Flange Strain Measurement in Shear Critical RC T-Beams · PDF fileIn general, the above...

1. INTRODUCTION The effect of the flange on the shear strength of an RCT-beam has been noted in several investigations to be animportant consideration in the assessment of existingstructures that is not well understood in the current stateof research. These include a comment by Klein andPopovic (1985) in the discussion of the shear evaluationprocedures in the then current concrete codes ofpractice, and most recently by Darwish et al. (2000) ina discussion of an article by ASCE-ACI Committee 445(1998) on the then current state of the art for the shearevaluation procedures.

It was a study by Placas and Regan (1971) that firstexplicitly identified an increase in the shear capacity with

an increase in the flange width of RC T-beams with webreinforcing. Fok (1972) undertook a study that includedT-beams with and without shear reinforcing. Thespecimens in this investigation were subjected to a lineload across the width of the flange. The author concludedthat only flange depth, and not flange width affectedthe shear strength. Chong (1980) tested a series of RCT-beams without web reinforcing subjected to a line loadalong the length of the span and made a similarconclusion to that of Fok, i.e. that increases in the flangedepth, not the width produced increases in shear strength.Taplin and Al-Mahaidi (2000) tested a series of RCT-beams with web reinforcing subjected to a line loadacross the width of the flange (similar to that of Placas

Advances in Structural Engineering Vol. 9 No. 4 2006 491

Flange Strain Measurement in Shear

Critical RC T-Beams

Craig Giaccio1, Riadh Al-Mahaidi2,* and Geoff Taplin3

1Ove Arup Consulting Engineers, 10 Wellington Road, Ballsbridge, Dublin 4, Co. Dublin,Republic of Ireland

2Department of Civil Engineering, Building 60, Monash University, Vic 3800, Australia3Maunsell Australia, Level 9, 161 Collins Street, Melbourne,Vic 3000, Australia

(Received: 3 May 2005; Received revised form: 6 February 2006; Accepted: 14 February 2006)

Abstract: This paper provides an analysis of the strain measurements anddistributions obtained from testing two reinforced concrete T-beam specimens for thepurpose of assessing the contribution of the flange to the shear strength. The specimenswere instrumented throughout the flange and the compressive zone of the web regionin order to obtain comprehensive data required for the understanding of shearresistance mechanisms and quantification of the flange contribution to the shearresistance of reinforced concrete T-beams. It was found that the formation ofshear cracking results in significant redistributions of strain through the measuredregion. Redistributions of compressive strains transversely away from the web regionand vertically away from the top surface of the flange were observed. The resultingdistributions throughout the specimen were highly nonlinear. In light of the results ofthis investigation, the assumptions made in the application of existing methodsavailable for prediction of the shear resistance of reinforced concrete T-beams arediscussed, and proposed improvements to these methods are also discussed.

Key words: shear, flange flexure, failure mechanisms, reinforced concrete, T-beams, strain redistribution, flangecontribution.

* Corresponding author. Email address: [email protected]; Fax: +61-3-9905-4944; Tel: +61-3-9905-4952

ASE_04_05_353-Al-Mahaidi 1/8/06 10:13 am Page 491

and Regan (1971)), and reported a trend of increasingshear strength with increasing flange width. Giaccio et al.(2002) examined a series of web reinforced RC T-beamssubjected to a concentrated point load (circular point loadwith diameter approximately equal to the web width ofthe specimens), and found that both flange width andflange depth influenced the shear strength; the resultsindicated that the flange width has the most pronouncedinfluence on the shear strength of this type of specimen.In general, the above indicates that the flange proportionsof an RC T-beam with web reinforcing have an effect onthe shear strength of this type of specimen.

Other investigations into the shear strength of RCT-beams have been undertaken in the past. These includestudies by Ferguson (1953), Al-Alusi (1957), Swamy(1969), Sway and Qureshi (1971). The common threadof all these investigations is the study of the effect ofvariables common with rectangular beams on the shearstrength of the specimens. These variables are thosesuch as shear span to depth ratio, percentage of webreinforcing, web geometry, material properties, andpercentage of longitudinal reinforcing. The effect of theflange on the shear strength was not isolated in any ofthese investigations.

Giaccio et al. (2002) suggested that when compared toa rectangular beam of identical web proportions,reinforcing percentages, and material properties(subsequently termed the identical rectangular beam),the most significant additional contribution to shearresistance offered by an RC T-beam will result from theenlarged compression region. The affect that the flangemay potentially have on the aggregate interlockcontribution, the stirrup contribution, and the dowelaction contribution is not discounted. The potentialincreases in these contributions may arise owing to affectthat the increased stiffness will have on the curvature ofT-beam in comparison to an identical rectangular beam.The increased stiffness will result in a decreasedcurvature at the same load for a T-beam in comparison toan identical rectangular beam potentially resulting in adecreased demand on the other mechanisms of shearresistance owing to the lower strains on a given crosssection. This is not further discussed in this paper.

The calculation of the effective flange width forflexure that is used in many concrete codes is based onwork by Levi (1961) and Brendel (1964). The work ofthese authors was a collation of studies that used linearelastic theory to calculate the effective flange width ofT-shaped solids under a variety of different loadingconfigurations that was compiled in the 1920’s. Thisformulation of the effective flange width does notconsider the strain redistributions that occur followingcracking of an RC T-beam and may not be suitable for

calculation of the effective flange width in the shearresistance of an RC T-beam.

There are some analytical methods that have beendeveloped with the capability of predicting the shearstrength of an RC T-beam. Placas and Regan (1971)developed a method that has the capability ofcalculating of the shear capacity of an RC T-beam. Theimplementation of this method requires the input of theeffective width of the flange in shear resistance in orderto predict the shear capacity. There is no such analyticalmethod available for this calculation specifically forshear resistance of RC T-beams, therefore the methodsprescribed Levi (1961) and Brendel (1964) are the onlymethods available for making such a prediction. Theserely on the linear elastic methods.

The Modified Compression Field Theory (MCFT)(Vecchio and Colins 1986), and the further developmentof this theory, the Disturbed Stress Field Model(Vecchio 2002), as well as the Softened Truss Model(Hsu 1988 ; Pang and Hsu 1995) are analyticalprocedures that require the discretisation of a concretecross section into a series of layers throughout the depthto calculate the section capacity. Vecchio and Collins(1988) developed a simplified method to calculate theshear strength of RC T-beams. The method applies adual section analysis of an RC beam and requires anassumed strain gradient throughout the depth at eachcross section used in the analysis to predict the shearcapacity. The assumed strain gradient presented in thestudy was linear throughout the depth.

Hoang (1997) presented an idealised failuremechanism of an RC T-beam and implemented theplasticity formulation to explicitly include the flangeproportions in the resulting shear strength predictionequations. The mechanism is shown in Figure 1. Thismechanism is representative of the beam shearmechanism of shear failure of web reinforced RCT-beams reported in Giaccio et al. (2002) and Giaccio(2003). This formulation assumed that compressivestresses are distributed in a 1:2 ratio across the width ofthe flange to calculate the effective width of the flangefor shear resistance, and allowed the implementation ofthe plasticity method.

This paper discusses the detailed instrumentationof two web reinforced RC T-beam specimens toinvestigate the strain redistribution in the flange and thecompression region of the web of an RC T-beam thatarises from the formation of shear cracking. The strainsare analysed to determine the validity of assumptionsused in state of the art methods of calculating shearresistance of RC T-beams and to understand the sourcesof nonlinearity that prevail in RC T-beams following theformation of the shear failure mechanism.

Flange Strain Measurement in Shear Critical RC T-Beams

492 Advances in Structural Engineering Vol. 9 No. 4 2006


2. RESEARCH SIGNIFICANCEThis paper forms part of a research program that is aimedat examining the role of the flange in the resistance of aweb reinforced RC T-beam subjected to shear, as well asquantifying the contribution that the flange makes to theoverall shear resistance of this type of structural element.

3. EXPERIMENTAL PROCEDURE3.1. Specimen Details

Two specimens were selected for detailed examination ofthe distribution of flange strain in the flange andcompression region in the web. As the primary focus ofthe research programme was on web reinforced shearcritical RC T-beams, the specimen proportions wereselected using the results of an investigation by Giaccio etal. (2002) into the effect of the geometry of the flange onthe shear capacity of RC T-beams. This investigation was

based on 30 experimental results. This study detailed theexistence of an upper bound to the effectiveness ofincreases in flange width on the shear resistance.Specimens in this study were intended to be identical totwo specimens tested by Giaccio et al. (2002) representingthis upper bound. The decision to select two specimenswith differing flange depths was intended to allowcomparison of the flange contribution to shear resistanceof specimens with varying flange depths.

These specimens had an overall depth of 305 mm,flange width of 465 mm, web width of 140 mm. The twodifferent flange depths studied in this investigation were75 mm and 100 mm. A cross section of these specimensis shown in Figure 2. The span of the specimens was 3.0m. The yield strength of the flexural bars was 340 MPa,the yield strength of the stirrups was 300 MPa, and theconcrete cylinder strength was 50 MPa.

Craig Giaccio, Riadh Al-Mahaidi and Geoff Taplin


Tension cracking on top of flange

Crushing under load point on top of flange

Applied Load

Point load across width of web

Intersection of flange crack and web crack

Plan of Idealised Mechanism for a Point Loaded T-beam

bf.ef

1:2 1:2

Line load across width of flange

Intersection of flange crack and web crack

Plan of Idealised Mechanism for a Line Loaded Flange

bf.ef

Elevation of Idealised Mechanism

1:2 1:2 1:2

1:2

Figure 1. Failure mechanism assumed in Hoang (1997)

465

100

140

205

45

6.5 mm Diameter Stirrups @225 mm crs.

5 × 20 mm Diamter Longitudinal Bars

6.5 mm Diameter longitudinal flange

bars at 75 mm centres

140

465

75

5 × 20 mm Diamter Longitudinal Bars

6.5 mm Diameter longitudinal flange

bars at 75 mm centres 230

40

6.5 mm Diameter Stirrups @ 225 mm crs.

Beam 1 Beam 2

Figure 2. Cross sections of specimens used in experimental investigation


3.2. Instrumentation

The layout of the gauging to measure concrete strains isshown in Figure 3. Figure 3(a) shows each of thelocations of the longitudinal gauges that were appliedacross the width of the flange and throughout the depth.The gauges throughout the depth of the flange alignedvertically. In each of the two specimens, a gauge wasprovided in the web below the underside of the flange togain further insight into the distribution throughout theweb. This was located approximately 40 mm below theunderside of the flange on Beam B1, and 50 mm belowthe underside of the flange on Beam B2. Strain gaugeswere not placed on the reinforcing bars.

Figure 3 also shows the notation used for the twosections of instrumentation, Section A and Section B thatare used in this paper. The discussions that ensue in thispaper refer to the left and right hand flange overhang.This refers to overhangs as they are seen on the crosssection in Figures 2 and 3.

The decision to locate strain gauges at three pointsacross the width and depth of the flange was based on thephysical limitation of the internal gauges. The use of anymore rows of embedded strain gauges could havesignificantly impacted on the results of strain because ofthe large area of protective coating around the embeddedconcrete gauges.

Instrumentation was also provided to determine themagnitude of the transverse strains thus allowing theirinfluence on the compressive response of the concrete tobe determined using available analytical models. Theseare shown in Giaccio et al. (2004) to produce nosignificant affect on the principal compressive strains onthese specimens and are not further discussed.

The gauges were offset from the edge of the load pointto avoid localised effects of the load. The distance used

in these experiments was determined from the results ofa finite element analysis to be 150 mm. This is close to avalue of D/2 (where D is the total depth of the specimen).

3.3. Testing Procedure

The specimens were subjected to a single point load. Thetotal span of the specimens was 3000 mm. The shear spanwas 800 mm, corresponding to a shear span to effectivedepth ratio (av/d) of 3.0. This was selected to ensure thatthe shear failure mechanism had developed to a significantextent at the failure of the specimen. The 145 mm diametercircular loading imprint was applied to the specimen via a controlled displacement of 0.009 mm/s. Theexperimental set up is illustrated in Figure 4.

3.4. Method of Analysis

To examine the affect of the formation of crackingassociated with the development of the shear failuremechanism, the following aspects of the experimentalwork are discussed in this paper.

1. The results of ultimate strength and failuremechanisms

2. The distribution of strains with applied load3. The variation of strains throughout the depth at

an indicative location in the flange overhangs,and at the centre of the width of the web. Thesevariations were shown at loads after significantredistributions of strains associated withcracking were observed.

4. RESULTS OF ULTIMATE STRENGTHAND FAILURE MECHANISMS

4.1. Beam B1

The failure mechanism displayed by specimen B1 wasone where the specimen exhausted its load carrying



Line of support

Surface gauges

110 mm to surface gauges, 80 mm to embeddable gaugesLongitudinal surface gauges

Load Embedded concretegauges

Line of stirrup beyond

Support bars for embedded gauges

Section ASection B

1 2 3 4 5 6 7

1 - Denotes gauging row number

Figure 3. Strain gauging used in the experimental work

ASE_04_05_353-Al-Mahaidi 1/8/06 10:13 am 94

capacity as the concentrated point load punched throughthe web and flange of the T-beam. This failuremechanism was described in Giaccio et al. (2002) as thebeam punching shear mechanism. Figure 5 shows aphoto of the failure mechanism. It shows the locationwhere the load point punched through the top surface ofthe flange. It also shows that in addition to the usualdiagonal web cracks associated with the shear failuremechanism, a large crack traversed the width of theflange intersecting the row of gauging farthest from theload point (Section B).

Figure 6 shows the load deflection response. Onreaching peak load, the specimen exhibited a non-ductile response. The formation of the punching shearmechanism was sudden, as was the resulting loss in loadcarrying capacity associated with the development ofthis mechanism. Failure occurred at a peak load of Pu = 212 kN which corresponded to a peak appliedshear of Vu = 155 kN.

The critical diagonal web crack that was present atfailure formed at an applied load of 85 kN. Anotherdiagonal web crack was observed to occur at 91 kN. Inaddition to these cracks, a crack on the top surface of theflange was observed. This crack intersected Section Bof the strain gauges. Analysis of the strain gauge resultsat Section B indicated that the strains were significantenough to cause cracking at a load of approximately 175 kN. This is assumed to be the load at whichthe transverse crack formed in the discussions thatfollow.

4.2. Beam B2

Beam B2 exhibited a ductile flexural failure. Figure 7shows a photo of the failure mechanism. When the peakload of 238 kN was reached, the specimen began toundergo large plastic deformations without any increasein the reaction forces. Diagonal web cracks associatedwith the formation of the shear failure mechanism were



800

3000

4000

1773

3385

1267

2235A

A

Support

Test Specimen

Reaction Frame

Loading Jack

Loading plate

Section A-A

Figure 4. Schematic of experimental set up

Punching of load point

Lateral crack across

Critical diagonal web cracks

Figure 5. Photo of failure mechanism of Beam 1

50

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App

lied

Load

(kN

)

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250

2 4 6 8

Deflection (mm)

0 10

Figure 6. Load deflection curve for Beam 1


observed at 78 kN, 86 kN, and the most significant ofthese cracks formed at a load of 212 kN. Four significant

flexural/flexural shear cracks formed at failure on thisspecimen. The load at which these initiated during theexperiment was not monitored.

Figure 8 shows the load deflection response. Thepeak load was Pu = 238 kN as indicated, whichcorresponded to a sectional shear of Vu = 174 kN.

5. RESULTS AND DISCUSSION OF FLANGESTRAIN MEASUREMENT

Not all gauges could be located exactly at the positionsshown in Figure 3 because of interferences byreinforcing bars. To allow simple analysis and discussionof the strains that were measured, results were linearlyinterpolated to locations that were equidistant throughoutthe width and depth of the flange. Results presented inthis paper are these linearly interpolated results.

5.1. Beam B1

5.1.1. Strains in the flange of the beam

Figures 9–10 show the variation of strain with load thatwas recorded in the flange overhangs for Beam B1. Forclarity of presentation, the strains in each flangeoverhang are presented separately. Strain gauges atSection B began to fail at an applied load of 200 kN asa result of the crack on the top surface of the flangeintersecting this row of gauges. For consistency ofpresentation, the results of measured strains vs. appliedload are not shown beyond an applied load of 200 kN.

Figure 9 shows the results for the gauges at Section A.These plots show that the trend of the change in strainwith the increasing applied load was similar for allgauges located at similar distances from the top surfaceof the flange. This was generally true for the magnitudes,



Well developeddiagonal web cracks

Crushing of compressionconcrete

Figure 7. Photo of failure mechanism for Beam 2

App

lied

Load

(kN

)

0

50

100

150

200

250

300

5 10 15 20 25 300 35Deflection (mm)

Figure 8. Load deflection curve for Beam 2

–600

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0

100

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0 40 80 120 160 200

Load (kN)

Str

ain

(µε)

Row 1 Top Row 1 Mid Depth Row 1 U/Side



–600

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0

100

200

0 40 80 120 160 200

Str

ain

(µε)




(a) Left Hand Flange Overhang (b) Right Hand Flange Overhang

Load (kN)

Gauges on undersideof flange

Gauges on top of flange

Figure 9. Strains measured in the flange at section A on Beam B1


although in some instances there were differences inmagnitudes of gauges located at the same distance fromthe top surface of the flange.

From the start of the test until 40 kN, the strains at alllevels of depth from the top surface of the flange wereincreasing and compressive. At 40 kN, the influence of aflexural crack became evident with strains on theunderside of the flange beginning to reverse in trend. Ata load of 85 kN (corresponding to the appearance of thefirst diagonal web crack), the trend of change in strainwith applied load changed on all surfaces. The strains onthe underside of the flange began to reverse and becameincreasing and tensile. This was accompanied by thestrains on the top surface increasing in the rate of changeof strain with applied load. The gauges at the centre ofdepth of the flange were largely unaffected by theformation of this crack. Although the load at whichthis occurred corresponded to the formation of thediagonal web crack, the change in trend is most consistentwith the influence of the growth of a flexural crack.

At a load of approximately 140 kN, the trend of thechange in strain with load on the top and bottom surfacesof the flange can be observed to have reversed. Thestrains on the underside of the flange decreased in tensilemagnitude, further becoming compressive strains, whilstthose on the top surface of the flange began to decreasein compressive magnitude. At a load of 175 kN, a suddensharp magnification in these trends was observed. Thisindicates that a vertical redistribution of strain occurredat this section to accommodate the crack on the topsurface of the flange. Compressive stresses were forced

down throughout the depth of the flange.It can be observed from Figure 9 that the reversal in

trend of change in strain with applied load occurred at aload of approximately 190 kN on some gauges. All ofthese gauges are located in the column of gaugesadjacent to the flange. This change in trend appears tobe consistent with a flexurally dominant behaviour ingauges adjacent to the web.

Figure 10 shows the results of the gauges at SectionB on Beam B1. The trend of change in strain withapplied load is generally similar to that observed atSection A until a load of 140 kN. The reversal of strainson the top and bottom surface of the flange at thisSection resulting from the formation of the crack on thetop surface of the flange is more pronounced than wasobserved at Section A. At this Section, the crackintersected the gauges on the top surface as is reflectedby the high tensile strains present as the last set of resultspresented at 200 kN. The gauges on the underside of theflange also underwent a significant reversal such thatthey displayed the highest magnitude of compressivegauges throughout the experiment.

The reversals of strain on the top and bottom surfaceof the flange are a result of a redistribution of strain thatis caused by the formation of the transverse crack on thetop of the flange. This redistribution arises to allow theflange to accommodate the crack that forms the shearfailure mechanism corresponding to Figure 1. Thevertical redistribution associated with the formation ofthe crack on the top surface forced compressive strainsaway from the top surface of the flange.



0 40 80 120 160 200

Load (kN)




0 40 80 120 160 200

Load (kN)




–600

–400

–200

0

200

400

600

–600

–400

–200

0

200

400

600

800


Str

ain

(µε)

Str

ain

(µε)



Figure 10. Strains measured in the flange at section A on Beam B1


5.1.2. Strains in the web of the beam

As the trend of change in strain with applied load isreasonably similar for gauges in the flange overhangs,one representative row of gauging is used to comparestrain distributions throughout the depth with gauges inthe flange and in the web region. This comparison isshown in Figure 11. The loads selected for plotting werethose close to significant strain redistributions discussedin the previous section. Gauges in Row 2 of the flangewere selected for comparison with the web gauges.

Part (a) of Figure 11 indicates that the distribution ofdepth throughout the flanges at Section A remainedgenerally linear following the significant redistributionsthat occur throughout the loading history. At load valuesof 190 kN and 200 kN some strain nonlinearity becomeevident as compressive strains on the top surface beginto decrease while compressive strains at the centre ofdepth of the flange and on the underside of the flangecontinued to increase.

Part (b) indicates that the distribution of strains atSection B were linear throughout the loading historyincluding at the peak load. The strain distributionmaintained a linear profile throughout the depth whilethe redistribution occurred to accommodate the crack onthe top surface of the flange.

Part (c) of Figure 11 indicates that the only part of theloading history that produced a linear strain gradient atSection A through the depth was prior to the formationof the diagonal web cracks. Following the formation ofthese cracks, strains in the flange remained mostly linearwith compressive strains in the order of 400–500 µε onthe top surface of the flange, and tensile strains on theunderside of the flange increasing sharply with load to amagnitude of 4470 µε at the peak load. However, theweb gauge that was located 40 mm below the bottomsurface of the web exhibited mostly compressive strainsin the order of 200 µε for the majority of the loadinghistory. Tensile strains began to develop on this gaugefollowing the formation of the crack on the top surfaceof the flange. The unusual distribution of strain throughthe depth of the web indicates that the diagonal webcracks influence the strains producing a sectionaldistribution throughout which is highly nonlinear.

Part (d) of this figure also indicates that the only partof the loading history that produced a linear straingradient at Section B through the depth was prior to theformation of the diagonal web cracks. Following theformation of the diagonal web cracks, the strainsmeasured in gauges located within the depth of the flangeremain linear, even during the vertical redistributions of



(c) Section A Web (d) Section B Web

0

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80 kN 120 kN 160 kN 180 kN 212 kN

Line of Top of Flange

Line of U/Side of Flange

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80 kN 120 kN 160 kN 180 kN 212 kN



0

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80 kN 120 kN 160 kN 190 kN 212 kN



0

25

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–600 –400 –200µε µε

µε µε

0 200

80 kN 120 kN 160 kN 190 kN 212 kN



(a) Section A Row 2 (b) Section B Row 2

Dep

th fr

om T

op o

f Fla

nge

(mm

)

Dep

th fr

om T

op o

f Fla

nge

(mm

)D

epth

from

Top

of F

lang

e (m

m)

Dep

th fr

om T

op o

f Fla

nge

(mm

)

Figure 11. Strains distributions throughout the depth of Beam B1


strains to accommodate the crack on the top surface of theflange. However, large tensile strains were recorded onthe gauge located 40 mm below the underside of theflange for most of the loading history.

Comparison of parts (a) and (c), i.e. the distributionof strain between the flanges and web at Section A,illustrates that as the tensile strains increased at thejunction of the flange to web interface the compressivestrains on the underside of the flange and at the centre ofdepth of the flange also increased, indicating atransverse redistribution of strain across the width of theflange. It is suggested that this was in part a result ofdecreasing compressive strains on the top surface of theflange.

Figure 12 shows the crack pattern on the specimenwith the location of Section A and B of gauges alongwith lines to indicate the locations of the centre lines of

the embedded gauges. With this superposition of thelocation of these gauges in relation to the cracks thatwere present at failure, it is very clear that the interactionof two separate diagonal web cracks influenced the straindistribution. The distribution of strain through the depthat Section A at the peak load in Figure 11 (shown in athicker line) indicates that the diagonal web crack thatformed and intersected with the flange to web interfacewas much more developed at failure than the crack thatintersected the gauge 40 mm below the underside of theflange. The distribution of strain through the depth atSection B in Figure 11 indicates compression at the levelof the soffit of the flange from the vertical redistributionof strain accompanying the formation of the crack on thetop surface of the flange as well as tension at the gauge 40 mm below the soffit of the flange. This tension onthe latter gauge is a result of the gauge intersectinga diagonal web crack. The resulting strain distributionowing to these complex interactions of cracks is highlynonlinear and is not that which corresponds to a planesection.

5.2. Beam B2

5.2.1. Strains in the flange of the beam

Figures 13–14 show the variation of strain with loadrecorded in the flange overhangs for Beam B2. Forclarity of presentation, the strains in each flangeoverhang are presented separately. Gauges performedwell until the peak load was reached. Once the specimenstarted exhibiting ductility, the gauges began to fail. Thestrain gauge results presented in the discussion that



Centreline of embedded gauges

Section ASection B

Load

Location of transversecrack on flange

Figure 12. Illustration of crack pattern with location of embedded

gauges for Beam B1


0 50 100 150 200 250

Load (kN)




0

0 50 100 150 200 250

Load (kN)




–400

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–200

–100

0

100

–500

200

–600

–500

–400

–300

–200

–100

100

200

Str

ain

(µε)

Str

ain

(µε)



Figure 13. Strains measured in the flange at section B on Beam B2


follows are those up until the peak load of 238 kN wasreached. Strains recorded during the ductile response arenot presented.

Figure 13 shows the results for the gauges at SectionA on Beams B2. These plots show that the trend of thechange in strain with the increasing applied load wasvery similar for all gauges located at similar distancesfrom the top surface of the flange. In general, themagnitudes of the gauges were also very similar. As thediagonal web cracks formed and propagated, magnitudesof the strains on the top and bottom surfaces began tovary across the width of the flange overhangs.

At a load of approximately 40 kN, influence of flexuralcracking became evident with the reversal of strains onthe underside of the flange from increasing compressive,to increasing tensile. This was accompanied with anincreasing gradient of increasing compressive strains onthe top surface of the flange with applied load.

At a load of approximately 120 kN, the trend of changein strain with increasing load on the top and bottom flangesuddenly reversed. As the load subsequently increased, thetrend in change in strain on the top surface of the flange withapplied load immediately reversed to become increasingcompressive with a lower gradient than that which wasobserved prior to this change in trend. The tensile strains onthe underside of flange continued to decrease. No physicalchange in the specimen was observed at this load.

The formation of a significant diagonal web crack ata load of 212 kN caused sharp variations in the trends ofthe change in strain with applied load on the top andbottom surface of the flanges. On the top surface, themagnitude of the compressive strains quickly decreased,

and then continued to remain reasonably constant untilthe failure load. The strains on the underside of theflange rapidly decreased at this load and subsequentlycontinued on their decreasing trend becoming small andcompressive at the peak load.

Although some small discontinuities were observedin gauges located at the centre of the depth of the flangeat loads associated with those causing significantchanges in trends of strain on the top and bottom surfaceof the flange, no significant change in trend arose duringthe loading history.

Figure 14 shows the results of the gauges at SectionB on Beam B2. Similar redistributions to thosediscussed at Section A were also observed at Section B.The most pronounced difference in the trends betweenSections A and B is the magnitude of the change instress that occurred on the top and bottom surface of theflange on the formation of the large diagonal web crackat a load of 212 kN. The decrease in compressive strainon the top surface of the flange and the increase incompressive strain on the bottom surface were such thatthe magnitude of strain at these levels of the flange wasvery similar at the peak load.

The gauges at the centre of the depth of the flangewere largely unaffected by the development of thefailure mechanism throughout this experiment.Although some small discontinuities were observed atloads associated with those causing significant changesin trends of strain on the top and bottom surface of theflange, no significant change arose. It can be observedthat the gauge at the centre of depth in row 2 at SectionB did exhibit larger magnitudes than other gauges.




0 50 100 150 200 250

Load (kN)




0 50 100 150 200 250

Load (kN)




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–50

0

50

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–350

–300

–250

–200

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–50

0

50

100

Str

ain

(µε)

Str

ain

(µε)



Figure 14. Strains measured in the flange at section B on Beam B2


5.2.2. Strains in the web of the beam

As the trend of change in strain with applied load isreasonably similar for gauges in the flange overhangs,one representative row of gauging is used to comparestrain distributions throughout the depth with gauges inthe flange and in the web region. This comparison isshown in Figure 15. The loads that the distributionscorrespond to are those just prior to the onset of diagonalweb cracking (75 kN), prior to the redistribution at 120 kN (110 kN), after the redistribution at 110 kN (180 kN), after the third diagonal crack formed (215 kN),and at the peak load (238 kN). Gauges in Row 1 of theflange were selected for comparison with the web gauges.

Part (a) of this figure shows that the distribution ofstrains throughout the depth of the flange at Section Aremained mostly linear throughout the loading history.At Section B however, the distribution through the depthshown in part (b) of Figure 15 did become nonlinear inthe flanges following the formation of the significantdiagonal web crack at 212 kN. The distributions at 215 kN and 238 kN show a reduction in strain on the topsurface of the flange whilst the strains at the centre ofdepth and on the underside of the flange continued toincrease. This is similar to that observed in Beam 1 prior

to the formation of the crack on the top surface of theflange. However, in this specimen, the flexural failureoccurred before this shear crack could develop.

Part (c) of Figure 15 indicates that the straindistribution displayed for the loads selected was notlinear throughout the depth. In the early stages ofloading, the gauge located 50 mm from the underside ofthe flange exhibited strains that did not fit the lineartrend. As the loading progressed, the strain measuredfrom this gauge became high in tensile magnitudefollowing the formation of the significant diagonal webcrack at 215 kN. The strains on the top surface of theflange also began to decrease following the formation ofthis web crack accompanied by a reversal of strains onthe bottom surface of the flange. It appears that theredistribution to accommodate the formation of thecrack on the top surface (similar to that of Beam B1)was underway when flexural failure occurred.

Part (d) of Figure 15 indicates that the straindistribution displayed for the loads selected was not linearthrough the depth. At this section, linear distributions areobserved through the depth of the flanges for all loadsconsidered, however, the gauge located 50 mm from theunderside of the flange did not fit a linear trend for the



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(a) Section A Row 2 (b) Section B Row 2

(c) Section A Web (d) Section B Web

Figure 15. Strains distributions throughout the depth of Beam B2


loads selected. Following the redistribution at 140 kN, thestrains on top surface of the web began to decrease whilethose measured at gauges at the centre of the depth of theflange and at the underside of the flange continued toincrease in magnitude with applied load. The highesttensile strains at the level of the soffit of the flange wererecorded prior to the formation of the significant diagonalweb crack at 212 kN. Following the formation of thisdiagonal web crack, the strains at this location decreasedsignificantly, becoming compressive at the peak load.The gauge embedded in the web below the soffit of theflange displayed high and increasing tensile strainsfollowing the formation of this diagonal web crack.

Comparison of part (b) and part (d), i.e. thedistribution of strain between the flanges and web atSection B, illustrates that as the tensile strains increasedat the junction of the flange to web interface, thecompressive strains on the underside of the flange and atthe centre of depth of the flange increased, indicating atransverse redistribution of strain across the width of theflange. This will in part be a result of decreasingcompressive strains on the top surface of the flange.

Figure 16 shows an illustration of the crack pattern onthe specimen with the location of Sections A and B ofgauges along with lines to indicate the locations of thecentre lines of the embedded gauges. With thissuperposition of the location of these gauges in relationto the cracks that were present at failure, it is very clearthat the interaction of two separate diagonal web cracksinfluenced the strain distribution. The distribution ofstrain throughout the depth at Section A at the peak loadin Figure 15 (shown in a thicker line) indicatescompressive strains throughout the flange, and hightensile strains at the gauge 50 mm below the undersideof the flange. The high tensile strains are a result of theintersection with a diagonal web crack as illustrated inthis Figure. The distribution of strain through the depthat Section B in Figure 15 indicates that tensile strainswere present at the flange to web interface for themajority of the loading history while the gauge 50 mmbelow the underside of the flange was displaying

compressive strains. At the peak load, a diagonal webcrack intersected the gauge 50 mm below the soffit ofthe flange resulting in significant tensile strainsprevailing. The magnitude of the tensile strainsdecreased at the level of the soffit of the flange at thepeak load. The resulting strain distribution owing tothese complex interactions of cracks is highly nonlinearand is not that which corresponds to a plane section.

6. DISCUSSION OF THE RESULTSThe results of the instrumentation programmedemonstrate that the formation of the cracks associatedwith the shear failure mechanism produce significantredistributions of strain in the flange and compressiveregion of the web. These redistributions prevail boththroughout the depth and transversely across the width ofthe flange. The most pronounced redistributions observedin the tests presented in this work were throughout thedepth of the flange and compressive region of the web.

The redistribution of strain throughout the depth isassociated with the formation of the transverse crack onthe top surface of the flange. It is suggested that thedevelopment of this crack forces compressive strains onthe top surface of the flange that result from bending atthe cross section downward through the flange toaccommodate the development of this crack. Thisdownward movement of compressive strains is requiredin a cross section in order to maintain equilibrium at thecross section.

The redistribution of the strains throughout the widthof the flange is associated with the propagation of thediagonal web crack to the flange-web interface. It issuggested that as a diagonal web crack propagates toand begins to penetrate the flange, compressive strainsat the flange-web interface that result from bending areforced transversely into the flange overhang toaccommodate the propagation of this crack. Thistransverse redistribution of compressive strains isrequired in a cross section in order to maintainequilibrium at the cross section.

Analytical methods such as those developed byPlacas and Regan (1971) that require estimation of theeffective width in shear resistance require considerationof a complex series of redistributions of strain toaccommodate the shear failure mechanism that is notonly cross sectional in nature, but interacts with theshear span. Linear elastic methods that form the basisfor calculation of the effective width of the flange inflexure cannot be adopted due to these redistributions.

The simplified method developed for implementationof the MCFT relies on the assumption of a strain gradient.The strain gradient suggested in the formulation is one oflinear variation throughout the depth. The results of this



Centreline of embedded gauges

Section ASection B

Load

Region ofcrushed concrete

Figure 16. Illustration of crack pattern with location of embedded

gauges specimen B2


investigation show that the strain distribution at shearfailure within the shear span is highly non linearthroughout the depth of the flange and into the web,therefore indicating that the assumption that is made inthis implementation may be a source of error in itsapplication to RC T-beams. Implementation of thismethod to calculate the shear capacity of RC T-beamsrequires the input of a strain gradient representative ofthat which arises from the shear failure mechanism.

The crack pattern that prevailed at failure inSpecimen B1 was similar to that hypothesised by Hoang(1997) in the development of a plasticity based methodto calculate the shear capacity of RC T-beams. Thestrain distribution in Specimen B2 at failure indicatedthat the magnitude of the compressive strains on the topsurface of the flange decreased, and compressive strainsdeveloped on the bottom surface of the flange at bothsections of instrumentation when the formation of theshear failure mechanism was interrupted by the failureof the specimen in flexure. This indicates that the crackon the top surface of the flange was developing whenthe specimen failed in flexure. These results, along withthose presented in Giaccio et al. (2002), indicate thatthis failure mechanism is an adequate representation ofthe shear failure mechanism in RC T-beams. Thisfailure mechanism could be used as a basis to derivea strain gradient to implement into strain based methodsof calculating the shear resistance of RC T-beams

7. CONCLUSIONSThis paper presented the results of an investigation intothe distribution of longitudinal strains through the widthand depth of two web reinforced RC T-beams. Theinfluence of the formation of shear cracks was discussed,as were the redistributions of strain that accompaniedthese cracks. Assumptions made in the application ofstate of the art methods available for prediction of theshear resistance of RC T-beams were discussed in lightof the results of this investigation, and improvements tothe prediction of shear strength using these methods werealso discussed.

The following conclusions are drawn from this work:1) Formation of the shear failure mechanism

resulted in strain redistributions throughout thewidth and depth of the flange as well as thecompressive region of the web.

2) Transverse redistributions of strain from the webto the flange at a cross section occurred in orderto accommodate the propagation of diagonalweb cracks into the flange.

3) Vertical redistributions of strain at a crosssection occurred as the formation of thetransverse crack on the top surface of the flange

forced compressive strains downward in theflange.

4) Linear strain distributions throughout the depthof a section, and distributions of straincalculated throughout the width of the flange ofan RC T-beam using linear elastic analysis arenot valid for the implementation of analyticalmethods that are reliant on assumed straindistributions.

5) The mechanism in Hoang (1997) adequatelyrepresents the shear failure mechanism of RCT-beams as validated in these tests and thosepresented in Giaccio et al. (2002). This mechanismcould be used as a basis for developing a straindistribution throughout the width and depth of anRC T-beam that would eliminate a source of errorin the implementation of methods of predictingshear resistance of RC T-beams that are reliant onassumed strain distributions.

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concrete T-beams with varying shear span”, ACI Journal, Vol.

53, pp. 1067–1077.

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T-beam. Part II: flange contribution”, Submitted to ACI

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publication in the Proceedings of the 18th ACMSM Conference,

Perth, Australia.




Giaccio, C. (2003). Flange Effectiveness in the Resistance of

Sectional Shearing Forces in Web Reinforced RC T-Beams

Subjected to a Concentrated Point Load, PhD Thesis, Department

of Civil Engineering, Monash University, Victoria, Australia.

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study on the effect of flange geometry on the shear strength of

point loaded RC T-beams”, Canadian Journal of Civil

Engineering, Vol. 29, No. 6, pp. 911–918.


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K.L., pp. 462–472.

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Denmark, pp. 32.

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Craig Giaccio is a Senior Bridge Engineer with Ove Arup Consulting Engineers,

based in Dublin in the Republic of Ireland. He received his BE(Hons) from the

University of Adelaide, and his PhD from Monash University. His professional

interests include the economic design of bridge structures, analysis and design of

reinforced and prestressed concrete structures, finite element analysis of concrete

structures, and the fatigue life prediction of steel structures. He is a member of

IABSE, IEAust, and IEI and undertakes external reviewing duties for the Structural

Engineering International Journal.

Riadh Al-Mahaidi is Head of the Structures Group in the Department of Civil

Engineering at Monash University in Melbourne, Australia. Be received his BSc

degree from the University of Baghdad and his MSc and PhD from Cornell University.

He is a member of ACI-ASCE Committee 447, Finite Element Analysis of Concrete

Structures. His research interests include analysis and design of reinforced and

prestressed concrete elements and structures, finite element modelling of concrete

structures, strength assessment of concrete bridges and rehabilitation of structures

using FRP composites. He is a member of IEAust, ASCE, ACI, IABSE and IIFC.




Geoff Taplin is a Principal Engineer-Structures with Maunsell Australia Pty. Ltd.

Based in Melbourne, Australia. His career has spanned both consulting engineering

and academia in the field of structural engineering. Prior to joining Maunsell

Australia, he was a Senior Lecturer in Structural Engineering at Monash University in

Melbourne, Australia. He has experience in building and bridge structures, and

strength assessment of bridges, he is a member of the Technical Committee of the

International Association of Bridge and Structural Engineering, and is Chairman of

their Structural Engineering Documents Board. He has a PhD and MEngSc, both from

Monash University.


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