NATIONAL SCIENCE FOUNDATION GRANT NO. ENG74-21131

FINAL REPORT

PART 3

Report SM77-2

EFFECT OF REINFORCING BAR SIZEON SHEAR TRANSFER ACROSS A

CRACK IN CONCRETE

by

Alan H. Mattock

REPRODUCED BYNATiONAL TECHNICALINFORMATION SERVICE

u. S. DEPARTMENT OF COMMERCESPRINGFIELD, VA. 22161

Department of Civil EngineeringUniversity of Washington

September) 1977 .

TECHNICAL REPORT STANDARD TITLE PAGE-

1. Repo" N". T2. Gov.,nment Ac<:~.. ion No. 3. Recip.ent'l Cotoloi No.

SM77-2A. Titl. and Subtitle 5. R~po'l Dot..

EFFECT OF REINFORCING BAR SIZE ON SHEAR <; 1077

TAANSFER AC ROSS A CAACK IN CONC RETE 6. P.,fo,ming C'ionil0tion Cod..

7. Author'sl - r8. P ..<Io,on,ng O,ganozation Report No.Alan H. Mattock I SM77-2 .'

9. Perfo,ming O,goni 10lion Name and Add,.... 110. Work Unit No.

Unlversity of Washington11. c.ontract or G'ont No.Department of Civil Engineering ENG 74-21131Seattle, Washington 9819513. Typ. of R..p",t and Pe'iod Covered

12. Sponloring Agency Name ond Add,.... Final Re~ort, Part 314 Oct. ~74-

National Science Foundation 30 Sept. 1977Washington, D.C. 20550 14~ Sponsoring o\g..ncy Cod.

15. Supplem..ntory Notes

.16. Abstract The total study is concerned with the shear transfer strength

of reinforced concrete subject to both single direction and cyclical-ly reversing loading, the latter simulating earthquake conditions.The primary topics studied were the 'influence of the existence inthe shear plane of an interface between concretes cast at differenttimes, and the influence of reinforcing bar diamet~r on sheartransfer across a crack in monolithic concrete.

This Part 3 of the Final Report is concerned with the effect ofsize of reinforcing baron shear transfer across a crack in concrete,under both monotonic and cyclically reversing shear. Nonotonic andcycl ically reversing shear transf~r tests were made of initiallycracked concrete push-off specimens, having reinforcement varyingfrom #4 to #18 in size.

Some' reduction in shear transfer strength occurred as the barsize was increased from #8 to #18, but the ~onotonic loadingstrength of all 'specimens ~as conservatively predicted by the shear-friction equation. The strength under reversed cyclic loading wasabout 0.8 of the strength under monotonic loading.

17. K.y Words 18. Distribution Stoleme"t ~--n~Y--/

connections, precast concrete,reinforced concrete, reinforcing tv rfll~ --4 '4;,IJ~ f.e<bar, seismic loading, sheartransfer. In I~./lj\ #71'/ 1::71/6 '/

lV')jY1' ¢-P,)j.;J 1- 5/ 7S19. Security Clossil. (of this repo't) 20. Socu,i ty Clossi!. (of thi s pagel 22. P,ice

None None Kl\of~4el

\'

PREFACE

This study was carried out in the Structural Research Laboratory of

the University of Washington. It was made possible by the support of

the National Science Foundation, through Grant No. ENGR74-21131.

Contributions were made to the execution of this project by graduate

student research assistants, A. Bhalaik and D. Novstrup.

TABLE OF CONTENTS

I INTRODUCTION

1.1 Background

1.2 Scope of the Entire Study

1.3 Sub-Division of the Final Report

1.4 Background to this Part of the Study

II EXPERIMENTAL STUDY

2.1 Scope

2.2 The Test Specimen

2.3 Materials and Fabrication

2.4 Initial Cracking

2.5 Testing Arrangements and Instrumentition

2.6 T~sting Procedures

II I TEST RESULTS

3.1 Ultimate Strength and Loading History

3.2 Specimen Behavior

IV DISCUSSION OF TEST RESULTS

4.1 General Behavior

4.2 Ultimate Strength

V PRINCIPAL CONCLUSIONS

REFERENCES

APPENDIX A - NOTATION

APPENDIX B - DATA FROM MONOTONIC LOADING TESTS

APPENDIX C - TYPICAL DATA FROM CYCLIC LOADING TESTS

;;

Page

1

1

1

2

2

4

4

4

6

8

9

10

13

13

13

17

17

27

32

34

Figure

2.1

2.2

2.3

LIST OF FIGURES

Title

Specimen details.

Arrangements for test.

Inverting specimen in cyclic loading test.

3. 1 Typical appearance of a monotonic loading specimen afterfailure.

3.2 Typical appearance of a cyclic loading specimen afterfailure.

3.3 Variation of shear stiffness with number of cycles ofloading, C4A.

3.4 Variation of shear stiffness with number of cycles ofloading, CSA.

3.5 Variation of shear stiffness with number of cycles ofload i ng, C1OA •

3.6 Variation of shear sti ffness with number of cycles ofloading, C14A.

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Variation of effective shear stiffness with percent ofcycles of load causing failure.

Variation of shear stiffness near zero shear, with per­cent of cycles of load causing failure.

VariatioQ 8f damping factor calculated according toJacobsenl l . .

Calculation of damping factor according to Jacobsen(lO) .

Variation of d9~~~ng factor calculated according toHawkins et al. l )

Calculation of damping factor according to Hawkins et al .(11).

Comparison of shear-slip relations for M4A and C4A.

Comparison of Shear-slip relations for MBA and CBA.

iii

Figure

4.9

4.10

4.11

4.12

Title

Comparison of shear-slip relations for M10A and C10A.

Comparison of shear-slip relations for M14A and C14A.

Variation of (Reinforcement Stress)/(Separation) withbar diameter, in shear transfer push-off tests and bondpu l1-out tes ts .

Variation of ultimate shear transfer strength with rein­forcing bar diameter.

iv

I - I NTRODUCTI ON

1.1 Background

The purpose of this study has been to obtain further information on shear

transfer in reinforced concrete subject to both single direction and cyclically

reversing shear. In this connection, II shear transfer II is defined as the transfer

of shear across a specific plane or crack in the concrete. Failure in shear

transfer appears as slip along the plane or crack, under the action of a constant

or decreasing shear force.

The principal topics included in the study were,-

(1) the influence on shear transfer behavior, of the existence in the

shear plane of an interface between concretes cast at different times.

(2) the influence of reinforcing bar size on shear transfer across a

crack in monolithic reinforced concrete.

The overall objectives of this study have been to improve understanding of

the mechanics of shear transfer in reinforced concrete, and to develop design

recommendations for shear transfer in reinforced concrete subject to static or

cyclically reversing loading conditions.

1.2 Scope of the Entire Study

Tests have been made of II pus h-off li type specimens and such modified versions

of the simple push-off type of specimen as will permit the desired loading

condition to be imposed on the specimen.

The following variables have been included in the test program:-

1. The use of composite or monolithic specimens.

2. The compressive strengths of the concretes cast against one another.

3. The condition of the face of the precast concrete against which

other concrete is cast, i.e. smooth or deliberately roughened, bond deliberately

broken or not.

1

2

4. The existence of a crack in the shear plane.

5. The shear transfer reinforcement parameter pfy.

6. The size of the reinforcing bars used as shear transfer reinforcement.

7. The type of loading, i.e., single direction and cyclically reversing

shear.

1.3 Sub-Division of the Final Report

Part 1 of the final report described(l) that part of the study concerned

with shear transfer across interfaces between concretes cast at different times,

when subject to monotonically increasing shear.

Part 2 of the final report described(2) that part of the study concerned

with shear transfer across interfaces between concretes cast at different times,

when subject to cyclically reversing shear.

Part 3 of the final report describes that part of the study concerned with

the effect of size of reinforcing bar on shear transfer across a crack in con-

crete, under both monotonic and cyclically reversing shear.

1.4 Background to this Part of the Study

Data so far published on shear transfer behavior has been obtained in

tests in which the shear transfer reinforcement was less than 3/4 inch diameter*.

Wlthin this range of sizes it was shown(3) that the shear transfer strength is

only influenced by change in bar size to the extent that the shear transfer

reinforcement percentage, p, is changed; i.e. if both bar size and spacing are

changed so that p is not changed, then the shear transfer strength is unchanged.

Although the range of bar sizes included in previous tests covers the bar

sizes used in many circumstances in precast concrete construction, an increasing

number of design situations are arising where it is necessary to use larger bar

*This statement relates to tests in which the reinforcement is embedded in and. bonded to the concrete.

3

sizes as shear transfer reinforcement. This is occurring in both precast con-

crete construction and cast-in-place concrete construction. An extreme case

occurs in the design of nuclear reactor containment vessel walls.

It has been proposed by some engineers that the II shear friction" design

concepts contained in ACI 318-71(4), which are based on data from tests of

specimens reinforced with fe1ative1y small sized bars, should be applied to the

membrane shear design of a containment vessel wall reinforced with #14 or #18

reinforcing bars. This would be a considerable extrapolation.

The transfer of shear across a crack involves a combination of resistance

to shearing off of local IIhigh spots,1I (or asperities,) on the crack faces,

frictional resistance to sliding of one crack face over the other, and dowel

action of the reinforcing bars. The relative contributions of each of these

to shear transfer resistance depends upon the intensity of shear stress, the

hardness and roughness of the crack faces, and the amount and possibly the

size of the shear transfer reinforcement.

At the commencement of this study it was considered that the role of rebar

dowel forces in the development of shear transfer strength, was ana1agous to

the role of dowel forces in stud shear connector behavior in composite steel

and concrete construction. Research(5) has shown that the useful strength of

stud shear connectors of diameter greater than about 1 inch, is limited by

splitting of the concrete as a result of dowel action, rather than by the

tensile strength of the stud. It was considered possible that a similar limita­

tion might be found in the case of large size reinforcing bars used as

shear transfer reinforcement. It therefore appeared desirable to establish

the maximum bar diameter for which current shear transfer design procedures

are valid.

II - EXPERIMENTAL.STUDY

2.1 Scope

This experimental study was concerned with the influence on shear transfer

across a crack in monolithic concrete, of the size of reinforcing bar used as

shear- transfer reinforcement. In particular, it was desired to establish the

maximum bar diameter for which current shear transfer design procedures are

valid.

The variables included in the study were,-

1. The size of reinforcing bar

2. The loading history of the test specimens,­

(a) monotonically increasing load,

(b) cyclically reversing load.

2.2 The Test .Specimen

A push-off specimen with two shear planes, each of 1000 in~ area, was used

for. both the monotonic loading and cyclically reversing load tests. Details of

a typical specimen reinforced with bars size 11 or less, are shown in Fig. 2.1.

In the case of specimens reinforced with #14 or with #18 bars, straight bars

with anchor plates on their ends were used instead of closed hoops. The

specimen was supported on the bearing strips and was loaded concentrically,

by a load distributed over most of the width of the specimen between the two

shear planes. This produced a shear in each shear plane equal to half the

applied load, together with a small moment.

One of the objectives of the tests was to establish the maximum bar dia­

meter for which current shear transfer design procedures are valid. It was

therefore decided to hold the reinforcement parameter as nearly constant as

possible, and to make it as close as possible to the value of pfy corresponding

to the maximum allowable shear transfer stress according to Se:. 11.15 - shear-

4 -

° 5

friction of ACI 318-71. For a concrete compressive strength f~, of 4000 psi,

theOmaximum allowable shear transfer stress is 800 psi. The corresponding

value of pfy is 571 psi, (using ~ = 1.4 for a crack in monolithic concrete.)

It was considered that this approach to the design of the specimens would be

conservative, since, if the potential strength of this quantity of reinforce­

ment could be developed using a particular bar size, then it should also be

possible to develope the full potential strength of any smaller quantity of

the same size of reinforcing bar.

The numbers of bars crossing the shear plane in each specimen is shown

in Table 2.1, together with the measured values of the reinforcement yield

strength and the consequent actual values of pfy . The average value of pfy

for the 8 specimens subject to monotonic loading was 540 psi, but individual

values of pfy varied from 495 psi to 590 psi. This was because of the

variation of the yield strength between different sizes of bars, (although all

were nominally 60 grade bars,) and the fact that only a whole number of bars

could be used in a specimen.

Six #10 bars were provided outside and parallel to the two shear planes,

to act as compression reinforcement in the vicinity of the supporting bearings.

These bars were machined to the same length, and a ~ inch deep hole was drilled

and tapped in each end to fit a 3/8 inch diameter machine screw. The screw

was used to attach each #10 bar directly to the bearing shoes at top and

bottom of the specimen. This ensured that this compression reinforcement

would be loaded directly by end bearing against the bearing shoe above the

support bearing. #8 bar auxiliary reinforcement was also provided as shown.

Six 1 inch diameter prestressing bars, (fy = 100 ksi,) were provided adjacent

to the end faces of the specimen and passing through the top and bottom bearing

6

plates. These bars served both to clamp the bearing plates to the specimen, and

also to make more uniform the compressive stresses under the bearing plate.

1 inch diameter, 12 inch long pigtail anchors were provided at the middle

of each end face, to which swivel lifting plates were subsequently attached.

In the numbering of the specimens, the first letter indicates the type of

loading to which the specimen was subjected, (i.e. Mfor monotonic and C for

cyclically reversing,) the number is the size of bar used as shear transfer

reinforcement in the specimen, and the final letter was to distinguish between

duplicate specimens, if necessary.

2,3 Materials and Fabrication

The specimens were made from Type III Portland Cement, sand and 3/4 inch

maximum size glacial outwash gravel. The concrete was obtained from a local

ready-mixed concrete supplier. The nominal mix proportions were 1:2.98:4.26,

with a 3 inch slump. However, as delivered, the slump varied considerably.

It was therefore necessary to monitor the concrete strength from day to day

and to test the specimen when the concrete strength was close to the target

strength of 4000 psi. The actual concrete strength at the time of test for

each specimen, is shown in Table 2.1.

The deformed bar reinforcement used,conformed to ASTM Specification A6l5.

The rebars were nominally of grade 60. The measured values of yield strength

are shown in Table 2.1. The closed hoops were each made from two U-shaped bars,

welded together on the shorter sides of the hoop. In specimens M8A, C8A and

MllA, it was necessary to provide an additional single bar at the middle of

the specimen. In M8A and C8A it was possible to anchor this bar by providing

a hook at each end. In the case of MllA it was necessary to weld a plate on

each end of the bar in order to anchor it.

7

The #14 and #18 bar reinforcement was in the form of 54 inch long straight

bars s each end of which was provided with an anchor plate, (3 x 6~ x 6~ inch

for #14 bars, 4 x 8~ x 8~ inch for #18 bars.) The anchor plates were ,attached

to the bars using a patent tapered thread. The bar and anchor plate assemblies

were supplied by Fox-Howlett Industries. The tapered thread was of the same

pattern as that used in tlfe Fox-Howlett IINo-slip Coupling ll for large diameter

rebars. The tensile tests of the #14 and #18 bars were made using similar

assemblies, pulling against the anchor plates at each end. In these tensile

tests, failure occurred approximately at the tensile strength of the bars, far

in excess of the yield strength.

The specimens were cast lying on their side, (as in Sec. A-A of Fig. 2.1.).

The inner bearing plates were incorporated in the form, so that the concrete

should be cast against them and uniform contact be thus ensured. The forms were

otherwise of plastic coated plywood, braced by a frame of steel angles. The

vee-shaped grooves used to define the shear plane~ were formed by stiff, steel

members, to ensure dimensional accuracy.

The specimens were cured in the form under a polythene sheet, for three

days. The companion cylinders were also cured for three days in their

moulds, sealed by a polythene bag placed over their ends. The specimen and

companion cylinders were then stripped and were immediately coated with a

sealer to prevent the escape of moisture. By doing this, it was thought that

the curing conditions for the concrete in the cylinders would more closely

approximate those of the concrete in the large specimen; than if both had been

left unsealed to dry in the ambient atmosphere of the laboratory. The majority

of the specimens were tested at an age of about 5 days, but specimen M4A had

to be held to age 15 days before the concrete strength reached 4000 psi.

8

After stripping and sealing the specimens, the prestressing bars were

threaded through the holes formed in the specimens, and were each stressed to

40 kips tension. The outer bearing plates were then bolted in place ..

2.4 Initial Cracking

·Before testing, a crack was formed in each of the shear planes of each

specimen. This was done by pressing vee-shaped steel bars into opposite vee­

grooves on the front and back faces of the specimen, using the same Baldwin

testing machine used for the shear tranfer tests. The opening of the crack was

taken as the average reading of dial gages mounted across the crack at each

end of the shear plane. Measurements were also made of the strain in the

shear transfer reinforcement at the shear plane.

The objective in the cracking process, was to form a crack with a residual

width of O.Ol"in. after the load was removed from the vee-shaped steel bars.

To achieve this, it was found to be necessary to load the specimen until an

average crack width under load of about 0.025 in. was produced. This was con­

siderably greater than had been necessary in the smaller. scale specimens tested

previously. It is believed the difference in behavior is due to bond slip

occurring over a larger length of bar in the larger specimens than in the

small specimens, leading to greater crack widths under load as a result of elas­

tic strain in the bars. The load required to produce a crack width of 0.025 in.

was found to decrease as the rebar size increased. This is thought to be due

to the fact that, for a given load on the specimen, the bond stresses would be

greater for the large size bars than for the smaller size bars, hence the load

at which extensive bond slip would occur would decrease as the rebar diameter

increased.

The maximum crack width under load and the residual crack width for each

of the two cracks in each specimen, are shown in Table 2.2 Also shown in this

9

table are the maximum stress in the rebar under load~ and the residual stress

in the rebar after the cracking process was completed~ at each of the two

cracks in each specimen.

2.5 Testing Arrangements and Instrumentation

The specimens were tested using a 2.4 million pound capacity~ Baldwin

hydraulic testing machine. The specimen was supported on the two lower bearing

strips~ (see Fig. 2.1,) through roller bearings resting on the base plate of

the testing machine, as may be seen in Fig. 2.2. The roller bearings were

provided to ensure that lateral dilation of the specimen would not be restrain­

ed by the testing machine base.

The load was applied concentrically to the middle part of the specimen,

through a double thickness 24 x 20 in. steel plate~ attached to the end of a

steel box section extension of the upper cross-head of the testing machine,

as shown in Fig. 2.2. To ensure a uniformly distributed load on the specimen,

a sheet of ~ in. thick fiber board was placed between the steel plate and the

top face of the specimen, and a spherical seat was provided between the steel

plate and the end of the cross-head extension. The steel box section cross­

head extension was strain gaged, so that it could be used as a load cell to

monitor the load during tests.

Both the slip (or relative motion parallel to the shear plane of the

concrete on opposite sides of the crack,) and separation (or relative motion

normal to the shear plane of the concrete on opposite sides of the crack,)

were measured continuously, for both shear planes, during the shear transfer

tests. The measurements were made using linear differential transformers as

the sensing elements of slip and separation gages, which were attached to

reference points embedded in the face of the specimen. The separation gages

10

were located at mid-height of the shear planes~ and the slip gages were located

3 inches away. The embedded reference points were l~ inches either side of

the shear planes. The slip and separation gages were calibrated direc~ly

before test by imposing known displacements on them.

One eighth inch gage length, foil type, electrical resistance strain gages,

were attached to one of the shear transfer reinforcing bars located near mid­

height of the shear planes. One gage was located where the bar crossed each

of the two shear planes, and an additional gage was attached to the bar 8 inches

from shear plane No.2. The gages were attached to the inside face of the bar

on a horizontal diameter~ so as to avoid registering flexural strains due to

dowel action of the reinforcement. The gages were sealed and were covered

with a strip of butyl rubber, so that they should not be subjected to forces

from the adjacent concrete~ either during the initial cracking procedure or

during the shear transfer test.

The strain gages, the slip and separation gages, and the load cell were

monitored continuously by a Sanborn strip chart recorder.

2.6 Testing Procedures

2.6.1 Monotonic Loading Tests - The specimen was first subjected to a

monotonically increasing load up to an arbitrarily defined service 10ad~ equal

to half the load corresponding to the calculated ultimate shear. The load

was then reduced to zero. The specimen was then subjected to a monotonically

increasing load until failure occurred. Failure was considered to have occurred

when the applied load could not be increased further, and slip and separation

both increased rapidly.

The ultimate shear was calculated using the shear-friction equation con­

tained in Sec. 11.15 of ACI 318-71.

11

(2.1)

In calculating the ultimate shear, the capacity reduction factor ~ was taken

as unity, since both the material strength properties and the dimensions of

the specimens were accurately known. The coefficient of friction ~, was

taken as 1.4, as prescribed for a crack in monolithic concrete. The actual

value of f y was used, although this was in excess of 60 ksi in all cases.

In the case of M14A and C14A, the upper limit of 800 psi for the calculated

ultimate shear stress specified in Sec. 11.15.3, was ignored.

2.6.2 Cyclically Reversing Shear Tests ~ The specimen was first sub­

jected to a monotonically increasing load, up to 50 percent of the load

corresponding to the ultimate shear calculated using Eq. (2.1). The load was

then reduced to zero. The specimen was then lifted from its supporting

bearings, by chains hanging from the testing machine cross-head and connect-

ed to the swivel lifting plates located at the middle of each end face of the

specimen. While hanging from the cross-head, the specimen was inverted, as

shown in Fig. 2.3. It was then lowered onto the roller bearings and the loading

plate was brought into contact with the top of the specimen. The load was

then once again increased monotonically to 50 percent of the load corresponding

to the calculated ultimate shear, and subsequently reduced to zero. This

second loading produced shear in the shear planes, of opposite sign to that

produced by the first loading. The specimen was lifted and rotated back to its

starting position. This completed one cycle of loading.

The process described above was repeated until 10 cycles of loading had

been completed. The maximum positive and negative values of shear were then

increased by 8 percent of the calculated shear transfer strength, i.e. to

· 12

+ 58 percent of Vu (calc.) for the next 5 load cycles. After each succeeding

5 cycles of load, the maximum positive and negative values of shear were in­

creased by the same increment of 8 percent of the calculated shear transfer

strength. This process was repeated until failure of the specimen occurred.

III - TEST RESULTS

3.1. Ultimate Strength and Loading History

The ultimate shear transfer strengths of the monotonically loaded speci-

mens are given in Table 3.1. The loading history and the ultimate shear

transfer strength, of each of the specimens subjected to cyclically reversing

loading, are shown in Table 3.2.

The ultimate shear is defined as the maximum shear carried by one of the

*shear planes of the specimen during the test. In a cyclic loading test this

may be either the maximum shear to which the shear plane has been cycled, or the

maximum shear reached when the maximum shear was being increased at the end of

a group of cycles of loading to a constant maximum shear.

Specimen failure was characterized by both slip and separation increasing

rapidly, with the load carried by the specimen either held constant or decreasing.

3.2 Specimen Behavior

3.2.1 Monotonic Loading Tests - No damage to or cracking of the concrete,

was observed during both the initial loading and the reloading to service load.

Slip and separation occurred at all levels of load, as may be seen in Figs. Bl

through B10; however, the values at service load were very small. In Table 3.3

are shown values of the slip due to applying the service load, both on first

loading and on reloading, together with the residual slip on removal of the

service load after first loading. Also shown in Table 3.3 are the secant

shear stiffnesses at service load, on both first-loading and on reloading.

A few fine diagonal tension cracks formed adjacent to the shear planes at

loads about 25 percent above the service load. These cracks grew in length

as the load was increased, but did not exceed 0.01 in. in width until very close

to the ultimate shear. Typical crack patterns after failure are shown in Fig. 3.1'.

*Because of the symmetry of the specimen, and of the loading and support systems,it was assumed that the shear in e.ach shear plane was equal to half the loadapplied to the specimen.

13

14

At loads approaching ultimate, cracks formed in the top face of the center

part of the specimens, around the perimeter of the loading head. This was

apparently due to the high bearing stress under the loading head, which was

approximately equal to f' at ultimate. These cracks propagated only a fewcinches into the concrete in most specimens, travelling diagonally outward. In

some cases they linked wit~ the cracks in the shear plane a few inches from

the top of the specimen. In specimens M4A and C4A these cracks travelled almost

vertically, parallel to the front and back faces of the specimen, and linked

with splitting cracks in the plane of the shear transfer reinforcement. After

the test of C4A, it was possible to pry off the concrete along the plane of

this crack, over the whole depth of the specimen.

In some specimens, compression spalling of the surface of the concrete

occurred close to the bearing shoes, at loads approaching failure. This dis­

tress was locallized, however, and is not thought to have affected the shear

transfer behavior of the specimens.

The slip and the separation both increased at an increasing rate as

failure was approached. The values of the slip and the separation at ultimate

strength are listed in Table 3.1, together with the angle of inclination to the

shear plane, of the direction of relative motion of the two faces of the crack

at ultimate.

Failure occurred so abruptly in the case of M6A~ M9A and Ml8A, that it

was not possible to obtain slip and separation data after the maximum load

was reached. Failure was still fairly abrupt in the other specimens, probably

due to release of elastic strain energy from the testing machine, which was

working near to its maximum capacity at ultimate load.

The variation of the stress in the shear transfer reinforcement with the

applied shear and with the measured separation across the crack, is shown in

15

Fig. 811 through 818 and Fig. 819 through 826 respectively.

3.2.2 Cyclic Loading Tests - In the cyclic loading tests also, no damage

to or cracking of the concrete, was observed during loading to service load.

Fine diagonal tension cracks were first observed at maximum shears a little

above service load. These cracks initiated close to the shear planes, and grew

in length as the maximum shear per load cycle was increased. The width of the

cracks did not exceed 0.01 in. until close to failure. The typical appearance

of a specimen after failure can be seen in Fig. 3.2.

The general behavior of these large scale test specimens, and the form of

the shear-slip and slip-separation curves, wa~ similar to those observed in the

previous cyclic loading tests (2) of smaller scale specimens.

Samples of the shear-slip and slip-separation curves for each specimen,

are shown in Appendix C. These curves show examples of behavior at service

load, at intermediate loads and approaching failure. Also shown in Appendix C

are shear - steel stress curves, and separation - steel stress curves, for every

fifth load cycle. These data relate to the cracked shear-plane in which failure

eventually occurred. In these figures, positive shear and positive slip are

shear and slip measured in the direction in which shear was first applied to

the specimen. The separation plotted, is the change in separation due to

application of shear to the specimen. To obtain the total separation, the

initial crack width must be added to the separation shown in the figures of

Appendix C.

As can be seen from the figures of Appendix C, the response of the speci-

mens changed as the number of cycles of loading, and the level of loading in­

creased. Specimen response to the first cycle of loading is characterized by

a gradual reduction in shear stiffness as the applied shear is increased, in

16

both positive and negative directions; and by retention of most of the slip

produced by the maximum shear, until the shear reduces to about half of its

maximum value. Response to succeeding cycles of load is characterized by a

low shear stiffness at low values of shear, and a gradual increase in shear

stiffness with increase in shear in both the positive and negative directions.

The "Effective Stiffness" will be defined as the slope of a line joining

the points of maximum positive and negative shear and slip, in the shear-slip

hysteresis loop for a particular cycle of load. In Figs. 3.3 through 3.6 are

shown the effective stiffness and the stiffness near zero shear for successive­

ly increasing cycles of load, for each of the specimens. It can be seen that

both stiffnesses decrease as the number of cycles of load increase. The shear

stiffness for low values of shear also decreases relative to the effective

stiffness, for the same cycle of loading, as the number of load cycles increases.

The increase in slip with each loading cycle was initially very small,

but increased as the value of the maximum applied shear increased. As the

load which caused failure was approached, the tangent shear stiffness tended

to decrease as the maximum shear was approached in each cycle. Failure

occurred when the shear stiffness under increasing load reduced to zero, after

which the slip increased rapidly, even though the shear was decreasing.

The slip-separation curves are approximately crescent shaped. Their

exact shape, and their symmetry with respect to the separation axis, was pre­

sumably a function of the profile of the crack faces in each particular case.

As the maximum shear per load cycle increased, both slip and separation at

maximum shear increased. Approaching failure, the separation at zero shear also

increased substantially with each cycle of loading. This increase in separation

at zero shear, occurred in the same load cycles in which the tangent shear

stiffness-started to decrease approaching maximum shear.

IV - DISCUSSION OF TEST RESULTS

4.1. General Behavior

When shear acts along a crack which is crossed at right-angles by reinforc­

ing bars, shear is transferred across the crack as a result of three types of

action.

1. By friction between the faces of the crack; due to the tension force

developed in the reinforcement, as a result of separation of the rough crack

faces when slip occurs.

2. By direct bearing of asperities projecting from the faces of the crack.

3. By dowel action of the reinforcing bars crossing the crack; i.e. direct

resistance of the bars to shearing action at the crack.

The relative importance of each of these contributions to shear transfer resis­

tance varies with the intensity of the shear stress and the prior shear loading

history.

4.1.1 Monotonic Loading Tests - For applied shears up to about half the

ultimate shear, the slip along the crack in these tests was very small.

(typically less than 0.005 in.,) and the shear-stiffness was consequently very

high. This can be seen in Figs. Bl through 88 and also in Table 3.3. The

separation across the crack was also very small at this stage of loading,

being about the same as the slip. As a consequence of the small separation

across the crack, the reinforcement was not strained very much due to the

applied shear. This can- be seen in Figs. 811 through B18, in which the measured

shear transfer reinforcement stress is plotted against the applied shear. It

can be seen that the increase in reinforcement stress up to "service load ll

was typically less than 5 ksi, while the average measured total reinforcement

stress at service load in all the specimens was 11.6 ksi. It appears therefore,

that in the service load range, only a small part of the. shear transfer resis-

17

18

tance developed, is due to friction between the crack faces as a result of

straining of the reinforcement caused by separation across the crack faces.

The small slips which occurred at service load lead to the conclusion

that, at this stage of loading, little is contributed to shear transfer resis­

tance by dowel action of the reinforcing bars crossing the crack. The average

slip at service load was 0.0022 in .. Dowel action tests at Cornell University(6)

showed that for a No, 11 reinforcing bar, the dowel action shear resistance

was 3,8 kips for a slip of 0.0022 in. on first loading. In specimen MllA,

5 No, 11 bars cross the shear plane. It appears therefore that of a service

load shear of 347 kips for MllA, dowel action could only have resisted about

19 kips, i.e. about 5 percent.

For the same specimen MllA, the clamping force across the crack correspond­

ing to the average measured reinforcement stress at service load would be 90.5

kips. Using a coefficient of friction of 0.8, this clamping force would

develop a shear resistance of 72 kips, i.e. about 21 percent of the service

load shear. It appears therefore that at service 10a9, 256 kips or 74 percent

of the shear transfer resistance was being supplied by direct bearing of asperi­

ties projecting from the faces of the crack.

When the applied shear is increased beyond about 50 percent of the ultimate

shear, both slip and separation increase more rapidly. This is probably a

result of a combination of shearing off and over-riding of asperities on the

crack faces. The more rapid increase in separation also results in a more

rapid increase in reinforcement stress, so that at ultimate shear the recorded

stresses were at or very close to the reinforcement yield point. (The average

reinforcement stress measured at ultimate shear was 62.7 ksi.)

19

If it is assumed that, at ultimate shear, the reinforcement developed its

yield strength, the average clamping force for all specimens would have been

540 kips .. The corresponding shear resistance due to friction would have

been 432 kips, or about 40 percent of the average of the measured ultimate

shears. That is, about 60 percent of the ultimate shear was being resisted by

a combination of dowel action and resistance to shearing off of asperities on

the crack faces. The proportions of the ultimate shear carried by these two

actions individually, cannot be deduced from the available data. Unfortunately,

the Cornell University dowel action tests (6) only provide data for first

loading up to a slip of 0.016, which occurred at a shear of 15 kips. At this

slip, specimen MllA was carrying a shear of 840 kips. If it is assumed

that the dowel resistance of the No. 11 bars was not affected by the axial

tension stress in them, the resistance to shear by dowel action in MllA at a

slip of 0.016 in. was 75 kips or 9 percent of the applied shear. It appears

therefore that at ultimate shear, a major part of the shear transfer resis-

tance is provided by the resistance to shearing off of asperities on the faces

of the crack. Shear transfer failure after monotonic loading is probably

initiated by the shearing off of asperities on the faces of the crack.

The direction of motion of one face of the crack relative to the opposite

face is inclined at angle a to the crack, where a = tan- l (separation/slip).

The average value of a at ultimate shear in these large scale tests was 44°.

The average value of a at failure in previous smaller scale shear transfer

tests(1)(7) of cracked, monolithic specimens made of sand and gravel concrete

was 32°. The larger value of a in the large scale tests, (Acr = 1000 in. 2),

as compared to the value found in the smaller scale tests, (Acr = 50 in. 2), is

probably due to the crack in the large specimen having a more irregular profile

20

than that in the smaller specimen. In both cases, the crack was produced by

applying line loads simultaneously to front and back of the specimen. However,

in the large specimen the line loads were 25 inches apart, while in the

smaller specimen they were only 5 inches apart. It appears likely that the

path of the crack would II wander ll from the shear plane more in traversing

the 25 inch thickness of t~e large specimens than in traversing the 5 inch

thickness of the smaller specimens. This greater irregularity of the crack

profile, i.e., greater roughness of the crack faces, may also have affected

the ultimate shear strengths attained in these tests, as is discussed in

Section 4.2.2.

The average slip at failure in the crack that failed, in these tests was

0.063 in. as compared with an average slip at failure of 0.022 in. the previous(1)(7)

comparable smaller scale shear transfer tests. It is believed that this dif­

ference in behavior is due to the greater length of reinforcing bar over which

bond slip could occur in the large scale specimens as compared to the smaller

scale specimens. (About 25 inches/shear plane as compared with 10 inches.)

In order to develop the yield strain of the reinforcing bars, a larger total

elongation of the bars would be necessary in the large scale specimens than in

the smaller scale specimens, i.e. a larger separation across the crack would

be necessary in the larger specimens than in the smaller specimens. Hence

a larger slip would be needed in the large scale specimens than in the smaller

scale specimens in order to develop the yield strength of the shear transfer

reinforcement.

4.1.2 Cyclic Loading rests - The general behavior of these large scale

specimens was very similar to that previously observed(2) in cyclic loading

tests of smaller scale specimens. The behavior of these large scale specimens

21

supports the following hypothesis concerning the mechanics of shear transfer

behavior, which was proposed previously(2) on the basis of the smaller

scale tests.

At low values of shear, on first loading, the shear stiffness is very

high and very little separation occurs. As discussed in 4.1.1, this behavior

indicates that at this stage most of the resistance to shear is due to the

direct bearing of asperities on the faces of the crack. Slip would result

from local crushing of asperities and would be very small. As increasing

numbers of the asperities are crushed, the intensity of bearing pressure on

the remaining asperities would increase more rapidly than the applied shear.

The deformations would therefore increase more rapidly, and the shear stiff­

ness would therefore decrease. This is the behavior observed in the first

quarter of the first cycle of loading.

When the shear is reduced to zero, the only force tending to return the

slip to zero is that due to the,elastic deformation of the reinforcing bars

and of the concrete against which they bear, as they develop dowel action.

This restoring force is resisted by friction and any interlocking effect

that may exist between the crack faces. The slip cannot return toward zero

until the applied shear becomes less than the net restoring force. This

would account for the observed behavior on unloading.

As the shear is increased in the reverse direction for the first time,

the mechanisms by which shear resistance ;s developed will be the same as on

first loading. The behavior on unloading will also be similar to the behavior

on first unloading in the opposite direction.

In subsequent load cycles, in order for the asperities to be brought into

bearing, a slip must occur almost equal to the maximum slip which has previously

22 .

occurred. Whilst this slip is occurring, shear resistance is developed only

by dowel action of the reinforcement and by any small friction existing

between the crack faces. The shear stiffness at low shears is consequently

much lower than on first loading. When the asperities come into bearing,

their resistance to deformation results in a sharp increase in resistance to

shear and an increasing tangent shear stiffness until maximum shear is reached.

On removing the shear~ the response and probable mechanism of behavior

are the same as in the first cycle. When the shear is reversed in direction,

the response and mechanism of behavior is the same as described above.

When the maximum shear is increased at the end of each group of cycles,

additional damage is done to the surfaces of the crack by shearing off of

additional asperities, and the slip increases. With each cycle of load, the

crack faces are abraided and become smoother. This reduces the resistance

to shear which can be developed at low shears, resulting in a reduction in

shear stiffness at low values of applied shear.

As the maximum shear per cycle increased it was observed that both the

slip and separation at maximum shear increased. This would lead to the

development of larger dowel forces and tensile strains in the bars. It is

therefore probable that, approaching failure, an increasing fraction of the

shear is resisted by friction between the crack faces and by dowel action of

the reinforcing bars.

In the load cycles preceding failure, the separation at zero shear in­

creases markedly, the tangent shear stiffness approaching maximum shear starts

to decrease, and both slip and separation at maximum shear increase signifi­

cantly in each load cycle. This behavior is probably due in large part to the

local crushing of the crack faces. Some of the mortar particles produced by

this crushing becomes trapped between the faces of the crack, wedging it open,

23

and acting like "ball bearings ll when the crack faces move relative to one

another. Progressive yielding Of the reinforcing bars, under the combination

of direct tension and of bending and shear resulting from dowel action, will

also contribute to deterioration in behavior at this stage. (The effect on

the stress in the reinforcement, of increasing separation at zero shear, can

be seen in Figs. C41 through C47.)

It can be seen in Figs. 3.3 through 3.6, that the effective stiffness and

the stiffness near zero shear, both decrease substantially as the number of

cycles of loading increase. The effective stiffness decreases with increasing

cycles of load, even without any increase in the maximum shear per load cycle.

This behavior contrasts with that observed previously(2) in the tests of

smaller scale specimens. In that case, after about the first five cycles of

loading, and for maximum shears less than about 75 percent of ultimate shear,

the slip at maximum shear per cycle did not change significantly, (i.e. the

effective stiffness did not change significantly.) This difference in

behavior may be related to a progressive break-down in bond between the shear

transfer reinforcement and the concrete in the large scale specimens, when

subjected to a cyclic load of constant amplitude.

In Fig. 4.1, the effective stiffness, (expressed as a percentage P~e of

the initial effective stiffness,) has been plotted against the number of load

cycles, (expressed as a percentage Pc of the number of load cycles to cause

failure.) It can be seen that, for the incrementally increasing loading

history used in these tests, the effective stiffness of the large scale speci-

mens is approximately related to the number of cycles of loading by,

Pse = 100 - 0.9Pc (4.1)

24

Also plotted in Fig. 4.1 are data from the smaller scale (Acr = 50 in. 2),

cracked monolithic specimen LC2, tested previOuSly(2). This specimen had a

reinforcement index pfy ' approximately the same as the average pfy for the

large scale specimens. It can be seen that after the first five cycles of

load, the effective stiffness remained at about 90 percent of the initial

effective stiffness, until the number of cycles of load reached about 60 per­

cent of the load cycles to cause failure, (and the shear reached about 75

percent of the ultimate shear.) Under subsequent cyclic loading, the effec-

tive stiffness decreased at an increasing rate as failure was approached.

As already indicated above, it is thought that the difference in behavior

may be due to the more favorable bond and anchorage conditions in the smaller

scale specimens than in the large scale specimens.

The ratio of the stiffness near zero shear (So) to the effective stiff­

ness (Se) in the same load cycle, varied from about 0.4 for the first load

cycle to about 0.3 for the load cycle before failure; but there is consider­

able scatter in the data. In Fig. 4.2, the stiffness near zero shear (ex­

pressed as a percentage of the initial effective stiffness), is plotted against

the number of cycles of load (expressed as a percentage of the number of load

cycles to cause failure.) Also plotted in Fig. 4.2 is a line which corresponds

to the equation,

SolS = 0.40 - P /1000e c

This equation implies that the ratio S /S varies linearly with the number ofo eload cycles, from a value of 0.4 for the initial cycle of loading, to a value

of 0.3 just before failure occurs. It can be seen that although there is

considerable scatter in the data, the line corresponding to equation (4.2) re­

flects the trend of th~ data reasonably well.

(4.2)

25

It should be noted that the slip and separation data obtained in the test of

specimen C4A is somewhat erratis and in some respects is not consistent with the

data obtained in the tests of CSA, Cl~ and Cl4A. It is believed that the data

obtained from specimen C4A is not so reliable as that obtained in the other three

cyclic loading tests.

In Tables 4.1 through 4.3 are given the maximum shear, the energy dissipated

per load cycle, (i.e. the area within the shear-slip hysteresis loop, Ah), the

energy absorbed as the load is increased in each cyc}e, (i.e. the area A1 shown

in Fig. 4.6b), the damping factor, the effective stiffness and the stiffness

near zero shear, for approximately every fifth cycle of loading of specimens CSA,

C10A and C14A. The damping factor has been calculated both according to

Jacobsen(10) and according to Hawkins et al.(ll)~

Jacobsen proposed that the damping factor be calculated using,

_ 1 Area within hysteresis loop.Sl - 21T -Area under II skel eton curve ll

•

Jacobsen proposes that for hysteresis curves of the type obtained in these

tests, the skeleton curve should be as indicated in Fig. 4.4. No attempt was

made to draw skeleton curves for the shear-slip hysteresis loops obtained in

these tests. Instead, it was assumed that the skeleton curve divides the hys­

teresis loop into two equal areas, and hence equation (4.3) can also be stated

as,--

where Ah and A, are as indicated in Fig. 4.6. The damping factor calculated

in this way has a maximum possible value of 0.318.

(4.3)

(4.3A)

26

Hawkins et al.(ll) proposed that the damping factor be calculated

using,--

~ _ 1 Energy dissipated in one load cycle.2 - 2w . Energy absorbed in increasing the

load in one load cycle

where Ah and Al are also as indicated in Fig. 4.6. The damping factor calcu­

lated in this way has a maximum possible value of 0.159.

The concept of an equivalent viscous damping factor is being strained

severely when it is used to characterize hysteretic behavior of the type

found in these shear transfer tests .. The significance of individual numerical

values obtained is questionable, but it is thought that the trends in varia-

tion of the values are of interest. In Figs. 4.3 and 4.5, the damping factors

~l and ~2 are plotted against number of load cycles (expressed as a percentage

of the number of load cycles to·cause failure.) The results of the three tests

are very consistent. The damping factor decreases after the first cycle of

loading, as the hysteresis loop becomes pinched in shape. Then, until about

80 percent of the cycles to cause failure, the damping factor is essentially

constant, indicating reasonably stable conditions regarding damage to the crack

faces. As further cycles of loading are applied, the damping factor increases

at an increasing rate. This rapid increase in the damping factor coincides

with a significant increase in separation across the crack at zero shear, and

is probably related to the occurrence of severe damage to the crack faces as

failure is approached. It can be seen from Tables 4.1 through 4.3, that during

this same time the energy dissipated per cycle increases by about 300 percent

in the last 5 load cycles before failure.

(4.4)

(4.5)

(4.5A)

(4.6)

(4.6A)

27

In Figs. 4.7 through 4.10 comparisons are made of the shear-slip relations

for companion specimens subjected to monotonic loading and to cyclic loading.

The data shown in each case is that relating to the cracked shear plane in which.

failure eventually occurred. For the cyclic loading tests, the slips shown are

equal to half the change in slip as the shear changes from the maximum positive

value to the maximum negative value in a particular load cycle. It can be seen

that in the case of the specimens reinforced with #8, #10, or #14 bars, the

slip at a given level of load was always greater in the specimen subjected to

cyclic loading than in the companion specimen subject to monotonic loading.

As indicated above, there are some doubts as to the reliability of the data

obtained from the test of specimen C4A and it is believed that the comparison

shown in Fig. 4.7 should be discounted. The less stiff behavior of the other

specimens subjected to cyclic loading, as compared to that of companion specimens

subject to monotonic loading, is probably due to the progressive abrasion of

the crack faces as they are rubbed backward and forward against one another.

4.2 Ultimate Strength

4.2.1 ~onotonic Loading Tests - In Table 4.4 a comparison is made

for each specimen, between the measured ultimate shear strength and

the ultimate shear transfer strength calculated, (1) using the shear-friction

equations,

Vu (calc)l = ~Avf~

= ~A pf ~ but t ~0.2f'A nor 800 ~Acr y c cr cr

and, (2) using the modified shear friction equation,

Vu (calc)2 = HO.8Avffy + 400 Acr ]

= ~Acr[0.8pfy + 400] but t ~0.3f~Acr

Since dimensions and material strengths were known accurately, ~ was taken as

1.0· in the above equations.

28

It is seen that both equations yield conservative estimates of the ultimate

strengths of these specimens. It therefore appears that either of these

equations could be used for design purposes in situations involving the use

of large diameter bars, providing that adequate anchorage is provided for the

bars on each side of the shear plane.

If a straight, large diameter bar crossed a single crack and was anchored

by bond only on each side of the crack, then there could be some question as

to whether the yield strength of that bar could be developed as a result of

separation occurring across the crack 5 due to shear acting along the crack.

This, because bond slip would probably occur over a considerable length of

bar on each side of the crack, requiring a large separation across the crack

in order to strain the reinforcement to its yield point. In Fig. 4.11 a compari­

son is made of the values of the ratio (Reinforcement Stress)/(Separation),

measured in these large scale push-off tests, with a comparable ratio obtained

from anchorage bond pull-out tests(8,9) of large diameter reinforcing bars. In

the case of the pull-out tests, the value plotted is equal to the ratio (two

times displacement at loaded end of embedded bar)/(stress in bar). This is-

appropriate, since in the push-off tests the bars are being pulled from the

concrete on both sides of the crack. The agreement is good for the #10 bar

and reasonably good for the #14 and #18 bars, despite the fact that in the push­

off specimens anchor plates were provided at each end of each #14 and #18 bar.

If a lower bound value of 1000 ksi/in. is assumed for the large diameter' bars,

a separation of 0~06 in. would be required to develop a yield strength of

60 ksi. Separations of this magnitude were obtained in some of the push-off

specimens tested. It therefore appears that under monotonic loading, it should

be possible to develop the yield strength of straight large diameter bars cross-

ing a crack, and relying on bond for anchorage.

29

If moment acts across the crack as well as shear acting along it, there

would be no concern regarding development of the yield strength of bars cross­

ing the crack, since the separation across the crack would not then depend only

on the shearing action and the roughness of the,crack faces.

It is not possible to show the effect of reinforcing bar diameter on the

shear transfer strength dir~ctly, by plotting the measured shear transfer

strength, since the value of the reinforcement parameter pfy varied between the

specimens, as previously discussed. The modified shear friction equation (4.2)

has previously been shown to reflect the effect on ultimate shear transfer

strength, of change in pfy. In Fig. 4.12, tharefore, a plot has been made of

Vu(test)/Vu(calc')2 versus reinforcing bar diameter, where V(calc')2 is the

shear transfer strength calculated using the modified shear friction equation (4.6).

This plot shows the change in ultimate shear transfer strength if the reinforcing

bar size is changed, while holding the reinforcement parameter pfy constant. It

can be seen that, for bar diameters greater than 1 inch, the ultimate shear

transfer strength tends to decrease as the bar diameter increases. The ultimate

strength using #18 bars is 15 percent less than when #8 bars are used. This

trend may be due to the development of larger dowel forces per bar in the

larger reinforcing bars, because of their greater flexural stiffness. These

larger dowel forces could lead to local crushing and splitting of the concrete

adjacent to the reinforcing bars, leading to the reduction in shear transfer

strengths seen in Fig. 4.12. However, despite the reduction in strength with

increase bar diameter, all the specimens had ultimate strengths in excess of

the calculated strength. It is therefore, not considered necessary to reduce

the calculated ultimate shear transfer strength when large diameter reinforcing

bars are used.

30

Specimen M4A yielded a much lower ultimate strength than the other speci­

mens.. On examination after failure, a crack was found to have occurred in the

plain of the reinforcing bars, parallel to the front and back faces of the

specimen. This crack extended downward from the edge of the loading head on

the top of the center section of the specimen. It is believed that this crack

may have occurred due to a combination of four effects, -- (1) high splitting

tensile stresses due to anchorage bond stresses,caused by close spacing of

the reinforcing bars, (less than 2 in. centers); (2) splitting tensile stresses

caused by bearing of the bars on the concrete as dowel action developes;

(3) displacement of concrete in the plane of the bars by the large number of

bars present; and (4) the development of spalling tensile stresses on the top

face of the specimen, at the edge of the loading head. Similar cracks were

found in the companion cyclically loaded specimen C4A. Despite its relatively

low strength, this specimen was still stronger than the calculated ultimate

strength.

The relatively high values of ultimate strength obtained in these large

size push-off specimens, are thought to have been due to the greater roughness

of the crack faces in these large specimens, as compared with the smaller scale

specimens tested previously. The reason for this greater roughness was discussed

in Section 4.1.1. The greater roughness of the crack faces would enable a

larger shear to be resisted by direct interlock of asperities on the crack faces.

4.2.2 Cyclic Loading Tests - The ultimate strengths of the cyclically

loaded specimens were in all cases less than the ultimate strengths of their

companion monotonically loaded specimens. In Table 4.5 a comparison is made

of the ultimate strengths of cyclically and monotonically loaded companion

specimens. Except in the case of the specimens reinforced with #4 bars, the

31

strength under cyclic loading was about 80 p~rcent of the ·strength under mono­

tonic loading. This is in agreement with the results of previous cyclic

loading tests(2) of smaller scale push-off specimens. The higher ratio for

specimen C4A is probably due to the ultimate strength of the companion mono­

tonically loaded specimen being low, rather than the strength of C4A being

unusually high. This is apparent in Fig. 4.12. It therefore appears that

the recommendation for design previously made(2), i.e., to assume that the

strength under cyclic loading is 80 percent of the strength under monotonic

loading, is also valid when large diameter reinforcing bars are used. It is

probable that the reduction in shear transfer strength under cyclic loading is

mainly due to a progressive abrasion of the crack faces, leading to a reduced

contribution to shear transfer resistance from direct interlocking of asperities

on the crack faces. It is also probable that under cyclic loading, the shear

resistance due to dowel action would reduce due to fatigue break down of the

concrete against which the reinfprcing bars are bearing.

The shear transfer strengths developed in these tests are considerably in

excess of those obtained in tests at Cornell University(6), although the general

form of the shear-slip curves was similar in both cases. The difference in be~

havior is probably due to the positive anchorage provided for the shear transfer

reinforcement in these tests, and also due to the provision of reinforcement

adjacent to the shear plane, which prevents a premature failure due to excessive

cracking of the concrete adjacent to the shear plane. In a design situation, it

is necessary to consider both the transfer of shear across the crack and the

ability of the adjacent concrete to carry the shear force, and to provide

reinforcement to resist diagonal tension cracking if necessary.

v - PRINCIPAL CONCLUSIONS

. Based on the test data reported, the following conclusions may be drawn

concerning shear transfer across a crack in monolithic concrete, crossed at

right-angles by reinforcing bars.

1. The shear transfer strength of cracked monolithic concrete, subjected

to monotonic loading, may conservatively be calculated by either-the shear­

friction equation (4.5) or by the modified shear-friction equation (4.6), regard­

less of reinforcing bar size, providing that adequate anchorage is provided for

the reinforcing bars.

2. For a given reinforcement index, the shear transfer strength of cracked

monolithic concrete decreases about 15 percent as the reinforcing bar size

increases from #8 to #18. (However, the strength is still greater than the

strength calculated using either Eq. (4.5) or Eq. (4.6).)

3. The shear transfer strength of cracked monolithic concrete subjected

to cyclically reversing shear may, for design purposes be taken as 80 percent

of the calculated shear transfer strength for monotonic loading.

4. At service load, under monotonic loading, the transfer of shear across

a crack is primarily due to direct bearing of asperities on the faces of the

crack, secondarily due to friction between the crack faces, and to a very minor

extent due to dowel action of the reinforcement.

5. At ultimate strength, under monotonic loading, the transfer of shear

across a crack is primarily due to both direct bearing of asperities dn the

faces of the crack and to friction between the crack faces, and to a minor extent

due to dowel action. (The proportionate contribution of friction to shear

transfer resistance can be expected to increase as the reinforcement index pfy

increases.)

32

33

6. Under cyclic loading) it is probable that at ulti-mate strength the contri­

butions to shear transfer strength of direct bearing of asperities and of dowel

action of the reinforcement) are both reduced relative to their contributions

under monotonic loading.

7. At a given level of shear stress, the shear stiffness under cyclic

loading is less than under monotonic loading.

8. Under cyclic loading, the effective shear stiffness decreases as the

number of load cycles increases; and just before fa~lure the effective stiffness

will have decreased to about 10 percent of its initial value.

9. Under cyclic loading, the shear stiffness near zero shear is initially

about 40 percent of the effective stiffness, and decreases to about 30 percent

of the effective stiffness for the same load cycle, as failure is approached.

10. Under cyclic loading, the hysteretic damping is approximately constant

after the first cycle of loading, up to about 80 percent of the cycles of

loading causing failure; after ~hich it increases rapidly.

11. In design situations involving shear transfer across a crack, attention

must also be paid to the diagonal tension cracking resistance of the concrete

adjacent to the primary crack, and appropriate reinforcement must be provided

if necessary.

REFERENCES

1. Mattock, A.H., "Shear Transfer Under Monotonic Loading, Across an InterfaceBetween Concretes Cast at Different Times,1I University of Washington,Structures and Mechanics Report SM76-3, September, 1976.

2. Mattock, A.H., IIShear Transfer Under Cyclically Reversing Loading, Across anInterface Between Concretes Cast at Different Times," University ofWashington, Structures and Mechanics Report SM77-1, June, 1977.

3. Hofbeck, J.A., Ibrahim, 1.0. and Mattock, A.H., IIShear Transfer in ReinforcedConcrete,1I Journal of the American Concrete Institute, Vol. 66, No.2, Feb. 1969,pp. 119 - 128.

4. IIBuilding Code Requirements for Reinforced Concre~e", (ACI 318-71), AmericanConcrete Institute, 1971.

5. Viest, I.M., IIInvestigation of Stud Shear Connectors for Composite Concreteand Steel I-Beams, II Journal of the American Concrete Institute, Vol. 52, No.8,April 1956, pp. 875 - 891,

6. White, R.N., and GergelY9 P., IIShear Transfer in Thick Walled ReinforcedConcrete Structures Under Seismic Loading," Annual Report for NSF GrantAEN 73-03178 A01, Dept. of Structural Engineering Report No. 75 - 10,Cornell University, Dec, 1975.

7. Mattock, A.H., IIEffect of Aggregate Type on Single Direction Shear TransferStrength in Monolithic Concrete,·' University of Washington, Structures andMechanics Report SM74-2, August, 1974.

8. Rostasy, F.S., and Hognestad, E., "Pilot Bond Tests of Large Reinforcing Bars ,IIJournal of the American Concrete Institute, Vol. 32, No.5, Nov. 1960,pp. 576 - 579.

9. Hassan, F.M., and Hawkins, N.M., IIEffects of Post-Yield Loading Reversals onBond Between Reinforcing Bars and Concrete,1I University of Washington,Structures and Mechanics Report SM73-2, March 1973.

10. Jacobsen, L.S., IIDamping in Composite Structures ,II Vol. 2 of Proceedings,2nd World Conference on Earthquake Engineering, Tokyo and Kyoto, Japan, 1960,pp. 1029 - 1044.

11. Hawkins, N.M., Mitchell, D., and Hanna, S.N., "Effects of Shear Reinforcementon the Reverse Cyclic Loading Behavior of Flat Plate Structures," CanadianJournal of Civil Engineering, Vol. 2, 1975.

34

TABLE 2. 1 - PROPERTIES OF TEST SPECIMENS

Specimen No. of bars Reinft. Reinft. pfy Concrete ConcreteNo. Crossing Area, Avf Yield (psi) Compn. TensileShear Plane (in. 2) Point, fy Strength Strength(3)(ksi) f~ (psi) f t (psi)

M4A 42 8.40 65.25 548 4075(2) 374M6A 20 8.80 62.12 547 4125(2) 420.M8A 11 8.69 61.23 532 4800(2) 390M9A 8 8.00 67.63 541 4650(2) 390

M10A 6 7.62 67.50 514 3940(2) 420MllA 5 7.80 63.40 495 4190(2) 370M14A 4 9.00 65.60 590 4300(2) 485M18A 2 8.00 68.75 550 4300(2) 410

C4A 40 8.00 68.90 551 3470 (1) ---3730(2) LIT11

C8A 11 8.69 60.75 528 4305(1 ) ---5235(2) 487

C10A 6 7.62 65.56 4·99 3850(1 ) ---4120(2) 368

C14A 4 9.00 65.60 590 3485(1) ---4630(2) 470

(1) Concrete strength at beginning of test, measured on 6 x 12 in. cylinders.

(2) Concrete strength at end of test, measured on 6 x 12 in. cylinders.

(3) Concrete splitting tensile strength measured on 6 x 12 in. cylinders.

TABLE 2.2 - DATA FOR INITIAL CRACKING

Specimen Crack Maximum Residual Maximum ResidualNo c No. Crack Crack Steel Steel

Hidth Width Stress Stress(in. ) (in.) (ksi) (ksi)

M4A 1 0.030 0.012 56.7 16.42 0.022 0.013 38.8 9.8

M6A 1 0.025 0.010 50.3 12.02 0.024 0.010 48.1 9.8

M8A 1 0.023 0.009 26.2 4.72 0.025 0.009 32.5 5.3

M9A 1 0.025 0.010 33.1 8.82 0.025 0.011 35.2 6.6

Ml0A 1 0.023 0.010 23.3 1.12 0.024 0.010 36.0 3.2

MllA 1 0.025 0.010 43.4 1.72 0.026 0.011 41.0 1.9

I M14A 1 0.025 0.010 -- (1) -- (1)2 0.025 0.011 34.3 7.8

M18A 1 0.025 0.011 2::(1 ) 4.~2 0.025 0.011 -- 1)

C4A 1 0.024 0.010 24.2 12.82 0.024 0.010 30.0 --

C8A 1 0.025 0.010 30.7 15.02 0.025 0.010 26.5 14.0

ClOA 1 0.023 0.011 10.4 2.82 0.023 0.010 23.8 3.0

C14A 1 0.027 0.010 29.5 6.42 0.026 0.010 16.0 9.3

(1) Defective gage.

TABLE 3.1 ~ RESULTS OF MONOTONIC LOADING TESTS

Specimen Shear Sl i p at Separation Angle(3} Ultimate(4}No. Plane and Failure at Failure a Shear

Crack No. (in. ) (i n.) (degrees) Strength(kips)

0

M4A 1 0.053 0.037 35 8652(1) 0.114 0.085 41

M6A 1 0.023 0.030 52 11502(1) 0.061 0.054 42

M8A 1 0.022 0.010 25 11482(1) 0.047 0.046 46

M9A 1(2) 0.042 0.060 55 11502(2) 0.046 0.035 42

M10A 1 0.021 0.017 46 10102(1) 0.059 0.070 57

MllA 1(1) 0.081 0.068 42 1091

2 0.051 0.033 37

M14A 1 0.019 0.019 46 11372(1) 0.065 0.060 46

M18A 1(1) 0.052 0.048 42 991

2 0.041 0.044 53

(1) Crack that failed first.

(2) Both cracks failed simultaneously.

(3) Inclination to the shear plane of the slip~separation curves at ultimateshear. ~.

(4) Shear carried by one shear plane.

TABLE 3.2(a) - RESULTS OF CYCLIC LOADING TESTS

Specimen loading History 51 ip at (1) Separation (l Ultimate(2)No. Failure at Failure Shear

load Range of Load (in. ) (in.) StrengthCycles ±% of (kips)

Vu (calc.)r

C4A 1-10 5011-15 5816-20 6621-25 7426-30 8231-35 9036-40 9841-42 106 0.081 0.060 816

C8A 1-10 5011-15 5816-20 6621-25 7426-30 8231-35 9036-40 9841-45 10646-50 11451-55 122

56 123 0.106 0.091 910

Cl0A 1-10 501l~15 5816-20 6621-25 7426-30 8231-35 9036-40 9841-45 10646-49 114 0.098 0.083 796

s6

TABLE 3.2(b) - RESULTS OF CYCLIC LOADING TESTS

Specimen Loading History Slip at(l) separation(l Ultimate(3)No. Failure at Failure Shear

Load Range of Load (i n. ) (i n. ) StrengthCycles +% of (kips)

V\1 Tcalc.)

C14A 1-10 5011-15 5816-20 6621-25 74 .26-30 8231-35 9036-40 9841-45 10646-48 114 0.060 0.047 940

(1) The values of slip tabulated are equal to half the change in slip betweenthe maximum positive and negative shears in the last complete load cyclebefore fa i1ure.

(2) The values of separation tabulated are the averages of the values measuredat the maximum positive and negative shears in the last complete load cyclebefore failure.

(3) Shear carried by one shear plane.

TABLE 3.3 - SERVICE LOAD BEHAVIOR INMONOTONIC LOADING TESTS

Specimen Service On 1st loading Residual On reloadingNo. load slip

shear Slip Shear after Slip Shearstress -3 stiffness loadin~

"(in.xlO-3)stiffness

(psi) (in.xlO ) (ks i Ii n.) (in.xlO- ) (ks i Ii n.)

M4A 384 2.63 146 1.80 1.38 278"

M6A 383 2.25 170 1.25 1.00 383

MBA 373 2.81 133 1.25 1.63 229

M9A 379 2.00 190 1.50 1.00 379 "

M10A 360 1.31 270 1.00 0.75 480

MllA 347 1.85 187 1.60 1.00 347

Ml4A 413 2.25 184 0 1.75 236

M18A 385 2.63 146 1.90 1. 25 308

TABL

E4.

1-

DEFO

RMAT

ION

BEHA

VIOR

OFSP

ECIM

ENCS

A

It

.Lo

adV

A hA 1

Dam

p;nq

Fact

orE

ffec

tive

Sti

ffne

ssI

Cyc

lem

ax.

(lb

.;n

./;n

.2 )(l

b.i

n./

in.2 )

13(1

)13

(2)

Sti

ffne

ssN

ear

Zero

(kip

s)1

2(k

si/i

n.)

Shea

r(k

si/ i

n.)

137

01.

08.1

.54

0.17

30.

112

109

45

537

00.

571.

120.

109

0.08

192

37

1037

00.

531.

140.

097

0.07

487

34

1542

90.

811.

630.

104

0.07

9~

8731

2048

80.

952.

180.

088

0.06

980

28

2554

71.

893.

660.

111

0.08

265

25

3060

62.

404.

640.

111

0.08

256

18

3566

53.

176.

280.

107

0.08

053

21

4072

44.

098.

380.

103

'0.

078

4718

4578

36.

0111

.44

0.11

40.

084

4214

5084

311

.40

19.3

00.

133

0.09

430

7

5490

126

.51

35.3

70.

191

0.11

920

5

5590

146

.27

55.9

10.

225

0.13

215

4

(1)

Cal

cula

ted

acco

rdin

gto

Jaco

bsen

(lO

)

(2)

Cal

cula

ted

acco

rdin

gto

Haw

kins

etal.

(ll)

~

TABL

E4

.2-DEFOR~TION

BEHA

VIO

ROF

SPEC

IMEN

C10

A

Load

V max

.A h

A 1D

ampi

nqF

acto

rE

ffec

tive

Sti

ffn

ess

Cyc

le(k

ips)

(lb

.in

./in

.2 )(l

b.i

n./

in.2 )

a(1

)S

(2)

Sti

ffn

ess

Nea

rZ

ero

12

(ksi

/in.

)Sh

ear

(ksi

Iin.

)

..1

350

0.93

1.28

0.18

00.

115

126

56

535

00.

530.

970.

121

0.08

810

950

1035

00.

591.

060.

122

0.08

810

244

1540

50.

711.

300.

119

0.08

711

043

2046

10.

991.

890.

112

0.08

398

40

25.

517

1.44

2.56

0.12

40.

089

9127

3057

31.

993.

920.

108

0.08

170

21

3562

93.

136.

130.

109

0.08

154

15

4068

54.

148.

160.

108

0.08

147

14

4574

19.

6916

.00

0.13

80.

096

298

4879

638

.85

48.6

30.

212

0.12

715

4

(l}

Cal

cula

ted

acco

rdin

gto

Jaco

bsen

(lO

)

(2)

Cal

cula

ted

acco

rdin

gto

Haw

kins

etal

.(11

)

~

TABL

E4.

3-

DEFO

RMAT

ION

BEHA

VIOR

OFSP

ECIM

ENC1

4A

Load

VA h

A1

Dam

ping

Fac

tor

Eff

ecti

veS

tiff

ness

Cyc

lem

ax.

S(1

)S

(2)

Sti

ffne

ssN

ear

Zero

(kip

s)(l

b.i

n./

in.2

)(l

b.i

n./

in.2

)1

2(k

siii

n.)

Shea

r(k

si/i

n.)

141

30.

941.

380.

166

0.10

916

771

541

30.

631.

180.

116

0.08

514

563

1041

30.

691.

440.

100

0.07

611

042

1547

90.

872.

040.

085

0.06

710

030

2054

51.

423.

030.

097

0.07

491

26

25.

611

1.93

3.91

0.10

40.

078

7817

3067

72

,95

5,86

0.10

70.

080

6720

3574

34.

408.

410.

113

0.08

357

14

4081

05.

7011

.12

0.11

00.

082

4913

4587

614

.94

26.4

10.

125

0.09

028

8

4694

033

.57

45.5

90.

185

0.11

723

8

4794

058

.56

71.5

40.

221

0.13

016

6

(1)

.Cal

cula

ted

acco

rdin

gto

Jaco

bsen

(10)

(2)

Cal

cula

ted

acco

rdin

gto

Haw

kins

eta1

.(11

)

~

TABLE 4.4 - COMPARISON OF CALCULATED AND MEASUREDULTIMATE SHEAR TRANSFER STRENGTH

Specimen pfy Vu (test) Vu (calc) 1 Vu (test) Vu (ca1c)2 Vu (test)No. (psi) (kips) (ki ps) Vu (calc) 1 (kips) V (cal c) 2u

t~4A 548 865 767 1.13 838 1.03

M6A 547 1150 766 1.50 838 1.37.M8A 532 1148 "745 1.54 826 1.39

M9A 541 1150 757 1.52 833 1.38

M10A 514 1010 720 1.40 811 1.25

MllA 495 1091 693 1.57 796 1.37

M14A 590 1137 826 1.38 872 1.30

M18A 550 991 770 1.29 840 1.18

C4A 551 816 771 1.06 841 0.97

C8A 528 910 739 1.23 822 1.11

C10A 499 796 699 1.14 799 1.00

C14A 590 940 826 1.14 872 1.08

Vu (calc)l = ~pfyAcr (lb.), with ~ = 1.4

Vu (calc)2 = (0.8pfy + 400)Acr (lb.)

TABLE 4.5 - COMPARISON OF ULTIMATE STRENGTH FORMONOTONIC AND CYCLIC LOADING

Cyclic MonotonicLoading Loading

Specimen Specimen Vu (cyclic)

Specimen Ultimate Specimen Ultimate Vu (monotonic)No. Shear No. Shear

(kips) (kips)

C4A 816 M4A 865 0.94

C8A 910 M8A 1148 0.79

C10A 796 M10A 1010 0.79

C14A 940 f114A 1137 0.83

-A

pigtailanchorfor swivelliftingplate

1 in. dia.prestressingbars in 1i in •ID tubes.

..::t

..::t

pbearing

bearing plates

(\J(\J

C\1(\J

I 1 ~Ir1'9 ~

shoes 'I 'y"Y/ / / // / .AviE[W7/ / / / / /v / L/bearing1j~j / / / / /U/

,,1--,"/;.f.// ////'P - /

""-'".-- 'I~

1 __ i IM \

,II ;tV

1'-- I 1---I I .

I I I.

\ I,!/I

No. & Rize

Iof hoopRiJ varieR 0

..::t , ~I """ 1=~~

~ 1= Ik=-.::=

~I I ---l

~'-- it-

~;;;

""'"'I::: p::::: ::::::

~ -c: ""SHEAR PLANE. ,/ I

I"l~I ,..

II (40 x 25 in Ieach) .

II . II

i J 1 I --,. It- - - l..I...--../J),J 1 , v,

I 1.4'll.

I """'" . ,-I~

v w//////if/ I I 'l-

! '791//////.F /Av '// / / / /~1~9~ r// / / / / / ' ,1//l 26 y;~ LW I~

stri s""""""

A-

1824

54 --\.---+------r~~---;;poot

.-iIN

'. C"'\;~---""""""" J~L-'

'-----60----Jj ''-2-l------+-'~

18

Section A--A

Fig. 2.1 - Specimen detailR

All dimensionsin inches.

--,T

,",'''\~:·~''',''

','''.,1'''',".,·'.·.·

~VJ.."

""_'

.,l.~d/

,'.....

..(~

,I····

:'.'!~

'~-

'C-';

'"\

,.i~_......

~~';

\

Fig

.2.

2-

Arr

ange

men

tsfo

rte

st

~

"F

ig.

2.3

-In

vert

ing

spec

imen

incy

clic

load

ing

test

!\i \

\i ,r-';:

Fig. 3.1 - Typical appearance of a monotonicloading specimen after failure

'~1~,'~~~'f;..;.;.;.

Fig. 3.2 - Typical appearance of a cyclicloading specimen after failure

\

)60

:320

280

605040:302010

,'0

\\\ / Effective Stiffness, 5e\ 0,\10'

\~\\\\\

-6. 0\ \\ 0_\ x'bStiffness near\ 6.--lt \ zero shear, So

\ I \

Li 1--4 '0\ \A \

.....~ 0 ......\ 0

\1--A 0,

.b.--6. 'Cbh--

o

80

40

240-•~

..-f...........-ffI) 200~-

Cycles of Load

Fig. :3.3 - Variation of shear stiffness with number ofcycles of loading, C4A.

180

160

140

120........s::<r4

"- \ Effective Stiffness, Se<r4 \to 100 " /~- (9" 9, p,

o '0 \fI.l 80 '0l:I.i 0\Q) \s:: \lHlH \<r4

CD"~

60Cf.)

'00,'0>" c?

StiffneE'l~ near " "-"40 "~,,~zero Rhear. SO CO,,

-~--~\

Cb,. l':I.--420 ~ b.--lt::. ,

--b, --~.... \. ~ 0

'Lh--D.

0 10 20 30 40 50 60

Cycle~ of Loa.d

Fig. 3.4- Varia.tion of shear stiffness with number ofcycles· of loading, C8A.

r

180

160 -

140 -

I I I I I I

-

-

-•$::.....

..............to~-

q ~Effect1ve StiffneRR, Se1.20 1-\ -

\\

CO, 7 "\'c?\\100 I-

'0 -

'm\\

80 I- \ -\

Cf1\,

60 I- \ -~ stiffness near

~,,,~zero shear, So ,'0

6.--lh--~__b, \

40 - 0, -\\

,\ \

~--6. CO\ \

20 ~-~\

'- \ -. '~-~ b

'YJ.

I I I I '~ f

0 10 20 30 40 50 60

Cycles of Load

Fig. 3.5 - Variation of shear Rtiffness with number ofcycles of loading, Cl0A.

180

"-

'%,',Stiffness near

\ zero shear, So

'4:1'\

'~,, 1\~ " ~,) & I\.

L:l 'A"'D.'~,~

\\\\,oI\,,o\ 1\ /Effective Stiffness, Se

\ I \,I \o ,

°0,'00

\\

\

~\,,CD, a

'''6 \,q

\

0,,'qo

\o

20

40

140

120

160

-•~

'""-'"lG 100~-

o 10 20 30 40 50 60

Cycles of Load

Fig. 3.6 - Variation of shear stiffness With number ofcycles of loading, C14A.

LC2(2) o - C4A

,I 6. - C8A

0+ + o - Cl0A

+ + 0- C14A6Q. 6.

0 +0

0

0 '6

0 ~ 0 +o 6. D.0"'-

0 @60

Fae 100 - 0.9Pc0 6. +=

00

O,,~

20 40 60 80 100

Percent of Cycles to Failure, Pc

100G>m~

o

..lCmG>

C 80\-tor'C

+>CI)

Q)~

or'C

~ 60Q)

c.-.e.-..ril

rotas

or'C

~ 40$:l

H

e.-..o+>s::~ 20J.4G>.~

Fig. 4.1 - Variation of effective shear stiffness withpercent of cycles of load causing failure.

0 050 0- C4A

8.- C8ArDrD 0- Cl0A0.> 0s:

0- C14Aase...

~ft-<

rD~ 40as,pen..

0""0.>as;:. 0CI)~ 0.s::,proo

Corresponds to,Q)~, 0Oft-< 30 0J..te.-. 0

0.>P::! '6 So/Se = 0.4 - Pc/1000Nr-t

J..tas <>CI5~o.>,pz~

s:rDH 20u;o.>e... 0s::o

6.e... 0ft-<,p~s:,pQ) o 6.tl)O

J..t

~orf 10 <>""'LtJ~

0 20 40 . 60 80 100

Percent of Cycles to Failure, Pc

Fig. 4.2 - Variation of shear stiffness near zero shear,with percent of cycles of load causing failure.

I I I I I

0.3 ~ I::::. - c8A -o - Cl0A0- C14A

~

~ qj.. 0.2J.t f-

01::::.-

0

~~()

~I":tc

€w8~ 0 ,60 0,6 a~ 01::::. <P ~qoI f:{)

~0.1 f- l:::.O 0 -

0as0

I I , I I

0 20 40 60 80 100

Percent of Cycles to Failure, Pc

Fig. 4.3 - Variation of damping factor calculat~d accordingto Jacobsen(10) .

"Skeleton curve"

Slip

Fig. 4.4 - Calculation of damping factor according toJacobsen(10}

I I I I I

0.15 - /:).- C8A -o - C10A

qj0- c14A~ @ <:P-..M 0.10 I-

~0~

B 0 o 0()

& ~CISj{) 6 06 0 6 @AI'r-!

o 6°~~~p., 0.05 I- -ElCIS0

oI

20I

40I

60I

80I

100

Percent of Cycles to Failure, Pc

Fig. 4.5 - Variation of damPirf)factor calculated accordingto Hawkins et al.{ .

Area Ai(energyabsorbed)

Area Ah(energydissipated)

Fig. 4.6 - Calculation of(da~Pin~ factor according toHawkins et al. 11)

a50

100

150

1500

.i

IIi.

,,

iI

II

II

I11

500

1200

- ~ - ~ ...., 0:::: cr:

.w

900

:::r:

(J) w I­ W 0::::

U Z o u o w ~ -J 0­

0­ cr:

300

+C4

AM

4A

1200

.

900

600

300

011

II

II

II

II

II

II

II

I0

a50

100

150

SL

IP.

10-3

(INCH

ES)

~F

ig.

4.7

-C

om

par

iso

no

fsh

ear

-sli

pre

lati

on

sfo

rM

4Aan

dC

4A.

o~

100

1@

1500iiiiiiiiiiii

II

II15

00

1200~

-112

00-. ~ ~ igO

Ol(+

'.M

8A

++

++

+C

8A-i

900

(J:)

W I-

W 0:: U z 8600~

I-B

--I

600

Cl

w - -' ll..

ll..

a:30

0~1

~30

0

01

'I

II

II

II

II

II

II

II

o~

100

1~

SLIP

lIE10

-3(I

NCHE

S)

o

~F

ig.

4.8

-C

om

par

iso

no

f~h

e9.r

-sli

pre

la.t

ion

sfo

rM

8Aan

dC

8A.

\J~

·0

5010

015

015

00.iii

i•iii

•iii

Ii

.150

0

1200~

1120

0.

..-~ X

.'-

J

0:::: a: ~

9001

-./

'----

---l

900

(f) w

+++

I- w

+-H

t+----

.M

IOA

---

0::::

+tt-

L>

Z-H

Hr

CD-l

600

u..

Cl

+W 1-

-04

*..

J0

-+

0- a:

+30

01

300

~

0',

,,

,,

,I

,I

I,

,,

,I

0a

5010

015

0S

LIP

lI(1

0-3

(INC

HE

S)

Fig

.4

.9.-

Com

pari

son

of

shear

-sli

pre

lati

on

sfo

rM

l0A

and

Cl0

A.

o50

100

150

1500

.i

•I

.I

I•

iI

•I

•i

II

.150

0

~1200~

-112

00-

MI4

A~ ~ \o

J

0::: ~900~

/..

.+

+C

I4A

-I90

0en w I-

W 0:::

U z 86

00

1-

fft-

-I60

0Q W 1

-4 -! a... a...

a:30

0U.

~30

0

~ ~

O'

II

I'.

I,

Ii

II

,I

II

II

o50

100

150

SLI

PlIE

10-3

(INC

HE

S)

i

Fig

.4

.10

-C

om

par

iso

no

fsh

ear

-sli

pre

lati

on

sfo

rM

14A

and

C14

A.

o

oM6A

o..,M4A

2000

M8Ao.

M9A° Jiassan &:5f/Hawkins (9 )

Ml0AO

M11A 0 (j114A

1000

M1.8Ao

o

Reinforcing Bar Diameter (in. )

Fig. 4.11- Variation of (Reinforcement Stress)/(Separation)with bar diameter, in shear transfer push-offtests and bond pull-out tests.

~/

1.5

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0

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0.7 + Cyclic loading ...1I

0.60 0.5 1.0 1.5 2.0 2.5

Reinforcing Bar Diameter (in.)

Fig. 4.12 - Variation of ultimate shear transfer strengthwith reinforcing bar diameter.

f y

APPENDIX A

NOTATION

= Area of shear plane, sq. in.

= Area of reinforcement crossing the shear plane, sq. in.

= Compressive strength of concrete measured on 6 x 12 in.cylinders, psi.

= Yield point stress of reinforcement, psi.

Vu = Ultimate shear force, kips.

Nominal ultimate shear stress, psi.

Coefficient of friction used in shear-friction calculations.

Avf/A cr

Capacity reduction factor, as per Sec. 9.2 of ACI 318-71.

APPENDIX B

DATA FROM MONOTONIC LOADING TESTS

Fi g. Title

Bl Applied concrete shear - slip curves, Specimen M4A

B2 Applied concrete shear - slip curves, Specimen M6A

B3 Applied concrete shear - slip curves, Specimen M8A

84 Applied concrete shear - slip curves, Specimen M9A

B5 Applied concrete shear - slip curves, Specimen M10A

86 Applied concrete shear - slip curves, Specimen M11A

87 Applied concrete shear - sl i p curves, Specimen M14A

B8 Applied concrete shear - sl ip curves, Specimen Ml8A

B9 Slip - separation curves for crack that fail ed inSpecimens M4A, M6A, M8A, M9A.

B10, Slip - separation curves for crack that failed inSpecimens M10A, MllA, M14A, M18A.

811 Applied concrete shear - steel stress curves, Specimen M4A

B12 Applied concrete shear - steel stress curves, Specimen M6A

B13 Applied concrete shear - steel stress curves, Specimen M8A

B14 . Appl i ed concrete shear steel stress curves, Specimen M9A

815 Appl ied concrete shear - steel stress curves, Specimen M10A

816 Applied concrete shear - steel stress curves, Specimen r11lA

B17 Applied concrete shear - steel stress curves, Specimen M14A

B18 Applied concrete shear - steel stress curves, Specimen M18A

B19 Steel stress - separation curves, Specimen M4A

B20 Steel stress - separation curves, Specimen M6A

Fig. Title

B21 Steel stress separation curves, Specimen MBA

822 Steel stress - separation curves, Specimen ~19A

823 Steel stress - separation curves, Specimen M10A

B24 Steel stress - separation curves, Specimen ~111A

825 Steel stress - separation curves, Specimen Ml4A

826 Steel stress - separation curves, Specimen M1BA

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APPENDIX C

TYPICAL DATA FROM CYCLIC LOADING TESTS

(Data presented is for the crack in which failure occurred).

Figure Title

Cl Shear - sli~ curves, C4A, cycles 1 - 5

C2 Shear - slip curves, C4A, cycles 6 - 10

C3 Shear - slip curves, C4A, cycles 21 - 25

C4 Shear - slip curves, C4A, cycles 36 - 40

C5 Shear - slip curves, C4A, cycles 41 - 42

C6 Shear - slip curves, CSA, cycles 1 - 5

C7 Shear - slip curves, CSA, cycles 6 - 10

C8 Shear - slip curves, CSA, cycles 21 - 25

C9 Shear - slip curves, C8A, cycles 46 - 50

C10 Shear - slip curves, CEA, cycles 51 - 56

Cll Shear - slip curves, C10A, cycles 1 - 5

C12 Shear - slip curves, C10A, cycles 6 - 10

C13 Shear - slip curves, C10A, cycles 21 - 25

C14 Shear - slip curves, C10A, cycles 41 - 45

C15 Shear - slip curves, C10A, cycles 46 - 49

C16 Shear - slip curves, C14A, cycles 1 - 5

C17 Shear - slip curves, Cl4A, cycles 6 - 10

C18 Shear - slip curves, C14A, cycles 21 - 25

C19 Shear - slip curves, C14A, cycles 41 - 45

CW Shear - slip curves, C14A, cycles 46 - 48

t!'- - I

Figure Title

'e2l Slip -. separation curves, C4A, cycles 1 - 5

C22 Slip - separation curves, C4A, cycles 6 - 10

C23 Slip - separation curves, C4A, cycles 21 - 25

C24 Slip - separation curves, C4A, cycles 36 - 40

C25 Slip - separation curves, C4A, cycles 41 - 42

C26 Slip - separation curves, CSA, cycles 1 - 5

C27 Slip - separation curves, CSA, cycles 6 - 10

C28 Slip - separation curves, CsA, cycles 21 - 25

C29 Slip - separation curves, CSA, cycles 46 - 50

C30 Slip - separation curves, CSA, cycles 51 - 56

C3l Slip - separation curves, C10A, cycles 1 - 5

C32 Slip - separation curves, C10A, cycles 6 - 10

C33 Slip - separation curves, C10A, cycles 21 - 25

C34 Slip - separation curves, C10A, cycles 41 - 45

C35 Slip - separation curves, C10A, cycles 46 - 49

C36 Slip - separation curves, Cl4A, cycles 1 - 5

C37 Slip - separation curves, C14A, cycles 6 - 10

C38 Slip - separation curves, C14A, cycles 21 - 25

C39 Slip - separation curves, C14A, cycles 41 - 45

C40 Slip - separation curves, Cl4A, cycles 46 - 48

C4l Shear - steel stress curves, C4A, cycles 21 - 42

C42 Shear - steel stress curves, CSA, cycles 1 - 25

C43 Shear - steel stress curves, CSA, cycles 30 - 56

C44 Shear - steel stress curves, C10A, cycles 1 - 25

C45 Shear - steel stress curves, C10A, cycles 30 - 49

e _2/

Figure Title

C46 Shear - steel stress curves, Cl4A, cycles 1 - 25

C47 Shear - steel stress curves, Cl4A, cycles 30 - 48

C48 Separation - steel stress curves, C4A, cycles 25 - 42

C49 Separation - steel stress curves, CSA, cycles 1 - 25

C50 Separation ~ steel stress curves, CSA, cycles 30 - 56

C51 Separation - steel stress curves, C10A, cycles 1 - 25

C52 Separation - steel stress curves, C10A, cycles 30 - 49

C53 Separation - steel stress curves, C14A, cycles 1 - 25

C54 Separation - steel stress curves, C14A, cycles 30 - 48

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FIG.-C2~SLIP-SEPRRRTION CURVES9C4R

uf

10.0?5.005.00a-5.00-10.0015 •00 iii iii iii iii iii iii iii iii iii iii iii iii Iii I...,

10.00

CYCLE 6-10

:!:.. .5 Vu(calc)

CRACK # 2 10.00

5.001- I -l 5.00(f)w:r:uzI-i...-

,1 01 I -I 0a......lIf

a..I-i

......J(f) -5.00t- I ~ -l -5.00

-10.00 -10.00

-15 .00 I I I I I I I I I I I I I I I I I I I I I I I I I I I , I I I I I I I I I I I I J -15 .00-10 .00 -5.00 0 5.00 10.00

SEPARATION * 10-3 (INCHES)

FIG.-C2~SLIP-SEPRRRTION CURVE5,C4R

t25

-5.00 o 5.00 10.00 15.0030 .OO~' , , , , , I , ' I'I , , , ~' , I I , I I , I , , , , I , , , , , , , , '~ 30.00

CYCLE 21-25

±. .74 vu{calc)

20 .OO~ CRACK # 2 -l 20.00

-20.00-20.00

10.00r I -l 10.00(J)w::r:uz.-.....,

IQ 01 1 1 0I0~

lIE

CL......J(J) -10.00 r- I ~ ~ ztj!P"- -i-10 .00

-30 •.00 I t I I I I I I I , I , I I I I I I , I I I I I I I I I I I I I I I , I I I I I 1-30.00-5.00 0 5.00 10.00 15.00

SEPARATION ~ 10-~ (INCHES)

FIGQ-C2~SLIP-SEPRRRTIONCURVES,C4R

u~

70.0?20.050.0030.0010.0012010 •00

ISO'i iii I I Iii iii iii iii i iii iii I Iii TT',,'n"T-r-~~J II Iii Iii I

80.0

CYCLE 3'6,:,"40

+ .98 v ( ")- u ca.LC

CRACK # 2 80.0

,..... 40.0~ I -f 40.0(f)w:c(JzI-f

"'-'

III 01 I /~ ./ I 0/' 1 7'I(:)~

lIE

Q..I-<

..J(f) -40.0 ~ IJ I II \ l , -f -40.0

-80.0 -80.0

-120 .0 I I I , , ! I I I I I I I , I , I I I I I I I I I , I I I I I I I I I I I I I I I -120 .0-10.00 10.00' 30.00 50.00 70.00

SEPARATION lIE 10- 3 (INCHES)

FIG.-C2~SLIP-SEPRRRTIDN CURVES,C4R

u·1

80.0

-80.0

70.0?20.050.0030.0010.00

CRACK # 2

CYCLE 41-42

.±. 1.06 Vu(calc)

80.0

12010 •00•0· I I iii iii iii iii iii iii iii iii iii Ti'jJr-r-.....,,...,_~r ...iii iii i I

-80.0

..... 40.0 r- I / /' / -1 40.0(J)w:r:uz~

'-'

to 01 I { 7r I 0J 7

0.......

lIE

0.............J(J) -40.0 ~ I / I / -l -40.0

-120.0 I I I I I I I I ! I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1-120.0-10.00 10.00 30.00 50.00 70.00

SEPARATION * 10-3 (INCHES)

FIGu-C25tSLIP-SEPRRRTION CURVES,C4R

tJ-O

20.0?5.0015.0010.005.00o15.00 iii iii iii iii iii iii iii iii iii I Iii iii iii iii i

10.00

CYCLE 1-5

+ .5 V ( 1)- u ca c

CRACK # I10.00

5.00 I-- -1 5.00(J)w:r:uzI-<

~

tn 0l\1 I aI0......

*CL..........J(J) -5.001-- -I -5.00

-10.00 -10.00

-·15 •do I I I I I I I , I I I I J I I I I I I I I I I I I , I , I I I , I I I I I I I I I -15 .00a 5.00 10.00 15.00 20.00

SEPARATION * 10-3 (INCHES)

FIG.-C26,SLIP-SEPRRRTION CURVES,C8R

MY

a 5.00 10.00 15.00 20.0015 •00 ~ I I I I I I I I I I I I I i I I I I I I I I I I I I I I I I I I i I I i I I I~ 15.00

Cy\CLE 6-10

+.5;V( 1)- ' u ca c

10.001-CRACK # I

-l 10.00

-10.00 -10.00

-15 •00 I I I I I I I I I I I I I I I I I I I I , I I I I I I I I I I I I , I I I I I I J -15 .00o 5.00 10.00 15.00 20.00

SEPARATION * 10-~ (INCHES)

FIG. -C27, 5L IP-SEPRRRT I ON CURVES, C8R

CStJ

0 5.00 10.00 15.00 20.0015 •00 Eiii I i I I I I I I Iii I I I I I I i I I I 1I I I I I Iii I I I I I 13 15.00

CYCLE 21-25,

±.. .. 714 Vu(calc)

10.00t-CRACK # I -1 10 .00

...... S.OO!- \U' -I 5.00(J)w:r:uz-.....

It). o~~ 1 aI'0.....

lie

0--....JCf.) -5.00 /- ~ -1 -5.00

-10.00 -10.00

-15 .00 I I ! , I i I I i I I i I I I I i I I I I I I I I I ! I I I I I I I I i I I I I I 15. 0005.00 10.00 15.00 20.00

SEPARATION * 10-~ (INCHES)

FIG .. -C28,SLIP-SEPRRRTION CURVES,C8R

c~1

ao.ogo.oo60.0040.0020.00o60 .00 Iii I I I • iii i i f i I I I I J iii • I f iii iii Iii iii i » i I

40.00

CYCLE 46-50+ 1.14 V ( 1)- . u ca c

CRACK # I40.00

,..... 20.001- ~ -i 20.00Cf)w:cuz............

to 01 I \I ~ 8 'I I 0I r t1111

0..-I

lIE

Q........-lCf) -20 .00 I- ~ -1-20.00

-40.00 -40.00

-60 .00 '. r I I , I , I , , I , J I I , I I , I I I I I I I I I I , I , , , I , I I I I I -60 .00o 20.00 40.00 60.00 ao.oo

SEPARATION * 10-3 (INCHES)

FIG .. -C29, SL IP-SEPRRRT I ON CURVES, C8R

t~cL-

-40.00

o 20.00 40.00 60.00 80.0060.00 Fill I I I 1 I .1 I ( I I I I I i I I I I , I I i I I , 1 I 17 1 Iii 1 Ii 60.00

. CYCLE 51-56

c+ 1 •.22 V ( 1)- u ca c

40.00r CRACK # I / / / -I 40 .00

-40.00

,... 20.00r ~/ -I 20 .00enw:I:UZ-'-'

f? 01 1111 III I I -I I I 0I

0.-..~

a....-....Jen-20 .00 r ~'\ '{ \ \ -1-20.00

-60 .00 I I 1 I I 1 I I I I I 1 I I I I 1 I I I I I I I I I 1 I I 1\1 I \1 I I I I I , 1 I -60 .00o 20.00 40.00 60.00 80.00

SEPARATION * 10-3 (INCHES)

FIG.-C3QSLIP-SEPRRRTION CURVES,C8R

c-JJ-

20.0?5.0015.0010.005.00a15 .00 iii iii iii iii iii iii I i I I iii iii iii iii iii iii I

CYCLE 1-5

1. •5 VUe calc)

~ CRACK # 210.00 10.00

5.00r- -\ 5.00(f.)WIUZ~

"'-J

f() or'M\\ I I aI·0.-4

lIE

a..........-1(f.) -5.00 r- -\ -5.00

-10.00 -10.00

-15. 00 I I I I I I I I I I I I I , I I I I I I I I I I I I I , I I I I I I I I I I I I '-15.00a 5.00 10.00 15.00 20.00

~EPARATION lIE 10-3 (INCHES)

FIGa-C31,SLIP-SEPRRRTION CURVESpCl0R

c~f

0 5.00 10.00 15.00 20.0015 •00rI 1 , , I , , , " I ':' , , , I , , , I , I , , , I I , , , , I , , , , '~ 15.00

CYCLE 6-10

±. .5 vu(calc)

10.00 f=- CRACK # 2 -=l 10.00

-10.00-10.00

5.001- -i 5.00CJ:JWIUZ.....'-'

tt> Dlil I 0Ja......

*CL.....--1(f) -5.001- -i -s .00

-15 •00 I I I ! I I I I I I I I I I I I I I I I I I I I I I I I ! I I I!! I I I I I I I -15 .00. 0 5.00 10.00 15.00 20.00

SEPARATION * 10-3 (INCHES)

FIG.-C32,SLIP-SEPRRRTION CURVES,Cl0R

~~

0 5.00 10 .. 00 15.00 20.0015 •DO ~' I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I~ 15.00

CYCLE 21-25

~ .±.- •74 IV {u calc)10.001- CRACK # 2 -1 10 .00

.-- 5.00 I- ~ , /'f// -f 5.00(f)w:cuz...........,

t() O~ I~-\ \\U i aJ0.....)If

0-..........I(J) -5.001- -...

~ -5.00

-10.00 -10.00

-15. 00 I I I I I I I I ! I I I I I I I I I ! I I I I I I I I I I I I I I I , I I I I I '-15. 00o 5.00 10.00 15.00 20.00

SEPARATION * 10-3 (INCHES)

FIG a -C33, SL IP-SEPRRRT ION CURVES, C1OR

~

a 20.00 40.00 60.00 80 .. 0060 •00 ~I iii iii I I I I I I I i I I I I I I I I j I I j I j I I I I t I I I Iii 60.00

CYCLE 41-45+ 1.06 V ( ];)- u cae

40.00 I- CRACK # 2 -t 40.00

,.... 20.00r -t 20.00<r.JW:cuz......~

«) 01 I 'I pI, I 01 1\ II

0.....)If

CLl-4

-1<r.J-20 .00 r ~ -t-20 .00

-40.00 -40.00

-60 .00 I I I I I I I I I ! I I I I I I ! I I I I I I I I I I ! I I f I I I I , I I I I '-60.00o 20.00 40.00 60.00 80.00

SEPARATION. 10-5 (INCHES)

FIG Q -C3't, SL IP-SEPRRRT ION CURVES 9 C1OR

031

0 30.0 60.0 90.0 120.090.00F' I I I II I I I I I I I I I I I I I Iii i I I I I I I I i I I iii I I Ii 90.00

CYCLE 46-49

+ 1.14 V ( 1)- u ca c

CRACK # 260.00 I- -I 60.00

-60.00

-90 .00 I I I , I , I I ! ! I I 'i' I I I I I I I I I , I t. I I I I I ! I I I I I ! I 1-90.00a 30 .0 60 •a 90 .0 120 •a

SEPARATION ~ 10-3 (INCHES)

-60.00

,.... 30.00r f/ f/ // -1 30.00CJ)w:r:uz..............

H1 01 \A IA \I I 0Ia.-4

)IE

CL.......-lCJ) -30.00 I- t.J \ \. """-.1-. -1-30.00

FIG.-C35, SLIP-SEPRRRTION CURVES ,C10R

ciS/J

10.00

lS.0?S.007.S0o-7.S0

CYCLE 1-5

~ .5 Vu(calc)

CRACK # I

~15.0015 .. 00 r i I Iii iii iii iii Iii ii' iii ii' i , , iii iii iii i i

10 .. 00

..-.. S.. OOr- l.-4 4 5.00(fJW::I:UZ-.......

tQ 01 '\~ I al "-~

0.-4

*CL1-4

....J(fJ -S .00f- I -i -S .00

-10 .. 00 -10.00

-15.00'1 I I I I I I I I , I I I , I I I I I , I I I I I I i I I , I I I I I I I I I '-15.00-lS.00 -7.50 a 7.50 15.00

SEPARATION * 10-3 (INCHES)

FIG.-C36,SLIP-SEPRRATION CURVES,C14R

G3r

-10.00

-15.00 -7 ..50 0 7.50 15.0015.00 Fl , I I , I I I I I I I I I I I I I I I' iii I I I I I I I I I I I I I I 'i 15.00

CYCLE 6-10

±.. •5 Vu ( ca.lc)

10 .001-CRACK # I

I -1 10.00

-10.00

r-'> ..J .uu,- r .lr//7ff -. 5.00(J)W:J:UZ............

ttl 01 ~ 1 a,O'-lIE

CL.....-.J(J) -5.00 r- I -f -5.00

-15 .00 I I , I I , ! I I I I I I I I I I I I I I. I I I I I I I ! I I ! I I I I I ! I ! I -15 .00-15.00 -7 ~50 0 7.50 15.00

SEPARATION. 10-3 (INCHES)

FIG .. -C37, SLIP-SEPRRRTlaN CURVES .C14R

~1(J

30.0~0.0020.0010.00a-10.0030 .00 f'"'"ITI' iii iii I iii iii j iii iii J iii iii iii iii iii i

20.00

-20.00

CYCLE 21-25

±... •774 vu( calc:)

CRACK # I20.00

...... 10.00r I~ -I 10.00CJ)W:I:UZ........,

110 or ~ a,0-If

a.......-ICJ)-10 .oor I . -1-10.00

-30 .00 I I.' ! , , , , I I I ! I I I I I I , I I I I I I I ! U I I I I I I I I I I I '-30.00-10.00 0 10.00 20.00 30.00

SEPARATION. 10-3 (INCHES)

FIG&-C3~SLIP-SEPRRRTIONCURVES,C14R

c! 11/

40.00

ao.ogo•oo60.0040.0020.00

CYCLE 41-45

±.. 1.06., Vu(calc)

CRACK # I

o60.00, iii iii iii iii iii i , , ii' iii iii i , , iii iii Iii i

40.00

..- 20.00 .... I 4 20.00enw:I:UZ--

to 01 '&& I 0I0.....•0--...Jen-20 .OQj- -1-20.00

-40.00 -40.00

-60.00 I I I I I I I I I I I I I I I I I I , I I I , I I I I I I I I , I , I I I I I , J -60 .00o 20.00 '40.00 60.00 80.00

SEPARATION. 10-3 (INCHES)

FIG.-C39,SLIP-SEPRRRTlaN CURVES,C14R

~;(~

o 20.00 40.00 60.00 80.0075 ..00 I I I I I I I i I I I I I I I I I I I I I OLD I I I I I I I I I I I I I I I I 75.00

50.00

-50.00

CYCLE 46"':4-6

+ 1.14 V { 1)- . u ca c)

CRACK # I50.00

-50.00

..... 25.001- )'/1/ -1 25.00enIJJ:I:UZ....'-"

W) 01 I \I \ \ ; 0I \ 1: \

0'..-c

IE

(L..........J(J) -25 ..00 I- \~ -l-25.00

-75.00' ! I ! I I ! I I I I I ! I I I ! I ! I I I ! ! I I I I ! I ! I I I I I I I I I '-75.00o 20.00 40.00 60.00 80.00

SEPARATION ~ 10-3 (INCHES)

FIG.-C40,SLIP-SEPARATION CURVES,C14A

L~

-750

o 20.00 40.00 60.00 80.001000Eill I I 1 1 I 1 I I 1 I I Iii I I I i I I Iii 1 I I I I I I Iii I I 13 1000

CYCLE 25,30,35'

40,41,42

750E- CRACK # 2 J ~ / ~ 750

-750

500F- ) III /1/ // -j 500,......~~

---a::: 250f:. / / If// / // / / .:j 2500:W:cCf)

wl- DE r (I I \: / .......... .......... l 0W I I Ia:::uz0u

fa -2501=- \\ '\\\ '\ ""'- I -1 -250......-lCLCL0:

-500f \\ " \"" II ~ -500

-1000 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I II -1000o 20.00 40.00 60.00 80.00

STEEL STRESS (KSI)

FIGa-C41,SHERR-STEEL STRESS CURVES,C4R

e-I/f

375.0

-375.0

40.0~00.030.0020.0010.00

CYCLE.1,5,IO,

15,20,25

CRACK If I

I I I I I I , I I I I I I I ' I I I I [ I VI , I I I , I I I , I I , , I , I I I I -500 .. 010.00 20.00 30.00 40.00

STEEL STRESS (KSI)

250.0L ifill .J

'"'~~'-'

.:f 125.00=: 125.0 t- IIffi:t:(J)

WJ- OE- t", ] 0W0=:UZ0uffi-125.0 E- . 1\ -3-125.0..-.c....J0..0..a:

-250.0E- \\\\\ \ -3-250.0

FIG.-C42SHEAR-STEEL STRESS CURVES,C8A

~!/5

-750

, I I I , t I I I I ' I , , I , I ;_ f , , I , , , , , , I I , I , J , , , , , , 1-100020.00 40.00 60.00 80.00

STEEL STRESS (KS!)

o 20.00 40.00 60.00 80.001000P , i , ii' iii iii , , i , i , I , , iii , ii' I , I , I , i I I '3 1000

CYCLE 30,35,40,45,50,55,56

750E- CRACK # I LII / I -3 750

500L. I /TUII I I I :J,-..

~~.....,0:::: 2501:- '111// / .:J 250a:lJJ:I:enlJJl- DE au ) I

(.~ 0W I

0::::UZ0ufiJ -250E- \. ,~\\ . \ -3 -250.........Ja..a..a:

r \1I1l\\ \ -,-500

FIG.-C4~SHERR-STEEL STRESS CURVES,C8R

~1~

o 10.00 20.00 30.00 40.00500.aLi iii Iii i Iii iii iii Iii iii iii iii iii iii iii i U 500.0

375.0

-375.0

CYCLE. 1,5,10,

15,20,25

CRACK # 2

, I I I , I I , , , , , , , »' , I , , I I I I I , , , I , I I I , , , , , I ~ -500 .010.00 20.00 30.00 40.00

STEEL STRESS. (KSI)

250.0E " j 250.0.-~~....,0:: 125.0t- II .:J 125.0ffi::I:(f)

~ OE lNtk- 3 0l.IJ0::UZ0u

fB-125.0E- \ \1 \ \\ \ -3-125.0.........J0..0..a:

r:: 1\.,,\/\ "- ,-250.0

FIG.-C4~SHERR-STEEL STRESS CURVES,C10R

~f1

o

250

500

750

-500

-250

.-750

CYCLE 30,35,4045,48,49CRACK # 2

I I , I , , , , I I , , , , , , , , , , , , , , , , I I ' , I , , , , , I , I ..U -1 00020.00 40.00 60.00 80,00

STEEL STRESS CKSI)

20.00 40.00 60.00 80.00I f Iii Iii iii i til I I I i I I I , , , C i , Iii Iii iii iii I 1000

0:::

ffi3.i~IJ.Ja::::U

~U

ffi -250.....-J

&

-~::c'""'

FIG Il-C45, SHERR-STEEL STRESS CURVES, ClOR

{AI/J

375.0

-375.0

CYCLE 1,5,10,

15,20,25CRACK # I

I ' I I I , , , , I , , , , , , , I , I 'If .' , , I I I , I , , , , , , , , ! 1-500.010.00 20.00 30.00 40.00

STEEL STRESS (KSI)

10.00 20.00 30.00 40.00iii iii i , iii iii j II II iii iii Iii iii Iii iii iii iii 500.0

250.0r: , II/III /I .:J,...

enQ.

::s:-~ 125.0t:- II/I f ~ 125.0ffi::cenw..... OE qJ( ] 0w0:::UZ0u

fi3-125.0E- l \\\~\ -3-125.0--J0-0-a:

r \ \\\\ \ \ \ \ \ ,-250.0

FIG. - C46, SHEAR-STEEL STRESS CURVES, C14R

t1/!

750

-750

80.0~00060.0040.0020.00

5001: 11111111 / I ;.J-~-x.....

0::: 250E- /11// / / / -3 250ffi::I:enwf- OE KIt ~\ '( \: ] 0W0:::U

BuG:l -250E ~,,~ \. '\. -3 -250........J0-0-a:

r ,~'\ '\'\. " " '\ .,-500

-1000 C! I I I , , ! I , I , , , , , , , , , I I , I , , , I , I , , , U J , , , n -1000o . 20.00 40.00 60.00 80.00

STEEL STRESS (KSI)

FIG.-C4~SHERR-STEEL STRESS CURVES,C14R

~5p

o 20.00100 .0 en i i ( I ! •

P 4

CYCLE 25,30,35,40s4I,42CRACK If' 2

40.00 60.00 80.00100.0

80.0 80.0

o

20.0

80.00oI I , i , , ,'f'l2%'1t=H.J I I , I ! I I , I I ! I I I , ! I I ! , I , I I I I I

o 20.00 40.00 60.00STEEL STRESS (KSI)

20.0

,-,.(f)W::I:UZ:; 60.0 l- /'... /~ -1 60.0~

ICJ.,-<

~

zc::J

~ 40.01- I / II I -1 40.0a:u::a:CLw(f)

FIG.-C4~SEP.-STEEL STRESS CURVES,C4R

t~/

o 10.00 20.00 30.00 40.0050 .00 I I I I Iii iii Iii Iii i , iii iii i t iii iii iii t i i t i J50 .00

CYCLE r,5,10,

15,20,2540.00l- CRACK # I 40.00

o

10 ..00

20.00

30.00

40.0010.00· 20.00 30.00STEEL STRESS (KSIl

00

•zo~20.00a:0::::a:0-

~

,...

~z~30.00

tc')io~

FIG.-C4~SEP.-STEEL STRESS CURVES,C8R

tJ:J--

80.0

CYCLE 30,35,40,45,50,55,56CRACK # I

80.0

o 20.00 40.00 60.00 80.00100 .0iii iii iii Iii iii iii I I I I I I I I I i I I I iii I i I I i I I 100 .0

40.0

20.0

60.0

80.00 020.00 40.00 60.00STEEL STRESS (KSIl

,...(J)

is~ 60.0.....,

•s:::: 40.0a:0::a:I:L

lli

tpo......

FIG.-C50SEP.-STEEL STRESS CURVES,C8A1

t5J

30.0020.0010.00 40.00I I I iii iii iii iii iii Iii iii iii iii iii iii I iii i 50 _00

40.00

,....

~::30.00

MIto.....•~~20.00a:0::::a:0­w(J)

CYCLE 1,5,10,

15,20,25

CRACK # 2

10.00 20.00 30.00STEEL STRESS (KSI)

40.00

30.00

20.00

10.00

o40.00

FIG.-C51 SEP.-STEEL STRESS CURVES,CIOAI

of

o 20.00 40.00 60.00 80.00100 ..0 r I I I I I I I I I I I I I i I f' r I I I I I I I I I I i I I I I I I I I I I I I 100 .0

CYCLE 30,35,4045,45,48,49CRACK # 2

40.0

20.0

80.0

60.0

80.00 020.00 40.00 60.00STEEL STRESS (KSI)

00

•e~ 40.0a:0::a:0­w(f;)

..-00

~u~ 60.0-

tc')Io.....

FIG.-C5~SEP.-STEEL STRESS CURVES,C10A

c5J

o 10.00 20.00 30.00 40 ..0050 ..00 E' I I r r r I I I I I I I I r r r I I J I r I r I I I I r J r r r I , 11r 1350.00

'CYCLE 1,5,10,15,20,25CRACK # I

40.00~ -140.00

-ff35z-30.00'""

J()

•o.-4

•a~20.00a:0:::a:0-

~

10.00

00 10.00 20.00 30 .. 00STEEL STRESS (KSI)

30 ..00

20.00

10.00

40.00 0

FIG.-C5~SEP.-STEEL STRESS CURVES,C14R

~..tP

o

20.0

40.0

60.0

80.0020.00 40~00 60.00STEEL STRESS (KSI)

0 20.00 40.00 60.00 80.00100.0 100.0

CYCLE 30,35,40,

45,47 'p48

CRACK # I

80.0 80.0

20.0

•zo~ 40.0a:0::::a:fu(f.)

-ffi5z~ 60.0

I()Io~

FIG.-C5~SEP.-STEEL STRESS CURVES,C14R