Design of Simply-Supported Composite Beams with · PDF fileDesign of Simply-Supported Composite Beams with Large Web Penetrations Design Booklet DB1.3 OneSteel Market Mills Composite

Design of Simply-SupportedComposite Beams withLarge Web Penetrations

Design Booklet DB1.3

OneSteel Market MillsComposite Structures Design Manual

February 2001


DB1.3–ii Simply-Supported Composite Beams Edition 2.0 - February 2001Design of Simply-Supported Composite Beams with Large Web Penetrations

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. Cameron Chick *Dr. Daya Dayawansa *Dr. Chong Chee Goh *

Mr. Rodney Wilkie ** Formerly BHP Melbourne Research Laboratories

Reviewed by

Dr. Brian UyThe University of New South Wales

Edition 1.0 - April 1999Edition 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 Simply-Supported Composite Beams DB1.3–iiiDesign of Simply-Supported Composite Beams with Large Web Penetrations

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 of Simply-Supported Beams with Large Web Penetrations” was the third design booklet of the CompositeStructures Design 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.


DB1.3–iv Simply-Supported Composite Beams Edition 2.0 - February 2001Design of Simply-Supported Composite Beams with Large Web Penetrations

ContentsPreface ............................................................................................................. iv

1. SCOPE AND GENERAL1.1 Scope ..................................................................................................... 11.2 General................................................................................................... 1

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

3.1 Strength Design...................................................................................... 43.2 Deflection Calculation............................................................................. 7

4. DESIGN MODELS4.1 General................................................................................................... 94.2 Strength Design Model ........................................................................... 94.3 Deflection Design Model........................................................................ 12

5. DESIGN APPROACH5.1 General................................................................................................... 135.2 Overall Design Approach........................................................................ 135.3 Strength Design...................................................................................... 135.4 Deflection Calculation............................................................................. 15

6. DESIGN RULES6.1 General................................................................................................... 166.2 Application .............................................................................................. 166.3 Strength Design...................................................................................... 186.4 Design Moment and Shear Capacities - Composite Beams .................. 186.5 Design Moment and Shear Capacities - Bare Steel Beams................... 206.6 Stability Considerations .......................................................................... 216.7 Detailing.................................................................................................. 216.8 Deflection Calculation............................................................................. 23

7. AIDS FOR STRENGTH DESIGN7.1 General................................................................................................... 267.2 WEBPENTM Spreadsheet Program ........................................................ 267.3 Design Capacity Tables.......................................................................... 27

8. WORKED EXAMPLES8.1 General................................................................................................... 288.2 Beam and Penetration Data ................................................................... 288.3 Example 1 .............................................................................................. 298.4 Example 2 .............................................................................................. 32

9. REFERENCES ..................................................................................................... 39

APPENDICESA. Nominal Moment Capacity - Composite Beam ...................................... 40B. Nominal Moment Capacity - Bare Steel beam ....................................... 44C. Design Capacity Tables.......................................................................... 46D. Notation .................................................................................................. 85


Edition 2.0 - February 2001 Simply-Supported Composite Beams DB1.3–vDesign of Simply-Supported Composite Beams with Large Web Penetrations

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.

The additional design information necessary to allow large web penetrations to be incorporated intosimply-supported bare steel and composite beams is presented in this booklet. Design issues withrespect to strength and deflection control are addressed. The non-composite bare steel state arisesduring construction prior to the concrete hardening.

Large rectangular and circular penetrations are often made in the steel web of composite beams forthe passage of horizontal building services. This allows the plenum height to be reduced when usingeconomical, standard UB and WB steel sections. However, large penetrations weaken a compositebeam locally and reduce its overall flexural stiffness, and therefore their effect must be considered indesign.

Neither the Steel Structures Standard AS 4100 nor the Composite Beam Standard AS 2327.1contains design provisions for large web penetrations. The rules provided in the booklet for designingbare steel beams with large penetrations are compatible with AS 4100. For the composite state, therules are compatible with AS 2327.1, and have been proposed as an acceptable method of design tobe referred to in Amendment No. 1 of this Standard expected to be published this year.

Information is also given to assist design engineers to understand the engineering principles onwhich the design methods are based. This includes:

(a) explanatory information on important concepts and models;

(b) the limits of application of the methods; and

(c) worked examples.

Design capacity tables are given in Appendix C to simplify the strength design process. Theinformation provided can be used to design for either the bare steel or composite states. The tablescover a range of situations involving 300PLUS® UB and WB steel sections supporting a compositeslab and incorporating large web penetrations. A spreadsheet program named WEBPENTM isavailable to assist with the strength design calculations.

Although these design aids are intended to make the design process more efficient, it is essentialthat the user obtain a clear understanding of the basis of the design rules and the design approachby working through this document and the relevant parts of associated design Standards such as AS4100 and AS 2327.1.


Edition 2.0 - February 2001 Simply-Supported Composite Beams DB1.3–1Design of Simply-Supported Composite Beams with Large Web Penetrations

1. SCOPE AND GENERAL1.1 ScopeThe additional design information necessary to allow large web penetrations to be incorporated intosimply-supported bare steel and composite beams is presented in this booklet. Design issues withrespect to strength and deflection control are addressed. The steel beam must be a doubly-symmetric I-section.

The overall beam design for the bare steel and composite states is assumed to have been carriedout in accordance with AS 4100 [1] and AS 2327.1 [2], respectively.

The penetrations may be (see Fig. 1.1):

• rectangular or circular in shape (within the specified limitations);

• unreinforced, or reinforced (in accordance with the specified details) ; and

• concentric or eccentric to the centroid of the steel section.

The application of the strength design method is defined by the conditions given in Section 6.2.

(a) Circular unreinforced (b) Rectangular unreinforced

(c) Circular reinforced (d) Rectangular reinforced

Figure 1.1 Acceptable Types of Web Penetrations

This document should be read in conjunction with the design booklet Design of Simply-SupportedComposite Beams for Strength, DB1.1 [3] and AS 2327.1, noting that some relevant material fromthese documents has not been duplicated herein.

In accordance with Clause 5.2.3.1 of AS 2327.1, the effect of holing of the steel beam due to a webpenetration may be ignored provided the greatest internal dimension of the penetration is not greaterthan 0.1 times the clear depth of the web. It follows that penetrations larger than this should beconsidered as large, and their effect determined in accordance with the information provided in thisdocument.

1.2 General

The strength design method presented herein is based on a method recommended by an ASCETask Committee [4]. The method has been verified with some experimentally-based investigationsconducted in Australia, and modified to suit Australian design practice and conform to relevantAustralian Standards. Further details about the development of the strength design method can befound elsewhere [5,6].


DB1.3–2 Simply-Supported Composite Beams Edition 2.0 - February 2001Design of Simply-Supported Composite Beams with Large Web Penetrations

The deflection design method has been developed from work originally presented by Tse andDayawansa [7]. Further information about this method can be found in [5].

Large rectangular and circular penetrations are often made in the steel web of composite beams forthe passage of horizontal building services. This allows the plenum height to be reduced when usingeconomical, standard UB and WB steel sections. However, large web penetrations weaken acomposite beam locally and reduce its overall flexural stiffness. Neither the Steel StructuresStandard AS 4100 nor the Composite Beam Standard AS 2327.1 contains design provisions forlarge web penetrations.

The strength design method was adopted after a detailed review of four proposed methods, viz.ASCE Task Committee [4], Redwood and Cho [8], Lawson [9] and Oehlers and Bradford [10]. Themethod adopted for Australian design practice, proposed by ASCE Task Committee [4], has beenmodified to conform to the relevant Australian Standards. The suitability of the modified method hasbeen verified on the basis of an Australian experimental program. A reliability analysis has beenconducted using the results of the experimental program and other experimental data available fromoverseas literature, to determine an appropriate value for the strength factor, φ [11]. In this regard,consideration has also been given to the improved performance of a composite beam that can bederived by placing DECKMESH™ [12] in the region of a penetration [13]. Accordingly, it isrecommended herein that this reinforcing product is used in the region of each web penetration whenthe profiled steel sheeting is deemed perpendicular to the steel beam. (Note: this product is notsuitable to be used in situations when the sheeting is parallel to the steel beam – refer to designbooklet DB1.2 for further guidance.)

The cost implications of choosing between reinforced or unreinforced web penetrations is animportant consideration during the design stage, noting that the intention of using penetrations is notonly to obtain an acceptable floor-to-floor height, but also a more cost-effective structure. For thispurpose, it is recommended that a rational method of costing steelwork is used which takes intoaccount the specific labour and material costs involved in fabricating the penetrations including anysteel plate reinforcement [14].



2. TERMINOLOGYSome important terminology used in this booklet is summarised in this section. Reference shouldalso be made to Section 2 of DB1.1 and Clause 1.4.3 of AS 2327.1 for additional terminology.

Bottom T-SectionThe portion of the steel beam cross-section lying below the penetration.

High Moment End (HME)The end of a penetration subjected to the higher primary bending moment.

Low Moment End (LME)The end of a penetration subjected to the lower primary bending moment.

Primary Bending MomentThe bending moment at a beam cross-section due to overall bending action ignoring secondaryeffects (see Fig. 3.2).

Rigid ArmA part of a beam assumed to be rigid in the model used for deflection calculations.

Secondary Bending MomentThe additional bending moment induced in the top and bottom T-sections as a result of Vierendeelaction over the length of the penetration (see Fig. 3.2).

Steel T-SectionThe bottom T-section or the top T-section, excluding the concrete flange in the case of a compositebeam.

Top T-SectionThe portion of the steel beam cross-section lying above the penetration, inclusive of the concreteflange in the case of a composite beam.

Vierendeel ActionThe development of secondary bending moments in the top and bottom T-sections due to thepresence of vertical shear force across the penetration.

Web Penetration ReinforcementSteel plates or flat bars continuously welded to one or both sides of the web of the steel beam, asclose as practicable to the top and bottom horizontal edges of the penetration.



3. DESIGN CONCEPTS3.1 Strength Design

Behaviour in the Region of a Web PenetrationA large rectangular or circular penetration made in the steel web of a simply-supported steel orcomposite beam weakens the beam locally by reducing both the moment and shear capacities. Thisreduction in strength can be partly overcome by welding steel plates or flat bars to the web along thehorizontal edges of the penetration as reinforcement. However, the economics of using webpenetration reinforcement needs careful consideration.

In the absence of vertical shear force, the moment capacity of a beam cross-section at a large webpenetration is reduced as a direct result of the loss of steel web area. Vertical shear force at thepenetration gives rise to a more complex state of equilibrium as a result of Vierendeel actionoccurring over the length of the penetration. This action causes additional secondary moments todevelop in the top and bottom T-sections. Its effect becomes more pronounced as the penetrationlength increases and as the shear-to-moment ratio increases, which explains why both of thesefactors need to be controlled during design.

The main features that become visible in the region of a web penetration at ultimate load are shownin Fig. 3.1. The most-highly stressed areas are located at the high- and low-moment ends of thepenetration, denoted HME and LME, respectively. These features are briefly explained as follows.

The secondary moments may be sufficiently large to cause the slab to crack perpendicular to thesteel beam, both in the top face at the LME and the bottom face at the HME. The combined effectsof flexure, shear and Vierendeel action can lead to yielding in the top and bottom T-sections, andplastic hinges can form at their ends.

In many cases, large differential vertical deflection between the two ends of the penetration occurswhen a major diagonal crack forms in the concrete slab directly above the penetration. This crackcan lead to a sudden drop in the load-carrying capacity of the composite beam, significantly reducingits ductility [13]. Large tensile forces develop in the shear connectors at the HME region of thepenetration [15], particularly prior to the onset of the diagonal crack. The likelihood of diagonalcracking in the slab can be influenced by a number of factors, such as: the moment-shear ratio; thegeometry of the profiled steel sheeting; the orientation of sheeting ribs; and the slab reinforcement.

Support

Steel yielding Bottom T-Section

Concretecracking

Diagonalcracking

Top T-Section

Concretecrushing

LMEHME

Primarybendingmoments

Shearforce

Figure 3.1 Behaviour at Ultimate Load



When the sheeting ribs are orientated perpendicular to the longitudinal axis of the steel beam, thediagonal crack initiates at the top of the ribs and rapidly propagates through the cover slab causingfailure. Tests show that the behaviour of a composite beam with the sheeting laid perpendicular tothe steel beam can be significantly improved if the width of this crack is controlled using special steelreinforcement in the concrete slab [13]. This steel reinforcement was originally developed to preventrib shearing failure in composite edge beams [16,17,19], and is now commercially available asDECKMESH [12].

Primary and Secondary Bending MomentsThe existence of primary and secondary bending moments in the region of a large web penetration isillustrated in Figure 3.2.

Primary bendingmoments

M*HM*L

Top T-Section

Bottom T-SectionHMELME

(a) Primary bending moments on beam at web penetration

Secondary bendingmoments

(b) Secondary bending moments on T-Sections

Top T-Section

HME

LME

V*b

V*b

V*t

V*t

Bottom T-Section

Vierendeel deformationin T-Sections

Figure 3.2 Primary and Secondary Bending Moments in the Region of a Web Penetration

Effect of Web Penetrations on Maximum Compressive Force in Concrete FlangeIn a simply-supported composite beam, the maximum compressive force that can develop in theconcrete flange at any particular cross-section can be governed by various factors such as thestrength and distribution of the shear connectors, the tensile capacity of the steel section, thecompressive strength of the concrete, etc. When a web penetration is incorporated in the steelbeam, this can reduce the compressive force that can develop in the concrete flange at some of theother cross-sections of the composite beam, as shown in Fig. 3.3 (where it is assumed that theshear connector distribution remains unchanged after the introduction of the web penetration, andthat they are uniformly spaced). Design rules to cater for this situation are given in Clause 6.6 of AS2327.1.

Design Moment CapacityThe design moment capacity at the web penetration is calculated at the HME, in accordance with therequirements of AS 2327.1, while accounting for:

(a) the depth of the penetration;



(b) any horizontal reinforcement at the top and bottom edges of the penetration; and

(c) the degree of shear connection ( β ) at the HME of the penetration.

The effect of vertical shear force is ignored, and therefore, so are secondary bending momentsarising from Vierendeel action.

Case (a) Force in concrete flange is not affected by web penetration (i.e. F = nHfds ≤=Fcc)

Case (b) Force in concrete flange is affected by web penetration (i.e. F = nHfds >=Fcc)

nH shear connectors

Maximum momentcross-section

Force in concreteflange Fcc

Fcc

F = (nH)afds

Force in concreteflange Fcc

Beam with noweb penetration

Beam withweb penetrationFcc

Assumptions:(a) fds corresponds to (nH)a in Case (a) and (nH)b in Case (b)(b) Shear connectors are uniformily distributed

F = (nH)bfds

Beam with noweb penetration

Beam withweb penetration

x

x

Figure 3.3 Influence of Web Penetration on Maximum Compressive Force in Concrete Flange

Design Vertical Shear CapacityIn the case of composite beams without large web penetrations designed in accordance withAS 2327.1, it is assumed that the shear force is resisted by the steel beam alone when calculatingthe design vertical shear capacity. This simplifying assumption is considered too conservative atcross-sections within a web penetration when a significant portion of the steel web has beenremoved. It is assumed that the concrete slab also contributes to the design shear capacity of thecomposite beam, if the combined design shear capacity of the top and bottom steel T-sections isinsufficient to resist the design vertical shear force.

The model used to determine the nominal vertical shear capacity of a composite beam in the regionof a web penetration is presented in Section 4.2.

Moment-Shear Interaction



In accordance with the strength design method given in AS 2327.1, the nominal moment capacity ofa cross-section of a composite beam without a web penetration is assumed to be affected by shearwhen the shear ratio, γ , is greater than 0.5 (see Clause 6.4 of AS 2327.1). In this case, the nominalmoment capacity is assumed to reduce linearly with the shear ratio until the entire steel web is fullyutilised resisting shear, and hence makes no contribution to moment capacity. When γ =10. , theonly contribution to the moment capacity from the steel section is due to the steel flanges. Theresulting tri-linear moment-shear interaction curve is shown in Fig. D3.2 of AS 2327.1.

It should be noted that a different moment-shear interaction relationship, defined by a continuouscubic equation, as shown in Fig. 4.1, is adopted in the web penetration design method. This samemoment-shear interaction equation is used by ASCE Task Committee [4], Redwood and Cho [8] andOehlers and Bradford [10].

Penetration ReinforcementThere are numerous ways of reinforcing web penetrations to minimise the loss of strength andstiffness that can arise due to their presence. Some of these reinforcing arrangements are shown inFig. 3.4. However, the strength design formulae given in Section 6 have been derived assuming thesteel plate or flat bar reinforcement is continuously welded to the web, as close as practicable to thetop and bottom horizontal edges of the penetration. Therefore, only the reinforcement arrangementsshown in Fig. 3.4(a) are valid for use with this document.

3.2 Deflection CalculationThe method given in this booklet can be used to calculate the total deflection of a simply-supportedbare steel or composite beam incorporating a large web penetration.

Basis of Calculation for Composite BeamThe method requires the following two deflection components to be calculated and added together toobtain the total deflection of a composite beam:

(a) total deflection of the beam with no web penetration, calculated in accordance with thesimplified method given in AS 2327.1; plus the

(b) additional deflection due to the presence of the web penetration.

The simplified method given in AS 2327.1 accounts for the effects of long- and short-term loadingand partial shear connection. The additional deflection component due to the presence of thepenetration can be calculated for both long- and short-term loading conditions. The second momentsof area of the T-sections required for this calculation are determined ignoring the effects of partialshear connection.

In calculating the additional deflection component in (b), the bending, shear and Vierendeeldeformations within the length of the penetration are taken into account, and the remaining parts ofthe beam on either side of the penetration are assumed to be two rigid arms. These rigid arms areassumed to undergo no deformation, but their rotations contribute to the deflection of the beam.

The method assumes linear elastic behaviour and hence does not account for deflections due toplastic or buckling deformations in any part of the beam. Concrete shrinkage and creep effects areaccounted for separately.

The additional deflection for a beam with multiple penetrations can be obtained by summing theadditional elastic deflections due to the individual penetrations.



(a) Horizontal reinforcement welded to web

(b) Horizontal and vertical reinforcement welded to web

(c) Penetration edge reinforced with flats

(d) T-Sections strengthened

(e) Diagonal reinforcement

Note: The design method is applicable for penetrations with reinforcement arrangement (a) only.

Figure 3.4 Arrangements of Web Penetration Reinforcement



4. DESIGN MODELS4.1 GeneralThe design models used in the strength and deflection design methods and their limits of applicationare briefly explained in this section. The limits of application arise mainly from the parameter rangescovered in experimental and theoretical studies undertaken to verify the models. This may explainsomewhat arbitrary nature of some of the limits of application. Nevertheless, the limits encompass arange sufficiently wide for most practical applications. These limits are described in detail inSection 6.

4.2 Strength Design Model

Strength Design CriterionThe strength design criterion for a web penetration in a bare steel or composite simply-supportedbeam is represented as the following cubic moment-shear interaction equation,

* *MM

VVφ φb u

� � +�

��

��

3 3

≤ 1.0 (4.1)

where, M * and V * are the design bending moment and shear force, respectively, at the mid-lengthof the penetration; φMb is the design moment capacity of the beam cross-section at HME of the

penetration; and φVu is the design shear capacity for the segment of beam over the length of thepenetration.A value of 0.9 has been chosen for the capacity factor, φ, in Eq. 4.1 based on the findings of areliability analysis on the experimental results [11]. This value is the same as that used for bendingand shear strength, in AS 4100 for bare steel beams and in AS 2327.1 for composite beams.

The curve described by Eq. 4.1 is shown graphically in Fig. 4.1, and the design combinations of

( )M V* *, falling within the shaded area represent satisfactory designs which satisfy the criterion.

00

1.0

1.0 A

B

M*φMb

+

3 3≤ 1.0Region where

Q

M*φMb

V*φVu

V*φVu

P - Corresponding to a satisfactory designQ - Corresponding to an unsatisfactory design

P

Figure 4.1 Moment-Shear Interaction Model



When the design bending moment, M * , and design shear force, V * , at the mid-length of thepenetration have been calculated, the next step of the strength design calculation is to determine thevalues of φMb and φVu at the penetration.

Design Moment CapacityThe design moment capacity, φMb , at a penetration is calculated at the HME in accordance withAS 2327.1 using rectangular stress block theory. In this calculation, the shear force at the cross-section is assumed to be zero. The degree of shear connection, β , at the cross-section is calculatedusing Clause 6.6 of AS 2327.1 and accounting for the reduced steel section due to the penetration.

Design Shear CapacityThe design shear capacity, φVu , at a web penetration is calculated as the sum of the contributionsfrom the top and bottom steel webs and the concrete flange. In this calculation, the effect of overallbending at the cross-section is ignored, while the flexural stresses in the top and bottom T-sectionscaused by Vierendeel action due to shear are determined.

The following assumptions are made in the calculation:

(a) the net axial force in the top and bottom T-sections is zero;

(b) a simplified version of the von Mises yield criterion is used to account for the interactionbetween shear and bending stresses;

(c) the plastic neutral axes of the top and bottom T-sections due to Vierendeel action lie in theirrespective steel flanges; and

(d) a width of 3Dc of the concrete flange contributes to the shear capacity of the top T-section, ifthe shear capacity of the steel web of the top T-section is fully utilised.

These assumptions greatly simplify the design model while not significantly affecting the accuracy ofthe calculation.

Limits of Applicability of the Strength Design ModelThe strength design model is primarily formulated for rectangular web penetrations in a simply-supported bare steel or composite beam. Circular web penetrations are designed by converting thecircular penetration into an equivalent rectangular penetration. Web penetration size, shape andlocation limits are given in Section 6.2.

Reinforcement

Reinforcement

(a) Single-sided reinforcement (b) Double-sided reinforcement

x

x

Section x-x

Figure 4.2 Web Penetration Reinforcement Arrangements



Web penetrations may be either unreinforced or reinforced, and possibly eccentric to the centroid ofthe steel beam section. It is assumed that any web penetration reinforcement is continuously weldedas close as practicable to the top and bottom horizontal edges of the penetration. In addition, thereinforcement shall be rectangular in cross-section and shall not exceed the dimensions specified inSection 6.7. Acceptable reinforcement arrangements are shown in Fig. 4.2 for a rectangularpenetration.

P

a L0 b

L

RA RB

Top T-Section

Bottom T-Section Rigid arms

Pθ'L

θ'L θ'H θ'H

P

δ's

a bL

L0

(c) Shear deformation and induced discontinuity

(d) Additional deflection due to shear

PθL

θL θH θH

(a) Idealised beam model for calculation of additional deflections

(b) Additional deflection due to bending

Figure 4.3 Deflections of the Beam



The steel section shall be compact or non-compact in accordance with the requirements ofAS 2327.1. Slenderness limitations have been imposed in the region of the web penetration to avoidbuckling of the webs of the T-sections and overall buckling of the top T-section in compression.These limitations are given in Section 6.6. As the resistance of bare steel and composite beams tolateral and flexural-torsional buckling may be lowered with the introduction of a web penetration, theeffect of reduced lateral and flexural-torsional buckling loads also needs to be considered in design.

The strength design method is not applicable to beams subjected to significant load fluctuations,which may lead to fatigue.

4.3 Deflection Design Model

Deflection Component Without a Web PenetrationThe deflection of the beam without a penetration is determined by the simplified method specified inAppendix B of AS 2327.1. This method is based on elastic bending theory, and uses the effectivesecond moments of area of the beam, which accounts for partial shear connection.

Additional Deflection Components due to Web PenetrationThe additional deflection components due to bending and shear deformations at the web penetrationare determined using a model where only the top and bottom T-sections at the penetration areassumed to undergo deformation. The remaining parts of the beam on both sides of the penetrationare assumed to be rigid (see Fig. 4.3(c)). These rigid arms, which are connected to each end of thepenetration, rotate in order to maintain compatibility with the local deformations at the penetration, asshown in Fig. 4.3.



5. DESIGN APPROACH5.1 GeneralThe purpose of this section is to explain the design approach adopted in this booklet. Rules for thestrength and deflection design of simply-supported bare steel and composite beams incorporatinglarge web penetrations are covered in Section 6. The restrictions applicable to the strength designmethod are given in Section 6.2.

The overall design approach covering strength and deflection design is illustrated in Fig. 5.1 as aflowchart.

5.2 Overall Design Approach It is assumed in the overall design approach that a preliminary design of the beam without webpenetrations has been completed prior to the web penetration design. Therefore, the basicparameters such as relevant material properties, the size of the steel beam, dimensions of theconcrete slab, distribution of shear connectors, etc., are all assumed to be known. It is also assumedthat the deflection of the beam without web penetrations has been calculated and that any specificdeflection criteria are known.

The aim of the web penetration design procedure is to determine whether the proposed webpenetration can be placed at the preferred location without violating the strength and deflectiondesign criteria. An unreinforced penetration is initially tried with the aim of minimising cost.

If the design criteria are not satisfied for a trial size and location of the web penetration, the optionsavailable to the designer for improving the design include:

(a) changing the location of penetration;

(b) changing the steel beam size; or

(c) adding penetration reinforcement.

The parts of the overall design approach that are covered by the strength and deflection designmethods provided herein are shown below the horizontal dashed line in Fig. 5.1.

5.3 Strength Design The aim of the strength design procedure presented in this section is to ensure that the strengthdesign criterion given by Eq. 4.1 is not violated in the region of the web penetration.

When multiple web penetrations are made in a beam, the method can be used to design eachpenetration separately provided the geometric restrictions in relation to the spacing of the webpenetrations are satisfied.

The main steps of the strength design procedure are described in the following sub-sections.

Size and Location of Web Penetration

The size and location of the web penetration shall satisfy the geometric constraints given in Section6.2. These represent the limits of applicability of the strength design method.

Design Action Effects

The design action effects, M * and V * , are calculated at the mid-length of the web penetration.

Strength Design CriterionThe strength design criterion for a web penetration is represented by the cubic moment-shearinteraction equation given as Eq. 4.1. Therefore, once M * and V * are known, the strength designmethod simply consists of calculating the design moment and shear capacities, φMb and φVu , andchecking that Eq. 4.1 is satisfied.



Start

Strength design ofbeam without web penetration

Calculation of deflectionof beam without web penetration

Choose the size of theweb penetration

No

Yes

Strength designcalculation

Yes

No

Stop

Geometricconstraints

satisfied?

Choose the location of the web penetration

Strengthdesign criterion

satisfied?

Calculate additional deflectiondue to web penetration

NoDeflectiondesign criteria

satisfied?

Yes

Design complete

Calculate M* & V*

NoStability &detailing criteria

satisfied?

Yes

No

Changelocation of web

penetration?

Yes

No

Addpenetration

reinforcement?

Yes

Change steelsection

Addreinforcement

Design of beamwithout web penetration

Web penetrationdesign

Figure 5.1 Flowchart of the Overall Design Approach

Design Moment CapacityThe design moment capacity, φMb , is calculated at the HME using rectangular stress block theorygiven in AS 2327.1, while accounting for the height of the web penetration, any web penetrationreinforcement present and the degree of shear connection β at the HME.



In the calculation of φMb , it is necessary to know the compressive force in the concrete flange at theHME, FcH , which depends on the distribution of shear connectors along the beam, previouslydetermined for the strength design of the beam without any web penetrations.The shear force, V * , at the cross-section is assumed to be zero for this calculation. Hence the valueof φMb represents the point “A” on the moment-shear interaction curve shown in Fig. 4.1.Design Shear CapacityThe design shear capacity, φVu , is determined as the summation of the nominal shear capacities ofthe top and bottom T-sections, Vt and Vb , respectively, times the capacity factor, φ. Although theoverall bending moment at the penetration is assumed to be zero for this calculation, Vierendeelaction due to vertical shear force acting across the penetration is accounted for which gives rise tosecondary bending moments. The value of φVu represents the point “B” on the moment-shearinteraction curve shown in Fig. 4.1.

5.4 Deflection CalculationThe total deflection is calculated as the sum of three components (as shown in Fig. 5.2), viz:

(a) deflection of beam without a web penetration, calculated in accordance with the requirementsof AS 2327.1 (Fig. 5.2(a));

(b) deflection due to secondary bending within the length of the penetration (Fig. 5.2(b)); and(c) deflection due to shear deformation within the length of the web penetration (Fig. 5.2(c)).

The design method has been formulated assuming only one web penetration in the beam. However,deflections from multiple penetrations may be superimposed as linear elastic behaviour is assumed.

(a) Bending deflection of beam with no penetration

P

a L0 b

x

L

δg(x)

δH(x)

θHθL

θ'L (b) Additional bending deflection (from rigid-arm model)

(c) Additional shear deflection (from rigid-arm model)

(d) Total deflection of beam

δv(x)

θ'H

δt(x)

Figure 5.2 Deflection Components of Beam



6. DESIGN RULES6.1 GeneralThe design rules for the strength and deflection design of simply-supported bare steel and compositebeams incorporating large web penetrations are presented in this section. The web penetrations maybe circular or rectangular in shape, unreinforced or reinforced, and located either concentrically oreccentrically to the centroid of the steel section.

The restrictions applicable to the strength design rules are given in Section 6.2.

The strength design objectives and criteria are given in Section 6.3.

The design rules for calculating the design moment and shear capacities, φMb and φVu , forcomposite beams are given in Section 6.4.

The design rules for calculating φMb and φVu for bare steel beams, a special case of the moregeneral method applicable to composite beams, are given in Section 6.5.

The stability considerations applicable to the strength design are given in Section 6.6, and thedetailing requirements are given in Section 6.7.

Design rules for calculating the additional vertical deflection due to a web penetration are given inSection 6.8.

6.2 ApplicationThe proposed size and location of the web penetration must be checked prior to performing thedesign calculations to ensure compliance with the requirements of the strength design method givenin this section. In addition, the size and location of penetrations may also be governed by the stabilityconsiderations given in Section 6.6.

Circular Penetrations

The design formulae presented are for rectangular penetrations. However, circular penetrations canbe designed using the same formulae by assuming that a circular penetration of diameter D isequivalent to a rectangular penetration of the following dimensions.

(a) L0 = 0 45. D .

(b) For unreinforced circular penetrations:

h0 = D for the calculation of Mb ; and

h0 = 0 9. D for the calculation of Vu .

(c) For reinforced circular penetrations:

h0 = D for the calculation of Mb and Vu .

Steel Section

The steel section shall be a doubly symmetric I-section. The design methods are only applicable ifthe steel beam plate elements are compact or non-compact in accordance with the requirements ofAS 2327.1. Only the effective portion of any non-compact plate elements shall be used in thestrength and deflection calculations. The steel section shall also conform to the stabilityconsiderations given in Section 6.6.

Profiled Steel Sheeting

The profiled steel sheeting shall conform to the requirements of AS 2327.1. For the purposes ofdesign, the sheeting shall be considered to be parallel to the steel beam (i.e. λ = 10. ) if the angle



between the beam and the sheeting ribs is less than or equal to 15 degrees. Otherwise it shall beconsidered perpendicular (i.e. λ = 0 0. ).

Size of Rectangular and Circular Penetrations

Acceptable geometry for a beam incorporating web penetrations is given in Fig. 6.1. The location anddimensions of web penetrations shall be such that:

(a) ( )L h0 0 3 0/ .≤

(b) h D0 0 7≤ . s

(c) s Dt s≥ 015.

(d) For bare steel beams, s Db s≥ 015. ; and

for composite beams, s Db s≥ 012.

(e) ( / )L s0 12t ≤ and ( / )L s0 12b ≤

(f) For bare steel beams, ( / / )L h h D0 0 06+ s ≤ 5.6; and

for composite beams, ( / / )L h h D0 0 06+ s ≤ 6.0

a ≥=Ds L0

Ds h0 ≤=0.7Ds

st ≥=0.15Ds

sb ≥=0.15Ds (bare steel)sb ≥=0.12Ds (composite)

L0/h0 ≤ 3

e

P

+ve e

Centroidal axisof steel beam

Mid-height ofpenetration

L0/sb ≤ 12

L0/st ≤ 12

Figure 6.1 Beam Geometry

Proximity to Concentrated Loads and Supports

The distance from the nearer end of the penetration to the edge of a support shall be not less thanthe overall depth of the beam, Ds . When a beam with a web penetration is subjected to aconcentrated load, the following requirements shall also be satisfied.

(a) No concentrated load shall be located within the length of a web penetration.(b) Bearing stiffeners shall be provided at the loading point when a concentrated load is applied;

- closer than Ds 2 to the nearer edge of the penetration unless,

dt

f1250w

yw� � ≤ 70 and b t

tff w

f

yf−� �

2 250≤ 9 (6.1)

- closer than Ds from the nearer edge of the penetration unless,

dt

f1250w

yw�

��

�� ≤ 87 and b t

tff w

f

yf−�

��

��

2 250≤ 11 (6.2)

The design of bearing stiffeners shall be in accordance with the requirements of Clause 5.14 of AS 4100.



6.3 Strength Design

Design ObjectivesThe objective of the strength design method is to ensure that the strength design criterion is notviolated in the region of the web penetration. It is also necessary to check that the beam issufficiently strong to resist any local instability of the steel beam plate elements around thepenetration, which can cause lateral buckling of the top T-section or flexural-torsional buckling of thebeam. The latter two modes of buckling apply only to bare steel beams.

Strength Design CriterionThe strength design criterion is given in the form of a cubic moment-shear interaction equation:

* *MM

VVφ φb u

� � +�

��

��

3 3

≤ 1.0 (6.3)

where, M * and V * are the design action effects at the mid-length of the penetration; and φMb andφVu are the design moment and shear capacities at the penetration, respectively. The value of φshall be taken as 0.9.

6.4 Design Moment and Shear Capacities - Composite Beams

Design Moment CapacityThe design moment capacity, φMb , at the HME of the web penetration is calculated usingrectangular stress block theory in accordance with AS 2327.1. The design moment capacity of thenet section at the penetration, including any web penetration reinforcement, shall not exceed that ofthe composite cross-section without the web penetration.

The formulae needed to calculate φMb are given in Appendix A. The calculation procedure is brieflydescribed below.

(a) Calculate the compressive force in the concrete flange, FcH , and the degree of shearconnection, β , using Para. A2.

(b) Determine the depth of the compressive zone in the concrete flange, dc , and the forcecomponents in the cross-section using Para. A3.2.

(c) Determine the design moment capacity, φMb , using the appropriate case given in Para. A3,depending on the depth of the compressive zone in the cross-section, dh .

The formulae given in Appendix A are based on the following assumptions:(a) the composite beam cross-section is comprised of a concrete flange and a doubly-symmetric

steel I-section;(b) penetrations may be either reinforced or unreinforced;(c) the reinforcement, if any, above and below the penetration are of the same dimensions and

are located horizontally as close as practicable to the edges of the penetration; and(d) sheeting ribs are deemed to be either perpendicular or parallel to the steel beam.

Design Shear CapacityThe design shear capacity in the region of a web penetration in a composite beam is given as:

φVu = φ( )V Vt b+ (6.4)where Vt and Vb are the nominal shear capacities of the top and bottom T-sections, respectively. Thenominal shear capacity, Vu , shall satisfy the conditions given in Eqs 6.37 or 6.41, as applicable.

The nominal shear capacity of the bottom T-section, Vb , is calculated as follows:



Vb = 6

3+

+≤

µ

νb

bpb pbV V (6.5)

where, µb = 2F dV s

r r

pb b(6.6)

sb = ( )D h es − +0 02 (6.7)

νb =Ls

0

b(6.8)

sb = sb , or (6.9)= ( )s A bb r f− 2 [when the penetration is reinforced and

6

31

+

+≤

µ

νb

b

]

Vpb = 0 6. f s tyw b w (6.10)The nominal shear capacity of the top T-section, Vt , is calculated as follows:

Vt =6

3+

+

µ

νt

tptV ≤ V f Apt c vc+ 0 29. ' (6.11)

where, µ t = 2F d F d F d

V sr r ctH ctH ctL ctL

pt t

+ − (6.12)

s t = ( )D h es − −0 02 (6.13)

ν t =Ls

0

t(6.14)

s t = s t , or (6.15)= ( )s A bt r f− 2 [when the penetration is reinforced and

63

1+

+≤

µ

νt

t

]

Vpt = 0.6 yw t wf s t (6.16)Fr = f Ayr r (6.17)

FctH = min.( , , ( ))F n f F F FHc ds tf tw r+ + (6.18)The distance dctH from the top of the steel cross-section to the line of action of FctH is determinedas:

dctH = DFf bcctH

c'

cf1.7− (6.19)

FctL = ( )F n n fctH H L ds− − (6.20)where, fds is calculated in accordance with AS 2327.1 based on nH shear connectors.The distance from the top of the steel section to the line of action of FctL is determined as:

dctL = ( )1− +λ hFf brctL

c'

cf1.7 (6.21)

If 6

3+

+

µ

νt

t

> 1.0 in Eq. 6.11, then the nominal shear capacity of the top T-section, Vt , shall be

limited by the following condition:

FctH ≤ ( )f t b t A fyf f f w r yr− + (6.22)



In this case, dctH , FctL , and dctL are all to be recalculated based on the value of FctH in Eq. 6.22,and µ t shall be recalculated from Eq. 6.12. The nominal shear capacity of the top T-section is thendetermined as:

Vt =µν

t

tptV (6.23)

but limited by,

Vpt ≤ Vt ≤ V f Apt c vc+ 0 29. ' (6.24)

where, Avc = ( )( )3 1D D hc c r− − λ (6.25)

6.5 Design Moment and Shear Capacities - Bare Steel BeamsThe design rules given in this section for bare steel beams have been derived using the moregeneral rules for composite beams given in Section 6.4.

Design Moment CapacityThe design moment capacity, φMb , at the HME of the penetration is based on the net section at the

penetration and determined using rectangular stress block theory. The value of φMb shall notexceed the design moment capacity of the steel section without the penetration.

The formulae presented in Appendix B for the calculation of φMb are only applicable when thefollowing requirements are satisfied:

(a) the steel beam is a doubly-symmetric I-section; and

(b) the reinforcement, if any, above and below the penetration is of the same dimensions and islocated as close as practicable to the horizontal edges of the penetration.

Design Shear CapacityThe design shear capacity, φVu , of a bare steel beam in the region of a web penetration isdetermined by evaluating the geometric parameters µ t , ν t , µb and νb for the top and bottom T-sections, and summing the components Vt and Vb , whereby;

φVu = φ( )V Vt b+ (6.26)where Vt and Vb are the nominal shear capacities of the top and bottom T-sections, respectively.

The nominal shear capacity of the bottom T-section shall be calculated as follows:

Vb =6

3+

+≤

µ

νb

bpb pbV V (6.27)

where, µb =2F dV s

r r

pb b; (6.28)

sb = ( )D h es − +0 02 (6.29)Vpb = 0 6. f s tyw b w (6.30)

Fr = f Ayr r (6.31)

and νb =Ls

0

b; (6.32)

sb = sb , or (6.33)= ( )s A bb r f− 2 [when the penetration is reinforced and

63

1+

+≤

µ

νb

b

]



The nominal shear capacity of the top T-section, Vt , can be calculated using Eqs 6.27 to 6.33 withVt , µ t , ν t , Vpt and s t substituted for Vb , µb , νb , Vpb and sb , respectively.

6.6 Stability Considerations

Web BucklingThe strength design method is generally applicable to the design of web penetrations in beams forwhich,

dt

f1

250w

yw� � ≤ 87 (6.34)

More specifically,(a) for beams where,

dt

f1

250w

yw�

��

�� ≤ 70 (6.35)

then Lh

0

0≤ 3.0 (6.36)

and Vu ≤ 0 4. f t D Vyw w s c+ (6.37)

where, Vc = min.(Vpt ( / )µ υ − ≥1 0 , 0 29. f Ac'

vc ) (6.38) for composite beams, and

= 0 for bare steel beams.(b) for beams where,

70 < dt

f1

250w

yw�

��

�� ≤ 87 (6.39)

then Lh

0

0≤ 2.2 (6.40)

and Vu ≤ 0 27. f t Dyw w s (6.41)

Buckling of Top T-sections

For rectangular penetrations where M V D* */ ( )s > 20 and ν t > 4 , the top T-section of a bare steelbeam shall be designed as a compression member with an effective length equal to L0 , inaccordance with the requirements of AS 4100. Buckling is unlikely to occur in the top T-section of acomposite beam or in reinforced T-sections.

Flexural-Torsional Buckling

In the case of bare steel beams, the effect of the penetration on flexural-torsional buckling of themember shall be considered. No specific guidelines are provided in this document.

Note: Some guidance on buckling of beams with web penetrations can be found in [18].

6.7 Detailing

Spacing Between Multiple PenetrationsTo be treated as an individual penetration, the clear spacing, S , between multiple penetrations inboth composite and bare steel beams shall satisfy the following requirements.



For rectangular penetrations:

S ≥

�

��

�

�

��

�

�

��

φ

φ

u

u00

-1max

VVV

V

L,h. *

*

(6.42)

For circular penetrations:

S ≥

�

��

�

�

��

�

�

��

φ

φ

u

u

-151

VVV

V

D,D..max *

*

(6.43)

where, Vu is the nominal shear capacity of the steel beam without a penetration and D is thediameter of the penetration.The spacing between multiple penetrations in composite beams shall also satisfy,

S ≥ [ ]max. ,L D0 2 s (6.44)When these criteria are not satisfied, the possible reduction in the strength of the member due tointeraction between penetrations shall be considered. However, no guidelines are provided in thisdocument for this assessment.

Penetration ReinforcementTypical reinforcement details are shown in Fig. 4.2. The reinforcement shall be provided inaccordance with the following requirements.

(a) The outstand of the reinforcement shall be compact in accordance with the requirements ofAS 4100.

(b) The reinforcement shall be continuously welded parallel and as close as practicable to thehorizontal edges of the penetration.

(c) The area of reinforcement along each edge of the penetration shall satisfy the condition:

Ar ≤ 0 3 0. t Lffwyw

yr�� (6.45)

(d) The reinforcement shall be extended beyond each end of the penetration by a distance notless than L0 4/ or ( . ) /0 87A tr w , whichever is greater.

(e) The design capacity of the weld within the length of the penetration shall not be less than twicethe nominal tensile capacity of the reinforcement.

(i.e. design capacity of weld ≥ × ×2 fyr cross-sectional area of one reinforcement plate or flat

bar.)(f) The design capacity of the weld beyond each end of the penetration shall not be less than the

nominal tensile capacity of the reinforcement.

(i.e. design capacity of weld ≥ ×fyr cross-section area of reinforcement.)

(g) Reinforcement shall be provided equally along the top and bottom horizontal edges of the webpenetration.

A single-side reinforcement arrangement shall not be used unless all of the following conditions aresatisfied:

Ar ≤Af

3(6.46)


Edition 2.0 - FebrDes

Lh

0

0≤ 2.5 (6.47)

st

ft

w

yw

250≤ 23 (6.48)

st

fb

w

yw

250≤ 23 (6.49)

and MV D

*

*s

≤ 20 at the mid-length of the penetration. (6.50)

Slab ReinforcementIt is recommended that DECKMESHTM be provided in region of the web penetration when thesheeting ribs are deemed perpendicular to the steel beam (see Fig. 6.2), to control the diagonalcracking shown in Fig. 3.1. Only one panel width (450 mm) is required.

L0 min. 600min. (600,a)

LME HME

beam

BHP DECKMESH

Figu

Corner RadiiThe corner radgreater.

6.8 Defle

GeneralThe total defle

where,

δg( )xδb( )x

δv ( )x

Shear Force C

The design shVt

* and Vb* , re

DECKMESH

Notes:(a) BHP DECKMESH is available in modules of length 600 mm(b) BHP DECKMESH is required only when sheeting ribs are deemed perpendicular to

Notes:(a) DECKMESH is available in modules of length 600 mm and width 450 mm.(b) DECKMESH is required only when sheeting ribs are deemed perpendicular to steel

beam

uary 2001 Simply-Supported Composite Beams DB1.3–23ign of Simply-Supported Composite Beams with Large Web Penetrations

re 6.2. DECKMESHTM Recommended in the Region of a Web Penetration.

ii of a rectangular penetration shall be not less than 2tw or 16 mm, whichever is

ction Calculation

ction δt ( )x at a point x (see Fig. 5.2) on the beam is expressed as:

δt ( )x = δ δ δg b v( ) ( ) ( )x x x+ + (6.51)

= deflection at point x of the beam without the penetration;= deflection at point x due to bending from Vierendeel action within the length of

the penetration; and= deflection at point x due to shear deformation within the length of the penetration.

arried by Top T-Section

ear force, V * , is assumed to be shared between the top and bottom T-sections as spectively. For bare steel and composite beams, Vt

* shall be determined as follows:



(a) For concentric penetrations in bare steel beams:

Vt* = V *

2(6.52)

(b) For eccentric penetrations in bare steel beams:

Vt* = V

R

*

( )1+ (6.53)

where, R =

LEI

k LGt s

LEI

k LGt s

03

0

03

0

12

12

b

B

w b

t

T

w t

+

+

��

��

(6.54)

kT and kB are the appropriate shear coefficients for top and bottom T-sections. A value

for R of 1.2 is considered suitable for I-sections used in practice.

(c) For composite beams:

Vt* = V * (6.55)

Additional Bending Deflection

The additional deflection due to secondary bending occurs as a result of the rotations of the rigidarms as shown in Fig. 4.3(c) and 4.3(d).

To determine these rotations, the differential primary moment across the penetration and thesecondary moment due to Vierendeel action must first be determined.

The differential design bending moment, Md* , acting across the web penetration is calculated as:

Md* = M MH

*L*− (6.56)

where, MH* and ML

* are the design bending moments at the high and low moment ends, respectively.

The secondary moment induced by Vierendeel action across the web penetration is defined as:

Mse* = −

V Lt*

0

2(6.57)

where Vt* is the shear force carried by the top T-section, and is calculated using Eqns 6.52, 6.53 or

6.55, as appropriate.

Hence, the rotations at the low and high moment ends of the web penetration are given as:

θL = ( )( ) ( )M I L L b L M I L b L

EI I Lse*

d*

t

t

0 02

0 0 0 0

0

2 3 2 3 2

6

− + − +��

�� (6.58)

θH =( )

−+

��

�� −

M I M I L

EI Id*

t se*

0

tL

2

20

0θ (6.59)

where I0 is the second moment of area of the gross cross-section including the web penetration, It

is the second moment of area of the top T-section, and b Land are the dimensions shown in Fig. 4.3(a).

The additional bending deflection, δb , of the beam due to the web penetration is given as:

For x a≤ ;

δb( )x = xθL (6.60)



For x a L≥ + 0 ;

δb( )x = ( )L x− θH (6.61)

Additional Shear DeflectionThe additional deflection due to shear deformation in the T-sections causes the rigid arms to rotateas shown in Fig. 4.3(c) and (d). These rotations, θL

' and θH' , are calculated as follows:

θL' =

23

0LbLδs

'(6.62)

θH' =

δθs

'

L'

b�� − (6.63)

where the additional shear deflection ignoring geometric continuity (see Fig. 4.3(c)) is given by:

δs' = kV L

Gs tt

t w

*0 (6.64)

The additional deflection, δv , of the beam due to the web penetration is given as:

For x a≤ ;

δv ( )x = xθL' (6.65)

For x a L≥ + 0 ;

δv ( )x = ( )L x− θH' (6.66)



7. AIDS FOR STRENGTH DESIGN7.1 GeneralTo assist the design of penetrations in accordance with the method given in Section 6, a series ofdesign tables and a spreadsheet program named WEBPENTM are provided.Details about WEBPENTM are given in Section 7.2.

The major calculation effort in the strength design method is spent determining φMb and φVu at thepenetration. The design tables allow these values to be readily determined for a wide range ofsituations covering both bare steel and composite beams. These design tables are suitable for useduring the preliminary design stage as well as for final design. A brief description of the tables isgiven in Section 7.3 and the tables are given in Appendix C.

7.2 WEBPENTM Spreadsheet ProgramThe WEBPENTM spreadsheet program runs on Microsoft® EXCELTM Version 7. The design tablesgiven in Appendix C were generated using WEBPENTM.The input data required for the spreadsheet includes:

(a) Steel section data - chosen from an in-built section library that includes all relevant propertiesfor UB and WB sections.

(b) Concrete flange data: b D fcf c c'

cand, , .ρ

(c) Profiled steel sheeting data: rib height; and angle of sheeting ribs to steel beam longitudinalaxis.

(d) Geometry of the penetration: rectangular/circular, height/diameter, length and eccentricity.(e) Shear connector data: nominal shear capacity; number of shear connectors from the HME to

the nearer end of beam; and number of shear connectors within the length of the penetration.(f) Penetration reinforcement data: plate width; thickness; and nominal yield stress.

(g) Design action effect data: M * and V * values at the mid-length of the penetration.

For a given configuration with M * and V * values at the penetration having been determined, thespreadsheet will calculate the design capacities φMb and φVu and plot the design point in relation tothe moment-shear interaction curve, allowing the designer to determine whether or not the trialgeometry and location of the penetration is satisfactory. The designer can easily trial severalcombinations of penetration geometries and locations until a satisfactory solution is obtained. Atypical moment-shear interaction curve output from WEBPENTM is shown in Fig. 7.1.



WEBPENTM RESULTS

0100200300400500600700800900

0 200 400 600 800

SHEAR FORCE (kN)

MO

MEN

T (k

Nm

)

Figure 7.1 Typical Output of WEBPENTM

7.3 Design Capacity TablesThe design capacity tables given in Appendix C can be used to calculate φMb and φVu for a widerange of bare steel and composite beams with concentric web penetrations of various proportions.The parametric range covered in the tables is given in Table 7.1. A detailed description of theparameters given in the tables and how the tables may be used to calculate φMb and φVu is given inParagraphs C2 and C3, respectively.

Table 7.1 Parametric Range of Design Capacity Tables

Parameter Range

Flange width ( bcf ) 1200, 1600 and 2100 mm

Concrete strength ( fc' ) Grades 25 and 32

Slab thickness ( Dc ) 120 mm

Direction of sheeting ribs Perpendicular ( λ = 10. ) andparallel ( λ = 0 ) to steel beam

Steel beam(300PLUS®)

700WB115 to 800WB192310UB32 to 610UB125

Penetration size Circular: h0 / Ds = 0.3, 0.5 & 0.7

Rectangular:

h0 / Ds = 0.3, 0.5 & 0.7; and

L0 / h0 = 1.0, 1.5 and 2.0



8. WORKED EXAMPLES8.1 GeneralTwo worked examples are presented to demonstrate the strength and deflection design methodsgiven in Section 6. They involve the design of a web penetration in an unpropped simply-supportedcomposite beam for Construction Stage 3 (i.e. bare steel beam), and the in-service condition, asdefined in AS 2327.1:Example 1

Strength design of a bare steel beam with a rectangular web penetration for Construction Stage 3,using hand calculations and the design capacity tables given in Appendix C.Example 2

Strength and deflection design of a composite beam with a rectangular web penetration for the in-service condition, using hand calculations and the design capacity tables given in Appendix C.It is assumed that the composite beam without the penetration has been designed in accordancewith AS 2327.1.

8.2 Beam and Penetration DataThe beam data and the preferred size and location of the penetration are given in Table 8.1:

Table 8.1 Worked Example Geometry and Properties

Span ( L ) = 10.5 m

Spacing of secondary beams = 2.6 mSteel beam = 410UB53.7, 300PLUS®

( D b t ts f f wmm, mm, mm, mm,= = = =403 178 10 9 7 6. .d f f1 yw yfmm, MPa, MPa= = =381 320 320 )

Slab depth ( Dc ) = 120 mm (composite slab, hr = 55 mm)

Orientation of sheeting = Sheeting ribs perpendicular to the steel beam

Concrete strength ( ′fc ) = 25 MPa

Density of concrete = 25 kN/m3 (including allowance for reinforcement)Superimposed dead load = 0.3 kPa (services and ceilings)Reducible Live load = 4.0 kPaShear connectors = 19 mm diameterPenetration = Penetration centreline located at 3300 mm from the support

h0 = ( )225 0 56mm s= . D , L0 = ( )425 19mm 0= . h

Concentric with no reinforcement (see Fig. 8.1), therefore( )s s D ht b s mm= = − =0 2 89

The assumptions made in the calculations are as follows:(a) the steel and composite beams are assumed to be simply-supported during construction and

the in-service condition; and(b) the maximum ponding deflection of the profiled steel sheeting equals 10.4 mm.



3088

L=10500

L0=425

h0=225

f'c= 25 MPa

410UB53.7, BHP-300PLUS

x

3300

6987

Dc=120

Figure 8.1 Beam Geometry

8.3 Example 1This worked example demonstrates the strength design procedure for a web penetration in a baresteel beam for Construction Stage 3, using hand calculations and design capacity tables given inAppendix C.

Calculation of Design Action Effects at Mid-Length of Web PenetrationThe minimum nominal loads for construction given in Paragraph F2 of AS 2327.1 are used.The effective span and tributary area are calculated in accordance with the requirements ofAS 2327.1.

Span ( )L = 10.5 mTributary area = 27.3 m2

Steel beam self-weight = 0.5 kN/mWeight of slab (including ponding) = (0.12 m + 0.7x2.6/250) x 25 kN/m3 x 2.6 m = 8.3 kN/m

Dead load (G) = 0.5+8.3 = 8.8 kN/mReducible Construction live load = ( ) ( ) ( )[ ]10 27 3 23 46 23 10 0 6 2 6. . / . . .− − − × − × = 2.4 kN/m

∴ Live load (Q) = 2.4 kN/mDesign load (W) = 1.25 x 8.81 + 1.5 x 2.4 = 14.6 kN/m

Support reaction = 76.6 kN

∴ At mid-length of web penetration:M * = 173 kNmV * = 28.4 kN

Preliminary CheckEnsure the conditions given in Section 6.2 are satisfied:

• ( )h D D0 225 0 7= ≤mm = 0.56 s s. � Satisfactory

• for bare steel beams: ( )L h h D0 0 06 5 2 5 6+ = ≤s . . Satisfactory in Construction Stage 3

• ( )s Dt smm mm= ≥ =89 0 15 60 5. . Satisfactory

• for bare steel beams: s Db smm= ≥89 015. Satisfactory in Construction Stage 3

• no concentrated loads are applied to the beam, thus loading does not restrict the position of theweb penetration Satisfactory



• distance to nearest end support = 3088mm > sD Satisfactory

• the ratios L s0 t , L s0 b = 425/89 = 4.8 < 12 Satisfactory

• the slenderness of the web will also influence the maximum allowable length-to-height ratio of apenetration and the maximum nominal shear capacity of the member (see Section 6.6).

For 410UB53.7, dt

f1

250w

yw� � = 56.7 < 70

Therefore,Lh

0

0≤ 3.0; and

for bare steel beams, Vu ≤ 0 4. f t Dyw w s

Strength Design by Hand Calculation

Design Moment CapacityDetermine the depth of the compressive stress zone, dh , and nominal moment capacity, Mb , of thesteel cross-section at the HME of the web penetration, using the formulae given in Paragraph B2 ofAppendix B.

As the penetration is concentric and unreinforced, Ftw = Fbw (= A ftw yw = 190 kN) and Fr = 0. Inaddition Ftf = Fbf (= 621 kN) (as the 410UB53.7 section is compact in accordance with AS 2327.1).

Therefore, using Eqs B1 and B2 for Case1;

dh =( )t f s t F F F F

t fw yw t f r bw bf tf

w yw

+ + + + −22

=( )7 6 320 89 0 10 9 2 0 190 3 621 3 621 3

2 7 6 320. . .

.× × + + × + + −

× ×E E E

= 89.0 mmand

Mb = ( ) ( ) ( )F d t t f d t s dtf h f w yw h f t h− + − + −� �/ 2 22 2

( ) ( )( )+ + − − + − − +F D s s d F D d s tr s t b h bw s h b f2 2

( )+ − −F D d tbf s h f / 2

= ( ) ( )[ ]621 3 89 10 9 2 7 6 320 89 10 9 0 22 2E × − + × − +. / . .

( )( )+ + − − +0 190 3 403 89 89 10 9 2E .( )+ − −621 3 403 89 10 9 2E . /

= 303 kNm

Therefore, the design moment capacity of the cross-section at the penetration is; φMb = 273 kNm

Design Shear CapacityFrom Eq. 6.4,

φVu = φ( )V Vt b+Nominal shear capacity of the bottom T-section:

Using Eqs 6.27 to 6.33,

Vb = 63

++

≤µ

νb

bpb pbV V



where, µb = 2F dV s

r r

pb b = 0 (since unreinforced)

νb =Ls

0

b = 425

89 = 4.78

and Vpb = 0 6. f s tyw b w = 0 6 320 89 7 6. .× × × = 130 kN

Therefore, Vb = 6 04 78 3

130 130++

× ≤.

kN

= 48.9 kN

Nominal shear capacity of the top T-section:

Using the same equations as for the bottom T-section calculations,

Vt = 48.9 kNThe design shear capacity is,

φVu = ( )φV Vt b+ = ( )0 9 48 9 48 9. . .× + = 88 kNTo satisfy the web buckling considerations given in Section 6.6,

Vu (=97.8 kN) ≤ 0 4. f t Dyw w s

≤ 0 4 320 7 6 403. .× × × = 392 kN O.KTo satisfy the considerations for buckling of the top T-section given in Section 6.6,

( )M V D* *s = 15.1 < 20 criterion satisfied

Moment-Shear InteractionApplying the moment-shear interaction relationship given in Eq. 6.3,

173273

28 488 0

3 3

� � + �

��

��

.

.= 0.29 ≤ 10. strength criterion satisfied

Strength Design using TablesSince h D0 s/ .= 0 56 for the penetration, determine φMb and φVu values by interpolating betweenthe values obtained from Table C26 for h D0 s/ .= 0 5 and Table C27 for h D0 s/ .= 0 7 .

Design Moment CapacityValues of the design moment capacity of a bare steel beam with a web penetration, φMb.0 , are givenin the fifth column of the tables. By interpolation, the design moment capacity are calculated as,

φMb = ( )269 0 56 0 50 7 0 5

269 255− −−� � × −. .

. . = 265 kNm

Design Shear CapacityValues of the design shear capacity of a bare steel beam with a web penetration are given in thecolumns with headings φVu.0 for different web penetration aspect ratios.

Since L h0 190 = . for the penetration, first interpolate between the columns corresponding toL h0 150 = . and L h0 2 00 = . in each table, and then interpolate between those values to determine

φVu.0 corresponding to h D0 0 56s = . .

Value of φVu.0 from Table C26 = ( )137 19 152 0 15

137 113− −−� � × −. .

. .= 118 kN


45 35− −−� � × −. .

. . = 37.0 kN



φVu = ( )118 0 7 0 560 7 0 5

118 37+ −−� � × −. .

. . = 93.6 kN

Moment-Shear InteractionApplying the moment-shear interaction relationship given in Eq. 6.3,

173265

28 493 6

3 3�

��

�� + �

��

��

.

.= 0.31 ≤ 10. strength criterion satisfied

8.4 Example 2This worked example demonstrates the strength design procedure for a web penetration in acomposite beam (described in Section 8.2) for the in-service condition, using hand calculations anddesign capacity tables given in Appendix C.

It is assumed that the composite beam without the penetration has already been designed inaccordance with AS 2327.1. The resulting shear connector distribution given in Fig. 8.2 shows thatthe number of 19 mm shear connectors from HME to the nearer end of the beam is 9 (i.e. nH = 9 ).

14

12

10

8

6

4

2

00 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 10500

LME HME

Position along the Beam

No.

of C

onne

ctor

s Recommended shear connectordistribution (from COMPBEAMTM)

nH= 9nL= 8

Figure 8.2 Shear Connector Distribution

Design Action Effects at Mid-Length of Web PenetrationThe effective span and tributary area are calculated in accordance with AS 2327.1.

Span ( )L = 10.5 mTributary area = 27.3 m2

Total dead load of beam (G) = 8 8 0 3 2 6. . .+ × = 9.6 kN/m

From Section 4 of AS 1170.1, the permissible live load reduction equals,75 35027 3

8%− =.

∴ Reducible live load (Q) = 4 x 0.92 x 2.6 = 9.6 kN/mDesign load (W) = 1.25 x 9.6 + 1.5 x 9.6 = 26.4 kN/m

Support reaction = 138.6 kN

Therefore, at mid-length of the web penetration: M * = 138 6 3 3 26 4 3 3 22. . . . /× − × = 314 kNm

V * = 138 6 26 4 3 3. . .− × = 51.4 kN

Preliminary CheckIn addition to the preliminary checks performed in Example 1 for the bare steel beam, the followingadditional checks must be made for the composite beam.



Effective Width of Concrete Compression FlangeUsing Clause 5.2.2 of AS 2327.1,

bcf = ( )2 105008

26002

1782 8 120× + ×min. , ,

= 2098 mm

Web BucklingCheck for web buckling conditions given in Section 6.6:

For 410UB53.7, dt

f1

250w

yw� � = 56.7 < 70

Therefore, Lh

0

0≤ 3.0; and

Vu ≤ 0 4. f t Dyw w s + min.(Vpt t t( / )µ υ − ≥1 0 , 0 29. f Ac'

vc )

Compressive Force in Concrete Flange at HMEThe compressive force in the concrete at the HME of the web penetration, FcH , is calculated usingthe equations presented in Paragraph A2 of Appendix A.

The compressive capacity of the concrete flange, Fc , is calculated as follows:

Fc = Fc1 + Fc2

Fc1 = ( )0 85. f b D hc'

cf c r−

= ( )0 85 25 2098 120 55. × × × − = 2898 kN

Fc2 = 0 85. f b hc'

cf rλ= 0 85 25 2098 0 0 55. .× × × × = 0 kN

Therefore, Fc = 2898 kN

Since nH = 9,fds = φk fn vs

= 0 85 118 0189

89. . .× − � ��

��

�� × = 84.7 kN

Therefore, n fH ds = 9 84 7× . = 762 kN

From Eq. A7,

Fs = Afi yii

ne

=1

= ( )2 178 10 9 320 2 89 10 9 7 6 320× × × + × − × ×. . . = 1622 kNFrom Eq. A8,

FcH = min.( , , )F n f Fc H ds s

= min.( , , )2898 762 1622 = 762 kNFrom Eqs A10 and A9,

Fcc = min.( , )F Fc s

= min.( , )2898 1622 = 1622 kNβ = n f FH ds cc ≤ 1

= 762 / 1622 = 0.47



Strength Design by Hand Calculation

Design Moment CapacityUse the formulae given in Para. A3.2.From previous calculations,

FcH = 762 kNFc = 2898 kNFs = 1622 kNFc1 = 2898 kNFr = 0 kN (penetration is unreinforced)

Since F FcH c≤ ,

dc = ( )F b fcH cf c'0 85. [Eq. A11]

= ( )762 3 0 85 2098 25E . × × = 17.1 mmSince top flange is compact,

Ftf = b t feff f yf = 178 10 9 320× ×. = 621 kN [Eq. A12]

Since ( )F F F Fs tf cH s− < ≤2 , Case 2 in Para. A3.2 is applicable.

From Eq. A20,dh = 128 mm

From Eq. A21,

Mb = 408 kNmTherefore, the design moment capacity of the composite cross-section at the penetration is:

φMb = 367 kNm

Design Shear CapacityFrom Eq. 6.4,

φVu = φ( )V Vt b+The nominal shear capacity of the bottom T-section, Vb , is the same as that calculated for the baresteel beam in Example 1.Therefore,

Vb = 48.9 kNThe nominal shear capacity of the top T-section, Vt , is calculated as:

Vt = 63

++

µν

t

tptV ≤ V f Apt c vc+ 0 29. ' [Eq. 6.11]

where, Vpt = 0.6 yw t wf s t [Eq. 6.16]= 0.6 × × ×320 89 7 6. = 130 kN

ν t =Ls

0

t = 425

89 = 4.78 [Eq. 6.14]

and µ t = 2F d F d F dV s

r r ctH ctH ctL ctL

pt t

+ − [Eq. 6.12]

FctH = min.( , , ( ))F n f F F FHc ds tf tw r+ + [Eq. 6.18]= min.( , , ( ))2898 762 621 190 0+ + = 762 kN

where, dctH = DFf bcctH

c'

cf1.7− = 120 762 103

− ×× ×1.7 25 2098

[Eq. 6.19]

= 111.5 mm



FctL = ( )F n n fctH H L ds− − =762 10 1 84 7 103 3× − × ×. [Eq. 6.20]= 677.3 kN

dctL = ( )1− +λ hFf brctL

c'

cf1.7 = 55 677 3 10

2098

3+ ×

× ×.

1.7 25 [Eq. 6.21]

= 62.6 mm

Therefore, µ t = 0 762 10 1115 677 3 10 62 6130 89

3 3+ × × − × ××

. . . = 3.68

and Vt = 63

++

µν

t

tptV = 6 3 68

4 78 3130+

+×.

.= 122 kN

Check, Vt ≤ V f Apt c vc+ 0 29. ' = 130 0 29 25 23 4+ ×. .= 164 kN O.K

Therefore, Vt = 122 kNSubstituting the values of Vb and Vt in Eq. 6.4,

φVu = ( )φV Vt b+ = ( )0 9 122 48 9. .× + = 154 kNTo satisfy the web buckling conditions given by Eqs 6.37 and 6.38 in Section 6.6,

Vu (=171 kN) ≤ 0 4. f t Dyw w s + min.(Vpt ( / )µ ν − ≥1 0 , 0 29. f Ac'

vc )≤ 0 4 320 7 6 403. .× × × +min.(130 3 68 4 78 1 0( . / . )− ≥ ,

0 29 25 23 4. .× )≤ 392 kN O.K

To satisfy the condition for buckling of the top T-section given in Section 6.6,( )M V D* *

s = 15 < 20 criterion satisfied O.K

Moment-Shear InteractionSubstituting the calculated values of M * , V * , φMb and φVu in Eq. 6.3,

314367

514154

3 3

� � + �

��

��

. = 0.66 ≤ 10. strength criterion satisfied

Strength Design using TablesSince h D0 s/ .= 0 56 for the penetration, determine φMb and φVu values by interpolating the valuesobtained from Tables C26 and C27 that correspond to h D0 s/ .= 0 5 and h D0 s/ .= 0 7 , respectively.

Design Moment CapacityInterpolating between Tables C26 and C27 to calculate β �� Fcc and nmax �for the penetration withh D0 s/ .= 0 56 ,

β = ( )0 79 0 56 0 50 7 0 5

0 79 0 70. . .. .

. .− −−� � × − = 0.76

Fcc = ( )1710 0 56 0 50 7 0 5

1716 1527− −−� � × −. .

. . = 1653 kN

nmax = ( )19 0 56 0 50 7 0 5

19 17− −−� � × −. .

. . = 18

The number of studs to HME, nH = 9 OK since nH < nmax (see Fig. 3.3)



From previous calculations,

FcH = 762 kN and β = 0.47Interpolating between Tables C26 and C27 to determine the design moment capacities φMb.0 andφMb.5 corresponding to h D0 s/ .= 0 56 ,

φMb.0 = ( )269 0 56 0 50 7 0 5

269 255− −−� � × −. .

. . = 265 kNm

φMb.5 = ( )385 0 56 0 50 7 0 5

385 341− −−� � × −. .

. . = 372 kNm

Now, interpolate between the values of φMb.0 and φMb.5 to determine φMb corresponding toβ = 0 46. ,

φMb = ( )265 0 46 0 00 5 0 0

372 265+ −−

�

��

�� × −. .

. . = 363 kNm

Design Shear CapacityFirst interpolate between the columns corresponding to L h0 150 = . and L h0 2 00 = . in Tables C26and C27 to determine φVu.0 and φVu.5 for L h0 190 = . ,


137 113− −−� � × −. .

. .= 118 kN


201 182− −−� � × −. .

. .= 185 kN


45 35− −−� � × −. .

. . = 37.0 kN


102 90− −−� � × −. .

. .= 96 kN

Secondly, interpolate between these values to determine the moment capacities φVu.0 and φVu.5

corresponding to h D0 s/ .= 0 56 ,

φVu.0 = ( )118 0 56 0 50 7 0 5

118 37− −−� � × −. .

. . = 94 kN

φVu.5 = ( )185 0 56 0 50 7 0 5

185 96− −−

�

��

�� × −. .

. . = 158 kN

Finally, interpolate between the values of φVu.0 and φVu.5 to determine the value of φVu

corresponding to β = 0 46. ,

φVu = ( )158 0 5 0 460 5 0 0

158 94− −−

�

��

�� × −. .

. . = 153 kN

Moment-Shear InteractionSubstituting the calculated values of M * , V * , φMb and φVu in Eq. 6.3,

314363

514153

3 3

� � + �

��

��

. = 0.68 ≤ 10. strength criterion satisfied

Deflection CalculationsIn this example, the additional deflection component calculated corresponds to short-term loadingduring the in-service condition. The design load, W , for short-term loading is given as:

W = G Qsup + ψs = 0 78 0 7 9 6. . .+ × = 7.5 kN/mThe design action effects at the web penetration resulting from the in-service loading are:



V * = 14.6 kN (calculated at the mid-length of the penetration)

MH* = 92 kNm

ML* = 86 kNm

From Eqs 6.56 and 6.57,Md

* = M MH*

L*−

= 92-86 = 6 kNm

Mse* =

−V Lt*

0

2

= − ×14 6 0 4252

. . = -3.1 kNm

The second moment of area of the composite cross-section at the web penetration can be calculatedas,

I0 = 510 106×××× mm4

Similarly, the second moment of area of the top T-section can be calculated as,

I t = 30 90 106. ×××× mm4

The modular ratio used in these calculations was based on the short-term properties of the concretein accordance with AS 2327.1.

Additional Deflection due to BendingFrom Fig. 8.1,

a = 3088 mm and b = 6987 mmFrom Eq. 6.58,

θL =( )( ) ( )M I L L b L M I L b L

EI I Lse*

d*

t

t

0 02

0 0 0 0

0

2 3 2 3 26

− + − +��

��

=

( )( )( )

− × × − × × + ×

− × × × × + ×��

��

× × × ×

31 6 510 6 425 2 425 3 6987 2 425

6 6 30 9 6 425 3 6987 2 4256 2 5 510 6 30 9 6 10500

2.

..

E E

E EE E E

= 137 10 6×××× −−−− rad

θH =( )

−+�

�� −

M I M I L

EI Id*

t se*

0

tL

2

20

0θ

=( )

−× + × − × ×

× × ×− −6 6 30 9 6 2 31 6) 510 6 425

2 2 5 510 6 30 9 6137 6

E E E EE E E

E. ( .

.= 63 7 10 6. ×××× −−−− rad

Therefore, the additional bending deflections at the HME and at midspan are:

δb at the HME = 6987 63 7 10 6× × −. = 0.4 mmδb at midspan = 5250 63 7 10 6× × −. = 0.3 mm

Additional Shear DeflectionThe additional shear deflection is determined from the rotation at the HME resulting from the shearforce carried by the top T-section.

From Eq. 6.64, δs' =

kV LGs t

t

t w

0



=( )

12 14 6 10 42580 10 89 7 6

3

3. .

.× × ×× × ×

= 0.1 mm

From Eq. 6.62, θL' =

2 0LbLδs

'

3

= 2 425 0146987 10500× ×

× ×.

3 = 541 10 9×××× −−−− rad

From Eq. 6.63, θH' =

δθs

'

Lb�� − '

= 0 146987

541 10 9.� � − × − = 19 5 10 6. ×××× −−−− rad

Thus, the additional shear deflections at the HME and at mid-span are:

δv at the HME = 6987 19 5 10 6× × −. = 0.1 mmδv at midspan = 5250 19 5 10 6× × −. = 0.1 mm

Total Additional DeflectionsThe total additional deflection of the beam at the in-service condition is the sum of the bending andshear components.

( )δ δb v+ at the HME = 0.4+0.1 = 0.5 mm

( )δ δb v+ at midspan = 0.3+0.1 = 0.4 mmFor this particular example, the additional deflections due to the penetration are not significant.



9. REFERENCES

1. Standards Australia, Steel Structures, AS 4100-1990.

2. Standards Australia, Composite Structures, Part 1: Simply-Supported Beams, AS 2327.1-1996.

3. OneSteel Market Mills, Design of Simply Supported Composite Beams for Strength (To AustralianStandard AS 2327.1-1996), Composite Structures Design Manual DB1.1, 2nd Ed., February, 2001.

4. American Society of Civil Engineers, Task Committee on Design Criteria for CompositeStructures in Steel and Concrete, Proposed Specification for Structural Steel Beams with WebOpenings, Journal of Structural Engineering, ASCE, 118(12), 1992, pp. 3315-3349.

5. Chick, C.G., Dayawansa, P.H. and Patrick, M., Design of Composite Beams with Large SteelWeb Penetrations, 15th Aust. Conf. on the Mech. of Struct. and Mat., Melb., Australia, 1997,pp. 159-164.

6. Chick, C.G., Dayawansa, P.H. and Patrick, M., Strength Design of Simply-Supported CompositeBeams with Large Steel Web Penetrations, Aust. Struct. Engg. Conf., Auck., New Zealand, 1998,pp. 159-166.

7. Tse, D. and Dayawansa, P.H., Elastic Deflection of Steel and Composite Beams with WebPenetrations, The Structural Engineer, J. of the Inst. of Struct. Eng., 70(21), 1992, pp. 372-376.

8. Redwood, R.G. and Cho, S.H., Design of Steel and Composite Beams with Web Openings,J. Construct. Steel Research, 25, 1993, pp. 23-41.

9. Lawson. R.M., Design for Openings in the Webs of Composite Beams, CIRIA Special Publication51, CIRIA/SCI, London, 1987.

10. Oehlers, D.J. and Bradford, M.A., Composite Steel and Concrete Structural Members:Fundamental Behaviour, Pergamon, 1995.

11. Chick, C.G., Dayawansa, P.H. and Goh, C.C., Reliability Analysis to Determine φ-factor forStrength Design of Web Penetrations, BHP Melbourne Research Laboratories Report.

12. OneSteel Reinforcing, DECKMESHTM, September, 2000.

13. Patrick, M., The Application of Structural Steel Decking in Commercial and Residential Buildings,Malaysian Structural Steel Association Convention, (Paper 6), December, 1998.

14. Watson, K.B., Dallas, S., van der Kreek, N. and Main, T., Costing of Steelwork from Feasibilitythrough to Completion, Steel Construction Journal, AISC, 30(2), 1996.

15. Patrick, M., Tse, D. and Wilkie, R., Combined Shear-Tension Testing of the Hilti HVB ShearConnector, Structural Steel PSSC ’95 4th Pacific Structural Steel Conference, Vol. 3, Steel-Concrete Composite Structures, Pergamon, 1995, pp. 203-210.

16. Patrick, M., Dayawansa, P.H. and Watson, K.B., A New Reinforcing Component for PreventingLongitudinal Shear Failure of Composite Edge Beams, Structural Steel PSSC ’95 4th PacificStructural Steel Conference, Vol. 3, Steel-Concrete Composite Structures, Pergamon, 1995,pp. 101-108.

17. Patrick, M., Dayawansa, P.H., Eadie, I., Watson, K.B. and van der Kreek, N., AustralianComposite Structures Standard AS 2327, Part 1: Simply-Supported Beams, Steel ConstructionJournal, AISC, 29(4), December, 1995, pp. 2-40.

18. Redwood, R.G. and Shrivastava, S.C., Design Recommendations for Steel Beams with WebHoles, Can. J. Civ. Engg., 7(4), 1980, pp. 642-650.

19. OneSteel Market Mills, Design of the Shear Connection of Simply Supported Composite Beams(To Australian Standard AS 2327.1-1996), Composite Structures Design Manual DB1.2, 1st Ed.,February, 2001.



APPENDIX ANOMINAL MOMENT CAPACITY - COMPOSITE BEAM

A1 GeneralThe equations required to determine the nominal moment capacity, Mb , of a composite beam cross-section with a web penetration are presented in this appendix. It is assumed that at the penetrationthe steel beam is a doubly-symmetric I-section. The equations are derived using the cross-section atthe HME of the penetration and are based on rectangular stress block theory.

A2 Forces at the HME of Penetration

Compressive Capacity of Concrete FlangeThe design compressive capacity of the concrete flange, Fc , is given as:

Fc = F Fc c1 2+ (A1)

where, Fc1 = ( )0 85. f b D hc'

cf c r− (A2)

Fc2 = 0 85. f b hc'

cf rλ (A3)Fc1and Fc2 are the design compressive capacities of the concrete flange above and within the depthof the steel sheeting ribs, respectively. Parameter λ in Eq. A3 is dependent on the orientation of thesheeting ribs with respect to the longitudinal axis of the steel beam, expressed as a function of theacute angle θ between the sheeting ribs and the longitudinal axis of the steel beam.

λ = 10. for 0 15< ≤θ (A4)λ = 0 0. for θ >15 (A5)

Design Shear Capacity of Shear ConnectorsThe design shear capacity, fds , of a shear connector acting in a group of n connectors is given as:

fds = φk fn vs (A6)where, φ is the capacity factor for shear connectors, taken as 0.85 (see Table 3.1 of AS 2327), andthe load sharing factor, kn , is given by Eq. 8.3.4.(2) of AS 2327.1 as:

kn = 118 0 18. . /− nThe values of fvs are given in Section 8 of AS 2327.1.

Nominal Capacity of Steel Cross-sectionThe nominal tensile capacity of the steel section, Fs , is given as the sum of all the nominal tensilecapacities of the steel elements at the web penetration cross-section, i.e.:

Fs = Afi yii

ne

=1(A7)

where, Ai and fyi are the cross-sectional area and yield stress, respectively, of the componentscomprising the steel the top flange, the steel web at top T-section, the penetration reinforcement (ifpresent), the steel web at the bottom T-section and the steel bottom flange.

Maximum Compressive Force in Concrete FlangeThe maximum compressive force that can develop in the concrete flange at the HME of thepenetration, FcH , is given as:

FcH = min.( , , )F n f Fc H ds s (A8)

and the degree of shear connection at the HME of the penetration, β , is given as:



β = min.( / , )n f FH ds cc 1 (A9)

where, F cc = min.( , )F Fc s (A10)

A3 Nominal Moment Capacity of Composite Beam Cross-Section

A3.1 Compression in Part of Steel BeamWhen part of the top flange, or part of the top flange and part of the web in the top and bottom steelT-sections of the steel beam are in compression, account shall be taken of the slenderness of eachof these plate elements either partially or fully in compression, in order to determine the effectiveportion of the steel beam. The effective portion of the steel beam shall be determined in accordancewith Clause 5.2.3 of AS 2327.1.

A3.2 Nominal Moment CapacityEquations are formulated to enable the calculation of nominal moment capacities based onrectangular stress block theory. The depth of the compressive stress block in the concrete flange,dc , measured from the top face of the concrete flange, is given as:

dc = ( )F b fcH cf c'0 85. (A11)

Depending on the magnitude of the compressive force FcH in the concrete flange, the nominal

moment capacity of the composite beam cross-section with a penetration, Mb , can be determinedusing the formula below.

The following force terms will be used:

Ftf = A ftf.eff yf (A12)Ftw = A ftw yw (A13)Fr = A fr yr (A14)

Fbw = A fbw yw (A15)Fbf = A ff yf (A16)

where, Atf.eff = b teff f (A17)and beff is the effective width of the top flange of the steel beam, noting that beff equals bf whenthe top flange is compact.

Case 1:

If ( )F F FcH c1 c2≤ + and F FcH s≥ , the plastic neutral axis of the composite cross-section is located inthe cover slab of the concrete flange. The depth of compressive zone, dh , and the nominal moment

capacity of the composite cross-section, Mb , are given by:

dh = ( )D h F Fc r cH c1− (A18)

Mb = ( ) ( )F d F D t dcH h tf c f h2 2+ + −/

( )( ) ( )+ − + + + − + −F D d s t F D d s stw c h t f r c h t b2 2 2

( )( )+ − + − +F D d D s tbw c h s b f 2

( )+ − + −F D d D tbf c h s f / 2 (A19)



Case 2:

If ( )F F F Fs tf cH s− < ≤2 , the plastic neutral axis of the composite cross-section is located within thetop flange of the steel beam. The depth of compressive zone, dh , and the nominal moment capacity

of the composite cross-section, Mb , are given by:

dh = Dt b f F F F F F

b fcf eff yf tw r bw bf cH

eff yf+

+ + + + −22 (A20)

Mb = ( ) ( )F d d b f d DcH h c eff yf h c− + −2 22

/

( ) ( )( )+ + − + − + +b f D t d F D d s teff yf c f h tw c h t f2

2 2/

( )+ − + − +F D d s s Dc tr h b s2 2

( )( )+ − + − +F D d D s tbw c h s b f 2

( )+ − + −F D d D tbf c h s f 2 (A21)

Case 3:

If ( )( ) ( )F F F F F Fs tf tw cH s tf− + < ≤ −2 2 , the plastic neutral axis of the composite cross-section is

located within the top web of the steel beam. The depth of compressive zone, dh , and the nominal

moment capacity of the composite cross-section, Mb , are given by:

dh =( )f t D s t F F F F F

f tyw w c t f r bw bf tf cH

yw w

2 22

+ + + + + − −(A22)

Mb = ( ) ( )F d d F d D tcH h c tf h c f− + − −2 2/

( ) ( )[ ]+ − − + + −t f d D t D s dw yw h c f c t h2 2 2/

( )+ − + − +F D d s s Dr c h t b s2 2

( )( )+ − + − +F D d D s tbw c h s b f 2

( )+ + − −F D D d tbf c s h f / 2 (A23)

Case 4:

If ( )( ) ( )( )F F F F F F F Fs tf tw tr cH s tf tw− + + < ≤ − +2 2 , the plastic neutral axis of the composite cross-

section is located within the top stiffener of the steel beam. The depth of compressive zone, dh , and

the nominal moment capacity of the composite cross-section, Mb , are given by:

dh =( )f b D s t F F F F F F

f byr r c t r r bw bf cH tw tf

yr r

2 22

+ − + + + − − −

….(A24)Mb = ( ) ( )F d d F d D tcH h c tf h c f− + − −2 2/

( )( )+ − − +F d D s ttw h c t f 2

( ) ( )[ ]+ − − + + + −b f d D s t D s dr yr h c t r c t h2 2 2

( )+ + − − +F D D d s tr c s h b f 2

( )( )+ − + − +F D d D s tbw c h s b f 2

( )+ + − −F D D d tbf c s h f / 2 (A25)



Case 5:

If ( )( ) ( )( )F F F F F F F F F Fts f tw tr br cH s tf tw tr− + + + < ≤ − + +2 2 , the plastic neutral axis of the compositecross-section is located within the bottom stiffener of the steel beam. The depth of compressivezone, dh , and the nominal moment capacity of the composite cross-section, Mb , are given by:

dh =[ ]f b D D s t F F F F F F

f byr r c s b r bw bf cH tw r tf

yr r

22

( )+ − + + + − − − −


( )( ) ( )+ − − + + − − +F d D s t F d D s ttw h c t f r h c t r2 2

( ) ( )[ ]+ − − + + + − + −b f d D D s D D s t dr yr h c s b c s b r h2 2 2/

( )( )+ − + − +F D d D s tbw c h s b f 2

( )+ + − −F D D d tbf c s h f / 2 (A27)

Case 6:

If ( )( ) ( )( )F F F F F F F F F F F Fts f tw tr br bw cH s tf tw tr br− + + + + < ≤ − − − −2 2 , the plastic neutral axis of thecomposite cross-section is located within the bottom web of the steel beam. The depth ofcompressive zone, dh , and the nominal moment capacity of the composite cross-section, Mb , aregiven by:

dh =( )f t D D s t F F F F F

f tyw w c S b f bf r tw tf cH

yw w

2 2 22

+ − − + − − − −


( )( ) ( )+ − − + + − − − +F d D s t F d D D s stw h c t f r h c s t b2 2 2

( ) ( )[ ]+ − − + + + − −t f d D D s D D t dw yw h c s b c s f h2 2 2/

( )+ + − −F D D d tbf c s h f / 2 (A29)



APPENDIX BNOMINAL MOMENT CAPACITY - BARE STEEL BEAM

B1 GeneralThe simplified equations required to determine the nominal moment capacity of a bare steel beamwith a web penetration are presented in this appendix. The equations are derived based on thefollowing assumptions:

(a) the steel beam is a doubly-symmetrical I-section;

(b) the penetration may be either reinforced or unreinforced;

(c) the reinforcement above and below the penetration have the same dimensions; and

(d) the penetration reinforcement is located as close as practicable to the penetration edges.

In all cases, the nominal moment capacity of the bare steel section with web a penetration, Mb , shallnot exceed that of the bare steel section without the penetration, Ms .

B2 Nominal Moment Capacity of Bare Steel SectionAs discussed in Section A3.1, the effective portion of the steel beam shall be determined inaccordance with the requirements of Clause 5.2.3 of AS 2327.1. Depending on the sizes of the steelbeam and the web penetration, the nominal moment capacity of the bare steel section can bedetermined using the formulations below.

The force terms given by Eqs A12 to A16 of Appendix A will also be used.Case 1:

If F F Ftw r bw≥ +2 , the plastic neutral axis of the steel section is located within the steel web of the

top T-section. The depth of compressive zone, dh , and the nominal moment capacity, Mb , of the

steel section, Mb , are given by:

dh =( )t f s t F F F F

t fw yw t f r bw bf tf

w yw

+ + + + −22

(B1)

Mb = ( ) ( ) ( )F d t t f d t s dtf h f w yw h f t h− + − + −� �/ 2 22 2

( ) ( )( )+ + − − + − − +F D s s d F D d s tr s t b h bw s h b f2 2

( )+ − −F D d tbf s h f / 2 (B2)Case 2:

If F Ftw bw> and F F Ftw r bw< +2 , the plastic neutral axis of the steel section is located within the topreinforcement of the steel beam. The depth of compressive zone, dh , and the nominal moment

capacity of the steel section, Mb , are given by:

dh =( )b f s t F F F F F

b fr yr t r r bw bf tw tf

r yr

22

− + + + − −(B3)

Mb = ( ) ( )( )F d t F d s ttf h f tw h t f− + − +/ 2 2

( ) ( )+ − + + −� �b f d s t s dr yr h t r t h2 2

2/

( ) ( )( )+ − − + + − − +F D d s t F D d s tr s h b r bw s h b f2 2

( )+ − −F D d tbf s h f / 2 (B4)



Case 3:

If F Ftw bw< and F F Ftw r bw+ >2 , the plastic neutral axis of the steel section, dh , is located within thebottom reinforcement of the steel beam. The depth of compressive zone, dh , and the nominal

moment capacity of the steel section, Mb , are given by:

dh =( )b f D s t F F F F F

b frr yr s b r bw bf tw tf

r yr

2 22

− + + + − − −(B5)


( )+ − +F d s tr h t r 2

( ) ( )+ − + + − + −� �b f d D s D s t dr yr h s b s b r h2 2

2/

( )( ) ( )+ − − + + − −F D d s t F D d tbw s h b f bf s h f2 2/ (B6)

Case 4:

If F F Ftw r bw+ <2 , the plastic neutral axis of the steel section is located within the bottom web of thesteel beam. The depth of compressive zone, dh , and the nominal moment capacity of the steel

section, Mb , are given by:

dh =( )t f D s t F F F F

t fw yw s b r bf tf tw r

w yw

2 22

− − + − − −(B7)


( )+ − − +F d D s sr h s t b2

( ) ( )+ − + + − −� �t f d D s D t dw yw h s b s f h2 2

2/

( )+ − −F D d tbf s h f / 2 (B8)



APPENDIX C DESIGN CAPACITY TABLES

C1 GeneralThe design capacity tables given in this appendix can be used to calculate φMb and φVu at apenetration for a range of bare steel and composite beams with unreinforced web penetrations,placed concentric to the centroid of the steel beam cross-section. The values of φMb and φVu canthen be used in the moment-shear interaction equation (Eq. 6.3) to check that the strength designcriterion is satisfied.

The design shear capacities in the tables have been calculated assuming that the number of shearconnectors over the web penetration is equal to one. The parametric range covered in the tables isgiven in Table 7.1.

C2 TablesParameters in TablesThe parameters given in the design capacity tables are described below.

Column

No.

Parameter Description

2 βmax The maximum degree of shear connection that can be achieved at across-section with the web penetration, calculated with respect to thecross-section without the web penetration, i.e. βmax = Fcc / Fcc . If thevalue of β at the proposed location of the penetration is greater thanβmax , then the force in the concrete flange will be affected (see Fig. 3.3).

3 Fcc The force corresponding to βmax , i.e. F Fcc max cc= β . This is themaximum force that can be developed in the concrete flange at a cross-section with the web penetration.

4 nmax The number of 19 mm studs required to develop Fcc .

5 - 7 DesignMomentCapacities

The values of φMb.0 , φMb.5 and φMbc given are the design momentcapacities of the composite beam cross-section at the web penetration,calculated ignoring the effect of shear force, corresponding to β = 0.0,0.5 and 1.0, respectively. The design moment capacity of a bare steelbeam with the web penetration can be read directly from Column 5.

8 - 10 DesignShearCapacitiesfor CircularPenetrations

The values of φVu.0 , φVu.5 and φVuc given are the design shearcapacities of a composite beam cross-section at the circular penetration,calculated ignoring the effects of primary bending, corresponding to β =0.0, 0.5 and 1.0, respectively. These values have been calculatedassuming an equivalent rectangular penetration with L D0 0 45= . andh D0 0 9= . . The design shear capacity of a bare steel beam with the webpenetration can be read directly from Column 8.

11 - 19 DesignShearCapacitiesforRectangularPenetrations

The values of φVu.0 , φVu.5 and φVuc given are the design shearcapacities of a composite beam cross-section at the rectangularpenetration, calculated ignoring the effects of primary bending,corresponding to β = 0.0, 0.5 and 1.0, respectively. Three sets of valuesare given for L0 / h0 equal to 1.0, 1.5 and 2.0. The design shear capacityof a bare steel beam with the web penetration can be read directly fromColumns 11, 14 and 17, as appropriate.



C3 How To Use TablesThe data required to use the tables are as follows, noting that Dc = 120 mm, hr = 55 mm and300PLUS® steel must be used.

(a) Beam cross-section data: steel section, bcf and λ .

(b) Concrete grade, fc' .

(c) Number of shear connectors, nH , from the end of the beam to HME, and the force n fH ds .The value of fds corresponding to nH can be calculated in accordance with Cl. 8.3.4 ofAS 2327.1.

(d) Shape of penetration: circular or rectangular.

(e) Size of the penetration: the ratios ( h D0 / s ) and ( L h0 0/ ) for rectangular penetrations or( D D/ s ) for circular penetrations.

Rectangular PenetrationsThe calculation steps for a composite beam with a rectangular penetration are as follows:

(a) Select the appropriate design table based on bcf , fc' , λ and h D0 / s or D D/ s .

(b) Read βmax from Column 2 of the table.

(c) If βmax = 10. , it indicates that F Fcc cc= and therefore the force in the concrete flange is notaffected by the web penetration.

(d) Read Fcc from the table.

(e) If n f FH ds cc> , then the force n fH ds is limited to Fcc (see Fig. 3.3(b)). The condition

n f FH ds cc≤ can also be satisfied by ensuring nH used in the calculations does not exceedthe value of nmax given in Column 4.

(f) Calculate β = ≤n f FH ds cc/ .10 .

(g) Calculate φMb corresponding to β by linear interpolation using φMb.0 , φMb.5 and φMbc , as

appropriate, which correspond to β = 0.0, 0.5 and 1.0, respectively.

(h) Select the columns of shear capacity data corresponding to the value of ( L h0 0/ ) for thepenetration. Interpolate between the columns for intermediate values of ( L h0 0/ ).

(i) Calculate φVu corresponding to β by linear interpolation using φVu.0 , φVu.5 and φVuc , as

appropriate, which correspond to β = 0.0, 0.5 and 1.0, respectively.

(j) Use the moment-shear interaction equation given in Eq. 6.3 and check whether or not thestrength criterion is satisfied. Reference should be made to Fig. 5.1 to consider the optionsavailable in the event that the design is unsatisfactory.

For bare steel beams, the value of β is taken as zero and the design moment and shear capacities

are directly read from the φMb.0 column, and the φVu.0 column corresponding to the values of( L h0 0/ ) for the penetration.

Circular PenetrationsFor circular penetrations, the same procedure described above is used except that the shearcapacity is calculated using the values of φVu.0 , φVu.5 and φVuc given in Columns 8-10 in the tables.



INDEX TO DESIGN CAPACITY TABLES

Table No.bcf

(mm)fc

'

(MPa)λ

hD

0

s

or DDs

C1 1200 25 0.0 0.3C2 1200 25 0.0 0.5C3 1200 25 0.0 0.7C4 1200 25 1.0 0.3C5 1200 25 1.0 0.5C6 1200 25 1.0 0.7C7 1200 32 0.0 0.3C8 1200 32 0.0 0.5C9 1200 32 0.0 0.7

C10 1200 32 1.0 0.3C11 1200 32 1.0 0.5C12 1200 32 1.0 0.7C13 1600 25 0.0 0.3C14 1600 25 0.0 0.5C15 1600 25 0.0 0.7C16 1600 25 1.0 0.3C17 1600 25 1.0 0.5C18 1600 25 1.0 0.7C19 1600 32 0.0 0.3C20 1600 32 0.0 0.5C21 1600 32 0.0 0.7C22 1600 32 1.0 0.3C23 1600 32 1.0 0.5C24 1600 32 1.0 0.7C25 2100 25 0.0 0.3C26 2100 25 0.0 0.5C27 2100 25 0.0 0.7C28 2100 25 1.0 0.3C29 2100 25 1.0 0.5C30 2100 25 1.0 0.7C31 2100 32 0.0 0.3C32 2100 32 0.0 0.5C33 2100 32 0.0 0.7C34 2100 32 1.0 0.3C35 2100 32 1.0 0.5C36 2100 32 1.0 0.7



TABLE C1: bcf = 1200 mm, fc' = 25 MPa, λ = 0.0 ( i.e. sheeting ribs perpendicular to beam), h D0 s or D Ds = 0.3,

Dc = 120 mm, hr = 55 mm, Steel Grade = 300PLUS®

Shear Connection Design Moment Design Shear Capacities (kN)Steel Limits Capacities (kNm) Circular L0/h0 = 1.0 L0/h0 = 1.5 L0/h0 = 2.0

Section βmax Fcc(kN)

nmax φMb.0 φMb.5 φMbc φVu.0 φVu.5 φVuc φVu.0 φVu.5 φVuc φVu.0 φVu.5 φVuc φVu.0 φVu.5 φVuc

800WB192 1.00 1658 19 1864 2162 2379 591 591 591 591 591 591 591 591 591 591 591 591800WB168 1.00 1658 19 1587 1883 2076 587 587 587 587 587 587 587 587 587 587 587 587800WB146 1.00 1658 19 1405 1698 1870 580 580 580 580 580 580 580 580 580 580 580 580800WB122 1.00 1658 19 1107 1401 1546 574 574 574 574 574 574 574 574 574 574 574 574700WB173 1.00 1658 19 1475 1740 1902 519 519 519 519 519 519 519 519 519 519 519 519700WB150 1.00 1658 19 1244 1507 1658 515 515 515 515 515 515 515 515 515 515 515 515700WB130 1.00 1658 19 1100 1359 1492 507 507 507 507 507 507 507 507 507 507 507 507700WB115 1.00 1658 19 922 1182 1301 502 502 502 502 502 502 502 502 502 502 502 502610UB125 1.00 1658 19 840 1076 1188 757 757 757 757 757 757 670 716 685 587 627 600610UB113 1.00 1658 19 750 982 1080 707 707 707 707 707 707 626 671 641 548 588 561610UB101 1.00 1658 19 707 937 1030 707 707 707 707 707 707 627 672 642 549 589 562530UB 92.4 1.00 1658 19 576 782 860 603 633 603 603 603 603 534 586 562 467 513 492530UB 82.0 1.00 1658 19 502 703 770 562 592 579 562 562 562 498 550 539 436 482 472460UB 82.1 1.00 1658 19 447 627 696 505 535 535 505 505 505 447 499 493 392 444 432460UB 74.6 1.00 1658 19 404 579 642 461 492 492 461 461 461 408 456 456 358 410 405460UB 67.1 1.00 1658 19 360 528 587 428 458 458 428 428 428 379 423 423 332 385 385410UB 59.7 1.00 1658 19 291 439 496 351 382 382 351 382 382 311 347 347 272 328 328410UB 53.7 1.00 1658 19 269 413 470 340 370 370 340 370 370 301 336 336 263 317 317360UB 56.7 1.00 1658 19 245 381 435 318 349 349 318 349 349 282 315 323 247 297 297360UB 50.7 1.00 1658 19 217 347 399 288 319 319 288 319 319 255 296 302 223 269 269360UB 44.7 0.98 1619 18 192 318 371 269 300 300 269 300 300 238 282 287 209 251 251310UB 46.2 0.98 1619 18 175 285 345 228 259 259 228 259 259 202 256 256 177 236 240310UB 40.4 0.94 1527 17 160 260 317 206 236 236 206 236 236 182 234 234 159 222 222310UB 32.0 0.88 1111 13 113 198 242 182 212 212 182 212 212 161 210 210 141 191 193





Shear Connection Design Moment Design Shear Capacities (kN)Steel Limits Capacities (kNm) Circular L0/h0 = 1.0 L0/h0 = 1.5 L0/h0 = 2.0Section βmax Fcc

(kN)nmax φMb.0 φMb.5 φMbc φVu.0 φVu.5 φVuc φVu.0 φVu.5 φVuc φVu.0 φVu.5 φVuc φVu.0 φVu.5 φVuc











TABLE C4: bcf = 1200 mm, fc' = 25 MPa, λ = 1.0 ( i.e. sheeting ribs parallel to beam), h D0 s or D Ds = 0.3,









Shear Connection Design Moment Design Shear Capacities (kN)Steel Limits Capacities (kNm) Circular δg L0/h0 = 1.0 L0/h0 = 1.5 L0/h0 = 2.0Section βmax Fcc



































































































































TABLE C24: b c f

= 1600 mm, fc' = 32 MPa, λ = 1.0 ( i.e. sheeting ribs parallel to beam), h D0 s or D Ds = 0.7,



























































































Appendix DNOTATION

The notation used in the booklet is the same as that used in AS 2327.1 where possible.

Abw = cross-sectional area of steel web of the bottom T-sectionAf = cross-sectional area of steel flangeAr = cross-sectional area of steel plate reinforcement along top or bottom edge of penetrationAtf.eff = cross-sectional area of steel top flange, based on beff or bf as appropriateAtw = cross-sectional area of steel web of the top T-sectionAvc = effective area of concrete slab for shear = ( )3 1D D hc c r− −( )λa = distance from LME to support, away from web penetration (see Fig. 5.2(a))b = distance from HME to support, away from web penetration (see Fig. 5.2(a))bcf = effective width of concrete slab compression flange, calculated in accordance with

AS 2327.1beff = effective width of steel beam top flangebf = width of steel beam top flangebr = width of penetration reinforcementD = diameter of circular penetrationDc = overall depth of concrete slabDs = overall depth of steel beamd1 = clear depth between steel beam flanges ignoring fillets or weldsdc = depth of the rectangular stress block in concrete slabdctH = distance from top of steel flange to line of action of FctH

dctL = distance from top of steel flange to line of action of FctL

dh = depth of compression zone in the cross-section measured from the top of the cross-sectiondr = distance from outside edge of steel flange to centroid of steel plate reinforcementE = Young’s modulus of steele = the vertical eccentricity of the web penetration with respect to the mid-height of the steel

cross-section (+ve when toward the concrete compression flange, see Fig. 6.1).Fbf = capacity of steel beam bottom flangeFbw = capacity of steel web of bottom T-sectionFc = compressive capacity of concrete flange (= Fc1 + Fc2 )Fcc = compressive force in concrete flange corresponding to complete shear connection for the

cross-section without web penetration at strength limit stateFc1 = compressive capacity of concrete cover slab within slab effective widthFc2 = compressive capacity of concrete between steel sheeting ribs within slab effective width

Fcc = compressive force in concrete flange corresponding to complete shear connection for thecross-section with web penetration at the strength limit state

FcH = force in concrete flange at HMEFctH = calculated value of compressive force in concrete slab at the HME of the penetration at

strength limit state, considering the area of top steel T-section only (see Eq. 6.18)FctL = calculated value of compressive force in concrete slab at low moment end of the

penetration corresponding to FctH (see Eq. 6.20)

Fr = capacity of steel plate reinforcement along one edge of penetration = f Ayr r ≤ ( ) /f t Lyw w 2 3Ftf = axial capacity of top steel flange (= b t feff f yf )Ftw = axial capacity of top steel web



Fs = tensile capacity of the steel cross-section with the web penetration

fc' = 28-day characteristic compressive cylinder strength of concrete

fds = design shear capacity of a shear connector in a set of nH connectors according toAS 2327.1

fvs = nominal shear capacity of a shear connectorfyf = yield strength of flange in steel beamfyi = yield strength of components in steel beams, either, flange, web or steel plate

reinforcementfyr = yield strength of steel plate reinforcementfyw = yield strength of web in steel beamG = nominal dead loadG = shear modulus of elasticityGsup = superimposed dead loadHME = high-moment end of penetrationh0 = height of penetrationhr = height of the steel ribs of profiled steel sheetingI0 = second moment of area of the gross cross-section including the web penetrationIb = second moment of area of the bottom T-sectionIt = second moment of area of the top T-sectionk = a shear coefficient for I-sections (=1.2)kB = shear coefficient for bottom T-section (=1.2)kn = load-sharing factor for shear connectorskT = shear coefficient for top T-section (=1.2)L = span of the beamLo = length of web penetrationLME = low-moment end of penetrationM * = design bending moment at mid-length of web penetrationMH

* = design bending moment at HME

ML* = design bending moment at the LME

Md* = differential design bending moment across the web penetration

Mse* = secondary moment induced by Vierendeel deformations across the web penetration (see

Fig. 3.2)Mb = nominal moment capacity at the HME of web penetration ignoring the effect of vertical

shear forceMb.0 , Mb.5 and Mbc = nominal moment capacity at the HME ignoring the effect of vertical shear

force, corresponding to β = 0.0, 0.5 and 1.0, respectivelyne = number of steel elements in a cross-section with a web penetrationnH = number of shear connectors between end of beam adjacent to penetration, at HMEnL = number of shear connectors between end of beam adjacent to penetration, at LME

nmax = number of 19 mm headed stud shear connectors required to develop the force Fcc

Q = live loadR = stiffness ratio for deflection calculations (see Eq. 6.54)S = clear spacing between multiple penetrationssb = depth of bottom T-sections t = depth of top steel T-section

sb = effective depth of bottom T-section, accounting for the movement in plastic neutral axiswhen the penetration is reinforced (see Eq. 6.10)



s t = effective depth of top steel T-section, accounting for the movement in plastic neutral axiswhen the penetration is reinforced (see Eq. 6.15)

t f = thickness of steel flangetr = thickness of steel plate reinforcementt w = thickness of steel webV * = design vertical shear force at mid-length of web penetrationVu = nominal shear capacity of the beam cross-section at the strength limit state

Vt* = design vertical shear force carried by the top T-section

Vpb = nominal shear capacity of steel web of the bottom T-section ignoring the effects of bendingVpt = nominal shear capacity of steel web of top T-section ignoring the effects of bendingVb = nominal shear capacity of bottom T-section including the effects of secondary momentsVc = contribution of concrete flange to shear capacityVt = nominal shear capacity of top T-section including the effects of secondary momentsVu = nominal vertical shear capacity of a beam cross-section without a penetration

Vu = nominal shear capacity of a beam cross-section with a penetration

Vu.0 , Vu.5 and Vuc = nominal shear capacity of composite beam cross-section at the penetration,

calculated ignoring the effects of primary bending moments, corresponding to β = 0.0, 0.5and 1.0, respectively

W = design loadx = distance to a beam cross-section from support

βmax = maximum degree of shear connection that can be achieved at cross-sections within the

length of a penetration, i.e. = FF

cc

cc

β = degree of shear connection calculated using Fcc , e.g. β = F FcH cc/ at HMEδb = additional deflection in the beam due to bending deformation at the web penetrationδb( )x = value of δb at a point on the beam distance x from supportδg = deflection of the beam calculated ignoring the effects of the penetrationδg( )x = value of δg at a point on the beam distance x from support

δs' = additional shear deflection ignoring geometric continuity (see Eq. 6.64)

δt = total deflection (see Eq. 6.51)δt ( )x = total deflection at a point on the beam distance x from support (see Eq. 6.51)δv = additional shear deflection due to a web penetrationδv( )x = value of δv at a point on the beam distance x from supportφ = capacity factor relevant to a strength limit stateλ = factor accounting for angle between sheeting ribs and steel beam - see Fig. 5.2.2.2(b)µb , µ t = dimensionless ratio relating secondary bending moment contributions of concrete and

web penetration reinforcement to the product of the plastic shear capacity and depth of thesteel T-section (see Eqs 6.6 and 6.12, respectively)

θ = acute angle between the steel ribs of a composite slab and longitudinal axis of steel beamθH , θL = rotations due to bending deformation at the HME and LME of penetration, respectively

θH' , θL

' = rotations due to shear deformation at the HME and LME of penetration, respectively

νb , ν t = aspect ratio L s0 / b and L s0 / t for bottom and top T-sections, respectively

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