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The Structural Behaviorof Higher Strength Concrete
by
Narayan Babu D. Hiremagalur
B. E. , Bangalore University, 19 82
A MASTER'S THESIS
submitted in partial fulfillment of the
requirements for the degree
MASTER OF SCIENCE
Department of Civil Engineering
KANSAS STATE UNIVERSITYManhattan, Kansas
1985
'
Mi TABLE OF CONTENTS.TV
Iff5
M?7A115D5 btllOM
iAGE
List of Tables III
List of Fi gures V
Chapter 1 - Introduction 1
Present Usage 1
Objectives 3
Chapter 2 - Selection of Materials 4
Introduction 4
Cement 4
Coarse Aggregate 6
Strength 7
Maximum Size and Graduation 7
Particle Shape and Surface Texture 8
Cleanliness 8
Mineralogy and Formation 8
Aggregate- Paste Bond 9
Fine Aggregate 9
Water 10
Admixtures 10
Chapter 3 - Literature Survey For Compressive Stress Block 12
Chapter 4 - Test Specimen and Method of Testing 15
Method of Testing 15
Strain Gages 17
Chapter 5 - Experimental Work and Results 18
Casting 18
l&BLfi 3E CONTENTS (Continued)
PAGE
Curing 18
Instrumentation and Apparatus 18
Test Procedure 19
Results and Discussion of the Results 20
Strain Behavior 23
Chapter 6 - Summary and Conclusions 25
Summary 25
Conclusions 2 5
Recommendations For Future Work 26
Appendix I References 27
Appendix II a) Mix Proporations 30b) Derivation of Ultimate Strength Factors 31
kik3, k2c) Steel Frame dm Q df 33d) Computer Program for Calculating 5— & 3— 34
e) Calibration of Minor Load P2 36
Appendix III - Tables and Figures 37
Appendix IV - Notation
Acknowledgements
ii
LIST QE TABLES
TABLE PAGE
5.0 Information about the test specimens 3 8
5.1 Cylinder data corresponding to Beam I 39
5.2 Cylinder data corresponding to Beam II 40
5.3 Cylinder data corresponding to Beam III 41
5.4 Cylinder data corresponding to Beam IV 42
5.5 Stress-strain relation for cylinder #1, 43corresponding to Beam I
5.6 Stress-strain relation for cylinder #2, 44corresponding to Beam I
5.7 Stress-strain relation for cylinder #2 45corresponding to Beam II
5.8 Stress-strain relation for cylinder #1 46corresponding to Beam II
5.9 Stress-strain relation for cylinder #1 47corresponding to Beam III
5.10 Stress-strain relation for cylinder #2 48corresponding to Beam III
5.11 Stress-strain relation for cylinder #1 50corresponding to Beam IV
5.12 Load-Strain data for flexural test of Beam I 51
5.13 Load-Strain data for flexural test of Beam II 53
5.14 Load-Strain data for flexural test of Beam III 55
5.15 Load-Strain data for flexural test of Beam IV 57
5.16 Load and average strain at each level for flexural 59test of Beam I
5.17 Load and average strain at each level for flexural 61test of Beam II
5.18 Load and average strain at each level for flexural 63test of Beam III
5.19 Load and average strain at each level for flexural 65test of Beam IV
JLIST .QE TABLES (Continued)
TABLE PAGE
5.20 Load and ultimate strength factors for Beam I 67
5.21 Load and ultimate strength factors for Beam II 69
5.22 Load and ultimate strength factors for Beam III 71
5.23 Load and ultimate strength factors for Beam IV 73
5.24 Load and stress data for flexural test of Beam I 75using equations (4.1) and (4.2)
5.25 Load and stress data for flexural test of Beam II 78using equations (4.1) and (4.2)
5.26 Load and stress data for flexural test of Beam III 80using equations (4.1) and (4.2)
5.27 Load and stress data for flexural test of Beam IV 82using equations (4.1) and (4.2)
5.2 8 Load and stress data for flexural test of Beam I 84using equations (4.1) and (4.2) and cylinderstress-strain curve
5.2 9 Load and stress data for flexural test of Beam II 86using equations (4.1) and (4.2) and cylinderstress-strain curve
5.30 Load and stress data for flexural test of Beam III 87using equations (4.1) and (4.2) and cylinderstress-strain curve
5.31 Load and stress data for flexural test of Beam IV 88using equations (4.1) and (4.2) and cylinderstress-strain curve
iv
LIST OF FIGURES
FIGURE PAGE
2.1 Effect of various brands of type I cement on 89concrete compressive strength (20)
2.2 Effect of various cements on concrete 90
compressive strength (2)
2.3 Effect of size of coarse aggregate on 91
compressive strength in different types ofconcrete (adapted from Ref . 5)
2.4 Maximum size aggregate for strength efficiency 92
envelope (15)
2.5 Compressive strength of concrete using two 93
sizes and types of coarse aggregate for 7500psi concrete (1) .
2.6 Compressive strength of high-strength concrete 94
using three sizes and types of coarseaggregate.
2.7 Slump vs. time when using superplasticizer 95
(11)
4.1 C-Shape structural element for flexure test. 96
4.2 Concrete stress-strain relations (7) 97
4.3 Reinforcement layout 98
4.4 An arbitrary section A-A with rebar arrangement 99
at each leg (11)
4.5 An arbitrary section of column part with rebar 100arrangement (11)
5.1 Cylinder compressive stress-strain curve for 101Beam I
5.2 Cylinder compressive stress-strain curve for 102Beam II
5.3 Cylinder compressive stress-strain curve for 103Beam III
5.4 Cylinder compressive stress-strain curve for 104Beam IV
5.5 Location of strain gages vs. strain for Beam I 105
LIST OF FIGURES (continued)
FIGURE PAGE
5.6 Location of strain gages vs. strain for Beam II 106
5.7 Location of strain gages vs. strain for Beam 107III
5.8 Location of strain gages vs. strain for Beam IV 10 8
5.9 Stress block of Beam I 109
5.10 Stress block of Beam II 110
5.11 Stress block of Beam III 111
5.12 Stress block of Beam IV 112
5.13 Axial load vs. strain for gages 4 and 5 for 113Beam I
5.14 Axial load vs. strain for gages 4 and 5 for 114Beam II
5.15 Axial load vs. strain for gages 4 and 5 for 115Beam III
5.16 Axial load vs. strain for gages 4 and 5 for 116Beam IV
5.17 Stress factors k_, k,k, vs. concrete strain for 117Beam I
z j. j
5.18 Stress factors k, , k, k, vs. concrete strain for 118Beam II « J. J
5.19 Stress factors k, , k.k, vs. concrete strain for 119Beam III x J
5.20 Stress factors k_ , k.k, vs. concrete strain for 120Beam IV * ± J
5.21 Condition at ultimate load in test specimen 121
5.22 f vs concrete strain for Beam I 122
5.23 fQ
vs concrete strain for Beam II 123
5.24 fQvs concrete strain for Beam III 124
5.25 £ vs concrete strain for Beam IV 125
5.26 mQvs concrete strain for Beam I 126
vi
FIGURE
LIST OF FIGURES (continued)
PAGE
5.27 mQ
vs concrete strain for Beam II 127
5.2 8 mQ
vs concrete strain for Beam III 128
5.29 m vs concrete strain for Beam IV 129
5.30 Average f from Eq. (4.1) and (4.2) vs. strain 130for Beam II
5.31 Average f from Eq. (4.1) and (4.2) vs. strain 131for Beam IV
vii
Chapter 1
INTRODUCTION:
The term high strength concrete is relative to any
assemblage of concrete technologists. Most concrete
technologists classify concrete as follows:
2500 - 6000 Psi > Normal strength concrete;(13.8 to 41.5 MPa)
6000 - 12000 Psi > Higher strength concrete;
(41.5 MPa - 83 MPa)
> 12000 Psi > High strength concrete.
(> 83 MPa)
In this report higher strength concrete implies
concrete of strength 6000 Psi (41.5 MPa) and above.
A few years ago concrete of 5000 Psi (34.5 MPa) and
above was considered high strength concrete. But, today
with the development of new materials, admixtures and
processers, even concrete of 6000 Psi (41.5 MPa) is
considered normal strength concrete.
PRESENT USAGE:
There are many advantages in using higher strength
concrete over normal strength concrete.
a) Higher strength concrete has greater load carrying
capacity than normal strength concrete. This helps in
reduction of member dimensions and hence dead weight is
greatly reduced.
b) Higher strength concrete is very advantageous in
compression members. In columns, if the section is
decreased the self weight decreases, and the stress due
to self weight is much lower, hence greater external
load can be taken.
c) The' precast and prestress industry is the largest user
of higher strength concrete. In prestressed concrete
members, the moment due to self weight is decreased,
higher external moment can be taken, and the efficiency
of the structure is increased. In prestressed concrete,
concrete strengths of up to 10000 Psi (68.9 HPa) have
been used.
d) It is not particularly advantageous to use higher
strength concrete in slabs, as thin sections have more
deflections.
Higher strength concrete is being used extensively in
New York and Chicago. In the Chicago area concrete of
10,000 Psi (18.9 MPa) was used in at least six different
buildings (21) . Nuclear power plants require concrete in
the 8000 Psi (55 MPa) range.
OBJECTIVES
a) To study the compressive and flexural behavior of higher
strength concrete [11,000 Psi or 75.8 MPa] made with
Kansas aggregate, in order to verify proposed stress-
strain relationships and to study the shape of the
stress block.
b) To compare the cylinder and flexural stress-strain
curves.
c) To find Poisson's ratio.
d) To determine strain at f ' and at rupture.
e) To determine modulus of elasticity.
CHAPTER 2
SELECTION M materials
INTRODUCTION
Material selection is an important factor in the
production of higher strength concrete as it has to meet
requirements for workability and strength development.
Locally available materials should be used to fullest
advantage, subject to suitability, to make the production
of higher strength concrete economical. Once the materials
are selected, the remaining variables should be studied to
develop an optimum mix on the basis of strength, cost and
field performance.
CEMENT
The strength of a mix is proportional to the strength
of the cement. As reported in the state-of-the-art report
of high-strength concrete [24] published in the ACI Journal
"The choice of Portland cement for high strength concrete is
extremely important. Unless high initial strength is the
objective, such as in prestressed concrete, there is no need
to use a Type III cement. Furthermore, within a given
cement type, different brands will have different strength
development characteristics because of the variations in
compound composition and fineness that are permitted by ASTM
C 150".
Walker and Bloom (see Ref. 5) presented values of
compressive strength for concrete from different cement
suppliers and offered the following conclusions:
a) Average strength for different cements varied
substantially.
b) At least one-half of the individual cement differs from
shipment to shipment sufficiently to have an effect on
uniformity of concrete strength.
c) There is a need for better control of uniformity of the
cement within individual sources.
Figure 2.1 (20) shows the effect of various cement
types on concrete compressive strengths based on mixes
having the same workability (5) . Type I (standard) or Type
II (low heat) cement should be recommended for high strength
concrete mixes and the same brand of cement is to be used
throughout the job (5) . Type III cement is too finely
ground and results in rapid setting, accelarated heat of
hydration, and high early strength development with rela-
tively moderate strength gains at 91-day or one year inter-
vals (5) .
In the present investigation, a mix developed by
Nikaeen (11) was used. Type I cement was used. Figure 2.2
shows that Type I cement gives the highest compressive
strength at all ages.
COARSE AGGREGATE
As coarse aggregate comprises a major portion of the
volume, it is very important to use proper coarse aggregate
in developing higher strength concrete. Kaplan (8) has
reported that the use of different coarse aggregates has a
marked effect on the strength of concrete with the same mix
proportions. Depending on the aggregates, a difference of
40% in flexural strength and 29% in compressive strength
were obtained in Kaplan's experiments.
The strength, up to 5000 Psi (34.5 MPa) depends
essentially on the quality of the hardened cement paste that
holds the aggregate particles together. The aggregate at
this strength level and above always has a much greater
strength than the cement paste. The following factors
should be considered in selecting a coarse aggregate for
higher strength concrete.
a) Strength
b) Maximum size and gradation
c) Particle shape and surface texture
d) Cleanliness
e) Mineralogy and formation
f) Aggregate-cement bond
STRENGTH
The aggregates chosen for higher strength concrete
should have a crushing strength at least equal to the
hardened cement paste. Most good quality aggregates have
crushing strength in excess of 12000 Psi (83 MPa) and,
hence, strength is not a major problem in the production of
higher strength concrete.
MAXIMUM SIZE AND GRADATION
Several researchers (3, 4, 10) have shown that in
higher strength concrete the compressive strength increases
when the maximum size of aggregate decreases. However, it
is obvious that there should be some limitation in order to
keep drying shrinkage and creep to a reasonable and
practical value. A maximum size of 0.4 in. (10 mm) is
recommended for most cases (10). Figures 2.3 and 2.4 show
the size effect of coarse aggregate on compressive strength.
In Figure 2.4, it is indicated that the smaller size
aggregate provides the most efficient use of cement in
higher strength concrete. This higher strength efficiency
which is obtained when using smaller aggregate is due to
greater bond between the cement and coarse aggregate because
of the increase in surface area. However, there is a
different optimum size for each aggregate and for each level
of strength desired, depending on the economics of the
situation. Therefore final batching for each job is highly
recommended.
PAKTICLE SHAPE AND SURFACE TEXTURE
In the research done by Carrasquillo, Ramon and Nil son
(5) , it is indicated that the ideal coarse aggregate for
high-strength concrete appears to be clean, cubical, angu-
lar, 100% crushed stone with minimum flat size and elongated
particles. It is also stated that if all other factors are
equal, crushed stone coarse aggregate produces higher
strength concrete than does a rounded aggregate. In
Figures 2.5 and 2.6, the compressive strength of concrete
using different types of coarse aggregate is shown.
CLEANLINESS
Coarse aggregate used in higher strength concrete
should be free of dust coating, because the dust content
causes an increase in the fines, and consequently an
increase in the water requirement of the resulting concrete
mixture. Hence, the water-cement ratio increases and the
strength decreases. Washing the crushed stone coarse
aggregate may not always be necessary, but is always
recommended (22) .
MINERALOGY AND FORMATION
As discussed above, the compressive strength of
concrete increases when using crushed stone as the coarse
8
aggregate. This is not only because of the shape of the
aggregate but also due to its mineralogy. The Waterways
Experiment Station has done some work on the effect of
mineralogy on concrete strength. They achieved 17 000 Psi
(117 MPa) using granite rock (14) .
AGGREGATE-PASTE BOND
When high-strength concrete is desired, the aggregate
paste-bond should be strong, a good quality aggregate with a
suitable surface texture should be used.
The aggregate-paste bond is known to decrease with
increasing water-cement ratio and increasing the size of
aggregate. Alexander (1) found that the cement-aggregate
bond to a 3 inch particle was almost 1/10 of that to a
corresponding 1/2 inch particle.
FINE AGGREGATE:
The gradation and particle shape of fine aggregate are
very important factors in the production of higher strength
concrete. Fine aggregate has a great effect on the water
requirement and consequently the strength of the concrete
mix. In sand of the same grading, a 1% increase in fine
aggregate voids may cause a 1 gallon per cubic yard increase
in water demand (6) .
One of the important functions of fine aggregate in
conventional concrete is its role in providing workability
and good surface finishing. Since higher-strength concrete
contains a large amount of cement paste, the role of fine
aggregate in providing workability and good finishing is not
so crucial. Fine aggregates with a fineness modulus between
2.7 and 3.2 have been most satisfactory (9). Blick (2)
reported that fine aggregates with fineness modulus below
this range might produce low strength and "sticky mixes". A
reduction of the amount passing the No. 50 and No. 100 sieve
on the lower side of the specification limit from ASTMEC-33
is suggested. Such reductions have shown an increase in
compressive strength of 500 to 1000 Psi (3.5 to 7.0 MPa)
(15).
In this investigation, Kaw River Sand with a maximum
sieve size of No. 4 was used.
WATER
Studies (6,20) have shown that water meeting specifica-
tion ASTM C-94(19) has no harmful effect on high-strength
concrete. Therefore, water meeting ASTM C-94 is adequate.
ADMIXTURES
Due to the low water-cement ratio, high-strength
concrete has low slump and workability is not adequate. A
chemical admixture called superplasticizer or "super water
reducer" can be used to improve workability and slump. This
admixture actually reduces the friction angle between the
10
water and surface of contact and causes the mix to be more
workable. It is important to note that this effect is for a
limited time and the mix changes to its original property
after a short time. Therefore superplasticizer increases
the slump within a limited time without altering the
compressive strength, because the slump will go back to its
original position as if no admixture was used in the mix.
Figure 2.7 shows the effect of superplacticizer on the slump
versus the time on a mix with water cement ratio of 0.35
(11). It is believed to have a similar effect on all other
mixes. In this investigation, the brand of superplacticizer
used was Sikament. The quantity of superplacticizer used
was in accordance with the mix proportion developed by
Nikaeen (11) . As slump decreases rapidly with time, it is
important to consider this effect on the job site.
"
£HAEIE£ 1
LITERATURE SURVEY FOR COMPRESSIVE STRESS BLOCK
The ultimate strength of reinforced concrete members
subjected to flexure and axial loading can be predicted
using the equivalent rectangular stress distribution in the
concrete compressive zone. In designing, the ratio of the
depth of the equivalent compressive stress block to the
depth of the actual one, and « , the extreme fibre compres-
sive strain, are to be known. Based on beam tests, using
concretes with compressive strength less than 6000 psi,
(41.3 HPa) the American Concrete Institute (ACI) (17) sug-
gested values for p. , depending on the concrete strength.
In 1975, a minimum value of p , equal to 0.65, was sug-
gested by the ACI. The validity of this stress block, has
always been in question with regard to higher-strength con-
crete. Hence, there is a need to study the shape of the
stress block in higher strength concretes.
Many views have been expressed concerning high strength
concrete, but the views are not consistent and they
contradict each other.
In the work done by Leslie, Rajagopalan and Everard
[9], they concluded:
12
a) The ACI building code rectangular stress block does
not predict the behavior of beams with f ' above
8000 psi (55 MPa)
.
b) Further research is warranted with respect to
maximum strain in concrete for f' exceeding 8000
psi (55 MPa)
.
c) Pending further tests, a triangular stress block
with an extreme fibre stresses of f' and zero
stress at the neutral axis is recommended as a
conservative model for predicting the behavior of
beams with f'c above 8000 psi (55 MPa).
In the work done by Wang, Shah, and Naaman [16] , the
following conclusions were made:
a) The rectangular stress distribution gives a suffi-
ciently accurate prediction of ultimate loads and
moments for reinforced concrete beams and columns
made with high strength concrete.
b) The value of maximum concrete compressive strain at
ultimate was always higher than 0.003 in/in.
In the work done by Nikaeen [11] , he concludes:
a) The shape of the stress block at ultimate changes
from rectangular to parabolic type as the strength
increases, because he found that the position of
the concrete internal reaction force is k_ = 0.37
at ultimate condition for higher strength mix
13
(i.e., £'c
= 9500 psi, 65 Mpa) . This value is very
close to 0.375 which is the center of gravity of a
parabolic stress block rather than 0.5 which is the
center of gravity of a rectangular stress block,
b) The strain behavior of high strength concrete is
different from normal strength concrete, because
strain at the ultimate condition is less than
0.003 in/in. proposed by ACI code (17) or it might
be greater than that proposed by ACI, but it
decreases with time drastically. Therefore, a more
conservative value of 0.002 in/in. was recommended.
14
CHAPTER A
TEST SPECIMEN AND METHOD OF TESTING
In 1955, Hognestad, McHenry and Hanson [7] formulated
the ultimate strength design criterion for concrete. In
their work, they used a special C-shaped structural element.
Tensile stresses were completely eliminated in the test
region of the specimen, by applying loads at two points and
varying them such that the neutral axis remained at the face
of the test specimen throughout the test.
The test specimen had a central unreinforced test
region, and reinforced brackets at the end of the test
specimen which accomodated the two thrusts.
The test reported here was done on a similar specimen
and the dimensions were as used by Nikaeen [11] (Fig 4.1)
.
In this test, the method and analogy adopted by Nikaeen
are very closely followed in order to investigate the
behavior and shape of the stress block in the higher
strength concrete beam section.
METHOD OF TESTING
Suitable tension, compression, and shear reinforcement
were placed in the end bracket to assure that failure would
occur in the central, unreinforced test region. A major
thrust P1 was applied and the neutral axis was maintained at
15
the face of the test specimen throughout the test. Strains
were measured over the test region.
In investigating the behavior and shape of the stress
block, the method and equations developed by Hognestad,
McHenry, and Hanson [7] were used. To formulate the
ultimate strength design criterion, they derived some
equations and used a C - shaped structural element. The
present ACI code for ultimate strength theory is based on
their work. They formulated stress in concrete fibres as a
function of strain in those fibres. They also showed that
stress-strain relationships for concrete in concentric
compression are indeed applicable to flexure (Figure 4.2
shows this fact) . The following equations which permit
stress to be expressed in terms of measured strain and other
known parameters were developed by them [see 7] .
dfQ
fc " 8cd^ + f
o (4.D
dmfc = 8cdT + 2m
o (4.2)c
Pl + p2
fo " —be"
(4-3)
plal
+ ?2 a2
be 2(4.4)
where
16
f = Concrete compressive stress in outer fiber ofthe beam;
» = Concrete strain in outer fiber of the beam;c
P. = major thrust;
P, = minor thrust;
a, and a_ are lever arms;
b is the width and c is the depth of the testingregion.
The details are shown in Figure 4.1.
Figure 4.3 gives the reinforcement layout of the test
specimen. Figures 4.4 and 4.5 give the sections at A-A and
B-B respectively (see Figure 4.1).
STRAIN GAGES
Strain gages were used to measure strains. The strains
were monitered by an automated data acquisition system
controlled by a model 2E Apple Computer.
Ten of Micro Measurement EA-06-7 50DT-120 electrical
resistance strain gages were used on the test beam of the
locations shown in Fig. (4.1).
17
CHAPTER 5_
EXPERIMENTAL WORK AND RESnT.TS
CASTING
The specimens were cast horizontally on a level
surface. Vibration was used to consolidate the concrete.
There was a minimum cover of 3/8 in. The mix proportions
used for all the 4 specimens are shown in Appendix Ila.
Some 3x6 in. cylinders were cast at the same time with each
mix.
CURING
Twenty-four hours after casting, the specimen was taken
out of the mold and then placed in a 100% humidity curing
room. All the specimens were in the curing room for 52
days. The specimens were then taken from the curing room
and were kept in a 50% humidity environment for 7 days in
order to prepare them for the test. Table 5.0 shows details
of the test specimens. Cylinders corresponding to each
specimen were taken out at the same time as the specimen.
INSTRUMENTATION AND APPARATUS
The location of the strain gages used to measure the
strain can be seen in Fig. 4.1. The major load P^, Figure
4.1, is applied by a 300,000 lb, load-controlled testing
18
machine through a system of bearing plates and rollers. The
minor load P„ is applied by a hydraulic jack through a steel
frame shown in Appendix II-c. A pressure gage system,
calibrated prior to the test, was used to control the load.
TEST PROCEDURE
Tables 5.1, 5.2, 5.3, and 5.4 give the average compres-
sive stress for the 3x6in cylinders corresponding to the 4
test specimens. Two strain gages were mounted on some
cylinders and strain was recorded as a function of load up
to failure. Cylinders were tested on the same day that the
corresponding structural element was tested in order to
determine the strength of the mix. The data are in the
tables 5.5 and 5.6 corresponding to beam I, 5.7 and 5.8
corresponding to beam II, 5.9 and 5.10 corresponding to beam
III, and 5.11 corresponding to beam IV. Cylinders corre-
sponding to structural elements I and II and some of the
cylinders of structural element III were tested on a machine
which was not functioning properly. Hence, the strength of
the mix corresponding to specimen IV (f' = 11100 psi or
76.49 MPa) was used in all the 4 specimens in computing the
stress factors.
The test specimen was loaded in such a manner that the
neutral axis always coincided with the outside face of the
specimen. The location of the neutral axis is shown in
Figure 4.1. After each increment of major thrust P., the
19
corresponding increment was such that the average strain
across the neutral surface was approximately zero. This
was monitored by connecting the strain gages on the neutral
face to a wheatstone bridge and maintaining zero potential.
The load and strain at each level were recorded and the
procedure repeated up to failure. The zero strain surface
represents the neutral axis of the specimen and the opposite
side of the cross section represents the extreme compressive
surface. The recorded data for specimens I, II, III, and IV
are shown in 5.12, 5.13, 5.14, and 5.15 respectively. The
average strain at each level is given as a function of load
and is in Tables 5.16, 5.17, 5.18, and 5.19 corresponding to
the 4 specimens.
RESULTS AND DISCUSSION OF THE RESULTS
The average values of cylinder stress-strain data of
Tables 5.6, 5.7, 5.10, and 5.11 corresponding to Specimens
I, II, III, and IV are plotted in Figures 5.1, 5.2, 5.3, and
5.4 respectively. Using the corresponding cylinder stress-
strain curve and the strain values for the flexure test
(indicated in Tables 5.16, 5.17, 5.18, and 5.19) the stress
values at each loading level could be directly determined.
The variation of strain along the depth is shown for beams
I, II, III, and IV in Figures 5.5, 5.6, 5.7, and 5.8 respec-
tively. The shape of the stress block for beams I, II, III,
20
and IV are shown in Figures 5.9, 5.10, 5.11, and 5.12
respectively. The average values of flexural strain at the
inner face (maximum compression) are plotted against load in
Figures 5.13, 5.14, 5.15, and 5.16 for beams I, II, III, and
IV respectively.
To determine the ultimate strength factors, k^k^ and k2
the equilibrium concept is used. The details are shown in
Appendix Il-b. By equilibrium of forces and moment from
Figure 5.21, k^k^r and k 2can be determined.
C p l + p21 J bcf£ bcfc
Pi a-, + P, a,
*' l T ^\ P2)c
< 5 - 2 >
k2
The values of k n k-,, k, and -r—.— can be measured directlyklk3
from zero up to failure. The individual value of the coef-
ficient kg is the ratio of maximum compressive stress in the
beam (i.e., f cmax flexural test) to the corresponding
average cylinder strength f,!,. To calculate k^, which is the
shape factor, k^^ and k2are to be evaluated. The values
of ultimate strength factors are given in Tables 5.20, 5.21,
5.22, and 5.23 for beams I, II, III, and IV. The ultimate
strength factor k2 indicates the position of the resultant
reaction force which is produced by concrete.
21
Figures 5.17, 5.18, 5.19, and 5.20 show the values of
^1^2 and ^2 computed by equations (5.1) and (5.2) as a
function of strain e c at the compression face for Beams I,
II, III, and IV. The term k 2 indicates the position of the
resultant force in the concrete from the outer fiber of the
beam. Figure 5.18 shows that the position of the resultant
force is 0.32 at lower loads and 0.36 at ultimate condition.
In beam II, k2changes from 0.32 at lower loads to 0.36 at
ultimate (Figure 5.19). From Figure 5.19, 5.20, and 5.21,
one can see that k2
changes from 0.31 to 0.35. This indi-
cates that the stress block is more triangular than rectan-
gular or parabolic, but it tends to become closer to para-
bolic towards the ultimate. Beam I unlike the other three
beams had k2changing from 0.37 to 0.43 which indicates the
stress block appears to be close to a rectangular shape.
The curve pattern for beam I looks exactly like the curves
for the other three specimens but it seems to be shifted.
This may be due to some error in conducting the experiment.
The f,!, value corresponding to the beam IV cylinder was
used in calculating k3 for all the four specimens as the
cylinders corresponding to the other beams were tested in a
defective machine. The outer fiber stress is calculated
using equations 4.1 and 4.2 for all the specimens. The
results are given in the Tables 5.24, 5.25, 5.26, 5.27,
5.28, 5.29, 5.30, and 5.31 corresponding to beams I, II,
22
Ill, and IV. A computer program was used to find the dif-
ferential parts. Tables 5.28, 5.29, 5.30, and 5.31 give
flexural stresses using both the methods i.e., Equations
4.1, 4.2, and the cylinder stress- strain curve, for compari-
son purpose for beams I, II, III, and IV.
Figures 5.22, 5.23, 5.24, and 5.25 show the values of
f Q (Equation 4.3) as a function of strain b at the compres-
sion face for the four beams respectively. Figures 5.26,
5.27, 5.28, and 5.29 show the values of mQ (Equation 4.4) as
a function of strain e c at the compression for the four
beams respectively. Figures 5.30 and 5.32 give average f c
from Equation (4.1) and Equation (4.2) vs. strain for beam
II and beam IV respectively.
Comparing the area of the ACI stress block (17), with
the area of the parabolic, stress block, we have
0.85 f^O-^Jb = k-^f^bc or
klk3
?1. 85
The values of fly, so calculated are 0.88, 0.8, 0.8, and 0.72
for beams I, II, III and IV respectively. This is higher
than the ACI recommended value of 0.6 5.
The modulus of elasticity corresponding to cylinders of
Beam III and Beam IV were 6.71 x 10 6 psi (0.462 GPa) and
6.67 x 10 psi (0.459 GPa) respectively. This was found to
be nearly equal to the modulus of elasticity calculated from
23
American Concrete Institute formula (17), which was
6.36 x 10 6 psi (0.438 GPa). The Poisson's ratio
corresponding to a cylinder from Beam II was found to be
0.23.
STRAIN BEHAVIOR
The maximum recorded strains corresponding to Specimens
I, II, III, and IV are 0.00330 in/in., 0.00303 in/in,
0.002 80 in/in. 00021 in/in. respectively. Maximum recorded
cylinder strains at stress near ultimate corresponding to
Specimens I, II, III, and IV are 0.0021 in/in., 0.00243
in/in., 0.002116 in/in. and 0.00203 in/in. respectively.
The cylinders had maximum recorded strain values less than
0.003 in/in. Two of the beams had maximum recorded strain
values greater than 0.003 and two of them had maximum
recorded strain values less than 0.003 in/in. Therefore, a
more conservative value of 0.0025 in/in. is recommended.
Reference (12) has also suggested a similar value. Nikaeen
[11] has suggested a very conservative value of 0.002 in/in.
24
CHAPTER 5.
SDMMARY MD CONCLUSIONS
SUMMARY
Four "dogbone" shaped [7] beams of higher strength
concrete were tested to investigate their structural bending
properties. The beams were loaded such that zero strain was
maintained at the outer face. The beams were made out of
concrete of 11000 psi (76 Mpa) . A number of 3"x 6" cylin-
ders corresponding to each beam were tested in concentric
compression. The main objective of this experiment was to
study the shape of the stress block of failure for higher-
strength concrete. The following conclusions were made from
the test results.
CONCLDSIONS
1. Higher-strength concrete has a brittle mode of failure
and failure is sudden without any formation of cracks
before failure. The failure line passes through the
stone and not through the interface of mortar as in
normal strength concrete. [This was also observed by
other investigators (12, 11)].
2. The values of k, near the ultimate condition for beams
II, III, and IV were 0.36, 0.36 and 0.35. These values
25
are very close to 0.375 the value for a parabolic
stress distribution. Thus higher strength mixes appear
to have a parabolic stress distribution of failure in
bending.
3. Strain-behavior in higher strength concrete is
different from normal strength concrete and is observed
to be less than the ACI proposed value of 0.003 in/in.
A more conservative value of 0.0025 in/in. is recom-
mended.
4. The modulus of elasticity may be estimated by the ACI
formula (17) (Eq. 10).
5. The value of Pi in higher strength concrete is greater
than the ACI recommended value of 0.65.
RECOMMENDATIONS FOR FUTURE WORK
For higher-strength concrete to be effectively used in
the future, intensive research should be conducted. Higher-
strength concretes of ranges 11,000 psi to 15000 psi (75.8
MPa to 103.4 MPa) should be tested to determine the
structural behavior in bending. Also, experiments should be
done on a larger scale i.e., more beams should be tested to
get consistent results and some definite code requirements
should be developed.
26
APPENDIX J
references'
1. Alexander, K. M. , "Factors controlling the Strength andthe Shrinkage of Concrete," Construction Review . Vol. 33,No. 11, Nov. 1960, pp. 19-29.
2. Blick, Ronald L. , "Some Factors Influencing High StrengthConcrete," Kederji Concrete . April 1973.
3. Bloem, D.L. and Gaynor, R.D. "Effect of AggregatesProperties on Strength of Concrete," American ConcreteInstitute Journal . Vol. 60, No. 10, October 1963, pp. 1429-1455.
4. Burgess, A. J., Ryell, J., and Bunting, J., "High-StrengthConcrete for the Willows Bridge," American ConcreteInstitute Journal . Vol. 67, No. 8, August 1970, p. 611.
5. Carrasquillo, Ramon L. , Nilson, A.H. , and Slate, Floyd 0.,"The Production of High-Strength Concrete," Research ReportNo. 7 8-1 . Department of Structural Engineering, CornellUniversity, Ithaca, May 1978, p. 2.
6. Freeman, Sidney, "High-Strength Concrete," Publication No.15176, Portland Cement Association, 1971 (Reprint from
.aoii£in Concrete . 1970-71) , p. 19.
7. Hognestad, Eivind, Hanson, N.W. , and McHenry, Douglas,"Concrete Stress Distribution in Ultimate Strength Design,"Journal .Of ihs American Concrete Institute . Dec. 1955, Vol.27, No. 4, pp. 455-47 9.
8. Kaplan, M.F. , "Flexural and Compressive Strength of Concreteas Affected by the Properties of Coarse Aggregate," AmericanConcrete Institute Journal . Vol. 55, May 1959, pp. 1193-1208.
9. Leslie, Keith E. , Rajagopalan, K. S. , and Everard, Noel J.,"Flexural Behavior of High-Strength Concrete Beams," A£IJournal . Vol. 73, No. 9, September 1976, pp. 517-521.
10. Mather, Katherine, "High-Strength Concrete, High DensityConcrete," (ACI Summary Paper), American Concrete InstituteJournal . Proceedings, Vol. 62, No. 8, August 1965, pp. 951-962.
27
11. Nikaeen, Ali, "The Production and Structural Behavior ofHigh-Strength Concrete." A Master's Thesis . Department ofCivil Engineering, Kansas State University, 1982.
12. Nilson, Arthur H. and State, Floyd 0., "StructuralProperties of Very High-Strength Concrete," Second ProgressRePP ft £113^. 76-Q8752, Department of Structural Engineering,Ithaca, New York, January 1975.
13. Perenchio, W. P. , "An Evaluation of Some of the FactorsInvolved in Producing Very High-Strength Concrete, " BulletinJSfij. RD014. Portland Cement Association, 1973.
14. Saucier, Kenneth L. , "High- Strength Concrete, Past, Present,Future," Concrete International. American ConcreteInstitute, Vol. 2, No. 6, June 1980, pp. 46-50.
15. Smith, E. E. , Tynees, H.O. , and Sauciet, K.L. , "HighCompressive Strength Concrete, Development of ConcreteMixtures, " Technical Documentary Report No^. XDS 63-3114 .
D.S. Army Engineer Waterways Experiment Station, VicksburgMississippi, February 1964, p. 44.
16. Wang, Pao-Tsan, Shah, Surendra P., Naaman, Antoine E.
,
"High-Strength Concrete in Ultimate Strength Design,
"
Journal Qi ihS Structural Division . ASCE, No. 197 8, pp.1761-1773.
17. "Building Code Requirement for Reinforced Concrete (ACI 318-83)," American Concrete Institute, 1983.
18. "Cement; Lime; Ceilings and Walls (including manual ofcement testing)", Annual Book of ASTM Standard . Part 13,1976.
19. "Concrete and Mineral Aggregates (including Manual ofConcrete Testing) ," Annual Book of. ASTM Standard , part 14,1974.
20. "High-Strength Concrete," First Edition, Manual q£ ConcreteMater ials-Aggregates . National Crushed Stone Association,January 1975, p. 16.
21. "High-Strength Concrete in Chicago High-Rise Buildings,"lasJs Force Report No^. 5_, Chicago Committee on High-RiseBuildings, Feb. 5, 1977.
22. "High Strength Concrete-Crushed Stone Makes the Difference,"Third Draft, Presented at the January 1975 National Crushed
28
Stone Association Convention in Florida, November 1974, p.31.
23. "New York Gets Its First High-Strength Concrete Tower,"Engineering News- Records. Vol. 201, No. 18, November 2,197 8, p. 22.
24. "State-of-the-Art Report on High-Strength Concrete,"Reported by ACI Committee 363, Ad jlojirjial, Vol. 81, No. 4,July-August 1 9 84 .
25. Tentative Interim Report on High-Strength Concrete, AmericanConcrete Institute Journal . Proceedings, Vol. 64, No. 9,September 1967, pp. 556-557.
29
APPENDIX II
a. MIX PROPORTIONS (Based on trial mix done by Nikaeen
(ID)
Proportions used for 1 cu ft.
Materials Quantity
Cement, Type I 31.93 lb
Quartz ite 49.65 lb
Sand 60.88 lb
Water 8.28 lb
Super pi asticizers 340 ml.
1 lb. = .45 kg
30
b. Derivation of ultimate strength factors k.k,, k 2
b,
V%V
(\
—
• • •
c
/ lc=,
T=Asfy
L)bc
Figure a: Force Couple System
Without any assumptions we obtain the equilibrium equation offorce and moment:
Fx = 0, T = C > T » k
1k3
fj. be
M1*3 - fj. be(1.1)
M = T(d ^2°1 C(d - k,c)
2 " c " Tc c Cc (1.2)
Applying the same concept to the test specimen shown in figure
5.21, we have C= P, + p..
Substituting in Equation (1.1) we obtain
*ilc, -
Pl + P
21*3 " bef ' (1-3)
31
where f ^ i s the cylinder compressive strength.
Mu " pl al
+ p2a2
Substituting in Equation (1.2)
kd P
l al + p2a2
2 * c (P1+ P2)c
d = c for the test specimen
Therefore:P1&1 + P2 a2
K2 = 1 "
(Pl + p2 ) c
32
c. STEEL FRAME
The minor load P2 is applied by a hydraulic Jack through
a steel frame shown below (Adapted from Ref. 11).
^xCw^JT
CUT SECTION
_BEAM
-ROLLER
.MOVABLE PLATE
.RAM
1 in = 25.4 mm
33
d_ cmo df o. Computer Program For Calculating -rr-, -— , f_, m~ and f,
Q£ C u C *
10 INPUT -NO. OF DP.TB POINTS N"?-)N20 DIM X (N) , YIN) ,fl(31 , DYIN1, Z (N)
M N2 m N - 24a dim Bi:,3),aB(3,;i,sf(3)so FOR I 1 TO NSa PRINT"DP.TO POINT NO. " 1
1
70 INPUT"X(I)«?-|X<I)SO INPUT-Y(II-?")Y(II30 INPUT"Z(I)-?"|ZU>100 NEXT I
lie FOB T-l TO 212« FOR I - 3 TO N2IS* FOR J • 1 TO 3ite b<j, : )- i
ise u - I - 3 • Jise B(J,2> - XIIJ) .- X(I)178 B<J,3> " 9<J,2)-2ise next j190 FOR J 1 TO 32ee FOR K - 1 TO 32i
e
BS(J, k> • e220 FOR L • 1 TO S230 SB(J.K) - BB(J,K) - 3(L,J1- B(L.K)2*0 NEXT L.K.J250 FOR J - 1 TO 3260 BF<J> - e270 FOR K » 1 TO S280 IK - I - 3 * K290 IF T-2 THEN Y(I)-Z<I>200 IF T-2 THEN Y(IK>-Z(IK1310 BF(J) • BFCJ) » B<K,J) Y(IK)320 NEXT K, J330 - 3B(l.l) • (BBI2.2) • 3B(3,3) - 9B<£. 21 • BB (3, 2) > - 56(1,21 • 96(2, 11 *
BB(3, 31
340 - D » BBC1.21 • BB(2,31 • BB(3, 1) - BB<1,3: • (BB(3,2) • BB (2. 11 - BB(2,2)• BB(3. 1)
>
330 E - BB(l.l) • <BF(2)»BB(3, 3) - BB (2. 3> »BF (3) 1 - BF ( 1 UMBB (2, 1 1 »BB (3, 2) -
3B(2. 3) • 3B(3, 11 1
360 E - E • 3BC1.31 • (BB(2, 11 • 3F(31 - 3FI21 • 3B(3, 111
370 C(21 - E/D380 £ - BB(l.l) • (BB(2. 21 • BF<3) - BF<21 • SB(3,21) - BB(1,21 * (BB(£. 11
• BF(3) - BF(2) BB<3, 111390 I E - 3F(11 • CBS (2. 11 • 3BI2.21 - 3B(2, 21 • 38(3, 11!400 CI31 - E/D410 IF I - 3 THEN 4SO420 IF I - N2 THEN 310430 DY(I) -0(2)440 SOTO 360430 DY(I - 21 - C(2) • 2 • C<3) • (X<1) - X (31 1
460 LPRINT"DY/DX (11-" ;DY(11470 0Y(21 - C(21 • 2 • CC31 • (X(21 - X(3)l4aO LPRINT "OY/DX (21-" ?DY(2)490 DY(I) . C(21300 GOTO 360
34
3ia OYU) » C<2)32a DY(I l) - C<2) * a • C<3> * <X(I » 1) - XII))33a LPRINT "DY/DXCjI * lt")-"|DY<I + 1)
3*a OY<I • 2) - C(2) • 2 • C(3) * <X(I * 2) - XI I))330 LPRINT "DY/DXC'lI * 8) ")«" lDY< I * 2)36a LPRINT "OY/DX(', |I|")-")DY(I)373 NEXT I
38a IF TO 1 THEN sia39a LPRINT "STRAIN AT COMP FACE Fa DF/0saa GOTO 638Sia LPRINT "STRAIN AT COMP FACE ITO OM/062a FOR M-l TO N53a IF T-2 THEN Y<M>«2»Z<M>64a F»X <M)*OY<M)-fY(M)63a IF T-2 THEN Y<M)-Z(KI)Sea LPRINT TABC3) X <K1> TAB(23) YCM) TAB(4a) DY(M) TAB(Sa) r
673 NEXT Kl
saa next tesa END
35
e. Calibration of the minor load P2
Pressure (Psi) Load (lb)
75 500
150 1000
235 1500
315 2000
395 2500
475 3000
550 3500
625 4000
700 4500
750 4850
800 5200
1 psi =6.89 kPa1 lb = 4.45 N
36
APPENDIX III
TABLES
AND
FIGURES
37
jjCO
<uEl
3
2
S. o•HJJ10
suo*Jc
oI
.a
a9JJ —
.
n
10 10
aV —
>t-H(0 "O5<HUJ 3o m
o o
oi 5
10 «a<u co -H
M• 3U
Zc
ai
ch aijj jja aa a
sai
S „ai oCJ~j
jju ia
v IXjj(0
3
oto
ojj
r? *r Tf COCO 00 CO V.
ovo
oJJ
oJJ
r* VO
CO CO
\fi in oOH iH (N
tp a CO *3- CO GO«3> ^ .
co mvo c-»
m-s.
VO CO
CN HVO CO
en ihCM IN
VO CO
CO
0>
a o
o
S 0. H H5a> -h H HJ H
4•H O E E1 gO 0] 10 10 a
&£ CD Hi 0) 0)
ca a (3 caCO CO
38
Table 5.1
Cylinder Data Corresponding to Beam I*
No. of 3x6 in. Load Stress
Cylinders Area in lb. psi
1 7.07 55,000 7779
2 7.07 56,500 7991
3 7.07 55,000 7779
4 7.07 53,500 7567
5 7.07 50,000 7072
6 7.07 53,500 7567
SZ£»f ' average = —t^c b
- 4*P = 7626 psi
1 in = 25.4 nun
1 lb = 4.45 N
1 psi =6.89 KPa
* while testing these cylinders, the machine was notfunctioning properly and hence the strength indicatedis not the true strength of the mix.
39
Table 5.2
Cylinder Data Corresponding to Beam II*
No. Of 3x6 in. Load Stress
Cylinders Area in lb. psi
1 7.07 63,000 8911
2 7.07 69,000 97 60
3 7.07 65,000 9194
4 7.07 64,000 9052
5 7.07 66,000 9335
6 7.07 64,000 9052
f ' Average =6
= Z*f = 9220 psi
1 in = 25.4 mm
1 lb = 4.45 N
1 psi = 6.89 kPa
* while testing these cylinders, the machine was notfunctioning properly and hence the strength indicatedis not the true strength of the mix.
40
Table 5.3
Cylinder Data Corresponding to Beam III*
No. of 3x6 in Load Stress
Cylinders. 2
Area in lb. psi
1 7.07 76,000 10,750
2 7.07 68,500 9,6 89
3 7.07 68,500 9,6 89
4 7.07 68,000 9,618
5 7.07 67,000 9,477
6 7.07 75,000 10,622
7 7.07 67,500 9,547
fc
Avei age =71 f
c 695927 " 7
= 9920 psi
1 in '= 25. 4 mm
1 lb = 4.45 N
1 psi = 6.89 kPa
* while testing these cylinders, the machine was notfunctioning properly and hence the strength indicatedis not the true strength of the mix.
41
Table 5.4
Cylinder Data Corresponding to Beam IV
No. Of 3x6 in Load Stress
Cylinders Area in lb. psi
1 7.07 78,000 11,033
2 7.07 72,000 10,184
3 7.07 80,000 11,315
4 7.07 82,000 11,598
5 7.07 80,000 11,315
6 7.07 78,600 10,750
7 7.07 81,800 11,570
f ' Aw,=>r ^n<a _£ fc m 777CC = 111 1 n «r..'
1 in = 25.4 mm
1 lb = 4.45 N
1 psi =6.89 kPa
42
Table 5.5
Stress-Strain Relationship for Cylinder #1
Corresponding to Beam I
Load(Lb)
Stress(psi)
StrainReading in
Gage #1
(m)
StrainReading inGage #2
(m)
Average(m)
5,000 707 - 32 - 216 - 124
10,000 1420 - 57 - 420 - 23 9
15,000 2120 - 117 - 615 - 366
20,000 2 830 - 220 - 7 93 - 506
25,000 3540 - 360 - 965 - 662
30,000 42 40 - 52 4 -1140 - 831
35,000 4950 - 707 -1330 -1019
40,000 5660 - 937 -1560 -1248
45,000 6370 -1190 -1820 -1500
50,000 7070 - 240 - 276 - 258
1 lb = 4 .45N
1 psi = i5.89 kPa
43
00 « •* a —
.
as «*-t > 3J -« Wu O m H *a a.u a +J as —
'
> oa W «<
H•
Of) » tSa G U %r* iH u -->.
«J *o c >. «u <a *4 IA BO 1-w <D
m OSHH
00 W i-l
a S U =tfc ~tfa a > o 3,^ « -H w oo —
-
d «e -" e ooeo «0 -rt *-.
01 3 « -H U0\ iH ^
00 00 <Na P B % ^^.
•H O (U
03 a -J 0) aU OS oO
a a at
n OS •n »
00 00 iHs s a 4fc ,-*
«OS T3 hJ « =1
h RS 00*j V a aBfl OS ^ ©
•a ~
33
44
Table 5.7
Stress-Strain Relationship For Cylinder #2
Corresponding to Beam II
Strain Strain Average Strain Strain
Load Stress Reading Reading of Reading Reading
(Lb) (psi) in Long in Long Longitudinal in in Poisson's
Gage #1 Gage #2 Strain Transverse Transverse Ratio(ue) (ue) Readings Gage #1 Gage #2
(ue) (|ie) (ue)
4 2 2
5,000 707 37 - 280 - 158 30 19 .155
10,000 1420 - 56 - 290 - 173 18 28 .133
15,000 2120 - 102 - 368 - 234 48 43 .194
20,000 2830 140 - 570 - 355 82 55 .193
25,000 3540 - 184 - 785 - 485 125 70 .201
30,000 4240 - 255 - 938 - 596 161 81 .203
36,200 5120 - 344 -1080 - 713 200 97 .208
40,000 5660 - 474 -1258 - 866 250 117 .212
43,000 6080 - 570 -1370 - 972 288 134 .217
46,000 6510 - 645 -1460 -1050 317 145 .220
49,000 6930 - 717 -1540 -1130 346 158 .223
52,000 7360 - 805 -1640 -1220 381 177 .229
55,000 7780 - 901 -1750 -1330 415 196 .230
58.000 8210 - 996 -1860 -1430 449 218 .233
61,000 8630 -1110 -2000 -1560 496 244 .237
63,000 8910 -1240 -2160 -1700 559 271 .244
64,000 9050 -1422 -2440 -1930 627 284 .236
1 lb = 4.45N
1 psi = 6.89 kPa
45
Table 5.8
Stress-Strain Relationship For Cylinder #1
Corresponding to Beam II
Load(Lb)
Stress(psi)
StrainReading in
Gage #1(lie)
StrainReading in
Gage #2
(at)
Average(us)
- 508 - 13
5,000 707 - 110 - 253 - 121
10,000 1420 - 219 - 253 - 236
15,000 2120 - 315 - 402 - 358
20,000 2830 - 403 - 546 - 474
25,000 3540 - 516 - 689 - 602
30,000 4240 - 627 - 816 - 721
33,000 4670 - 707 - 904 - 806
36,000 5090 - 784 - 988 - 886
39,000 5520 - 865 -1080 -.970
42,000 5940 - 945 -1160 -1054
45,000 6370 -1020 -1240 -1130
48,000 6790 -1110 -1347 -1230
51,000 7210 -1200 -1450 -1325
54,000 7640 -1290 -1550 -1424
57,000 8060 -1390 -1670 -1530
60,000 8630 -1490 -1797 -1645
62,000 8770 -1576 -1930 -1750
64,000 9050 -1670 -2060 -1870
66,000 9340 -1770 -2080 -1930
1 lb = 4
1 psi =.45 NS.89 kPa
46
Table 5.9
Stress-Strain Relationship For Cylinder #1Corresponding To Beam III
Strain StrainLoad Stress Reading in Reading in Average(Lb) (psi) Gage #1
(lie)
Gage #2(lie)
(|18)
6 3 4
2,000 280 - 54 - 45 - 50
5,000 707 - 115 - 116 - 115
10,000 1420 - 239 - 224 - 231
15,000 2120 - 359 - 356 - 357
20,000 2830 - 463 - 484 - 474
25.000 3540 - 570 - 623 - 597
30.000 4240 - 673 - 753 - 713
33.000 4670 - 738 - 830 - 784
36,000 5090 - 810 - 916 - 863
39,000 5520 - 879 - 999 - 939
42,000 5940 - 950 -1080 -1020
45,000 6370 -1023 -1165 -1090
48,000 6790 -1110 -1260 -1180
51,000 7210 -1200 -1360 -1280
54,000 7640 -1290 -1460 -1380
57,000 8060 -1390 -1571 -1480
60,000 8490 -1510 -1700 -1600
63,000 8910 -1650 -1830 -1740
66,000 9340 -1840 -2010 -1930
67.500 9550 -2090 -2150 -2120
1 lb - 4.45 N1 psi = 6.89 kPa
47
o w h ta a!H U B *• at wH O 1 « §
* *a a <o a.
•MO «CO OS (9
u so c« a -~
-
Ph -H i.H aA »<a %<A <a a ~a M « w <o wo 4-1 •O '" ao 3.H &n S on 3 -•*-> © fl 9St PC O
hJ
oa
a ,_,
•H a a<3 •h ah M -*4 tHw w> -a %V3 CO a o —1 h •H ** fl> «
[A d at a w
2d
i-( fH »H fH CS
I I
1* •* *o o oiH O t- v> en
1 1 1
oI-l
1
O 00 oo\ o* hO i-i CO
48
« a «h m —«
<a w u T3 a.
aoU
a> ao « a w<
>3
a •* <s•h so<d %<tf tt *>*
u m -m a
(3 Q
w is .-1 so a.
3d
Zin oo
49
Table 5.11Stress-Strain Relation for Cylinder #1
Corresponding to Beam IV
Load(lb)
Stress
(psi)
1 psi = 6.89 kPa
StrainReading in
Gage #1
(lis)
StrainReading in
Gage #2
(ue)
Average(lie)
5,000 707 - 36 - 161 - 99
10,000 1410 - 161 - 238 - 200
15,000 2120 - 284 - 313 - 298
20,000 2830 - 401 - 432 - 417
27,000 3820 - 517 - 603 - 560
30,000 4240 - 655 - 609 - 632
35,000 4950 - 740 - 698 - 719
39,000 5520 - 811 - 881 - 846
43.000 6080 - 868 - 960 - 914
46,000 6510 - 941 -1051 - 969
49,000 6932 -1010 -1120 -1050
52,000 7360 -1140 -1120 -1130
55,000 7780 -1290 -1190 -1240
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o o o OA c* « An m •» <r VI so
83
Table 5.28: Load and Stress Data for Flexural Test of
Beam I Using Eq. 4.1 and Eq. 4.2 and
Cylinder Stress-Strain Curve
Maj or
Thrnst P,
(lb)
AverageMinor Strain at f
cAverage of
Thrnst Pj Compression Eq. (4.1) and (4.2)(lb) (ue) (psi)
fcUsing
Cylinder StressStrain Curve (psi)
10,000 - 64 - 528 - 458
10,000 183 - 118 - 683 - 840
20,500 550 - 247 - 1580 - 1740
30,000 850 - 363 - 2430 - 2530
40,400 1180 - 488 - 3280 - 3370
50,400 1410 - 599 - 4030 - 4090
60,400 1720 - 726 - 4840 - 4900
70,000 2020 - 845 - 5620 - 5630
80,000 2300 - 963 - 6350 - 6330
90 , 000 2590 -1080 - 7010 - 7010
100,000 2840 -1230 - 7680 - 7810
110,000 3180 -1370 - 8480 - 8560
120,000 3430 -1500 - 9220 - 9180
125,000 3530 -1570 - 9660 - 9490
130,000 3630 -1650 -10600 - 9870
135,000 3750 -1710 -11000 -10000
140,000 3820 -1750 -11300 -10200
145,000 3950 -1820 -11000 -10500
150,000 4070 -1910 -10500 -10800
155,000 4130 -2000 -10400 -11100
160,000 4230 -2100 - 9660 -11400
84
Table 5.28 Continued
MajorThrust P,
(lb)
MinorThrust P,
(lb)
AverageStrain at
Compression(us)
feAverage of
Eq. (4.1) and (4.2)
(psi)
fcUsing
Cylinder StressStrain Curve (psi)
162,000 4220 -2160 - 9750 -11500 »
162,700 4220 -2200 - 9660 -11700
165,000 4230 -2260 -10200 -11800
170,000 4280 -2370 -10900 -12000
175,100 4350 -2490 -11300 -12300
179,600 4350 -2610 -11400 -12400
185,000 4350 -2730 -11500 -12500
190,000 4330 -2880 -11300 -12500
205,000 3170 -3340 -10200
lib = 4.45 N
1 psi = 6.89 kPa
* values of stress from this point on obtained from extrapolated curve.
85
Table 5.29: Load and Stress Data for Flexural Test of Beam II
Using Eq. (4.1) and Eq. (4.2) and Cylinder Stress-Strain Cnrve
MajorThrust P,
(11>)
AverageMinor Strainat f Average of f Using
Thrust Pj Compression Eq. (4.1) and (4.2) Cylinder Stress(lb) ((is) (psi) Strain Curve (psi)
9,500 - 129 - 894
19 , 800 600 - 240 - 1770
30,000 670 - 301 - 2320
40,500 1380 - 495 - 3240
50,000 1900 - 631 - 4080
60,100 2360 - 764 - 5060
70,000 2670 - 885 - 5850
80,000 2970 -1000 - 6600
90,100 3330 -1140 - 7350
100,000 3670 -1270 - 8010
119,800 4320 -1560 - 9310
129,500 4570 -1720 - 9880
139,500 4830 -1860 -10300
149,400 5050 -2040 -10700
154,500 5150 -2150 -10900
159,500 5170 -2250 -10900
164,500 5220 -2350 -11200
169,400 5230 -2480 -11200
175,000 5320 -2610 -11100
180,000 5320 -2740 -10800
185,000 5320 -3070 - 9580
- 915
- 1690
- 2100
- 3410
- 4300
- 5130
- 5870
- 6570
- 7350
- 8040
- 9410
-10100
-10700
-11300
-11600 *
-11800
-12000
-12200
-12400
-12500
-12500
lib = 4.45 N 1 psi - 6.
* values of stress from this
89 kPa Failure at 195,000 lb
point on obtained from extrapolated curve.
86
Table 5.30: Load and Stress Data for Flexnral Test of Beam III
Using Eq. (4.1) and Eq. (4.2) and Cylinder Stress-Strain Cnrve
MajorThrnst P<
(lb)
MinorThrnst P,
(lb)
Aye rageStrainat f Average of fusing
Compression Eq. (4.1) and (4.2) Cylinder Stress(us) (psi) Strain Carve (psi)
10,000 - 57 - 490 - 408
10,000 400 - 149 - 785 - 1060
20,000 800 - 273 - 1650 - 1920
30,000 1150 - 389 - 2550 - 2700
39.000 1500 - 513 - 3320 - 3530
50,000 1875 - 650 - 4210 - 4420
60,000 2220 - 776 - 5050 - 1680
70,000 2500 - 895 - 5800 - 1940
80,400 2875 -1030 - 6560 - 6740
90,000 3200 -1160 - 7210 - 7450
100,000 3580 -1310 - 7970 - 8240
110,000 3920 -1460 - 8620 - 8980
120,000 4166 -1600 - 9290 - 9590
130,000 4170 -1750 - 9800 -10200
140,000 4733 -1930 -10400 -10900
150,500 5000 -2130 -10800 -11500 *
160,000 5270 -2320 -11000 -12000
165,000 5280 -2430 -11500 -12200
170,000 5330 -2570 -11600 -12300
175,000 5350 -2690 -11600 -12500
185,000 5270 -2810 -11800 -12500
lib = 4
* valnei
45 N 1 psi =
of stress from
6.89 kPa
this point on
Failure at 195,
obtained from extr
000 lb
apolated cnrve.
87
Table 5.31: Load and Stress Data for Flexure Test of Beam IV
Using Eq. (4.1) and Eq. (4.2) and Cylinder Stress Strain Curve
MajorThrust P,
(lb)
MinorThrust P,
(lb)
AverageStrainat f Average of f Using
Compression Eq. (4.1) and (4.2) Cylinder Stress(ue) (psi) Strain Curve (psi)
7,000 - 23
10,000 - 39
11,500 200 - 117
20,000 650 - 203
30,000 1010 - 329
40,000 1520 - 482
50,500 1860 - 613
60 , 100 2300 - 755
70,300 2890 - 934
80 , 000 3150 -1050
90,000 3370 -1160
100,00 3870 -1330
110,100 4120 -1470
120,000 4580 -1660
130,000 4820 -1800
140 , 000 5000 -1950
149,500 5220 -2120
159,000 5430 -2320
164,400 5330 -2420
- 324
- 477
- 782
- 1480
- 2360
- 3193
- 3960
- 4790
- 5880
- 6580
- 7400
- 7960
- 8560
- 9450
-10100
-10700
-10900
-11000
-10900
- 173
- 286
- 834
- 1430
- 2290
- 3330
- 4180
- 5080
- 6160
- 6830
- 7450
- 8310
- 9030
- 9860
-10400
-11000
-11500
-12000
-12100
lib - 4.45 N 1 ps
* values of stress from this
L = 6.89 kPa Failure at 170,000 lb
point on obtained from extrapolated curve.
88
12,000
Type I
11,000
en
a.
X© 10,000zUJcrKwtu>CO
S 9.000Ea.3oo
8,000 -
stone
admixture
3 ± 1/2" slump
J_28
AGE DAYS
56 90
Figure 2.1: Effect of Various Brands of Type I Cementor. Concrete Compressive Strength (20)
89
12,000
10,000
8,000l-
Age, days
Figure 2.2: Effect of Various Cements onConcrete Compressive Strength (2)
90
1 1
. nr iiJ— 1 ' --»^^^z ^^^ S^
u/fef £ 1 -
o .roA 9/ -o e v•V jP/o •! 5 .5 o t»«<* K *
^ 5^=°—•*?!-Ik yS^ >E^Uu {/ 4 5 < -
1
1/8/1/ 600
iaM
'mi<D
-V.I*
— tn\m
*-i«
J'«i« E
c
aoc
oa
o2
*— -E -
cs -< u
c
isd 'q;5uej|s 3A!ss3jduioo
91
10
a
e
<r>
o
inQ.
JOs
ca>
c75
4-
el
7,000 PSi
6,000 P
5,000 PSi
2,000 PS"
3,000 PSi
4,000 PS'
Slump - 3.8 to 5.8 in.
Cure 28 days , moisl
Max. size aggregate, in., log scale
Figure 2.4: Maximum Size Aggregate for StrengthEfficiency Envelope (15)
92
<0Q.
oZUJcrl-cn
UJ>en<nUJ(XQ.
Oa
9,000 -
8,000
7.C00
6,000-
5,000
823-Jb CEMENT/ c-y
I00-* FLY ASH/c-yWATER REDUCER
Figure 2.5: Compressive Strength of Concrete Using TwoSizes and Types of Coarse Aggregate for7,500 psi Concrete (1 )
93
I-ohicrHCO
Hi>COCO_
11,000-
- 10,000 -
9,000 -
8,000-
7,000
Figure 2.6: Compressive Strength of Kigh-StrengthConcrete Csing Three Sizes and Typesof Coarse Aggregate
Q 4
1
1s
i
1•n o
6Mo
s
o
I
LU
S E
o04
O « a>' r- « o t t)
("'.) dwms
95
96
in
in
en_
UJ
zoo
.001 .002 aoz .004 o .001 .002 .003 .004 .005STRAIN -FLEXURAL TESTS STRAIN -COMPRESSION TESTS(5BY8BY 16-IN PRISMS) (6 BY I2-IN CYLINDERS)
Figure 4.2: Concrete Scress-Strain Relations (.7)
97
l /a OIA- WtR£
ALL OIMEMSONSIN INCHES
Is 23.4 mm
"Igura 4.3: aaiaiorcamanc Layout (11)
98
h-6/8'
Cos 45*>a
WO. 3 BARS AT 3.3
SECTION A -A (SEE FIG. 4.2,4^l"» 22.4mm ' '
a - the lag siza of stirrup
Figure 4.4, An Arbitrary Section A-A «WtRebar Arrangement at Each Lag (11)
99
NO. 4 BAflS
3.3*
/0.373 11
3.25* ,1/8 01A-1
t I0.875"
1
0.373 3.23* ,_0.373 "
3*
SECTION B-8(SSS PIS •*. 2)
I "=23.4mm
"igure 4-5: An Arbitrary Section of Coliarn ParrWith Rabar Arrangement (XI)
100
7000-
MAX STRESS 7567 PS I
(52 MPa)
Note: Testing machine not functioning properly.
200 400 S00 300 1000 1200 1400 ISOO 1800 2000
STRAIN IN (MICRO IN/IN)
1 Psi - S.S9 kPa
Figure 5.1: Cylinder Compressive Stress-StrainCarve for Beaa I, Data from Table 5.6
101
Note: Testing machine not functioning properly.
200 100 600 800 1000 i 200 1*00 1600 1600 2000
STRAIN IN frtlCRH IN/TNI
1 Psi =6.89 IcPa
Figure 5.2: Cylinder Compressive Stress-StrainCurve for Beam II, Data from Table 5.7
102
I I 000-
I 0000-
9000
aooo-
7000sT
R
E sooo.ss
I 5000-N
S 4000-
3000
2000-
1000'
1AX STRESS.| og
|
a pS]
(73 MPa)
200 «00 600 800 i 000 1200 MOO 1600 ,800 2000
, _ .
STRAIN IN (MICRO IN/IN!1 Psi » 6.89 kBa
Figure 5.3: Cylinder Compressive Stress-StrainCurve for Beam III, Data from Table 5.10
103
I I 000'
I 0000'
3000-
r rooo-4
5 5000-
S000
3000
200 400 600 900 1000 1 200 HOO iSOO 1800 aooo
STRAIN IN (MICRO IN/IN)
Figure 5.4: Cylinder Compressive Stress-StrainCurve for Beam IV, Data from Table 5.11
104
soc! ooo i 500 coao
STRAIN (MICRO IN/IN]
2500
1 in. = 25.4 mm
1 lb = 4.45 N
Load in lb
Figure 5.5: Location of Strain Gages vs. Strain for Beam I
105
SOO 1000 1S00 2000 2500 30C
STRyUNCMCRO IN. /IN.)1 in. » 25.4 nun Load in lb
1 lb = 4.45 N
Figure 5.6: Location of Strain Gages vs. Strain for Beam II
106
in. 25 .4 mm
iooo isoo jooo
S'SAIN (MICRO \H. 'JM.'
2SO0
Load in lb
1 lb - 4.45 N
Figure 5.7: Location of Strain Gages vs. Strain for Beam in
107
30000so; oo30000
I 200001-19300
1 in. » 25.4 nun
1 lb = 4.45 N
900 i 200 1 600
STRAIN (MICRO IN. /IN.
I
2000 240
Load in lb
Figure 5.8: Location of Strain Gages vs. Strain for Beam IV
10 8
3.0
2.5
SOO0 3000
s t »ess(°s:>
1 in = 25.4 mm, 1 psi 6.89 kpa
1 lb = 4.45 N
Load in lb
Figure 5.9: Stress Block of Beam I
109
s.o-4
i.5
4.0-
3.5
2000 4000 S000 8000
STRESS (PSD
1 in = 25.4 mm, 1 psi =6.89 kpa
1 lb = 4.45
Load in lb
Figure 5.10: Stress Block of Beam II
110
2000 *000 6000 8000i 2000
STRESS 'PS I!
1 in = 25.4 mm, 1 psi =6.89 kpa Load in lb
1 lb = 4.45 N
Figure 5.11: Stress Block of Beam III
111
2000 4000 0000I 2000S000 8000
STRESS (PSD
1 in = 25.4 mm, 1 si = 6.89 kpa Load in lb
1 lb = 4.45 N
Figure 5.12: Stress Block of Beam IV
112
320000
200000-
1 30000
Failure at 205,000 lb
J00 1000 IJOO 2000 2«0O 3000 3J00
AW STRAIN IN SASCS «UmCM IN. /IN.)
1 lb - 4.45 N
Figure 5.13: Axial Load vs. strain for gaces 4 and 5for Seam I
113
MO 1200 1S00 2000 2S00
*VS STHAIM IN GAOSS *«<mCSO tM./W.I
1 lb - 4.45 H
3000
Figure 5.14: Axial Load vs. strain for gages 4 and 5for Beam II
114
Failure at 195,000 lb
soo 1000i soo 2000 asoo
*.VE STSAIN [N SACES 4«(MCS0 IN. /I?).
I
joeo
1 lb - 4.45 N
Figure 5.15: Axial load vs. strain for gaces 4 and 5for Beam Iir'
115
(1*)
1 lb
100 800 1300 ISOO 2000
VE STRAIN IN SACSS 4*5MOW IN. /IN.)
4.45 H
2«50
Figure 5.15: Axial load vs. strain for gages 4 and 5for Beam iv
116
Vl/3
1 OOO 1 500 2000
STSAINIMICHO IN. /IN.
I
2500 3000
Figure 5.17: Stress Factors k, , k_k. Vs. Concrete StrainFor Beam I * J. J
117
SCO ,00° >50O 2000 2S00 3000
STSAImmcRO IK. 'IN.)
Figure 5.18, Stress Factors ^ ^ vs. Concrete StrFor Beam IIam
118
500 ,000 1500 2000 2500 3000
STRAIN tPIICRO IN./1N.)
Figure 5.19: Stress Factors k,, k^ltj Vs. Concrete Strain
For Beam III
119
0.50-
0.00-
400 300 I 200 I 600
STRAIN (MICRO IN./1M.)
Tl^ure 5.20: Stress Factors k2< k1k^
v3/8
Vl/3
2400
Figure 5.20: Stress Factors k_, lt.lt Vs. Concrete StrainFor Beam IV
2' 13
120
STRAIN
b»3i i
i
i
I"* 25.4mm
Figure J. 21: Condition ac Ulclmace Load in Test Specimen
121
a iooo
3000
500 1000 iSOO 2000 2500 3000 3S00Vlt STRAIN IN CAGES 44S!MICS0 IN. 'IN.'
1 psi = 6.89 kPa
Figure 5.22: f vs concrete strain for Beam I
122
9000-f
rooo
5000
5000
3000-
2000-
500 1000 ,500 2000 2500 3000
WE STHA1N IN SAGES US (MICRO iN.'IM.'
1 psi =6.89 kPa
Figure 5.23: f vs concrete strain for Beam II
123
9000-1
7000
sooo-
5000
'00 1000 ,500 2000 2500 300
AVE STRAIN IN SAGES 4*5 (MICRO iN.'lN.'
1 Psi = 6.89 kPa
Figure 5.24: f vs concrete strain for Beam III
124
7000-
8500.
WOO
?ooo
4500
3500-
3000
2100
2000
;500-
500-
100 90" 1200 ;S00 2000 2100
AVE STRAIN IN OAGES *4S (MICRO if).'!M.>
1 psi =6.89 kPa
Pigure 5.25: fo vs concrete strain for Beam IV
125
3 WO ,000 ,500 2000 2500 J000 35
AVE STRAIN [H 5A0ES «4301tCS0 iN.'t*.'1 psi = 6.89 kPa
Figure 5.26: m vs concrete strain for Beam I
126
5000-
4S00-;
3500-
3000-
lpsi =6.89 kPa
3 500 1000 ;500 iOOO 2500 300;
*VE STRAIN IN GAGES **S(MICSO iN.'IN.'
Figure 5.27: siq vs concrete strain for Beam II
127
2500
*VE STRAIN iN GAGES *« (MICRO IN. 'IN.'1 psi =6.89 kPa
Figure 5.28: n^ vs concrete strain for Beam III
128
1Q0O-
won
2000-
,500'
500
3 100 900 I 200 i 600 2000
AVE STRAIN IN GAGES '45 (MICRO IN. MM."
1 psi = 6.89 kPa
Figure 5.29: mQ vs concrete strain for Beam IV
129
1 3000-
1 2000-
a^.
1 1 000-
10000-
9000-
3000-
Sr
R 7000^£S
5000-
S
3000-
/
4000-
3000-
2000-
1000-/
a-
500 1000 1500 200C 23CO
AVE STRAIN IN GAGES 445 (MICRO III. 'IN.'
1 psi » 6.89 ka
Figure 5.30: Average f c from Bq (4.1) and (4.2) vsstrain for Beam II
130
800 1200 i600 2000 2400
WE STRAIN IN GAGES **SCMCS0 IN. 'IN.!
1 psi = 6.89 ka
Figure 5.31: Average f c from Eq (4.1) and (4.2) vsstrain for Beam IV
131
APPENDIX IV
NOTATION
e = strain.
e c= strain at compression face.
a = level arm.
b = width of beam.
c = depth of beam.
d= distance for outermost fiber to center of gravityof steel.
f c = stress in concrete at different levels of loading.
f'c= concrete cylinder strength.
f , m cross-section stress parameters.
fy
= estimated allowable strength in reinforcement.
h = height of beam.
kj, k2 , IC3 = ultimate strength factors (k,, k, areshape factors and k, is the position ofconcrete internal force from outermostcompresion fiber.
C = concrete internal force.
As= area of reinforcement.
M moment.
Mu = ultimate moment.
Pj = axial load applied by testing machine (i.e., major thrust)
P2 = eccentric load applied by hydraulic ram system(i.e., minor thrust).
T = force carried by reinforcement.
y = depth of stress block.
132
ACKNOWLEDGEMENTS
The author is greatly indebted to his major professor, Dr.
Staurt E. Swartz, for invaluable advice and guidance during his
study at Kansas State University and carrying out this
investigation.
Sincere thanks are due to Dr. Robert R. Snell, Head of the
Department of Civil Engineering, for providing financial support
for this project. Sincere thanks are extended to Dr. Cecil Best
for his guidance. Appreciation is also due to the other
committee member, Dr. Teddy 0. Hodges.
Special thanks to Mr. Ali Nikaeen who helped me in this
project.
Special appreciation is expressed to Russell L. Gillespie,
Civil Engineering technician, for his guidance and help in using
the facilities.
Special thanks also to Ms. Christy Schroller, Word
Processor of the Electrical and Computer Engineering Department,
for typing this thesis.
133
The Structural Behaviorof Higher Strength Concrete
by
Narayan Babu D. Hireraagalur
B.E. , Bangalore University, 1982
AN ABSTRACT OF A MASTER'S THESIS
submitted in partial fulfillment of the
requirements for the degree
MASTER OF SCIENCE
Department of Civil Engineering
KANSAS STATE UNIVERSITYManhattan, Kansas
1985
ABSTRACT
An experimental investigation into the structural
bending properties of plain beams of higher strength
concrete was performed.
The objective of this study was to obtain further
information on the shape of the compressive stress block at
failure for higher strength concrete beams.
Four "dogbone" shaped beams were cast with an unre-
inforced test region. Loads were applied so that bending
was produced in the unreinforced test region and the neutral
axis maintained at the outer surface of the test region.
Experimental data were obtained up to the failure of
the test specimen and the k 2 values of beams II, III, and IV
were 0.36, 0.36, and 0.35. These were very close to 0.375,
the k2 value for a parabolic stress distribution.
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