Shear Deformation of Steel Fiber-Reinforced Prestressed Concrete Beams
International Journal of Concrete Structures and Materials
Shear Deformation of Steel Fiber-Reinforced Prestressed Concrete Beams
Deuck Hang Lee
Kang Su Kim
Thomas H.-K. Kang
Steel fiber-reinforced prestressed concrete (SFRPSC) members typically have high shear strength and deformation capability, compared to conventional prestressed concrete (PSC) members, due to the resistance provided by steel fibers at the crack surface after the onset of diagonal cracking. In this study, shear tests were conducted on the SFRPSC members with the test variables of concrete compressive strength, fiber volume fraction, and prestressing force level. Their localized behavior around the critical shear cracks was measured by a non-contact image-based displacement measurement system, and thus their shear deformation was thoroughly investigated. The tested SFRPSC members showed higher shear strengths as the concrete compressive strength or the level of prestress increased, and their stiffnesses did not change significantly, even after diagonal cracking due to the resistance of steel fibers. As the level of prestress increased, the shear deformation was contributed by the crack opening displacement more than the slip displacement. In addition, the local displacements around the shear crack progressed toward directions that differ from those expected by the principal strain angles that can be typically obtained from the average strains of the concrete element. Thus, this localized deformation characteristics around the shear cracks should be considered when measuring the local deformation of concrete elements near discrete cracks or when calculating the local stresses.
SFRPSC; shear; prestressed concrete; steel fiber; shear deformation; shear strength
It is generally known that prestressed concrete (PSC)
members without transverse reinforcement have brittle
failure modes in shear with a rapid load decrease after diagonal
(Hawkins and Ghosh 2006; Avendan˜ o and Bayrak
2011; Padmarajaiah and Ramaswamy 2001)
. On the other
hand, steel fiber-reinforced prestressed concrete (SFRPSC)
members have higher shear strength and deformation
capability compared to conventional PSC members because of
the resistance of steel fibers at the crack surface after
(Narayanan and Darwish 1987; Batson et al.
1972; Tan et al. 1996; Padmarajaiah and Ramaswamy 2004;
Furlan and Hanai 1999; Hwang et al. 2015; Thomas and
Ramaswamy 2006; Liu et al. 2009; Tadepalli et al. 2011;
Campione 2014; Colajanni et al. 2012; Dinh et al. 2010;
Spinella et al. 2012; Tadepalli et al. 2015; Islam and Alam
2013; Karl et al. 2011)
. The shear behavior of the SFRPSC
members results from very complex mechanisms, and the
local behavior at the crack surface of SFRPSC beams is very
difficult to understand. In recent studies
(Tan et al. 1996;
Hwang et al. 2015; Vecchio and Collins 1986; Watanabe and
, the smeared models that take into account the
average strain and local behavior at the crack surface have
shown great advances, while few studies have been
performed with detailed measurements and analysis on the local
behavior of discrete cracks. In this study, in order to better
understand the shear behavior of SFRPSC beams by looking
into both the global and local behavior, shear tests were
conducted using SFRPSC members with the primary test
variables of concrete compressive strength, fiber volume
fraction, and prestress level. The local behavior around the
cracks of the specimens was measured using a non-contact
image-based displacement measurement system. The local
behavior was then analyzed along with the shear behavior.
2. Experimental Program
In this study, a total of five SFRPSC beam specimens were
manufactured and tested as summarized in Table 1. The
specimens were named according to the concrete
compressive strength (H or N), prestressing force level (P0, P1, or
P2), and fiber volume fraction (F0 or F1). As shown in
Fig. 1a, the specimens had a T-shaped cross-section, and
were 300 mm in height and 100 mm in web width. For all
specimens, eight deformed bars with a diameter of 13 mm
(D13) were placed in the concrete flange, and two deformed
bars with a diameter of 22 mm (D22) were placed on the
tension side. In addition to the tension reinforcement, one
and two strands with a diameter of 12.7 mm were placed in
the P1 and P2 specimens, respectively, while the HP0F1
specimen, which was not prestressed, was reinforced with a
D13 bar that had a cross-sectional area similar to the
12.7 mm diameter strand. As shown in Fig. 1b, D10 stirrups
with two legs were placed on the right side of the specimens
at spacings of 130 mm to induce shear failure only on the
left side. Two-point loads were applied on the specimens
with a clear span of 2100 mm and a shear span of 750 mm.
As shown in Table 1, the jacking forces (Ppj) applied to the
P1 and P2 series specimens were 132.3 and 232.2 kN,
respectively, and their effective prestressing forces (Pe)
measured by strain gauges installed on the strands were
about 128 and 218 kN on average, respectively. The concrete
compressive strengths ranged from 57.1 to 67.8 MPa in the
H series specimens and from 42.6 to 43.8 MPa in the N
series specimens. SD400 steel reinforcements were used for
the reinforcing bars, and 1860 MPa low-relaxation strands
were used for the prestressing strands. Hooked steel fibers of
30 mm in length, 0.5 mm in diameter, and a yield strength of
981 MPa were used, and the fiber volume fraction of all
specimens was 1.5 %.
As shown in Fig. 2, targets were installed between the
loading point and the support at intervals of 50 mm in the
vertical and horizontal directions, and the three-dimensional
coordinates of each target were measured by an image-based
displacement measurement system. Using this system, the
relative displacements between any two targets can be
measured, and therefore the amount of deformation and
strain could be obtained at all locations on the side of the
beam. In this study, the crack opening and slip behavior
around critical cracks as well as the average shear strains in
the entire shear span of the specimens were analyzed.
3. Test Results
Figure 3 shows the load–displacement relationship of the
specimens with the marks on the diagonal cracking load
(Vcdr) and the ultimate load (Vmax), while Fig. 4 shows the
longitudinal bars (D13)
longitudinal tendons (ϕ12.7) or re-bar(D13)
longitudinal bars (D22)
Fig. 1 Section properties and specimen details (unit: mm). a Cross section properties (specimens P0, P1, P2 from the left),
b specimen details.
Fig. 2 Image-based displacement measurement system.
a Targets for measuring displacements (unit: mm),
b measurement equipment.
crack patterns of the specimens at ultimate loads. As shown
in Figs. 3 and 4, all specimens underwent shear failure. In
the case of the NP1F0 specimen, which is a conventional
PSC member without steel fibers, only a diagonal crack
appeared without any flexural crack. The load decreased
suddenly at diagonal cracking, and shear failure occurred
without a significant load increase compared to the diagonal
cracking load. For the other specimens with steel fibers
(SFRPSC beams), the load continued to increase without a
degradation in stiffness when both flexural cracks and
diagonal cracks occurred. The cracks developed to the
bottom of the compression flange, and the SFRPSC beams
showed shear failures which occurred immediately after
reaching the maximum load. It is noted that part of the test
data for the post-peak behavior of the HP2F1 specimen
could not be measured because the testing equipment
malfunctioned at the last point shown in Fig. 3. The diagonal
cracking strength (Vcdr), represented by triangular markers in
Fig. 3, was significantly higher in all other specimens than in
the NP1F0 specimen, which confirms that the steel fibers
contributed to significant increases in the diagonal cracking
loads of PSC members. In addition, the diagonal cracking
strengths of specimens HP1F1, NP2F1, and HP2F1 were
higher than those of the HP0F1 specimen because those
specimens were prestressed. With respect to the shear
strength (Vmax), represented by the circular markers in
Fig. 3, the specimens with steel fibers and a higher prestress
level had higher shear strengths; the HP2F1 specimen thus
showed the highest shear strength.
As shown in Fig. 4a, the NP1F0 specimen without steel
fibers had a single diagonal crack, and most of the
deformation was concentrated on the crack. In contrast, a large
number of flexural and shear cracks occurred in the
specimens with steel fibers as shown in Figs. 4b to 4e. It was also
observed from the crack patterns of the NP2F1 and HP2F1
specimens that the inclination angles of the critical cracks
were lower in the specimens with high prestress levels.
3.2 Average Strain and Local Displacement
In this study, the detailed measurements of average shear
strain and local deformation behavior were obtained from
the targets attached to the specimens. The average shear
strain of the entire shear span (cxy) was calculated from the
displacement data from the four outermost targets attached to
the surface of the web concrete; the results are shown in
Fig. 5. Comparing the shear stress–strain relationships
(vucxy) shown in Fig. 5 and the load–deflection curves shown in
Fig. 3, it can be seen that shear stiffness rapidly decreased
and shear strains increased significantly before reaching the
maximum load. This obviously means that the members
failed in shear after some components of the shear resistance
mechanisms reached their limits. This pattern can also be
observed in Fig. 6 which shows the contributions of shear
deformation (ds) and flexural deformation (df ) to vertical
deflection. Here, the vertical deflection caused by shear
deformation (ds) was calculated by multiplying the shear
strain shown in Fig. 5 (cxy) by the shear span length (a),
while the vertical deflection caused by flexural deformation
(df ) was calculated by subtracting the deflection caused by
shear deformation (ds) from the total deflection (dtot). The
load–deflection relationships of the HP1F1 specimen shown
in Fig. 6a demonstrate that the deflection caused by flexural
deformation increased linearly until reaching the failure
load, and the vertical deflection of the member was
dominated by flexural deformation until the load reached about
250 kN. After the appearance of the shear cracks, the vertical
deflection caused by shear deformation increased
significantly because of the rapid degradation of shear stiffness.
The same pattern was observed in the HP2F1 specimen
shown in Fig. 6b.
Using the displacement data obtained from four target sets
attached close to the cracks, as shown in Fig. 7, the local
deformation behavior near the shear cracks can be analyzed
in more detail. As presented in Fig. 8, crack slips (Ds) and
openings (Dw) were calculated as:
Ds ¼ dx cos h
dy sin h
Dw ¼ dx sin h þ dy cos h
where dx and dy are the displacements in the longitudinal
direction and the vertical direction, respectively, and h is
the crack angle, for which this study used the average
angles of the main critical crack in the web concrete
(Figs. 4 and 7).
Figure 9 shows the crack opening and slip behavior of
the test specimens at each target layer location presented in
Fig. 7. It is noted that some targets (layer 1 of the HP1F1
specimen and layer 3 of the NP2F1 specimen) were
detached during the experiment due to the surface spalling
of concrete, and that such data could not be presented in
Fig. 9. In addition, the target displacements were measured
until the maximum load for the HP2F1 specimen and its
crack opening and slip behavior is shown in Fig. 10.
According to Fig. 9a, the NP1F0 specimen without steel
fibers exhibited significantly larger crack openings (Dw)
than crack slips (Ds), and the opening-to-slip ratio (Dw=Ds)
remained almost constant until the end of the experiment.
Few changes were observed in the slope, even after
reaching the maximum load, as represented by the vertical
line in the figure. In addition, the magnitudes of the crack
openings (Dw) and slips (Ds) in all layers were very similar,
*marker : diagonal cracking
and the crack openings (Dw) were larger than in the other
test specimens. This is because the NP1F0 specimen had
only one diagonal crack, and consequently all local
deformations concentrated on this critical crack, while multiple
diagonal or flexural cracks occurred in the other specimens
with steel fibers. In the HP0F1 specimen that was not
prestressed (Fig. 9b), the crack openings (Dw) were found
to be slightly larger than the slips (Ds); the differences,
however, were not significant. This means that the
displacements occurred at about 45 relative to the crack
surface. As the crack angle of the HP0F1 specimen was
approximately 43 (Fig. 4), this result demonstrates that
most displacements around the crack occurred in the
vertical (y-axis) direction.
In the HP1F1 specimen shown in Fig. 9c, the differences
between the crack openings and the slips were comparable to
those of the NP1F0 specimen shown in Fig. 9a, but the
magnitudes of the crack openings and the slips were smaller
than in the NP1F0 specimen because of the resistances of
steel fibers. The opening and slip displacements increased
drastically when the shear strain increased by 0.03, after
which the opening and slip displacements of the HP1F1
specimen were similar to those of the NP1F0 specimen. This
means that the resistance provided by steel fibers was
significantly degraded due to the large shear strains after this
point. The NP2F1 specimen shown in Fig. 9d exhibited
significant differences between the crack openings and crack
slips. The magnitude of crack openings was predominant,
while the magnitude of slips was very low. Since the crack
angle decreased as the prestress level increased, the slip
displacements around the critical diagonal crack seemed to
be controlled effectively in the NP2F1 specimen that had the
highest prestress level among the specimens.
Figure 10 shows enlarged representations of the crack
opening and slip displacements shown in Fig. 9 until the
maximum loads, and Fig. 11 shows them against the shear
stress. The NP1F0 specimen shown in Fig. 11a exhibited
rapid increases in the crack opening and slip displacements
right after a diagonal crack occurred. After that point, as
shown in Fig. 10a, the opening and slip displacements
increased almost linearly as the shear strain increased. As
shown in Fig. 10b, the HP0F1 specimen exhibited a
significant increase in opening and slip displacements after the
strain reached approximately 0.0025. The crack opening and
slip displacements at the maximum load were larger than
those of the NP1F0 specimen having no steel fiber because
the maximum load of the HP0F1 specimen was much higher
than that of the NP1F0 specimen. Furthermore, because the
HP0F1 specimen was not prestressed, it exhibited larger
opening and slip displacements than the HP1F1, NP2F1, and
HP2F1 specimens that were prestressed. According to
Fig. 10c, the HP1F1 specimen also exhibited an increase in
opening and slip displacements at a shear strain of 0.0015,
where the shear stiffness decreased rapidly (Fig. 5).
Compared to the NP1F0 specimen having no steel fibers, the
HP1F1 specimen with steel fibers exhibited low magnitudes
of openings and slips at a similar strain level by forming
multiple shear cracks, which means that the steel fibers were
very effective for crack control. According to Fig. 10d, the
NP2F1 specimen exhibited an increase in the openings in
layer 4 when the shear strain was approximately 0.001, with
the openings occurring sequentially from layer 4 to layer 1.
In addition, layer 1 showed distinctively smaller
displacements than the other layers along all the loading stages,
because the neutral axis was still below layer 1 even until the
maximum load reached. As shown in Figs. 10e and 11e, the
HP2F1 specimen exhibited lower deformation than did the
0.02 0.03 0.04
average shear strain
: original shape
other specimens, which indicates that deformation can be
very effectively controlled by prestress and fiber
Through the comparisons of the shear stress–strain
behavior and the local opening and slip behavior between
the NP1F0 specimen without steel fibers and the other
specimens with steel fibers, the behavioral difference by the
fiber reinforcement can be clearly observed. The shear strain
of the NP1F0 specimen increased abruptly immediately after
diagonal cracks appeared (Fig. 5). At this point when the
shear strain was approximately 0.0005 (Figs. 10a and 11a),
the slopes of the opening and slip also rapidly changed.
Then, the opening and slip displacements increased at a
constant rate without a significant change in the slope until
the maximum load was reached. Because the tensile
resistance of concrete in the direction perpendicular to the
diagonal crack disappeared immediately after diagonal
cracking, the angle of principal strain was changed, and
consequently the slope of openings and slips was changed.
Since then, however, there was no change in the resistance
mechanisms, and little change therefore occurred in the slope
of the openings and slips until after the maximum load was
reached. On the other hand, the other specimens, which were
reinforced with steel fibers (i.e., HP0F1, HP1F1, NP2F1, and
HP2F1), showed no significant change in their shear
stiffness when shear cracks occurred (Fig. 5). Instead, the shear
strains increased after a significant increase in loads or even
near their maximum loads. This can also be observed in
Figs. 10b to 10e, in which the slopes of the opening and slip
changed significantly in accordance with the rapid increase
in shear strains a long time after diagonal cracking. The
reason for no significant change in their shear stiffness as
well as the slopes of slips and openings soon after diagonal
cracking is that the steel fibers replaced the tensile resistance
of the concrete that was lost at diagonal cracking. The steel
fibers at the crack surface continuously resisted until they
reached their bond strengths. Some fibers started to be pulled
out at the crack opening of approximately 0.5–1.0 mm as
: original shape
-2 0 2
longitudinal displacement, dx (mm)
shown in Figs. 10b to 10e, at which the slopes of the
openings and slips changed significantly.
3.3 Principal Directions of Average Strains and Local Displacements
In concrete members subjected to shear force, the angle of
principal strain (h) is closely related to the contributions of
shear resistance mechanisms, and it can be calculated as
(Tadepalli et al. 2011; Vecchio and Collins 1986;
Watanabe and Lee 1998)
h ¼ 12 tan 1
where cxy is the average shear strain, ex is the longitudinal
strain, and ey is the vertical strain. In order to obtain the shear
strain (cxy) in Eq. (3), the average displacement and strains
measured from any part of a member have been used in most
experimental studies. Then, the shear strains (cxy) are, in fact,
dependent on the measuring ranges of the test specimen, and
consequently the angles of the principal strains (h) calculated
from Eq. (3) differ. More importantly, the angles of the
principal strains calculated from Eq. (3) differ from the
directions of local displacements around the cracks that form
Figure 12a shows the angles of the principal compressive
strains of the HP1F1 specimen calculated using Eq. (3) with
the displacement data from four targets around the locations
of the four layers shown in Fig. 7. The principal strain
angles at each layer were initially between 30 and 45 , and
then decreased until stabilized at about 26 with a shear
strain of 0.02. As shown in the drawing on the top right side
of Fig. 12a, when the three targets attached to the concrete
piece moved down only along the vertical direction (y-axis)
due to cracking, the angle of principal compressive strain
would not be calculated as zero, say 25 –35 or so, which is
because the angle is calculated in an average manner.
Figure 12b shows the vertical displacement (dy) with respect to
the longitudinal displacement (dx) obtained from the
coordinates of two targets located at each layer and measured
until immediately after the maximum load was reached.
Across all the four layers, the longitudinal displacements
(dx) were 1 mm or smaller, during which the vertical
displacements (dy) increased up to about 10 mm. This means
that the vertical displacement (dy) was dominant over the
longitudinal displacement (dx) in the specimen. In addition,
the longitudinal displacement (dx) occurred mostly before
the maximum load, during which the displacement
directions of the concrete around the crack [tan(dx/dy)] were
between 10 and 20 relative to the vertical axis. After the
maximum load was reached, only vertical displacements
subsequently occurred, and the displacement directions of
the concrete component below the crack were almost
vertical, i.e., 0 relative to the vertical axis, which significantly
differed from the principal angles of the average strains
(approximately 26 ), as shown in Fig. 12a. For a proper
interpretation of analysis results on shear behavior, such a
difference should be carefully considered in both smeared
(Tan et al. 1996; Hwang et al. 2015; Vecchio
and Collins 1986; Watanabe and Lee 1998)
(Oh and Kim 2004; Walraven 1981; Li et al.
In this study, shear tests were conducted on steel
fiberreinforced and/or PSC members, and their localized behavior
around the critical shear cracks was systematically measured
by a non-contact image-based displacement measurement
system. Based on the investigation conducted in this study,
the following conclusions were drawn:
1. The test results showed that steel fibers and prestress
were very effective in increasing the shear cracking
strength and the ultimate shear strength of concrete
2. In the specimens reinforced with steel fibers, the applied
load increased continuously with little change in
stiffness even after diagonal cracking, and the cracks
were well controlled.
3. The shear stiffness of the specimens reinforced with
steel fibers started to significantly decrease when the
crack opening was about 0.5–1 mm because the fibers
resisting at the crack surface started to reach their bond
4. The angle of average principal strain was calculated
using the displacement data obtained from the targets
attached to the surface of the concrete members. The
angle was about 26 under large shear strain. However,
the actual deformation directions of the concrete
elements around the cracks ultimately differed
significantly. In particular, the actual deformations of concrete
elements around the cracks occurred only in the vertical
direction when the vertical displacement was more than
5. The principal angles of average strains were found to
differ considerably from the directions of local
displacements around the cracks, and this difference
therefore needs to be well understood when the shear
behavior or the local behavior around the cracks are
simulated by an analysis model.
This work was supported under the framework of
international cooperation program managed by National Research
Foundation of Korea (No. 2014K2A2A2000659).
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