Shear transfer inreinforced concrete withmoment or tensionacting across theshear planeAlan H. MattockProfessor of Civil EngineeringUniversity of WashingtonSeattle, Washington

L. Johal and H. C. ChowFormer Graduate StudentsDepartment of Civil EngineeringUniversity of WashingtonSeattle, Washington

Reports results from acomprehensive investigationto study the shear transferstrength of reinforcedconcrete. Specificdesign recommendationsare proposed.

Alan H. Mattock

76

In the design of precast concrete con-nections it is frequently necessary to

consider the transfer of moment andnormal force across a shear plane, aswell as shear. Such a situation occursat the interface between a corbel (orbracket) and its supporting column.

The ACI Building Code, ACI 318-71, 1 permits the use of the shear-fric-tion provisions of Section 11.15 for thedesign of corbels in which the shearspan to depth ratio a/d is one-halfor less, providing the limitations on thequantity and spacing of reinforcementin corbels specified in Section 11.14 areobserved.

In using shear-friction according toSection 11.15 of ACI 318-71 to designthe reinforcement crossing the inter-face between the corbel and the col-umn, the following assumptions aremade:

1. The concurrent action of momentacross the shear plane will not reducethe effectiveness of the reinforcementcrossing the shear plane in resistingshear, i.e., no interaction betweenmoment and shear transfer.

2. The shear transfer reinforcementneed not be uniformly distributed overthe shear plane but may be distributedso as to be more effective in resistingmoment.

3. If a normal tension force actsacross the shear plane, it may be pro-vided for by providing reinforcementadditional to that required for sheartransfer and having a yield strengthequal to the tension force, i.e., linearinteraction between shear and normalforce.

Before this study was undertaken, nosystematic experimental study had beenmade to validate these assumptions.However, their use within the limits im-posed by Section 11.14 of ACT 318-71is justified by the fact that they lead togenerally conservative estimates of theyield strength (or ultimate strength if

A comprehensive study ofthe shear transfer strength ofreinforced concrete, subjectto both single direction andcyclically reversing loading(the latter simulatingearthquake conditions), iscurrently in progress at theUniversity of Washington.This paper reports that partof the study concerned withthe effect of normal forceand moment in the shearplane on single directionshear transfer strength.Tests are reported of corbeltype push-off specimens andof push-off specimens withtension acting across theshear plane. It was found that1. Moments in the shear

plane less than or equalto the flexural ultimatemoment of the shearplane do not reduce theshear transfer strength.

2. Tension across the shearplane results in areduction in sheartransfer strength equal tothat which would resultfrom a reduction in thereinforcement parameterpf„ by an amount equal tothe tension stress.

A future paper will extendthe results of thisinvestigation to lightweightconcrete and provide a firmbasis for corbel design.

PCI JOURNAL/July-August 1975ҟ 77

ato

u u (varies)stub columnҟ vҟclosed stirrups,

10 size and spacingvaries

N

SHEAR PLANE_la

A—ҟ —A'corbel"

_!_ :iiiJ JT

0N —la

d1

All dimensionsCD CO CO CO in inchesN N N N

IҟIҟIҟI

Section

U[____2 2•1

Fig. 1. Corbel type push-off specimen (Series A, B, C, and D).

the main tension reinforcement did notyield) of those corbels tested by Krizand Raths2 which satisfy the require-ments of Section 11.14.

This was demonstrated in the Re-port3 of ACI-ASCE Committee 426,Shear and Diagonal Tension. How-ever, the limitations contained inSection 11.14 of ACI 318-71 are quitearbitrary. They simply reflect the rangeof various parameters included in Krizand Raths' tests for which satisfactorybehavior was obtained, and the ranges

of these parameters were chosen arbi-trarily when their test program wasplanned.

It appeared that if the assumptionslisted above could be validated in amore general manner, then the use ofshear-friction concepts in corbel designcould be extended beyond the arbitrarylimits set out in Section 11.14, withconsequent simplification of design pro-cedures. This study was therefore un-dertaken with the following objectives:

1. To determine the effect of mo-

78

SHEAR PLANE

4 0 high strengthbolt anchored insteel spiral

Series E4 #3 stirrupsSeries F6 #3 stirrups

4II dimensionsin inches

71!: 7 —{

—4#6Section at

ti mid—height—4 #6

t— ^— --- 14

Fig. 2. Push-off specimen for test with tension across shear plane(Series E and F).

ment acting on the shear plane, on theshear which can be transferred across ashear plane by a given quantity andarrangement of reinforcement.

2. To study the influence of the ar-rangement of the reinforcement cross-ing the shear plane on the shear andmoment which can be transferred ac-cross the shear plane.

3. To determine the effect of a ten-sion force acting normal to the shearplane, on the shear which can be trans-ferred across the shear plane.

Experimental Study

Six series of specimens were tested. Se-ries A through D were corbel typepush-off specimens, as shown in Fig. 1.Series E and F were standard push-offspecimens, except that anchorages wereprovided on opposite sides of the shearplane through which a tensile forcecould be applied across the shear plane(see Fig. 2).

PC! JOURNAL/July-August 1975 79

Table 1. Data concerning corbel type push-off specimens.

Arrangement of Shear Concrete (2) Eccentricity Ultimate

Specimen Transfer Reinforcement Compressive Tensile of Applied Load Vu

ObserveFailure

No. Strength Strength LoadMode

fc (psi) fct (psi) a (in.) (kips)

Al 3975 395 0 60.00 Shear

A2 Uniformly distributed 4130 410 2.50 60.00 Shear

A3over shear plane

4200 415 5.00 41.25 Flexure

A4 3895 385 7.50 31.50 Flexure

B1 Distributed in upper 3890 380 0 52.00 Shear

B2 part of shear plane 4125 410 5.00 51.50 Flexure

Cl 3980 395 0 50.50 Shear

C2 3915 385 5.00 53.00 Shear

C3 Concentrated at top 3805 375 6.00 51.00 Shear

C4 of shear plane 4210 420 6.66 40.50 Flexure

(d - 8.5 in.)

D1 3920 385 0 39.00 Shear

D2 4090 400 5.70 36.00 Flexure

(1) Measured on 6 x 12 in, cylinders

(2) Split cylinder tensile strength measured on 6 x 12 in. cylinders

(3) Reinforcement in Series A, B & C, 3 #3 bar closed stirrups, A ef = 0.66 in. 2 , f = 53.0 ksiReinforcement in Series D, 1 #4 bar closed stirrup, A vf = 0.40 in. 2 , fy = 53.0 ksi

Data concerning the specimens ofSeries A through D are shown in Table1 and data concerning the specimens ofSeries E and F are shown in Tables 2and 3, respectively. All specimens weremade from sand and gravel concretewith 3/4 in. maximum size aggregateand a design strength of 4000 psi at thetime of test.

Corbel type push-off testsThe specimens were tested using aBaldwin hydraulic testing machine toapply a load V at distance a from theshear plane, as shown in Fig. 1. Thisresulted in a shear V and a moment Vaacting in the shear plane simultaneous-ly. The "corbel" part of the specimenwas made to project above the top ofthe "stub column" in order that theload V could be applied in line with theshear plane in certain of the tests, i.e.,a = 0.

Typical arrangements for test areshown in Fig. 3. The specimen wasstood on the lower platten of the testingmachine and was loaded through the

system of rollers shown. The fixed up-per roller served to define the point ofapplication of the load and the lowerfree rollers prevented the testingmachine from restraining horizon-tal movement of the "corbel" relativeto the remainder of the specimen.

The 2-in, thick steel bearing plateresting on the top face of the "corbel"was anchored to the corbel by an em-bedded screw anchor at the side of thecorbel remote from the point of appli-cation of the load, when zero eccentric-ity or a very large eccentricity wasused. Measurements were made of slipalong the shear plane and separationacross it using 0.000I-in. dial gages,mounted on the specimen as shown inFig. 3.

Mast4 pointed out the need to consid-er the case of a crack existing in theshear plane before shear acts. There-fore, prior to test, the specimens werecracked along the shear plane by apply-ing line loads to their front and rearfaces. These loads were applied

80

Table 2. Data concerning Series E push-off specimens with tension acrossshear plane.

SpecimenNo.

Concrete (2)CompressiveStrength

f (psi)

concreteTensile

Strength

fct (psi)

YieldPoint

f (ksi)

ReinforcementParameter

Pfy (Psi)

Normal(4>Stress

°Nx (Psi)

f + o(p y Nx )

(psi)

Vv =U

Au

cr

(psi)

ElC (1} 3855 359 51.8 543 0 543 881

E2C 4220 397 52.1 546 -100 446 929

E3C 3960 343 52.7 552 -163 389 714

E4C 3820 362 50.5 529 -200 329 673

E5C 4020 383 52.3 548 -300 248 527

E6C 3985 373 50.9 533 -400 133 369

ElU 4060 372 52.7 552 0 552 1089

E4U 3860 392 49.1 514 -200 314 946

E6U 4120 335 50.8 532 -400 132 607

Shear transfer reinforcement area A5f = 0.88 in. 2 in all Series E specimens, (4 #3 bar closed stirrups).

(1) C denotes specimens initially cracked; U denotes specimens initially uncracked.

(2) Measured on 6 x 12 - in. cylinders.

(3) Split cylinder tensile strength measured on 6 x 12 - in. cylinders.

(4) Tension negative, Compression positive.

Table 3. Data concerning Series F push-off specimens with tension acrossshear plane.

SpecimenConcrete (2)CompressiveStrength

f (psi)

Concrete (3)TensileStrength

fct (Psi)

StirrupYieldPoint

f (ksi)

ReinforcementParameter

ofy (psi)

NormalStress

aNx (psi )

(pf + o )y Nx

(psi)

v = Vuu A

cr

(psi)

F1C` 1) 4220 350 50.1 787 0 787 988

F4C 3890 336 51.3 806 -200 606 839

F6C 4150 380 51.7 812 -400 412 804

FlU 4035 420 52.2 820 0 820 1369

F4U 4175 354 53.2 836 -200 636 1143

F6U 4245 389 51.0 801 -400 401 1066

Shear transfer reinforcement area A vf = 1.32 in. 2 in all Series F specimens. (6 #3 bar closed stirrups).

(1) C denotes specimens initially cracked; U denotes specimens initially untracked.

(2) Measured on 6 x 12 - in. cylinders.

(3) Split cylinder tensile strength measured on 6 x 12 - in. cylinders.

(4) -ension negative, Compression positive.

PCI JOURNAL/July-August 1975ҟ 81

Fig. 3. Arrangements for test ofcorbel type push-off specimen.

through steel wedges with the speci-men in a horizontal position. The dila-tion of the specimen across the shearplane was measured during the crack-ing operation, using dial gages mount-ed in a reference frame. The width ofcrack produced was about 0.01 in. inthe region of the reinforcement crossingthe crack.

The specimens were subject to an in-crementally increasing load to failure.Failure was regarded as having oc-curred when the load could not be in-creased further and slip increased rap-idly. At each increment of load readingswere taken of slip and separation, andthe growth of any cracks was markedon the specimen. Due to the nature ofthe instrumentation used, it was notpossible to obtain data relating to thefalling branch of the load-slip and load-separation curves.

Behavior—No additional cracking oc-curred during the testing of the speci-mens loaded along the shear plane (i.e.,

a = 0). In the case of the specimensloaded with an intermediate eccentric-ity (i.e. insufficient to cause a flexuralfailure), diagonal tension cracks oc-curred in the "stub column" duringtest, but they did not link up with thecrack in the shear plane. At failure,minor compression spalling occurredadjacent to the crack in the shear plane,in the specimens loaded with zero orintermediate eccentricity.

Both flexural cracks and independentdiagonal tension cracks formed in the"stub column" of those specimens load-ed at an eccentricity sufficiently large tocause a flexural failure. The flexuralcracks started in the top face of thestub column and propagated downwardand towards the shear plane. In somecases a flexural crack linked up with thecrack in the shear plane.

In flexural failures extensive com-pression spalling occurred in the con-crete adjacent to the lower end of theshear plane and the shear plane crackopened wide at the top of the shearplane. Failure became less sudden asthe eccentricity of the applied load in-creased and the failure mode changedfrom shear to flexure.

Both slip and separation occurred atall levels of loading. These have beenreported in detail elsewhere. It wasfound that for zero eccentricity of load(i.e., shear only in the shear plane), theultimate slip increased as the distribu-tion of the reinforcement changed fromuniform distribution over the shearplane to concentration at the upper endof the shear plane.

It appears that when a crack in ashear plane is subject to shear only,then only that part of the crack crossedby the reinforcement is fully effectivein resisting slip. By concentrating thereinforcem"nt, the average shear stressis increased in that part of the shearplane fully effective in resisting slip, ascompared with the case of uniformlydistributed reinforcement. This may be

82

the reason for the increase in slip.In the case of specimens with uni-

formly distributed reinforcement theultimate slip increased as the eccentric-ity of the load increased, except for A4in which a flexural failure occurred at aload only about half that sustained inshear. This trend in behavior may alsobe due to an increase in the effectiveaverage shear stress. In this case themoment acting in the shear plane re-sults in only part of the shear planebeing subject to compression and theaverage shear stress in that part of thecrack across which compression actswill therefore be greater than when thewhole length of the crack is active inresisting shear.

In the specimens having the rein-forcement concentrated near the top ofthe shear plane there is little variationin ultimate slip with eccentricity ofload. This is probably due to the fact

that the length of the crack subject tocompression and therefore active in re-sisting shear will not change appreci-ably going from small to large eccen-tricity, although its location willchange. For zero or small eccentricity,that part of the crack crossed by the re-inforcement will be subject to compres-sion, while for large eccentricities thatpart of the crack lying in the flexuralcompression zone of the "corbel" willbe subject to compression, but thelength of crack involved is probablysimilar in both these cases.

Ultimate strength—In Figs. 4 and 5 themeasured ultimate strengths are com-pared with the calculated strengthswhich correspond to shear failure andflexure failure. The calculated shearstrength V,u (calc.), is obtained usingthe shear-friction provision of Section11.15 of ACI 318-71, with p = 1.4 for

NQ

Da)

N

a,0E

H5

® ` `^V(flex.) Series CAi A2;o o^ҟ0 -

BIҟV(flex.),B2ҟC2

>O C I _

\

ҟB2 pC3 -

V„(Calc.) ҟo ^^` C4Shear Frictionҟ\ A3

50ҟ OA4\ -V(flex.) Series A

0.66 in2 -

p.fy = 583 psiҟSeries A, B a C0ҟfc = 4000 psi -

0ҟiҟ2ҟ3ҟ4ҟ5ҟ6ҟ7ҟ8ҟ9ҟ10

Eccentricity of Load, aҟ(in.)

Fig. 4. Variation of ultimate shear with eccentricity of applied load(Series A, B, and C).

PCI JOURNAL/July-August 1975ҟ 83

60

50ҟ

'U)n

40

y 30

20E

n 10

VU(calc.), Shear Friction

Avf = 0.40in?P.fy = 353 psiҟSeries Dfc = 4000 psi

V t 'L a 4 0 b ( tS U

Eccentricity of Load, aҟ(in.)

Fig. 5. Variation of ultimate shear with eccentricity of applied load (Series D).

1.4/DI

ҟ

—AIҟ OA2 •D2

ҟ

BIҟ C2B2

ҟ

/CIҟ ^ A—C3

C4

Shear Transfer- MomentInteraction Diagramappropriate for designҟ1

1

1.2

M1

C.)

y 0.8

N 0.6

— 0.4

0.2

OA3

oA4

0ҟ0.2ҟ0.4ҟ0.6ҟ0.8ҟ1.0ҟ1.2ҟ1.4ҟ1.6

M„(test)/ M„(caIc.)

Fig. 6. Interaction of shear and moment transferred across a crack.

84

a crack in monolithic concrete, and set-ting 4) = 1.0 since the materialstrengths and specimen dimensions areknown accurately.

The calculated shear correspondingto flexural failure V (flex.), is obtainedby dividing the calculated ultimate mo-ment capacity by the eccentricity ofloading. The ultimate moment capacitywas calculated using the assumptionsset out in Section 10.2 of ACI 318-71,

being taken as 1.0 in this case also.It can be seen that if the calculated

strength is taken to be the lesser of V,,,(tale.) and V (flex.), then in all casesthe actual strength exceeds the calcu-lated strength. It appears that the ulti-mate shear which can be transferredacross a crack is not significantly affect-ed by the presence of moment in thecrack, providing the applied moment isless than or equal to the flexural capac-ity of the cracked section.

A comparison of the strengths ofSpecimens Al, B1, and C1 which wereall reinforced with three #3 bar stir-rups, indicates that a small decrease inshear strength resulted when the dis-tribution of the reinforcement waschanged from uniformly distributed toconcentrated at one end of the shearplane. This is probably due to the localincrease in shear stress in the latter casedue to the reinforced part only of theshear plane effectively resisting shear.It should be noted however, that theshear capacity was still greater than.the calculated capacity for all threespecimens.

The greater conservatism of Speci-men Dl than CI, although both havetheir reinforcement concentrated nearthe top of the shear plane, is due to thelower reinforcement parameter of Spe-cimen Dl (353 psi), as compared to thatof Specimen Cl (583 psi). The shear-friction equation is most conservativefor low values of pf, and becomes pro-gressively less conservative as pfy in-creases.

The flexural capacity of SpecimensA3 and A4 is considerably greater thanthe calculated capacity because the cal-culation assumes that the maximumstress that can be developed in the re-inforcement is the yield stress. In thiscase the effective flexural reinforcementratio is very low and consequently theupper reinforcement was strained intothe strain hardening range, resulting ina reinforcement stress considerablygreater than the yield stress. This oc-curred to a lesser extent in SpecimenD2 where the flexural reinforcement ra-tio was 0.8 percent, but did not occurin Specimen C4 where the flexuralreinforcement ratio was 1.3 per:ent.This is the trend to be expected.

The interaction of shear and momentin all the specimens tested is shown inFig. 6. The test eccentricities for Speci-mens A2, B2, C2, C3, and 02 weredeliberately chosen to check whetherthe shear transfer strength according toshear-friction theory could be devel-oped simultaneously with the calculat-ed flexural ultimate strength, i.e., themost severe interaction situation. Theresults obtained indicate that the sheartransfer strength according to shear-friction theory and the flexural ultimatestrength can be developed simultane-ously across a crack in monolithic con-crete.

Section 11.14 of ACI 318-71 allowsthe shear-friction provisions of Section11.15 to be used for the design of cor-bels providing a/d is less than 0.5. Theresults obtained in this study indicatethat at least for the case of vertical loadonly, this arbitrary limit on a/d is un-necessary, provided the corbel is de-signed for shear according to the shearfriction provisions of Section 11.15 andfor flexure using the assumptions ofSection 10.2. The value of a/d atwhich flexure will begin to control andreduce the shear transfer strength be-low. that. _ calculated according to the"-shear-friction theory, will depend on

PCI JOURNAL/July-August 1975ҟ 85

Fig. 7. Arrangement for test of push-off specimen with tension acting

across shear plane.

the distribution of the reinforcementover the shear plane.

Push-off tests with tensionacross the shear planeThe specimens were tested using aBaldwin hydraulic testing machine toapply a load V concentric with theshear plane as shown in Fig. 2. Thisproduced shear without moment in theshear plane. Simultaneously, tensionacross the shear plane was producedby pulling on the pairs of high strengthbolts anchored in the specimen on op-posite sides of the shear plane. The ten-sion force was provided by a pair of 20-kip capacity rams, acting through shortdistribution beams as may be seen inFig. 7.

Both the shear V and the tensileforce were measured using SR4 gageload cells. The slip and separation weremeasured by linear differential trans-formers attached to reference points

embedded in the concrete on oppositesides of the shear plane. Both the lineardifferential transformers and the loadcells were monitored continuously dur-ing the tests using a Sanborn strip chartrecorder.

Prior to test, those specimens indi-cated in Tables 2 and 3 were crackedalong the shear plane by applying lineloads to their front and rear faces. Theloads were applied through steelwedges with the specimen in a horizon-taI position. The dilation of the speci-men across the shear plane was meas-ured during the cracking operation,using dial gages mounted in a refer-ence frame. A crack width of approx-imately 0.01 in. was produced.

The tensile force across the shearplane was applied before the specimenwas subjected to shear loading, andwas maintained constant during thetest. The shear load was then increasedcontinuously until failure occurred.Failure was regarded as having oc-curred when the shear load could notbe increased further and slip increasedrapidly.Behavior of initially cracked specimens—When the tension force across theshear plane was applied, additionalseparations of up to 0.0012 in. weremeasured, the magnitude of the sep-aration increasing with increase in theapplied stress. Both slip and separationoccurred from the commencement ofshear loading.

These measurements have been re-ported in detail elsewhere. 5 No diagon-al tension cracks occurred in the SeriesE initially cracked specimens, but a fewoccurred in the more heavily rein-forced initially cracked specimens ofSeries F. Failure of this type of speci-men was characterized by a rapid in-crease in slip and separation, and bycompression spalling of the concreteadjacent to the shear plane.

(Separation is caused by the over-rid-ing of roughness on the crack faces.

86

This will be accompanied by very highlocal compression stresses at the pointsof contact of the crack faces, whichmust be the cause of the compressionspalling observed adjacent to the crackat failure.)Behavior of initially uncracked spe3i-mens—When the largest tensile stress(400 psi) was applied to the initiallyuncracked specimens E6U and F6Ufine cracks occurred near the shearplane and roughly parallel to it. An ad-ditional "separation" of about 0.001 in.was recorded in these cases.

When shear was applied to the ini-

tially uncracked specimens no slip orseparation was recorded until shortdiagonal tension cracks commenced toform across the shear plane. Thesecracks were first observed at shearstresses of from 330 to 700 psi, theshear stress at cracking decreasing asthe tensile stress across the shear planeis increased. The inclination of the di-agonal tension cracks to the shear planevaried from about 10 to 40 deg, theinclination decreasing as the tensionstress across the shear plane increased.

Failure was quite brittle and wascharacterized by the extension of one

la0o

Specimens initially cracked

1600ҟfc - 4000 psi , fy = 50 ksiModified push-offtests. ^^ҟQ

1400 ҟq

1200 Series E 8 F, this study. Push-offҟtests with tensionacross the shear plane.

1000 qA qVVu s Previous pus -off

(psi ® q tests.

800-0 0ҟSymbol Urtx Qfy•

600 q q 0 variesa • Tension 540 psi

(varies)400 A Tension 800 psi

(varies)q Q Compression varies

Wnn (varies)

0ҟ200ҟ400ҟ600ҟ800 1000 1200 1400

( P fy + o)ҟ(psi)

Fig. 8. Comparison of shear transfer strength of initially cracked specimenstested in this program with that of "push-off" and "modified push-off" speci-

mens tested previously.

PCI JOURNAL/July-August 1975ҟ 87

Specimens initially uncracked

fc _ 4000 psi , fy - 50 ksi

Series E 8 F, this study. q qPush-off tests with tensionҟA q

across the shear plane.O q q

`^\Modified push-offtests.

•ҟPrevious push-off tests.

•ҟ13ҟ Symbol Nx efy

q 0 variesҟ-

• Tension 540 psiq (varies)

A Tension 800 psiҟ-(varies)

Q Compressionҟvaries(varies)

1800

1600

1400

1200

1000Vu

(psi)800

600

400

200

0 200 400 600 800 1000 1200 1400

(pfy + 6-Nx)ҟ(psi)

Fig. 9. Comparison of shear transfer strength of initially uncracked speci-mens tested in this program with that of "push-off" and "modified push-off"

specimens tested previously.

of the larger diagonal tension cracksroughly parallel to the shear plane, link-ing up with other diagonal tensioncracks, and by compression spalling ofthe concrete, particularly near the endsof the shear plane.

The slip which occurred at all levelsof load in the initially cracked speci-mens was greater than that which oc-curred in companion initially uncrackedspecimens. The slip at ultimate loadtended to decrease as the tensile stressacting across the shear plane increased.

In the case of the initially uncrackedspecimen, the "slip" is not a true slip

but rather the component parallel tothe shear plane of the relative motion ofthe two halves of the specimen, due torotation and compression of the in-clined concrete struts formed by thediagonal tension cracking.

The reduction in "slip" at ultimatein an initially uncracked specimen asthe tensile stress across the shear planeincreases, is consistent with the reduc-tion in the angle between the diagonaltension cracks and the shear plane,(and hence between the inclined con-crete struts and the shear plane), as thetension across the shear plane increases.

88

1800

1600

1400

1200

1000Vu

(psi)800

600

400

200

0

Specimens initially cracked_ҟfc' se 4000 psi , fy 01= 50 ksi

• - Series E, 9fy ^= 540 psiA - Series F, pfy 800 psi

/

vu = (?fy + ONx)?(e fy 0 o- + 0.5) /'/Nx

but t 0.25 f nor 1200 psi//

(}J = 1.4)ҟ®/•/• ' /

AҟAҟ800psi

• Shear Friction

•ҟV„ = (pfy + a-Nx)r

but 1 0.2ff nor 800 psi

(r = 1.4)

200 400 600 800 1000 1200 1400

(pfy + a-Nx) (psi)

Fig. 10. Comparison of shear transfer strength of initially cracked concretehaving a tension stress across shear plane, with the strength predicted by

current ACI Code and PCI Handbook equations.

In the case of the initially crackedspecimens, it may be that because ofthe increasing initial separation of thecrack faces as the tension across theshear plane increased, less slip becamenecessary to over-ride the minor rough-ness of the crack faces and causefailure.Ultimate strength—The ultimate sheartransfer strength of the specimens isshown in Tables 2 and 3, in the form ofnominal shear stresses at failure of thespecimens.

In Figs. 8 and 9, the shear transferstrengths obtained in the tests of initial-

ly cracked and initially uncracked push-off specimens, respectively, are plottedagainst (pff + o z ). Also plotted inthese figures are shear transfer strengthdata obtained previously in simplepush-off tests 6 and in modified push-off tests7 in which compression actedacross the shear plane simultaneouslywith the shear.

In making these plots, a positivevalue of o- corresponds to a compres-sive stress across the shear plane and anegative value of cr corresponds to atensile stress across the shear plane.

In both the initially cracked concrete

PCI JOURNAL/July-August 1975ҟ 89

1800

1600

1400

1200

1000vu

(psi) 00

600

400

200

0

IҟIҟIҟI ҟI

Specimens initially cracked.q - push-off tests, f' 4000psi• - ii ii ii ff= 2500 psiO - modified push-off tests, f 4000psi0 - push-off tests with tension acrossҟOq q

the shear plane, fc= 4000psiA - pull-off tests, fc = 5100psiҟq

v„ = 400 +

0.8(pf/_f4OOOPsi

q / , /^but I- 0.3f0 O / 0.3f, for

0

q

O /••q ,O,//K^^n 0.3fe for fc= 2500psi

vu = 33.5 (pfy + aN)

N

Recommended minimum(Pfy t o-Nx) = 200psi

200 400ҟ600 800 1000 1200 1400

(9fy + o-NX )ҟ(psi)

Fig. 11. Comparison of shear transfer strength of initially cracked concretewith and without direct stress across shear plane with strength predicted

by equations proposed by Mattock 9 , 1 ° and Birkeland.II

and the initially uncracked concrete,the grouping of the data points in thesefigures indicates that the change inshear transfer strength which occurswhen (pt + o) is varied is thesame whether this parameter ischanged by varying pf, or a-N„. This in-dicates that it is appropriate to com-bine the normal stress crN5 with the re-inforcement parameter when calculat-ing shear transfer strength.

In Fig. 10, the shear transfer strengthof the initially cracked push-off speci-mens with tension across the shearplane are plotted against the parameter

(pff + o-). Also plotted in this figureare lines corresponding to the shear-friction provisions of Section 11.15 ofACI 318-71 (solid line) and the designequation contained in Section 6.1.9 ofthe PCI Design Handbook” (dash line).(Note that the capacity reduction factordi was taken as 1.0 in both cases, sincethe material properties were accuratelyknown for these specimens.)

It can be seen that for this sand andgravel concrete, both equations yieldconservative estimates of shear transferstrength.

For the situation in which a tension

90

force N,, acts across a shear plane areaA,,., the shear-friction equation for de-sign:

vu.= (4)Pfv +arx)µ (1)

nating these disadvantages, have beenproposed previously by Birkeland :'1

v24 = 33.5- / p7 (6)and by Mattock:°"°

becomes: v,, = 400 + 0.8 pf2, (7)

v. = (4)A 8fr/A — Nu/A,,)JL (2) but not less than 0.3 f .or

= 4A 8f„ — N. (3)

where A$ is the total area of steel cross-ing the shear plane and 0 is the ca-pacity reduction factor (0.85 for shear).Hence

çbA8f2, = V,,/p. + N,,that is

A,—+----V.. N,, (4)

orA,, = A, f + A tɁ(5)

where A„j is the area of reinforcementrequired to carry the shear V,, accord-ing to shear-friction, and At is the areaof reinforcement required to carry thetension force N,,, acting across the shearplane.

The test results shown in Fig. 10theref )re validate the assumption madein Section 11.15 of ACI 318-71 that thetotal amount of reinforcement neededto carry a shear V,, and a tension N,,across a crack may be obtained by sim-ply adding together the area of rein-forcement required to resist the shear[according to Eq. (11-30)], and thearea of reinforcement required to resistthe tension force N,,.

While the shear-friction equation hasthe advantage of simplicity, it also hasthe disadvantages of being rather con-servative for small values of pfy andof artificially limiting the maximum ul-timate shear transfer stress to 800 psi.The PCI equation is an attempt toremedy the second disadvantage, buthas the disadvantage of complexity.

Alternate simple expressions forshear transfer strength, aimed at elimi-

These alternate design equationshave previously been validated only forthe case of shear alone acting in theshear plane. In Fig. 11 they are ex-tended to the case of shear and directstress acting across the shear-plane, andare compared with measured sheartransfer strengths of initially crackedsand and gravel concrete, both withand without direct stress acting acrossthe shear plane.

It can be seen that both expressionsare applicable to this general combina-tion of stress, Birkeland's parabola be-ing slightly more conservative thanMattock's straight line. Use of either ofthese relationships (suitably modifiedby the inclusion of the capacity reduc-tion factor 4)) would lead to more eco-nomical shear transfer designs than arecurrently yielded by the shear-frictionprovisions of ACI 318-71.

In design, either of these relation-ships could be used to design the rein-forcement required for shear transfer,and then the reinforcement required tocarry the tension across the shear planeshould simply be added to the shear re-inforcement.

Conclusions for Design

On the basis of the study reported here,the following conclusions are drawnconcerning shear transfer in sand andgravel concrete.

1. The simultaneous action of a mo-ment less than or equal to the flexuralultimate strength of the cracked sectionwill not reduce the shear which can betransferred across the crack.

PCI JOURNAL/July-August 1975 91

2.. The arbitrary limitation of a/d toless than 0.5 when shear-friction is usedin corbel design, contained in Section11.14 of ACI 318-71, should be re-placed by a requirement that both theflexural and shear capacity of corbelsshall be checked according to Sections10.2 and 11.15 of ACI 318-71, respec-tively.

3. If both moment and shear are tobe transferred across a crack, then inorder to be fully effective the sheartransfer reinforcement should be locat-ed in the flexural tension zone.

4. It is appropriate to add the nor-mal stress °N' to the reinforcement pa-rameter pfy when calculating sheartransfer strength in both initiallycracked and initially untracked rein-forced concrete. (ONE is positive whencompression and negative when ten-sion.)

5. The shear friction provisions ofSection 11.15 of ACI 318-71 yield aconservative estimate of the shear trans-fer strength of reinforced concrete, bothwith and without a tension stress act-ing across the shear plane. The resultsobtained validate the assumption madein these provisions that the totalamount of reinforcement needed tocarry a shear V,, and a tension N^,

across a crack may be obtained by sim-ply adding together the area of rein-forcement required to resist the shear[calculated using Eq. (11-30)], andthe area of reinforcement required toresist the tension force N.

6. The equation proposed in Section6.1.9 of the PCI Design Handbook foruse when p f, exceeds 600 psi, yieldsconservative results for the case when anormal stress UN,, acts across the plane,providing (p f5 -{- O'Nx) is substituted forpf^ in the equation. (cr is positivewhen compression and negative whentension.)

7. The alternate shear transfer de-sign Eq. (6) and (7) proposed by Birke-

land" and Mattock9.10 are equally ap-

plicable to the general case of bothshear and direct stress acting across ashear plane. Use of these equations indesign (suitably modified by the inclu-sion of the capacity reduction factor (P),instead of the shear "friction equation,would lead to economies.

Appendix—Notation

A,,.ҟ= area of shear plane, sq in.A, = total area of reinforcement

crossing shear plane whenboth shear and tension act,sq in.

A = area of reinforcement neces-sary to resist tension forceN,,, sq in.

A,f = area of shear-friction rein-forcement, sq in.

a = eccentricity of applied loadwith respect to shear plane,in.

d = distance from extreme com-pression fiber to centroid oftension reinforcement, in.

= compressive strength of con-crete measured on 6 x 12-in.cylinders, psi

f1t = splitting tensile strength ofconcrete, measured on 6 x 12in. cylinders, psi

f y = yield point stress of reinforce-ment, psi

= ultimate moment of resis-tance, in.-kips

N. = ultimate tensile force actingacross shear plane simultan-eously with V,,, kips

V(flex) = M,G/a

V,u = ultimate shear strength, kipsuu = nominal ultimate shear stress,

psi

t = coefficient of friction used inshear-friction calculations

92

P = A,g /A,,,. when both shear andtension act

p e Arf/Acr when shear only acts

6 = externally applied normalstress acting across shearplane, psi (compression posi-tive, tension negative)

= capacity reduction factor, asper Section 9.2 of ACI 318-71

Acknowledgment

This study was carried out in theStructural Research Laboratory of theUniversity of Washington. It was joint-ly supported by the National ScienceFoundation, through grant No. GK-33842X, and by the Prestressed Con-crete Institute, through its PCI Gradu-ate Fellowship program.

References

1. "Building Code Requirements for Rein-forced Concrete (ACI 318-71)," Ameri-can Concrete Institute, Detroit, 1971.

2. Kriz, L. B., and Raths, C. H., "Con-nections in Precast Concrete Structures—Strength of Corbels," PCI JOURNAL,V. 10, No. 1, February 1965, pp. 16-61.

3. ACI-ASCE Committee 426, "The ShearStrength of Reinforced Concrete Mem-bers," (Chapters 1 to 4), Journal of the

Structural Division, ASCE, V. 99, No.ST6, June 1973, pp. 1091-1187.

4. Mast, R. F., "Auxiliary Reinforcement inConcrete Connections," Journal of theStructural Division, ASCE, V. 94, ST6,June 1968, pp. 1485-1504.

5. Mattock, A. H., "Effect of Moment andTension Across the Shear Plane on Sin-gle Direction Shear Transfer Strength inMonolithic Concrete," Report SM 74-3,Department of Civil Engineering, Uni-versity of Washington, Seattle, Wash-ington, October 1974.

6. Hofbeck, J. A., Ibrahim, I. 0., and Mat-tock, A. H., "Shear Transfer in Rein-forced Concrete," ACI Journal, V. 66,No. 2, February 1969, pp. 119-128.

7. Mattock, A. H., and Hawkins, N. M.,"Research on Shear Transfer in Rein-forced Concrete," PCI JOURNAL, V.17, No. 2, March-April 1972, pp. 55-75.

8. PCI Design Handbook, PrestressedConcrete Institute, Chicago, 1971.

9. Mattock, A. H., "Shear Transfer in Con-crete Having Reinforcement at an Angleto the Shear Plane," American ConcreteInstitute Publication SP-42, Shear inReinforced Concrete, 1974, pp. 17-42.

10. Mattock, A. H., Discussion of the pa-per, "Modified Shear-Friction Theoryfor Bracket Design," by B. R. Herman-sen and J. Cowan, ACI Journal, V. 71,No. 8, August 1974, pp. 421-423.

11. Birkeland, H. W., Class Notes forCourse, "Precast and Prestressed Con-crete," University of British Columbia,Spring 1968.

Discussion of this paper is invited.Please forward your discussion toPCI Headquarters by December 1, 1975.

PCI JOURNAL/July-August 1975ҟ 93