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Behavior and Design of Shear Connections for Loadbearing Wall Panels Harry R. Foerster Graduate Student Department of Civil Engineering University of Manitoba Winnipeg, Manitoba, Canada Sami H. Rizkalla Professor Head of the Structures Division Civil Engineering Department University of Manitoba Winnipeg, Manitoba, Canada J. Scott Heuvel Manager of Engineering Con-Force Structures Limited Winnipeg, Manitoba, Canada D inring the past decade, use of precast loadbearing shear wall panels for high rise construction has become very popular due to the high quality control achieved at the precast concrete man- ufacturing plant and the ease of panel assembly and erection at the project site (Fig. 1). In the structure, the precast panels are tied together using continuity reinforce- ment bars and mechanical shear con- nectors. The gap between the panels, which is required for alignment, is nor- mally filled with a dry pack grout. This grouting system eliminates the use of falsework and minimizes the use of temporary supports. Current design sources'- 3 provide only limited information about the behavior and ultimate shear carrying capacity of the connections described in this paper. The information available in the liter- ature lo mainly describes the shear fric- tion mechanism and the dowel action of initially cracked concrete to concrete surfaces. The results of such studies cannot be directly applicable to the pre- described connections due to the pres- ence of the dry pack grout layer between the two concrete surfaces. 102

Transcript of Behavior and Design of Shear Connections for Loadbearing ... · PDF fileBehavior and Design of...

Page 1: Behavior and Design of Shear Connections for Loadbearing ... · PDF fileBehavior and Design of Shear Connections for Loadbearing Wall Panels Harry R. Foerster Graduate Student Department

Behavior and Design ofShear Connections for

Loadbearing Wall Panels

Harry R. FoersterGraduate StudentDepartment of Civil EngineeringUniversity of ManitobaWinnipeg, Manitoba, Canada

Sami H. RizkallaProfessorHead of the Structures DivisionCivil Engineering DepartmentUniversity of ManitobaWinnipeg, Manitoba, Canada

J. Scott HeuvelManager of EngineeringCon-Force Structures LimitedWinnipeg, Manitoba, Canada

D inring the past decade, use of precastloadbearing shear wall panels for

high rise construction has become verypopular due to the high quality controlachieved at the precast concrete man-ufacturing plant and the ease of panelassembly and erection at the project site(Fig. 1).

In the structure, the precast panels aretied together using continuity reinforce-ment bars and mechanical shear con-nectors. The gap between the panels,which is required for alignment, is nor-mally filled with a dry pack grout. Thisgrouting system eliminates the use of

falsework and minimizes the use oftemporary supports.

Current design sources'- 3 provide onlylimited information about the behaviorand ultimate shear carrying capacity ofthe connections described in this paper.The information available in the liter-aturelo mainly describes the shear fric-tion mechanism and the dowel action ofinitially cracked concrete to concretesurfaces. The results of such studiescannot be directly applicable to the pre-described connections due to the pres-ence of the dry pack grout layer betweenthe two concrete surfaces.

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RESEARCH SIGNIFICANCE'the main objective of this study is to

investigate the behavior of differenttypes of connections typically used inpractice for precast concrete loadhear-ing shear wall panels, The study at-tempts to identify the contribution ofeach component used for these types ofconnections at various limit states. Theresults of the experimental programwere used to refine and calibrate pro-posed rational mathematical modelsintroduced to predict the strength ofsuch connections before and aftercracking.

EXPERIMENTAL PROGRAM

Test SpecimensA total of ten specimens were tested.

Dimensions of all the precast panelswere identical, with a thickness of 200mm (77/s in.) and overall dimensions of1660 mm and 1290 mm (65% and 50Y4in.), as shown in Fig. 2. The dimensionscorrespond to a prototype scale of theprecast panels typically used for highrise construction. A typical reinforce-ment detail of the panel used for all thespecimens is shown in Fig. 3. The fiveconnection configurations used in thisprogram are as follows:• Type I: Dry pack grout only.• Type II: Dry pack grout and 25M (No.8) continuity bars.• Type III: Dry pack grout, 25M (No. 8)continuity bars, and shear connectorsType A.• Type IV: Dry pack grout, 25M (No. 8)continuity bars, and shear connectorsType B.• Type V: Shear keys with dry packgrout.

Details of the above connections areshown in Fig. 4_

The average compressive strength ofthe normal weight concrete and the drypack grout used for each specimen weredetermined using standard 150 x 300

SynopsisFive different connections for load-

bearing wall panels were subjected tomonotonic shear load up to failure.Two levels of preload, applied normalto the connection, were used. Thedifferent connection configurations in-cluded dry pack grout, continuityreinforcement steel bars, mechanicalshear connectors with two differentanchorage details and dry packedshear keys.

Test results were used to evaluatethe friction coefficient factor and to re-fine and calibrate a proposed rationalmathematical model introduced topredict the shear carrying capacitybefore and after cracking.

mm (6x12 in.) concrete cylinders and 75mm (3 in.) cubes, respectively. The con-crete, supplied by a local ready-mixconcrete company, had a maximumaggregate size of 14 mm ('/2 in.) and anaverage slump of 75 min (3 in.). The re-inforcement bars were Grade 400W (58ksi) and the shear connection plateswere 300W (43 ksi) steel, according toCSA CAN3-516.1-M84.9

Each specimen consisted of two pre-cast panels as shown in Fig. 5. All pa-rameters, such as steel details and con-crete material, were kept constant. Thetwo panels were connected after 28 daysusing the various connection detailspreviously described. Specially de-signed temporary steel brackets wereused for specimens with dry pack groutonly.

The dry pack grout mix consists of twoparts concrete sand, one part normalportland cement and approximatelyone-half part water. The mix was placedand compacted into the 20 mm (^ in.)wide joint space between the twopanels. The mixture was of a dry con-

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Fig. 1. Precast high rise building.

sistency, which allowed for tamping andcompaction of the material.

Electric resistance strain gages wereused to measure the strains of the con-tinuity bars and the shear connectorplates. The average strains of the con-crete and the dry pack were measuredusing mechanical strain gages at various

locations, as shown in Fig. 6 for a typicalspecimen. Linear variable differentialtransducers were also used to monitorthe deformation parallel and perpen-dicular to the joint.

Figs. 2 and 3 (opposite page) show thepanel configuration and the typical re-inforcement of the panel,

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L 540 r50 1070

0rn

Oery

16 60

25.4 mm = I inch

Fig. 2. Panel configuration.

Fig, 3. Typical reinforcement of panel.

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20 mm widegrouted'pint

spacetypical

Continuity bars i 25 M 770mm c/c(No.B) reinforcing welded {centered into 75x75xL0 (3x3x 3/B) the connection)angle iron) typical

Type I Type II

Shear connectortype A

(5 to ang le weldedto angle iron

with connection ate)

'Shear connectortype B

(15M (No 5) reinforcingand plate withcorrection plate I

II 225 E4BOXXType III

Type ITL

I00mm70mmtypical

typical35 mm _ Dry pack groutedtypical shear keys

4 Shear key lugstypical

25.4 mm = I inchType y I MF = 145 psi

Fig. 4. Connection configurations.

TESTING APPARATUSAND PROCEDURE

Each specimen was positioned verti-cally into the testing machine as shownin Fig. 7. It should be noted that the testspecimens were rotated 90 degrees withrespect to Figs. 2, 5 and 6 for testingconvenience. The joint centerline of thespecimen was aligned with the verticalcenterline of the top and bottom heads

of the testing machine.To study the dead load effect, two

levels of preload, equivalent to 2 MPaand 4 MPa (290 psi and 580 psi), wereapplied normal to the joint. A post-ten-sioning scheme consisting of four hy-draulic jacks, Dywidag bars and a seriesof plates designed to allow deformationof the joint was used to measure theapplied preload as shown in Fig. 8. Anadditional post-tensioning scheme was

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Fig. 5. Specimen configuration.

Typ, DemecGauge Locoticn- F 150

___7 .LLApplied 100Shear

35

25.4 mm = I inch

Fig. 6. Mechanical strain gage locations.

used at the outer edges of each panel toprevent premature failure of the panel atthe loading zones.

The testing procedure was started byapplying the normal preload to the de-

signed level, followed by an initialreading of all the instrumentation. Thetesting machine was used to apply thevertical shear load in increments of 100kN (22.5 kips). At each increment, all

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Fig. 7. Test setup. Fig. 8. Preload apparatus.

readings of the instrumentation were re-corded, followed by marking of thecracks. The experiment was terminatedafter extensive deformation and signifI-cant drop of the load carrying capacitywas observed. Descriptions of the testedspecimens, including the material prop-erties of the concrete and dry pack grout,are given in Table 1.

OVERALL BEHAVIORA sunnnary of the test results and

overall behavior of the specimens arediscussed in this section. For detailedinformation, consult Ref. 10.

Connection Types and Behavior

Connection Type I (Dry Pack GroutOnly) — Typical displacement of thejoint parallel to the applied shear loadfor Specimen SP21 under a preloadlevel of VIPs (580 psi) is shown in Fig. Fig. 9. Typical failure of Connection Type I.

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Table 1. Summary of variables considered in experimentalprogram.

Normalpreloadlevel

(MPa)Specimen

markType of

connection

Concretecompressive

strengthf, (MPa)

Dry packcompressive

strengthfo (MPa)

SPI 1 1 31.9 46.4SPI2 II 32.3 49.7

2 SP13 III 43.5 56.6SPI4 IV 46.5 66.5SP12C Precracked 43.2 59.4

TI

SP21 1 41.5 56.6SP22 II 34.5 67.6

4 SP23 III 49.3 56.9SP24 TV 52.8 60.2SP25 V .32.4 59.6

\ rte: I MPa – 145 psi.

O SP I I

• SP21

Hciiiiii 25.4 mm = I inchI kN = 0.225 kips

0 2 6 In 14 IR 7;

DISPLACEMENT (mm)

Fig. 10. Load-displacement relationship of Connection Type I.

(600

1400

1200

1000

800

600

400

200

0

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1400

1200

z 1000

800

600

400

200

0

• SP 120 SP 22• SP 12C

25.4 mm = I inchkN = 0.225 kips

'- 2 6 In 14 rR 2

DISPLACEMENT (mm)

Fig. 11. Load-displacement relationship of Connection Type II.

Ij 9. The joint exhibited insignificantdeformation prior to cracking of thegrout. Substantial and sudden dis-placement, accompanied by significantloss of stiffness and the load carryingcapacity, was observed at the initiationof cracking of the grout layer as shown inFig. 10. The specimen exhibited asteady deterioration of the load carryingcapacity due to smoothing of the inter-face surfaces with increased displace-ment. The resistance after cracking wasproportionate to the level of the appliedpreload normal to the joint.

Connection Type II (Dry Pack Groutand Continuity Bars) — Similar to JointType 1, the defonnation was insignif-icant before cracking, as shown in Fig.

– -- - 11 for Specimens SP12 and SP22 underthe two predescribed preload levels.The presence of the continuity bars en-hanced the resistance after cracking due

• to the effect of dowel action. The loadFig. 12. Typical failure of Connection Type II. carrying capacity steadily increased by

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1600

1400

1200

1000z

6000

600

400

200

0

O SP I30 SP 23

25.4 mm = I inchI kN = 0.225 kips

0 2 6 IC) 14 OR 2;

DISPLACEMENT (mm)

Fig. 13. Load-displacement relationship of Connection Type III.

subjecting the joint to large deformationas illustrated in Fig. 11.

It should be noted that the highercracking load of Specimen SP22 couldbe attributed to the significantly highercompressive strength of the dry packgrout used for this specimen. The be-havior of the precracked specimen,SP12C, was identical to Specimen SP12after cracking, as shown in Fig. 11.Typical failure of this type ofconnectionis shown in Fig. 12 for Specimen SP12C.

Connection Type III (Dry Pack, Con-tinuity Bars and Shear Connectors TypeA) — Use of inechanical shear connec-tors with Anchorage Detail A in additionto the continuity bars and dry pack grouthad no influence on the joint behaviorbefore cracking of the grout, as observedfor Specimens SP13 and SP23. How-ever, the gradual reduction of the stiff-ness rather than the sudden drop of theload carrying capacity, shown in Fig. 13,was evidence of the additional contri- Fig. 14. Typical failure of Connection Type III.

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1500

1400

1200

1000

800

_j 600

400

200

0

0 5P 14• SP 24

25.4 mm = I inchkN = 0.225 kips

?u 2 F, Ifl I4 IR 9:

DISPLACEMENT (mm)

Fig. 15. Load-displacement relationship of Connection Type IV.

bution of the shear connectors. Behaviorof the specimen suggested also that thepresence of the mechanical shear con-nectors enhanced the clamping actionand the overall ductility of the joint, asevidenced by the large deformation be-fore failure (as shown in Fig. 14) forSpecimen SPI3.

Connection Type IV (Dry Pack, Con-tinuity Bars and Shear Connectors TypeB) — The only difference betweenJoints Type III and Type IV lies in theanchorage detail used for the shear con-nector, as described in Fig. 4. The be-havior before cracking of SpecimensSPI4 and SP24 with Anchorage Type Bwas identical to that of specimens withT ype A anchorage. However, bothspecimens with Type B anchorage ex-hibited a faster rate of stiffness reduc-^iLion, as shown in Fig, 15. This behaviorcould be attributed to earlier bond fail-ure of Anchorage Detail B in compar-

Fig. 16. Typical failure of Connection Type IV. ison to Detail A. Typical failure of this

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1600

1400

1200

z 1000

o 800

a 600

400

200

0

• SP 25

25.4 mm = I inchI kN = 0.225 kips

0 2 6 10 14 I8 2:

DISPLACEMENT (mm)

Fig. 17. Load-displacement relationship of Connection Type V.

type of connection is shown in Fig. 16for Specimen SP24.

Connection Type V (Dry Pack, ShearKeys) — One specimen with dry packmultiple shear keys connection, SP25,

i''was tested in this program. As illustratedin Fig. 17, the behavior indicates agradual loss of stiffness due to the pro-gressive formation of failure surfaces,which are due to the seating charac-teristics of the keys and continuous lo-calized crushing of the concrete andgrout as shown in Fig, 18. Continuouscracking of the grout results in graduallosses in the stiffness rather than thesudden drop of load resistance observedin other types of connections. As shownin Fig. 18, the ultimate resistance oc-curred as a result of the completecracking of the concrete at the bases of *j • r„ .^ a sr.the shear lugs. Using the shear keysconnection increased the load carrying "' R

capacity by approximately 40 percentwhen compared to the plain surface Fig. 18. Failure of Connection Type V.

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16 0

1400

1200

Z 1000

800

d 600

400

200

0

• SP 21O SP 22♦ SP 23

L SP24

■ SP 25

25.4 mm = I inchI kN = 0.225 kips

0 2 6 in

DISPLACEMENT (mm)

Fig. 19. Behavior of all connections under a preload of 4 MPa (580 psi).

L.® 2 MPa® 4MPo

0

cc>-F- 1.1J

UD0

0 i -il

0TYPE Y II III IV

JOINT CONFIGURATIONI MPa = 145 psi

Fig. 20. Ductility ratio of the differentconnections.

114

- grouted joint. Further experimentalwork is now in progress to examine thebehavior of various shear keys config-urations at different preload Ioad levelsnormal to the joint.

Behavior of the five different types ofconnections considered in this program,under a preload level of 4 MPa (580 psi),is shown in Fig. 19.Ductility

Ductility of the various types of con-nections tested in this program was de-termined based on the total energy ab-sorbed by the joint at a selected dis-placement of 5.4 mm (7/a2 in.), achievedby all the tested specimens. Fig. 20compares the measured ductility of thevarious joints to the ductility of the drypack connection, Type 1, at the twopreload levels. Obviously, using me-chanical shear connectors clearl y en-hanced the ductility by an average of 80percent. It should also be noted thatusing shear keys connection improvedthe ductility by 65 percent.

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z 1600Z

QO 12000z

U800

0wtU

400uJa

2 •2'221 S^^

SP t4 6 2313•

12 91•II

0 400 800 1200 1 600

MEASURED CRACKING LOAD (kN}I kN = 0.225 kips

Fig. 21. Predicted and measured cracking loads.

Cracking StrengthBased on the iiieasured experimental

results, it was found that regardless ofthe type of mechanical shear connectorsused, the cracking strength stress, Vcr,depends on the tensile strength of thegrout, f, and the level of the appliedpreload, Q,,, as follows:

ver =4 r,rn +f^) (1)

Accordingly, the cracking load of theconnection, Vtr, can be estimated basedon the area of the concrete interfacealong the cracked surface,A^, as follows:

17cr = Aevcr (2)

Using an estimated tensile strength ofthe grout, ft , in terms of the ultimatecompressive strength, f;, of 0.5could lead to a very reliable predictionof the cracking load. This is shown inFig. 21.

Ultimate ResistanceCurrent design sources'' were used to

predict the ultimate resistance of thejoints in this study, and the results werecompared to the measured values asshown in Fig. 22. Using the well-knownfriction theory48 and including the weldarea of the mechanical shear connectoras part of the clamping action, the ulti-mate shear resistance of the connection,V,,, on the contact surface A,, could bedetermined as follows:

Model 1:

V,, = µ(o,, + p ,u + p f,)A= (3)

where pb is the percentage of steel of thecontinuity bars of yield strength f

11, and

pw is the percentage of steel of the weldarea of yield strength f.

For an average coefficient of friction,A, of 0.7 based on the measured ultimateload, the predicted ultimate shear re-sistance of the various connections

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acl• ,^ CPCI

• PCI

2000

1600z

0 12000

0uJ

800CDwXa-

400p /^

• ACIO PCI• CPCI

0 I If I I I iI I 1 i i N

0 400 800 1200 1600 •.•

MEASURED LOAD (kN)I kN = 0.225 kips

Fig. 22, Predicted and measured ultimate loads.

1600SP 24 23

Z 1200_x

9 g/S13N

aa0J 8000wF-Uawa 400

SP 12C

lxO• MODEL IO MODEL 2O PROPOSED MODEL

01 I I I I 1 I f I I I I I. ....I I I

0 400 800 1200

1600

MEASURED LOAD (kN)I kN = 0.225 kips

Fig, 23. Prediction capability of existing and proposed models.

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WELD1I 225

III lI

III II3-25M-- —3-25MIIII ^- I I _thFL00R

20 mm I I 1r--^ I j 1

DRY-PACK i IiiI i iit I II

8200mm

A5 /25M = 500 mm225.4 mm = I inch

Fig. 24. Design example.

tested in this program is compared to themeasured values in Fig. 23.

This model could be modified by con-sidering the shear resistance of theweld, V, as an additive component tothe shear friction as follows:Model 2:

V. = A(v,, + p&f,)A C + V. (4)

where V. is the shear strength of theweld, A.„ of the mechanical shear con-nector:9

VW -- 0.5Auf9(5)

Predicted ultimate shear resistanceusing Model 2, Eq. (4), and a frictioncoefficient factor of 0.7 is compared tothe measured values in Fig. 23.

The proposed model introduced inthis investigation is to evaluate the ulti-mate shear resistance of the joint as asummation of the contribution of eachindividual component. The componentsare the friction due to aggregate inter-lock at the joint, the shear resistance dueto dowel action of the continuity bars,and the shear resistance of the weld asfollows:

Proposed Model;

V9 = + AJ /, +V, (6)

where Ab is the area of the continuitybars.

The predicted ultimate shear resis-tance based on the proposed modelusing a friction coefficient factor of 0.7 isalso given in Fig. 23. The prediction re-liability of this model appears to hesuperior to Models 1 and 2. The overes-timation of the strength of SpecimenSP24 could be attributed to the prema-ture failure of Anchorage Detail B usedfnr this connection.

NUMERICAL EXAMPLEConsider a 200 mm (8 in.) precast con-

crete loadbearing shear wall panel at thefourth floor of a 26-story high rise apart-ment complex (see Fig. 24). The re-quired problem is to determine the ul-timate shear resistance of a typical shearconnection.

To solve the problem, assume that thefollowing information is given (see nextpage);

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Equivalent dead load at the connectionIevel = 360 kN/in (24.7 kips/ft).Total horizontal shear load at the con-nection level = 800 kN (180 kips).Yield strength of the continuity bars:f = 400 MPa (58 ksi),Yield strength of the welding electro-rod: f,,, = 480 MPa (69.6 ksi).Compressive strength of the concrete:f^• = 40 MPa (5 ksi).

It should be noted that the methoddescribed in this paper is based solelyon the effect of shear loads, Therefore,one-half of the length of the panel willhe considered in evaluating the shearresistance of the connection in order toaccount for the presence of bendingmoments.

Based on the specified dead load, thestress normal to the connection is:

= 360a',,

= 1.8 MPa (261 psi)200

The area of the contact surface is:8200

Ae = (200)2 11

820x103 mni 2 (1271 in.2)Using an estimated tensile strength of

the grout, f„ of 0.5 v7 the crackingstrength of the connection can he esti-mated using Eq. (2):

V. =[820x103til2.96(1.8+2.96)110-5= 3077 kN (692 kips)

Based on the proposed model, Eq. (6),the nominal ultimate shear resistance ofthe connection can be predicted:

Vu = x 103) + 6(500)V 3

+ U,5 (J2 x 225) (480) 1 I0-'

= 2146 kN (483 kips) 1

The ultimate resistance is consid-

erably higher than the factored load discto wind:

Vr= 1.7(800) = 1360 kN (306 kips)Since the cracking strength exceeds

the ultimate shear resistance of the con-nection, the deformation of the connec-tion will he insignificant,

CONCLUSIONSThe various limit states behavior of

the connection typically used for precastconcrete loadbearing shear wall panelsis determined, Based on the test resultsof ten prototype specimens, it was foundthat regardless of the mechanical con-nectors used, the cracking strength de-pends on the tensile strength of thegrout and the level of the preloadapplied normal to the joint.

A proposed mathematical modelbased on the individual contribution ofeach component of the connection is in-troduced. The predicted ultimate shearresistance of the connection was foundto be in good agreement with the mea-sured values.

The results of a pilot specimen testedwith a shear keys connection indicatedsuperior performance in comparison tothe typical connections, Further re-search is currently in progress to inves-tigate the behavior of the shear keysconnection with dry pack grout.

ACKNOWLEDGMENTThis study was performed in the De-

partment of Civil Engineering at theUniversity of Manitoba, with financialassistance from Con-Force StructuresLimited, Winnipeg, Manitoba, and theNational Research Council of Canada,IRAP program.

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REFERENCES1. ACI Committee 318, "Building Code

Requirements for Reinforced Concrete(ACT 318-83)," Detroit, Michigan, 1983.

2. PCI Design Handbook -Precast andPrestressed Concrete, Third Edition,Prestressed Concrete Institute, Chicago,Illinois, 1985.

3. Metric Design Manual, Canadian Pre-stressed Concrete Institute, Ottawa,Ontario, Canada, 1987.

4. Birkeland, P. W., and Birkeland, H. W.,"Connections in Precast Concrete Con-struction," ACI journal, Proceedings V.63, No. 3, March 1966, pp. 345-367.

5. Mast, R. F., "Auxiliary Reinforcement inConcrete Connections," Journal ofthe Structural Division, ASCE, V. 94,No. ST6, Jane 1968, pp. 1485-1504.

6. Hotbeck, J. A., Ibrahim, 1. 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.,

"Shear Transfer in Reinforced Con-crete — Recent Research," PCI JOUR-NAL, V. 17, No. 2, March-April 1972, pp.55-75.

8. Mattock, A. H., "Shear Transfer in Con-crete Having Reinforcement at an Angleto the Shear Plane," Shear in ReinforcedConcrete, ACI Special PublicationSP-42, V. 1, 1974, pp. 17-42.

9. Steel. Structures for Buildings -LimitStates Design (CAN3-516.1-M84), Cana-dian Standards Association (CSA), Rex-dale, Ontario, Canada, 1984.

10. Foerster, H. R., "Behavior of the Con-nection Typically Used in Precast Con-crete Load Bearing Shear Wall Panels,"MSc Thesis, Civil Engineering Depart-ment, University of Manitoba, Winnipeg,Manitoba, Canada, 1987.

APPENDIX - NOTATION

A b = area ofcontinuity barsA, = contact area of concrete inter-

face subject to compressivestresses

A^ = throat area ofweldf^ = compressive strength of concretefv = compressive strength of dry pack

groutft = tensile strength of dry pack grout

= yield strength of continuity barsf„u = yield strength of weld

v^.r = cracking strength of connectionVrr = cracking load of connectionV,, = ultimate shear resistance of con-

nectionV,n = shear resistance of weldµ = coefficient of frictionpp = percentage of steel of continuity

barsp, = percentage of steel of weld areavR = compressive stress norrnal of con-

nection

* * t

NOTE: Discussion of this paper is invited. Please submityour comments to PCI Headquarters by October 1, 1989.

PCI JOURNAL/January-February 1989 119