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Proc. of the 13th fib International PhD Symposium in Civil Engineering
Aug 26 to 28, 2020, Marne-la-Vallée, Paris, France
1
Bond stress distribution of ribbed steel bars in
reinforced concrete with short bond length under
various loading conditions
Marc Koschemann, Manfred Curbach
Institute of Concrete Structures,
Technische Universität Dresden,
August-Bebel-Straße 30/30a, 01219 Dresden, Germany
Abstract
In the course of bond research of reinforced concrete for the past decades, the pull-out test with a bond
length lb of 5 times the bar diameter ds established as the standard to investigate the local bond behav-
iour. Despite the known disadvantages of this test setup, results of pull-out tests build the basis for bond
stress-slip relationships like the approach of fib Model Code 2010 [1]. Current investigation at the
Technische Universität Dresden focus on the bond behaviour and the bond stress distribution for ribbed
bars with short and very short bond lengths under various loading conditions. The investigations include
different types of specimens and the targeted use of fibre-optic measuring technology.
1 Introduction
The success story of reinforced concrete is based on the targeted exploitation of the material properties
of concrete under compression and of reinforcing steel under tensile stress. The interaction between
concrete and steel reinforcement, known as bond, is essential for reinforced concrete. In separation and
bending cracks, the reinforcement transmitts tensile forces by itself, but to both sides of the crack these
forces are reintroduced into the concrete due to the bond action. Thus crack widths and crack spacings
are decisively dependent on the bond behaviour. In addition, the bond action influences the construc-
tions stiffness at the cracked state and the resulting load-deformation behavior of a reinforced concrete
(RC) element.
In the course of bond research on reinforced concrete over the past 100 years, it can be assumed
that more than 30 parameters influence the bond behaviour [2]. Besides the material properties of the
individual components and the loading conditions, the configuration of the test setup and especially the
bond length in the specimen have a significant influence on experimental results. In this article the
experimental and instrumental setup, test results and the procedure of evaluation are shown. Further-
more, the questions of a suitable bond test and what local bond behaviour means are discussed.
2 Bond behaviour in experimental tests
2.1 Bond tests and bond stress distribution
The suitability of test setups for investigating bond behaviour has been the subject of controversial
discussion since the beginning of the 20th century [3]. The most used test to evaluate the bond behav-
iour of steel reinforcement is the pull-out test (PO) according to RILEM [4]. It is known for the com-
paratively simple setup and easy way of specimen production.
However, the main weaknesses of the RILEM pull-out test are the large concrete cover and the arch
effect of the reacting forces (Fig 1). This effect causes a transverse pressure in the bond zone, what
increases the bond resistance and subsequently leads to an overestimation of the bearing capacity. How-
ever, the load capacity increase can not been quantified by a study so far. Due to the minimum edge
length of the test specimen of at least 200 mm or 10.0 times the bar diameter ds, the minimum concrete
cover is at least 90 mm, respectiveliy ≥ 4.5 ds. The large concrete cover represents a high level of con-
finement, which is necessary to achieve the highest possible bond resistance, the so called pull-out
failure.
For real structural elements, the concrete cover is usually in the range between 20 and 55 mm.
Depending on the bar diameter, this normally corresponds to 1.0 to 4.0 ds. According to Vandewalle
[5], a concrete cover of 2.5 to 3.5 ds is required to achieve a failure by bar pull-out. Therefore, the
13th fib International PhD Symposium in Civil Engineering
2
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various
loading conditions
concrete cover of most of the structural elements does not comply this criterion and the reinforcement
has an insufficient level of confinement to reach the maximal bond resistance, which can be achieved
by pull-out tests.
Fig. 1 Left: scheme of pull-out test; middle: scheme of beam-end test; right: modes of bond failure
The lower concrete cover leads to a change of the failure mode towards a more or less sudden splitting
failure. Depending on the transverse reinforcement, both failure modes appear in combination (Fig. 1
right), which may be definded as “splitting-induced pull-out failure”. Anyway, an insufficient level of
confinement leads to a premature failure and a reduction of the bond resistence. Hence, the pull-out test
does not accurately represent stress states and the boundary conditions of bond zones of real RC ele-
ments. However, the pull-out test is suitable for testing the influence of individual material parameters
such as concrtes strength and rib geometry. In contrast, test configurations such as the beam test and
the beam-end test (BE) represent the bond conditions of real RC components in a better way (Fig. 1
middle). The force flow within the the specimen does not cause any transverse stresses in the bond zone
and the concrete cover is adjustable. However, the associated guidelines and standards specify a bond
length of 10 ds instead of 5 ds in the pull-out test [4], [6]. The comparison of results of bond tests with
differently specified specimen types therefore includes the influence of different bond lengths [7].
=
=∙
4∙
(1)
As early as 1905, Bach [8] determined the decrease in the length-related bond resistance τ (1) with
increasing bond length on the basis of tests with plain steel bars. Bach saw the cause of this behaviour
in the elasticity of the pull-out bar. As the tensile force decreases, the strain along the embedded bar
also decreases. The assumption of a uniform distribution of the bond stress along the bond length is
therefore not applicable for longer bond lengths. Mörsch [9] found a plausible explanation for this
phenomenon. Fig.2 left shows the tension stress σs of the bar and the bond stress distribution along the
bond length for different load stages. The local bond stress maximum shifts from the loaded to the
unloaded end of the bond length as further the load reaches the bond resistance of the embedded bar.
Close to the load limit (Stage III), the load is mainly transmitted by the rear part of the bond length.
Areas closer to the loaded end are already damaged, but can still transfer minor load due to friction
between the bar and concrete. Depending on the local slip, each point within the bond length is at a
different bond stress state. Consequently, the mean value calculated under the assumption of a uniform
distribution is smaller than the local maximum. Therefore the average bond stress decreases with in-
creasing bond length.
Fig. 2 Left: bond stress distributions at different loading stages according [9], taken from [2];
right: typical bond stress to slip curve
These findings were confirmed by the investigations of Mains for ribbed bars [10]. By means of strain
gauges distrubted along the pull-out bar of long test specimens, Mains could reveal the non-uniform
distribution of bond stresses for different load levels.
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various loading
conditions
Marc Koschemann, Manfred Curbach
3
2.2 What means local bond behaviour?
To describe local failure criterias of bond between reinforcement and concrete, bond tests with short
bond lengths are usually carried out. According to Model Code 2010[1] it is possible to consider an
average local bond to local slip relationship for short bond lengths. For the definition of a short bond
length lb the magnitude of lb ≤ 5 ds has been established in scientific practice, which is in accordance
with the standard for the pull-out test by RILEM [4].
Nevertheless, the experimental results of [11] and [12], for example, indicate that the length-related
bond stress continues to increase even for shorter bond lengths. Therefore, for a bond length of 5 ds, the
bond stress is not uniformly distributed along the bar and the bond behaviour cannot be considered
local. An accurate description of the local bond-slip relationship allows to derive generally valid state-
ments about the bond behaviour of ribbed reinforcing steel in concrete for any bond length by means
of theoretical approaches such as the differential equation of the sliding bond [13] eq 2. In addition to
the closed solution by using special approach functions for τ(x), equation (2) can also be solved by
stepwise integration. Martin [13] suggests a step size of one rib spacing for that, which corresponds to
roughly 0.6 ds for common rebars. On the other hand, the step size should be equal to the bond length
in the experiments on which the associated local bond law is based.
2()
²=()∙
∙ −()∙
∙
(2)
()=(())
(3)
Reference [1] provides a mean bond-stress to slip relationship, where the maximum bond strength τmax
is defined in dependence to the square root of the mean concrete’s compressive strength fcm, see eq. 3.
This is valid for pull-out failure under well confined concrete (concrete cover ≥ 5 ds).
= 2.5 ∙�
(3)
= 0.45 ∙
(4)
In contrast to this, the investigations of Huang et al. [14] revealed much higher bond stresses than
expected by the bond model of MC2010[1]. Based on their results of 28 pull-out tests with a bond
length of 2.5 ds, they introduced a linear approach to describe the maximal bond stress in case of pull-
out failure for normal and high strength concrete, see eq. 4.
Local bond to slip relationships are often used to calculate crack width for different loading sitiua-
tions. Rohling [15], for example, calculated the increase in crack width under permanent load using the
bond-oriented crack theory by Krips [16]. The input parameters for these calculations were the results
of pull-out tests with a bond length of 5 ds. However, Rohling points out, that the quality of these
calculations depends on how accurately the local bond law represents the actual conditions in the struc-
tural element. This applies in the same way for numerical investigations of bond behaviour like [17].
For few years now, fibre-optic sensing technology is offering the possibility of quasi-continuous
measurement of strain values at intervals of less than one millimeter. Distributed optical fibre sensors
(DOFS) have already been successfully applied in reinforced concrete for crack detection and strain
measurements in concrete, [18] and [19]. Applied in bond tests, this method allows to record local and
time-related changes within the bond zone. This makes it possible to record local failure criteria and
define local bond stress-slip relationships.
2.3 Specifics of tests with short bond length
When carrying out tests with short bond lengths, some effects have to be taken into account, which are
usually not relevant for bond lengths of 5 ds and even more. In general, for short bond lengths, different
arrangements and imperfections in the bond zone have a bigger impact on the results, which is mostly
reflected in a larger scatter.
Fig. 3 Left: bond stress-slip curves for different rib arrangements [17]; right: rib arrangements
13th fib International PhD Symposium in Civil Engineering
4
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various
loading conditions
By means of numerical simulations, Zobel [17] shows that the exact position of the ribs within the bond
zone have considerable influence on the results of tests with short bond lengths. Depending on the
arrangement, two or three ribs are involved in the force transmission for a bond length of 2 ds. Therfore,
the ultimate bond stress can vary up to 25% from the average (fig. 3), which covers the scatter of the
experimental results from [20] well.
Another influencing factor is the diameter of the bond breaker. Usually plastic sleeves are used to
define the bond length within the specimen and to ensure a free pre-length of at least 5 ds. However,
the plastic sleeve is also an interference for the load transfer, which leads to an early cone-typed failure
of the first concrete key. Zobel [17] investigated the influence of the ratio of diameters between bond
breaker and bar dh/ds with the result, that an increase of this ratio causes a decrease in bond strength
(fig. 4). As bigger the diameter of the bond breaker is, as further in reaches the failure cone and pre-
damages the bonded zone. This affects the test results with very short bond lengths more than for longer
bond lengths.
Fig. 4 Left: bond stress-slip curves for different ratios dh/ds [17]; right: bond zone after pull-out
failure
3 Experimental methods
3.1 General
Current investigations at the Technische Universität Dresden focus on the bond behaviour and the bond
stress distribution of ribbed steel bars under various loading conditions, including monotonic, cyclic
and long-term loading. The investigations compromise approx. 250 individual tests, 130 carried out so
far, on three specimen types and different concrete grades reaching from normal to high strength con-
crete.
3.2 Material properties and test program
Different kinds of concrete are used, reaching from a mean uniaxial strength of fcm = 30 MPa up to fcm =
120 MPa. In the test carried out so far, one normal strength concrete named C40 and two high strength
concretes named C80 and C120 were used. These two are self-compacting concretes, whereas the C40
must be compacted. All kinds of concrete have a maximum grain size of 16 mm. The compressive strength
and splitting tensile strength were determined on 10 cm cubes. The cylinder compressive strength was
calculated with a conversion factor, which was determined in advance for each concrete using 6 standard
cylinders (d =15 cm). Table 1 shows the properties of the concretes after a minimum test age of 56 days.
Table 1 Concrete properties
Type fc,cube100 [MPa] cal. fc,cyl [MPa] fct,sp,cube100 [MPa] E-Modul [MPa]
C40 55.6 48.6 3.9 34000
C80
110.5
96.1
5.6
40800
C120 141.5 123.0 6.6 51900
The nominal bar diameter ds is 16 mm in all tests and the pull-out bar is made of B500 B (yield strength
fyk = 500 MPa). The bars are provided with a pressed-on sleeve to apply the loading. The bond breakers
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various loading
conditions
Marc Koschemann, Manfred Curbach
5
are plastic tubes with a diameter of dh = 25 mm, what means a ratio of dh/ds = 1.56. The experimental
programme includes systematic investigations of the influence of the bond length on the ultimate bond
stress using pull-out tests and beam-end tests as well. The pull-out tests were configured according to
[4] with a cover of 92 mm (c = 5.75 ds), but with a lead length of 120 mm. The beam-end test allows
different configurations of concrete cover, transverse reinforcement and supplies a more realistic stress
state inside the specimen. Fig. 5 shows the configureration for a bond length of 2 ds and a cover of 2 ds.
Fig. 5 Configureation of beam-end specimen
The number of ribs and their location, individually for each embedment length, as well as the number
of two stirrups Ø6 within the bond zone were kept the same in all of the tests (Fig. 5 right). Table 2
gives an overview about the monotonic loaded tests carried out so far.
Table 2 Test programme
Concrete
Test
c= 2.0 (BE)/5.75 (PO); l
b
=
l
b
=2.0 d
s
; c=
rotated
no
stirr. shif-
ted
Σ
1.0
2.0
2.5
3.0
4.0
3.0
4.0
90°
180°
C40
BE
4
8
-
3
4
-
-
-
-
-
-
19
C80
BE
4
20
-
3
3
3
3
3
3
3
3
48
PO
4
6
-
3
3
-
-
-
-
-
-
16
C120
BE
3
13
2
3
3
3
3
3
3
3
3
42
PO
4
6
-
3
-
-
-
-
-
-
-
13
The different configurations are used to investigate the influence of the bond length (col. 3-7), for beam-
end tests the influence of concrete cover (col. 8 and 9), a rotation of the bar around the longitudinal axis
(col. 10 and 11), the removal of transverse reinforcement (col. 12), and a shift of the rib arrangement
by half a rib spacing (col. 13).
The specimens are made in series of 3 or 4 samples out of the same batch. The bar is placed in
horizontal position during casting and the beam-end specimens are concreted upside-down to ensure
good bonding conditions. After demolding the samples are covered with moist cloths for 6 days and
then stored indoor until testing. The monotonic tests are executed path-controlled and are also used as
refernce for tests with cyclic and long-term loading. For the cyclic experiments, the specimens are
exposed to a tensile loading with a lower stress level of 0.4 τult and an upper stress level of 0.7 to 0.8
τult depending on the static bond strength τult of each series. Further information about the cyclic tests
can be found in [21]. The continuation of the test programme includes further monotonic tests on nor-
mal-strength concretes as well as long-term tests. In addition, tensile tests under long-time loading are
planned, the results of which will be used to validate calculated crack widths.
3.3 Instrumentation and fibre-optic sensing
By default, the slip at the unloaded end of the bar is measured by contact-free displacement transducers
(LVDT). For beam-end tests another LVDT is attached at the loaded end and two more LVDTs are
placed right above the bond zone, one longitudinal and one in transverse direction, to record the growth
13th fib International PhD Symposium in Civil Engineering
6
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various
loading conditions
of cracks on the upper surface. The measurement distance is 100 mm for both of them. The force is
measured with a load cell, which is connected with the hydraulic cylinder. All signals were sampled
with a rate of 5 Hz.
In addition, DOFS has already been used in some tests and will be used more in upcoming series.
The hair-thin sensors with a polyimid coating are applied direcly to the pull-out bars with cyanoacrylate
adhesive and enable the quasi-continuous recording of strains along the bar with a resolution of
0.65 mm per measured value. In tests carried out so far, a sensor fibre was redirected several times
outside the bond zone so that it was applied along both sides of the two longitudinal ribs. Therefore the
sensor passes through the bond zone four times. Within the bond zone, the sensor is covered with a thin
layer of silicone to prevent bonding with the concrete. Protective tubes are arranged outside the bond
zone (fig. 6).
Fig. 6 Applied sensor fibre and protective tube; left: at the longitudinal rib; middle: in groove
through the inclined ribs; right: with support frame in helix form.
In preliminary tests, the sensors are applied at different positions on the bar with the help of grooves in
order to identify strain differences within the reinforcement’s cross-section. By means of support
frames, the sensor fibres are also placed in the surrounding concrete of the bond zone for some samples
and can detect strains in the circumferential direction.
4 Results and discussion
Looking at the experimental results for monotonic loading and a bond length of lb = 2 ds (fig. 7 left), it
can first be seen that an increase of concrete compressive strength results in higher bond strength. All
test results are above the approach according to MC 2010, eq. (3). On the other hand, there is good
agreement with the linear approach according to [14], eq. (4), although this applies especially to the PO
setup and lower bond strengths were determined in the BE tests.
Fig. 7 Left: relationship of bond strength and concrete compressive strength; right: relationship of
average bond strength and bond length (with mean concrete strength for each concrete type)
This phenomenon is even more noticeable for bond lengths longer than 2 ds (fig. 7 right). The reason
for this is the lower concrete cover in the BE setup, which reduces the confinement effect. For bond
0
10
20
30
40
50
60
70
035 70 105 140
Bond strength τmax [MPa]
Concrete compressiv strength fcm [MPa]
0
10
20
30
40
50
60
70
016 32 48 64 80
Ave. bond strength τmax [MPa]
Bond length lb[mm]
l
b
= 2.0 d
s
BE: c= 2.0 ds
PO: c= 5.75 ds
BE: c= 2.0 d
s
PO: c= 5.75 ds
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various loading
conditions
Marc Koschemann, Manfred Curbach
7
lengths of 2 ds or more, the big ring tensile forces cause splitting cracks, which lead to premature failure
and reduced bond strength. The crack propagation of these cracks was recorded during the tests (see
3.3) and the crack patterns were subsequently documented.
However, no cracks were found on the concrete surface in BE tests with lb = 1 ds. According to this,
the same failure mode occurred as in the PO tests, which also explains the almost identical test results
for this bond length. The test results also confirm the influence of bond length even for short bond
lengths lb < 5 ds. In BE tests, a doubling of the bond length from 2 to 4 ds was observed to reduce the
bond strength by approx. 30%. With the PO setup, this effect is less significant. The reason for this are
probably the higher absolute pull-out forces at longer bond lengths, which increase the splitting effect
and lead to larger crack widths in BE specimens. After the splitting is occurred, only the two stirrups
ensure a certain level of confinement, which depends on the ring tensile forces. Anyway, for both spec-
imen types and all three concretes, a decrease in bond strength is observed for a bond length of lb = 1 ds.
The cause of this can be found in fig. 4 right. As the first concrete key cannot support itself due to the
bond breaker, a breakout cone forms early on. The depth of this cone does not participate in the further
load transfer or only by friction and depends on the diameters of the bar and the bond breaker. Under
the selected conditions, the depth of the breakout cone is approx. 7 mm, which shortens the effective
bond length accordingly. For the bond length of lb = 16 mm, this means a shortening of the transmission
length by almost half, for lb = 64 mm only by roughly 10%.
Fig. 8 Left: steel strain curves for different load levels; right bond stress distribution along the
bond length
To detect those effects, differences and changes in load transfer within the bond zone during experi-
mental tests, DOFS are used. Fig. 8 left shows steel strain curves along the pull-out bar within the bond
zone for different load levels. It is noticeable that the strain curve for a low load level takes on a slightly
concave shape. By increasing the load, the shape changes to a convex course, which indicates a redis-
tribution of the load transfer. Through local derivation of the strain curves, it is possible to obtain the
bond stress distribution along the bar (Fig. 8 right). If the stress distribution at 0.4 Fmax can still be
declared as quasi uniform, a doubling of the load causes a redistribution towards the middle of the bond
length. At the time of failure, the force is mainly transmitted through the last concrete key, resulting in
a local bond stress of almost twice the mean value. Hence, it can be stated that there is a redistribution
of stress from load close to load far areas during the progress of damage, which confirms Mörsch’s
theorie [9].
5 Conclusion and Outlook
In this paper, recent investigations on local bond behaviour at short bond lengths were presented. Based
on a literature review and the results of over 130 individual tests under monotonic load, it is shown that
the bond stress distribution cannot be assumed to be uniform even for short bond lengths. By means of
DOFS, it was determined that a redistribution of the load transfer within the bond zone occurs during
the damage progress. In addition, local bond stresses could be detected, from which local failure criteria
can be derived.
Further investigations will address the effects of different loading situations such as fatigue and
creep on the internal load transfer in the bond zone. Subsequently, local bond stress to slip relationships
are described, which serve as a basis for determining crack widths.
13th fib International PhD Symposium in Civil Engineering
8
Bond stress distribution of ribbed steel bars in reinforced concrete with short bond length under various
loading conditions
Acknowledgements
The presented studies are funded by the German Federal Ministry of Economic Affairs and Energy
(BMWi, project No. 0324016B and project No. 1501601). In addition, a thank goes to the Otto-Mohr-
Laboratory, Technische Universität Dresden, for carrying out the test and the good cooperation.
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