investigation in t 00 muns
DESCRIPTION
Investigation in t 00 MunsTRANSCRIPT
AN INVESTIGATION INTO THEUNCONFINED COMPRESSIVE STRENGTH OF CONCRETE
by
BISWAJIT MUNSHI
B.E., University of Calcutta, 1978
A MASTER'S THESIS
submitted in partial fulfillment of the
requirements for the degree
MASTER OF SCIENCE
Department of Civil Engineering
KANSAS STATE UNIVERSITYManha t tan , Kansas
1987
I/O 1
Approved by:
Major Professor
TABLE OF CONTENTS A11S07 3CH422
Page
LIST OF TABLES Hi
LIST OF FIGURES v
CHAPTER 1 INTRODUCTION AND HISTORICAL REVIEW 1
1 .
1
Introduction 1
1.2 Historical Review 2
CHAPTER 2 SCOPE OF INVESTIGATION 6
CHAPTER 3 MATERIALS, MIXTURES, SPECIMENS, AND INSTRUMENTATION .
.
8
3.
1
Materials 8
3.1.1 Fine aggregates 8
3.1.2 Coarse aggregates 8
3.1.3 Cement 8
3.2 Molds 8
3.3 Proportioning, Mixing, and Curing 12
3.3.1 Mix Design 12
3.3.2 Mixing and Casting Procedures 13
3.3.3 Curing 13
3.4 Specimen Preparation 14
3.5 Instrumentation 15
CHAPTER 4 TEST PROCEDURES 17
4.
1
Cylinder Specimens 17
4 .
2
Beam Specimens 18
4.2.1 Difficulties and Precautions 19
CHAPTER 5 TEST RESULTS 21
5.1 Cylindrical Specimens with Varying Diameter-to-
Height Ratios and End Conditions 21
i
Page
5.1.1 Normal-weight Concrete 21
5.1.2 Light-weight Concrete 22
5.2 Mechanical Properties of Cylinders with Varying
Diameter-to-Height Ratios 23
5.3 Beam and Companion Cylinder Specimens 24
5.3.1 Normal-weight Concrete 24
5.3.2 Light-weight Concrete 26
CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 28
APPENDIX A TABLES 52
APPENDIX B METHOD OF ANALYSIS OF DATA FOR BEAM SPECIMENS 75
APPENDIX C BIBLIOGRAPHY 82
ACKNOWLEDGEMENTS 85
ABSTRACT
li
LIST OF TABLES
Table Page
Al Cylinder Set #1 : Sulfur-Capped (with residual oil),
PVC Molds. Normal-weight aggregate 53
A2 Cylinder Set #2 : Sulfur-Capped (with TFE) , PVC Molds.
Normal-weight aggregate 54
A3 Cylinder Set #3 : Sulfur-Capped (without residual oil),
PVC Molds. Normal-weight aggregate 55
A4 Cylinder Set #4 : Ground Surface (without TFE), PVC
Molds . Normal-weight aggregate 56
A5 Cylinder Set #5 : Ground Surface (with TFE), PVC Molds.
Normal-weight aggregate 57
A6 Cylinder Set #6 : Standard Sulfur-Capped (with residual
oil) , PVC Molds. Light-weight aggregate 58
A7 Comparision of Ultimate Stress in Cylinders of Diameter-
to-Height Ratio of 1.00 and 0.50. Light-weight concrete,
Paper Molds 59
A8 Cylinder Stress-Strain Data. D/H = 0.85 60
A9 Cylinder Stress-Strain Data. D/H = 0.45 61
A10 Cylinder Stress-Strain Data. D/H = 0.31 62
All Cylinder Stress-Strain Data. D/H = 0.23 63
A12 Cylinder Stress-Strain Data. D/H = 0. 19 64
A13 Cylinder Stress-Strain Data. D/H = 0. 16 65
A14 Cylinder Stress-Strain Data. Standard 3-in.-by-6-in.
Cy 1 inder 66
A15 Load-Stress Data, BeamBl, Normal-weight aggregate 67
A16 Computation of df/dG, Beam Bl 68
iii
Table Page
A17 Computation of dm/d€, Beam Bl 69
A18 Cylinder Stress-Strain Data, Companion Cylinder to Beam Bl 70
A19 Load-Stress Data, Beam B2, Light-weight aggregate 71
A20 Computation of df/d€, Beam B2 72
A21 Computation of dm/d€, Beam B2 73
A22 Cylinder Stress-Strain Data, Companion Cylinder to Beam B2 74
IV
LIST OF FIGURES
Figure Page
I General Arrangement of Cylinder Molds 9
2A Assembled Cylinder Molds 10
2B Hold-Down Detail of Molds 11
3 Influence of Diameter- to-Height on Relative Compressive
Strength, Cylinder Set 1 30
4 Influence of Diameter-to-Height on Relative Compressive
Strength, Cylinder Set 2 31
4A Linear Regression for Data in Left Half of Figure 4 . . . . 32
5 Influence of Diameter-to-Height on Relative Compressive
Strength, Cylinder Set 3 33
6 Influence of Diameter-to-Height on Relative Compressive
Strength, Cylinder Set 4 34
7 Influence of Diameter-to-Height on Relative Compressive
Strength. Cylinder Set 5 35
8 Influence of Diameter-to-Height on Relative Compressive
Strength, Cylinder Set 6 36
8A Linear Regression for Data in Left Half of Figure 8 . . . . 37
9 Stress vs. Axial Strain Curve for Cylinder with
D/H = 0. 16 38
10 Stress vs. Lateral Strain Curve for Cylinder with
D/H = 0. 16 39
II Stress vs. Axial Strain Curve for Cylinder with
D/H = 0. 19 40
12 Stress vs. Lateral Strain Curve for Cylinder with
D/H = 0. 19 41
v
Figure Page
13 Stress vs. Axial Strain Curve for Cylinder with
D/H = 0.23 42
14 Stress vs. Lateral Strain Curve for Cylinder with
D/H = 0.23 43
15 Stress vs. Axial Strain Curve for Cylinder with
D/H = 0.31 44
16 Stress vs. Lateral Strain Curve for Cylinder with
D/H = 0.31 45
17 Stress vs. Axial Strain Curve for Cylinder with
D/H = 0.45 46
18 Stress vs. Axial Strain Curve for Cylinder with
D/H = 0.85 47
19 Stress vs. Lateral Strain Curve for Cylinder with
D/H = 0.85 48
20 Stress vs. Axial Strain Curve for 3-in.-by-6-in.
Standard Cy 1 inder 49
21 Stress vs. Lateral Strain Curve for 3-in.-by-6-in.
Standard Cy 1 inder 50
22 Comparision of Stress vs. Axial Strain for Beam Specimen
and 3-in.-by-6-in. Companion Cylinder (Normal-weight
Concrete) 51
Bl C-Shaped Structural Element (Beam Specimen) used for
Determining Unconf ined Strength of Concrete 78
B2 Plan of Beam Specimen (showing reinforcement detail) ... 79
B3 Sections of Beam Specimen 80
B4 Loading Frame to apply minor load, P2 81
vi
CHAPTER 1
INTRODUCTION AND HISTORICAL REVIEW
1.1 Introduction
Uniaxial compressive tests are the most widely accepted norm for
evaluating the quality of concrete. The standard cylinder test (ASTM
C39: Standard Test Method for Compressive Strength of Cylindrical
Concrete Specimens (1)) is simple and provides an excellent means for
the quality control of concrete in industry, and is the basis for
assessing the mechanical properties of concrete which are essential to
the design of concrete structures.
However, the value of ultimate compressive strength obtained from
the standard uniaxial compression test, and followed religiously, is,
in fact, higher than the true strength of concrete in uniaxial
compression. Incorrect measurements of strength and elastic
properties are obtained because of the development of non-uniform
stresses throughout the specimen caused by friction between the end
surfaces of the specimen and machine platens, which prevent it from
expanding laterally.
Attempts have been made throughout this century to investigate
the stress distribution within cylindrical specimens. Investigators
have also studied the effect of specimen geometry and end conditions
on the "uniaxial" compressive strength. However, a practical approach
to the problem of trying to find a thumb-rule or guideline relating
the strength obtained in the standard test to the true strength in
unconfined compression is yet to be established. The following
historical review traces significant experimental and theoretical work
in this area.
1.2 Historical Review
The effect of different end conditions on compressive strength
was recognised as early as 1900 by Foeppl (2). He conducted
experiments in which he eliminated end friction to a degree, and
observed the modes of failure. His experiments on cubes showed that
specimens with paraffin on the bearing surfaces failed at a lower
ultimate strength than those without. The modes of failure were
entirely different. The former failed by splitting in a direction
parallel to a vertical face, whereas the latter failed in a pyramidal
shape.
It was not until 1924 that Gonnerman (3) made an extensive study
of this problem. He studied the influence of uneven end surfaces and
of different methods of capping on the strength in compression of
concrete cylinders from four different mixtures. He used neat cement
paste, mixtures of gypsum and port land cement, gypsum, and a variety
of other interfacing materials, such as beaverboard, white pine,
millboard, leather, sheet lead, cork, and sheet rubber. He observed
that the introduction of rubber sheets resulted in the greatest
reduction in apparent strength — 50 percent for a 1:3-1/2 concrete.
In the following year, Gonnerman (4) conducted a study on the
effect of size and shape of test specimen on compressive strength.
Cylinders 1-1/2 in. to 10 in. in diameter and two diameters in length,
12 in. in length ranging from 3 in. to 10 in. in diameter, 6 in. in
diameter ranging from 3 to 24 in. in length, cubes 6 and 8 in., and
square prisms 6 by 12 in. and 8 by 16 in. were tested at ages from 7
days to 1 year. A decrease in strength ratios of 5 percent and 10
percent in cylinders of height-to-diameter ratios of 3.0 and 4.0 (in
comparision to cylinders of height-to-diameter ratio of 2.0) was
observed. The curves presented in the paper indicate that the fall in
strength ratio versus height-to-diameter ratio is quite steep, even at
height-to-diameter ratios greater than 4.0.
In 1941, Troxell (5) investigated the effect of some other
capping materials such as Hydrostone (a gypsum product), Castite (a
sulfur-silica mixture), oiled steel shot, dry steel shot, and Plaster
of Paris. He concluded that, regardless of the end conditions of the
cylinders before capping, a higher strength and greater degree of
uniformity of strength for the same quality of concrete are obtained
with Hydrostone or Castite caps. Plaster of Paris caps gave lower
strengths, especially for high-strength concrete.
A study by Johnson (6) in 1942 on the effect of height of test
specimens on compressive strength reinforced previous observations.
Johnson concluded that a correction factor should be applied for
specimens for which the length is greater than twice the diameter.
Price (9) mentions specimen geometry as one of the factors
influencing compressive strength of concrete test specimens.
In 1956, Neville (10) reported results on the testing of cube
specimens of 2.78 in., 5 in., and 6 in. The mean strength of 2.78-in.
cubes was higher than that of either the 5-in. or the 6-in. cubes.
Werner (11), in 1958, studied the effect of capping materials on
the compressive strength of concrete cylinders and concluded that
capping materials did have a distinct effect on the strength.
In 1964, Newman and Lacnance (12) reported an extensive study
conducted at the Imperial College in London. They investigated mainly
the deformational behaviour of specimens with different geometries
(prisms 4 in. square with heights ranging from 4 in. to 20 in.). They
measured lateral and longitudinal deformations. The lateral
deformation at about mid-height was most for the smallest specimens,
gradually diminishing with increasing specimen height. They showed
that tangential stresses were induced at the ends of the specimen, but
dropped rapidly with increasing distance from the ends. Axial
stresses again were seldom uniform, and they concluded that axial
stress concentrations could occur.
In 1965, Hughes and Bahramian (13) recognized the need for a
modified uniaxial test. They used 4-in. cubes and prisms 4 in. by 4
in. by 9-5/8 in., and initially introduced inter layers of
polytetraf luoroethylene between the specimens and the bearing platen,
but finally decided on using pads consisting of a polyester film
(Melinex, gauge 100), a grease containing 3 percent molybdenum
disulphide (Molyslip), and a hardened aluminum sheet, 0.003 in. thick
(MGA). They observed that lateral strains were reduced considerably
at some stress levels as a result of the MGA pads.
In 1969, Kupfer. Hilsdorf and Rusch (14) developed a steel brush
device with filaments 5 mm. by 3mm. and spaced 0.2 mm. apart. The
idea was that the bristles would produce axial loads, but, because of
their own small lateral stiffness, would deflect, and therefore would
not produce lateral restraint at the specimen ends. A comparable
device had been developed earlier by the Kaiser-Wilhelm Institute
(15). It consisted of a cone with base angles equal to the angle of
friction between steel and concrete; the end effect would be to
produce uniaxial compression. However, this method, though suitable
for testing metals, was not suited to concrete because of the
difficulty in evaluating the friction between steel and concrete
consistently.
In 1973, Schickert (16) published a detailed study on the
influence of frictional restraint on fracture modes. He used steel
brushes and aluminum sheets to minimize end friction and showed that
with aluminum sheets, the strength of test specimens was 92 percent of
the compressive strength obtained using steel platens. He also showed
that steel brushes reduced the strength to 81 percent of that obtained
using steel platens.
Most recently, Basunbul (17) concluded from his work that for
test specimens of height-to-diameter greater than or equal to 2, the
frictional constraint had no apparent influence on strength, which is
contrary to what other investigators have found.
In summary, the apparent ultimate strength of concrete and the
lateral and longitudinal stress distributions within it are
significantly affected by end frictional conditions, and by the
geometry of the specimen.
CHAPTER 2
SCOPE OF INVESTIGATION
The present investigation was designed to evaluate a method for
determining the strength of concrete in truly unconfined uniaxial
compression and then to test the method in the context of a design
application.
Data of earlier investigators suggest that the apparent strength
of concrete in compression (fc) is inversely proportional to the
aspect ratio (H/D) of the test specimen; that is, fc vs. H/D is a
rectangular hyperbola translated from the origin in the direction of
fc. If so, a simple variable transformation of the form, x = 1/x,
should yield a straight line with a y-intercept equal to the
displacement of the horizontal asymptote of the corresponding
rectangular hyperbola along the y-axis. The fact that correction
factors to be applied to strengths obtained from cores of H/D less
than 2 (ASTM C42: Standard Method of Test for Obtaining and Testing
Drilled Cores and Sawed Beams of Concrete (1)) are approximately
linear following variable transformation supports this hypothesis.
In order to test this hypothesis, five sets of six replications
of cylinders of six different aspect ratios, all cast from a single
normal-weight concrete mixture, and a similar set cast from a single
light-weight concrete mixture, were to be tested in compression in
accordance with applicable portions of ASTM C39 (1). Among the five
sets of normal-weight concrete cylinders, end conditions were to be
altered to vary the frictional restraint. Coincidental ly, the
elastic modulus and Poisson's ratio were to be measured for a
representative set.
Finally, ultimate stresses determined in a field of unconfined
uniaxial compression in a structural element were to be compared with
the unconfined cylinder strengths estimated as described above. The
classic specimen of Hognestad, Hanson, and McHenry (23) was to be used
for this purpose.
CHAPTER 3
MATERIALS, MIXTURES, SPECIMENS, AND INSTRUMENTATION
3.1 Materials
3.1.1 Fine Aggregates
The fine aggregate used was a uniformly graded local sand from
the Kaw River Valley. The sand was first dried in air, and then dried
in an oven for 24 hours, sieved through a standard No. 4 sieve, and
stored in sealed containers.
3.1.2 Coarse Aggregates
The coarse aggregate used was a locally available pseudo-
quartzite for normal-weight concrete, and a locally manufactured
expanded shale for light-weight concrete. Both aggregates were
uniformly graded to a maximum size of 3/4 in..
3.1.3 Cement
The cement used was ordinary port land cement, Type I. It was
stored in sealed drums pending use.
3.2 Molds
Molds for cylinders with different diameter-to-height ratios were
made from PVC Schedule 80/40 pipes of internal diameter 2-7/8 inches.
We proposed to make six different sizes of cylinders with
diameter-to-height ratios ranging from approximately 0.17 to 1.00.
Six cylinders molds of each size were fabricated into a gang of 36
molds for any one set. A shop drawing of the gang mold is shown in
Figure 1. Figure 2A is a photograph of the assembled mold. Figure 2B
shows the hold-down detail.
The beam mold consisted of a wooden base and 3/4-in.-thick
8
Height of
Cylinder Mold3,6,9,12,15 & 18"
No. reqd.
6 each
Schedule 80 PVC pipe threadedbottom 2" and slit longitudinally
PVC sheet
SECTION 1 - 1
45" (approx.)
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36 nos. 3" 0/D PVC pipe segments (Schedule 40)threaded inside and welded to 1" thick PVC sheet
General Arrangement of Cylinder Molds
Figure 1
Figure 2A: Assembled Cylinder Molds,
10
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11
plexiglass walls. The plexiglass was fixed to the base with 1/2-in.
angles and round-head screws 1-1/2 in. long. The joints were sealed
with tape to prevent leakage.
Holds for companion cylinders to the beams were paraffin-coated
paper molds complying with ASTM C39 (1).
The inner surfaces of the PVC cylinder molds and the beam forms
were oiled lightly before concreting.
3.3 Proportioning, Mixing, and Curing
3.3.1 Mix Design
The mixture proportions used for normal-weight, high-strength
concrete were those developed and used in earlier work on the
investigation of the stress-block of high-strength concrete at Kansas
State University (24). Those used for light-weight concrete were
recommended by the aggregate manufacturer. Proportions and pertinent
properties are shown in the following tabulation:
Material
Portland cement (c)
Water (w)
Coarse aggregate
Fine aggregate
Property
Weight of material per eft. of concrete, lb.
Normal-weight Light-weight
27.5
9.0
49.7
60.9
35.2
12.3
31.9
49.0
w/c, by wt.
Slump, in.
fc, psi
0.33
2+1/2
9600
0.35
2+1/2
7000
12
3.3.2 Mixing and Casting Procedures
The batched ingredients were mixed in a power-driven, rotary-drum
mixer of 3.5 cubic feet capacity.
To minimize variation among batches, uniform procedures were
followed, especially when specimens were cast from two separate
batches of concrete, as in the case of the beam specimens.
A "buttermix" with a quarter cubic foot of concrete was mixed and
discarded before the first full batch was mixed, to eliminate
differences between the first batch and subsequent batches.
Dry ingredients were mixed for 30 seconds. Water was poured in
gradually over the next 30 seconds, and mixing was continued for 4
minutes. The concrete was then discharged into a large pre-dampened
pan, and a standard slump test was performed immediately thereafter.
The concrete in cylinder molds was tamped with a 3/8-in. rod with
rounded head as the concrete was placed in layers of about 3 inches.
Subsequently the molds were vibrated on a shaking table. The molds
had been secured to the vibrating table prior to concreting. The
formwork of the beam and its companion cylinder molds was filled to
half the depth with concrete from the first batch and finished with
material from the second.
Five sets of cylinders were fabricated with normal-weight
concrete and one with light-weight concrete.
3.3.3 Curing
All specimens were covered with polyethylene sheets to prevent
loss of moisture.
The cylinder specimens were stripped from their molds after 24
13
hours and put in a standard curing room. The cylinders in any
particular batch were subsequently removed from the curing room on the
same day and kept in the laboratory until time of test.
The beam specimens could not be stripped the next day and
handled, due to strength considerations. The beams were stripped
after a period of seven days after casting. The companion cylinders
were stripped simultaneously and placed in the curing room. The beam
specimens and its companion cylinders were cured in exactly the same
manner for the same period of time.
3.4 Specimen Preparation
The ends of the test specimens were prepared as follows-"
Cylinder Set Description
1 Normal-weight concrete.Standard sulfur-capped with residual oil.
2 Normal-weight concrete.Standard sulfur-capped with powderedtetraf luoroethylene.
3 Normal-weight concrete.Standard sulfur-capped without residual oil.Ends degreased.
4 Normal-weight concrete.Ground surface without powderedtetraf luoroethylene.Ends degreased.
5 Normal-weight concrete.Ground surface with tetraf luoroethylene.
6 Light-weight concrete.Standard sulfur-capped with residual oil.
A given set of 36 cylinders (six different heights, six of each
size) were taken out of the curing room at the same time, and left to
14
dry out for a day under ambient room conditions.
Sulfur-capping was done in accordance with ASTM C39 (1). The
capping base was provided with new guides for cylinders of average
diameter 2-7/8 in.
The capping was checked for perpendicularity to the long axis of
the specimen by placing the capped specimen on a plane horizontal
surface and checking it with a spirit level. If the bubble shifted
from the center, the specimen was re-capped. The smallest specimens
posed difficulty in capping and had to be capped several times before
satisfactory results were obtained.
Two sets of cylinders had ground surfaces. The surface cast
against the PVC plate was already plane and perpendicular to the long
axis of the specimen. This end of the specimen was chucked up in a
lathe. The other end was faced with a diamond cutting tool at a high
r.p.m. and slow cross-feed. The cuts were made in small increments,
and the resultant end surfaces were extremely smooth to the touch. No
coolant was required for the facing operation.
In this operation, the smaller cylinders posed no problem. But
with the larger sized cylinders, there remained a distinct possibility
that the cylinder could slip out of the chuck and be damaged in the
process. A steady-rest was therefore fabricated to accomodate lateral
forces induced in the cutting process.
3.5 Instrumentation
Lateral and axial strains were measured to evaluate the modulus
of elasticity, E, and Poisson's ratio for cylinders of different
diameter-to-height ratios.
15
Six cylinders of different heights from Cylinder Set 3 (sulfur-
capped, without residual oil) were instrumented for this purpose. Two
axial gages 180 degrees apart and two lateral gages diametrically
opposite to each other at mid-height were used.
Electric-resistance strain gages, 2 in. long, were installed in
accordance with the recommendations of the manufacturer.
The beam specimens were instrumented following the same
procedures. The gages were located as shown in Figure Bl. One 3-in.-
by-6-in. companion cylinder was also instrumented with two axial
strain gages 180 degrees apart.
16
CHAPTER 4
TEST PROCEDURES
4.1 Cylinder Specimens
Cylinder specimens with prepared end surfaces were marked
individually for identification. Three diameter measurements were
taken with a caliper reading to the nearest 0.001 in., and an average
of the three was computed. This average diameter was used in all
subsequent computation. Measurements of height were also recorded.
For capped surfaces, the height was taken to include the caps. The
cylinder was centered in the testing machine to the best of our
ability. For centering the specimen, we relied on markings on the
base plate. Two lines intersecting at 90 degrees, and tangent to a
circle of diameter 2-7/8 in., were drawn on the base plate with a
carbide-tipped scriber. A small steel angle section was aligned with
the etching on the base plate. The cylinder was brought into position
so that its sides touched the angle. The angle was removed before
loading.
The difficulty with this procedure was that the cylinders were
not perfectly circular in cross-section, as is evident from the data
presented in Tables Al to A6 (Appendix A). The specimens may not have
been truly centered, but the ultimate stress values which do not have
a wide standard deviation indicate that the technique was sound.
The testing machine used was a load-controlled Emery-Tatnal 1
300,000-lb. hydraulic testing machine. The machine platen was brought
to bear on the cylinder, and load was applied at a uniform rate to
failure. The load at failure was recorded and divided by the cross-
17
sectional area to give the "uniaxial" compressive stress.
Strain data for the cylindrical specimens of different diameter-
to-height ratio were recorded with a Vishay-Ellis Digital Strain
Indicator. The cylinders were loaded to predetermined load levels
with approximately equal increments, and the strains corresponding to
particular loads were recorded automatically.
Since failure was sudden in most cases, it was not possible to
record the strains corresponding to the ultimate load. However, in
most cases, we were successful in recording strain data close to
failure.
4.2 Beam Specimens
Loading on the beam consisted of a major thrust, PI, and a minor
thrust. P2, as shown in Figure Bl. The objective was to load the beam
in a manner such that the neutral axis coincided with the outer face
of the specimen. The approximate zero strain surface represents the
neutral axis of the flexural member while the opposite face represents
the extreme compressive side.
The beam was placed in a standing position in the Emery-Tatnall
machine to apply the major load PI. The minor load P2 was applied
using a hydraulic ram and a yoke as shown in Figure B4. The hydraulic
ram was placed in series with a load cell. The load cell was hooked
to a digital readout which displayed readings to the nearest 10 lb.
The loading yoke was secured to the machine, and the load cell
was bolted to the yoke, to prevent damage to either at failure.
An initial major thrust was applied, and the yoke was placed in
position. This was done to prevent tension developing on the outer
18
face due to the weight of the yoke.
The strain indicator was zeroed at this point, and initial
readings at this load level were recorded. The major thrust was then
increased. The hydraulic ram was operated to apply an eccentric load
until the indicated strains at the outer face were zero. At this
point, the minor load and the corresponding compressive strains were
recorded. This procedure was repeated incrementally until failure
occurred.
The recorded load-strain data and computations to arrive at a
value for compressive stress of concrete at failure, along with test
results of the 3-in.-by-6-in. companion cylinders are presented in
Tables A15 through A22.
4.2.1 Difficulties and Precautions
The beam specimens weighed over 300 lb. Hence, handling was a
problem. Moreover, the mid-section, the test region, was unreinforced
(as shown in Figure B2), and extra caution had to be exercised in
order not to fracture this region in transporting the beam.
Centering the beam in the machine, so that the load PI could be
applied concentrically, was another major problem. The beam had a
tendency to tilt slightly as a result of defective form-work. This
difficulty was overcome by capping the loading region of the beam with
Hydrostone, and levelling it with a spirit level.
Keeping the strain at zero on the outer face was also a difficult
task. This was achieved, however, to some degree of accuracy by
careful operation of the hydraulic ram.
The digital display for the minor load usually jumped around with
a variation of 40 lb. between the highest and lowest readings. Aver-
19
ages of the highest and lowest readings were interpreted as the
operative value of P2.
Following failure, the entire system was unstable; so everything
was slung with rope from the testing machine cross-head.
20
CHAPTER 5
TEST RESULTS
5.1 Cylindrical Specimens with Varying Diameter-to-Height Ratios and
End Conditions
5.1.1 Normal-Weight Concrete
The results obtained from the five sets of cylinders of normal-
weight concrete are presented in Tables Al through A5 (Appendix A).
In all cases, fc is the mean of stresses corresponding to
ultimate loads in cylinders identified as "B" (standard cylinders).
Individual cylinder strengths, f. are divided by fc. This ratio,
f/fc is plotted against D/H. The plots are shown in Figures 3
through 7.
A linear regression analysis yields the following straight-line
fits with corresponding correlation coefficients, R:
Cylinder Description Eqn. of st. line RSet y = f/fc & x = D/H
1 Sulfur-capped, with residual oil y = 0.347x + 0.834 0.957
2 Sulfur-capped, with TFE y = 0.169x + 0.884 0.742
3 Sulfur-capped, without residual oil y = 0.301x + 0.863 0.941
4 Ground surface, without TFE y = 0.346x + 0.847 0.975
5 Ground surface, with TFE y = 0.192x + 0.893 0.855
In general, a linear fit seems to be good, judging from the high
correlation coefficients. However, it may be noticed that Set 5 and
especially Set 2 have a lower correlation coefficient than the other
three sets. A segmental linear fit was tried for Set 2. Figure 4A
21
shows one segment of the fit (D/H = 0.85 excluded). The equation of
the line of best fit is y = 0.373x + 0.833, with a higher correlation
coefficient of 0.804. Interestingly enough, the intercept is much
lower (0.833 against 0.884), which makes it comparable to sets without
TFE. It appears that the effect of TFE is most pronounced for the
smallest cylinders. In the complete absence of friction we would
expect a straight line fit parallel to the x-axis, of the form y = c,
c being the intercept of the y-axis.
The intercept in all five cases lies between 0.834 and 0.893.
The intercept represents the correction factor needed to convert the
ultimate strength of the standard cylinder to the true uniaxial
compressive strength.
The strengths of cylinders cast in paper molds indicate a
reduction in strength as compared to cylinders cast in PVC molds. In
Table Al, where the end conditions were exactly the same for cylinders
cast in PVC and paper molds, a reduction in strength of 2.2 percent is
indicated. This result is consistent with the findings of Burmeister
(25).
5.1.2 Light-Weight Concrete
Results for the set cast with light-weight concrete are presented
in Table A6, and a plot of these results is shown in Figure 8.
The analytical procedure followed is the same as for Cylinder
Sets 1 through 5 for normal-weight concrete.
A linear regression analysis of the plot of f/fc (y) versus D/H
(x) yields:
y = 0.161x + 0.886, with a correlation coefficient of 0.77.
22
The intercept is higher than that obtained for normal-weight
concrete (0.886 compared to 0.834) with cylinders having identical end
conditions. On inspection of the plot, it is seen that a segmental
linear fit would be more appropriate, giving a higher correlation
coefficient and a lower intercept.
We did notice a peculiar phenomenon in light-weight concrete.
The ultimate stresses in cylinders identified as "A" and "B" were
approximately the same.
Two sets of nine cylinders, of diameter-to-height ratios of 0.5
and 1.0 cast with light-weight aggregate were cast. They were capped
with sulfur and tested. The strengths were identical again. The
results are shown in Table A7.
The behavior of light-weight concrete seems to be entirely
different to normal-weight concrete, in so far as cylinders of D/H
ratios of 0.5 and 1.0 are concerned. The established difference of 15
percent in D/H ratios of 0.5 and 1.0 for normal-weight concrete is not
noticed in light-weight concrete.
5.2 Mechanical Properties of Cylinders with Varying Diameter- to-
Height Ratios
The stress-strain data are presented in Tables A8 to A14. These
cylinders were taken from Set 3.
The plots of axial stress vs. axial strain and axial stress vs.
lateral strain are presented in Figures 9 through 21.
Modulus of elasticity, E, and Poisson's ratio are found at
0.45fc. The results are tabulated on the next page.
23
D/H Modulus of Elasticity, E, psi Poisson's Ratio
0.16 4.8 E +06 0.21
0.19 4.9 E +06 0.22
0.23 5.1 E +06 0.23
0.31 5.2 E +06 0.25
0.45 5.3 E +06 *
0.85 5.4 E +06 0.22
* Lateral strain gage malfunction.
The standard sulfur-capped 3-in.-by-6-in. cylinder cast in a
paper mold gave a modulus of elasticity value of 5.1 E +06 psi (ACI
formula gives 4.9 E +06 psi), and a Poisson's ratio of 0.22.
The results indicate a significant difference in the modulus of
elasticity with change in specimen geometry, about 11 percent between
cylinders of D/H = 0.85 and 0.16.
Poisson's ratio at mid-height increases from 0.21 at D/H = 0.16
to 0.25 at D/H = 0.31. Lateral strains in the cylinder with D/H =
0.45 could not be determined due to strain gage malfunction. However,
the cylinder with D/H = 0.85 yielded a Poisson's ratio of 0.22, which
does not tally with the trend indicated by the other cylinders.
Newman and Lachance (12) have reported similar results. In general,
the differences in Poisson's ratio and in lateral strain at mid-height
for varying height of specimens is about 16 percent for the concrete
used in the test.
5.3 Beam and Companion Cylinder Specimens
5.3.1 Normal-weight concrete
24
The method of analysis is presented in Appendix B.
The values of df/dG and dm/dG are computed using the first
derivative of the equation of the curve of best fit for the plots of f
vs. € and m vs. 6. A quadratic regression analysis was done (Tables
A16 and A17), and the residuals indicate that the predictive equations
are satisfactory.
The compressive stresses at the inner face of the beam, computed
from an average of the two stress values obtained from the equations
fc = 6 ( df/dt ) + f,
and fc = 6 ( dm/d€ ) + 2m,
are presented in Table A15. Hence, compressive strain, 6, can be
plotted against fc (average) (Figure 22).
A standard sulfur-capped 3-in.-by-6-in. companion cylinder cast
in a paper mold was also instrumented and tested. The stress-strain
data are presented in Table A18. These stress-strain values are also
plotted in Figure 22. Ultimate stress values of all the companion
cylinders (including the one which was instrumented) are presented
below:
CylinderSet
Ultimate load,
P. lb.
Area, A,
sq. in.
Stress,P/A,
Mean, Std.
Dev. ,
psi psi psi
1 54400 7690
2 59000 8350
3 53400 7.07 7550 7870 350
4 55800 7890
The final compressive stress in the beam that could be computed
from the available data was at a major load , PI, of 115000 lb. A
25
reasonable procedure to find the ultimate compressive stress would be
to extrapolate the preceding data. The differences indicate that the
ultimate compressive stress in the beam would be (7260 + 70) equal to
7330 psi. This is a 7 percent reduction from the ultimate compressive
stress of the 3-in.-by-6-in. cylinders.
This percent value does not reflect the predicted "true" uniaxial
compressive stress value, which was found to be about 15 percent lower
than the ultimate compressive strength of cylinders with D/H
approximating 0.5.
There are two factors for this, namely, (a) the difference in
strengths of cylinders cast in cardboard and paper molds PVC molds;
and, (b) the test region in the beam was 5 in. by 5 in. by 16 in.,
giving D/H value of 0.31.
From Table Al. it may be observed that reduction for factor (a)
above is about 2.2 percent, and the additional reduction for factor
(b), from Figure 3, is 10 percent. This adds up to an additional 12.2
percent, over and above the 7 percent already shown, making a total
reduction of about 19 percent of the compressive strength of the
standard cylinder.
Hence, it may be reasonably argued that the reduction in
compressive strength is a valid proposition, and a reduction of about
15 percent is not at all unreasonable.
5.3.2 Light-weight concrete
Computations similar to those made for the beam specimen made
with normal-weight concrete are presented in Tables A19 through A21.
Stress-strain data for a companion cylinder is tabulated in Table A22.
26
Results for all the companion cylinders are presented below.
Cylinder # Ultimate load, Area, A, Stress, Mean, Std.
P, lb. sq. in. P/A. Dev.,
psi psi psi
1 40200 5690
2 41900 5930
3 40900 7.07 5790
4 43200 6110
5 44000 6220
5950 220
However, the value computed for ultimate compressive strength in
the beam is 7220 psi, greater than the compressive strength of 5950
psi computed in the standard 3-in.-by-6-in. cylinders.
Numerical computation seems to be correct. The raw data also
look good, and so do the polynomial curve-fits. The reason for this
apparent anomaly is not clear.
27
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
The test results of Cylinder Sets 1 through 5 cast in normal-
weight concrete indicate that the strength of concrete determined by
the standard cylinder test is higher than its strength in truly
uniaxial compression by some 11 to 17 percent, based on linear
regression analysis. When the data from Cylinder Set 2 are subjected
to a segmental linear regression analysis, the correlation coefficient
improves, and the standard cylinder strength becomes 17 percent higher
than the estimated strength in unconfined compression. The data from
Cylinder Set 5 also appear to be segmental.
The apparent discontinuity in the slopes of these two data sets
is not understood. The bearing surfaces of the cylinders of both sets
were lubricated with powdered tetraf luoroethylene, but it is not clear
that that fact is all or part of the cause of the anomaly. Further
research is necessary if it is to be understood.
Test results for Cylinder Set 6 cast in light-weight concrete
indicate a reduction of 11 percent, based on linear regression
analysis. Based on a segmental linear analysis, the reduction is 17
percent, with a corresponding improvement in the correlation
coefficient. Replicate testing indicates that the anomaly is real,
but the cause is not yet clear.
Apparently, the strength of concrete in truly unconfined
compression is of the order of 85 percent of the strength determined
from standard cylinders tested in accordance with ASTM C39 (1).
In the case of normal-weight concrete, ultimate stress determined
28
in the Hognestad-Hanson-McHenry structural element compared well with
the estimated strength in unconfined compression. In the case of
light-weight concrete, the ultimate stress was significantly higher
than the estimated strength in unconfined compression. Again, the
apparent anomaly in the latter case is not understood, and further
work is needed to clarify it.
The measured secant modulus of elasticity is affected
significantly by specimen geometry. In this instance, an increase in
aspect ratio of three resulted in a reduction of about 10 percent in
the secant modulus. Over the same range of aspect ratio, Poisson's
ratio varied between 0.21 and 0.25.
The evidence presented here strongly suggests that standard test
methods for determining the strength of concrete in compression and
the secant modulus of elasticity are significantly unconservative for
normal-weight concrete, though not necessarily so for light-weight
concrete. It is recommended that research be continued to explain the
anomalies encountered, to identify and explain other anomalies, and
ultimately to generate an extensive data base as a significant
resource for review and revision of methods of test and design codes.
29
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APPENDIX A
TABLES
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APPENDIX B
METHOD OF ANALYSIS OF DATA FOR BEAM SPECIMENS
75
METHOD OF ANALYSIS OF DATA FOR BEAM SPECIMENS
In 1955. Hognestad, Hanson, and McHenry (23) outlined a criterion
for ultimate strength design. Their work was later accepted as a
basis for formulating the American Concrete Institute recommendations
for ultimate strength design (ACI Standard 318-77).
Their study involved determining the stress block, and the
factors Kl, K2, and K3 which define it. They also defined stress at a
particular fiber as a function of strain, starting from basic
assumptions of structural mechanics.
They used a C-shaped structural element similar to the one
illustrated in Figure Bl.
In the above-mentioned publication, equations defining stress as
a function of strain are given as follows:
fc = 6 ( df/d€ ) + f, and
fc = € ( dm/dG ) + 2m, where
f = ( PI + P2 ) / be. and
m = ( Pl.al + P2.a2 ) / bc~2.
The symbols used above are defined as follows:
fc : concrete compressive stress in extreme fiber of the beam;
G : concrete strain in extreme fiber of beam;
PI : major thrust;
P2 : minor thrust;
al and a2 : lever arms.
(Refer to Figure Bl for physical interpretation of the
nomenclature.
)
76
The reinforcement detail is shown in Figures B2 and B3. The
loading frame along with location of the hydraulic ram and load cell
are shown in Figure B4.
In our investigation to determine the unconfined compressive
strength of concrete, we used a specimen (referred to as the beam
specimen throughout the body of the text) as illustrated in Figure Bl.
The method of analysis was that developed by Hognestad, Hanson, and
McHenry (21).
77
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Figure B2 : Plan(Showing Reinforcement Detail)
79
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80
Figure B4 : Loading Frame to apply minor load, P2,
81
APPENDIX C
BIBLIOGRAPHY
82
BIBLIOGRAPHY
1. ASTM Annual Book of Standards, current edition.
2. Foeppl, A., "Mitteilungen aus dem Mech.", Tech. Lab. der KoenigsTech. Hochschule, Munchen, Hefte 27, 1900.
3. Gonnerman, H.F., "Effect of End Condition of Cylinder in
Compression Tests of Concrete", Proceedings, American Society for
Testing and Materials, Volume 24, Part II, 1924, pp. 1036-1063.
4. Gonnerman, H.F., "Effect of Size and Shape of Test Specimen onCompressive Strength of Concrete", American Society for Testing andMaterials, Proceedings, Volume 25, Part II, 1925, pp. 237-250.
5. Troxell, G.E., "The Effect of Capping Methods and End ConditionsBefore Capping Upon the Compressive Strength of Concrete TestCylinders", Proceedings, American Society for Testing and Materials,Volume 41, 1941, pp. 1038-1044.
6. Johnson, James W., "Effect of Height of Test Specimens onCompressive Strength of Concrete", Bulletin, American Society forTesting and Materials, Number 120, January, 1943.
7. Tucker, J., "Effect of Length on the Strength of Compression TestSpecimens", Proceedings, American Society for Testing and Materials,Volume 45, 1945. pp. 976-984.
8. Mather, B., "Effect of Type of Test Specimen on Apparent CompressiveStrength of Concrete", Proceedings, American Society for Testingand Materials, Volume 45, 1945, 802-809.
9. Price, W.H., "Factors Influencing Concrete Strength", PRoceedings,American Concrete Institute, Volume 47, 1951. pp. 417-432.
10. Neville. A.M., "The Influence of Size of Concrete Test Cubes onMean Strength and Standard Deviation", Magazine of Concrete Research,London, August, 1956, pp. 101-110.
11. Werner, G., "The Effect of Capping Material on the CompressiveStrength of Concrete Cylinders", Proceedings, American Society forTesting and Materials. Volume 58, 1958, pp. 1166-1181.
12. Newman, K., and Lachance, L., "The Testing of Brittle Materialsunder Uniform Uniaxial Stress", Proceedings, American Society forTesting and Materials, Volume 64, 1964, pp. 1044-1067.
13. Hughes, B.P., and Bahramian, B., "Cube Tests and UniaxialCompressive Strength of Concrete", Magazine of Concrete Research,Volume 17, Number 53. December. 1965.
83
14. Kupfer, H., Hilsdorf, Hubert K., and Rusch, Hubert, "Behavior of
Concrete Under Biaxial Stresses", American Concrete Institute
Journal, Volume 68, Number 8, August, 1969.
15. Seibel, E., and Pomp, A., "Die Ermittlungen der Formanderungsfest-igkeit von Matallen durch den Stanchversuch Mitt.", Kaiser-WilhelmInstitute, Eisenforsch, Dusseldorf, Volume 9, 1927, p.157 (as
reported by Timoshenko, S., in "Strength of Materials, Part II",
0. Van Nostrand and Co., Inc., Princeton, N.J., N.Y., 1958).
16. Schickert, G., "On the Influence of Different Load ApplicationTechniques on the Lateral Strain and Fracture of ConcreteSpecimens", Cement and Concrete Research, Volume 3, 1973,
pp. 487-494.
17. Basunbul, Islam Ahmed, "The Influence of End Friction and Length-to-Diameter Ratio on the Behavior of Concrete Cylinders", Ph.D.
Dissertation, University of California, Davis, 1981.
18. Davin, M.. "Remarks on the Compression Test with Rubber Caps",
International Union of Testing and Research Laboratories for
Materials and Structures (RILEM), Bulletin, Number 32, 1956,
pp. 49-57.
19. Hansen. H., Nielsen, K.E.C., Kielland, A., and Thau low, S.,
"Compressive Strength of Concrete — Cube or Cylinder", Bulletin,RILEM, Number 17, December, 1962, pp. 23-30.
20. Sigvaldason, O.T., "The Influence of Testing MachineCharecteristics upon the Cube and Cylinder Strength of Concrete",Magazine of Concrete Research, Volume 12, Number 57, December,1966, pp. 197-206.
21. Mills, Laddie L., and Zimmerman, Roger M., "Compressive Strengthof Plain Concrete Under Multiaxial Loading Conditions", AmericanConcrete Institute Journal, Proceedings, Volume 67, Number 10,
October, 1970, pp.802-807.
22. Farrar, N.S., "The Influence of Platen Friction on the Fracture ofBrittle Materials", Journal of Materials, JMLSA, Volume 6, Number4, December 1971. pp.889-910.
23. Hognestad. E. . Hanson, N.W.. and McHenry, D.. "Concrete StressDistribution in Ultimate Strength Design", Journal of the AmericanConcrete Institute, December, 1955, pp. 455-479.
24. Nikaeen, A., "The Production and Structural Behavior of High-Strength Concrete", M.S. Thesis, Kansas State University, 1982.
25. Burmeister, R.A. , "Tests of Paper Molds for Concrete Cylinders",Proceedings, American Concrete Institute, Volume 47, 1951, p. 17.
84
ACKNOWLEDGEMENTS
The author wishes to express his sincere appreciation to Dr.
Cecil H. Best, under whose guidance this study was carried out, and to
Dr. Stuart E. Swartz and Dr. Albert N. Lin for their helpful
criticism.
Sincere thanks are also due to Dr. Robert R. Snell, Dr. James K.
Koelliker, Dr. Fredric C. Appl, Messrs. Gary Thornton. Russell L.
Gillespie, Brian Holle, Ali Nikaeen, and Ms. Peggy Selvidge. Dr.
Snell provided office and laboratory space, equipment, and a portion
of the funding. Dr. Koelliker provided instruction and guidance in
the use of microcomputers and software. Dr. Appl made his research
diamond-tooled lathe available, and Mr. Thornton instructed the author
in its use and crafted the steady-rest needed in the facing of longer
specimens. Mr. Gillespie taught the author to machine the PVC
cylinder molds, to refit elements of the loading yoke for the beam
specimens, and to weld the reinforcing bars for the beam specimens.
Messrs. Holle and Nikaeen, fellow graduate students, helped the author
in experimental work. Ms. Selvidge gave invaluable guidance relative
to Graduate School rules and regulations in general, and to thesis
requirements in particular.
Major funding for the project was generously provided through
grants from Ash Grove Cement, Buildex, and Dudley Williams &
Associates, and through contributions to the KSU Foundation from C. H.
Best, D. W. Kershaw, Kershaw Ready-Mix Concrete & Sand Company, and
Professional Engineering Consultants, P.A.
85
AN INVESTIGATION INTO THEUNCONFINED COMPRESSIVE STRENGTH OF CONCRETE
by
BISWAJIT MUNSHI
B.E. , University of Calcutta, 1978
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
1987
ABSTRACT
The standard cylinder test (ASTM C39 : Standard Test Method for
Compressive Strength of Cylindrical Concrete Specimens — Annual Book
of ASTM Standards Section 4 - Construction) is used universally to
determine the uniaxial compressive strength of concrete.
However, the value of ultimate compressive strength obtained from
the standard uniaxial compression test, is, in fact, higher than the
true strength of concrete in uniaxial compression.
It is generally believed as a result of the work of several
investigators throughout this century that the strength in uniaxial
compression of cylindrical test specimens is significantly affected by
the end frictional conditions and the geometry of the specimen.
The present investigation was designed to develop a method for
determining the strength of concrete in truly unconfined uniaxial
compression and to test the method in the context of a design
application.
A coincidental part of the investigation was to study lateral and
axial deformational charecteristics and other mechanical properties
for specimens with different geometries.
Results from this work show that apparently the strength of
concrete in truly unconfined compression is in the order of 85 percent
of the strength determined from standard cylinders tested in
accordance with ASTM C39.