Empirical calculation method of residual flexural tensile strength [f.sub.R,1] of SFRC.
Kelpsa, S. ; Augonis, M. ; Dauksys, M. 等
1. Introduction
Fibre reinforced concrete (FRC) is cement based composite material.
Basically, the concrete has a low tensile strength, low strain capacity,
and it fails in brittle manner. The addition of the fibre improves the
mechanical properties of concrete, especially the post-cracking
properties [1, 2].
The steel fibre reinforcement has been studied and developed
intensively over past four decades, and now it is lots of different
fibre in the market. The fibre can be made of different materials, such
like steel, carbon, synthetic, glass and others. However, the steel
fibre is the most commonly used for the structural purposes. Length,
shape, and the cross section of the steel fibre are various. Numerous
researches have been performed to develop better bond between the fibre
and matrix of concrete [3]. Despite of that the circular cross section
hooked end steel fibre is one of the most widely used because of the
simplicity of manufacturing and the good bonding parameters [1, 2, 4,
5].
It is known that fibres bridge the cracks and transfer the tensile
stress across the cracked sections. Therefore, the concrete becomes more
ductile and durable material, cracks are restricted, and even bearing
capacity of the member can be enhanced. Nevertheless, the application of
the steel fibre is still limited. There are two main reasons for these
limitations: first--lack of the generally accepted design method,
second--complicated (experimental) determination of the post-cracking
properties of steel fibre reinforced concrete (SFRC). Although it is not
generally accepted design method, however there are some design
proposals, and some countries already have its design standards or
recommendations [1, 6-13]. Nevertheless, the second problem still
remains open.
The determination method of the post-cracking parameters is
prescribed by the design method, and usually it is experimental.
Residual flexural tensile strength [f.sub.R,1] is the mostly applied
parameter for the SLS (crack width) calculations. This parameter should
be established from the experiments, and later recalculated to residual
tensile stress ([[sigma].sub.fb] = k[f.sub.R,1]). Coefficient k can
differ in different crack width calculation methods (0.40-0.45). Mean or
characteristic values of [f.sub.R,1] could be used depending on the
crack width calculation method. Recalculation methods are also described
together with the crack width calculation methods [1, 6, 8-10, 12-14].
In order to use the discussed crack width calculation methods the
tests are necessary for the determination of residual flexural tensile
strength [f.sub.R,1]. Method of these tests is given in EN
14651:2005+A1:2007 [14]. Nevertheless, these tests require time and
other resources, therefore it would be great practical benefit if it
would be possible to calculate [f.sub.R,1] without it. Even in those
cases where designer is responsible only for specifying the requirements
of residual tensile strength the calculation method of [f.sub.R,1] could
help to analyse and choose the most economical solution.
Calculation of the residual flexural tensile strength is
complicated due to the random distribution of the steel fibre in the
concrete, due to a large variety of the fibre types, due to the
different fibre bond and other aspects. Despite of that, it could be
found in the literature some calculation proposals of SFRC post-cracking
properties [1, 3, 15-19]. Most of these methods are developed using
experimental results. But still, none of these methods is intended for
the calculation of the residual flexural tensile strength [f.sub.R,1].
The new calculation method of the residual flexural tensile
strength ([f.sub.R,1]) is presented in this paper. The method was
developed using 60 series of three-point bending test (446 prisms). 12
test series (132 prisms) has been tested by authors, and results of
remaining series has been taken from the references [2, 15, 20, 21-34].
Only hooked end steel fibre was used for this method. The scatter of the
experimental results and the relative errors of the method are
discussed. The recommendation for designers and researchers are given.
2. Testing procedure and results
In order to determine [f.sub.R,1] the three-point bending tests
were performed according to the regulations of EN 14651:2005+A1:2007
[14]. The scheme of three-point bending test is given in Fig. 1. Loading
was performed according to a deformation control. The method allows to
measure force-displacement or force-CMOD (crack mouth opening
displacement) relations. When the displacement of the beam reaches 0.46
mm or CMOD reaches 0.5 mm, then the value of load is recorded and the
residual flexural tensile strength [f.sub.R,1] is calculated according
to Eq. (1).
10 test series have been performed in Kaunas University of
Technology (KTU) and 2 test series in Norwegian University of Science
and Technology (NTNU). In order to develop precise calculation method
more experimental results of three-point bending tests were taken from
the references [2, 15, 20-34]. The information about the test series and
its specimens is given in Table 1.
[FIGURE 1 OMITTED]
[f.sub.R,i] = 3[F.sub.R,i]l/2b[h.sup.2.sub.sp], (1)
where [F.sub.R,i] is load corresponding with CMOD = [CMOD.sub.j] or
[delta] = [[delta].sub.j] (j = 1, 2, 3, 4), l is span length, b is width
of the specimen, [h.sub.sp] is distance between the tip of the notch and
the top of the specimen.
Two types of concrete were used--traditionally vibrated and
self-compacting SFRC. Traditionally vibrated SFRC was up to series No 41
(inclusive). All remaining series were made of self-compacting SFRC.
Compositions of SFRC are not given in this paper because of huge number
of different mixes. The main parameter which was used in further
calculations is the average compressive strength of SFRC
([f.sub.cm,fb])--given in Fig. 2. The compressive strength of SFRC
([f.sub.cm,fb]) was determined for every series, together with the
residual flexural tensile strength ([f.sub.R,1]).
[FIGURE 2 OMITTED]
The large scatter of the residual flexural tensile strength was
obtained almost in all the series. The maximum relative error between
the specimens of the same series was 71.3% (6th series). The average
coefficient of variation of all series with known standard deviation (50
series) was 16.6%. While the average coefficient of variation of
traditionally vibrated SFRC (31 series) was 19.2%, and 12.4% of
self-compacting SFRC (19 series). Standard deviation of these
coefficients was 7.65, 7.60 and 5.75, respectively. As an example
stress-CMOD relation of ninth test series is given in Fig. 3. The
coefficient of variation is equal to 23.43% here.
[FIGURE 3 OMITTED]
3. Analysis of relevant factors
In order to calculate the residual flexural tensile strength
[f.sub.R,1] the main factors which has an influence on the post-cracking
properties of SFRC should be established:
* Fibre length--[l.sub.fb];
* Fibre diameter--[d.sub.fb];
* Aspect ratio--[l.sub.fb]/[d.sub.fb]
* Fibre material properties (tensile strength)--[f.sub.y,fb];
* Fibre cross-section--shape of the section;
* Fibre shape--deformated shape of the fibre;
* Fibre content--[V.sub.fb];
* Fibre orientation;
* Bond strength between fibre and matrix of concrete;
* Others.
The fibre length and the fibre diameter are ones of the main
parameters as well as the aspect ratio of the fibre. Vandewalle
determined that very short and short fibers are more effective for the
narrower cracks, and the longer fibres are more effective for the larger
cracks [20]. The fibre length also defines the embedment length. This is
especially important for thick, short hooked end steel fibre and low
strength concrete. When the embedment length is too short then the
fibre(s) is pulled out of the concrete with or without the surrounding
matrix. The fibre diameter defines the cross section of the fibre as
well as it influences the concrete spalling in the crack surface. The
aspect ratio defines the contact surface between the fibre and concrete
matrix and so the stress level before the fibre de-bonding [15, 32].
The material that the fibre is made of defines such significant
properties as the tensile strength of fibre ([f.sub.y,fb]), modulus of
elasticity (E) and others. The tensile strength ([f.sub.y,fb]) defines
the maximum available stress level in the fibre as well as the limit of
the fibre bond [15, 16]. The modulus of elasticity (E) defines the
deformations of the fibres as well as deformations of cracked SFRC
members. However, while all the fibre is made of steel the modulus of
elasticity (E) is approximately the same and it becomes not relevant for
this research.
The different shape of the fibre defines the bond between the fibre
and the concrete matrix. The circle shape of cross-section is the least
effective comparing with other shapes such like rectangular, triangular
or especially with the cross-section shape of the "Torex"
fibre. However, the circular cross-section is the most common in
practice and therefore only this cross-section shape was used in this
research [3, 4].
To pull out the straight fibre which is perpendicularly embedded to
concrete surface, the pulling force should exceed the shear stress-slip
reaction (adhesion + friction). In order to improve the bond the
deformed shape of the fibre was started to use. Lots of types of
deformed steel fibre are in the market today--crimped (wavy), hooked
end, with end paddles, with end buttons, etc. Nevertheless, the hooked
end steel fibre is one of the most widely used. Usually, the hooked end
steel fibre is produced from cold-drawn wire. To pull out such fibre,
despite of the mentioned shear stress-slip reaction, the hooked end
should be deformed into the straight during the pull-out. The extra pull
out force depends on hooks, material properties, etc [3, 4, 15, 32]. For
this research only the hooked end steel fibre was used (some fibre are
given in Fig. 4).
The fibre content has the direct influence on the post-cracking
properties of SFRC. This parameter is used in every proposal of
calculation of the post-cracking properties [1, 3, 5, 15-18].
Nevertheless, in some proposals its influence is nonlinear. The main
reason is the group effect, i.e. when the number of fibres being pulled
out from the same area considerably increases the bond strength per
fibre decreases [15, 35].
[FIGURE 4 OMITTED]
It is known that fibres can distribute and orientate randomly in
concrete. Due to the random fibre orientation the angle between
longitudinal axis of the fibre and the pull-out direction can be not
equal to zero, which means that snubbing and spalling effects start to
come hand in hand. The higher inclination angle the higher force is
needed to pull-out the fibre due to snubbing effect. Meanwhile the
higher inclination angle the lower force is needed to pull-out the fibre
due to spalling of concrete in the crack. In more details these two
effects are described in references [15, 35]. Also, depending on the
orientation the number of fibres crossing the crack can differ
significantly as well as post-cracking properties of SFRC [16, 35].
The orientation of steel fibre in SFRC can be described using the
orientation factor. Theoretically, when all the fibres are orientated in
one direction the orientation factor is equal to 1.0. This factor is
equal to 0.637 when fibres are randomly orientated in plane, and it is
equal to 0.5 when fibres are randomly orientated in space. The
orientation factor can be calculated according to the Eq. (2) using the
number of fibres per cross-section of SFRC [16, 19, 32]:
[alpha] = [n.sub.fb][A.sub.fb]/[A.sub.c][V.sub.fb], (2)
where [n.sub.fb] is a number of fibres per area of SFRC; [A.sub.fb]
is cross section area of single fibre; Ac is cross section area of SFRC;
[V.sub.fb] is fibre content (fibre volume ratio).
To evaluate the influence of the fibre orientation on the residual
tensile strength a capacity factor ([[eta].sub.0]) is used, which is
calculated according to the literature [16]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)
where [alpha]--the fibre orientation coefficient.
It is recommended in some calculation proposals of post-cracking
properties that the fibre bond strength should be given from fibre
pull-out tests. However the bond strength between the fibre and the
matrix of concrete as well as resistance against the spalling can be
approximately defined by strength of the concrete. The tensile strength
of SFRC is used in some calculation proposals whereas the compression
strength is used in another [1, 5, 15, 17, 18, 35]. While the
compressive strength of SFRC ([f.sub.cm,fb]) can be simply
experimentally determined it was chosen to characterize the bond
strength between fibre and matrix of concrete.
Other factors also can influence the post-cracking properties of
the SFRC, such like local fibre distribution, local concentration of the
fibres, member size, uneven properties of the concrete matrix, etc. The
post-cracking properties can vary due to these factors. However, all
experiments were performed according to the standard method given in EN
14651:2005+A1:2007. Such factors as member shape and its size as well as
testing procedure are clearly described, and were the same for all
specimens. Also, the experimental data which was taken from the
references was limited. Therefore, it is assumed in this research that
only factors which were described earlier are essential and should be
considered in further research.
4. Analytical prediction of [f.sub.R,1]
The main factors which have the influence on the residual flexural
tensile strength ([f.sub.R,1]) are described in previous section. These
factors were combined while the most accurate calculation formula of
[f.sub.Rm,1] was deduced. First of all the mentioned factors were
partitioned in to three parts as it is given in Eq (4):
[f.sub.Rm,1] = [beta] x [gamma] x y, (4)
where the parameter [beta] depends only on the compressive strength
of SFRC [f.sub.cm,fb] (average value)--([beta] [member of]
[f.sub.cm,fb]), the parameter [gamma] depends on fibre length
[l.sub.fb], fibre diameter f the tensile strength of the fibre
[f.sub.y,fb], and the fibre capacity factor [[eta].sub.0] ([gamma]
[member of] [l.sub.fb], [d.sub.fb], [f.sub.y,fb], [[eta].sub.0]). The
function y depends on the fibre content V, (fibre mass per cube /
density of the fibre) and the fibre reinforcement efficiency factor
[k.sub.fb] - (y [member of] [V.sub.fb], [k.sub.fb]).
In order to find the best relations of the discussed parameters
some functions were analysed. The best relations were established when
the sequent functions were used:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
where [k.sub.c1], [k.sub.c2], [k.sub.c3], [n.sub.c1], and
[n.sup.c2] are coefficients which were combined while the most accurate
combination was found.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
where k, [n.sub.l1], [n.sub.l2], [n.sub.d1], [n.sub.y1],
[n.sub.y2], and [n.sub.[eta]1] are coefficients which were combined
while the most accurate combination was found.
The best fit function y = f (x) = [f.sub.Rm,1]/[beta] + [gamma] and
the coefficient of determination [R.sup.2] was established during
analysis (Fig. 5).
[FIGURE 5 OMITTED]
As it can be seen from Fig. 5 that two functions y were established
and compared (linear and second order polynomial). Due to higher
coefficient of determination ([R.sup.2]) the second order polynomial
function is used.
The only one difference between traditionally vibrated and
self-compacting SFRC was assumed--the orientation factor [alpha]. For
traditionally vibrated SFRC [alpha] = 0.60 and for self-compacting SFRC
[alpha] = 0.80. The capacity factor was equal to 0.467 and 0.733,
respectively. Such values of the orientation factor were chosen
considering the experimental results (including the results from
references) [21, 22, 24, 31, 33] and guidance from other references [13,
15].
As a result of this analysis the Eq. (7) is proposed for
calculation of the residual flexural tensile strength [f.sub.Rm,1] (mean
value). All experimental values of [f.sub.Rm,1] were compared with the
results calculated according to the Eq. (7). The average relative error
of calculated residual flexural tensile strength ([f.sub.Rm,1]) is 0%
due to the coefficient [k.sub.adj]. The maximum relative error reaches
50%, and the standard deviation of the ratio between calculated and
experimental results is 0.20. The comparison of calculated and
experimental values of [f.sub.Rm,1] is given in Fig. 6.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)
where the adjustment coefficient [k.sub.adj] is equal to 0.96 and
the fibre reinforcement efficiency factor - [k.sub.fb] =
[l.sub.fb]/50[d.sub.fb].
Although the maximum relative error is quite high, however higher
then 30 % relative error was reached only for 7 test series. Considering
the relative error between the specimens of the same series as well as
the relative error between the comparable series (such like 5th and 6th,
37th and 39th, etc.) the accuracy of the calculation method is
satisfactory.
[FIGURE 6 OMITTED]
5. Discussions
Two general orientation factors were assumed for two different
types of SFRC (traditionally vibrated and self-compacting). However,
despite of the clearly defined experimental program these factors
([alpha]) can vary depending on various other factors, such like
vibration time, vibrator, mixer, workability of mortar, etc. The
variations of the orientation factor could lead such high relative
errors for some test series. Also, the other factors such like actual
local fibre concentration, water cement ratio, precision and dimensions
of the fibre hooks could have a significant influence on [f.sub.R,1],
but these factors were not included into the research due to lack of
information.
The precision of the proposed calculation method could be revised
in future research after the inclusion of more experimental results as
well as the mentioned additional factors. In order to use this method
directly for particular structures (beams, walls, plates, etc.) the more
detailed analysis of orientation factor and its influence on fR1 is
required as well as possible adjustments of the method. The intended
application of the proposed calculation method is the same as tests
results of the standard beams, which should be cast and tested according
to EN 14651:2005+A1:2007 [14]. The indirect application is given in
related codes, standards and recommendations [8, 10, 12, 13].
6. Conclusions
1. The calculation method of the residual flexural tensile strength
([f.sub.Rm,1]) was developed using the experimental results of 446
standard beams. The important parameters: fibre length, fibre diameter,
tensile strength of the fibre, fibre orientation factor, fibre content,
and compressive strength of SFRC was included in the research. The
proposed calculation method is suitable for circular cross-section
hooked end steel fibre reinforced concrete, where the mean compressive
strength [f.sub.cm,fb] varies from 25 to 60 MPa and the fibre content
varies from 15 to 80 kg/[m.sup.3]. Method is suitable for the
traditionally vibrated and self-compacting SFRC.
2. The calculated residual flexural tensile strength ([f.sub.Rm,1])
could be applied in the SLS calculations (crack width calculations,
etc.) according to suitable codes, standards and recommendations. The
relative error of calculation method exceeded 30% in few cases. However,
comparing it with the deviations between separate specimens of the same
series the precision of the method is satisfactory. For the practical
purposes the method could be used as a first approximation in design.
The proposal and the related future research could lead to the reduction
or even to elimination of the necessary tests from the design process.
http://dx.doi.org/ 10.5755/j01.mech.21.3.9551
Received January 21, 2015
Accepted March 10, 2015
References
[1.] Jansson, A. 2007. analysis and design methods for fibre
reinforced concrete: a state-of-the-art report, Goteborg, Sweden:
Department of Civil--and Environmental Engineering Division of
Structural Engineering, Chalmers university of technology.
[2.] Vandewalle, L. 2007. Postcracking behaviour of hybrid steel
fiber reinforced concrete, Proceedings of FraMCoS-6, 1367-1375.
[3.] Naaman, A.E. 2003. Engineered steel fibers with optimal
properties for reinforcement of cement composites, Journal of Advanced
Concrete Technology 1(3): 241-252. http://dx.doi.org/10.3151/jact.L241.
[4.] Kaklauskas, G.; Ba?inskas, D.; Gribniak, V.; Jakubovskis, R.;
Ulbinas, D.; Gudonis, E.; Meskenas, A.; Timinskas, E.; Sokolov, A. 2012.
VGTU. Concrete structures reinforced by steel fibres and nonsteel bars.
Vilnius: Technika. 391p. (in Lithuanian).
[5.] Grunewald, S. 2004. Performance-based design of
self-compacting fibre reinforced concrete, PhD thesis, Technical
University of Delft.
[6.] Kelpsa, S; Augonis, M.; Dauksys, M.; Augonis, A. 2014.
Analysis of crack width calculation of steel fibre and ordinary
reinforced concrete flexural members, Journal of Sustainable
Architecture and Civil Engineering 6(1): 50-57.
http://dx.doi.org/10.5755/j01.sace.6.1.6336.
[7.] CNR-DT 204/2006, Guide for the design and construction of
fibre-reinforced concrete structures. CNR.
[8.] RILEM TC 162-TDF. 2003. Final recommendation of RILEM TC
162-TDF: Test and design methods for steel fibre reinforced concrete
sigma-epsilon-design method, Materials and Structures 36(262): 560-567.
http://dx.doi.org/10.1617/14007.
[9.] Jansson, A.; Lofgren, I.; Gylltoft, K. 2010. Flexural
behaviour of members with a combination of steel fibres and conventional
reinforcement, Nordic Concrete Research 42(2): 155-171.
[10.] Model Code of Concrete Structures 2010 (Final Draft). FIB.
[11.] DafStb Guideline, Steel fibre reinforced concrete. German
Committe for Reinforced Concrete.
[12.] ftSS 812310:2014 Design of fibre concrete structures, Swedish
Standards Institute.
[13.] design guideline for structural applications of steel fibre
reinforced concrete, SFRC Consorcium.
[14.] EN 14651:2005+A1:2007--Test method for metallic fibre
concrete. Measuring the flexural tensile strength (limit of
proportionality (LOP), residual), CEN/TC 229.
[15.] Dupont, D. 2003. Modelling and experimental validation of the
constitutive law ([sigma]-[epsilon]) and cracking behaviour of steel
fibre reinforced concrete, PhD thesis, Catholic University of Leuven,
Department of Civil Engineering.
[16.] Thorenfeldt, E.T. 2003. Theoretical Tensile strength after
cracking, fibre orientation and average stress in fibres, Workshop
Proceedings from a Nordic Miniseminar: Design Rules for Steel Fibre
Reinforced Concrete Structures, 43-60.
[17.] Naaman, A.E. 2003. Strain hardening and deflection hardening
fiber reinforced cement composites, Proceedings of the 4th International
RILEM Workshop on High Performance Fiber Reinforced Cement Composites
(HPFRCC4), 95-113.
[18.] Sujivorakul, C. 2012, RILEM bookseries. High performance
fiber reinforced cement composites 6. Model of hooked steel fibers
reinforced concrete under tension, Dordrecht--Heidelberg--London--New
York: Springer. 19-26.
[19.] Kanstad, T.; Juvik, D.A.; Vatnar, A.; Mathisen, A.E.;
Sandbakk, S.; Vikan, H.; Nikolaisen, E.; Dossland, A; Leirud, N.;
Overrein, G.O. 2011. COIN report: guidlines for sizing, execution and
control of fiber reinforced concrete structures.
[20.] Vandewalle, L. 2007. Mechanical properties of hybrid fiber
reinforced concrete, Proceedings of the 1st International Conference on
Sustainable Construction Materials and Technologies, 283-290.
[21.] Vandewalle, L.; Heirman, G. 2009. Properties of
Self-compacting fibre reinforced concrete, 4th International Conference
on Construction Materials: Performance, Innovations and Structural
Implications (CONMAT09), 406-411.
[22.] Vandewalle, L.; Heirman, G.; Van Rickstal, F. 2008. Fibre
orientation in self-compacting fibre reinforced concrete, 719-728.
[23.] Olimb, A.M. 2012. Testing of fibre reinforced concrete
structures: shear capacity of beams with openings, Master thesis,
Norwegian University of Science and Technology, Faculty of Engineering
Science and Technology, Department of Structural Engineering.
[24.] Prisco, M.; Ferrara, L.; Caverzan, A. 2012. Selfcompacting
fibre reinforced concrete: is the material really isotropic? 3[degrees]
Congreso Iberoamericano Sobre Hormigon Autocompactante Avances Y
Oportunidades, 17-31. Available http://www.autocompacto.net/
wp-content/themes/splendio/pdf/ponencias/ 03_ID02_MdiPrisco_def.pdf.
[25.] Flakk, O; Tordal, K.N. 2012. Testing of fibre reinforced
concrete structures: structural behaviour in the serviceability and
ultimate limit states, Master thesis, Norwegian University of Science
and Technology, Department of Structural Engineering.
[26.] Ferrara, L.; Caverzan, A.; Muhaxheri, M.; Prisco, M. 2012.
Identification of tensile behaviour of SFRSCC: Direct Vs. Indirect
Tests, Eighth RILEM International Symposium on Fibre Reinforced Concrete
(BEFIB 2012): Challenges and Opportunities, 209-221.
[27.] Dupont, D.; Vandewalle, L. 2003. Calculation of crack widths
with the (o -e) method, Proceedings of International RILEM Workshop on
Test and Design Methods for Steel Fibre Reinforced Concrete - Background
and Experiences, 119-144.
[28.] Buratti, N.; Mazzotti, C.; Savoia, M. 2010. Experimental
study on the flexural behaviour of fibre reinforced concretes
strengthened with steel and macrosynthetic fibres, Proceedings of
FraMCoS-7, 12861294.
[29.] Amirineni, K.C. 2009. Fracture properties of fiber reinforced
concrete, Master thesis, The Pennsylvania State University.
[30.] Alvarez, A.B. 2013. Characterization and modelling of SFRC
elements, Doctoral Thesis, Universitat Politecnica de Catalunya.
[31.] Hanssen, H.E.; Hallberg, M.A. 2013. Post-Tensioned fibre
reinforced flat slab, Master Thesis, Norwegian University of Science and
Technology.
[32.] Sandbakk, S. 2011. Fibre reinforced concrete: evaluation of
test methods and material development, PhD Thesis, Norwegian University
of Science and Technol [degrees]gy.
[33.] R0d, A.; Aspas, 0. 2013. Testing of fibre reinforced concrete
structures: shear capacity of beams with openings, Master thesis,
Norwegian University of Science and Technology.
[34.] Strack, M. 2008. Modelling of crack opening in steel fibre
reinforced concrete under tension and bending, Proceedings of the 7th
RILEM International Symposium on Fibre Reinforced Concrete: Design and
Applications --BEFIB, 323-332.
[35.] Naaman, A.E. 2008, Engineering materials for technological
needs. High-performance construction materials. Sci Appl. High
Performance Fiber Reinforced Cement Composites. Singapore: World
Scientific Publishing Co. Pte. Ltd. 91-153p.
S. Kelpsa *, M. Augonis **, M. Dauksys ***, A. Augonis ***, G.
Zirgulis *****
* Kaunas University of Technology, Studentu str. 48, LT-51367
Kaunas, Lithuania, E-mail: sarunas.kelpsa@ktu.edu
** Kaunas University of Technology, Studentu str. 48, LT-51367
Kaunas, Lithuania, E-mail: mindaugas.augonis@ktu.lt
*** Kaunas University of Technology, Studentu str. 48, LT-51367
Kaunas, Lithuania, E-mail: mindaugas.dauksys@ktu.lt
**** Kaunas University of Technology, Studentu str. 48, LT-51367
Kaunas, Lithuania, E-mail: algirdas.augonis@ktu.lt
***** Norwegian University of Science and Technology,
RichardBirkelands vei 1A, NO-7491 Trondheim, Norway,
E-mail: giedrius.zirgulis@ntnu.no
Table 1
Specimens of three-point bending tests
Series Reference No. of [l.sub.fb]/ [l.sub.fb], mm
No. spec. [d.sub.fb]
1 KTU * 6 50 50
2 KTU * 12 50 50
3 KTU * 12 50 50
4 KTU * 12 50 50
5 KTU * 12 50 50
6 KTU * 12 50 50
7 KTU * 12 69 52
8 KTU * 12 69 52
9 KTU * 12 67 50
10 KTU * 12 50 30
11 [28] 7 50 50
12 [15, 27] 8 48 50
13 [15, 27] 8 48 50
14 [21, 22] 6 65 40
15 [22] 6 63 25
16 [15, 27] 8 67 60
17 [15, 27] 8 67 60
18 [15] 6 67 60
19 [22] 6 67 60
20 [15, 27] 8 67 60
21 [15, 27] 8 67 60
22 [15, 27] 8 67 60
23 [15, 27] 8 67 60
24 [15] 6 67 60
25 [34] 16 67 60
26 [30] 6 64 35
27 [20] 6 64 35
28 [29] 4 64 35
29 [30] 6 64 35
30 [2] 6 64 35
31 [29] 5 64 35
32 [30] 6 80 60
33 [29] 5 80 60
34 [30] 6 80 60
35 [29] 5 80 60
36 [30] 6 81 50
37 [30] 6 81 50
38 [30] 6 81 50
39 [30] 6 81 50
40 [15, 27] 8 78 35
41 [15, 27] 8 78 35
42 [31] 6 63 50
43 [22] 6 65 40
44 [22] 6 65 40
45 [22] 6 65 40
46 [22] 6 63 25
47 [22] 6 63 25
48 [22] 6 63 25
49 [22] 6 67 60
50 [22] 6 67 60
51 [22] 6 67 60
52 [32] 6 67 60
53 [25] 5 67 60
54 [33] 6 67 60
55 [33] 6 67 60
56 [24, 26] ** 9 64 35
57 [24, 26] ** 4 64 35
58 NTNU * 9 80 60
59 NTNU * 9 80 60
60 [23] 6 80 60
Series [f.sub.y], [V.sub.fb],
No. MPa kg/[m.sup.3]
1 1200 25
2 1150 25
3 1200 30
4 1150 30
5 1150 35
6 1150 35
7 1500 15
8 1500 20
9 1150 30
10 1150 35
11 1100 20
12 1000 20
13 1000 60
14 1050 30
15 1700 30
16 1000 20
17 1000 20
18 1000 20
19 1000 30
20 1000 40
21 1000 40
22 1000 60
23 1000 60
24 1000 60
25 1000 75
26 1100 20
27 1100 30
28 1100 39
29 1100 40
30 1100 60
31 1100 79
32 1050 20
33 1050 39
34 1050 40
35 1050 79
36 1270 40
37 1270 40
38 1270 40
39 1270 40
40 1050 40
41 1050 60
42 1550 30
43 1050 30
44 1050 30
45 1050 30
46 1700 30
47 1700 30
48 1700 30
49 1000 30
50 1000 30
51 1000 30
52 1160 39
53 1160 80
54 1160 78
55 1160 78
56 1100 50
57 1100 50
58 1050 40
59 1050 40
60 1050 80
*--indicates that the tests have been performed by the authors. KTU
or NTNU is the name of the university where the tests have been
performed.
**--specimens were divided into two series because the mould filling
procedure was different and the orientation coefficients also
differed highly.
