Design of Anchorage-ZoneReinforcement in Prestressed

Concrete Beamsby Peter Gergely* and Mete A. Sozen**

NOTATIONThe symbols as used in the text aredefined as follows:

p — uniform stress on cross sec-tion due to prestress

c — distance to the longitudinalcrack from the bottom ofbeam

e — distance to the applied forcefrom the bottom of beam

P — applied forceL — distance from the end of the

beam to a cross section wherethe stresses are linear dueto P

M - unbalanced moment on a freebody formed by a longitudi-nal crack

T — total tensile force to be sup-plied by the stirrups

C — vertical compression force (onthe free body formed by ahorizontal crack)

h — height of the anchorage zone(or beam)

f ' — cylinder strength of concreteat the time of testing

F — force in one reinforcing barA — area of one reinforcing bars — slip of one reinforcing bar

w — crack widthf 8 — stress in stirrups

*Assistant Professor, Cornell University,Ithaca, N.Y.

**Professor, University of Illinois, Urbana,Ill.

E — modulus of elasticity of steelm — numerical factor in bond-slip

relationship

INTRODUCTION

The object of this paper is to in-troduce a simple method for the de-sign of transverse reinforcement torestrain anchorage-zone cracks andto present a series of test results toconfirm the validity of the method.

In prestressed beams, the pre-stressing force is introduced into theconcrete section either at a singleplane, as in the case of beams withmechanical anchorages, or over ashort length of the tendons, as in thecase of pretensioned bonded beams.In either case, the stress distributionover the section becomes linear, andconforms to that dictated by the ov-er-all eccentricity of the appliedforces, within a distance less thanthe height of the beam from thepoint of application of the force. Asthe applied force, concentrated at acertain level in the section, flows incurved patterns to conform to thelinear stress pattern, it sets up trans-verse tensile stresses. These stressesmay lead to longitudinal crackswhich can extend throughout thebeam span, thus . causing failure.Similar stress conditions exist inbonded members where the pre-stressing force is transmitted to theconcrete over a finite length.

April 1967 63

Calculated contours (1) of equaltransverse stresses in a rectangularprism loaded uniformly over a dis-tance equal to h/8 at an eccentricityof 3h/8 (where h is the depth of thesection) are shown in Fig. 1. It isseen that the tensile stresses can becategorized in two groups. The ten-sile stresses along the load axis reacha maximum a short distance fromthe plane at which the load is ap-plied. These stresses, to be referredto as "bursting" stresses, are general-ly associated with bearing failures.The transverse tensile stresses awayfrom the load axis reach a maximumat the loaded face. These, to be re-ferred to as "spalling" stresses, aremost often associated with anchor-age-zone cracking.

Various methods have been pro-posed by different authors to calcu-late the transverse stresses. Therelevant studies are reviewed in Ref-erences 1, 2 and 3.

Disagreement was noted amongthe results of some of the most wide-ly used methods. Finite differenceswere used in this investigation to ob-tain the elastic distribution. The re-sults are reported in Reference 1;however, these mathematical solu-tions are not discussed in this pa-per.

The usefulness of the methodsdealing with elastic stresses has tobe examined in view of the structur-al performance of the member. Onemay be primarily interested in themagnitude and the position of themaximum transverse stress in orderto predict crack initiation. However,the stress distribution can be ob-tained, at best, only under idealizedconditions. The initiation of a crackcan be estimated only if the tensilestrength of the concrete, under thecomplex conditions of stress, isknown. This is especially important

in the case of the spalling stressesthat are confined to a small area.Also, frequently there are initial(mainly shrinkage) cracks or differ-ential shrinkage stresses in themember that invalidate the "elastic"analysis. For these reasons, the use-fulness of the purely elastic stressapproach is limited in practice.

Hence, of the two important ques-tions: "What starts a crack?" and"What stops a crack?", the first onecannot be answered with sufficientease and accuracy. The new ap-proach, used in this investigation,was more concerned with the secondquestion. It attempted to find theeffects and the propagation of theanchorage zone cracks. This led tothe examination of the role of thetransverse reinforcement in confin-ing the crack. The method is directand it has resulted in a conserva-tive design procedure.

THE EFFECTS OF TRANSVERSEREINFORCEMENT ON CRACKING

The method of analysis of the ef-fect of transverse reinforcement ad-vanced in this paper is based on theequilibrium conditions of thecracked anchorage zone. The crack,admitted a priori, is to be restrainedby the stirrup to a prescribed width.

The common method of designingreinforcement for end blocks is tocompute the tensile stresses andforces according to some elastic so-lution and then to provide steel atan arbitrary working stress to carrythe total tensile force or part of it.This approach ignores some impor-tant aspects of the behavior of endblocks. There is inelastic action atrelatively low loads that changes thestress distribution. The concretemust be cracked before the rein-forcement comes into action. Theformation of a crack invalidates theelastic stress distribution. An initial

64 PCI Journal

P

El Tensile Stress ZoneFig. 1—Contours of Equal Transverse Stresses

crack (for example, at the junctionof the web and the flange, as foundin one of the test specimens of thepresent investigation) also modifiesthe elastic conditions. Even for anassumed elastic case, there is no gen-erally accepted solution. In addition,the tensile strength of the concreteunder complex conditions is notknown sufficiently.

The analysis presented in this sec-tion investigates the conditions in acracked end block in order to limitthe length and width of the crack.A method is presented for estimat-ing the position of the first crack.The equilibrium of the free body

bounded by the crack is investigatedin order to estimate the internalforces. The relationship between thewidth and length of the crack andthe stirrup force is also examined.The admitted longitudinal crack andthe inside end face of the anchoragezone delineate the free body. Thefollowing quantities enter the analy-sis: applied prestressing force, stir-rup force, the length and width ofthe crack, and the dimensions of theend block.

The forces acting on the free bodyhaving a rectangular section areshown in Fig. 2. The contribution ofthe tensile strength of the concrete

April 1967 65

is ignored. The crack and the ap-plied load are at distances of c ande from the bottom of the end block.The sketch on the top part of thefigure illustrates the beam with thefree body marked in full lines. Theprism is shown enlarged in the bot-tom part of the figure.

The applied force P produces alinear stress distribution at a dis-tance L from the end. To maintainequilibrium, there must be a momentM and a shearing force acting on thetop part of the prism. The moment isto be supplied by the tensile forceT in the reinforcement and by thecompression C in the concrete. Theheight of the free body (that is, theposition of the crack) will be de-termined from the condition that onthat longitudinal section the mo-ment will be the largest.

The moment on the longitudinalsection is:

M=P rc— e —(h) 2

C 2h- 3e—c+ 2hc ljVi (1)

This moment (and, hence, T and

C) changes with the height of thefree body, c. The moment takes ex-treme values for the following twovalues of c:

c1 = h2 and c2 = h (2)3(h-2e)The first of these gives the maxi-

mum moment, the second gives thezero moment on the top surface. Themagnitude of the former is:

_ h2 4h-9eMm"^ rP 127(h-2e)2 - e ] (3)

The maximum moment may alsooccur along the line of the load.This moment can be obtained fromthe general expression of the = mo-ment by setting e = c. This ;, yields

Me =2P 2 h—e (4)

Knowing the moment, the forcescan be calculated if the distance be-tween the forces can be estimated.The position of the tensile force isgiven by the center of gravity ofthe stirrup forces; the position ofthe centroid of the compressive forceis not known. It is somewhere be-tween the end of the crack and the

e fTIJi1T CP

Fig. 2—Forces on the Free Body

66 PC:] Journal

plane where the normal-stress dis-tribution becomes linear. If the po-sition of the compressive force isassumed to be at the end of thecrack, the design will be on the safeside. Thus, the length of the crackmust be known or assumed. In addi-tion to the relationship between themoment on the free body, the stirrupforce, and the crack length, thestirrup force and the crack widthmust also be related in order toestablish a crack width limitation.Force-slip relations can be obtainedfrom bond tests. The crack widthwill be twice the slip if the bar isanchored similarly on both sides ofthe crack. The elongation of the steelbetween the surfaces of the crackis compared with the slip. However,the usual bond values cannot beapplied directly here. The stirrupforces and the amounts of slip dealtwith in this problem are small, whilethe customary bond-slip relation-ships are usually used near the ulti-mate conditions. For this reason, theuniform bond stress used to approxi-mate the actual bond-slip distribu-tion is smaller than the values gen-erally used. The difference isillustrated in Fig. 3, where a uniformbond of 3Vf, (in force/length) wasused as an approximation at smallerforces, while 6-/f approximates theactual curve at high forces. Thismodification, corroborated by test re-sults, is used in the design specifi-cation presented in this paper.

COMPARISON WITH TEST RESULTS

The analysis presented in theprevious section is based on sim-plifying assumptions regarding theinteraction of forces and the develop-ment of cracks. An experimentalinvestigation was conducted to con-firm the assumptions and to investi-gate possible new approaches to the

Slip

Fig. 3—Approximations to the Force-Slip Curve

solution.The following factors and relation-

ships were examined in the experi-mental investigation reported here:the position of the crack, the effectsof the amount of reinforcement, thedifferences in the behavior of endzones with rectangular and I-shapedcross sections, the effect of the sizeof the loading plate, the variation ofthe forces and cracks with the ap-plied load, and the relationship be-tween the stirrup force and the crackwidth.

The position of the crack in thespalling zone is calculated fromEquation 2. The expression yields5.3 in. from the bottom for the rec-tangular beams used in this investi-gation. The crack was observed tooccur at about 5.5 in. from the bot-tom in seven of the nine test speci-mens without reinforcement (notreported in this paper). The samecalculated distance is 5.5 in. for theI-beams.

The measured relationship be-tween the stirrup strain at the crackand the applied load was linear upto the yielding of the reinforcement.The smaller reinforcement (No. 7USSWG) carried only little lessforce than the larger bar (No. 3 de-formed bar). The crack width, how-

April 1967 67

ever, was much larger in the case ofthe smaller size reinforcement.

When two reinforcing bars wereplaced in the specimen, they sharedabout equal portions of the totalforce. The bars were placed relative-Iy close (0.5 and 2 in.) to the endof the beams. The force in each ofthe bars was about equal to the forcein single bars, under equal loads.

The propagation of the cracks wascarefully noted. The larger amountof reinforcement restricted thecracks more effectively. The rate ofincrease of the crack width andcrack length with the applied loaddepends on the amount of reinforce-ment. With little reinforcement thecrack width increased much fasterthan the crack length. With suffi-cient amount of reinforcement thecrack length increased faster thanthe crack width.

According to the analysis, the un-balanced moment is smaller in theI-beams than on the rectangularbeams. This results from the smallermoment arm between the appliedload and the resultant of the longi-tudinal stresses on the free body.The ratio of the moments, for thesections used in this investigation, is1.8. The comparison of the behaviorof the rectangular and I-beams con-firmed this interesting difference.The stirrup strains (measured at thecrack in the spalling zone) werelarger in rectangular beams (about1.5 times in the case of the smallestamount of reinforcement) than inI-beams. Also, the cracks were widerand longer in the rectangular beams.These differences result from the dif-ferent flow of forces in the two sec-tions. In an I-beam with the forceapplied to the flange, a large portionof the force is confined to the flange.The force trajectories have smallercurvature. Consequently, the trans-

verse stresses are smaller in the endzones with I-shaped cross sections.In the rectangular beams the flowof stresses reaches more readily the"web" portion of the beam, with cor-respondingly larger stresses.

The ratio of measured stirrupforces in the rectangular and in theI-beams for specimens with ade-quate reinforcement (two No. 2bars) was 1.7, that agrees well withthe ratio of 1.8 given by the analysis.For insufficient amounts of reinforce-ment, the crack opens and the toppart of the beam participates lessand, hence, the ratio is smaller (1.5for one No. 2 bar and 1.1 for one No.7 USSWG). The ratio of measuredcrack widths in rectangular beamto that in I-beams was 1.4 for equalapplied loads. The ratio of cracklengths was about 2.5 for specimensreinforced with two No. 2 bars.

The agreement between the pre-dicted and measured stirrup forceswas good for both I-beams and rec-tangular beams except for rectangu-lar beams with little reinforcement.In this case the crack width wouldlimit the stirrup force in the designmethod. To illustrate agreement, atan applied load of 20 kips the pre-dicted stirrup force in an I-beamwith one No. 2 bar was 0.75 kips(using a moment arm equal to theheight of the beam less the distancebetween the stirrup and the end ofthe beam). The measured force was0.63 kips. In the case of two No. 2bars in I-beams the calculated forcewas 0.84 kips while the measuredforce was 0.88 kips. The correspond-ing values were 1.50 kips versus 1.54kips for rectangular beams.

The effect of the size of the load-ing plate on the spalling stressesand the stirrup forces was small.This supports the equilibrium anal-ysis. If the eccentricity of the ap-

68 PCI Journal

plied load is small, the effect of thesize of the loading plate is largerand may then be easily included inthe calculation. of the unbalancedmoment, or it can safely be neg-lected.

For the relationship between thestirrup force and the crack width, anaverage bond (in force/length) wasused in the form of m , where mis a numerical coefficient. This re-sults in the following expression

F2 (5)2mEA V f

where F is the force in one bar, A isthe area of one bar, s is the slip ofthe bar. This relationship representsa second degree parabola and sincethe actual variation has smaller cur-vature (is closer to being linear), theabove approximation is good at cer-tain intervals only, as it was ex-plained in the previous section. Forlow stirrup forces (No. 2 or No. 3bars) m = 4 can be used. This valueis reasonable if the limiting crackwidth is about 0.005 in.

The comparison between the ex-perimental and analytical results in-dicates the feasibility of a designmethod based on the approach ad-vanced above.

DESIGN RECOMMENDATIONS

The design method presented inthis paper is based on the method ofanalysis outlined above. In essence, itadmits the presence of a longitudinalcrack in the anchorage zone and isconcerned with the equilibrium ofthe beam portions on either side ofthe crack. Transverse reinforcementis provided to satisfy equilibrium forany possible position of the longi-tudinal crack. The force in the rein-forcement is calculated from themaximum of the unbalanced mo-ments, using an assumed moment

arm. The steel stress is controlled bya limiting crack width through an ap-proximate force-slip relationship. Thepivotal assumption is that there is alongitudinal crack in the anchoragezone. The prime role of the reinforce-ment is to confine the crack.

The method is best suited for thedesign of anchorage-zone reinforce-ment for loads of high eccentricitywhere the conditions of anchoragedo not influence the forces in thespalling zone. If the load has smalleccentricity, the size of the loadingplate influences the forces along theline of the Ioad, though the resultsgiven by this method are on the safeside. In the case of pretensionedtendons, the method can be used byarbitrarily concentrating the forcetransferred at a finite number ofpoints within the anchorage length.

The approach used results in astraightforward method suited foruse in the design office. First, themaximum moment acting on a longi-tudinal section is calculated, as de-scribed above. In order to estimatethe moment arm of the stirrup forcesand the compressive force of theconcrete, the crack length has to beknown. There is no practical way ofestimating this quantity. Since linearstress distribution is reached at a dis-tance of h (or less) from the endface, this value is taken as the upperlimit for the distance between thecompressive force and the end face.The stirrup force can be calculatedby dividing the known moment bythis assumed moment arm to obtainthe total stirrup force. Bond-slip re-lationships are used to check if thecrack width is less than a prescribedlimit. If the actual moment arm issmaller than the one defined above,the stirrups will be overstressed.Then the limitation on the crackwidth will modify the design. The

April 1967 69

method is illustrated below.An approximate expression for the

limit on the stirrup stresses can bederived from the bond-slip relation-ship presented above (Equation 5).It can be written as:

F2 = 4EAJ f (.ww (6)

or f8 = 4E \/w (7)

where w is the crack width, and f8is the stress in the stirrups. For f . _5000 psi, a representative concretestrength at release for prestressedconcrete, the value of the square rootof 4E \/ f , is 0.92>< 105 which canbe taken conservatively as 1.0 X 105.Therefore,

f8= 105 A psi (8)

Naturally, f8 should also be less thansome allowable stress. This limitingstress, with the equilibrium analysisdescribed above, constitutes the de-sign procedure.

The determination of the maxi-mum unbalanced moment is simpleand can be obtained by using alge-braic expressions. For I-shaped endzones the expressions are compli-cated and a trial and error proced-ure is necessary. However, for I-sections of common proportion, theuse of Table I (see Appendix) will fa-cilitate calculation of the posi-tion and the magnitude of the maxi-mum unbalanced moment. The tableis also applicable in the case of rec-tangular beams.

The maximum unbalanced mo-ment is given by the moment of theforces shown in Fig. 4, as follows.

11'1..ax = PB (x —GB) — (x — ax) FR— (x — ar — t) FT

— (x—ativ) Fw (9)

where PB is the resultant of the bot-tom group of prestressing forces. Theother quantities are shown in thefigure, and are defined by the fol-lowing equations:

Fig. 4—Definition of Symbols for Table I

70 PCI Journal

FR= (1- t(bfm(10a)2 v/t )

_u^3v- u- 3t (b-b') f.(10b)FT -6 )y

Fw = xb' fd 2v-xl(

(10c)2 v J

t 3v - 2taR_ 3(2v-t )

(Ila)

_ u_ 2v - u - 2t (11b)aT 2(3v-u-3t

x (\ 2 - x 1aw = l2v -x

(lie)

x = v - Vv2 - 2vcB

= v (1- /1- 2cB /v) (12a)

PB - FR - FTcB (12b)b, f

d

Table I gives FR, aR, FT, aT forvarious v/t and u/t values. Thenonly x and CB have to be determinedfrom the above equations for the usein the expression for Mm¢,. The letterv designates the distance to the neu-tral axis of the stresses due to thetotal prestressing force (using 0_

P/A-tMc/I) from the bottom of thebeam. The maximum moment occurseither on a plane given by x, or alongthe line of the resultant force if v islarge.Example: The transverse reinforce-ment will be designed for theAASHO standard beam No. 1, shownin Fig. 5. The area and the momentof inertia of the section are 276 in.2and 22,750 in4 ., respectively. The pre-stressing force is applied by 22strands in the bottom part of thesection and by two strands at thetop of it and anchored at the end ofthe beam. The center of gravity ofall the forces (a total of 336 kips) isat 6.17 in. from the bottom, while thesimilar distance for the resultant ofthe bottom strands is 4.37 in. Thecenter of gravity of the cross sectionis 12.59 in. from the bottom. Thebending stresses due to all prestress-ing forces are 2.41 ksi compressionand 0.24 ksi tension. Hence:

v = 25.4 in., u = 5 in., t = 5 in.,b = 16 in., b' = bin.fd = 2.41 ksi

(b - b') fa a = 24.1 k/in.u/t = 1, v/t = 5.1

Table I-Coefficients for the Determination of Forces and Their Position

vI

FR(b-b')tfa,

aR

t

u

FT

u(b-b')faaTU

0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2t

3 .833 .465 .284 .278 .272 .267 .304 .300 .296 .2923.5 .856 .472 .314 .310 .305 .300 .310 .308 .305 .3024 .875 .476 .338 .333 .329 .325 .315 .312 .310 .3084.5 .889 .479 .356 .352 .348 .346 .318 .316 .314 .3125 .900 .482 .370 .367 .363 .360 .320 .318 .316 .3155.5 .909 .483 .382 .379 .376 .373 .322 .320 .318 .3176 .917 .485 .392 .389 .386 .383 .323 .322 .320 .3196.5 .923 .486 .400 .398 .395 .392 .324 .323 .322 .3217 .929 .487 .407 .405 .402. .400 .325 .324 .323 .3227.5 .933 .488 .413 .411 .409 .407 .325 .324 .324 .3238 .938 , .488 .419 .417 .415 .412 .326 .325 .324 .324

April 1967 71

therefore, using the proper values inTable I:

FR = 0.901 x 5 x 24.1 = 108.5 k.aR = 0.482 x 5 = 2.41 in.FT = 0.368 x 24.1 x 5 = 44.3 k.aT =0.318X5=1.59 in.

cB = PB bF f FT = 10.74 in.a

x=25.4— X125.42 -2 x 25.4 x 10.74= 15.8 in.

(the position of the plane of themaximum moment)

Fw = xb2 f a (2y - x )157kiPs

x 3v-2xa`r = 3(2v—x = 6.70 in.,

hence the maximum moment is:Mm¢,. = 308 (15.8 — 4.37)

—108.5 (15.8 - 2.41)—44.3(15.8-1.59-5)—157 (15.8-6.7)

= 237 k-in.

The resultant of the stirrup forces isplaced at 5 in. from the end. Hence,the total stirrup force is 237/23=10.3kips. Try No. 3 bars, area 0.11 in.2The allowable stress is

105 .^ 1 0.005 = 21,400 psi,f8 —— v0.11 '

using an allowable crack width of0.005 in. If this is less than a limit-ing steel stress (say 30,000 psi), thetotal stirrup area required is:

10.3 0.48 in.21.4

Use three No. 3 two-legged stirrups,with a total area of 2 X 3 x 0.110.66 in.2

The first stirrup should be placedas close as possible to the end of thebeam. Also, careful mixing and plac-

ing of concrete is very important.For draped pretensioned strands thepoint of action of the resultant pre-stressing forces can be taken at 25diameters along the strands from theend. The stirrups should be well an-chored at the top of the beams andshould enclose all prestressing ten-dons. It is advisable not to have stir-rup spacing larger than h/5 over adistance of h from the end of thebeam. (Hence, one more stirrup maybe used in the above example.)

A similar procedure may be usedto investigate the cracking parallelto the sides of the beam. Verticalcracks may appear in wide beamswith prestressing forces anchoredclose to the side edges of the endface.

SUMMARY

The transverse stresses created bythe prestressing forces may cause

Fig. 5—AASHO Standard Beam No. 1

72 PCI Journal

longitudinal cracks in the end zonesof beams. Many uncertainties makethe prediction of the initiation of thefirst crack and the rate of propaga-tion of existing cracks difficult. Also,no simple measures are available toprevent cracking even if the condi-tions were known.

The analysis of the equilibriumof the cracked end zone yielded ex-pressions for the location of thecrack and the magnitude of the un-balanced moment which creates thetension forces in the transverse steel.A simple procedure resulted for thedesign of stirrups to restrain thecrack.

One series of tests confirmed theproposed method, the prediction ofthe location of the crack and theforces in the reinforcement. A sec-ond series of tests resulted in a force-slip relationship that was used todevelop an expression to limit thewidth of the crack. Both test seriesare briefly described in the Appen-dix.

The investigation brought out theimportance of the spalling stresses,transverse tensile stresses away fromthe line of the load, and showed thatfor eccentric prestressing forcesthese stresses are larger for rectan-gular than for I-shaped end blocks.

A table is included to simplify thedesign of stirrups based on the ap-proach developed in the paper.

ACKNOWLEDGMENTS

This study was carried out in theStructural Research Laboratory ofthe Department of Civil Engineer-ing at the University of Illinois aspart of a cooperative investigationof prestressed reinforced concretefor highway bridges sponsored bythe Illinois Division of Highwaysand the U.S. Department of Trans-portation, Federal Highway Adminis-tration, Bureau of Public Roads. The

opinions, findings, and conclusionsexpressed in this publication arethose of the authors and not neces-sarily those of the State of Illinois,Division of Highways, or the Bureauof Public Roads.

REFERENCES

1. Gergely, P., Sozen, M. A., and Siess,C. P., "The Effect of Reinforcement onAnchorage Zone Cracks in PrestressedConcrete Members," Structural ResearchSeries No. 271, University of Illinois,Urbana, 1963.

2. Lenschow, R. J., Sozen, M. A., "A Prac-tical Analysis of the Anchorage ZoneProblem in Prestressed Beams," ACIJournal, Proceedings Vol. 62, No. 11,Nov. 1965, pp. 1421-1439.

3. Hawkins, N. M., "The Behavior andDesign of End Block for PrestressedConcrete Beams," Research Report No.R58, Civil Engineering Laboratories,The University of Sydney, 1965.

APPENDIXEXPERIMENTAL INVESTIGATION

The experimental investigation,described briefly below consisted oftwo parts. The first part includedtests on unreinforced beams (10specimens) and beams with trans-verse reinforcement (25 specimens).Only the latter are reported here.The second part of the experimentalinvestigation attempted to establishempirical bond-slip relationships forthe use in the design method pre-sented in this paper.

For both parts the concrete wasmade of Marquette brand Type IIIPortland cement, and of aggregatewith maximum size of 3/s in. Thestrength of the concrete ranged from4500 to 5900 psi. Compression andsplit cylinder tensile strength testswere made for every batch.

Two kinds of transverse reinforce-ment were used: No. 2 deformedbars and No. 7 USSWG wires (withcross-sectional areas of 0.05 and0.025 in2 ., respectively).

April 1967 73

(a) Beams with transverse reinforce-ment orce-.ment

The dimensions of the beams areshown in Fig. Al. The specimenshad either rectangular or I-shapedcross sections.

The loading of the specimens pre-sented some difficulties. It was ex-cessively troublesome to keep an ex-ternal load aligned. After variousloading systems had been tried, theone shown in Fig. A2 was adopted.A T-1 steel rod was cast unbondedin the concrete. It was lubricated toprevent bond. Paper wrapping wasalso used in some cases but that waslater found to be unnecessary. Onone end of the specimen a steel bear-ing block with a bearing area of 6 x 3in. was used. A 50-ton center holejack pressed on the steel block withthe reaction supplied by a nut on theend of the rod. On the other end, thebearing area was 6 x 1.5 in. A dyna-mometer was placed between thisblock and the nut.

The instrumentation consisted ofelectric strain gages on the concrete,

placed transversely along longitudi-nal lines, strain gages on the trans-verse reinforcement and .0.0001 in.dials glued across the crack to meas-ure crack width. (In some cases me-chanical gages, Whittemore plugs,were also used to measure transversedeformations.)

In order to measure the stirrupstrains at the crack, the gages hadto be placed at the proper positions.Since the approximate location ofthe crack was known, the gage wasplaced at the corresponding eleva-tion, and a pre-crack was made byplacing a piece of plastic strip at thecenter of the gage to ensure crackingthere.

The development of cracks wasnoted during testing. The loadingwas applied in about 15 incrementsto failure. Each test took less thantwo hours.(b) Bond tests

Two kinds of bond tests weremade. The simple pull-out specimenswere 6-in, cubes with a single bar orwire protruding at the center of one

4 1 – 0°

N

2

:qC1J

Fig. Al—Nominal Dimensions of Test Specimens

74 PCI Journal

Center Hole JackN

T-1 Steel Bar Dynamometer

Loading Block Loading Block

Fig. A2—Test Setup

face. To simulate the conditions in pull-out specimens were loaded bythe end block, twin pull-out speci- a small jack pressing against themens were also made. In this case center of the block on an area of 4 xthere was no pressure on the con- 4 in. on one end and against a dyna-crete around the bar that would pro- mometer on its other end.duce confinement. Two symmetrical- The slip of the bars was measuredly placed bars were pulled at the with a traveling microscope. Ansame time. The twin pull-out tests electric strain gage on one of theare illustrated in Fig. A3. bars in the twin pull-out specimens

The single pull-out tests were served as a check on the loads in themade in the usual manner. The twin symmetrically placed bars.

Jack Pull-out Bar

N Dynomometer

U,

No. 3 Bar

Pll-out Bar

F--F PH H1Ii(

7 ::i,9

Fig. A3—Twin Pull-Out Specimens

Discussion of this paper is invited. Please forward your Discussion to PCI Headquartersbefore July 1 to permit publication in the October 1967 issue of the PCI JOURNAL.

April 1967 75