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Masters Theses Student Theses and Dissertations

1965

Effect of single stirrups on reinforced concrete beams Effect of single stirrups on reinforced concrete beams

Vinodbhai T. Patel

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EFFECT GF SINGLE STIRRUPS ON

REINFORCED CONCRETE BEAMS

BY .. VINOB:BHAI T. PATEL ) 11~1.)

A

THESIS

submitted to the faculty of the

UNIVERSITY OF MISSOURI AT ROLLA

in partial fulfillment of the r e quirement for the \ 1

Degree of

MASITER GF SCIENCE IN CIVIL ENGINEERING

Rolla, Mi s s ouri

1965

Approve d by

ii

ABSTRACT

This study was made to determine the location of

vertical stirrups and also to determine the amount of stir­

rup-steel required to prevent diagonal cracking. The study

is limited to rectangular) simply supported) reinforced con­

crete beams subjected to a concentrated point load at the

center of the span. Five sets) each containing three beams

were tested. Two sets were cast without stirrups and the

results were used to locate the stirrups for the remaining

tests. The other three sets were cast with one stirrup on

either side of the central load. Stirrups were of the 11 U11

type and formed from No. 9 and No. 11 steel wire and 3/16

inch diameter bar. Results indicated only a small increase

in moment carrying capacity between the first two sets and

the latter three. Some inconsistences between observed and

theoretical behavior are noted.

ACKNOWLEDGEMENT

The author wishes to express his sincere thanks to

Professor James E. Spooner~ of the Civil Engineering

Department~ for his valuable advice and encouragement

throughout the work.

iii

The author is also thankful to Dr. William A. Andrews

and the staff of the Civil Engineering for their advice and

assistance in preparing this thesis. The author wishes to

express his grateful appreciation to Mr. Raman A. Patel and

Mr. Vipin R. Shah for their help during the experiment.

The author is also indebted to the several members of

the Mechanics Department for their assistance on the use of

the testing machine.

iv

TABLE OF CONTENTS

Page

ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i i

ACKNOWLEDGEJYIENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

LIST OF FIG"URES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

I INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l

II REVIEW OF LITERATURE.......................... 2

III EQUIPJYIENT AND MATERIALS................ . ...... 12

A. Laboratory Equipment....................... 12

1 . Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2. Testing Machines. . . . . . . . . . . . . . . . . . . . . . . . 12

3. Forms ........................... ...... .. 13

B. Materials.................................. 13

l. Cement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2. Fine Aggregate.......................... 13

3 . Coarse Aggregate ........................ 13

4. Re inforcing Bar and Stirrups............ 14

C. Preparation of Specimens................... 14

IV TEST PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

A , Beams ... . ·. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

B. Cylinders .".......................... . .... . . 20

V DISCUSSION OF RESULTS... . .. ......... ... ....... 32

VI CONCLUSIONS ....... .. ......... .. ..... ... · · · · · · · 37

VII RECOMIVIEND.ATIONS .............................. .

BIBLIOGRAPHY.

APPENDIX".

. . . . . . . . . .. . . . . . . . .. . . . . . . . . .. . . . . . . . . . . .

VITA ................................... ............. .. .

v

Page

38

39

40

44

vi

LIST OF FIGURES

Figure Page

1 Comparison o~ Theoretical and Test Results

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

by Dr . Kani . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . l 0

Test Set Up ~or Beams and Anchorage Details ....

Determination o~ Points ''a'' and "bH ........... .

Crack Pattern at Failure ~or Set A ............ .

Crack Pattern at Failure ~or Set B ............ .

Cracking Zone ................................. .

Load-De~lection Curve ~or Beam .Set B .......... .

Crack Pattern at Failure ~or Set c .............

Crack Pattern at Failure ~or Set D ............ .

Crack Pattern at Failure ~or Set E .............

Load-De~lection Curves for Beam Set c ..........

Load-De~lection Curves ~or Beam Set D ..........

Load-De~lection Curves ~or Beam Set E . .........

Average Load De~lection Curves ............... .

Mohr's Circle ~or Combined Stress ............. .

Sieve Analysis ~or Fine Aggregate ..............

Sieve Analysis ~or Coarse Aggregate ............

Stress-Strain Curve for No. 6 Bar . .............

Stress -Strain Curve ~or No. 5 Bar . .............

17

19

22

23

24

25

26

27

28

29

30

31

33

36

41

41

42

43

Table

1

2

vii

LIST OF TABLES

Page

Concrete Mix Content........................... 14

Properties o~ Beams and Test Results........... 21

viii

LIST OF SUMBOLS

The symbols used are de~ined where they ~irst occur in

the text and are listed here in alphabetical order ~or con~

venience.

a =shear arm in inches.

=cross-sectional area ·o~ bent-up bar crossing the diag­onal crack in square inches.

cross-sectional area o~ tensile steel in square inches.

= cross-sectional area o~ vertical stirrups in square inches.

b =width o~ beam section in inches.

d = e~~ective depth o~ beam in inches.

~ct compressive strength of concrete in pounds per square inch at fourteen days.

~v = allowable stress in vertical stirrups in pounds per square inch .

~y = yield strength of stee l in pounds per square inch .

. :I moment of inertia of the cross-section with respect to neutral axis in inert+ . .

jd = internal moment arm in inches.

M = b ending moment in pound-inches .

Mer = critical bending moment in pound inches.

M~l = flexural bending moment in pound inches.

~0 = s um perimeters 9~ all effective bars crossing the section on tension side in square-inches .

P axial compressive load in pounds.

P~ = l oad at failure in pounds .

Pu = ultima t e load in pounds .

Pw = p erc entage of tensile steel .

Q first moment with respect to neutral axis of cross­sectional area cut off at a distance y from neutral axis in inch3 •

S spacing of vertical stirrups in inches.

U = bond stress in pounds per square inch.

V total vertical shear at a section in pounds.

Vc = shear resisted by the concrete compression zone.

v = unit shear stress in pounds per square inch.

a = inclination of bent up bar with respect to axis of beam.

~ = capacity reduction factor, ~ = 0.85 for diagonal tension, bond and anchorage as per ACI 318-63.

cr = direct stress in pounds per square inch

T = shear stress in pounds per square inch

ix

1

I INTRODUCTION

Generally reinforced concrete beams are designed for

maximum moment~ but in order .to develop this moment capacity

it is necessary to insure that the beam will not fail in

some other manner than bending. Thus the section must be

checked for resistance to a diagonal failureJ and where the

capacity of the unreinforced web is deemed inadequateJ stir­

rups are employed to provide sufficient strength. Although

a great amount of work has been expended on the problem of

shear and diagonal tension since the very beginning of

rational design of reinforced concreteJ renewed interest has

been shown in this problem during the last decade. The Ameri­

can Concrete Institute has strongly recommended that further

research be carried out to determine the mechanisms which

control shear failure of reinforced concrete members so that

it will be possible to develop fully rational design pro­

cedures. With this in mindJ the present investigation was

undertaken to determine the location of diagonal cracks and

the effect of a single vertical stirrup on the behavior of a

simply supported rectangular reinforced concrete beamJ sub­

jected to a centrally located concentrated load.

2

II REVIEW OF LITERATURE

As discussed in ACI-ASCE Joint Committee 326 report

11 Shear and Diagonal Tension ll ( 1) early developments in the

design of reinforced concrete before the year 1900 were in-

fluenced by two main ideas regarding the mechanisms of shear

failure in reinforced concrete members. One belief was that

the horizontal shear was the main cause of shear failure. This

seemed reasonable at a time when engineers were familiar with

the action of web rivets in steel girders and shear keys in

wooden beams for which shearing stresses were computed using

the classical equation derived for elastic materials.

where,

v = unit horizontal shearing stress at a distance y from

the neutral axis.

V = total vertical shear at the section.

Q = first moment with respect to the neutral axis of

the cross sectional area cut off at a distance y

from neutral axis.

I = moment of inertia of the cross section with respect

to neutral axis.

b = width of the cross section at a distance y from neu-

tral axis.

3

Reinforced concrete beams were treated as an extension of the

older materials assuming that the concrete alone could resist

low horizontal shearing stresses) and that vartical stirrups

acted as shear keys for higher shearing stresses.

The second beliefJ accepted by nearly all engineers to-

dayJ considered diagonal tension as the basic cause of shear

failures. The origin of the concept of diagonal tension is

uncertain) but a clear explanation was presented by W. Ritter

in the year 1899. He stated that stirrups resisted tension,

not horizontal shear~ and suggested design of vertical stir-

rups by the equa tion:i

where~

V = Av fv jd s

Av = total cross sectional area of vertical stirrups.

fv = allowable stress in the stirrups.

jd internal moment arm.

S = spacing of stirrups in the direction of the axis

of the member.

Ritter's ideas were not widely accepted at the timeJ but his

d e sign expression for vertical stirrups is similar to that

appearing in the design specificationsof most countrie s

todp:y .

The discussions among engineers of the two different

b e liefs continued for nearly a decade. In the year 1906,

E. Morsch of Germany pointed out that, if a state of pure

4

shear exists~ then a tensile stress of equal magnitude must

exist at a 45 degree plane, and he developed the equation

for nominal shearing stress widely used today,

v v b jd

Morsch 1 s data~ supported by tests by F. Von Emperger and E.

Probst, supported the argument for diagonal tension. By 1910~

a general acceptance of Ritter 1 s viewpoint of diagonal ten-

sion had been achieved although the concept of horizontal

shear has reappeared periodically in the literature even in

recent years. Today~ however, most design codes and speci-

fications throughout the world predicate their design pro-

cedures on the concept of diagonal tension.

The analysis of stirrup action known as the truss anal-

ogy was presented by the University of Illinois Engineering

Experiment Station in June 1927 in complete form and then with

simplifying assumptions. In the simplified form it is assumed

that the action of a reinforced concrete beam with stirrups

may be represented as that of a truss i n which the concrete

compression zone is the top chord, the tension reinforcement

is t he bottom chord, the stirrups or bent-up bars are the

t ension web members, and portions of the concre te web of beam

are compression members.

In the year 1908, the National Association of Cement

Users r e comme nd that the shearing strength of concrete

should be assumed at 200 psi and if the shearing stress ex-

5

ceeded this limit, a surricient amount or steel should be

introduced in such sections to overcome the deficiency. In

1910, the recommendations were changed such that in calcula-

ting web reinrorcement the concrete should be considered to

carry 40 psi and any excess over this should be resisted by

means or reinrorcement in tension. In 1913, the First Join·t

Committee or ACI-ASCE retained these general methods with

modification or allowable stresses. The allowable shearing

stress for beams with horizontal bars only, was set at 0.02

f c 1 ltlttlir'a: maximum value of 66 psi. Similarly, the allowable

shearing stresses ror beams thoroughly reinrorced ror shear

was set at 0.06. fc' with a maximum value or 198 psi. From

1917 to 1950, the general trend was toward the use of less

and less web reinrorcement, and the ceiling value or shear

stress was raised to 0. 075 fc 1 • In 1951, the American Con-:

crete Institute recommended that all plain bars must be hook­

ed and all deformed bars must meet the requirements of ASTM

specification A-305. A maximum shearing stress of 0.03 fc'

was specified for all beams without web reinforcement and a

ceiling or 0.12 rc' was specified for beams with web rein­

forcement.

In Germany, the maximum allowable stress was set at 64

psi for members without web reinforcement in 1904. This value

could be exceeded by 20 percent if web reinforcement was pro-

vided. In the U.Ss.R the formula:. for shear strength of a dia­

gonal section given in the nstandards and Technical Specifica­

tions for the Design of Plain and Reinforced Concrete Structure 11

6

of 1955~ was

V=m

where~

V = design shear force at the section.

Vc = shear force resisted by concrete compression zone.

~A = total cross sectional area of vertical stirrups v

cro~sing diagonal section.

~A0Sina = sum of cross sectional area of bent-up bars

crossing diagonal section.

fv = design stress of web reinforcement.

m = coefficient depending on various conditions; the

usual value is m = l

ms = coef,ficient depending on uniformity of steel~ e.g.

fqr hot rolled deformed bars ms = 0.9

IDn coefficient introduced to take into account the

possibility that web reinforcement does not always

yield prior to failure.

The strength in shear of an inclined diagonal section~

determined from the above equation~ depends on its angle of

inclination. When vertical stirrups are used without bent-up

bars~ the projected length of the critical diagonal section

corresponds to a minimum value of the expression (mnmsf~Av+

The National Building Code of Canada of 1953 specifies

that th~ m~ximum allowable . shear stress is 0.03 fc' for

7

members without web reinforcement and 0.12 f c ' for members

with proper web reinforcement.

The British Stardard Code of Practice CP 114 of 1957

follows the basic principles of the German code of 1916.

Where the shear stress exceeds the permissible shear stress

for concrete~ all shear must be resisted by the web reinf orce-

ment alone.

The American Concrete Institute Standards of 1963 (2),

spe cifies. that the shear stress permitted on a web without

reinforcement should not exceed 1.1~ for working stress

design at a distance ndn from the support unless a more de-

tailed analy sis is made. The s hear stresses a t s e ctions be-

tween the face of the support and the section a distance nd 11

therefrom should not be considered critical. With a more

d e tailed a n a lysis t he shear stress permitted on an unrein-

forced web shall not ex ceed that given by~

v =ftc' + 1300 Pw V d c

M

but not to e x c eed 1.75 f c T whe re ,

vc = shear stress carried by concrete.

Pw = As /bd

As = a r e a of stee l .

v = total s hear.

M = bending moment.

A gene ral and dir e c t comp a r i s ion of specif ications of

the four major c ountries ; U.S.A., Germany~ Bri t a in and t he

8

U.S.S.R. is not possible without simplifying assumptions. In

the ACI code, concrete strength is given by a cylinder strength,

fq', while in the other three countries, concrete strength is

given as an average cube strength, feu'· The specification

of the U.S.S.R. is entirely based on ultimate strength de-

sign, while the shear design methods of the other three coun­

tries are based on working load and allowable stress.

During the past decade the mechanism of shear failure

has commanded the renewed interest of many research workers

in dif~erent countries. The first clear realization of the

important parameters involved came with the experiments of

Clark (3). He put forward a diagram showing that the shear

at failure depends on the shear arm ratio a/d. He also show­

ed that for the same beams, the shear stress at failure

changes considerably with a little change in the a/d ratio.

B. Broms, in his paper (4), wrote that the flexural

cracks which form in reinforced concrete beams cause a

redistribution of stresses which results in secondary shear

and lateral tensile stresses. High secondary shear stresses

probably contribute to the development of diagonal tension

cracks, and it is possible that the horizontal cracks which

result from these lateral tensi1e stresses affect the failure

mechanism of the beam.

Bresler and Fister pointed out (5) th~t the strength of

concrete is a function of the state of stress and cannot be

predicted by limitations of tensile, compressive and she.aring

stresses independently of each other. For example,

9

concrete having pure compressive strength, fc', and shearing

strength of 0.08 fc', would fail under a compressive stress

of 0.5 fc 1 with the shearing stress increased to approximately

0.2 fc'. Therefore the strength of structural elements can

be properly determined only by considering the interaction

of the various components of the state of stress. Such con­

ditions as shrinkage, restraint to contraction or expansion,

foundation settlements, duration or loading and previous

stress history, may have an important effect on the state of

stress at the critical section~ and must be carefully evaluat­

ed, particularly with respect to possible reduction of

strength.

Dr. Kani pointed out (6) that under increasing load a

reinforced concrete beam is 'transformed into a comb-like struc­

ture. The analysis of this structural system has disclosed

that there are two di.:fferent mechanisms of structural behavior

possible. In the tensile zone the flexural cracks form ver~

tical concrete teeth and the compression zone becomes the

back-bone of the structure. As long as the capacity of the

concrete teeth is not exceeded~ beam-like behavior governs;

but after the resistance of the concrete teeth has been des­

troyed, a tied arch action remains. Figure 1 shows the

comparision of test results obtained from experiments con­

ducted by Dr. Kani and calculated data. The transformation

of the reinforced concrete beam into a tied arch weakens the

comb-like structure, but there will not be a sudden collapse

of the comb-like structure, if a/d is less than the value at

100

H ~

~ ~ 0 ~ 80 Q) 0.0 cd

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8

Figure 1 Comparison of Theoretical and Test Results by Dr. Kani

10

11

point A~ since the capacity o~ the remaining arch is higher

than the capacity of the concrete teeth. Therefore~ under

gradually increasing loads~ the trans~ormation o~ the beam

into an arch occurs gradually and the structure fails when

the capacity o~ the arch is exceeded. In the region between

points A and B~ the capacity of the arch is lower than the

capacity of the concrete teeth; thus when the capacity of the

concrete teeth is exceeded~ there will be a sudden collapse

of the beam since the capacity of the remaining arch is lower.

In the region beyond point B only flexural failure is possible.

III EQUIPMENT AND MATERIALS

A. Laboratory Equipment

1. Mixer

12

The concrete mixer used was a stationary, nontilting,

electrically operated mixer, having a capacity of three cubic

feet. It is manufactured by Lancaster Iron Works Inc.,

Lancaster, Pennsylvania. The interior surface was kept very

clean, dry and free from any foreign materials before use.

2. Testing Machines

Two types of Riehle Universal Testing Machines were

used. The first, used for compression test of cylinders,

had a range of 300,000 pounds, graduated in 1000 pound in­

crements and was hydraulically operated. It is located in

the Structural Laboratory of the Civil Engineering Department,

Rolla, Missouri.

The second, used to determine the . tensile strength of

reinforcing steel, has a load range of 60,000 pounds, graduat­

ed in 200 pound increments and is also hydraulically operated.

It is located in the Material Testing Laboratory, Mechanics

Department, Rolla, Missouri.

A Tinius Olsen Testing machine was used for testing

beams for flexural strength. It is mechanically operated

and has a load capacity ranging from zero to 10,000 pounds,

graduated in 10 pound increments. It is located in the Struc­

tural Laboratory, Civil Engineering Department, Rolla,

Missouri. It is manufactured by Tinius Olsen Testing Machine

13

Company, Willow Grove, Pennsylvania.

3. Forms

Two types of forms were used, one for casting beams and

the other for cylinders. The beam forms were made from 3/4

:inch plywood and had insdde d:i,mension Of 3. 75 X 6. 5 X 40.0

inches. They were kept thoroughly clean and well oiled before

pouring of the concre-te. The cylinders were standard 6 inch es

by 12 inches fo:r:rns of waxed cardboard with a smooththin metal

bottom.

B .. Materials

1 . . Cem~I?-t , . ' TypE( . 1 . cernent,., ,manufactured by . the Alpha Portland Cement

Company, Lemay, .. :r-'):issouri, . was used throughout the experiment.

2. Fine ~se~egate

. The ~j_ne ag;g;P,eg;.a.te used wcus a rive;Q sand from Meramec

River -near Pacific, Miss our:],, c.qntain:i.ng mo.::;tly chert and

q;uartz. A sieve analysis was made using a Rotap machine in

accordance with the 11 Standard Method of Test for sieve ,,

Analysis for Fine Aggregate, 11 ASTM Designation: C-136-46.

The results were plotted as shown in Figure 16 in the

Appendix. The fineness modulus. .was calculated as 2.5.

3. Coarse aggregate

The coarse aggregate used was c'rushed limestone obtained

from the Springfield, Missouri area. The sieve analysis was

lJl.ade in accordance -with the 11 Tenta ti ve Specifications for

Coarse Aggregate 11 , ASTM Designation: C-33-55 and results

were plotted as shown in Figure 11 in the Appendix.

14

4. Reinforcing bar and Stirrups

The reinforceing steel used was a n intermediate grade

steel witha yield strength of approximately 42,000 ps i . The

stress strain curves are shown in Figures 18 and 19 in t he

Appendix. The stirrups used were No. 9 and No.. ll galvanized

steel wire with cross sectional areas of 0.0172 and 0;0123

square inches_, respectively, and a 3/16 inch intermediate

grade s tee 1 bar wit h : a cross -sectional area of' 0. 0275 square

inches. Ultimate strengths were determined for the stirrup

materials and are shown in Table 2.

C. Preparation of' Specimens

The concrete mix was designed to have a slump of approx­

imately 2.75 inches and compressive strength approximately

equal to 3500 psi. at 14 days. The mix was designed using

the Portland Cement Association's "Design and Control of

Concrete Mixtures'', (7). The a mount of cement, fine aggre­

gate_, coarse aggregate and water used for each batch of con­

crete mix is shown in Table 1.

Table 1. Concrete Mix Content

Ingredient Weight in Pounds

Cement .56.4

Fine Aggregate 174.0

Coarse Aggregate 183.0

Water 34.98

The beams were cast according to the ''Standard Method of

Making and Curing Concrete Compression and Flexure Test

15

Specimens in the Laboratory, 11ASTM Designation: C-192-55.

Three cylinders were cast from each batch, cured in the moist

room at 100 percent relative humidity and an average tempera­

ture of 72 degree F,. Each batch produced about three cubic

feet of concrete which was sufficient to make three beams and

three cylinders.

All the materials were weighed on a Toledo Scale accurate

to one fourth of a pound~ , In preparing concrete, one third

of the water and all of the fine aggregate and coarse aggre­

gate was placed in the mixer. After mixing for about three

minutes, all the cement and the rest of the water was added

and mixed for an additional 2.5 minutes. A slump test was

made on each batch immediately after mixing and before plac­

ing concrete in the forms. The slump test was conducted in

accordance with ASTM Designation: 143-39.

The beam forms were thoroughly oiled and the reinforcing

bar was properly positioned with steel rebar chairs. The

reinforcing bar was clean and free from rust and grease.

The concrete was placed in two layers, rodded fifty times

per square foot per layer and the top surface trowelled

smooth. The cylinders were filled in three layers, each

layer being rodded twenty-five times.

The three series with stirrups were cast in a similar

manner. For the No. 9 and No. 11 wire stirrups series, the

stirrups were anchored by providing a concrete block on the

16

top of the beams, Figure 2, while for the 3/16 inch bar

series, the stirrups were anchored by providing a steel

plate across the top of the beam to which the stirrups were

welded, Figure 2.

The beams were kept for twenty-four hours outside the

curing room to prevent swelling of the wooden forms due to

moisture. A period of twenty-four hours was considered to

be the earliest time that the forms could be removed without

damaging the beams.

The cylinder forms were removed after curing had pro­

gressed for twenty-four hours outside the moist room; then

marked and placed in the curing room.

17

~--- - ----------- - - ----------- .:_ _ _______ -+-Location of stirrups ! l i ,-·Dial gage j r 9"--·r I . p I / Detail A and B

T -----~-~-\f~-- --- n T

s_tf __ :_ ___ L ______ - --- _:_ ___ ---- GJ 6t· ~8,75~ 8.7~

H------T---- 36!1 -----.----~ Aluminum plat~

P/2

311 Concrete cube

Detail A for No. 9 and No. 11 wire stirrups

p /2

-_··· 1"x3 l/2 11 xl/4n ~Steel Plate

1/8 11 .

Detail B for 3/16!1 bar stirrup

Figure 2 Test Set Up for Beams and Anchorage Details

18

IV TEST PROCEDURE

A. Beams .

To determine the positions of tension cracks, two

series of beams without stirrups were cast as mentioned in

Chapter III. In Set A of the beams, a No. 6 deformed bar was

used as a tensile reinforcement, while in Set B,a.No. 5 de­

formed bar was used. After fourteen days curing the beams

were tested in accordancewiththe ASTM Designation: C-79-49.

The beams were simply supported with a clear span of 36

inches, and a point load was applied at the center of the

span. Aluminum plates of 1.5 x 3.75 x 5/16 inch dimensions,

were grouted at the point of load and at the supports, using

plaster of paris. These plates were used to minimize any

failure in bearing. One dial gage, graduated in 0.0001 of

an inch, was installed at one fourth span as shown in Figure

2. An initial load of 500 pounds was placed on the specimen

and then released in order to set the zero reading. The

load was then applied gradually and deflection at intervals

of 500 pounds w:as :. recorded and the test was continued until

failure occured. Crack propagation was observed during the

test and marked with the aid of a pencil as shown in Figures

4 and 5. Time required for the above test varied from about

10 to 15 minutes.

To locate the position of vertical stirrups, points 11 a 11

and 11 b'1 were determined as shown in Figure 3. Point 11 a 11 is

19

near the top surface where the slope of the crack changes~

and point 11 b 11 is at the bottom surface where an extension~

of the crack meets the bottom surface. From the six beams

tested, the cracking zone was determined 'bY plotting these

11 all and 11 b 11 points as shown in Figure 6, and from this in­

formation the position of the vertical stirrups was located.

In addition to thisj a load and deflection curve was plotted

as shown in Figure 7. By mistake Set A was tested with the

knife edge improperly located; however, since the results

did not vary much from Set B, Set A results were utilized

for fixing the position of the vertical stirrups.

---------------b

Figure 3 Determination of Points 11 a" and 11b tt

After the location of the stirrups had been determined

as explain e d above, three identical sets of beams were cast,

each from one batch of concrete. Each set contained the

three different stirrups as shown in Table 2. The sti rrups

we re posi tione.d at 8 . 75 inches from the center line oftrebeam

as determined from Sets A a nd B. Afte r fourteen days of

curing the beams were tested as explained for Sets A and B

and the crack patterns are shown in Figures 8, 9 and 10 .

The load and deflection curves were p l otted for all the beams

20

as shown in Figures 11, 12 and 13 .

B. Cylinders ·.

The cylinders were capped with a sulf'ur compound at a

minimum of' one day before the test was conducted. They were

tested in accordance with the 11Standard Method of Test for

Compression Strength of Model Concrete Cylinders 11 J ASTM

Designation: C-39-49. The results are indicated in Table 2.

21

Table 2

Properties or Beams and Test Results

.,

Beam Tensile Type of ~c I Yield Ultimate Load

reinforce- web rein- ln point of load of at ment forcement psi tensile stirrups failure

rein- in lbs. Pf forcement p in psi u

fy

Set 6 bar None 3360 64000 7500 A

6500

8000 ..

Set 5 bar None 3740 42000 8200 B

7450

7800

Set 6 bar ll wire . 3530 43000 750 7900 c

9 wire 1050 . 88 00

3/ 16 11 bar 1540 8450

Set 6 bar ll wire 3790 43000 750 8200 D

9 wire 1050 8900

3/ 16" bar 1540 8420 --

Set 6 bar ll wire 3830 43000 750 7800 E

9 wire 1050 8700

3/ 16 11 bar 1540 8600

22

Front View

Back View

Figure 4 Crack Pattern at Failure for Set A

23

Front View

Back View

Figure 5 Crack Pattern at Failure ~or Set B

Set A

~

Set B

Note:

Stirrup r Location t

r ------ -- ·--··-·······-····· - ~ ·-·j l l

·-ts . 7 5 II ---J---s . 7 5 11 ---t-..

Figure 6 Cracking Zone

6 point a .in Figure 4 and 5

o poi nt b i n Figure 4 and 5

l

2

3

l

2

3

24

lOOOo rH·-rr-K--K++++~-~~-~HH~-+4~++++ I

v v

6ooo . H--'- -1-1-- · + -

t-t±-'t I I ; ·-f--+- 1-f-+ H -1-- - - - -r:! +-- -n--r--L . I ' ~14-f.. -1- --+- ·--+ ++ --.- 1---·r-t- -~ 1-r-, ·1-r- -~r - 7 - - + - --+- - ... -1--. --H- - 1- t-H++--1--f- , .1 . -~---+-- -- - - - --r+- - -r,

I 1 ' : I [' .J I I J -r ~--c- +-rr·- 1--f-y-1-- - - - · 1-+-- ----j--1·- --- J--+- f-1-- -·-j-rr+- t-i.ti · -+ - ~-- - ···- ,--1--j - -1-1-H--;-

1·- - · .,. - + -+-'- 1-- - -r--

4ooo . ,-- ·I-- + I---~- · · ~--;

, ___ B-1-:- - ll --' 1--f--1------~-- 1-.J ' ~ -- 1--f-i-- - . ,._~ I-f- -

· ; --1- --1-1- -I-I--+--I--1-.J-..J...-i-- ii-+-,J,...+-+--+--+-I---.J-.+---JFC.J-.+-+--I- --1- ·- .. 1-'-~- - - - ·-- - -.J-.-1---.J...--f-.~----+---c

0 400 800 1200

Deflection in lo-4 Inch

Figure 7 Load-Deflection Curve for Beam Set B

25

26

Front View

Back View

Fj_gure 8 Crack Pattern at Fai l~~~ f6r Set C

27

Front Vie w

~-.. ~·

Back View

Figure 9 Crack Patt ern at Fa ilure fo r Set D

28

Front View

Back View

Figu re 10 Crack Pattern at Failure ror Set E

!11-f--+-+-t-t+-H-+-H-' -11'--1---t-1-

Figure 11 Load-Deflection Curves for Beam Set C

29

' ·t-- + '--1---~+-t--r-L 7' ~", --! - -,- -f- -- I . -1- r- - I -~ ___; r-- · -+-+--+-t·--1-~- , , 1 I .

. l- . -~- --+~--h-- - __ j_ I tj!l~ ,1!11 +-H--H_----r-r++--,+ +H-1--1-- --r-- ---i- i-1-2 6o.oo H- H--r---++ '/ ~:. .- · -. -H-r-r , -., _ _j -(~ +-=t'-f---·>- ~J 1_,_+- - 'J_·---1-c--+-_:_ 1-! ,-~- -r , ·; / 1 • 1 n 1 1 1 ,

--+---+-+--+-+-+--r 'r- - +- , , , I , -j~--1-l-+--+! -+-+-+-+-1-+-- -++ ~--, 1~j~ _J_ n --,-'1-- --1--R,--r ---t -·.· - - - - - ' --1 l j-.+-i,-- --- --f---+-- --+--lc-t--+-t-t-t-+-+ . I I : I I ' - 1 i ! !

, - 71 , J_J__;_J__ r-H_+-~--W-1 J l_ j- -1---t-_-+-+-+-1-+-H--, 'I I H-' '-+---r--1--1--f-lH- '-+-t--i--f-+-t--r---r, +-1+--t--i-1--- H+t-f}t_~_ +-+-i-t- ---h--T--t 1 f- r +--r-J-~-r-H-l- 1

ir1 1"-T r·- -r---~-;- [r I ' 1 ' - I I ' i I __ 1 ' _ _I 1_ I J

0 , 400 800 1200

Deflection in lo-4 Inch

Figure 12 Load-Deflection Curves f'or Beam Set D

30

8000

6000

r . •-+-- · J.' '-- • _, -.II'e

~t.6 ~ 'l r:. '"" 1:.-,y -'(

f--- -I"

,u

"' .., .

v. 1'-'. j ...L I Vlj...l j .L. I"-

~ Gl

f---f-I ~

f--1--+---cl--+-+--l-+--+-+-1 / [7 H-1/-+-+-f-1--1-f---f---11--+-+---l-f - +--l-+-l---1--1--1--+-1---1--1--+--,

-+-+-, -+-+-!-+-+--++ I :i>J~ V_ i'C' +- f-- H--1-+-- ---- j !-+-++-+-!-+-+ t-r- -+-- i..< ' :--f-- - f--f-)-t ---;

De~lection in l0-4 Inch

Figure 13 Load-Deflection Curves for Beam Set E

31

32

V DISCUSSION OF RESULTS

As mentioned previously, the ultimate moment capacities

determined from Set A of the beams was considered to be in

error and was discarded since the knife edge of the testing

machine was not resting in the proper location. However,

since there was little disagreement between the A and B se­

ries, in the location of diagonal cracks, these results were

used to locate the position of the stirrups for the succeed­

ing tests.

Although beams Sets A and B had been designed on the

basis of Kani's work to produce a failure below the calculat­

ed ultimate moment capacity, see Figure 1, it is clear from

the results that this was not the case. Only a small in­

crease in moment capacity was produced by adding the stirrups.

However the failure of the Se t B, at 7.9 K without stirrups

was actually some 20% higher than the calculated ultimate

load of 6.5 K ~or No. 5 tensile steel. With stirrups and

No. 6 tensile steel the failure load of about 8.3 K agreed

quite well wi th the calculated value of 8. 7 K. No. explan­

ation of the ·behavior of the unreinforced section can be

presented.

The a/d ratio of 3.55 u s ed in these experiments should

have caused premature failure of the unreinforced web section

with respect to moment capacity. It is not too surprisin g

that the pre mature failure did not occur since many of t h e

v a lues n e c essary i n Kani rs equations a r e p ure gue s s -wo r k a t

this stage of development. The results do indicate, however,

10000

8000

2 6000 ~--=~ ·

:;:::: ..-I

'd eel 0

1--=l 4000

2000

33

__j_ l I - - f..- -i- ---

-

___,

I -N' ) '-! IN I :::. i: '

,.., 1 .,- I ....,

' .J, ,.'-'-' ..J•::l.

I

' .. h '""

" t 1/.: ' lhV

19 'l' ,..._

i ~ t- - ... l:!.b R ; 10 i lb:: ~ -;} . -

~ 1'1

~j: v

- f--f-- -I- 17 v - I

I T I~ I -! :

II ; - -I- -+ 1/ ., ·J l

I /

I •; 7

• 71 I

!· v , Jj I

' I I

·--+ -

1 I

; : II rt '

I A I I

I

iJ I -t I I

.-/i I -+ I I T v I I '

o· 400 800 -1200

Deflection in l0-4 Inch

Figure 14 Average Load Deflection Curves

34

that in order to achieve a premature failure~ which is neces-

sary in order to measure the effect of stirrups, it will be

necessary to use a smaller a/d ratio for this section.

It will be noticed from Figure 14 that the addition of

stirrups to the section did have an effect upon the stiff-

ness of the beam. There was a consistent decrease of deflec-

tion with the addition of stirrups. In addition, the stirr-

ups seem to have controlled the horizontal failure at the

ends which was evident in Sets A and B. Thus, it may be con-

eluded from thii::s meager evidence, that even for sections

with adequate shear capacity it may be advantageous to use a

nominal number of stirrups.

With l!U 11 type stirrups used, the ultimate load capacity

in tension for the stirrups were

No.ll wire = 2 x 750 = 1500 lbs.

No. · g wire= 2 xl050 = 2100 lbs.

3/16 inch bar= 2 x 1540 = 3080 lbs.

Since none of the stirrups used broke, it can be said that

at the location of the stirrups the concrete mus.t have

carried a shear force greater than

3.6 K = ($.3 - 1.5) K ~

According to the ACI Building Code (2), the ultimate s hear

force that the concrete at this section would be allowed to

carry would be (Art. 1701-c)

..

35

v = 2>i /f;' b d u

= 2 X 0.85 ~0 X 3.75 X 5.1

= 2 X .85 X 59.25 X 3.75 X 5.1

= 1.92 K

Thus the ACI Code seems to be quite conservative~ at least

~or this particular section .

The calculated ultimate bond stress was~

v'U = V,, C., M

(j zo jd

= 8. 3/2 0.85 X 1.963 X 4.56

= 547 psi

as compared to an allowable of 750 psi, by the ACI Building

Code. This would indicate a satisfactory design condition,

however, the horizontal failure along the line of the tensile

rein~orcement would indicate either excessively high bond

stresses or dowel. action . The cover of 1.1 inches may have

been inadequate although it is within the 3/4 11 a llowed for .

unexposed sur~aces .

In comparing the ~ailure patterns of Sets A and B with

Sets C, D and E Figures 4, 5, 8, 9, 10, it can be seen that

the addition o~ stirrups has ef~ected the patterns and in

general, has cause the cracks to fall within the bounds of

the stirrups. Comparing the results of sets C, D and E,

there appears to be some e~fects on the crack pattern caused

by stirrup size and concrete stren gth . It appears that the

larger stirrups tend to pull the sloping part of the crack

closer to the top surface . However, this observation is

36

strictly tentative since the evidence is far from sufficient.

With respect to concrete~ there is an increasing order of

strength through Sets C~ D, and E (Table 2) and there also

seems to be a consistant increase in the angle of the crack

with the beam axis. This would seem to be consistant with

a simPlified analysis of the combined stress condition in

the compression zone. Using a constant shear stress at a

point in the compression zone, the Mohrs' circle solution is

shown in Figure 15.

Figure 15 Mohr's Circle for Combined Stress

If tension produces cracking, tG indicates the angle the

crack makes with the axis of the beam. Since ~ > GA~ a

higher compressive strength leads to an increase in the slope

of the failure crack. Another inconsistency which cannot be

explained in the incre a se in failure load of the No. 9 wire

stirrups over the larger 3/16 inch bar stirrups.

VI CONCLUSIONS

1. The addition of stirrups confined the diagonal failure

cracks within the limits of the stirrups although there

is no large increase in the ultimate moment capacity of

the beams.

2. The addition of stirrups did cause an increase of the

stif1fness of the beam system as compared to the beams

without . stirrups.

37

3. There is some evidence that the use of a nominal number of

stirrupsJ even in a beam which is satisfactory with respect

to a diagonal tension failure, might be necessary in order

to control horizontal cracking at the level of tensile

reinforcement.

4. There is some indicationJ both experimentally and theo­

retically that higher concrete strength increases the slope

of the failure line with respect to the axis of the beam.

38

VII RECOMMENDATIONS

In order to ef~ectively measure the results of a single

stirrup~ it will be first necessary to obtain a beam with an

appreciable reduction in moment capacity. The section to be

obtained should have a reduction in moment capacity of about

60 percent.

The e~fect o~ different q/d ratios may be checked for

the same stirrup positions and also for di~ferent locations

of the stirrups.

. '

~

39

BIBLIOGRAPHY

1. Report of ACI-ASCE Joint Committee 326 11Shear and Diagonal Tension. 11 American Concrete Institute, 1962

2. nBuilding Code Requirements for Reinforced Concrete." ACI-318-63, the American Concrete Institute, 1963

3. Clark, Arthur P. 11Diagonal Tension in Reinforced Concrete Beams,,, Journal of the American Concrete Institute, Vol. 48, No. 2, October 1951, pp 145.

4. Broms, Bengt B. 11Stress Distribution, Crack Patterns and Failure Mechanisms of Reinforced Concrete Members", Journal of the American Concrete Institute, Vol. 61, No. 4, December 1964, pp 1535.

5. Bresler, B. and Pister, K. S. 11Strength of Concrete Under Combined Stresses 11 , Journal of the American Concrete Institute, Vol. 55, No. 3, September 1958, pp 321.

6. Kani, G. N. J. 11 The Riddle of Shear Failure and its 8olu­tion11, Journal of the American Concrete Institute, Vol. 61, No. 4, April 1964, PP 441

7. "Design and Control of Concrete Mixtures 11 , Tenth Edition, Portland Gement Association, Chicago, pp 15-16, 1952.

APPENDIX

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I

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20

0

J-ttt-Li i ; ,---1- · -·:-t· ' I ,-H:

#100 #50 #30 #16 H8 H4 3/8 11

Standard Square Mesh Sieves

Figure 16 Sieve Analysis for Fine Aggregate

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::s i>:l .0

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Figure 17

Square Mesh Sieves

Sieve Analysis for Coarse Aggregate

-1= 1-'

42

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v

50

I 40 r+ ~ ~~-rrr~~~-rrr~++~~~H-~~++++~~H-~~~~~

1!--t--t-+-ir-+-+-+-+-+-+-t-+-+-+-i'-+·-+++-+-f- - f-f- t-+-+-+-H -1-+-l- t--1-1-+-l-+-t-++-f-t-+--1-+-+-~-f- +-1-+·+-H -l-H -1--+-ii-++H-1--H -+-l-1-+ -r· + - f-- f- f-f- - - - -r-+-f-~ f- t-- -- ' . - c- - - - - -:_ L-+- c-f-i- - ' · - 1- ,_._(__ · r- --- ,- 1--H.- ·- - r- ·· -++-r- - 1 I I I ' . I ' I -1

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Figure 18 Stress-Strain Curve for No. 6 Bar

60

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H ..p 'CI).

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~-t-t-+++-+-+·+-t-t--t-t-+-l-+-t-+-+~+il-t-~~-+-+l -+-r+-+-++-!-~+~4~~+-+-t-t-+-+~

o·

Figure 19

Strain in

Stress-Strain

lo- 2 ;:·I p ch ~)\\ ?,r. t.\1 ::i . ,i--.'t 1$ ~.f ...

Curve for Nb . 5 Ba r

44

VITA

Mr. Vinodbhai T. Patel, son of Mr. and Mrs. Dr. Tulsibhai

K. Patel, was born on July 25, 1940~ in Sarsa~ Taluka Anand,

Gaharat State, India. He married Laxmiben, daughter of Mr.

and Mrs. Shanabhai A. Patel of Gopalpura, India, on May 11,

1961.

He received his primary and secondard education in Sarsa,

India. He received his college education from Vitthalbhai

Patel College of Science and Birla College of Engineering,

Vallabh Vidyanagar, Anand, Gujarat, India. He received his

Bachelor of Engineering Degree in Civil Engineering from Sadar

Vallabhbhai Vidyapetth (University) in June 1962.

From September 1962 to January 1964, he worked as a

Junior Engineer, in Public Works Department, Gujarat State,

India. He was appointed on the Kakarapar Irrigation Project

as Site Engineer.

He enrolled at the Missouri School of Mines and Met­

allurgy at Rolla in February 1964 to work towards his Master

of Science Degree in Civil Engineering.