, viz.:

• fsy.sh = 550 MPa for BHP Zinc-Hi-Ten steel up to 1.0 mm thick;

• Ash and Mu.sh which depend on tbm ;

• y sh and Κ which depend on β1;

• µ = 0.5; and

• Hr , which for Bondek II is a function of tbm and concrete compressive strength fc' or fcj

' .

If conventional reinforcement is present in the bottom face of the slab, its cross-sectional area, Ast+ ,

and design yield stress fsy need to be known. However, it is conservative to ignore its presence, andinitially this can be assumed to simplify the design calculations.

Calculation of Resultant Tensile Force in SheetingThe resultant tensile force, Tsh , at each PCC can be calculated taking into account the position ofthe cross-section relative to the ends of the sheeting and the sheeting support conditions, asexplained by the design model in Section 4.2.

Calculation of Design Positive Moment CapacityThe following simplified equations may be used to calculate the design positive moment capacity,φMuo

+ , at a PCC. These equations apply to both partial shear or complete shear connection regions,with or without conventional reinforcement.

φMuo+ = φ φT D y T

f bMc c

c' u.sh− −�� +0 5

0 85.

.Κ 5.6(1)

where T = T Tsh y.st+ 5.6(2)

y c =T y T y

Tsh sh y.st st+

5.6(3)

β1 =TT

sh

y.sh5.6(4)

Tsh and Ty.st are given in Eqs 4.2(1) to 4.2(4). Mu.sh is the nominal moment capacity of the sheetingalone (see Table C3.1), y st is the centroidal height above the slab soffit of the conventional bottom-face reinforcement, y sh is the height at which Tsh acts above the slab soffit (see Table C3.1), andΚ is a profiled steel sheeting bending factor which is a function of β1 (see Table C3.1).

In this formulation, the conventional reinforcement is assumed to be at its design yield stress.Equation 5.6(5) must be satisfied to ensure that this assumption is valid, otherwise the contribution ofthe conventional reinforcement should be ignored.

y st ≤ Df T T

f bcsy y.sh y.st

c'

−+ +( / )( )

.

1 600

0 85γ5.6(5)

In order to use the equations above, proprietary values of four parameters are required, viz. Ash ,y sh , Mu.sh and Κ (see Appendix C).

If Appendix C is used to calculate φMuo+ rather than Eq 5.6(1), it is first necessary to calculate β1

(see Eq. 5.6(4)), and to then use linear interpolation in the tables.



Moment Capacity CheckIf at any PCC there is insufficient moment capacity, the normal approach to be taken will be to eitherincrease tbm or add conventional tensile reinforcement to the bottom face. Alternatively, the overalldepth, Dc , may be increased, span, L , reduced, etc.

Minimum Strength RequirementThe issue of preventing sudden collapse was discussed in Section 3.6. It was explained that theminimum strength requirement M Muo uo min

+ +≥ ( ) will be satisfied at any PCC in positive bendingprovided the slabs are uniformly loaded, practically proportioned to meet normal deflection limits, andhave a span-to-depth ratio L D/ c ≥ 15 . It is also a requirement that Hr ≥ 100 kPa, a condition alwayssatisfied for the profiled steel sheeting products given in Appendix C used within their range ofapplicability.

Design for Vertical ShearThe design of positive-moment regions for vertical shear can be carried out using the informationgiven in Section 3.3 for the calculation of nominal positive vertical shear capacity Vuc

+ , andSection 4.3 showing the design model. The design equations are given in Section 6.8.



6. DESIGN RULES6.1 Design ObjectivesThe composite slab shall be designed for strength, serviceability, durability and fire, as appropriate toits intended use.Note : This booklet covers design for strength only. Major aspects of the design rules have beenexplained in preceding sections. The normal design procedure to follow is described in Section 5.

6.2 Limit State Requirements for StrengthThe composite slab shall be designed so that during Construction Stages 5 and 6, and the in-servicecondition defined in AS 2327.1:

(a) at every transverse cross-section, the design moment capacity, φMuo , is not less than thedesign bending moment, M * , i.e. φM Muo ≥ * , and

(b) at every transverse cross-section located a distance of at least Dc from the face of anysupport, the design vertical shear capacity, φVuc , is not less than the design vertical shearforce, V * , i.e. φV Vuc ≥ * .

The above requirements shall be deemed to be satisfied at every cross-section, if they are shown tobe satisfied at each relevant potentially critical cross-section (PCC) for bending or shear as definedin Section 5.3.The capacity reduction factor, φ , shall equal 0.8 in all cases concerning positive bending and shear,both during construction and the in-service condition. In negative-moment regions, the normalrequirements of Table 2.3 of AS 3600 shall apply.

6.3 ApplicationIn the application of the design rules, the following conditions shall be satisfied:

(a) The shear connection performance of the sheeting shall have been verified by adequatetesting and determined by an independent assessment using a procedure similar to that givenin Reference 12.

(b) The shear connection performance of the sheeting shall be deemed ductile, whereby itsmechanical resistance Hr and coefficient of friction µ can be treated in design asindependent of the amount of slip between the sheeting and the concrete. The value ofHr shall not be less than 100 kPa.

Note: Design values for Hr and µ can be found in Appendix C for Bondek II, Comform andCondeck HP. Composite slabs must incorporate sufficient transverse shrinkage andtemperature control reinforcement to control any longitudinal splitting of the concrete over thesheeting ribs at the strength limit state. In this regard, the requirement of Clause 9.4.3.4 ofAS 3600 for minor degree of control over cracking is sufficient.

(c) The steel strip from which the sheeting is roll-formed shall be BHP Zinc-Hi-Ten , which is hot-dipped, zinc-coated steel to AS 1397 with a design yield stress, fsy.sh , of 550 MPa for basemetal thickness, tbm , up to 1.00 mm.

(d) The geometry of the steel sheeting profile shall conform to the dimensions and tolerancesshown on the manufacturer’s production drawing. Sheeting with embossments less than thespecified lower characteristic value shall not be used compositely unless the value of Hr isrevised.

Note: Design values for Ash , y sh , Mu.sh and Κ for Bondek II, Comform and Condeck HP aregiven in Appendix C, as are acceptable values of base metal thickness, tbm . Lowercharacteristic values of embossment height can be found in Appendix C for Bondek II andComform.



(e) Material and construction requirements for conventional reinforcing steel shall be inaccordance with Clause 19.2 of AS 3600, and the design yield stress, fsy , shall be taken fromTable 6.2.1 of AS 3600 for the appropriate type and grade of reinforcement. The ductility classshall be L (OneMesh500™) or N (500PLUS® Rebar or BAMTEC®).

(f) The concrete compressive strength grade, fc' , and density, ρc , shall be in accordance with

Clause 1.1.2 of AS 3600, and any other restrictions that result from the limited range of testsperformed under item (a). In composite beam construction, the requirement of Clause 8.1 ofAS 2327.1 shall also be satisfied, viz. fc

' shall not exceed 40 MPa.

Note: The restrictions which apply to concrete compressive strength and density for compositeslabs incorporating Bondek II, Comform and Condeck HP are specified in Appendix C.

(g) Material and construction requirements for concrete shall be in accordance with Clause 19.1 ofAS 3600.

(h) The profiled steel sheeting shall not be spliced, lapped or joined longitudinally in any way.(i) The permanent support lines shall extend across the full width of the slab.(j) Similar to the requirement in Clause 4.2.3 of AS 2327.1, composite action shall be assumed to

exist between the steel sheeting and the concrete once the concrete in the slab has attained acompressive strength of 15 MPa, i.e. fcj

' ≥ 15 MPa. Prior to the development of compositeaction during Construction Stage 4 defined in AS 2327.1, potential damage to the shearconnection shall be avoided.

Note: Damage to the shear connection can be avoided by preventing either the imposition ofsignificant live loads on the slab, or the removal of any falsework or props supporting the slabor steel beams; or alternatively by back-propping the slab, or the steel beams, or both.

(k) Props to either the composite slab or steel beams supporting the slab may be removed duringConstruction Stage 5 provided: (i) the strength of the composite slab and any other relevantdesign criteria are checked; and (ii) the compressive strength of the concrete, fcj

' , is at least asgreat as the minimum value allowed for a particular profiled steel sheeting product accordingto item (f).

(l) All design loads acting on the slab during construction and the in-service condition shall beuniformly-distributed. Minimum design loads are specified in Section 6.4.

Note: Concentrated line loads arising from the removal of temporary construction props can beignored in accordance with Section 3.7.

(m) Holing of the sheeting due to the provision of vertical building services or installation offasteners through the soffit of the sheeting should be minimised and should not lead topremature yielding and fracture of the steel sheeting at the strength limit state. Self-drillingscrews may be used at lap joints.

Note: BHP Zinc-Hi-Ten steel does not exhibit strain-hardening. Therefore, yielding of the steelat even a small hole can cause the steel to fracture at this location. Full-scale slab tests haveshown that self-drilling screws used at lap joints have not unduly affected the ductility of theslabs. Design rules for holing have yet to be developed. In the interim, it is recommended thata conservative approach be adopted, viz.: (i) proprietary hanging systems should be usedwhenever possible in preference to systems requiring masonry fasteners to support services;(ii) holes for vertical services should be cut neatly and not over-cut; (iii) if a hole is placed in apositive moment region, depending on its exact location, size and the level of tensile force thatmight need to develop in the sheeting, consideration should be given to ignoring the presenceof the steel sheeting altogether, which may require additional conventional reinforcement to beprovided in the bottom-face of the slab.

6.4 Design LoadsMinimum dead and live loads for both propped and unpropped construction of composite slabs shallbe determined in accordance with AS 2327.1 and AS 1170.1. These nominal loads should beappropriately factored and combined in accordance with AS 1170.1 to give the design loads.



Composite slabs are designed assuming one-way action, and therefore reduction of uniformly-distributed live load is not appropriate.

6.5 Methods of Structural AnalysisThe Linear Elastic Analysis method of Clause 7.6 of AS 3600 shall be used to determine the designbending moments, M * , vertical shear forces, V * , and support reactions, R * , of indeterminate,continuous composite slabs. The effective span, Lef , shall be calculated in accordance withSection 4.5.

6.6 Moment RedistributionRedistribution of moments shall be permissible up to the limit defined in Clause 7.6.8 of AS 3600,with the following qualifications:

(a) the elastic bending moment distribution before redistribution shall be determined assuminguncracked cross-sections;

(b) the redistribution limit in each negative-moment region shall be based on the value of ku inthat particular negative-moment region only;

(c) the amount of redistribution is measured by the percentage of the moment beforeredistribution;

(d) redistribution of moments is permitted from negative-moment regions to positive-momentregions but not from positive-moment regions to negative-moment regions; and

(e) no redistribution of moments is permissible where the contribution of Class L reinforcementhas been included in the calculation of the design negative moment capacity, φMuo

− .

Alternatively, it shall be permissible to design slabs which are continuous over any support as simply-supported at that support, with the exception that cantilevers shall be treated as continuous.

6.7 Negative-Moment Regions

Bending StrengthFor the strength design of negative-moment regions, the presence of the sheeting in the slab shallbe ignored and the slab designed as an equivalent solid reinforced-concrete member. For thispurpose, the provisions of AS 3600 as they relate to the design of one-way slabs shall be used. For aslab which is continuous over any support but treated as simply-supported for strength at thatsupport, the design negative bending moment, M *− , at the support shall be taken equal to zero.

In calculating the design negative bending moment, M *− , an allowance for negative-to-positivemoment redistribution up to the limit specified in Clause 7.6.8 of AS 3600 may be made. Thus, theelastic design bending moment before redistribution, M *e

− , may be reduced in magnitude to obtainthe design negative bending moment after redistribution, M *− .

The design negative moment capacity, φMuo− , shall be calculated by multiplying the nominal negative

moment capacity, Muo− , by a capacity reduction factor, φ , as given in Table 2.3 of AS 3600. The

nominal negative moment capacity, Muo− , shall be calculated based on the principles of rectangular

stress block theory as defined in Clause 8.1.2 of AS 3600.

For potential hinge locations at which the neutral axis parameter, ku− , as defined in AS 3600,

exceeds 0.4, the requirements of Clause 8.1.3 of AS 3600 shall be satisfied. In the application of thisclause, it may be assumed that the minimum compressive reinforcement requirement is satisfied bythe presence of the steel sheeting in the negative moment region.



Minimum Bending StrengthThe minimum strength requirement M Muo uo min

− −≥ ( ) shall be satisfied when either the negativemoment region is part of a cantilever, or Class L reinforcement is used to provide negative momentcapacity. The minimum value of ku

− corresponding to M Muo uo min− −= ( ) is given by Eq. 5.5(16).

Detailing of Conventional Tensile ReinforcementConventional tensile reinforcement in negative-moment regions shall be detailed in accordance withthe relevant requirements for one-way slabs in Clause 9.1.3 of AS 3600.

Shear StrengthNegative-moment regions shall be designed for shear strength such that the requirements of Clause8.2, and therefore Clause 9.2.2(a), of AS 3600 are satisfied.

6.8 Positive-Moment Regions

Bending StrengthThe design positive moment capacity, φMuo

+ , shall be calculated by multiplying the nominal positivemoment capacity, Muo

+ , by a strength reduction factor, φ , which shall be taken as 0.8, irrespective ofthe degree of shear connection at the particular cross-section.

The nominal positive moment capacity, Muo+ , shall be calculated taking into account the degree of

shear connection which exists between the sheeting and the concrete. The simplified equation, Eq.5.6(1) in Section 5.6, may be used for this purpose. In calculating the design positive momentcapacity at any cross-section, the entire cross-section of the profiled steel sheeting products inAppendix C shall be assumed to be effective. Conventional longitudinal tensile and compressivereinforcement may be considered to contribute to the positive moment capacity at a cross-section,provided due allowance is made for the tensile development length, Lsy.t , for anchorage of thereinforcement in accordance with Section 13 of AS 3600.As explained in Section 4.2, the requirements of Clause 8.1.3 of AS 3600 which apply whenku

+ > 0 4. are not required to be satisfied when designing the positive moment regions of over-reinforced composite slabs, viz.: (i) top-face compressive reinforcement is not required; and(ii) φ = 0 8. irrespective of the value of ku

+ when calculating φMuo+ .

Minimum Bending StrengthThe minimum bending strength requirement of Clause 8.1.4.1 of AS 3600 shall be satisfied at allcritical cross-sections in positive-moment regions, where the critical cross-section within each spanis defined as the cross-section with the maximum value of M M* /( )+ +φ uo . If necessary, conventionaltensile reinforcement shall be provided to ensure that M Muo uo min

+ +≥ ( ) . The contribution of thesheeting and any conventional reinforcement shall be included in the calculation of Muo

+ (see Eq.5.6(1)), but excluded in the calculation of ( )Muo min

+ .

The value of ( )Muo min+ shall be calculated as follows:

( )Muo min+ = 01 2. f bDcc

' 6.8(1)

It was explained in Section 3.6 that:• Eq. 6.8(1) will be satisfied when designing uniformly-loaded composite slabs incorporating any

of the proprietary profiled steel sheeting products described in Appendix C, providedL D/ c ≥ 15 ; and

• Hr ≥ 100 kPa.



Sheeting End SupportThe ends of the sheeting (see Fig. 3.10):

• shall extend fully onto the support at a simply-supported discontinuous end of a slab;

• shall extend to the centre of the support where a slab is continuous but the support is designedas simply-supported for strength; and

• may extend partially onto the support where a slab is continuous and the support is designedas continuous for strength.

Note: It is acceptable to terminate the sheeting just before the discontinuous end of a slab toprovide any necessary cover to the end of the sheeting.

Detailing of Conventional Tensile ReinforcementThe termination locations of any conventional tensile reinforcement in positive-moment regions shallbe determined by extending the reinforcement a distance D Lc sy.t+ past the point at which it is nolonger required for strength. The requirements of Clause 9.1.3 of AS 3600 shall not apply.

Shear StrengthPositive-moment regions shall be designed for vertical shear strength, such that at every cross-section located a distance of at least Dc from the face of a support, the design positive verticalshear capacity, φVuc

+ , is not less than the design positive vertical shear force, V *+ .

The design positive vertical shear capacity, φVuc+ , shall be calculated as follows including the

contribution of the sheeting and any fully-anchored conventional reinforcement (see Fig. 4.3).(a) The positive-moment region of a continuous member shall be idealised as a simply-supported

member, with the hypothetical supports placed at the points of contraflexure in the elasticbending moment diagram resulting from uniform loading on all spans.

(b) At one end of the equivalent simply-supported member, a hypothetical line load shall be placedat a distance of 15. Dc from the face of the hypothetical support.

(c) The value of the line load at which the bending moment reaches the nominal positive momentcapacity, Muo

+ , at the loaded cross-section shall be determined using the equations inSection 5.6.

(d) For the calculated value of line load, the value of the vertical shear force at the end of themember being considered shall be taken as the nominal positive vertical shear capacity, Vuc

+ ,which shall be multiplied by the normal value of φ for bending equal to 0.8 to give the designpositive vertical shear capacity, φVuc

+ . This gives the following approximate equation:

φVuc+ =

c

uo

51 D.M +φ

6.8(2)

where φMuo+ (see Eq. 5.6(1)) is calculated at the location of application of the hypothetical line

load.As a simplification, for simple spans and the outer-edge support regions of end spans, the designvertical shear capacity (including the contribution of the sheeting but ignoring any contribution fromconventional reinforcement) may be calculated from the following equation:

φVbD

uc

c

+

=φ

µ[ . / ( )]

( . )15

15

2H M bDr u.sh c+−

6.8(3)

where φ is the value for bending equal to 0.8. This simplification comes about by assuming that bothy

c and the half-depth of the compressive stress block (=0.5T/(0.85f’

cb)) in Eq. 5.6(1) are zero, which

is a reasonably accurate approximation for cross-sections with a low degree of shear connectionsuch as those being considered.Design for types of shear failure that occur locally around a support or concentrated load (i.e.punching shear) is outside the scope of these rules.



7. WORKED EXAMPLES7.1 GeneralThe worked examples are used to explain the design approach given in Section 5 and the designrules given in Section 6.The examples are of an unpropped simply-supported slab and a continuous slab. In unproppedconstruction, the base metal thickness, tbm , is dictated by the formwork condition and the range ofthicknesses made available by the manufacturer. The slab span is also limited to about 2-3 metresfor the Australian profiled steel sheeting products Bondek II, Comform and Condeck HP mentionedin this booklet. On account of the short spans involved, the nominal overall slab depth, Dc , in asteel-frame building is normally 120 mm, the minimum required by AS 2327.1. Using normal-weightconcrete, this is also the minimum thickness for a 120 minute fire resistance period with respect tothermal insulation (see Table G1 of AS 2327.1). It will be seen from the examples that all threeprofiled steel sheeting products give similar solutions, despite having different Hr values as given inTable C2.1.

The index to the worked examples is given in Table 7.1.

Table 7.1 Index to Worked Examples

Example Pagenumber

Title

7.2-1 33 Define Design Situation for Two-Span Continuous Slab7.3-1 34 PCC’s in a Simply-Supported Slab7.3-2 34 PCC’s in a Continuous Slab7.4-1 35 Design not incorporating Moment Redistribution7.4-2 36 Design incorporating Moment Redistribution7.4-3 37 Design for Negative Vertical Shear7.5-1 37 Calculation of Design Positive Moment Capacity using

Appendix D7.5-2 40 Calculation of Design Positive Vertical Shear Capacity using

Appendix E7.5-3 41 Calculation of Design Positive Moment Capacity using

Equations

7.2 Definition of Design SituationIssues concerning the definition of the design situation for a continuous composite slab are brieflydiscussed in Section 5.2. Consideration will be given in the following example to the different optionsavailable for modelling the slab.

Example 7.2-1 Define Design Situation for Two-Span Continuous SlabIdentify the three design options available to model the interior support B shown in Fig. 7.1 that arewithin the scope of this booklet.

Profiled steel sheeting Interior support

UDL

A B CTransversereinforcement

Figure 7.1 Definition of Design Situation - Example 7.2-1



Solution

Option 1: Design interior support B as continuous without moment redistribution.Option 2: Design interior support B as continuous with moment redistribution up to the limit defined

in Clause 7.6.8 of AS 3600.Option 3: Design as two simply-supported spans, where the design negative bending moment at

the interior support B is taken as zero, i.e. 100 percent redistribution.

7.3 Identification of Potentially Critical Cross-SectionsThe rules for identifying of potentially critical cross-sections (PCC’s) are given in Section 5.3.Application of the rules is demonstrated using the examples given below.

Example 7.3-1 PCC’s in a Simply-Supported SlabDetermine the positions of PCC’s in the simply-supported slab shown in Fig. 7.2.

UDL

1 2 3 4

Dc

DcTransversereinforcement Profiled steel sheeting

Figure 7.2 Identification of Potentially Critical Cross-Sections - Example 7.3-1

Solution

The PCC’s are shown in Fig. 7.2 and explained below:PCC1: Cross-section of maximum positive design vertical shear force.PCC2: Cross-section two-thirds of the distance from the maximum positive moment position to

the nearer end of the sheeting, measured from the maximum positive moment position.PCC3: Cross-section one-third of the distance from the maximum positive moment position to

the nearer end of the sheeting, measured from the maximum positive moment position.PCC4: Cross-section of maximum positive design bending moment (mid-span).From symmetry, only one side of the slab needs to be considered.

Example 7.3-2 PCC’s in a Continuous SlabDetermine the positions of PCC’s in the two-span slab shown in Fig. 7.3.

Negative tensile reinforcement, Ast


Positive tensile reinforcement, Ast UDL

Developmentlength, Lsy.t

+ -

1 2 3 4 57

6Transversereinforcement

Figure 7.3 Identification of Potentially Critical Cross-Sections - Example 7.3-2

Solution

The PCC’s are shown in Fig. 7.3 and explained below:PCC1 - 4: See solution to Example 7.3-1.PCC5: Cross-section where reinforcement is terminated, taken at a distance equal to the

development length away from physical end of the reinforcement.PCC6: Cross-section of maximum negative design vertical shear force.



PCC7: Cross-section of maximum negative design bending moment.From symmetry, only one side of the slab needs to be considered.

7.4 Design of Negative-Moment RegionsThe simplified equations given in Section 5.5 will be used to calculate the quantity of negative tensilereinforcement, Ast

− , required at the interior support for the cases where no redistribution of moment isused, and where redistribution is up to the limit defined in Clause 7.6.8 of AS 3600.

Example 7.4-1 Design not incorporating Moment RedistributionDetermine the amount of negative tensile reinforcement, Ast

− , required at support B for design notincorporating moment redistribution. The design parameters are given in Fig. 7.4.


Slab span, Lef = 5200 mmSlab depth, Dc = 190 mmSlab width, b = 1000 mmLive load, Q = 7.5 kPaSuperimposed dead load, Gsup = 1.0 kPaDesign yield stress of reinforcement, fsy = 400 MPa (Class N) = 450 MPa (Class L)Cover, c = 25 mmTop reinforcement depth, dct = 30 mmConcrete density, ρc = 2400 kg/m3 (ρg =25kN/m3)Concrete strength, f'c = 32 MPa

Dc

Astdct

Lef Lef

Gsup,Q-

TransversereinforcementA B C

Figure 7.4 Two-Span Continuous Slabs - Example 7.4-1

Solution

Nominal Loads G = ρgD Gc sup+ [ ρ includes allowance for steel reinforcement and sheeting weight]

= 25 0 19 10× +. .= 5.75 kPa

Q = 7.5 kPa

Design Action EffectsDesign elastic bending moment:

M *e− = 0125 125 15 2. ( . . )× × + × ×G Q Lef

= 0125 125 5 75 15 7 5 5 22. ( . . . . ) .× × + × ×= 62.3 kNm/m

m *e− =

Mb d

*( )

e−

− 2

= 62 31000 160

1026.

×× [d − = D dc ct− = 190 - 30 = 160 mm]

= 2.43 MPa

500 MPa (Class N), or500 MPa (Class L)



From Eqs 5.5(12) to 5.5(15):

a1 = 1

a2 =2

0 85.*'φ

mf

e

c

−

= 2 2 430 85 0 8 32

×× ×

.. .

= 0.223

ku− = a a a1 1

22− −� � / γ [ γ = − − =0 85 0 007 28 0 822. . ( ) . ]fc

'

= 1 1 0 223 0 8222− −� �. / .

= 0.144 < 0.4Rearranging Eqs 5.5(2) and 5.5(3):

Ast− = 0 85. 'γbd f k

f

− −c u

sy

=500

144.0321601000822.085.0 ×××××

= 1030 mm2/m for Class N or Class L steel

Example 7.4-2 Design incorporating Moment RedistributionDetermine the amount of negative tensile reinforcement, Ast

− , required at support B for designincorporating moment redistribution to the limit defined in AS 3600. The design parameters are givenin Fig. 7.4.Solution

From Eqs 5.5(7) to 5.5(11):

Assume that ku− < 0.2,

a1 = 1

a2 =14

0 85.

.*'φ

mf

e

c

−

= 14 2 430 85 0 8 32

. .. .

×× ×

= 0.156

ku− = a a a1 1

22− −�

�� / γ

= 1 1 0156 0 8222− −�� . / .

= 0.099 < 0.2 (and 0.4)

Ast− = 0 85. 'γbd f k

f

− −c u

sy

=500

099.0321601000822.085.0 ×××××

= 708 mm2/m only for Class N steel (Class L steel may not be used)

This is a saving of 31% in the amount of steel required at the interior support comparedwith design not incorporating moment redistribution.



From Fig.5.3 for ku− < 0.2, the amount of moment redistribution is 30%, i.e. η = 0.3.

Note: In accordance with Fig. 5.1, there is no minimum strength requirement when Class N steel isused.

Example 7.4-3 Design for Negative Vertical ShearCheck negative vertical shear capacity for reinforcement given in Example 7.4-2.Solution

From elastic analysis with moment redistribution, the design negative vertical shear force at distanceDc away for support B is:

V *− = 52.8 kN/mFrom Clause 8.2.7.1 of AS 3600:

do = d − = 160 mm

β1 = 11 161000

. .× −� �do

= 11 16 1601000

. .× −� �

= 1.584 > 1.1β2 , β3 = 1bv = 1000 mm

φVuc− = φ β β βv 1 2 3 v o

c'

st

v ob d

f Ab d

−��

1 3/

= 33/1

101601000

70832160100011584.17.0 −×��

�

××××××××

= 92.5 kN/m > V *− = 52.8 kN/m

7.5 Design of Positive-Moment RegionsUse of the simplified equations given in Sections 5.6 and 6.8 for designing the positive-momentregions of composite slabs for flexure and vertical shear will be illustrated here.

Example 7.5-1 Calculation of Design Positive Moment Capacity using Appendix DFigure 7.5 shows a simply-supported composite slab subjected to a uniformly distributed load. Noconventional longitudinal reinforcement is included. The three proprietary products, Bondek II,Comform and Condeck HP, are designed in turn to demonstrate the use of the design positivemoment capacity tables given in Appendix D.

The sheeting thickness has been determined at the formwork stage. The additional designparameters assumed are given in Fig. 7.6.



DcProfiled steel sheeting

x1 = 1060

Lef = 1950 mm

Q

Slab span, Lef = 1950 mmSlab depth, Dc = 120 mmSlab width, b = 1000 mmLive load, Q = 10.0 kPaSuperimposed dead load, Gsup = 1.0 kPaConcrete density, ρc = 2400 kg/m3 (ρg =25kN/m3)Concrete strength, f'c = 25 MPa

Dc

85 85

Transversereinforcement

B1234325 325 325

PCC for shear, see Example 7.5-2 M*maxA

x3 = 410x2 = 735

Figure 7.5 Simply-Supported Slab - Example 7.5-1

Solution

From symmetry, the PCC’s for bending are shown in Fig. 7.6 as cross-sections 1, 2 and 3. Thedistance x of cross-sections 1, 2 and 3 from the nearer end of the sheeting are:

x1 = 1.060 m (mid-span)x2 = 0.735 m (i.e. Lef / .3 0 085+ )x3 = 0.410 m (i.e. Lef / .6 0 085+ )

Nominal Loads G = ρgD Gc sup+ [ ρ includes allowance for steel reinforcement and sheeting weight]

= 25 0 12 10× +. .= 4.0 kPa

Q = 10.0 kPa

Design Action EffectsThe design elastic bending moments for the PCC’s are:

M *(1)+ = 9.5 kNm/m

M *(2)+ = 8.5 kNm/m

M *(3)+ = 5.3 kNm/m

The design support reactions at supports A and B are:

R *A = R *B

= 19.5 kN/m

Cross-sections with Complete Shear ConnectionThe distance from the end of the sheeting, xcsc , which guarantees the attainment of complete shearconnection regardless of the support conditions, is calculated as:

xcsc =TH b

y.sh

r[Eq. 4.2(5)]



Tcsc = min. ( 0 85. ( )'f D h b Tc c r y.st− − ,Ty.sh ) [Eq. 4.2(2)]

= min. ( 0 85 0. ( )'f D h bc c r− − , A fsh sy.sh )

Table 7.2 Design information for Bondek II, Comform and Condeck HP (see Appendix C)

tbm hr Ash Hr µ

(mm) (mm) (mm2/m) (kPa)Bondek II 0.75 54 1259 381 0.5Comform 0.75 58 1172 235 0.5

Condeck HP 0.75 55 1215 210 0.5

Table 7.3 Tcsc for Bondek II, Comform and Condeck HP

xcsc Ty.sh 0 85. ( )'f D h bc c r− Tcsc

(m) (kN/m) (kN/m) (kN/m)Bondek II 1.82 692.5 1402.5 692.5Comform 2.74 644.6 1381.3 644.6

Condeck HP 3.17 668.3 1317.5 668.3

Since x1 , x2 and x3 are all significantly less than xcsc for each proprietary product, these cross-sections are all likely to exibit partial shear connection.

Calculation of Resultant Tensile Force in SheetingFrom Section 3.4, Eq. 4.2(1) and from symmetry:

Tsh = min( , , )T T Tsh.L sh.R csc

Tsh.L = Tsh.R

= H bx Rr A*+ µ

Table 7.4 Tsh for Bondek II, Comform and Condeck HP

At PCC-1, x1 = 106. m At PCC-2, x2 = 0 74. m At PCC-3, x3 = 0 41. m

T Tsh.L sh.R= Tsh T Tsh.L sh.R= Tsh T Tsh.L sh.R= Tsh

(kN/m) (kN/m) (kN/m) (kN/m) (kN/m) (kN/m)Bondek II 413.6 413.6 291.7 291.7 166.0 166.0Comform 258.9 258.9 183.7 183.7 106.1 106.1

Condeck HP 232.4 232.4 165.2 165.2 95.9 95.9

Calculation of Design Positive Moment CapacityFrom the tables in Appendix D, values of φMuo

+ may be obtained by linear interpolation. Values of

φMuo+ for Bondek II, Comform and Condeck HP are given in Tables D2.2, D3.2 and D4.3,

respectively.



Table 7.5 φφφφMuo++++ for Bondek II, Comform and Condeck HP


β1sh

y.sh=

TT

φMuo+ β1

sh

y.sh=

TT

φMuo+ β1

sh

y.sh=

TT

φMuo+

(kNm/m) (kNm/m) (kNm/m)Bondek II 0.60 39.8 0.42 32.3 0.24 22.9Comform 0.40 29.3 0.28 22.8 0.16 16.3

Condeck HP 0.35 27.7 0.25 22.1 0.14 16.1

Check M *+ ≤≤≤≤ φφφφM +uo at each PCCCheck design positive moment capacity, φMuo

+ , is not less than the design positive bending moment,M *+ , at each PCC:

Table 7.6 Check M M*++++ ++++≤≤≤≤ φφφφ uo at each PCC


M *(1)+ φMuo

+ M *(2)+ φMuo

+ M *(3)+ φMuo

+

(kNm/m) (kNm/m) (kNm/m) (kNm/m) (kNm/m) (kNm/m)Bondek II 9.5 39.8 8.5 32.3 5.3 22.9Comform 9.5 29.3 8.5 22.8 5.3 16.3

Condeck HP 9.5 27.7 8.5 22.1 5.3 16.1

Design for flexure OK.Note: In this example, the overall depth, Dc , has been assumed to be 120 mm. The overall depth,Dc , of a composite slab used in composite beam design in accordance with Clause 1.2.4 ofAS 2327.1, must not be less than the minimum value given in Table C1.1 corresponding to eachproprietary product.

Example 7.5-2 Calculation of Design Positive Vertical Shear Capacity using Appendix ECheck the design positive vertical shear capacity for the simply-supported slab shown in Fig. 7.5.Solution

From symmetry, PCC-4 is the critical cross-section for vertical shear. This cross-section is located adistance Dc from support A [Note: Beam flange width is ignored in this example].

V *(4)+ = 19 5 125 15 1000. ( . . ) /− × + × ×G Q Dc

= 19 5 125 4 0 15 10 0 120 1000. ( . . . . ) /− × + × ×= 17.1 kN/m

Check V *+ ≤≤≤≤ φφφφV+uc at PCC-4

From Appendix E, Table E2.1 for Bondek II with tbm = 0.75 mm, fc' = 25 MPa, Dc = 120 mm and µ =

0.5;

φVuc+ = 123.9 kN/m > V *(4)

+

From Appendix E, Table E3.1 for Comform with tbm = 0.75 mm, Dc = 120 mm and µ = 0.5;

φVuc+ = 87.3 kN/m > V *(4)

+

From Appendix E, Table E4.1 for Condeck HP with tbm = 0.75 mm, Dc = 120 mm and µ = 0.5;

φVuc+ = 88.2 kN/m > V *(4)

+



Example 7.5-3 Calculation of Design Positive Moment Capacity using EquationsCalculate the design positive moment capacity of cross-section 1 (see Fig. 7.6) which incorporatesconventional tensile reinforcement, for proprietary products Bondek II, Comform and Condeck HP.

Cross-sectional area of bottom-face reinforcement, Ast = 600 mm2/mCentroid height Ast from slab soffit, yst = 60 mmDesign yield stress of reinforcement, fsy = 400 MPaConcrete strength, f'c = 32 MPa

Dc=190


Positive tensile reinforcement, Ast

5200 5200

+Negative tensile reinforcement, Ast

-

+

+

1

x1R = 7372x1L = 3200TransversereinforcementA B C

Figure 7.6 Two-Span Continuous Slab Configuration - Example 7.5-3

Solution

For simplicity, assume that the design loads are such that µR *A = 18.0 kN/m.

Cross-sections with Complete Shear ConnectionThe distance from the end of the sheeting, xcsc , which guarantees the attainment of complete shearconnection regardless of the sheeting support conditions, is calculated as:

xcsc =TH b

y.sh

r[Eq. 4.2(5)]

From Eqs 4.2(3) and 4.2(4):

Ty.sh = A fsh sy.sh [see Table 7.8 for values, noting that fsy.sh = 550 MPa]

Ty.st = A fst sy+

= 310500480 −××= 240 kN/m

Check contribution of bottom-face reinforcement at its yield stress [Eq. 5.6(5)]:

( )y st max = Df T T

f bcsy y.sh y.st

c'−

+ +( / )( )

.

1 600

0 85γ [γ = 0.822 for fc

' = 32 MPa]

Tcsc = min. ( 0 85. ( )'f D h b Tc c r y.st− − ,Ty.sh ) [Eq. 4.2(2)]= min. ( 0 85 32 190 1000 1000 240. ( ) /× × − × −hr , A fsh sy.sh )

Table 7.7 Design information for Bondek II, Comform and Condeck HP (see Appendix C)

tbm hr Ash Hr µ

(mm) (mm) (mm2/m) (kPa)Bondek II 0.75 54 1259 431 0.5Comform 0.75 58 1172 235 0.5

Condeck HP 0.75 55 1215 210 0.5

500 MPa

480 mm2/m



Table 7.8 Tcsc for Bondek II, Comform and Condeck HP

( )y st max xcsc Ty.sh 0 85. ( )'f D h bc c r− Tcsc

(mm) (m) (kN/m) (kN/m) (kN/m)Bondek II 120.5 1.61 692.5 3459 692.5Comform 124.1 2.74 644.6 3350 644.6

Condeck HP 122.5 3.17 668.3 3432 668.3

Since x1 (= 3.2m) is greater than xcsc for each proprietary product, cross-section 1 is in completeshear connection in all cases. Also, since y st (= 60 mm) ≤ ( )y st max , the conventional reinforcementis at its yield stress.

Calculation of Design Positive Moment CapacityAt cross-section 1, since x1L (= 3200 mm) < x1R (= 7372 mm), Tsh.L < Tsh.R . Therefore, the resultanttensile force in the sheeting, Tsh is given as:

Tsh = min( , )T Tsh.L csc

Tsh.L = H bx Rr A*+ µ [where µR *A = 18.0 kN/m]From Eqs 5.6(1) to 5.6(4):

T = T Tsh y.st+ [Eq. 5.6(2)]

β1 =TT

sh

y.sh[Eq. 5.6(4)]

y sh [see Table C3.1]

yc =T y T y

Tsh sh y.st st+

[Eq. 5.6(3)]

φMuo(1)+ = φ φT D y T

f bMc c

c' u.sh− −�� +0 5

0 85.

.Κ [Eq. 5.6(1)]

Table 7.9 φφφφMuo++++ for Bondek II, Comform and Condeck HP (Complete Shear Connection)

Tsh T β1 y sh yc φMuo(1)+

(kN/m) (kN/m) (mm) (mm) (kNm/m)Bondek II 692.5 932.5 1.0 15.5 27.0 108.8Comform 644.6 884.6 1.0 13.4 26.0 104.6

Condeck HP 668.3 906.1 1.0 12.8 25.3 107.3Note: Since β1 = 10. , the term Κ = 0 , and therefore φMu.shΚ = 0 .



8. REFERENCES1. European Committee for Standardization (CEN), Eurocode 4: Design of Composite Steel and

Concrete Structures, Part 1.1: General Rules and Rules for Buildings, ENV 1994-1-1: 1992.

2. Patrick, M., A New Partial Shear Connection Strength Model for Composite Slabs, SteelConstruction Journal, Australian Institute of Steel Construction, Vol. 24, No. 3, August, 1990,pp. 2-17.

3. Patrick, M. and Bridge, R.Q., Partial Shear Connection Design of Composite Slabs, Journal ofEngineering Structures, Vol. 16, No. 5, 1994, pp. 348-362.

4. Johnson, R.P. and Anderson, D., Designers’ Handbook to Eurocode 4, Part 1.1: Design ofComposite Steel and Concrete Structures, Thomas Telford, London, 1993.

5. Johnson, R.P, Composite Structures of Steel and Concrete, Volume 1: Beams, Slabs,Columns, and Frames for Buildings, Second Edition, Blackwall Scientific Publications, 1994.

6. Bode, H. and Minas, F., Composite Slabs with and without End Anchorage under Static andDynamic Loading, International Conference on Composite Construction, Innsbruck, 1997.

7. Veljkovic, M., Behaviour and Resistance of Composite Slabs - Experiments and Finite ElementAnalysis, Doctoral Thesis, Dept. Civil and Mining Engng, Division of Steel Structures, LuleaUniversity of Technology, Sweden, 1996.

8. Patrick, M., Testing and Design of Bondek II Composite Slabs for Vertical Shear, SteelConstruction Journal, Australian Institute of Steel Construction, Vol. 27, No. 2, May, 1993, pp.2-26.

9. Beeby, A.W. and Narayanan, R.S., Designers’ Handbook to Eurocode 2, Part 1.1: Design ofConcrete Structures, Thomas Telford, London, 1995.

10. Proe, D.J., Patrick, M. and Goh. C.C., Simplified Design of Continuous Composite Slabsincluding Moment Redistribution and Crack Control, Fifteenth Australasian Conference on theMechanics of Structures and Materials, Melbourne, December, 1997, pp. 147-152.

11. Patrick, M., Shear Connection Performance of Profiled Steel Sheeting in Composite Slabs, Ph.D. Thesis, Department of Civil and Mining Engineering, University of Sydney, February, 1994.

12. Bridge, R.Q., Shear Connection Parameters for Bondek II, Comform and Condeck HP,University of Western Sydney - Nepean, May, 1998.

13. Wilkie, R. and Patrick, M., Embossment Measurement Procedures for Bondek II and ComformProfiled Steel Sheeting Products, BHP Research - Melbourne Laboratories, May, 1998.



APPENDIX AREFERENCED AUSTRALIAN STANDARDS

REFERENCE NO. TITLE

AS 1170.1-1989 Minimum design loads on structures, Part 1: Dead and live loads andload combinations.

AS 1397-1993 Steel sheet and strip — Hot-dipped, zinc-coated or aluminium/zinc-coated

AS 2327.1-1996 Composite structures, Part 1: Simply supported beams

AS 3600-1994 Concrete structures

AS 3600, Amt 1-1996 Amendment No. 1 to AS 3600-1994

DR 99193 CP Combined Postal Ballot/Draft for Public Comment Australian Standard,Amendment 2 to AS 3600-1994 Concrete Structures, Issued 1 May,1999

AS 3600 Supp1-1994 Concrete structures - Commentary

(Supplement to AS 3600-1994)

AS 3600 Supp1-1994,Amt 1-1996 Amendment No. 1

Doc. BD/32/4/96-2 Methods of test for elements of composite construction, Method 1: Slip-BlockTM Test, Committee Draft.

AS 4671 Steel reinforcing materials (to be published 2001)



APPENDIX BNOTATION

Parameters affected by the direction of applied moment are shown in this report with a minus sign (-)or plus sign (+) superscript to indicate negative-moment or positive-moment regions respectively.

Latin lettersAst Cross-sectional area of tensile reinforcement

Ash Cross-sectional area of base metal of profiled steel sheeting within width of slab b

a1 ,a2 Parameters used to calculate ku

b Width of slab considered

bb Width of opening at base of steel rib in a composite slab (see Fig. 1.2)

bcr Width of the concrete rib in a composite slab at mid-height of the steel ribs (= s br sr− )

bs Support width

bsr Width of steel rib in a composite slab at its mid-height (see Fig. 1.2)

bv Effective width of a web for shear

c Cover to conventional reinforcement

C Compressive force in concrete

d Effective slab depth in negative-moment regions, measured from bottom compressiveface to centroid of conventional tensile reinforcement

dct Top reinforcement depth, measured from the top face of the slab to the centroid of thereinforcement

do Effective slab depth for shear in accordance with AS 3600, measured from compressiveface to centroid of outermost layer of tensile reinforcement, being either sheeting orconventional reinforcement

Dc Overall depth of composite slab including sheeting

fc' Characteristic compressive cylinder strength of concrete at 28 days

fcj' Characteristic compressive cylinder strength of concrete at j days (see AS 2327.1)

fcf' Characteristic flexural tensile strength of concrete

fsy Design yield stress of conventional reinforcement

fsy.sh Design yield stress of sheeting measured in the spanning direction

G Nominal dead load

Gsup Superimposed uniform dead load

hr Height of rib of sheeting (maximum if height of rib types varies)

hs Height of longitudinal stiffener in profiled steel sheeting (see Fig. 1.2)

Hr Mechanical resistance of sheeting per unit width and length of slab

ku Neutral axis parameter, being the ratio at ultimate load of the depth to the neutral axisfrom the extreme compressive fibre, to d , as defined in AS 3600



L Slab span

Lef Effective span of a composite slab, i.e. span of slab assumed in design

Lsy.t Development length for tension, being the length of embedment required to develop theyield strength of a bar in tension

L1 Half-length of positive-moment region

m * Normalised design bending moment, m M bd* * /( )= 2

m *e Normalised elastic design bending moment, m M bd* /( )e e2*=

M * Design bending moment at a cross-section, calculated using the load combination forstrength, after allowing for any redistribution as permitted under Section 5.4

M *eElastic design bending moment at a cross-section, calculated using the load combinationfor strength and making no allowance for redistribution

M *max Maximum design bending moment

Muc Nominal positive moment capacity of a slab cross-section with complete shear connection

Muo+ Nominal positive moment capacity of a slab cross-section with complete or partial shear

connection

Muo− Nominal negative moment capacity of a slab cross-section

( )Muo min Minimum nominal moment capacity of a slab cross-section

Mu.sh Nominal moment capacity of bare profiled steel sheeting

Mu.st Nominal moment capacity of a slab cross-section due to conventional tensilereinforcement only

P Applied loadp Steel proportion

Q Nominal live load

R * Design support reaction

s Longitudinal slip measured in direction of sheeting ribs

tbm Base metal thickness of sheeting (nominal value)

T Total resultant tensile force at a cross-section

Tcsc Resultant tensile force in sheeting with complete shear connection

Tsh Resultant tensile force in sheeting at a cross-section

Tsh.L Maximum tensile force that can develop in the sheeting to the Left of a cross-section

Tsh.R Maximum tensile force that can develop in the sheeting to the Right of a cross-section

Ty.sh Yield force in sheeting at a cross-section

Ty.st Yield force in conventional reinforcement at a cross-section

V * Design vertical shear force at a cross-section

V *max Maximum design vertical shear force

Vuc Nominal vertical shear capacity of a cross-section of a composite slab without shearreinforcement

x Horizontal distance from a slab cross-section to either adjacent end of the sheeting



xcsc Distance from an end of the sheeting which guarantees the attainment of complete shearconnection

y sh Height at which Tsh acts above slab soffit, which depends on the degree of shearconnection

y st Centroidal height of conventional reinforcement above slab soffit

Z Section modulus of the uncracked section, referred to the extreme fibre at which flexuralcracking occurs

Greek lettersβ Degree of shear connection, β = T Tsh csc/

β1 Ratio of Tsh to Ty.sh , i.e. β1 sh y.sh= T T/

φ Capacity reduction factor for flexure

φv Capacity reduction factor for shear

γ The ratio at the strength limit state of the depth of the assumed rectangular compressivestress block to k du , as defined in Clause 8.1.2.2 of AS 3600

η Moment redistribution parameter

Κ Profiled steel sheeting bending factorµ Coefficient of friction between sheeting and concrete

ρ Overall density of slab including an allowance for the weight of steel reinforcement andsteel sheeting

ρc Density of concrete



APPENDIX CSTRENGTH DESIGN INFORMATION FOR PROPRIETARY

PROFILED STEEL SHEETING PRODUCTS

C1 GeneralThe following Australian products may currently be designed in accordance with this booklet:

• Bondek II, manufactured by BHP Building Products;

• Comform, manufactured by Woodroffe Industries Pty Ltd; and

• Condeck HPTM, manufactured by Stramit Industries.The geometry of each of these products, as given in the section of this manual ProductsManufactured from OneSteel and BHP Steel (Profiled Steel Sheeting From BHP Zinc-Hi-Ten ),conforms with the requirements of Clause 1.2.4 of AS 2327.1 (see Section 1.2). Therefore, they mayall be used in composite beam construction in accordance with this Standard. It follows from Fig. 1.2,that the overall depth, Dc , of a composite slab used in composite beam design must not be lessthan the minimum value given in Table C1.1 corresponding to each proprietary product.

Table C1.1 Minimum Overall Depth of Composite Slab to AS 2327.1

Proprietary product Height of sheeting ribhr (mm)

Minimum overall depth ofcomposite slab, Dc (mm)

Bondek II 54 120Comform 58 125

Condeck HP 55 120

All of these proprietary products must be manufactured from BHP Zinc-Hi-Ten , G550 galvanisedsteel for the information given in this appendix to be valid.

C2 Shear Connection ParametersAn independent assessment of test data available for each product has been made to determine thedesign values for the shear connection parameters Hr and µ [12]. In the case of Bondek II,information about the value of Hr was gained from a combination of slab and Slip-Block Test data,while slab data was only used in the assessment for Comform and Condeck HP. For all products, acommon design value of µ was derived from Slip-Block Test data.

Design values of the shear connection parameters, Hr and µ , are given in Table C2.1, and in thecase of the more critical parameter Hr , represent lower characteristic values of the test data with a95% probability of exceedance.

Table C2.1 Values of Hr and µµµµ for Design

Profiled steelsheeting product

Mechanical resistanceHr (kPa)

Coefficient of frictionµ

Bondek II 88 t fbm c' 0.5

Comform 235 0.5

Condeck HP 210 0.5

Note: Differences in the Hr values will affect the strength predictions. However, other factors suchas the availability of different sheeting thicknesses, the formwork condition, serviceability, fire



resistance, and restrictions applying to composite beam construction can impact on the design of acomposite slab. This is illustrated in the worked examples in Section 7.

The following restrictions apply to the use of the values of Hr given in Table C2.1:

(a) Bondek II1. The equation is valid for 0.60 ≤ tbm ≤ 1.00 mm.

2. The equation is valid for 20 ≤ fc' ≤ 40 MPa and 15 ≤ fcj

' ≤ fc

' MPa.

3. The lower characteristic embossment height is 2.5 mm with a 95% probability of exceedance.Embossment height is to be measured using a standard procedure [13].

(b) Comform1. The value is valid for 0.75 ≤ tbm ≤ 0.95 mm.

2. The value is valid for 20 ≤ fc'

≤ 40 MPa.

3. The lower characteristic embossment height is 1.0 mm with a 95% probability of exceedance.Embossment height is to be measured using a standard procedure [13].

(c) Condeck HP1. The value is valid for 0.75 ≤ tbm ≤ 1.00 mm.

2. The value is valid for 20 ≤ f’c ≤ 40 MPa.

Normal-weight concrete as defined in AS 3600 is to be used in all cases. Transverse reinforcementis also to be provided.

C3 Sheeting Cross-Section ParametersValues of sheeting cross-section parameters ( Ash , y sh , Mu.sh and Κ ) required for strength designare given below for each of the Australian products, and are applicable provided BHP Zinc-Hi-Ten,G550 galvanised steel is used. The values of base metal thickness, tbm , chosen for each productcorrespond to those given in the section of this manual Products Manufactured from OneSteel andBHP Steel (Profiled Steel Sheeting From BHP Zinc-Hi-Ten ).

When determining the values of these parameters, it has been assumed that for each product thesheeting cross-section is compact for the range of base metal thicknesses addressed. Slab testshave confirmed that this assumption is reasonable for the composite state. Therefore, Ash equals thegross cross-sectional area of the steel sheeting base metal, y sh is the height at which Tsh actsabove slab soffit, Mu.sh is the nominal moment capacity calculated using simple-plastic theory andalso based on the gross cross-section, and variable Κ is a profiled steel sheeting bending factorwhich defines the amount of moment carried by the sheeting.

Table C3.1 Values of Ash , ysh , Mu.sh and ΚΚΚΚ based on fsy.sh = 550 MPa

Profiled steelsheetingproduct

Cross-sectional

area of steelsheeting

Ash (mm2/m)

Height at which Tsh actsabove slab soffit

y sh (mm)

Nominal momentcapacity of baresteel sheetingMu.sh (kNm/m)

Profiled steelsheetingbendingfactor

Κ

Bondek II 1678tbm18 1

2β for 0 0 751< ≤β .

216 611. .β − for 0 75 101. .< ≤β13 8. tbm ( )1 1

2− β

Comform 1563tbm18 1

3β for 0 0 751< ≤β .

231 9 71. .β − for 0 75 101. .< ≤β10 7. tbm ( )1 1

3− β

Condeck HP 1620tbm16 1

3β for 0 0 751< ≤β .

241 1131. .β − for 0 75 101. .< ≤β116. tbm ( )1 1

3− β



APPENDIX DDESIGN POSITIVE MOMENT CAPACITY TABLES FOR

PROPRIETARY PROFILED STEEL SHEETING PRODUCTS

D1 GeneralThe tables presented in this appendix include no contribution from conventional reinforcement in thebottom of the slab, and are applicable provided BHP Zinc-Hi-Ten , G550 galvanised steel is used.The values of base metal thickness, tbm , chosen for each product correspond to those given in thesection of this manual Products Manufactured from OneSteel and BHP Steel (Profiled SteelSheeting From BHP Zinc-Hi-Ten ).

D2 Bondek II Slabs

Table D2.1 Bondek II Design Positive Moment Capacity, φφφφMuo++++ (kNm/m)

tbm = 100. mm; fc' = 25 MPa tbm = 100. mm; fc

' = 32 MPa

Dc Values of φMuo+ for β1 = Values of φMuo

+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 24.6 35.4 42.7 46.2 46.4 24.8 36.0 44.0 48.4 49.9110 26.1 38.3 47.2 52.1 53.7 26.2 38.9 48.4 54.3 57.2120 27.6 41.3 51.6 58.0 61.1 27.7 41.9 52.8 60.2 64.6130 29.0 44.3 56.0 63.9 68.5 29.2 44.8 57.3 66.1 72.0140 30.5 47.2 60.4 69.8 75.9 30.7 47.8 61.7 72.0 79.4150 32.0 50.2 64.9 75.7 83.3 32.1 50.7 66.1 78.0 86.8160 33.5 53.1 69.3 81.6 90.7 33.6 53.7 70.6 83.9 94.2170 35.0 56.1 73.7 87.5 98.0 35.1 56.6 75.0 89.8 101.5180 36.4 59.0 78.2 93.4 105.4 36.6 59.6 79.4 95.7 108.9190 37.9 62.0 82.6 99.3 112.8 38.0 62.5 83.9 101.6 116.3200 39.4 64.9 87.0 105.2 120.2 39.5 65.5 88.3 107.5 123.7210 40.9 67.9 91.5 111.1 127.6 41.0 68.4 92.7 113.4 131.1220 42.3 70.8 95.9 117.1 135.0 42.5 71.4 97.1 119.3 138.5230 43.8 73.8 100.3 123.0 142.3 44.0 74.3 101.6 125.2 145.8240 45.3 76.7 104.7 128.9 149.7 45.4 77.3 106.0 131.1 153.2250 46.8 79.7 109.2 134.8 157.1 46.9 80.3 110.4 137.0 160.6

Note: For β1= 0, φMuo+ = 11.0 kNm/m




tbm = 0 75. mm; fc' = 25 MPa tbm = 0 75. mm; fc

' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 18.6 27.0 33.1 36.6 37.8 18.7 27.3 33.8 37.8 39.7110 19.7 29.2 36.4 41.0 43.3 19.8 29.6 37.2 42.2 45.3120 20.8 31.5 39.8 45.4 48.8 20.9 31.8 40.5 46.7 50.8130 21.9 33.7 43.1 49.8 54.4 22.0 34.0 43.8 51.1 56.4140 23.0 35.9 46.4 54.3 59.9 23.1 36.2 47.1 55.5 61.9150 24.1 38.1 49.7 58.7 65.5 24.2 38.4 50.4 60.0 67.4160 25.2 40.3 53.1 63.1 71.0 25.3 40.6 53.8 64.4 73.0170 26.3 42.5 56.4 67.6 76.5 26.4 42.8 57.1 68.8 78.5180 27.4 44.7 59.7 72.0 82.1 27.5 45.1 60.4 73.3 84.0190 28.6 47.0 63.0 76.4 87.6 28.6 47.3 63.7 77.7 89.6200 29.7 49.2 66.3 80.9 93.1 29.7 49.5 67.1 82.1 95.1210 30.8 51.4 69.7 85.3 98.7 30.8 51.7 70.4 86.5 100.7220 31.9 53.6 73.0 89.7 104.2 32.0 53.9 73.7 91.0 106.2230 33.0 55.8 76.3 94.1 109.8 33.1 56.1 77.0 95.4 111.7240 34.1 58.0 79.6 98.6 115.3 34.2 58.3 80.3 99.8 117.3250 35.2 60.2 83.0 103.0 120.8 35.3 60.6 83.7 104.3 122.8




' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 14.9 21.9 27.0 30.2 31.7 15.0 22.1 27.5 31.0 32.9110 15.8 23.6 29.7 33.7 36.1 15.9 23.8 30.1 34.5 37.4120 16.7 25.4 32.3 37.3 40.5 16.7 25.6 32.8 38.1 41.8130 17.6 27.2 35.0 40.8 45.0 17.6 27.4 35.4 41.6 46.2140 18.5 28.9 37.7 44.3 49.4 18.5 29.1 38.1 45.2 50.6150 19.4 30.7 40.3 47.9 53.8 19.4 30.9 40.8 48.7 55.1160 20.2 32.5 43.0 51.4 58.2 20.3 32.7 43.4 52.2 59.5170 21.1 34.3 45.6 55.0 62.7 21.2 34.5 46.1 55.8 63.9180 22.0 36.0 48.3 58.5 67.1 22.1 36.2 48.7 59.3 68.4190 22.9 37.8 50.9 62.1 71.5 22.9 38.0 51.4 62.9 72.8200 23.8 39.6 53.6 65.6 76.0 23.8 39.8 54.1 66.4 77.2210 24.7 41.3 56.3 69.2 80.4 24.7 41.5 56.7 70.0 81.7220 25.6 43.1 58.9 72.7 84.8 25.6 43.3 59.4 73.5 86.1230 26.4 44.9 61.6 76.2 89.2 26.5 45.1 62.0 77.0 90.5240 27.3 46.7 64.2 79.8 93.7 27.4 46.9 64.7 80.6 94.9250 28.2 48.4 66.9 83.3 98.1 28.3 48.6 67.3 84.1 99.4




D3 Comform Slabs

Table D3.1 Comform Design Positive Moment Capacity, φφφφMuo++++ (kNm/m)


' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 20.6 31.5 39.7 44.0 44.4 20.7 31.9 40.7 45.8 47.2110 21.9 34.1 43.6 49.3 51.0 22.0 34.5 44.6 51.0 53.7120 23.2 36.7 47.5 54.5 57.5 23.3 37.1 48.5 56.2 60.2130 24.5 39.3 51.5 59.7 64.0 24.6 39.8 52.5 61.5 66.8140 25.8 41.9 55.4 64.9 70.6 26.0 42.4 56.4 66.7 73.3150 27.1 44.5 59.3 70.2 77.1 27.3 45.0 60.3 71.9 79.8160 28.5 47.2 63.2 75.4 83.6 28.6 47.6 64.2 77.2 86.4170 29.8 49.8 67.1 80.6 90.2 29.9 50.2 68.1 82.4 92.9180 31.1 52.4 71.1 85.9 96.7 31.2 52.8 72.1 87.6 99.4190 32.4 55.0 75.0 91.1 103.2 32.5 55.4 76.0 92.8 106.0200 33.7 57.6 78.9 96.3 109.8 33.8 58.0 79.9 98.1 112.5210 35.0 60.2 82.8 101.5 116.3 35.1 60.7 83.8 103.3 119.0220 36.3 62.8 86.7 106.8 122.8 36.4 63.3 87.7 108.5 125.6230 37.6 65.4 90.7 112.0 129.4 37.7 65.9 91.7 113.7 132.1240 38.9 68.1 94.6 117.2 135.9 39.0 68.5 95.6 119.0 138.6250 40.2 70.7 98.5 122.4 142.4 40.3 71.1 99.5 124.2 145.2


Table D3.2 Comform Design Positive Moment Capacity, φφφφMuo++++ (kNm/m)


' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 16.4 25.2 32.1 36.1 37.1 16.4 25.4 32.7 37.2 38.9110 17.4 27.2 35.2 40.2 42.3 17.5 27.5 35.8 41.3 44.0120 18.4 29.3 38.3 44.3 47.5 18.5 29.6 38.9 45.4 49.2130 19.5 31.4 41.4 48.5 52.6 19.5 31.6 42.0 49.6 54.3140 20.5 33.4 44.5 52.6 57.8 20.6 33.7 45.1 53.7 59.5150 21.5 35.5 47.6 56.7 62.9 21.6 35.8 48.2 57.8 64.6160 22.5 37.6 50.7 60.8 68.1 22.6 37.8 51.3 61.9 69.8170 23.6 39.6 53.7 65.0 73.2 23.6 39.9 54.4 66.1 75.0180 24.6 41.7 56.8 69.1 78.4 24.7 41.9 57.5 70.2 80.1190 25.6 43.7 59.9 73.2 83.6 25.7 44.0 60.6 74.3 85.3200 26.7 45.8 63.0 77.3 88.7 26.7 46.1 63.6 78.4 90.4210 27.7 47.9 66.1 81.5 93.9 27.8 48.1 66.7 82.6 95.6220 28.7 49.9 69.2 85.6 99.0 28.8 50.2 69.8 86.7 100.7230 29.8 52.0 72.3 89.7 104.2 29.8 52.3 72.9 90.8 105.9240 30.8 54.1 75.4 93.8 109.3 30.9 54.3 76.0 94.9 111.1250 31.8 56.1 78.5 98.0 114.5 31.9 56.4 79.1 99.1 116.2




D4 Condeck HP Slabs

Table D4.1 Condeck HP Design Positive Moment Capacity, φφφφMuo++++ (kNm/m)

tbm = 100. mm; fc' = 25 MPa tbm = 100. mm; fc

' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 22.8 34.5 43.0 47.0 46.8 23.0 35.0 44.2 49.1 50.1110 24.3 37.3 47.3 52.7 53.9 24.4 37.9 48.5 54.8 57.2120 25.7 40.2 51.6 58.4 61.0 25.8 40.7 52.7 60.5 64.3130 27.1 43.0 55.8 64.1 68.2 27.3 43.6 57.0 66.2 71.4140 28.5 45.9 60.1 69.8 75.3 28.7 46.4 61.3 71.9 78.6150 30.0 48.7 64.4 75.5 82.4 30.1 49.3 65.6 77.6 85.7160 31.4 51.6 68.7 81.2 89.6 31.5 52.1 69.8 83.3 92.8170 32.8 54.4 72.9 86.9 96.7 33.0 55.0 74.1 89.0 99.9180 34.2 57.3 77.2 92.6 103.8 34.4 57.8 78.4 94.7 107.1190 35.7 60.1 81.5 98.3 110.9 35.8 60.7 82.7 100.4 114.2200 37.1 63.0 85.8 104.0 118.1 37.2 63.5 86.9 106.1 121.3210 38.5 65.8 90.0 109.7 125.2 38.7 66.4 91.2 111.8 128.5220 40.0 68.7 94.3 115.4 132.3 40.1 69.2 95.5 117.5 135.6230 41.4 71.5 98.6 121.1 139.4 41.5 72.1 99.8 123.2 142.7240 42.8 74.4 102.9 126.8 146.6 42.9 74.9 104.1 128.9 149.8250 44.2 77.2 107.2 132.5 153.7 44.4 77.8 108.3 134.6 157.0




' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 20.6 31.2 39.1 43.1 43.4 20.7 31.6 40.1 44.8 46.0110 21.9 33.8 43.0 48.2 49.8 22.0 34.2 43.9 49.9 52.5120 23.2 36.3 46.8 53.4 56.2 23.3 36.8 47.8 55.0 58.9130 24.4 38.9 50.7 58.5 62.6 24.5 39.3 51.6 60.2 65.3140 25.7 41.5 54.5 63.6 69.0 25.8 41.9 55.5 65.3 71.7150 27.0 44.0 58.4 68.7 75.4 27.1 44.5 59.3 70.4 78.1160 28.3 46.6 62.2 73.9 81.8 28.4 47.0 63.2 75.5 84.5170 29.6 49.2 66.1 79.0 88.3 29.7 49.6 67.0 80.7 90.9180 30.8 51.7 69.9 84.1 94.7 31.0 52.1 70.8 85.8 97.3190 32.1 54.3 73.7 89.2 101.1 32.2 54.7 74.7 90.9 103.7200 33.4 56.8 77.6 94.4 107.5 33.5 57.3 78.5 96.0 110.1210 34.7 59.4 81.4 99.5 113.9 34.8 59.8 82.4 101.2 116.5220 36.0 62.0 85.3 104.6 120.3 36.1 62.4 86.2 106.3 122.9230 37.3 64.5 89.1 109.7 126.7 37.4 65.0 90.1 111.4 129.3240 38.5 67.1 93.0 114.9 133.1 38.6 67.5 93.9 116.5 135.7250 39.8 69.7 96.8 120.0 139.5 39.9 70.1 97.8 121.7 142.1






' = 32 MPa


+ for β1 =

(mm) 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0100 17.2 26.2 33.2 36.9 37.8 17.3 26.5 33.8 38.1 39.6110 18.3 28.4 36.4 41.2 43.1 18.4 28.7 37.0 42.4 44.9120 19.3 30.5 39.6 45.5 48.5 19.4 30.8 40.2 46.6 50.3130 20.4 32.6 42.8 49.7 53.8 20.5 32.9 43.4 50.9 55.6140 21.5 34.8 46.0 54.0 59.1 21.5 35.1 46.6 55.2 60.9150 22.5 36.9 49.2 58.3 64.4 22.6 37.2 49.8 59.4 66.3160 23.6 39.0 52.4 62.5 69.8 23.7 39.3 53.0 63.7 71.6170 24.7 41.2 55.6 66.8 75.1 24.7 41.5 56.2 67.9 76.9180 25.7 43.3 58.8 71.0 80.4 25.8 43.6 59.4 72.2 82.2190 26.8 45.4 62.0 75.3 85.7 26.9 45.7 62.6 76.5 87.6200 27.9 47.6 65.1 79.6 91.1 27.9 47.9 65.8 80.7 92.9210 28.9 49.7 68.3 83.8 96.4 29.0 50.0 69.0 85.0 98.2220 30.0 51.8 71.5 88.1 101.7 30.1 52.1 72.2 89.3 103.6230 31.1 54.0 74.7 92.4 107.1 31.1 54.2 75.4 93.5 108.9240 32.1 56.1 77.9 96.6 112.4 32.2 56.4 78.6 97.8 114.2250 33.2 58.2 81.1 100.9 117.7 33.3 58.5 81.8 102.0 119.5




APPENDIX EDESIGN POSITIVE VERTICAL SHEAR CAPACITY TABLES FOR

PROPRIETARY PROFILED STEEL SHEETING PRODUCTS

E1 GeneralThe tables presented in this appendix include no contribution from conventional reinforcement in thebottom of the slab, and are applicable provided BHP Zinc-Hi-Ten , G550 galvanised steel is used.The values of base metal thickness, tbm , chosen for each product correspond to those given in thesection of this manual Products Manufactured from OneSteel and BHP Steel (Profiled SteelSheeting From BHP Zinc-Hi-Ten ).

E2 Bondek II Slabs

Table E2.1 Bondek II Design Positive Vertical Shear Capacity, φφφφVuc++++ (kN/m)

tbm = 100. mm tbm = 0 75. mm tbm = 0 60. mm

fc' = 25 MPa fc

' = 32 MPa fc' = 25 MPa fc

' = 32 MPa fc' = 25 MPa fc

' = 32 MPa

Dc Values of φVuc+ for µ = Values of φVuc

+ for µ = Values of φVuc+ for µ =

(mm) 0 0.5 0 0.5 0 0.5 0 0.5 0 0.5 0 0.5100 108.8 163.2 113.4 170.1 85.7 128.5 89.7 134.5 71.4 107.1 75.0 112.5110 105.6 158.4 110.7 166.1 83.7 125.6 88.1 132.2 70.1 105.2 74.1 111.1120 103.6 155.4 109.1 163.7 82.6 123.9 87.4 131.1 69.5 104.3 73.8 110.7130 102.4 153.6 108.4 162.6 82.1 123.1 87.3 130.9 69.4 104.1 74.1 111.1140 101.9 152.8 108.3 162.5 82.1 123.2 87.7 131.6 69.7 104.6 74.7 112.1150 101.9 152.8 108.8 163.2 82.5 123.8 88.5 132.8 70.3 105.5 75.7 113.6160 102.3 153.5 109.7 164.6 83.3 124.9 89.7 134.5 71.2 106.8 77.0 115.4170 103.1 154.7 111.0 166.5 84.3 126.4 91.1 136.7 72.3 108.5 78.4 117.6180 104.2 156.4 112.6 168.9 85.5 128.3 92.7 139.1 73.6 110.4 80.1 120.1190 105.6 158.4 114.4 171.6 87.0 130.5 94.6 141.9 75.0 112.6 81.9 122.8200 107.2 160.8 116.4 174.7 88.6 132.9 96.6 144.9 76.6 114.9 83.8 125.7210 109.0 163.5 118.7 178.0 90.3 135.5 98.7 148.1 78.3 117.4 85.8 128.7220 110.9 166.3 121.1 181.6 92.2 138.2 101.0 151.4 80.1 120.1 87.9 131.9230 113.0 169.4 123.6 185.4 94.1 141.2 103.3 155.0 81.9 122.9 90.1 135.2240 115.1 172.7 126.2 189.4 96.2 144.2 105.8 158.7 83.8 125.8 92.4 138.7250 117.4 176.2 129.0 193.5 98.3 147.4 108.3 162.5 85.8 128.7 94.8 142.2



E3 Comform SlabsTable E3.1 Comform Design Positive Vertical Shear Capacity, φφφφVuc

++++ (kN/m)

tbm = 0 95. mm tbm = 0 75. mm


+ for µ =(mm) 0 0.5 0 0.5100 73.0 109.5 61.6 92.4110 70.0 104.9 59.6 89.4120 67.7 101.6 58.2 87.3130 66.1 99.2 57.4 86.0140 65.0 97.6 56.9 85.3150 64.3 96.5 56.7 85.1160 64.0 95.9 56.8 85.2170 63.9 95.8 57.1 85.7180 64.0 95.9 57.6 86.4190 64.3 96.4 58.2 87.4200 64.7 97.1 59.0 88.5210 65.3 97.9 59.9 89.8220 66.0 99.0 60.8 91.2230 66.8 100.2 61.8 92.8240 67.7 101.6 63.0 94.4250 68.7 103.0 64.1 96.2

Note: This table covers fc' = 25 and 32 MPa.

E4 Condeck HP SlabsTable E4.1 Condeck HP Design Positive Vertical Shear Capacity, φφφφVuc

++++ (kN/m)

tbm = 100. mm tbm = 0 90. mm tbm = 0 75. mm


+ for µ = Values of φVuc+ for µ =

(mm) 0 0.5 0 0.5 0 0.5100 78.7 118.0 72.5 108.7 63.2 94.8110 74.7 112.1 69.1 103.6 60.7 91.0120 71.7 107.6 66.6 99.8 58.8 88.2130 69.4 104.1 64.7 97.0 57.5 86.3140 67.7 101.6 63.3 94.9 56.7 85.0150 66.4 99.7 62.3 93.5 56.1 84.2160 65.5 98.3 61.7 92.5 55.9 83.8170 65.0 97.4 61.3 92.0 55.9 83.8180 64.6 96.9 61.2 91.8 56.0 84.0190 64.5 96.7 61.2 91.8 56.3 84.5200 64.5 96.8 61.4 92.2 56.8 85.2210 64.7 97.1 61.8 92.7 57.4 86.1220 65.1 97.6 62.3 93.4 58.1 87.1230 65.5 98.3 62.8 94.3 58.8 88.2240 66.1 99.1 63.5 95.3 59.7 89.5250 66.7 100.1 64.3 96.4 60.6 90.8

Note: This table covers fc' = 25 and 32 MPa.

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