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Scholars' Mine Scholars' Mine
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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Part of the Civil Engineering Commons
Department: Department:
Recommended Citation Recommended Citation Patel, Vinodbhai T., "Effect of single stirrups on reinforced concrete beams" (1965). Masters Theses. 5245. https://scholarsmine.mst.edu/masters_theses/5245
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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
+-"> s:: Q) C)
H Q) 60 P-1
40
20
+--+ =F "-'-· - ~+-
- --,_ --r-1-
,- -·
'
!
I
, t--r-c-I
' l I
I
! I I
' . I I
I
I
I v l-1--
I I I i
lt
0
+--1+-H-- --+-H---L---r- -1-~- -J++- ~- --+-++- -r--c- ·- I-
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--r- - '-+·--,---c--'-+ --r- H--r- I 1-f- t-H I i _l Tr I
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1--- I~ t:-_r- __ fl=_ !::.t"':. ::t. - --1--- f- - - --- 1-- r-1-"'f- - - - ~. xi? Ft~ ~- y=- -t--
f- P.~t- lrP RiJ Itt- !=; 1'-f--- - t-
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1'111
11
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/
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- !". ' l lltt31 V,, ft 1_1;~
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f"IY v i / 1 . 1-t-t--
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II
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rtl=> tn:q I I r- !... .... I
-
: :
I
4
Ratio a/d
-
~r- 1-1---
+- -· hii h~ ..
• I
r-.. ..... .
--I
6
_J r--r- -·
H -_: -- -
-
-
. I'- f-' - r-
!-' I " -r--f-1- -~
j-t- -I-t-+ r- -'--t I
·-j
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-- ~---~ ..J
- ·-
' 1-I
p -- ,_ r-h .. A r>J r.o
H - --I
t- r-1-
h -l__j_ I
L L I i
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
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#100 #50 #30 #16 H8 H4 3/8 11
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Figure 16 Sieve Analysis for Fine Aggregate
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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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~-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.