mechanism of shear transfer

8/11/2019 Mechanism of Shear Transfer

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Mechanism of shear transfer in a reinforcedconcrete beam

Akin A. Olonisakin and Scott D.B. Alexander

Abstract: This paper presents an analysis of the results of five tests conducted on four reinforced concrete beams. The

tests were performed principally to investigate the mechanics of internal shear transfer in a transversely loaded concrete

beam with no shear reinforcement. Test specimens consisted of simply supported wide beams with steel flexural

reinforcement. The reinforcement for two of the beams was epoxy coated. The shear span to depth ratios were 2.93,

3.32, and 3.81. Measured strains on the reinforcement were used to divide the total shear into its beam and arching

action components. In all tests, beam and arching action shear transfer mechanisms were found to coexist. Apart from

that with the longest span, all tests ended with rupture of the concrete along a diagonal failure surface. It is concluded

that shear failure may be caused by a shift in the internal mechanics of shear transfer from beam action to arching

action. Because this shift may be initiated by the yielding of reinforcement, it can be associated with the formation of

a plastic hinge. There was no observed effect on the mechanics of shear transfer that could be attributed to epoxy

coating of the reinforcement.

Key words: arching action, beam action, one-way shear, shear transfer, reinforced concrete beam, bond forces, bar force

gradient.

Rsum : Cet article prsente une analyse des rsultats de cinq tests conduits sur quatre poutres en bton arm. Les

test taient principalement effectus pour tudier la mcanique du transfert de cisaillement interne dans une poutre en

bton charge transversalement sans renforcement de cisaillement. Les spcimens de test consistaient de larges poutres

supportes simplement avec un renforcement en flexion en acier. Le renforcement de deux des poutres tait enduit

d'poxyde. Les rapports trave de cisaillement/profondeur taient 2,93, 3,22 et 3,81. Les contraintes sur le renforcement

mesures ont t utilises pour diviser le cisaillement total en composantes d'action de poutre et d'action de cintrage.

Dans tous les tests, il a t trouv que les mcanismes de transfert de cisaillement de l'action de poutre et de l'action

de courbure coexistaient. Hormis celui avec la trave la plus longue, tous les tests se sont termins par une rupture du

bton le long d'une surface d'effondrement diagonale. Il est conclu que l'effondrement de cisaillement pourrait tre

caus par un changement de la mcanique interne du transfert de cisaillement d'une action de poutre une action de

cintrage. Parce que ce changement pourrait tre initi par le flchissement du renforcement, il peut tre associ la

formation d'une charnire plastique. Aucun effet, qui pourrait tre attribu l'enduit en poxyde, n'a t observ sur lamcanique du transfert de cisaillement.

Mots cls : action de cintrage, action de poutre, cisaillement sens unique, transfert de cisaillement, poutre en bton

arm, forces de liaison, inclinaison de force de barre.

[Traduit par la Rdaction] O lonisakin an d A lexand er 81 7

Introduction

In a reinforced concrete one-way flexural member, ne-glecting tension in concrete, the bending moment M is ex-pressed as the product of the tensile steel force T and the

effective moment arm jd. One-way shear V is the gradientof bending moment along the length of the member. That is,

[1] V M

x

Tjd

xjd

T

xT

jd

x= = = +

d

d

d

d

d

d

d

d

( ) ( )

The first component of eq. [1] is the shear resulting froma gradient in steel tensile force on constant lever arm and iscarried by beam action. The beam action shear requiresbond forces between the concrete and the steel reinforce-ment and is conveniently modeled by a critical nominalshear stress. Beam action is characteristic of slender flexuralmembers (B-regions) and may be limited by yielding of thereinforcement or by bond failure. The second component ofeq. [1] is the shear resulting from a constant steel tensileforce acting on a varying lever arm and is carried by internalarching action. It requires only remote anchorage of thereinforcement. Shear transfer by arching action predomi-

Can. J. Civ. Eng. 26: 810817 (1999) 1999 NRC Canada

81 0

Received December 14, 1998.Revised manuscript accepted June 16, 1999.

A.A. Olonisakin and S.D.B. Alexander.1 Department ofCivil & Environmental Engineering, University of Alberta,Edmonton, AB T6G 2G7, Canada.

Written discussion of this article is welcomed and will bereceived by the Editor until April 30, 2000 (address insidefront cover).

1Author to whom all correspondence should be addressed(e-mail: [email protected]).


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nates in deep beams and regions adjacent to discontinuitiesor disturbances in either the loading or the geometry of themember (D-regions).

This paper reports tests on four wide-beam elements. Thebeams were companion specimens to two slab-column con-nection specimens, reported in Alexander et al. (1995). Thegoal of all of these tests was to examine the mechanisms ofshear transfer by experimentally measuring some of thecomponents of eq. [1]. In addition to applied loads and reac-tions, forces in the flexural reinforcement were estimated onthe basis of strain measurements and coupon test results. Asone of the shear mechanisms identified in eq. [1] requiresforce gradient in the reinforcement, it was thought that fac-tors affecting bond might also affect shear. Therefore, two ofthe beam specimens were built with epoxy-coated reinforce-ment while the remaining two were built with uncoated rein-forcement.

Test details

The test specimens consisted of four concrete beams,155 mm in thickness, 750 mm in width, and 1.4 m in length.All beams were simply supported and reinforced with a bot-tom mat of grade 400 No.15M bars spaced at 150 mm each

way. The main (longitudinal) bars were placed at an effec-tive depth of 128 mm. The transverse reinforcement, presentin a prototype structure as shrinkage and temperature rein-forcement, functioned in the test specimens mainly as crackinitiators. Figure 1 shows the geometry and reinforcementdetails for a typical test specimen. All specimens had a rein -forcing ratio of 1.04%. Test information and results are sum-marized in Table 1.

The steel reinforcing bars for all the test specimens camefrom the same batch with measured yield strength of425 MPa. Reinforcement for two beams, CB1 and CB2, wassent out to the industry to be epoxy-coated. The remainingspecimens, RB1 and RB2, were built with uncoated rein-forcement. Despite the fact that all the reinforcement was

taken from the same lot, the epoxy-coated bars had a slightlyhigher measured yield strength of 439 MPa after treatment.The compressive cylinder strength of the concrete used forall the test specimens was 32.5 MPa.

Tensile strains in the main bars were measured by threerows of gauges located at a distance of 75, 225, and 375 mm(sections 1, 2, and 3, respectively) on either side of the beamcentre-line. A total of 15 electrical resistance strain gaugeswith nominal resistance of 120 and gauge length of 5 mmwere used for each test specimen. To minimize the effects oftension stiffening, strain gauges were positioned at thepoints of intersection of the longitudinal and transverse bars

where it was deemed most likely that the beam would crack.The layout of the strain gauges is as shown in Fig. 1.

The loading and span dimensions for all the test beamsare as shown in Fig. 2. A central vertical load was applied

by means of a hydraulic jack operating between the beamsurface and a reaction frame. The load from the jack pointwas measured with a commercial load cell. Two tests,(a) and (b), were performed on specimen CB1. The remain-ing three specimens were each tested once to failure. InCB1(a), the jack load was transferred centrally to the beamthrough a 38 75 HSS. In the rest of the tests, the jack loadwas distributed to two central points on the beams by meansof a 200 mm steel channel section. All the beam specimenshad between 175 to 225 mm overhang on each side of thesimple supports to provide anchorage for the main bars.Beam deflections were measured with a linear variable dif-

1999 NRC Canada

O lonisakin and A lexander 811

Mark

Span

Depth

fy(MPa)

Type of

reinforcement

Vmax(kN) Failure mode

CB1(a) 3.81 439 Epoxy coated 113 Bending

CB1(b) 3.32 439 Epoxy coated 129 Shear/compression

CB2 2.93 439 Epoxy coated 130 Shear/compression

RB1 3.32 425 Uncoated 123 Shear/compressionRB2 2.93 425 Uncoated 128 Shear/compression

Table 1. Description of tests.

interval

750

4 @

150

128155

700 700

Line ofsymmetry

7 @ 150

Symm.

75

225

375

1stinterval

2nd

Longitudinal gauges

Section1

Section2

Section3

Fig. 1. Description of test specimens.


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ferential transformer (LVDT). The slippage between thesteel and concrete was monitored during the tests with hori-zontal LVDTs attached to the ends of the main bars.

At a reinforcing ratio of 1.04% and shear span to depthratios ranging from 2.93 to 3.81, the beams were expected tobehave as slender flexural members. Results of tests onbeams without stirrups, summarized in MacGregor (1997),suggest for predicting shear failure, the simplified method ofshear design in Standard A23.3-94 (CSA 1994) works bestfor reinforcing ratios of about 1%. At lower reinforcing ra-tios, the simplified method produces scattered and generallyunconservative predictions of strength, while at higher rein-forcing ratios the method tends to be a lower bound of thetest data.

Test results

The beam deflections and average strain readings in thelongitudinal bars recorded during the tests indicated reason-able symmetry about the midspan of the beams. As ex-pected, the transverse bars were effective in initiating cracksat the gauge locations.

Figure 3 shows the central jack load (P) versus the centraldeflection for all the test specimens. Apart from test CB1( a),all tests resulted in the rupture of the beam along a diagonalfailure surface. Anchorage failure was ruled out because noslippage between the steel and concrete was observed in thedisplacements monitored by the horizontal LVDTs. The fail-ures were judged to be shear/compression failures, althoughin the case of specimen RB1 rupture took place shortly afterthe formation of a folding mechanism. Figure 4 shows pho-

tos of the failed specimens. Test CB1(a) was stopped whenit became evident that the beam was developing a foldingfailure. The loading geometry was adjusted and the speci-men re-tested to failure as CB1(b).

Analysis of test results

Strain gauge readings were converted to bar forces usingthe results of coupon tests of the reinforcement. Making useof symmetry, there are five strain gauges located at each ofthe three sections defined in Fig. 1. At every load step, thebar forces determined for each set of five gauges were aver-aged to produce experimental measures of the bar forces, T1,T2 , and T3, at the corresponding sections. The subscripts 1,2, and 3 indicate the section number in Fig. 1.

From the average bar force values at sections 1, 2, and 3,the bar force gradient was computed over the first and sec-ond intervals at every load step. Figure 5 shows bar forcegradients over the second interval versus the central deflec-tion for the test beams. CB1(b) with epoxy-coated reinforce-ment and RB1 with uncoated reinforcement had similarloading geometry. Both reached a limiting bar force gradientof about 205 N/mm, after which the bar force gradient de-clined. CB2 with epoxy-coated reinforcement and RB2 withuncoated bars both reached maximum force gradients ofabout 255 N/mm. The maximum force gradient measuredfor CB1(a) was 228 N/mm.

In all cases, a decline in force gradient over a particularinterval is associated with the onset of yielding at the morehighly strained section defining that interval. However, wellin advance of any yielding, the force gradient over the inter-val softens. This softening may be the result of a gradual de-terioration of the bond between the steel bars and thesurrounding concrete. The authors were, however, surprisedthat there was no obvious correlation between the magnitudeof the force gradient and the presence or absence of epoxycoating. One possibility is that adhesion bond was not signif-icant in these specimens. Alternatively, it may be that thereare factors other than bond that have a more significant ef-fect on force gradient.

The values of force gradient measured in the beams com-pare closely with those values for two-way plates of200 N/mm reported by Alexander et al. (1995). This sug-

1999 NRC Canada

812 C an. J. C iv. E ng. Vol. 26, 1999

175 525 525 175

38 x 75 HSS

175 525 525 175

200 mm channel

225 475 475 225

200 mm channel

(a)

(b)

(c)

Fig. 2. Span dimensions and loading: (a) CB1(a);

(b) CB1(b) and RB1; and (c) CB2 and RB2.

0

50

100

150

200

250

0 2 4 6 8 10 12 14

Deflection (mm)

Totalload(kN)

CB1(a)

CB1(b)

RB1

CB2

RB2

Fig. 3. Load versus deflection.


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gests that there ought to be a fundamental link between one-and two-way shear.

To examine the mechanics of shear transfer more closely,it is first necessary to recast eq. [1] in terms that can be mea-sured experimentally. Conditions at successive sectionsalong the beam are used to approximate the gradient termsin eq. [1]. The bending moments at each section, M1, M2 ,and M3, are calculated at every load step using load cellreadings and the known geometry of the simply supportedbeam. For an interval between sections i and i + 1, eq. [1]can be rewritten as

[2] V M M

s

Tjd Tjd

s

i i i i=

=

+ +1 1( ) ( )

At each section, the tensile force T is calculated fromstrain gauge measurements. The effective internal momentarm, jd, at each gauge location is estimated as follows:

[3] j d M

T1

1

1

= ; j d M

T2

2

2

= ; j d M

T3

3

3

=

A tacit assumption behind eqs. [2] and [3] is that flexuraltension in the concrete is insignificant. Ideally, this requiresthat the beam be fully cracked and that the gauged sectionscoincide with crack locations. Because transverse reinforc-ing bars were placed at the gauged sections, cracks tended tooccur at the gauged sections. To establish that a section isfully cracked is more difficult. Where flexural tension in theconcrete is significant, eq. [2] will produce an estimate of jthat is well in excess of unity. Figure 6 shows the effective

moment arm factor j obtained from eq. [3] plotted againstthe central deflection for tests CB1(a), CB2, RB1, and RB2.Prior to cracking, the contribution of concrete tension to themoment of resistance of the beam results in a value ofj thatis not reasonable, exceeding unity. With significant flexuralcracking, the magnitude of j drops to a value between 0.5and 0.9.

Not surprisingly, Fig. 6 shows that section 1 cracks first,with cracking at section 2 following closely. In all cases,section 2 appears to be fully cracked at a deflection of 3 to4 mm. Cracking at section 3 is delayed until well after

1999 NRC Canada


Fig. 4. Photographs of failed specimens: (a) CB1 and CB2; and (b) RB1 and RB2.

0

50

100

150

200

250

0 2 4 6 8 10 12 14

Deflection (mm)

Barforcegradient(N/mm)

CB1(a)

CB1(b)

RB1

RB2CB2

Fig. 5. Measured bar force gradients.


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cracking at section 2. Section 3 cannot be considered fullycracked until the final 2 or 3 mm of deflection.

The significance of the preceding discussion is to limit theapplication of eqs. [2] and [3]. To apply eqs. [2] and [3] tothe first interval requires full cracking at sections 1 and 2.This means that the analysis at the first interval is valid at

deflections greater than about 3 to 4 mm. For the second in-terval the analysis is valid only near the end of each test,where full cracking at section 3 is a reasonable assumption.

As was the case for eq. [1], eq. [2] can be broken downinto two components, namely beam and arching action.

[4] V V V= +a b

Expanding the right hand side of eq. [2] leads to the fol-lowing expressions for beam and arching action shear.

[5] V j j d T T n

s

i i ib =

+

+ +( ) ( )1 1 1

2

[6] V j j n T T dn

s

i i ia =

+

+ +( ) ( )1 1 1

2

The term V is the total vertical shear; Va and Vb are thecomponents of the total vertical shear transferred by archingaction and beam action, respectively; n is the total number of

bars at each of the gauge location (n= 5 in all tests); and s isthe length of beam in shear between the two sections.

It should be noted that the values ofj, T, and Mare not in-dependent of each other. They are constrained to be stati-cally consistent. While eqs. [5] and [6] provide a criterionfor dividing the applied shear into its two fundamental com-ponents on the basis of strain measurements, those two com-ponents, namely Va and Vb, will always sum to the appliedvertical shear V.

Figures 7 to 11 show plots of total vertical shear ( P/ 2),arching shear(Va) and beam shear(Vb) against the central de-flection for all the test beams. In all graphs, the point of firstmeasured yielding of at least one bar at the more highly

1999 NRC Canada

814 C an. J. C iv. E ng. Vol. 26, 1999

0

0.5

1

1.5

2

0 2 4 6 8

Deflection (mm)

j

(c)

0

0.5

1

1.5

2

0 2 4 6 8

Deflection (mm)

j

(d)

0

0.5

1

1.5

2

0 5 10 15

Deflection (mm)

j

Section 1

Section 2

Section 3

(a)

0

0.5

1

1.5

2

0 2 4 6 8 10

Deflection (mm)

j

(b)

Fig. 6. Effective moment arm factor: (a) CB1(a); (b) RB1; (c) CB2; and (d) RB2.


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strained section is indicated with an asterisk. Figure 8 showsresults for test CB1(b) over only the second interval becausethe strain gauges at section 1 did not survive the unloadingsequence at the end of test CB1(a).

Comparing the (a) and (b) parts of Figs. 7, 9, 10, and 11,it can be seen that the contribution of arching action is moresignificant in the first interval than in the second interval.This is attributed to two factors. First, the first interval is incloser proximity to a point of load application than is thesecond interval. This would tend to favour arching actionover beam action. Second, strains are generally greater in thefirst interval with yielding of the reinforcement typical.

Since yielding of reinforcement limits force gradient, thespread of yielding is parasitic on beam action shear. Archingaction must pick up shear that is shed from the beam actionmechanism.

Over the second interval in tests CB2, RB1, and RB2, theshear carried by beam action reaches a fairly stable valueuntil reduced by the onset of yielding. This value rangedfrom a low of 80 kN in RB1 to a high of 95 kN in CB2. TestCB1(b) did not display the same level of stability in its beamaction shear component although this may have been a resultof its loading history. The maximum value of beam actionshear measured for CB1(b) was 78 kN, which is comparableto the other three specimens. It is noted that the higher val-

ues of beam action shear were not associated with uncoatedreinforcement, as was expected.

At failure over the second interval of specimens CB1(b),CB2, RB1, and RB2, beam action accounted for betweenone and two thirds of the total shear. Nevertheless, the totalshear/compression failure shears are relatively consistent,ranging from a low of 123 kN to a high of 130 kN. These

1999 NRC Canada


0

25

50

75

100

125

0 2 4 6 8 10 12 14

Deflection (mm)

Verticalshear(kN)

(b)

0

25

50

75

100

125

0 2 4 6 8 10 12 14

Deflection (mm)

Verticalshear(kN)

Beam action

Arching action

Total shear

(a)

Fig. 7. Components of shear for CB1(a): (a) first interval; and

(b) second interval.

0

25

50

75

100

125

150

0 2 4 6 8

Deflection (mm)

Verticalshe

ar(kN)

Beam action

Arching action

Total shear

Fig. 8. Components of shear for CB1(b).

0

25

50

75

100

125

0 2 4 6 8 10

Deflection (mm)

Verticalshear(kN)

Beam action

Arching action

Total shear

(a)

0

25

50

75

100

125

0 2 4 6 8 10

Deflection (mm)

Verticalshear(kN)

(b)

Fig. 9. Components of shear for RB1: (a) first interval; and



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failure shears compare reasonably with an unfactored resis-tance of 109 kN as given by the simplified method for sheardesign in Standard A23.3 (CSA 1994).

It is apparent from Figs. 8 to 11 that at shear/compressionfailure, the beam action mechanism is shedding load to thearching action mechanism. In all cases except that of thesecond interval of specimen CB2, the loss of beam actionshear is a consequence of yielding of the reinforcement. Inthe case of the second interval of CB2, the drop in beam ac-tion shear at failure is attributed to a loss of bond.

Discussion

While far from conclusive, these tests raise questionsabout the nature of shear failure. There is the question ofwhat shear force Vis appropriate to use for the computationof the nominal shear stress V bd/ in a slender beam. Theconcept of a limiting nominal shear stress is more consistentwith the beam action mechanism than with the arching ac-tion mechanism. Given that both arching action shear andbeam action shear contribute to the total shear at or near theultimate load, it is conceptually incorrect to assign all of theload to beam action. This means that even though the simpli-fied method for shear design given in Standard A23.3-94(CSA 1994) reasonably predicts the failure strength of the

beams, its underlying mechanics are not consistent with thebehaviour of the beams. For the tests reported here, beamaction accounted for only about one to two thirds of the totalfailure shear. Alternatively, if one considers the maximumvalues of beam action shear, then the appropriate unfactoredresisting shear stress would be about 78% of the criticalshear stress given in the standard.

It is worth noting that for all tests ending in a shear/com-pression failure, shear was being shed from the beam actionmechanism to the arching action mechanism. In most cases,this internal redistribution of shear was the result of yieldingof the reinforcement, which reduced the difference in barforce and hence the force gradient between successive sec-tions of the beam. However, the failures themselves may bethe result of some critical stress state that is associated withthe shifting of load from the beam action mechanism to thearching action mechanism.

Failure associated with shifting shear from a beam actionmechanism to an arching action mechanism has been ob-served before. Kani (1964) noted a significant increase in theshear capacity of deep beams with reduced bond of rein-forcement provided that the reinforcement was anchored atits ends. Kani reduced both the bond strength and stiffnessby casting soft concrete locally around the reinforcement.In one specimen, the reinforcement was debonded com-

1999 NRC Canada

816 C an. J. C iv. E ng. Vol. 26, 1999

0

25

50

75

100

125

150

0 2 4 6 8

Deflection (mm)

Verticalshear(kN)

(b)

0

25

50

75

100

125

150

0 2 4 6 8

Deflection (mm)

Verticalshear(k

N)

Beam action

Arching action

Total shear

(a)

Fig. 10. Components of shear for CB2: (a) first interval; and


0

25

50

75

100

125

150

0 2 4 6 8

Deflection (mm)

Verticalshear(k

N)

Beam action

Arching action

Total shear

a

0

25

50

75

100

125

150

0 2 4 6 8

Deflection (mm)

Verticalshear(kN)

(b)

Fig. 11. Components of shear for RB2: (a) first interval; and



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mechanism of shear transfer

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