22|The Structural Engineer – 21 February 2006

paper: persaud/symons

SynopsisTimber frame buildings may have low embodied energy, buthave the disadvantage of low thermal mass. Steel and concretecomposite construction provides good thermal mass but isbecoming less economic with the increasing cost of steel. Thispaper presents results from testing of a composite system thatallows the use of timber with improved structural efficiencyand increased thermal mass. The composite system consists ofa concrete slab cast on profiled steel decking actingcompositely with glue-laminated timber beams. Compositeaction is achieved with coach screw shear connectors betweenthe beams and slab. The connectors have been tested in ‘push-out’ shear tests and a three-point bend test of a full-scale floorslab has been completed. The composite system is more thanthree times as stiff and almost twice as strong as the samebeam/slab configuration without composite action. Existinganalytical and design methods are compared to finite elementpredictions and the experimental results and show goodcorrelation.

NotationA Cross sectional area (with subscript 1 or 2 to denote

concrete or timber respectively)E Modulus of elasticity(EI)eff Effective flexural stiffness determined from the γ design

method F Shape factor for shear deformable beamsG2 Shear modulus of timberI Second moment of areaK Slip modulus (subscript ser for serviceability or u for an

ultimate limit state value)M Bending moment (with subscript p to denote fully plastic

and y to denote yield with additional subscript d to indi-cate a design value or with subscript R,Partial to denotean ultimate moment of resistance of a composite crosssection)

N The internal normal force P Applied vertical loadRd Design shear resistance of the connectorb Breadth of component d Diameter of nail (or screw)e Centroidal distance between componentsf1cube Mean concrete cube strengthf1cyl Concrete cylinder strengthfh Embedment strength of timber (additional subscript d

indicates a design value)ft Tensile strength of timber (additional subscripts k or

mean indicate characteristic or mean strengths respec-tively)

fm Bending strength of timber h Height of component k Slip stiffness of shear connectionl Spanm Number of shear connectors p Sinusoidal distributed load (used with subscript 0 to

indicate the central value)s Connector spacingt Depth of penetration of connector into timber w Deflection x Distance between support and cross section being consid-

ered y Depth of the neutral axis in concrete δ Mid-span deflection of timber beam aloneγv Material safety factorρk Density of timberσ Stress in a material (additional subscripts M or N for

bending or normal stress)σy Yield stress of steel

IntroductionTimber-concrete composite construction is becoming increasinglycommon in continental Europe, in particular for the refurbish-ment of old buildings.This efficient floor system consists of timbermembers in the tensile zone, a concrete slab in the compressionzone and a shear connection between timber and concrete. Forrefurbishment applications a layer of concrete is cast in situ overa shear connection system fitted to an existing timber floor.However, there is also developing interest in using timber-concrete composite construction in new buildings. This is moti-vated by the low embodied energy of timber, a need for thermalmass and the increasing cost of steel.

Unfortunately buildings of pure timber construction do nothave the thermal mass necessary to contribute usefully topassive heating and cooling.Passive heating and cooling uses theheat capacity of the building itself to moderate internal temper-atures, and therefore reduces energy requirements for heatingand air-conditioning. Concrete has a high heat capacity andconsequently concrete buildings have an inherently highthermal mass. Timber-concrete composite construction allowsstructurally efficient use of both timber and concrete whilstretaining the high heat capacity of a concrete floor slab. Tomaximise the passive heating and cooling effect the slab soffitshould be exposed. Should this be aesthetically undesirable apermeable ceiling may be used. Kendrick1 has shown that up to85% of the passive thermal effect of an exposed soffit can beobtained with a thin perforated suspended false ceiling with anopen area of only 20%.

An efficient shear connection allows beam depths to be signif-icantly reduced when compared with a non-composite system.Composite action can be achieved by a variety of connectionsystems.Ahmadi and Saka2 showed that a reasonable improve-ment in the stiffness and strength of unconnected timber andconcrete floors can be achieved by connecting the timber andconcrete using plain vertically driven nails.Mungwa3 and Sonda4

extended this concept by testing composite floors connected usingspecially made vertical shear connectors. A refinement to thevertical type connection was proposed by Capozucca5 that allowsan axial prestress to be applied to the connector, thus increasingthe frictional contact force between the concrete and timber.Bathon and Graf6 proposed a system that uses a steel mesh,glued into a continuous slot in the timber along its length,as theshear connection. Fontana and Frangi7 tested a connectionsystem consisting of a recess cut into the timber across its width.This connection was further strengthened using a verticallyinstalled dowel to prevent separation of the timber and concrete.A drawback of vertical dowel connectors is that the relative slipbetween concrete and timber is primarily resisted by bending ofthe connector. Meierhofer8 has shown that installing connectorsat an angle to the interface of the timber and concrete can signif-icantly increase slip stiffness. When the timber slips relative tothe concrete the connectors are loaded axially as well as inbending. Similar tests are reported by Fontana and Frangi7. Amore detailed review of shear connection systems is given byPersaud9.

The long term behaviour of timber concrete compositesdepends on the creep of the concrete, timber and the shearconnection.Ahmadi and Saka2 tested a composite system undera sustained live load and observed that the deflection tended tostabilise after about 100 days, with a final midspan deflectionabout three times the instantaneous deflection. Tests byMeierhofer8 and Sonda4 on composite systems with various shearconnection systems showed similar behaviour.

Design and testing of a composite timberand concrete floor system

RichardPersaud

Dr DigbySymonsUniversity ofCambridge, Departmentof Engineering,Trumpington Street,Cambridge, CB2 1PZ

Received: 06/05Modified:Accepted: 08/05Keywords: Floors,Compositeconstruction, Testing,Beams, Glulam, Slabs,Eurocode 5, Finiteelement analysis

© Richard Persaud & DrDigby Symons

21 February 2006 – The Structural Engineer|23

paper: persaud/symons

Timber concrete composite systemAlthough several shear connection systems have been investi-gated or patented, many have impractical complex installationprocedures.The choice of connectors also depends on the type ofconstruction (pre-cast or in situ). In order to be successfullypromoted, timber concrete composite systems should be practi-cal and use readily available components. With this in mind,ordinary zinc plated steel coach screws were selected for thisexperimental investigation.

In order to minimise on-site construction time profiled steeldecking permanent formwork can be used to support a concretefloor slab cast in situ. It is lightweight, requires minimal main-tenance, adds stiffness to the concrete slab it is supporting,provides structural bracing during construction and has good fireresistance characteristics.The deck can also provide a temporaryplatform for access and storage of materials during construc-tion. The Holorib decking system (Richard Lees Steel DeckingLtd) was selected for these experiments.

Proposed applicationA typical new building application for the proposed timberconcrete composite system is a 15m wide office building built ona 7.5m × 6m grid.Profiled steel decking would be used as perma-nent formwork spanning between secondary glulam beamsspaced at 2m centres.These secondary beams span onto centraland edge primary glulam beams. The work described in thispaper has focused on the design and testing of the key compo-nents of this system:the secondary beams,slab and shear connec-tors.

Preliminary design of the composite system considered thesecondary beams as simply supported with a span of 7.3mbetween edge and primary beams. Design criteria were takenfrom the relevant sections of Eurocode 5, Part 1.110.An imposedfloor load of 3.5kN/m2, typical for office buildings, was used andallowance was made for a fire exposure of 1h. A 100mm thickconcrete slab was chosen, cast in situ on Richard Lees HoloribS280 0.9mm thick decking. Important considerations for thechoice of shear connector included ready availability and asimple,unambiguous, installation procedure.To minimise on-sitework a maximum of one shear-connector would be used in eachtrough of the decking at its intersection with the glulam beam.Consequently the shear connectors chosen for these experimentswere 16mm diameter,150mm long,zinc-plated steel coach screwsto be placed vertically, one per trough, as shown in Fig 1.Preliminary design suggested an adequate beam cross section ofgrade GL32 glulam timber would be 140mm wide and 630mmdeep.

Experimental workThe first phase of experimental work investigated the perform-ance of the shear connectors through push-out shear tests. Thesecond phase studied the behaviour of a full-scale floor slab in athree-point bend test.

Push-out shear testsThe push-out shear test has become the standard method ofestablishing the strength and fatigue performance of shearconnectors for steel and concrete composite beams. The typicalform consists of a short section of beam connected to two smallconcrete slabs by the shear connectors. The slabs are beddeddown onto a reaction floor and a load is applied to the upper endof the beam. The relative slip between beam and slab is thenmonitored.

Push-out shear tests of this geometry were used to test theperformance of the coach screw shear connectors in the timberand concrete composite system.The purpose of the experimentswas to quantify the load-slip relationship of the shear connectors,and in particular to determine the initial stiffness (slip modulus)of the connectors, which is necessary to check the assumptionsused in the initial design.

Fig 2 shows the shear test specimen. The concrete slabs oneither side of the timber beam were 1000mm long and 600mmwide. Each was 100mm deep and cast on Holorib S280 0.9mmdecking.Each steel decking sheet was initially fixed to the timberbeam using 4.5 × 20mm long self-drilling,self-tapping screws,twoper trough. In each trough of the decking, an ordinary 16mmdiameter, 150mm long coach screw was screwed into a pilot hole(drilled to a predetermined depth in the timber of 90mm) to serveas shear connectors between the timber and concrete. A total often coach screw connectors were used, five on each side of thetimber beam.A layer of A142 mesh reinforcement was placed ata depth of 30mm from the surface of the concrete to control crack-ing. Concrete cube strength at the time of testing was approxi-mately 32MPa. The glulam timber beam was Grade GL32, 630× 140mm in section and 1000mm long. The timber moisturecontent was 10.1%.

Two specimens were tested which gave almost identicalresponses (the maximum load recorded differing by less than 2%).Fig 3 shows the load per connector against slip response of oneof the specimens.The load was applied in loading and unloadingcycles. The maximum load in each cycle was increased in incre-ments of 2kN/screw up to 24kN/screw,after which a final loadingcycle was applied.The maximum load sustained by the shear testspecimen was 30kN/screw. At maximum load the slip of thetimber relative to the concrete was about 10mm. The test was

Fig 1. (left)Cross-section ofcomposite system

Fig 2. (right)Push-out shear testspecimen

Fig 3. Load-sliprelationship forcoach screw shearconnector

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finally stopped at a slip of 45mm, at which point the load haddropped to 15kN/screw.The concrete remained undamaged andnegligible horizontal separation between the timber and theconcrete was observed throughout the test.

The coach screws had an initial elastic stiffness of15.8kN/mm/screw up to an elastic limit of approximately 0.6mmslip (a load of approximately 10kN/screw). Beyond this pointsignificant hysteresis was observed in the loading and unloadingcycles. At a load of 24kN/screw a permanent slip of approxi-mately 2mm was measured after unloading. This softeningresponse gave an extremely ductile failure mode,which is attrib-uted to crushing failure in the timber around the screws andplastic deformation of the screws themselves.

The coach screws were observed to have failed in two distinctmodes.Some screws failed with a single plastic hinge developingat the interface of the concrete and timber,while others developeda double hinge, the additional hinge occurring in the portion ofthe screw embedded in the timber. The timber in front of thescrews showed significant bearing (compression) failure.

Full-scale slab testBased on the proposed building application a full-scale test wasperformed of a beam and slab composite system 7.5m long and2m wide.The slab was loaded by a single point load at mid-spanand the deflection, slip, strain profile in the cross section, andlongitudinal strain distribution on the surface of the concrete slabwere measured.

The test rig used for the full-scale composite beam and slab test

is shown in Fig 4. Pedestals and lateral restraints shown weresafety features that would have prevented excessive rotationsand/or lateral displacements in the event of unexpected insta-bility.These were never in contact with the specimen during thetest.

The preliminary design of the composite system was revisedbased on the push-out shear test results.This suggested a slightlywider but shallower timber section would be appropriate.A gradeGL28 glulam timber beam with a 160 × 405 mm cross-sectionwas used in the test. The measured moisture content of thetimber at testing was 9.6% (mean of 6 tests).The beam was 7.5mlong and was simply supported over a span of 7.3m. The shearconnection system tested in the push-out tests was reproducedfor this full-scale test:a combination of two 4.5 × 20mm long self-drilling self-tapping screws and one 16 × 150mm long coachscrew was used in each trough of the decking.The strength of theconcrete was checked prior to the slab test by testing three stan-dard 100mm × 100mm cubes. The average cube compressionstrength f1cube of the concrete used in the slab was 48 MPa.

Before load testing the natural frequency of the compositebeam and slab was determined using accelerometer data from animpulse response test. The response gave a measured value ofnatural frequency of 8.9Hz.

The composite beam and slab was load tested in three-pointbending. The load was applied in cycles, in increments of 20kNup to 120kN, before continuing to collapse. The relationshipbetween the load and mid-span deflection obtained from the testis shown in Fig 5.The relationship between the load and the rela-tive slip between the concrete and the timber at the supports (endslip) is shown in Fig 6.

The maximum load recorded (at failure) in the full-scale testwas 173kN, at a central deflection of 74.9mm. The compositesystem showed approximately linear elastic behaviour up toabout 50kN.There was no measurable end slip until the appliedload exceeded 14kN, this lag in response is attributed to frictionbetween the slab and timber beam.At the maximum load the endslip was 5.7mm.

No cracking in the concrete or separation between the deckingand timber was observed during the test and collapse occurreddue to a combined bending and tension failure in the timberbeam.This brittle failure of the timber was initiated in the regionof a knot in the lower laminates at mid-span, causing a crack topropagate vertically to about mid-depth of the timber,then longi-tudinally through the timber to about quarter-span (see Fig 7).

Throughout the test, strain gauges and extensometers wereused to monitor strains in the timber beam and concrete slabat mid-span. Three strain gauges were positioned on the sideof the timber beam: near the top, mid-depth and bottom of thebeam. Strain gauges were also placed on the top surface of theconcrete slab and clip gauge extensometers were placed acrossthe gap between adjacent troughs on the slab soffit (see Fig 7).These strain measurements may be extrapolated to give astrain profile through the whole depth of the composite section.Fig 8 shows the strain profile in the composite system at midspan at intervals of 20kN applied load. The figure shows thechange in position of neutral axis in the timber beam through-out the test. The strain profiles for 20kN and 40kN show thatfor the initial elastic response of the composite system the

Fig 4. Arrangement usedfor full-scale test

Fig 5. Load against mid-span deflection forfull-scale floor slab:experiment and FEprediction

Fig 6. Load against end slipfor full-scale floorslab: experiment andFE prediction

Fig 7. Failure of timberbeam at mid-span

21 February 2006 – The Structural Engineer|25

paper: persaud/symons

neutral axis of the timber is positioned near the interface of theslab and beam and the majority of the timber beam depth isworking in tension. However, as the applied load is increased,and the shear connection begins to yield, the axial force in thetimber beam remains approximately constant whilst thebending moment continues to increase.The neutral axis in thetimber beam drops towards mid-depth and the stiffness of thecomposite section degrades.

The slope of the strain profile is the curvature at that point. Ifit is assumed that the deflected shape of the timber is sinusoidalit can be shown that the slope of the measured strain profiles inthe timber beam give curvatures which are in very good agree-ment with the measured displacements of the composite section.However,the slope of the measured strain profiles in the concreteslab show a somewhat higher local curvature. The disparity islargest at the highest applied loads. This difference may beexplained by localisation of the bending in the concrete slab at thethin section between troughs under the loading point.

Strain gauges positioned at the centre and edges of the top ofthe slab at mid-span give an indication of the variation ofcompressive strain across the width of the slab. These straingauge results are shown in Fig 9. The variation is due to shearlag in the slab width.Because both the variation (< 25%) and themagnitude of the compressive strains are relatively small itseems reasonable to assume in the design that the full flangewidth of 2m contributes to bending resistance and the effect ofshear lag may be neglected.

Available design toolsDesign of timber concrete composites requires consideration ofpartial composite action. Because of the flexibility of the shearconnection between timber and concrete, slip occurs at the inter-face and the assumption of plane sections remaining plane doesnot hold for the composite section as a whole. (Fig 10 from Blasset al.11).

Existing design methods and guidance for timber concretecomposite construction are somewhat limited in the UK. Weexamine here relevant sections of Eurocode 5, an elastic analyt-ical solution for partial composite action, and the Elasto-Plasticmethod proposed by Fontana and Frangi7.

Material and section propertiesMaterial properties used in the design and analysis methodsconsidered here are summarised in Table 1. Experimentallydetermined values are listed together with Eurocode designvalues.

Glulam timber beamThe elastic modulus of the grade GL28 glulam timber beam wasexperimentally determined from a three-point bend test prior tocasting the slab above it. A load P was applied to give a centraldeflection δ of approximately 10mm.The Young’s modulus E wascalculated using the elastic deflection formula, taking account ofshear deformation,for the central deflection of a simply supportedbeam under a central point load:

E IPl

FG APl

48 42 2

3

2 2= +d ...(1)

where l is the span (7.3m), I2 the second moment of area, A2

the cross-sectional area and F the shape factor of the glulamtimber beam (F = 3/2 for rectangular sections). G2 is the shearmodulus of the timber and is assumed to be equal to E2/16.

Bearing strength was experimentally determined by indenta-tion tests. Both the experimentally determined modulus andbearing strength are in good agreement with Eurocode designvalues.

Characteristic (Eurocode) tensile and bending strengths arequoted in Table 1.In order to obtain a prediction of the failure loadof the composite beam mean tensile (ft,mean = 31.3 MPa) andbending (fm,mean = 41.7 MPa ) strengths for GL28 timber werecalculated from the characteristic strengths assuming a log-normal function with a coefficient of variation of 0.2 (followingFontana and Frangi7).

Concrete slabFor the purposes of design, concrete was considered to be anisotropic linear elastic material.The Young’s modulus of concreteE1 (in MPa) was calculated according to the CEBFIP12 recom-mendation:

.Ef

2 15 1010

cube1

4 13#= ...(2)

where the measured average cube strength ft,mean= 47.7 MPa,and therefore E1= 36.2 GPa.

Although the total depth of the concrete slab is 100mm, theslab does not have a uniform thickness because of the deckingprofile. As a result the axial and bending stiffnesses are lowerthan those for a slab with a uniform depth of 100mm. A two-

Table 1: Summary of material properties Property Unit Eurocode Experimental Eurocode

value value

Glulam timber Grade: GL28/GL32Elastic modulus E2 MPa 12085 /– 12000/13500Shear modulus G2=E2/16 MPa 755 /– 750/844Tensile strength ft,k MPa – 21/24Bending strength fm,k MPa – 28/32Characteristic density ρk kg/m3 – 410/440Mean density ρm kg/m3 – 490/530Bearing/embedment strength fh MPa – /31.8 28.6/30.7(for connectors d = 14.85mm)

ConcreteCube strength f1cube MPa 47.7 –Elastic modulus E1 MPa – 36200Coach screws (16mm diameter, 150 mm long)Ultimate strength (in tension) kN 49.6 –Yield stress σy (in tension) MPa 321.0 355.0Yield moment (in bending) My kNmm 140.0 155.0Plastic moment (in bending) Mp kNmm 421.0 465.0

Fig 8.Measured strainprofile in compositesection at mid-spanthroughout test

Fig 9. Distribution acrosswidth of slab ofcompressive strain intop surface of slab

26|The Structural Engineer – 21 February 2006

paper: persaud/symons

dimensional finite element model of a unit of the actual crosssection of the concrete slab was used to determine the depth,centre-line and Young’s modulus of an equivalent slab of uniformthickness with the same axial stiffness, centroidal position andbending stiffness. For this calculation it was assumed that axialcompression of the concrete slab would prevent tension develop-ing and therefore the uncracked concrete section was consid-ered. The equivalent slab was determined to have a depth of59.8mm,a centre-line 72.1mm above the top surface of the timberbeam and an elastic modulus of 0.975E1 (see Fig 11).

Shear connectorsThe coach screw shear connectors were experimentally tested intension and bending. The strengths obtained are listed in Table1.Initial design values assume a yield stress σy = 355MPa,some-what higher than the 321MPa measured, and therefore giveslightly higher strengths than those measured.

Design of shear connection systemStiffnessEmpirical expressions in Table 7.1,Section 7.1,of Eurocode 5 part1-110 can be used to determine the instantaneous slip modulusKser (resistance to slip in N/mm) of different fastener types usedfor a single shear plane timber to timber connection. For a steelto timber or concrete to timber connection (where one end of theconnector is essentially held rigidly) these expressions for Kser

should be doubled (see also Aicher et al.13). For dowels, bolts,screws or nails inserted into predrilled holes for a concrete totimber connection the slip modulus is therefore given as:

K d232 .

serm

1 5= t ...(3)

where d is the nail diameter (0.9d for a screw) and ρm is themean density of the timber.This expression is in excellent agree-ment with the experimentally measured initial slip modulus ofthe push-out shear tests described in this paper (Table 2).

Kser should be used for design for the serviceability limit state.For the ultimate limit state a reduced slip modulus Ku=2/3Kser

should be used. Alternatively, Ceccotti et al.14 recommend thatexperimental slip response data should be used. They suggestthat the secant modulus of the slip response at 40% and 60% ofthe ultimate shear strength should be used for Kser and Ku respec-tively.

StrengthThe ultimate strength of a doweled connection system in shearmay be determined using Johansen’s models, for which equationsare outlined in section 8.2 of Eurocode 5 part 1-110. Both thefastener and the wood are assumed to be perfectly plastic at theultimate limit state. The models predict a limit state load forseveral modes of failure. The governing mode depends on thecross section and yield strength of the fasteners, the thicknessesof the connected components and the ‘embedment strength’ of thefasteners.The embedment strength fh (or crushing strength) is ameasure of the resistance of the fastener to being forced laterallyinto the timber. This can be obtained from the empirical rela-tionship in section 8.3 of Eurocode 5, Part 1.110 for predrilled

holes:

. .f d0 082 1 0 01h k= -t _ i ...(4)

where d is the dowel diameter (or the shank diameter forscrews).

Although there are several failure modes outlined in theEurocode for timber to timber doweled connections, the assump-tion that the concrete remains undamaged in a concrete to timberdoweled connection limits the modes of failure to three.These areshown in Fig 12: Mode A, where the screw tears through thetimber; Mode B, where the screw develops a single plastic hingeat the interface between the timber and concrete; and Mode C,where the screw develops two plastic hinges.

The design resistance Rd of dowel type connectors according toJohansen’s theory is given as follows:

.

...( )

...( )

...( )

minR

f td

f tdf dt

M

M f d

Mode A

Mode B

Mode C

24

1

2 3

5

6

7

,

,

,

,

, ,

d

h d

h d

h d

y d

y d h d

2= + -

R

T

SSS

V

X

WWW

Z

[

\

]]]

]]]

_

`

a

bbb

bbb

where the subscript d indicates design values of strength(according to the appropriate material safety factors), t is thedepth of penetration of the dowel into the timber, and My is theyield moment of the shear connector. Note that we neglect theadditional ‘rope effect’ term in the Eurocode, which may be

Fig 10. (left)Partial compositeaction (from Blass etal11)

Fig 11. (right)Equivalent concreteslab of uniformdepth

Fig 12. Shear failure modesand designresistance versusembedment depth tof a connector

21 February 2006 – The Structural Engineer|27

paper: persaud/symons

allowed for the axial withdrawal capacity of the connector.Fig 12shows how the design resistance of each mode depends on t.Thedesign resistance is given in the non-dimensional form

/R M f d,d y h d and plotted against the non-dimensional dowelpenetration / /t M f d,y h d . The switch from mode A to mode Boccurs at / /t M f d,y h d = 1.4. Maximum design resistance isobtained with the switch from mode B to C with a depth of pene-tration / /t M f d,y h d = 4.9. For the 16mm coach screws tested inGL32 timber this gives an optimal penetration depth t of approx-imately 90mm.No further benefit is obtained from greater pene-tration as the design resistance is then limited to the doublehinge failure mode C. Once the dowel or screw will fail in ModeC the design resistance is relatively insensitive to the timbergrade. The difference between using GL28 and GL32 timber isonly 3.5%.

Using unmodified values of timber embedment strength fh

and the fully plastic bending moment of the connector Mp theseequations give a good prediction of the ultimate shear failure loadmeasured in the push-out shear tests (see Table 2). The coachscrew connectors in the push-out test were observed to havefailed in either Mode B or C, indicating that the 90mm depth ofpenetration was indeed close to optimal.

Two additional failure modes that should be checked are shearfailure of the connector and local crushing of the concrete.However, in practice these modes will not dominate for a timberto concrete connection. Design rules for these modes may befound in Eurocode 4,part 1.115.The shear capacity of the connec-tor can be determined from equation 8 using the yield strengthof steel σy and the fastener cross sectional area.

. / /R d0 8 4d y v2# v r cc m ...(8)

where γv = 1.25 is the material safety factor.

The design shear resistance offered by the concrete can bedetermined from equation 9 using the concrete cylinder strengthf1cyl= 0.8f1cube, and the elastic modulus of concrete E1.

. /R d f E0 29.

cd yl v2

1 10 5

# c_ i ...(9)

Eurocode 4,part 1.1,also requires that the minimum depth ofembedment of the shear connector in the concrete should not beless than four times the connector diameter d.

Partially composite beam behaviourStiffnessThe initial stiffness of the composite system can be determinedeither from an analytical or numerical solution to the differen-tial equation for partial composite action (Stüssi16), or from theapproximate ‘gamma method’ described in Annex B of Eurocode5 part 1-110. More detail is given in the Appendix to this paper.The gamma method provides an effective flexural stiffness (EI)eff

of the composite beam as a function of the slip modulus K andspacing s of the shear connectors.This effective stiffness may beused in standard elastic deflection calculations for serviceabilitydesign.Eurocode 5 specifies different deflection limits for instan-taneous and long term loading for the serviceability limit state(span/300 and span/200 respectively). Serviceability design forlong term loading requires a reduction of all the elastic materialconstants, including the slip modulus Kser, to account for creep.

Comparison with experimental resultsIn Fig 13 the deflected shape predicted by the exact analyticalsolution and by the approximate gamma method may becompared with deflections measured experimentally under acentral point load of 40kN. Note that for the gamma method we

have plotted the cubic solution for 3 point bending of a beam witheffective stiffness (EI)eff (but no separate shear deformation term).The predicted and measured central deflection stiffnesses arealso listed in Table 3. The difference between the exact andapproximate solutions is very small and there would be even lessdifference between the methods for the case of a uniformlydistributed load. Both methods closely match the experimentdespite the fact that they (unlike the finite element modeldescribed below) do not include shear deformation of the indi-vidual sub-components.For increased loads the problem is a non-linear one, with plastic slip and large deflections. Both of theanalytical solutions, because they are linear elastic solutions,will not give good results beyond the elastic range.Consequentlythe effort required to find an exact elastic analytical solution isunlikely to be justifiable in the design process and the gammamethod should be adequate for most serviceability calculations.

Ultimate strengthAnalytical solution and Gamma method: The gammamethod,although a linear elastic method, is used in the Eurocodefor ultimate limit state design by using a reduced elastic stiffnessKu = 2/3Kser for the connectors.We therefore use this approach topredict collapse loads for the composite beam using both char-acteristic and mean material strengths and take the sameapproach with the analytical method.When using these methods,the designer needs to check the maximum shear force in theconnectors and the stresses in the timber under combinedbending and tension, according to the relevant sections inEurocode 5. Ultimate strength is defined by the limit of eithercriterion.A disadvantage is that the design calculations requireknowledge of the instantaneous slip stiffness Kser, to which thesemethods are very sensitive.

Predictions of the failure load based on characteristic andmean timber strengths are given in Table 3. The analyticalmethod calculation based on mean strengths slightly underesti-mates the collapse load of the composite beam whilst the gammamethod based on mean strengths gives an overestimate.Nevertheless, the gamma method prediction based on charac-

Table 2: Summary of shear connection propertiesProperty Unit Eurocode experimental EuroCode

value valuePush out shear test

Initial slip stiffness Kser kN/mm/screw 15.8 15.8Yield strength (in shear) kN/screw 17.3 18.7 (My)Ultimate strength (in shear) kN/screw 30.0 32.4 (Mp)

Table 3: Predictions of analytical methods and FE analysisInitial stiffness First yield Ultimate strength Deflection at ULS

(KN/mm) (kN) (kN) (mm)

Predictions for non-composite and fully composite systems (ft,mean & fm, mean)Timber beam only 1.23 – 98.1 81.8Fully composite system 7.38 – 298.6 46.7Partially composite systemExperiment 4.06 40.9 172.6 74.9Analytical solution predictionsft,k & fm,k 4.24 – 121.3 32.7ft, mean & fm, mean 4.24 – 180.6 48.6 Gamma method predictionsft,k & fm,k 4.32 – 147.5 39.7ft, mean & fm, mean 4.32 – 219.6 59.1Elasto-plastic method predictionsft,k & fm,k – – 142.6 –ft, mean & fm, mean – – 177.7 –FEA 2D model 3.78 37.8 176.2 63.7FEA 3D model 3.61 46.4 168.3 60.4

Fig 13. Deflected shape ofhalf-span ofcomposite beamunder a 40kN centralpoint load

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teristic timber strengths gives a safety factor of 1.4 and shouldbe suitable for design.Elasto-plastic method: The elasto-plastic design method is anultimate limit state design method proposed by Fontana andFrangi7. The principal assumptions are that at the ultimatesection capacity the connectors are perfectly plastic and thetimber has attained its ultimate bending capacity. It is assumedthat timber and concrete behave linear elastically and that planesections remain plane within these subcomponents. The tensilestrength of concrete is neglected. The advantage of this methodover the gamma method is that, rather than considering theelastic stiffness of the connectors, the connectors are idealised asperfectly plastic.The sensitivity of the results to the slip stiffness,inherent in the elastic methods, is therefore eliminated.The ulti-mate moment of resistance MR,Partial of the partially compositebeam can be calculated from:

M mRh

hy b h

2 3 6,, dR Partial M

21 2

22

2

= + - + ve o ...(10)

where hi is the depth and bi the width of the sub-components. yis the depth of the neutral axis in the concrete (sub-component 1):

yb E

mR h Eh

, M

d

2 1 1

2 21#=

v...(11)

σ2,M is the bending stress in the timber cross-section at the ulti-mate limit state for timber subjected to combined bending andtension and therefore:

ff1,

,M

t

Nm2

2= -v

ve o ...(12)

where ft and fm are the tensile and bending strength of timberrespectively and σ2,N is the mean tensile stress in the timbercross-section:

AN

AmR

, Nd

22 2

= =v ...(13)

m is the number of shear connectors placed between thesupport and the critical cross-section (where each connector hasshear resistance Rd).

Using the shear resistance Rd of the connectors of30.2kN/connector from the shear test and the mean strengths ofthe timber, the load bearing capacity of the composite floor slabwas determined to be 177kN (see Table 3). This is very close tothe experimentally measured collapse load of 173kN.

The elasto-plastic method gives a good prediction of the ulti-mate strength of the composite system tested (see Table 3) andis more extensively validated by Fontana and Frangi7.

Finite element simulationsThe elastic and elasto-plastic models of partial composite behav-iour described above have been shown to give good predictions ofstiffness and ultimate strength respectively. However, neitherapproach provides predictions of both load and deflectionthroughout the non-linear response observed experimentally.Simple non-linear finite element (FE) models may be used topredict the complete response of the composite system and conse-quently can be useful tools in the design process. Additionaladvantages of FE analysis are the opportunity to model discreteconnectors and to consider three-dimensional effects.FE modelsof the composite system tested are described here.

Details of FE modelsThe finite element package ABAQUS 6.4.1 was used to model thecomposite timber and concrete system. Because of symmetry itwas only necessary to model half the span. Two types of FEmodel were used to investigate the behaviour of the composite:a simple two-dimensional analysis with both the timber andconcrete modelled using 2D shear deformable ‘B21’ beamelements and a second, three-dimensional, model in which theconcrete slab was modelled with four node,finite strain ‘S4R’ shellelements (with the timber beam modelled using 3D sheardeformable ‘B31’ beam elements).

Timber and concrete were modelled as linear elastic materi-als in ABAQUS with the elastic properties listed in Table 1.The

depth and elastic modulus of the concrete slab were modified asshown in Fig 11 to account for the non-uniform cross section.

Each shear connector was modelled as a discrete spring witha non-linear force displacement relationship.These springs werefixed to rigid links attached to the beam (or shell) elements usedto model the timber beam and concrete slab (see Fig 14).The non-linear response modelled was chosen to match the experimentallyobtained force-displacement response from the push-out sheartests (Fig 3), neglecting the loading cycles, as closely as possible.Although the push-out shear tests were conducted with GL32timber and the full-scale test with GL28 the load/slip responseof the shear connectors is expected to be relatively insensitive tothe timber grade and therefore very similar (recall that inJohansen’s models for connector failure strength the differencebetween GL28 and GL32 timber is only 3.5%).

Multiple step non-linear analysis was used,to account for bothnon-linear behaviour of the connectors and any geometric non-linearity caused by large displacements.A mesh sensitivity checkwas carried out to determine a suitable mesh density of the finalmodels. Based on this analysis, the mesh adopted used 15mmlong B21 or B31 beam elements and 75mm × 50mm S4R shellelements.

Comparison of results from FE simulations with experimentLoad/deflection responseThe load / deflection response of the 3D FE model may becompared with the experimental response in Fig 5 (the responseof the 2D model was very similar and is omitted for clarity).TheFE results closely simulate the behaviour of the composite floorin the elastic range,and up to about 100kN.Predictions at subse-quent loads are less accurate. The FE load deflection curve isinitially slightly less stiff than the experiment but is stiffer forloads over 100kN. The deflected shape predicted by the 2D FEmodel at 40kN is shown in Fig 13 and is slightly greater than theexperiment.However,at the collapse load,the deflection from theFE analysis was lower than the experiment by 16% and 17% forthe two and three dimensional models respectively (see Table 3).The lower experimental stiffness observed in the final stages islikely to be due to cracking in the concrete slab. The FE modelsdiscussed here use an uncracked flexural stiffness throughout.

Ultimate loadFailure predictions were obtained considering combined bendingand tensile stresses in the timber and the mean strengths fm,mean

and ft,mean. The predicted loads and deflections at failure of thetimber beam are given in Table 3. The 2D finite element modelpredicted that collapse of the composite floor slab would occur at176kN,while the 3D finite element model gave a predicted failureload of 168kN, both within 2% of the experiment. However,because the FE models do not account for concrete cracking,bothmodels underestimate the deflection at failure by about 15%.

End slipThe predicted end slip from the 3D FE model may becompared with the experimental response in Fig 6 (the verysimilar response of the 2D model is again omitted for clarity).Overall the prediction is a reasonable match to the experi-mental results. However, the delay in the appearance of end-slip in the experiment (which may be explained by frictionbetween the timber beam and slab) provides an initial dispar-ity between measurement and the model, while at higherloads the slip in the experiment is larger than that predicted.This greater slip is consistent with the difference in deflectionat the ultimate load seen in Fig 5.

Longitudinal stress distribution The three-dimensional FE model provided a prediction of the

Fig 14. Two dimensionalfinite element model

21 February 2006 – The Structural Engineer|29

paper: persaud/symons

variation in compressive stress across the concrete slab at mid-span due to ‘shear-lag’. The FE predictions are compared withexperimental strain gauge results in Fig 9.The FE prediction ofthe strains at the edges and near to the centre of the slabcompares well with the experimental measurements. Themaximum variation in the concrete strains across the 2m widthof the concrete slab in the FE model is about 28%.This shear lageffect might be expected to significantly reduce the effective widthof the slab, and therefore reduce the stiffness of the composite.However, the difference in initial stiffness between the 2D model(no shear lag) and 3D models is always less than 5% (see Table3). This indicates that shear lag in the slab has a negligibleminimal effect on the overall response of the composite system.We also note that that the magnitude of the compressive strainsis small compared to a typical failure strain for concrete andtherefore conclude that it is not necessary to consider a reduced‘effective width’ of the slab for either serviceability or ultimatelimit state design.

Conclusions The proposed composite floor system is structurally efficient andshould prove to be cost effective because of the savings in mate-rials resulting from reduced timber sizes and therefore floorheights. In addition, due to the thermal mass of the concreteslab, savings in cooling and heating costs in a building may beachieved.

In Table 3 the performance of the composite beam tested maybe compared to the predicted performance of the non-compositesystem (a 160mm by 405mm section timber beam acting alone)and a theoretical, fully-composite system where the slab is rigidlybonded to the timber beam and no slip occurs. The coach screwshear connection system tested increases the stiffness of thecomposite system to approximately three and a half times thatof a non-composite system and the strength by almost a factor oftwo.The fully-composite system would theoretically be six timesstiffer and three times stronger.As an alternative comparison weobserve that a non-composite timber beam of the same stiffnessas the composite system tested would have a 160mm wide by620mm deep section. Achieving the same ultimate strengthwould require a 160mm by 540mm section.Although final failureof the composite floor slab tested was brittle, being caused bytensile failure of the glulam timber beam, the non-linear slip ofthe coach screw shear connectors introduces significant ductilitybefore collapse. A fully-composite system would have no suchductility.

Strain gauges on the surface of the concrete indicated that theconcrete strains were low and shear lag is not a serious concernwith the flange width (i.e. secondary beam spacing) of 2m tested.

The elasto-plastic method was found to give a good estimateof the collapse load of the composite system and is recommendedfor ultimate limit state design. The shear connectors areassumed to be fully plastic and the only design parameter for theconnectors required is their shear resistance Rd. Johansen’sequations in Eurocode 510 have been found to be adequate forpredicting Rd . The depth of the screw embedment into thetimber can be chosen so that a double hinge failure mode willdominate, meaning that no benefit can be gained by deeperembedment.

The Eurocode γ method is a linear elastic method and is there-fore best used to describe the behaviour of the composite in thelinear elastic range. It is a useful design tool for the serviceabil-ity limit state. The method requires knowledge of the slip stiff-ness of the shear connectors.

Simple non-linear finite element models can be used to givequite reasonable predictions of the behaviour of full-scale compos-ite systems up to the collapse load. However, obtaining accuratepredictions will most probably require small-scale testing of theshear connectors to establish their non-linear load-slip response.This response may then be used as an input to the finite elementmodel.

AppendixElastic partial composite action A second order differential equation may be used to describe

elastic partial composite action. An analytical solution to thisequation can provide the elastic deflection,material stresses andinterface slip for prescribed boundary conditions. It is assumedthat the two sub-components are linear elastic, and that planesections remain plane in each.The connectors are modelled as auniform elastic shear layer of constant slip stiffness and negligi-ble thickness. For varying slip stiffness, or complex boundaryconditions, a numerical solution to the differential equation willbe required.

Consider a composite beam of two sub-components connectedby mechanical shear connectors with slip stiffness k.

k sK

= ...(14)

where K is the slip modulus per connector and s is the connec-tor spacing. Considering the total bending moment M(x) in thesection at a distance x from a support, a single differential equa-tion for the axial force N(x) in the sub-components can be formu-lated to describe the behaviour of the composite cross section (seeBlass et.al11 and Fontana and Frangi7).

dx

d N xkN x

E I E I

M x ek

2

2

2

1 1 2 2- =-

+p

__

_ii

i...(15)

where

E A E A E I E Ie1 12

1 1 2 2 1 1 2 2

2

= + ++

p ...(16)

The subscript i indicates the sub-component,1 for the concreteslab,2 for the timber beam.Ei is the elastic modulus,Ai the cross-sectional area, Ii the second moment of area and e the distancebetween the centroids of the sub-components (see Fig 10).

Analytical solution for 3-point bending For a beam of length l, loaded by a single point load P at mid-spanthe bending moment at a point x between the support and mid-span of the beam is:

< <M xP

x xl

for2

02

=_ i ...(17)

A general solution to equation 15 for this linear bendingmoment distribution is:

N Ae BeE I E I

Pex

2

k x k x

21 1 2 2

= + ++p

-p p

_ i...(18)

Applying boundary conditions for the simply supported beam(zero moment and axial force at the supports and no slip at mid-span) gives the following solution:

cosh

sinhN

E I E I

Pex

k kl

k x

22

21 1 2 2

=+

-p p p

p

_ d

a

i n

k

Z

[

\

]]

]]

_

`

a

bb

bb

...(19)

The curvature of the composite beam is given by:

dx

d wE I E I

N x e M x

2

2

1 1 2 2=

+

-_ _i i...(20)

where w is the deflection at any point in the beam, and there-fore

wE I E I

P

E I E I

e xx l

2 244 3

1 1 2 22

1 1 2 2

22 2=

+ +- +

p

C_ _

ci i

m* 4

...(21)where

cosh

sinhx

x l

k k k

k x

6 81

21

2 2

2 3= - + -

p p p

pC

J

L

KK

J

L

KKKKK a d

aN

P

OO

N

P

OOOOOk n

k

...(22)

Gamma method The ‘gamma method’ is an exact solution for partial compositeaction for simply supported spans subjected to loads that give abending moment that varies sinusoidally. It may be used as anapproximate result for other loading conditions. The method isintroduced in Annex B of Eurocode 5 part 1-110 and is outlined indetail in Blass et al11.An effective stiffness of the composite cross

30|The Structural Engineer – 21 February 2006

paper: persaud/symons

section is calculated as a function of the connector stiffness andthe geometric and elastic properties of the timber and concretesub-components.

The effective flexural stiffness (EI)eff of the composite systemaccording to the gamma method is:

EI E I E I Seff

1 1 2 2= + + c_ i ...(23)

where

SE A E AE A E A e

kl e

Sand

1

11 1 2 2

1 1 2 22

2 2

2=

+=

+

cr

...(24)

This effective stiffness can be used to give an exact solutionfor the deflection w under a sinusoidal load distribution pwhere

sin sinp pl

x w wl

x wEI

p land

eff

0 0 04

04

= = =r r

rd d

_n n

i

...(25)

However, the effective stiffness (EI)eff can also be used to calcu-late approximate deflections under other loading conditions. Forexample, the central deflection w0 under 3-point bending of asimply-supported composite beam with a central point load P (astested) is approximately:

wEI

Pl

48eff

0

3

._ i

...(26)

AcknowledgmentsThe research presented in this paper is part of an ongoingresearch project at the University of Cambridge. The generouscontributions to the project of Whitbybird, Lilleheden, RichardLees Steel Decking Ltd and Readymix are gratefully acknowl-edged.

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