Tailor Made Concrete Structures – Walraven & Stoelhorst (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8

Shear resistance of bridge decks without shear reinforcement

G.A. Rombach & S. LatteInstitute of Concrete Structures, Hamburg University of Technology, Hamburg, Germany

ABSTRACT: This paper presents experimental and numerical investigations of a research project, carried outto examine whether bridge deck slabs under concentrated wheel loads exhibit reserves of shear capacity, whichhave been neglected in the current Eurocode design provisions so far. Tests conducted on large-scale cantileverslabs under concentrated loads demonstrated significant load redistributions after the formation of bendingand diagonal shear cracks. The evaluation of the test results showed, that the current design formula leads torather conservative values of shear capacity for bridge deck slabs when combined with a shear force distributionaccording to linear elastic slab analysis. A beneficial effect of a tapered slab bottom on the shear capacity, asimplied by most codes, could not be verified with these tests.

1 INTRODUCTION

The design of concrete bridge deck slabs is of majorconcern since the introduction of the Eurocodes andthe German DIN Fachbericht 102 (DIN-Fb 102). Thecalculated shear capacity of slabs without stirrups andstaggered reinforcement according to the new designstandards, as illustrated in Figure 1, is often consid-erably smaller compared to the former regulationsi.e. DIN 1045:88. Thus, more massive constructionsor shear reinforcements are now required in bridgedeck slabs, whereas this was formerly not the case.This raises the question whether there is a lack ofsafety for existing deck slabs which have been build

Figure 1. Shear capacity of concrete slab strips without shear reinforcement according to DIN-Fb 102, EC 2, SIA 262 andDIN 1045:88.

mainly without shear reinforcement, or whether deckslabs under concentrated wheel loads exhibit reservesof shear capacity which have been neglected in thecurrent design provisions.

Determining the shear capacity of reinforced con-crete structures without shear reinforcement is a clas-sical problem of slabs. Despite this the majority ofresearch and experiments has so far concentrated onsimply supported beams or one-way spanning slabstrips (b/d < 4) with loads applied over the full widthof the specimens. Over the years an extensive databasecontaining three or four point bending tests fromvarious researchers was established. The design equa-tions of the EC2 and DIN-Fb 102 are based on an

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Figure 2. Comparison between the ratio a/d and the bend-ing moment to shear ratio for a beam and a slab withconcentrated load.

empirical evaluation of such a database. A similardatabase containing 374 well-documented tests waspublished by Reineck & Kuchma et. al. (2003). Thesignificance of many of those beam tests is, however,limited for bridge deck slabs. Unrealistic high longi-tudinal reinforcement ratios were chosen for many ofthe beams in the database to avoid bending failuresprior to the formation of critical shear cracks. In con-trast to this, the reinforcement ratio for bridge decksslabs with d > 250 mm and a reasonable maximumamount of reinforcement of asl < 25 cm2/m will typi-cally be below ρl = 1%. From the 374 beam tests only58 fulfill this constraint. Only 27 relevant test remain,if the focus is laid on slender beams (a/d ≥ 2.9) withparameters typical for bridge deck slabs (d < 550 mmand fck < 50 MPa).

Furthermore, the ratio of bending moment to shearforce m/v for beams is connected to the distance abetween load and support and is directly proportionalto the geometrical ratio a/d. This condition does notapply for bridge deck slabs under concentrated loads,where m/v depends on the distribution of shear andbending moments in the support region. Due to thelarger distribution of bending moments compared toshear forces in slabs, the ratio mmax/vmax of a slab isalways smaller than that of a beam as pointed out inFigure 2.

A critical assessment of the published experimentaldata in literature, thus, leads to the conclusion, that theconducted experimental studies so far did not containthe most relevant parameters for the design of bridgedeck slabs under concentrated wheel loads. There-fore, experimental and theoretical investigations ofthe shear capacity of reinforced concrete bridge deckslabs without shear reinforcement under concentrated‘wheel’ loads financed by the German Federal High-way Research Institute (BASt) have been carried outat the Institute of Concrete Structures at the HamburgUniversity of Technology.

2 TESTS OF REINFORCED CONCRETE DECKSLABS UNDER CONCENTRATED LOADS

2.1 Test specimens and load arrangement

The experimental program consisted of 12 load testson 4 large-scale test specimens of reinforced concretebridge deck slabs measuring 2.40 m in width and rang-ing from 5.68 m to 6.58 m in length with an overallslab thickness from 200 mm to 300 mm (Fig. 4). Eachtest specimen comprised two cantilever slabs of 1.65 mspan and a centre slab supported on two web beams.This offered the possibility to conduct two cantileverslab tests (V1 and V2) and one centre slab test (V3)with each specimen. While the centre slabs of tests V3and the cantilever slabs of tests V1 did not contain anyshear reinforcement the cantilever slabs of tests V2were equipped with stirrups. This paper will focusesonly on the cantilever slab tests. Further informationis available in Latte (2008).

The cantilever slabs of specimen VK1 weredesigned to represent a full-scale cantilever of a con-crete box girder bridge with 2.60 m span using trafficloads as prescribed by Eurocode 1. Because the designshear capacity according to Eurocode 2 is indepen-dent of the rate of bending the governing load caseis found by applying the wheel loads in a distance of2.5·d towards the support. To account for uniformlydistributed traffic loads and a reduction of the can-tilever slab length to feasible dimensions for the testapparatus a constant line load fq was applied over thefull width at the tip of the cantilevers. The specimenswere tested in a 1 MN test frame as shown in Fig-ure 3. The line load fq was applied with a secondaryhydraulic jack and kept constant during the wholeduration of each test. After applying the line load theslab was loaded by a concentrated load FQ appliedon a square loading plate 400 × 400 × 100 mm untilfailure.

To study the influence of a tapered slab bottomon the shear capacity two test specimen VK2 andVK3 with identical cross-sections at the web beamswere tested. While VK2 had a constant slab thick-ness of 250 mm, VK3 was laid out with a slopeof 1:15 reducing the slab thickness to 140 mm atthe outer edge. All other parameters were kept con-stant for the two tests. Figure 4 shows the geometry,dimensions and reinforcement layout of each testspecimen.

The load arrangements and concrete properties atthe time of testing are listed in Table 1. The reinforc-ing steel was of grade BSt 500 S with yield strengthof 550 MPa for the Ø16 longitudinal reinforcement inthe top layer. A normal ready-mix concrete of class C30/37 with a maximum aggregate size of dag = 16 mmwas used. The concrete cover was chosen to 45 mmas typical for bridges for VK1 and 25 mm for VK2 toVK4 respectively.

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Figure 3. Test setup and load arrangement of the cantilever test for test specimen VK1.

Figure 4. Dimensions and reinforcement layout of the test specimen VK1 to VK4.

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2.2 Test results

All slab tests V1 of cantilever without shear reinforce-ment showed a brittle shear failure with no yielding ofthe longitudinal reinforcement. Only small deforma-tions and fine cracks were visible at the top surfaces

Table 1. Concrete strength at the time of testing and loadarrangement.

Concrete* Line load ‘Wheel’ load

ρ fc,cyl fct,sp fq e a** a/dSpecimen – MPa MPa kN/m m m –

VK1 0.81 35.0 2.85 32.1 1.5 0.71 2.88VK2 1.16 46.0 3.42 22.5 1.5 0.71 3.27VK3 1.16 46.5 3.34 22.5 1.5 0.71 3.27VK4 1.20 42.5 3.23 – – 0.71 4.25

*Tests on cylinders Ø 150 mm h = 300 mm.** Distance between load center and edge of the web beam.

Figure 5. Load–deflection curves for the measured deformation of the cantilever tips.

Table 2. Measured and calculated failure loads.

Yield line with effectiveTest results Linear elastic FE model width of 2.40 m

Shear ShearBending

Shear Bendingcracking Yielding FailureFQ,ct∗ FQy ∗ ∗ FQu Fct,cal FQu/ Fy,cal Fvu,cal FQu/ Fmu,cal FQu/

Test kN kN kN kN Fct,cal kN kN Fvu,cal kN Fmu,cal

VK1V1 350 – 690 290 2.38 537 518 1.33 684 1.00VK1V2 – 671 758 – – 537 – – 684 1.11VK2V1 360 – 678 392 1.73 691 613 1.11 807 0.84VK2V2 – 808 877 – – 691 – – 807 1.09VK3V1 400 – 672 359 1.87 645 621 1.08 817 0.82VK3V2 – 808 870 – – 645 – – 817 1.06VK3V1 260 – 487 308 1.58 469 516 0.94 558 0.87VK3V2 – 548 590 – – 469 – – 558 1.06

* Deduced from the calculated vertical strains of the measured slab thickness variation** Beginning of yielding in the longitudinal reinforcement

before shear failure. In contrast to this the stirrup rein-forcement of the cantilever slabs V2 ensured a ductilebending failure with large deformations and plasticstrains in the longitudinal reinforcement accompaniedby wide crack openings over the full width of the slab.The load deflection curves for all cantilever tests areshown in Figure 5 a&b. The measured failure loadsare summarized in Table 2. The behaviour of the testspecimens will be explained for VK1 only, as all otherspecimens exhibited a similar failure mechanism.

The crack pattern of specimen VK1 after the twocantilever slab tests is shown in Figure 6. The crackson the side faces of the slabs propagated almost verti-cally. The characteristic diagonal shear cracks on theouter slab faces of test V1 were only visible after a pro-nounced drop of load FQ. The inclined crack is joinedby cracks propagating along the reinforcement layersresulting from dowel action. The bending shear crackpropagated along the reinforcement in the bottom layertowards the supporting web beam and cut through thecompression zone with a straight crack over the whole2.40 m width of the slab.

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Measuring the deviations of the slab thickness atvarious points throughout the tests made it possibleto detect the appearance of inclined cracks inside theslabs. Figure 7 a shows the load-strain-relation calcu-lated from the measured increase of slab thickness.From these vertical strains it can be followed thatthe first inclined bending shear crack inside the slabemerged in the middle of the slab and crossed the loca-tions of the measuring points W25 and W24 at loadlevels of FQ ≈ 350 kN and FQ ≈ 440 kN respectively.As can be observed from Figure 7b the formation ofthe first inclined shear bending cracks did not causean immediate increase of the concrete strains in thecompression zone. A local increase of concrete strainsin the centre of the slab could not be noticed untilloads above FQ ≈ 560 kN. At this load level the diag-onal shear crack had grown towards the compressionzone in the support region and was also detected in themeasuring points W27 and W28. The fully developedcrack in the centre of the slab did, though, not lead to adirect loss of bearing capacity. The sudden and brittleshear failure at a load of FQ = 690 kN did only occur

Figure 6. Crack pattern of test specimen VK1 after tests V1 without shear reinforcement on the left and V2 with shearreinforcement on the right.

Figure 7. Measured data for cantilever tests VK1-V1 without and V2 with shear reinforcement.

after the diagonal crack propagated over a larger widthof the slab.

In contrast to the test without shear reinforcementthe stirrups provided in cantilever slab V2 reduced thecrack width of the diagonal shear crack considerablyand lead to a ductile bending failure by yielding ofall reinforcements in the top layer with large crackopenings and deformations. The test was stopped ata load of FQ = 758 kN after considerable crushingof the concrete compression zone in the bottom wasobserved.

3 DISCUSSION OF TEST RESULTS

A three dimensional FE model using shell elementswith linear elastic material properties taking intoaccount the exact boundary conditions was used tocalculate the sectional forces. The bending momentcapacity calculated with the elastic model resulted inthe load value Fy,cal for which the onset of yielding isexpected. Assuming a straight yield line over the full

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width of the slab resulted in the calculated ultimatebearing capacity Fmu,cal .

The calculation of shear capacity was performedwith the sectional shear forces of the linear elasticmodel according to the common design approach for avertical section directly at the intersection of the slabwith the web beam. Mean values of shear capacitywere required to compare the calculated values to testresults. To calculate mean values of the shear capacitythe code equation had to be multiplied by a transfor-mation factor which was verified by an evaluation ofthe shear database published by Reineck & Kuchmaet al. (2003). The mean value of the shear capacity canbe calculated according to Equation 1.

The shear bearing capacity predicted with the loaddistribution according to the linear elastic model isdenoted Fct,cal in Table 2. Since all tests exhibited afailure over the full width of the specimens the loadcapacity Fvu,cal was calculated with an effective shearforce distribution over the full 2.40 m slab width. Notethat for the calculation of the load capacities in Table 2a reduction of the shear force due to an inclined com-pression cord was omitted for the tapered slabs ofspecimen VK1 and VK3.

Comparing the calculated values with the testresults it can be observed that the ultimate bendingcapacity of the slabs Fmu,cal could be predicted quitewell. The shear capacity according to the code withelastic shear force distribution leads to rather conser-vative values. The calculated value Fct,cal captures theonset of diagonal cracking in the slab structure at loadsFQ,ct , but the crack initiation does not immediately leadto failure of the slabs. Considering load redistributionsin the slab and utilising the shear capacity over thefull width for the calculation of Fvu,cal does far bettercapture the measured maximum load FQu.

It should be noted that, although the slab bottom ofVK3 was tapered 1:15 under otherwise identical con-ditions, the cantilever slab tests V1 of VK2 and VK3failed at the same load level with a difference of only1%. Many design codes allow for a possible reduction

Table 3. Comparison of failure load VK2V1 to VK3V1calculated with shear reduction due to Vccd .

Linear elastic FE model 2.40 m effective width

mct,cal vccd Fct,cal mvu,cal vccd Fvu,calTest kNm/m kN/m kN kNm/m kN/m kN

VK2V1 176 – 392 223 – 613VK3V1 210 72 460 281 96 817

of the design shear force due to an inclined compres-sion cord Vccd according to Equation 2 and 3. If thereduction would be taken into account the load bearingcapacity of test VK3 with tapered slab bottom wouldbe predicted to be higher than that ofVK2 (seeTable 3).Furthermore, taking in to account an influence of theinclined compression zone and a load distribution ofshear forces over the full 2.40 m width would lead toan unsafe estimation of the bearing capacity changingthe predicted failure mode to bending failure.

4 CONCLUSIONS

The failure loads of tests conducted on reinforced con-crete slabs without shear reinforcement under concen-trated loads were considerably higher than calculatedaccording to Eurocode 2 in combination with an effec-tive width based on an elastic FE solution. The onsetof diagonal shear cracking in the slabs could, though,be predicted with this design approach. The increaseof ultimate bearing capacity could mainly be relatedto redistributions and diffusion of concentrated loadsin concrete slabs.

Furthermore, it is concluded that for an efficientdesign against shear failure of concrete bridge deckslabs under wheel loads the provisions should take intoaccount the influence of bending strains on the shearcapacity. Since the ratio of bending moment to shearforce for slabs under concentrated loads considerablydiffers from that of beams, the real boundary condi-tions of bridge deck slabs are not modelled properlyby normal beam tests. Therefore, it will be necessaryto perform more tests and analyses of concrete slabsunder concentrated loads.

The experiments and theoretical studies addition-ally indicate the need to further investigate the influ-ence of an inclined compression chord on the shearcapacity of reinforced concrete bridge deck slabs withtapered bottom edges.

ACKNOWLEDGEMENTS

This Paper is partly based on a research project accom-plished on behalf of the German Federal Ministryof Transport, Building and Urban Affairs (BMVBS)represented by the Federal Highway Research Insti-tute (BASt), with the research number FE-Nr.15.418/2005/DRB. The author alone accounts for thecontent of this paper.

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The authors would like to express their gratitudeto the German Federal Highway Research Institute(BASt) for their support and financing of this research.

REFERENCES

Latte, S. 2008. Querkrafttragfähigkeit von Fahrbahnplattenohne Schubbewehrung. PhD thesis (in prep.). HamburgUniversity of Technology.

Muttoni, A. 2003. Schubfestigkeit und Durchstanzen vonPlatten ohne Querkraftbewehrung. Beton- und Stahlbe-tonbau 98 (2): 74–84.

Reineck, K.-H. & Kuchma, D. et. al. 2003. Shear databasefor reinforced concrete members without shear reinforce-ment. ACI Structural Journal 100 (2): 240–249.

Eurocode 1 2003. Basis of design and actions on structures –Part 3:Traffic loads on bridges; German version EN 1991-2:2003. Berlin: Beuth.

Eurocode 2 2004. Design of concrete structures – Part 1-1:General rules and rules for buildings; German version:EN 1992-1-1:2004. Berlin: Beuth.

DIN 1045-1 2001. Tragwerke aus Beton, Stahlbeton undSpannbeton Teil 1: Bemessung und Konstruktion. Berlin:Beuth.

DIN-Fachbericht 102 2003. Betonbrücken. Berlin: BeuthDIN 1045 1988. Beton und Stahlbeton – Bemessung und

Ausführung. Berlin: Beuth.SIA 262 2003. Betonbau. Zürich: Schweizerischer Ingenieur-

und Architekten-Verein.SIA 262/1 2003. Betonbau – Ergänzende Festlegungen.

Zürich: Schweizerischer Ingenieur- und Architekten-Verein.

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