DELFT UNIVERSITY OF TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
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Report 5-78-10
Static and dynamic testing of
concrete beams reinforced with
fibres and continuous bars
Ir. H.A. Körmeling
Prof. dr. ing. H.W. Reinhardt
Prof.dr. S.P. Shah
STEVIN LABORATORY
CONCRETE STRUCTURES
B e t o n
7 8 - 0 5
Stevin Laboratory
Stevinweg 4
2628 CN Delft
The Netherlands
Research nr. 1.2.76.09
March 1979
Technische Hogeschool Afdeling: Civl !e TechniekSteviuv;'L'3 1 poGlbas 5348 2600 GA Delft
/ qaXerLj
static and dynamic testing of concrete beams
reinforced with fibres and continuous bars.
Ir . H.A, Körmeli ng
Prof.Dr.-Ing. H.W. Reinhardt
Prof.Dr. S.P. Shah
No part of this report may be published without written
permission of the authors.
Contents
Preface Summary
List of notations
1 Testing of steel bar reinforced steel fibre concrete 1.1 Scope and objective
Test program Specimens
Static test equipment Dynamic test equipment Measuri ng
Control tests
Results and conclusions of the static tests
2.1 Results and discussion of the static tests 1 Compression test
2 Stress-strain curves
3 Beams without fibres and with fibres
4 Beams with 2 bars 0 4 without fibres and with fi bres
5 Beams with 4 bars 0 6 with fibres
6 Beams with 4 bars 0 10 without and with fibres 7 Load vs total crack width
8 Load vs max. crack width 9 Crack distance
10 Crack width and crack distance
The contributions of steel bars, steel fibres and concrete to the internal moment
Conclusions of the static tests
Results and conclusions of the dynamic tests 3.1 Introducti on
Results of the dynamic tests
Discussion of the results of the dynamic tests Crack width
Crack spacing
Conclusions of the dynamic tests 1.2 1.3 1.4 1.5 1.6 1.7 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.2 2.3 3.2 3.3 3.3.1 3.3.2 3.4 References Appendix
Preface This ri ed S.P. al mos prof e whi ch were n e e r i p a n y i D i V i s The t of th super work were The a gram searc 1 nves out i Shah t a y ssor. he g carri ng De ng te ion 0 est s e Roy V i s i 0 i n t h made u'thor for t h Gra t i g a t i 0 n c l o s e from Un ear at Before uided 1 ed out partmen sts on f Mater pecimen al Duch n of i n e beam by Th.A s would hei r en nt No . n on coop i V e r s D e l f t h i s a t e r i n th t , Di t h e m i al s s h a s M i l i g . A . tests • Stey like coura 1501 fibre erati ity 0 Uni V stay, on at e Ste vi si 0 ateri of th been tary H. Ve was n. to t gemen is al rei nfor on of se f n i i n o ersity o he has Delft. vin Labo n of Con al prope e Civil manufac Academy rhagen . performe ced cone veral pa is at Ch f Techno i ni ti ate The test ratory o Crete St rties we Engineer tured by (KMA) , B Most of d by A.v hank al1 parti ci t. Fi nanci al sup so gratefully ac
rete has been car-rti es . Prof .Dr . icago Circle spent logy as a visiting d the test program s reported here f the Civil Engi-ructures . Accom-re done by the ing Department.
the Laboratory reda, under the the experimental
.Rhijn, the drawings pants in this pro-port by Nato Re-knowledged.
SUMMARY
The main purpose of the testing program was to get an idea
about t h e i n f l u e n c e of steel fibres on the fatigue performance
of conventionally reinforced concrete beams. The influence of
three types of steel fibres with three various percentages on
the failure load, the cycles to f a i l u r e , the crack width and
the crack spacing should be investigated. Because it was
ex-pected that the effect of the fibres would vary with the
amount of steel bar r e i n f o r c e m e n t , three different
reinforce-ment ratios were applied. In order to can relate the results
most of the tests were carried out statically and dynamically
as w e l l . Each fatigue test had a constant amplitude.
The types of fibres used, were a straight one, a hooked one and a straight
one with paddles on both ends.
The percentages of fibres were 1 . 4 1 % , 0.89%, and 1.53%, by
volume respectively, and, as a r e f e r e n c e , non fibre reinforced
concrete was used. Besides the f i b r e s , continuous bars were
used as reinforcement. The steel quali ty was a FeB 500 Hi-bond
with diameters of 4 , 6 or 10 mm. The reinforcement ratios w e
-re a low one ( 0 . 1 7 % ) , a medium one (0.75%) and a high one
(2.09%) resulting in 2 0 4, 4 0 6, and 4 0 10 respectively.
The results of the static test showed a remarkable increase
in ducti1i ty. The addition of fibres to reinforced concrete
increased the ultimate moment and reduced crack width and
crack spacing. The benificial effects of the fibre addition
seemed to be proportional to the volume aspect ratio pl/d.
In the dynamic tests the fibre reinforcement has increased
the number of cycles to failure. This influence is more
List of notations
a crack spacing m m
b depth of the beam m m
c cover m m
d fibre diameter m m
h height of the beam m m
h-, lever arm m m
1 length of the beam m m
p volume percentage of fibres
%
pl/d volume aspect ratio
%
w crack width mm
X height of the compressive zone m m
Ag cross section area of steel bars m m ^
E(- modulus o f elasticity of concrete N / n m ^
Eg modulus of elasticity of steel N / m m ^
M Q ^ internal moment for concrete in tension NmmMg internal moment for steel Nmm N^^ concrete compressive force N N(,t concrete tensile force N '^fct fibre concrete tensile force N
Ng steel force N'
P load N
Ec compressive s t r a i n f o r concrete %o
£5 t e n s i l e s t r a i n f o r steel %o e^ t e n s i l e s t r a i n f o r concrete %o 6^ centre d e f l e c t i o n of the beam mm a^^ t e n s i l e stress of f i b r e concrete N/mm^
X curvature of the beam 1/mm 0) reinforcement r a t i o %
9
-afd. Civ'ie!3 Technirïk T.H. Stevinv,'3g 1 - D a l f t T E S T I N G OF S T E E L BAR R E I N F O R C E D S T E E L F I B R E C O N C R E T E B E A M S S U B J E C T E D T O S T A T I C A N D D Y N A M I C L O A D I N G .
1.1
S c o p e and o b j e c t i v e W h e n r ted to c r e a s e the pr to cal 1i kely wi dths T h e pr dy the ti onal f o r c e d m e n t : me use i n p r a m i n i m u f e r e n t h o o k s S o m e 0 1 o a d i n amp!i t Duri ng ti on , 46 b e a ei n f o cycl wi th eci se cul at t h a t and i m a r y infl ly re wi th 0.17, d cor cti ce m amo type at th f the g to ude f both curva ms (2 reed i c 1 0 the natu e the the defle obje uence i n f 0 r t h r e 0.75 respo and unt u s of ei r e se be f ai 1 u a t i g u S t a t ture 7 in and adi n i ncr re 0 se q addi cti 0 cti V of ced e di and nds the sed fibr nds ams re ( e 1 0 i c a and dyna prest g, th eased f sue u a n t i ti o n ns u n e of f i bre concr f fere 2.09 to a 1 owes i n th es we and f were stati adi ng nd dy crack m i c a ress ei r num h i n ti es of s der the s on ete nt V per bout t vo e CU re u i bre subj c 1 0 up nami wi d nd 1 ed c defl ber crea are tee! fati rese the beam ol urn cent the 1 ume rren sed: s wi ecte adi n to a c 1 0 th w 9 in oncrete ecti ons of 1oad se i s n not ac fibres gue loa arch re f a t i g u s. C o n e es of c by vol maxi mu is sub t des i g strai g th padd d to mo g ) w h i 1 b o u t on adi ng , e r e mad stati c s t r u and r e p e ot kn c u r a t will d i n g . p o r t e e beh rete o n v e n ume . m a m o s t a n t n p r a ht fi les a n o t o n e oth e mi 1 m e a s u e. A 1 oad e t u r e s a r e s u b j e e c r a c k w i d t h s i n -t i -t i o n . A l -t h o u g h own and the m e t h o d ely k n o w n , i t i s r e d u c e t h e c r a c k d h e r avi ou b e a m s t i 0 n a T h e h u n t n i a 11 y c t i c e b r e s , t the i c a 11 e r s t 1 i on r e m e n total i n g ) e w a s t r of CO w e r e r 1 r e i n f i g h e s t o r m a l l y b e ! ow . T h r e e f i b r e s ir e n d s y i n c r e 0 a con cycl es . ts of d of a b o w e r e te 0 stun v e stun -ei no r c e -vol u-used the d i f -wi th asi ng s t a n t ef 1 ec' ut s t e d . 1.2 T e s t p r o g r a m C o n c r e t e b e a m s w e r e 1 0 0 m m w i d e , 1 5 2 m m d e e p and 2 2 0 0 m m l o n g . They w e r e t e s t e d in f o u r - p o i n t l o a d i n g w i t h a s p a n of 2 0 0 0 m m and w i t h a c o n s t a n t b e n d i n g m o m e n t z o n e o f 8 0 0 m m . All t h e m e a s u r e m e n t s w e r e r e s t r i c t e d to t h e c o n s t a n t m o m e n t z o n e . T h e±
800i^
I
20001 1
1 1 1 ! F i g . 1 R e i n f o r c e m e n t d e t a i l sconventional reinforcement consisted of (FeB 500 Hi Bond steel) continuous deformed bars with diameters of 4,6 or 10mm.
Three different reinforcement ratios of 0.17, 0.75 and 2.09% were provided by using 2 bars of 4mm diameter (2 0 4 ) , 4 bars of 6mm diameter (4 0 6) or 4 bars of 10mm diameter (4 0 1 0 ) . To assure moment failure, shear reinforcement was provided in the shear-zone. The reinforcement details are shown in fig. 1. Beams with each reinforcement ratio were tested in static and dynamic loading. For each ratio, beams were made with concrete containing either no fibres or 3 different types of fibres shown in fig. 2. The volume percent of straight fibres, fi b r e s
hooked s i : — i |— d = O.Amm pl/d =69 straight d=0.4mm pl/d = 76 h r H 50 31 mm 2A mm mm 2.5 — H H paddled | ^ — ^ ^ — ^ d=0.8nnm A pl/d=96 F i g . 2 F i b r e t y p e s
with hooks, and fibres with paddles were respectively 1.41, 0.89 and 1.53%. These amounts were chosen so that concrete made with these fibres had comparable workability. The static and dynamic tests were also carried out for beams containing fibres but no conventional steel. The scope of the test program of the beams can be seen in Table A IV.
The static and dynamic tests were carried out in different test frames .
The dynamic loading test frame was specially designed to enable testing simultaneously of 4 different beams with only one pul-sator (fi g . 3) .
The load on each beam was measured through a load cell. The frequency of loading was about 3 cycles per second. For dynamic loading, the measurements were made after 1, 1 0 , 100, 1000, 10.000, 50.000, 100.000 and then every 100.000 cycles up to about one million cycles. Measurements were also made at the beginning and the end of the working day.
The d e f l e c t i o n s were measured j u s t b e n e a t h t h e l o a d p o i n t s and a t t h e c e n t e r w i t h d i a l gages w i t h a s c a l e g r a d u a t i o n o f 0.01mm the s t r a i n s on the top and the bottom of the beams
front-view
1 t e s t frame
8 load d e v i d i n g beam
10 hinge 11 load cell 55 testbeam 56 dynamic jackside-view
F i g . 3 Dynamic t e s t i n g equipment
were measured by extensometers (containing electric resistance strain gages) fixed between glued points on the top and bottom surfaces of the beam. (fig. 4)
2200
4x7A , 296 _
-"T T
^— -im -vmi i*Y •*•• ** f 1"^ *•!• 1 * * T* • —^^ • — —
Top view 1100
TE:
^j a
±
s:
500 ^'- 300J^
300 500 Side view 5x70 350'tAAAjyiTLruTLriJ
Bottom viewFig Scope of measurements on the beam
To aid in crack detection, beams were white washed.
Crack widths were measured with an i11 uminated microscope with a scale division of 0.01mm. The crack widths were measured on one side of the beam at distance of 10mm from the bottom sur-face. This was the location of continuous rebars . Cracks were marked with black lines after each loading step. At the end of the test the beams were photographed.
To controle the concrete quality cubes and cylinders were tes-ted in compression. For each diameter of reinforcing bars ten-sile stress-strain curves were made. (Appendix fig. A 17 - A 22)
Specimens
The specimens were cast in groups of six in wooden moulds. The two outer beams were provided for static testing, the middle four ones for fatigue testing. The premixed aggregate, the cement and the water was mixed in a vertical mixer after which the fibres were added. The hooked fibres were cast in the mix all together (producers a d v i c e ) , the straight and paddled ones were distributed by hand.
For the concrete mix a premixed aggregate of round coarse ma-terial (maximum diameter 16mm) and sand was used. The sieve analysis data of the aggregate are presented in Fig. A 23 and the slump, aircontent and compaction index in table A VII. The cement used was a portland A cement (Dutch standard) from one batch. The water to cement ratio was 0.48 while no plasticizers were used (see table A VIII).
Different amounts of three types of steel fibres were added to the concrete mix. The first type was a straight fibre, the second type was hooked at the ends, and the third one was
straight with paddles at both ends of the fibre.
IOOL 600 800 50 8x75 -,' q .l^^-^H^'m^l A01O B 3 *
w
'^ 1 50i
Ri/inn t 1*1* ^ <fiU . / 4 0 6B2
•ail 50i4=
6x100 , '81
0A /Fig. 5 Reinforcement types
Except these fibres steel bar reinforcement was used in a cer-tain number of specimens. Steel quality was FeB 500 Hi-Bond steel with diameters of 4, 6 and 10mm. The combinations made with plain concrete, fibres and steel bar reinforcement are presented in table A IV.
2 bars 0 4, 4 bars 0 6 or 4 bars and medium (0.75%) and a high (2 fibre types are shown in figure fi gures 5.
0 10 resulted in a low (0.17%) .09%) reinforcement ratio. The 2 , the reinforcement types in
The moulds were filled while the table vibration was acting.
The vibration was transfered in the 152mm direction, obtaining
in this way a more horizontal orientated m j r e distribution.
T T m ü l t T n e o ü s l y with the beams cylinders 1 0 150-300mm and 400mm)
were cast for obtaining stress-strain curves in compression.
^The cylinders were compacted in the same manner.
After casting the beams were kept in their moulds for ten days
covered with wet burlap. ^ Q
The temperature varied between 6 and 12 C.
After the demoulding the beams were covered with plastic foil
until transportation took an advance to Delft University. Un-^
til testing the specimens were kept in a moist room
X^ST
h u m i d i T y T
1.4 Static test equipment
the complete stress-strain curves
closed loop testing machine. In
testing machine an input function (such as a
rate of the specimen axial strain) is fed to
unit. The controlling unit compares the output
the input function and minimises the difference
through an adjusting amplifier. This amplifier regulates the
hydraulic system of the testing machine.
For the compression test,
were obtained by a 2000 KN
a closed loop
predetermi ned
a controlling
function with
It was decided to use the central strain of the specimen as a
controlling function. The axial strains of the specimens were
measured by an inductive device shown in fig. 6.
1
-*-T
T
o
o
i^L
The strains were measured over a gage length of 200mm and the displacement transducer was designed s o , that the actual dis-placements were magnified two times. When this central strain was used as the controlling parameter (the rate of the strain was kept constant at 50 microstra in per minute) all fibre reinforced concrete specimens failed in a controlled manner. During the test the bottom plate of the testing machine was fixed and the top plate was hinged.
Fig
Static testing equipmentmachine was designed for the static flexural steel Another testing
test (fig. 7 ) .
The test beam was supported at the bottom ends on small frames ( A ) . These frames were connected with steel bars (B) on the main frame ( C ) . The load was applied in the third points of the beam via small steel frames (D) connected with steel bars (E) on a loading beam ( F ) .
In the centre point of this loading beam a HP 20-10/200 10 tons (100 KN) capacity hydraulic jack (G) was placed.
To measure the forces a 100 KN
the loading beam and the jack.
The jack was hand-controlled. The
bed in chapter 1.6.
load cell (H) was fixed between
measurement system is descri'
1.5 Dynamic testing equipment
To save testing time, a dynamic testing equipment (fig. 3) was
develloped in which four beams could be tested with one
pulsa-tor at the same time. The maximum allowable frequency of the
whole system appeared to be three cycles per second. Two 20
tons (200 KN) hydraulic jacks connected with the pulsator
could manage two beams each. Because of the fact that
each beam needed its own maximum load, a load deviding system
was constructed (fig. 8) .
s
I'
Fig. 8 Load deviding system for beams in the dynamic test
The load deviding beam, on both ends connected with the test
beam frames could be loaded in any desirable point between the
ends by moving the jacks in a horizontal way.
The top-and the bottom side of the jacks were hinged.
In the hinged connection between the load deviding beam and
the test beam frame a 100 KN dynamic load cell was fixed for
measuring the loads. These load cells had a stiff connection
with the test beam frames from which both ends steel bars were
connected with the third points of the test beams.
Starting the dynamic loading, depending on the desired
amplitu-d e , 200 till 500 cycles were necessary to reach the appropriate
values. Stopping the machine took only a few cycles extra.
1.6 M e a s u r i n g
In the static test and the dynamic test as well the same measu-rements have been made. Only in the dynamic test the number of cycles till failure is an extra measurement. The other measure-ment concerns:
- load history - deflection - extension
- crack width, crack depth - crack distance
In the static test the load was applied in small steps in such a way that the first cracks appeared after three of four steps and the failure occured after nine or ten steps.
In the dynamic test the maximum load was applied on the beams in about five steps. The first ten cycles and the first 100 cycles were applied by hand-control after which the pulsator machine took over the job.
In static the measurements have been made after every step,
in dynamic only after 1, 10, 100, 1000, 10.000, 50.000, 100.000, 200.000 etc. Extra measurements were made in the beginning and at the end of the (working) day. All measurements were regi-strated by hand and written down on recording charts.
The force was measured with 100 KN (dynamic) load cells. In the dynamic test these load cells were connected to a oscilloscope for controlling force and amplitude.
The deflecti on measurement was situated beneatch the loading poinTs in the 800mm observati^on _zone at a distajice of 600 mm q^f the bearing points and in thje centre point'using 40mm dial jag^es with a scale graduation "óf O.Ö'lmm '
The gages were fixed on a metal frame with a span of 2000mm on the topside of the beam. One of the supports of the beam was fixed, the other hinged. For the extensi on measuring in the static test eight 74mm gange 1ength electri c extensometers we-re fixed at the top side of the beam between 9 points glued on the beam.
On the bottom side 10 electric extensometers with a gange length of 70mm were fixed. In the dynamic test only three electric
extensometers ( gage length 100mm, 150mm, 100mm) were used at the top side and only three ( gage length 100mm, 100mm, 100mm) on the bottom side (fig. 4 ) .
The development of crack width was controlled with the aid of a microscope with a scale division of 0.01mm. Cracks up to 2mm could be measured in this way. These microscope was built in the laboratory.
To recognise cracks in an early stage the beams were white washed. Cracks of 0.005mm could be detected by eye. All the
cracks were marked with black lines just beneath the crack to make the measurement easier. The development of crack depth was registrated on the beams by putting the scan number at the maximum observed depth. All the crack measurements were made on one side of the beams at a level of 10mm above the bottom, according the depth of the reinforcement bars (if applied). Crack distances were measured with a rule and were registrated.
All the deflection, force and extension data were fed to
punch-tapes for computer processing later on.
All beams have been photographed after the test to record the
crack depth development and the crack distances.
1.7 Control tests
To check the behaviour of the concrete in compression
stress-strain curves of cylinders 0 150-300 or 400mm have been m a d e .
From these curves the compression strength and the Young's
modulus could be determined.
These curves were produced with a deformation controlled
com-pression testing machine. By means of an extensionmeter the
extension in the middle zone of the cylinders was measured.
The strain rate was kept at 0.2%/minute. The age of the
speci-mens was 6 month. Data are given in appendix A 17 - A 23, A IX.
Uniaxial tension tests have not been made. The splitting tests
on cubes did not result in reliable data.
For the steel bars stress-strain curves have been determined,
A 16, A VI.
RESULTS AND CONCLUSIONS OF THE STATIC TESTS
2.1
Results and discussion of the static tests
2.1.1 Compression test
The results of the compression tests on cylinders 015O-3OOmm
and 015O-4OOmm are given in table A IX. Looking to the load
con-trolled test on cylinder 015O-3OOmm a difference can be noticed
between the plain concrete specimens and the fibre concrete
specimens.
The fibre concrete specimens are 1.1 till 1.25 times stronger
than the plain ones. The difference between the straight and
the hooked fibres is very small. The paddled fibre concrete
has a higher compressive strength.
Also for the 015O-4OOmm cylinders there is a difference between
the plain and the fibre concrete specimens.
The hooked fibre specimens gave rather low values for the
com-pressive strength, the other types behave b e t t e r .
2.1.2 Stress-strain curves
A clearer vision on the behaviour of the fibres in the concrete
during compression can be seen in the stress-strain curves
(fig. 9 ) . When the top load is reached for the plain concrete
60
50
AO
30
20
10
4stress N / m m '
P S I
f
/ / ^ / ^K
te,:-^ ^ ^ , _ ^ " ^ « ^ "^«^N
K^
X jk
^ 1F\^% MM \ ^^4 •1 tQcc\straight (76)
hooked (69)
plain concr.(O)
•9000
6000
3000
Strain
8 xlO
-3Fig. 9 Stress strain curves for compression
specimen the bond between the cement matrix and the aggregates
(sand and gravel) is lost and a failure will occur soon. The
fibres in the concrete start actually their work after the m o
-ment that the first cracks appear.
A large strain capacity can be noticed after reaching the maxi
mum load. This strain capacity can be seen as a function of
the pl/d ratio which is given in parentheses in the figures.
Besides this ratio, the influence of the shape of the fibres has surely an influence. Because of the fact that different volume percentages were used for the different fibre types, the influence of the shape of the fibre can not be determined from these results.
Beams without fibres and with fibres
The difference in behaviour of fibre reinforced concrete beams in comparison with plain concrete beams is shown in fig. A 24. Loading the beams till the top load resulted in a more or less 1 i near behavi our.
At the top load the plain concrete beam fails suddenly. The fibre reinforced concrete beams will reach the cracked stage at a load 40% higher than the static while the ultimate load is 70-80% higher.
After reaching the top load the load will diminish and the
deformation grows. Only the beams with the hooked fibres showed a larger deformation area between the first crack load and the top load.
This can be explained by streching effects of the hooks of the fibres after the first cracks have been appeared.
In het M-x-diagram (fig. A 25) the same phenomena can be noticed. Until the first crack the stiffness in all types of beams is nearly the same. The plain concrete beam fails while the fibre concrete beams show a growing curvature. Here the hooked fibres also show a different behaviour: a growing load over a larger area between first crack load and top load.
Straight and paddled fibres only show a difference in stiffness Conclusions are difficult to make because for this type of beam reinforcement the results are very sensitive for fibre
distri-buti on. .
Beams with 2 bars 0 4 without fibres and with fibres
The influence of fibres on the behaviour of beams with a low reinforcement ratio (0.17%) is illustrated in the P-6 and the M-X-diagrams (fig. A 26, fig. A 27).The first crack loads for beams with fibre addition are 40-50% higher, except for the hooked ones, while the ultimate load can be seen as a function of the volume aspect ratio pl/d. Relative values are given in Table I.
t y p e
f i b r e
hooked
s t r a i g h t
p a d d l e d
p 1 / d
%0
69
76
96
' ' f i r s t
c r a c k
1.0
1.08
1.58
1.50
p
ul timate
1.0
1.03
1.21
1.52
^ f i r s t
c r a c k
1.0
1.07
1.46
1.39
M
L1 timate
1.0
1.09
1.27
1.57
Table I First crack and ultimate strength for fibre concrete related to plain concrete
The hooked fibre concrete beams showed a bad fibre distribution in the failed cross section. Failure was caused always by a failure of the reinforcement steel.
Beams with 4 bars 0 6 with fibres
The difference in stiffness between the different fibre rein-forced beams is not so evident as for the lower reinforcement rati o's.
Between stiffness, ultimate load and pl/d ratio is no clear relation. At the moment of failure a few bars, mostly two, were broken in combination with a beginning failure of the
compression zone. See also fig.A 28 and fig. A 29.
In this test a non fibre reinforced beam was not available.
Beams with 4 bars 0 10 without and with fibres
In f i g . A 3 0 a n d fig. A 31 the results for the highest reinforce-ment ratios are given. The stiffness of the hooked fibre con-crete beams is a little bit smaller than when no fibres were added. The other fibre concrete types have a higher stiffness. The first crack loads are 2 - 20% higher according to a raising pl/d ratio, the ultimate loads are only 1% higher. The paddled fibres with the highest pl/d ratio do increase the ultimate load with 9%.
The failure of this high reinforced ratio beams was always cau-sed by a destruction of the compression zone. For the non-fibre reinforced beam a wedge shaped piece of concrete sprang away. The fibre concrete specimen showed the same wedge, but owing to fibres in the cracked zone the wedge was very difficult to remove.
In table A X a scope of static test data for load, flection and curvature is given.
moment,
de-From the P-6 and the M-X-diagrams for the beams we can see that a raising reinforcement ratio diminishes the influence of the fibres on the maximum load values.
To understand this phenomena we can assume that fibres have only an influence when the fibre volume is larger than a cer-tain amount of the steel bar volume. In the following table II the volumes of the bars and the steel fibres in a beam are gi ven.
In tablelllthe volume ratio of fibres and steel bars is given.
steel bars steel fibres concrete beam
2
4
4
0
0
0
4
6
10 r = 50.27 = 226 .19 = 628.32 = 270 = 390 = 450 = 30000cm
II II II II II n 0.17 0.75 2 0 1 1 100 09 89 41 53 0 vol .%2 0 4 4 0 6 4 0 10 hooked 5.37 1.19 0 .43 strai ght 7.76 1.72 0.62 paddled 8.95 1.99 0.72 In this fibres , / 2 , 12/
Table III Fibre volume/steel bar volume
last table a correction has to be made for the active i.e. from the fibres in the tension zone only 30-50% are active assuming a random distribution.
For the low reinforcement ratios there is an influence of pl/d on the stiffness of the beam till the maximum load has been reached. Higher reinforcement ratios do not show this effect so extremely. Sometimes the fibre concrete seemed to be less stiff thans non fibre concrete. The stiffness behavio-ur behind the top could not be measured because the test was load con-trol 1 ed.
2.1.7 Load vs total crack width (fig. A 32, A 33, A 34, A 35)
Putting fibres in a reinforced concrete beam a remarkable in-fluence is shown in the development of the crack width. For all types of bar reinforcement the larger total crack width is reached for the beams without fibres. The hooked fibres (pl/d= 69) show a better result, followed by the straight fibres
(pl/d = 8 1 ) .
The best behaviour was noticed by the paddled fibres with a pi/d ratio of 96.
The diminishing of crack width with a higher pl/d ratio seems to be independent of the reinforcement ratio. Unless the dif-ference in pl/d ratio, the difdif-ference between the straight and the hooked fibres is not so large probably due to the influence of the hooked ends.
The r e s u l t s o f t h e
P-w
total di ffi cultunreinforced fibre to interpret.
concrete beams are for
2.1.8 Load vs max. crack width (fig. A 36, A 37, A 38, A 39)
Fibres in concrete influence also the maximum crack width. For the same load a remarkable reduction in crack width can be ob-tained within the limit of one reinforcement ratio. The pl/d ratio is a parameter. Raising this ratio, the smaller the crack wi dths will be .
2.1.9 Crack distance (fig. A 40)
In the middle third zone the mean distance between the cracks in the ultimate moment case is determined. For the 2 0 4
reinforced beams the different amounts of fibres and/or the
The higher the pl/d ratio the smaller the distances a r e ,
compa-red with the beams with only bar r e i n f o r c e m e n t .
This difference is in the 4 0 6 case much s m a l l e r . No
compari-son could be made with the pure 4 0 6 reinforced beam because
this beam was not available for the static test. H o w e v e r , we
can assume that a raising pl/d ratio gives smaller crack
dis-tances. The beams with the highest reinforcement ratio show
the same tendency. Only the hooked fibres give a smaller
distan-ce then the straight f i b r e s . They do not follow the pl/d ratio
In table A XI the mean values of the crack distances are given
with the values for a 9 0 % confidence interval.
2.1.10 Crack width and crack distance
For all reinforcement ratios the total crack width will be
diminished. The higher the pl/d ratio is the smaller the total
crack width is.
The number of cracks on contrary shall increase with raising
bar r e i n f o r c e m e n t . A smaller crack width and a smaller crack
distance should be possible for high reinforcement ratios by
increasing the pl/d ratio until the workability is not possible
any m o r e .
2.2 The contribution of steel b a r s ,
the internal moment
steel fibres and concrete to
In a cross section of a beam the external moment must be in
equilibrium with the internal m o m e n t . Contribution to the
in-ternal moment can be expected from the steel b a r s , the steel
f i b r e s , the uncracked concrete in tension and the concrete in
c o m p r e s s i o n . A collaboration between steel bars and c o n c r e t e ,
the tension s t i f f e n i n g , may cause a stiffer behaviour of the
loaded beam, which can be determined from the test r e s u l t s .
For calculation of the internal moment an uncracked and a
cracked stage can be distinguished / 5 , 7, 1 1 , 1 2 / . In the
un-cracked stage the steel bar contribution can be calculated from
the measured top and bottom s t r a i n s , assuming a lineair strain
distribution over the height of the b e a m s . From fig. 10 equations
1 to 4 can be derived.
->^ in II -)^ot
>100
-^ F i g . 10 U n c r a c k e d s t a g eX =
e^^h
et^(h-x-c)
K'=li(1)
(2)
M = N^-Jth, =e;^-)«E^-)tA^-)fhi s s 1 s s s 1 h , = 2/3-jex+(h-x-c)(3)
(4)
In the uncracked stage no difference between fibre reinforced
concrete and non fibre reinforced concrete .behaviour in the
tension zone is assumed. The contribution of the concrete in
tension to the internal moment is given in formula 5.
M =M .-M
c ext s
ct 2/3^h2
(5)
(6)
In the cracked stage a tension crack limit is assumed at a
strain of 0..2%ofor plain concrete.
The stress block in the tension zone will change now according
to fig. 11.
^ 04 ur> ^ CJ ^ ^ X 7 (-^nnnn r v j ^c , / / ^0.2s
^ J 2 0 _ ^
N.
C i
/zL
y
/„
^ct
N.
Fig. 11 Cracked stage
An approximation of N^^ needs now a value for the Young's
modu-lus. From the compression tests a mean value of E=25000N/mm^
can be found. The contribution of the concrete tension zone is
given in formula 7 in which b is the width of the beam.
N _ = Ec^b^^
c t
^ ( 0 . 2 * 1 0 " ^ ) ^ ( 7 ) 2^e M ^= N ^ ( h . - x - X ^ 0.2^10"-^) c t Ct^ I ( 8 ) I n f i b r e r e i n f o r c e d c o n c r e t e t h e f i b r e s i n t h e t e n s i o n zone g i v e a r e a l c o n t r i b u t i o n t o t h e i n t e r n a l moment ( f i g . 1 2 ) . ^ IT) II - / •ut
y
'°°
X
CMX
Nfct
Fig. 12 Cracked stage with fibres
A rectangular stress distribution in the tension zone may be
used assuming a bi-linear pull-out diagram (fig. 1 3 ) . This
diagram consists of the junction of all pull-out diagrams of
the single fibres in the tension zone / I , 8, 1 0 , 1 1 , 1 2 / . The
pure tension contribution of the concrete N . will not be
con-sidered separately but will be a part of the tension
contri-bution of the fibre concrete N ^ ^ . .
f ct
Fig. 13 Assumed pull-out diagram for one fibre
The internal moment now consists of two c o n t r i b u t i o n s , one
of the steel bars and one of the fibres.
M. „. =N^^ .^h„+N^-xh, tot fct 2 s 1 h, =ix+(h-x-c) 1 3
h_ =2x + Hh-x)
L 3 ^ =^S^^S^A3(9)
( 4 ) (10) (11)From formula 9 the fibre influence can be c suits are given in fig. . A41,A42,A43,A44 in w stress ^izX is given as a function of the c ferent reinforcement ratios.
For {jj=2.09% the steel fibre contribution va ter of the steel bar contribution.
In the M-X-diagram's ( f i g . A 4 5 A 4 6 ) the infl on the behaviour of the reinforced concrete as the difference between the non fibre rei and the fibre reinforced ones. Analysing th fibre reinforced beams, a tension stiffenin in the M-X-diagrams as the difference betwe internal moment and the external moment. Th fibres on the tension stiffening is hardly
alculated. The re-hich the mean fibre urvature for dif-nished in the scat-uence of the fibres
beams can be seen nforced beam results e data of the non g effect is visible en the calculated e influence of the to give.
2.3 Conclusions of the static tests
a) The addition of fibres to plain concrete substantially in-creased the ductility. The deformation of the fibre concre-te beams was almost 20 times larger than the deformation of the plain concrete beams.
b)
c)
d)
The addition of fibres to conventionally reinforced concre-te increased the ultimaconcre-te moment. The contribution of the fibres to the ultimate moment (M^J was less, the higher the amount of reinforcement.
u
The addition of fibres to substantially reduces the That means, for a given lo beams with fibres had sma
conventi onally ack width
reinforced concrete crack width.
oad and a given reinforcement ratio, ller total and maximum crack width. The addition of fibres to conventionally reinforced concrete reduces the average crack spacing. The reduction is highest for the lowest reinforcement ratio.
It appears that the benificial effects of fibres is approxi-mately proportional to the parameter pl/d.
e) The reducing effect of fibres on the plain the reduction in deflection or and crack distances.
steel stress will ex-curvature, crack width
RESULTS AND CONCLUSIONS OF THE DYNAMIC TESTS
3.1 Introduction
From the preliminary static tests the ultimate value of the
load could be determinated. In literature / 2 , 3 / a two million
cycle fatigue limit was given for 41 to 4 7 % of the static
ul-timate strength and a 2 ^ 10^ cycle limit for 8 2 . 5 , 90 and 9 5 %
of the static ultimate strength both for fibre concrete without
bar reinforcement. Fatigue data for Hi-Bond steel can be found
from W a s c h e i d t / 4 / for larger diameters then used in our test.
Effect of bar sizes are given in ACI journal march 1 9 7 4 , which
learns that the fatigue strength of bars with smaller diameters
is expected to be higher. If a failure is wanted within one
million c y c l e s , a
a^
ax-dynamic ^t 0 • 53 . ajj-] t^^iate-stati c with
a stress amplitude of 0.40 ajjit. should be favourite.
Two different ways of calculation the influence of the fibres
on the stresses in the reinforcement bars can be used. The
first one ignores the benefit of the fibres resulting in too
high stresses in the steel for low reinforcement ratios.
This method however gives a good idea about the real fibre
con-tribution which will reduce steel bar s t r e s s e s . In the last part
of this chapter a real stress calculation has been made using
deflection and surface strain data from the m e a s u r e m e n t s . The
method is described in reference / 5 / .
3.2 Results of the dynamic tests
The first group of beams subjected to fatigue loading were the
beams with only fibre reinforcement. It seemed to be very
im-portant that the scatter in the Pyi^imate data for all beams
with the same r e i n f o r c e m e n t , is as less as possible / 6 / .
However for this group of beams the scatter was too large to
get reliable r e s u l t s . In table A XII these results are given.
They will not be discussed further. Deflection versus N-curves
are gi ven in fig. A 4 7 .
Test beams with 2 0 4 reinforcement steel were subjected to a
constant amplitude (0.35 Pjit. ) fatigue loading with a maximum
of 5 0 % of the static ultimate*loading.
Failure could be expected within 2 million cycles according
to data in literature. H o w e v e r , only the beams without fibres
failed within one million cycles. The failure was introduced
by a failure of the reinforcement b a r s . The beams with the
fi-bres had only a
yery
small increase in deflection (fig.A 4 8 )
and cracks were hardly visible. The conclusion was made that
the cyclic loading had not damaged the b e a m s . Data are shown
in table A XIII.
These same beams have been tested again in fatigue using a
higher maximum load (0.80 Pjit.)
^'^^
about the same amplitude.
Only the beam with the lowest fibre volume failed. A second
series 2 0 4 beams with a maximum load of 9 0 % and an amplitude
of 7 0 % P-ultimate showed a failure for all b e a m s . The
deflec-tion development is shown in figs, A 48 and A 49.
rfd. Civieb Techniek T.H. Si-viii.vsg 1. r De!:t
For the 4 0 6 beams one test was made with a maximum load of 73% P-ultimate and an amplitude of 6 0 % .
All beams failed. In a second series with lower maximum and amplitude values the beam with the highest pl/d did not fail. Deflection versus N-curves are shown in fig. A 50,Fatigue data are given in table A XIV.
Only one ser P,,-i+ ratio was
ies of the 4 0.84 a
Crack width measurement results do show the same behaviour as described for the deflection. These data were only measured in the constant moment zone. Table A XVI will summarize the crack distances for all the tested beams reinforced with steel bars.
Discussion of the results of the dynamic tests
The pl/d ratio seemed to be a very favorite ratio to describe the influence of the fibres on the fatigue life of steel bars and steel fibres reinforced concrete beams. The figures A52,A53 and A54 shows this parameter as a function of the number of cycles to failure. At each point the stress data of the parti-cular test are given calculated in accordance with the cracked-section elastic analyses, i.e. the fibre contribution is ignore The number between parenthesis is the steel stress at the top
load, the other one means the stress amplitude in the steel. From figs. A 53andA 54 i t can be seen that the number of cycles till failure increases with an increasing ratio pl/d. Moreover it is evident that the slope of the regression line becomes steeper with larger amount of bar reinforcement.
That means, the effect slowly diminishes if more bar reinforce-ment is present. This result could be expected because if there
is only a little bar reinforcement,any additional reinforcement (for instance fibres) must have a significant effect whereas this effect gets hidden where the concrete is already highly reinforced with bars. Fig. A52 shows that fact clearly: at a comparable stress level only one specimen failed before a million of cycles and the slope of a to be drawn regression
line would be very gentle.
The points on the left side are determined at different (higher stress levels and cannot be compared mutally. They indicate only the trend to lower numbers of cycles with increasing stres 1evel and ampli tude.
The test results of plain concrete are given on the bottom side of the graphs. From that the gain in fatigue life increases with decreasing reinforcement ratios.
To k nece stre face i rre ti on bed The betw renc vatu s tra now the ssary to sses dur strai n 1i able t and top in r e f . c u r v a t u r een the e b e t w e e re X is i ns , ace If X i s calc m e a s u r e d , th With the o-e
steel forces Knowing thes and external
real b e h a v i o u r o obtain the real ing the f a t i g u e m e a s u r e m e n t s at h e s e strai ns hav s u r f a c e s t r a i n / 5 / and will be e is a s s u m e d to two o u t e r d e f l e c n c e n t r e d e f l e c t also a r e l a t i o n ording to x= (e ulated from the en e and ^steel c u r v e s for the s are also k n o w n . e steel f o r c e s ,
m o m e n t m u s t be
f the fibres in the beams it is steel s t r e s s e s and the fibre l o a d i n g . Due to the fact that s u r -the b o t t o m of -the beams w e r e very e been c a l c u l a t e d from the d e f l e c -m e a s u r e -m e n t s . The -m e t h o d is descri-s u m m a r i z e d here descri-s h o r t l y .
be x = 8 6 / l ^ in which 1 = d i s t a n c e tion p o i n t s and 6 is the d i f f e ion and o u t e r d e f l e c t i o n . The c u r -b e t w e e n the -b o t t o m and top s u r f a c e
+ £
)/h
d e f l e c t i o n , h is k n o w n a n d e is
c a n b e d e r i v e d .
^
teel bars the steel s t r e s s e s and the e q u i l i b r i u m b e t w e e n internal g u a r a n t e e d . This ri te fore bars for wi th trib s i ng fore stee stre deer The res u The m o m e 1 oad the unti meth for e m e n t i n e a rel 2 0 uti on of t ed to 1 . Ot ss ar ease resul lts f cal CU nt co ing t momen 1 fai od fo medi u rati onjun iable 4 or to t he st tran her i e the i n te ts fo or 4 lated ntrib he st t of 1 ure r calcu m and 1 os howe ction t f i b r e 4 0 6 b he t o t a e e l s t r s f e r a n f 1 u e n c dynami nsion s r 2 0 4 0 6 i n steel u t i o n 1 eel str fai 1 ure o c c u r s .
1 a t i o
OW rev e r t
0 the stres ars t 1 mom esses part es re c ere tiff e are figs . stres i n e . esses . Ste n ste i nfor he in stee s cal he in ent r . Fib of th spons ep in ning shown A 59 s val It ca are el st el str c e m e n t f 1 u e n c 1 fibr culati creasi e s u l t s res w i ei r be ible f the c i n the in fi - A 62 ues ar n be s g r OW i n r e s s e s e s s e s rati e of e a m o on . S ng o f i n a 11 b ea r i n g
or an o m p r e t e n s gs . A s e e m e d t os . F o r h the a m o u n unt w a s t o , o n l y f the s t e e r e m a r k a b p u l l e d o c a p a c i ty i n c r e a s e ssi on z o n i1 e z o n e . 55 - A 58 o be favoui g h r e favoui n -t of s-teel 0 0 bigo r b e a m s
1 b a r c o n
1 e i n e r e a
-ut a n d a r e
to t h e
in s t e e l
e a n d a
a n d t h e
e g i v e n a l o n g t h e s t e e l
e e n t h a t d u r i n g t h e c y c l i c
g s l o w l y t i l l j u s t b e f o r e
w i l l i n c r e a s e s u d d e n l y
C r a c k w i d t h
In f i g u r e s A 63 - A 66 t h e g r a p h s a r e s h o w n o f t h e a v e r a g e c r a c k
w i d t h as a f u n c t i o n o f t h e n u m b e r o f c y c l e s . T w o p a r t s c a n b e
c l e a r l y d i s t i n g u i s h e d , a f i r s t p a r t w h e r e t h e a v e r a g e c r a c k
w i d t h g r o w s s l o w l y a n d a s e c o n d p a r t w h e r e t h e c r a c k s o p e n
v e r y f a s t w h i c h l e a d s s o o n to a f a i l u r e . T h e b e h a v i o u r is
very
s i m i l a r t o t h a t o f t h e l o a d - d e f l e c t i o n c u r v e s .
F o r t h e b e a m s w i t h r e i n f o r c e m e n t b a r s o n e m o m e n t o f s t a b l e
c r a c k g r o w t h w i l l b e e v a l u a t e d m o r e p r e c i s e l y . In t h e f i g u r e s
A67,A68,A69 t h e r e s u l t s o f t h e a v e r a g e c r a c k w i d t h in t h e p u r e
b e n d i n g z o n e a f t e r 1 0 . 0 0 0 c y c l e s a r e p l o t t e d vs t h e p l / d r a t i o
It can be seen that the pl/d ratio and,
Without fibres, the total crack width The influence of the stress level and too. Higher stress levels result in a shall be noted that the values of the
the fibres are more efficient the higher also, the smaller the bar reinforcement.
is the largest.
stress range is visible, shorter fatigue life. It static test at comparable those of the dynamic tests stress levels are always smaller than
The influence of the fibres and the reinforcement ratio on the difference between static and dynamic results is not quite as pronounced as for the normally reinforced specimens.
Crack spacing
The crack spacing a is commonly smaller with greater reinfor-cement ratio. That turns also out from f i g . A 7 0 f o r pl/d=0. There, the average crack spacing just before failure is about 100mm for 2 0 4 and between 30 and 40mm for 4 0 6 and 4 0 10 in the static case.
Thus the lower limit which is determined by the bond proper-ties of the steel, the concrete quality and the geometry of the
static withiout (—) hooi<ed (67) straight (81) paddleci (95) A s ( N / m m 2 ) (Cmax) 320(395) Ajy 385 (492) V \ 327 (All) \ ^ \ 330 (A02) I ' ^ ^~\
/ \/ X \
20^
/ A / \. •
iM) 60 80 100 120 140 160 * not failed 425(880)* / \ < ^ " y \ \ 366 (522) 374 (773)* ƒ --/ / -.vX 302 (690) 20 AC 60 80 100 120 crack spacing a. mmFig. 14 Relative frequency of crack spacing in static and dynamic tests
beam, seems to be about 25mm. This limit is not undercut, not even in the dynamic tests.
For the higher reinforcement ratios there is hardly any in-fluence of the fibres, too. Only at low reinforcement ratios both influences are evident: dynamic loading reduces the crack spacing and the higher pl/d ratio reduces it as well to a con-siderable extent.
The influence of the reinforcement ratio shall be illustrated by a few more diagrams showing the frequency distribution of the crack spacing.
On the lower part of fig. 14 , the distributions are rather dif-ferent for the four cases, i.e. at low reinforcement ratios the fibres contribute to the cracking behaviour. This effect is leveled at higher reinforcement ratios. That is true for the absolute value of the crack spacing and also for the scat-ter of the results. The right hand side gives the influence of dynamic loading. There can be seen that only for a low reinfor-cement ratio (2 0 4) the crack spacing decreases by dynamic loading whereas for higher reinforcement ratios there is no obvious difference between static and dynamic behaviour.
Conclusions of the dynamic tests The s the s that descr rei nf dimi n a gi V The i ment addi t stres ses w creep fibre Due t creas ame tati the ibe orce i she en s nflu rati i on ses ill of s . 0 th e al charac c part rati 0 the va ment i s the tati c ence i 0 and of fib in the i ncrea concre teristi are va pl/d is rious i ncrease crack w load an s more the hig res sub conti n se as a te in c cs as lid fo a sui nf1uen s the idth, d for di sti n her th stanti uous b resul ompres menti r the table ces . numbe crack a gi V ct th e pi/ ally ars . t of si on
oned in the conclusions of dynamic test. It turned out parameter in order to
It can be noted that fibre r of cycles to failure and
spacing and deflections for en number of cycles .
e smaller the bar reinforce-d ratio. It appears that the reduces the average tensile In fatigue loading these stres-debonding of the steel, dynamic and pull-out behaviour of the e same effects, deflections and crack widths will in-so.
REFERENCES
/ I / Bouter, C.; "Resultaten van uittrekproeven van 3 typen staalvezels ingestort in beton" ;Stevinrapport 1.79.3 materiaalkunde. Delft 1979.
I l l ACI SP44;"Fibre reinforced concrete 1974 American Con-crete institute.
IZl BoK, Gray ;"Fatigue of fibre concrete PhD Thesis"; Cal-gary 1977.
I^| Wascheidt, H.;"Dauerschwingfestigkeit von Betonstahlen im einbetonierten Zustand";Deutscher Ausschuss fur Stahl-beton; Heft 2 0 0 , Berlin 1968.
/ 5 / Reinhardt,H.W.;"Contribution of the fibres to the load bearing capacity of a bar-and fibre reinforced concrete beam; Stevinrapport 5-78-9 Delft, 1978.
/ 6 / Ball, C.;"Fatigue behaviour of steel fibre reinforced concrete.";MSC Clarkson College of Technology.Dpt.Civi1 Eng.; Potsdam NY, October 1967.
HI One^,T.; "The behaviour of bar reinforced steel fibre concrete beams in static testing"; Stevinreport 5-78-5, Delft, June 1978.
/ 8 / CUR 89 ;"Staalvezelbeton" ;Betonvereniging Zoetermeer 1977. / 9 / ACI Committee 544;"State of the art report on fibre
reinforced concrete"ACI Journal 1973 November, vol. 70 no. 11 pp. 729-744.
/lO/ Boer ,L.J.den ; "Fibre reinforced concrete."Conf . on proper-ties and applications of fibre reinforced concrete; TH Delft, Afd. Civil.Tech. ;Delft 1973.
/ll/ Swamy, R.N. ; "Testing and test methods of fibre cement com-posites" ;Ri 1 em symp. Sheffield 1978;The Construction Press /12/ Hannant,D.J. ; "Fibre cements and fibre concretes"; John
figures
Contents of appendix
page
A 15 Modulus of elasticity 37 A 16 Stress-strain curves rebars 38
A 17 - A 22 Force-strain curves for cylinders 39
A 23 Sieve analyses 44 A 24 - A 31 Load-deflection and moment-curvature diagrams 46
A 32 - A 39 Load-crack width diagrams 51 A 40 Crack distance (beams) 55 A 41 - A 44 Calculated fibre concrete stress-curvature
diagrams 57 A 45 - A 46 Contribution of concrete and steel to the
internal moment 59 A 47 - A 51 Deflection- N curves 60
A 52 - A 54 Influence of the volume aspect ratio on the
fatigue 1 ife 63 A 55 - A 62b Contribution of moments during repeated
1oadi ng 66 A 63 - A 66 Average crack width during repeated loading 74
A 67 - A 69 pl/d-average crack width diagrams at 10.000
cycles 77 A 70 Crack spacing a vs pl/d ratio for 2 0 4 and
4 0 10 reinforced beams 78 A 71 Fibre data 79 tables A IV - A V A VI A VII-A VIII A IX A X A XI A XII A XIII-A XII A XVI Scope of tests
Results of the steel tests Mix data
Compression cylinder strength Results of static tests
Crack distances in static tests
Fatigue results of beams without bar reinforcement
Fatigue results of beams with bar rei nforcement
Crack distances in dynamic tests
37 37 45 45 50 56 56 61 65
Rebar F i b e r s^ CÜ = 0% (i) = 0 . 1 7 % 2 0 4 to = 0 . 7 5% 4 0 6 CÜ = 2 . 0 9 % 4 0 10
None
Hooked
Strai ght
Paddled
2
2
2
(1)
(2)
(3)
(2)
(2)
(2)
(2)
- (1)
1 (2)
1 (2)
1 (2)
1 (1)
1 (1)
1 (2)
1 (2)
X*
Number of beams tested in static loading
( ) Number of beams tested in dynamic loading
Table A IV Scope of beam tests
0150x300mm 0150x400mm
plain concrete
hooked fibres
straight fibres
paddled fibres
4
3
2
2
2
2
Table V Scope of the cylinder tests
Di ameter
(mm) (inch)
Yield Stress'
N/mm2(PSI)
Ultimate
N/mm^
Stress
(PSI)
0 4
0 6
0 10
(0.16)
(0.24)
(0.39)
716
485
460
(4.94)
(3.35)
(3.17)
756
565
650
(5
(3
(4
22)
90)
49)
0.2% offset
Table A VI Results of the steel tests
N/mm2
plain
34800
35100
34200
37100
22800
20800
19000
15800
F i g . A 15 Modulus o f e l a s t i c i t y (N/mm^)s t r e s s N / m m
700
500
300
100
0
700
/ " / /1/
I<i>u
5 10 . . .
s t r e s s N / m
s t r a i n 7o
s t r a i n '/oo
700
500
300
100
stress N
/ / // m m
^ ^1
^10
— H
10 15 20
strain 7oo
F i g . A 16 S t r e s s - s t r a i n curves rebars
800
6 0 0
400
200
P ( k N )
8 C/oo)
1000
800
600
400
200
P(kN)
^ / / / - - ^ \ ^ \ \s
8
10
e (7oo)
F i g . A 17 F o r c e - s t r a i n curves f o r c y l i n d e r s 0 150x400 mm
(hooked f i b r e s )
P(kN)
ftnn .
0\J\Jfinn .
Ann
-9nn .
0
/ƒ
/ ^ v ^ ^ \V
"VJ —8
10
e (7oo)
1000
800
600
400
200
P(kN)
/ /ƒ
[Z
'X
\
\
. 1
s
^8 10
e (7oo)
Fig. A 18 Force-strain curves for cylinders 0 150x400 mm (straight fibres)
P(kN)
P(kN)
800
600
400
200
——^—1 I I I800
600
400
200
/ / / / ( ^ ~ 1 ^ ^ \V
4 6
e (7oo)
0 2 4 6
e (7oo)
F i g . A 19 F o r c e - s t r a i n curves f o r c y l i n d e r s 0 150x400 mm
(paddled f i b r e s )
800
600
4 0 0
200
P(kN)
/ / / / withoi fibres j tflnn ,
O V y U RCin .ouu
400 •
7nn .
0
P(kN)
A
1
I
/ / / without fibres8(7oo)
8(7oo)
Fig. A 20 Force-strain curves for cylinders 0 150x400 mm
(wi thout fi bres)
P(kN)
P(kN)
800 •
600
400
200
T n r
800
600
400
200
7 X 1 I •4
£ (7oo)
4
£ (7oo)
1000
P(kN)
800 —
600 •
400
200
1000
— 800
600
400
200
P(kN)
^ / / /f
- ^ ^ \ " " 1 1 -\ ^K
£ (7oo)
F i g . A 21 F o r c e - s t r a i n c u r v e s f o r c y l i n d e r s 0 150x300 mm ( h o o k e d f i b r e s )800
600
400
200
P(kN)
»800
600
400
200
P(kN)
4
£
(7oo)
£
(7oo)
Sknn -oUU600
200
0
P(kN)
1
1 \ . ^4 6
£
(7oo)
Fig. A 22 Force-strain curves for cylinders 0 150x300 mm (straight fibres)
sieves ace gram % % cum. gram
NEN 2560 cum.
16
8
4
2 mm 1 mm 500 pm 250 lam 125 pmst
tal
60
1195 2625 3205 3520 4070 4780 4925 5000 50001.2
22.7 28.6 11.6 6 .3 11 .0 14.22.9
1.5
1.2
23.9 52.5 64.1 70.4 81.4 95.6 98.5 100.060
1135 1430580
315
550
710
145
75
5000Type of concrete s 1 ump mm compacti on i ndex ai r content plain 7.0
with straight fibres 8.7 with hooked fibres 31.3 with paddled fibres 18.7
1.16 1.12 1 .10 1.10 2.7 2.8 2.9 3.0
Table A VII Data of concrete mix
Cement Portland A Sand Gravel (max. 16 mm) Water 400 kg/m^-^ 1425 kg/m^ -475 kg/m^ — 190 kg/m^ 70 kg/m^ 100 kg/m^ 120 kg/m^
(Mixing time concrete 5 min.; mixing time fibre con Crete 6 min. compaction time 6 min.)
Table A VIII Mix proportions
300 mm Load control 300 mm Central strain control 400 mm Central strain control N/mm' N/mm^ Mean N/mm' N/mm^ Mean N/mm' N/mm^ Mean without 32.93 41.37 37.15 hooked 39.44 42.27 42.50 44.87 straight 38.08 40.72 41.48 42.61 paddled 42.16 46.52 47.19 50.19 38 42, 45 48 49, 38 37, 40 42 50 08 72 27 61 57 08 24 23 67 42 44.85 41.73 39 40 42 39 43 95 06 10 27 01 43.97 46.57 43.52 43.63 40.70 41.14 45.27 43.57
![[W związku z recenzją Wł. Czaplińskiegoz wydawnictwa "Merkuriusz Polski", oprac. A. Przyboś, Kraków 1960, "PH" 54, 1963, z. 1, s. 144-147]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)