Kitoh, Hiroaki

Ohuchi, Hajime

Takahash, Kosuke

Tsunokake, Hisao

Osaka City University Repository

Mem. Fac. Eng., Osaka City Univ., Vol. 49, pp. 67-74 (2008)
Interface Shear Transfer of Diagonally Arranged Reinforcing Bars
under Repeated Loading
Kosuke TAKAHASHI*, Hiroaki KITOH**, Hisao TSUNOKAKE*** and Hajime OHUCHI****
(Received September 30, 2008)
Synopsis
We focus on dowel action, which is one of the shear transfer mechanisms on the crack interfaces of RIC
members. Therefore, we calTied out experiments Ullder repeated loading with the push-off type test specimens.
Our purposes are to examine shear transfer mechanism of rebar diagonally arranged on the crack interface and
also hysteretic characteristics of shear force vs. displacement. The following conclusions can be drawn: First,
shear transfer due to the dowel action could be explained by a cantilever model based upon linear moment
distribution assumption; Second, transfelTed shear force comprised of 15% for dowel action and 85% for axial
force action in case of rebar alTanged diagonally; Last, less energy absorption could be expected because of
dominate crack opening in concrete and, in conh'ast, rebar remained in elastic.
KEY WORDS: shear transfel~ dowel action, repeated loading
1. Introduction
It is impOJiant to investigate the shear transfer mechanism which includes aggregate interlock and dowel action
on the RC crack interface. This study focuses on only the dowel action. Many studies have been calTied out on the
dowel action due to a reinforcing steel bar, called as rebar hereafter, arranged perpendicularly onto the crack
surface. However, in general crack surface is not always perpendicular to the axial direction of the rebar, so that
the rebar can work as not only dowel but also axial action. Nevertheless, less study has been conducted on the
shear transfer of the rebar diagonally alTanged on the crack interface, in particular, Ullder repeated loading. Thus,
we calTied out experiments under repeated loading with five push-off type test specimens as shown in Photo. I.
The purposes of our study are to investigate the shear transfer mechanism of rebar diagonally ananged on
interface, and also hysteretic relation between applied shear force and relative displacement along the crack
interface.
* Student, Master Course of Department of Civil Engineering
** Associate Professor, Department of CiviI Engineering
*** Research Associate, Department of Civil Engineering
**** Professor, Department of Civil Engineering
-67-
2. Experiments
2.1 Test Specimens
Typical specimens we used are shown in Photo. I. A specimen was composed of L-shaped t\1vO concrete
blocks in asynunetric layout and a couple of the rebar connecting the blocks. Bold broken black lines in the
Photo. I , indicate the single layered rebar arrangement, which rebar was so-called D16 having nominal diameter
and cross sectional area were 16nun and 199 rnn12, respectively. Furthennore, bold line segments also denote
uni-axial strain gauge arrangements on the rebar. In each specimen, moreover, another action for shear transfer
on the interface than action due to the rebar was removed by a thin acryl plate.
Two of the test parameters were an interface opening distance "e" and also a rebar arranged angle" ex " to the
interface as shown in Photo. I. As shown in Photo. I(b), the distance "e" in specimens group B was intended to
draw a potential plastic behavior of the rebar. The plastic behavior to be expected is capable for the damping
equipment. On the other hand, as shown in Photo.l(c), the angle" ex" in specimens group C was implemented to
identify shear transfer mechanism ofrebar diagonally arranged on interface.
The mechanical properties of the material used herein are also listed in Table 2.
(a) (b) (c)
Photo. I Specimens
Table.l Test Parameters
Group Tag e a Photo.!
A A-O-90 0 90° (a)
B B-15-90 15mm 90° (b)
B-30-90 30mm 90° (b)
C C-O-45 0
45° (c)
C-0-30,60 0 30, 60° (c)
Rebar(D16)
Strain Gauge
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Table.2 Material Propeliies
Materials Properties Values
Elastic Modulus 183 [GPa]
Rebar
Yield Stress 349 [MPa]
Compressive Stress 36.2 [MPa]
Tensile Stress 2.60 [MPa]
Concrete
Elastic Modulus 29.0 [GPa]
Poisson's Ratio 0.21
2.2 Test Procedure
An example of the test setup we used is shown in Photo.2. Screw cutting round bars embedded both on top and
bottom surfaces of the specimen were to be connected to the testing machine.
Repeated loading tests were controlled based on an incremental displacement. Prescribed displacements were
O.Smm, I.Omm and I.Smm with three cycles for each the displacement. Relative displacement along the interface
was measured by a displacement gauge as shown in Photo.3, and also axial and bending strains of the rebar were
observed by the couple ofuni-axial strain gauges as shown in Photo. I.
.'
Photo.2 Installed Test Specimen Photo.3 Displacement Gauge
3. Test Results
3.1 Crack Pattern
The crack pattern of A-O-90 is shown in Fig.! (a). Remarkable splitting cracks from the interface were observed
both on the front and rear surfaces along the rebar arrangements. Similar crack patterns were, moreover, found in
the specimens group B with distance "e" as shown in Fig.l (b). On the other hand, in the specimens group C with
angle" a: " , none of the splitting cracks could appear along the rebar alTangements as shown in Fig.l (c). These
cracks significantly affected the shear transfer mechanism described hereafter.
-69-
-(a) A-0-90
g;
II
(b) B-30-90
Fig.l Crack Pattern
(c) C-0-30,60
3.2 Load Displacement Hysteretic Characteristics
3.2.1 Load-Displacement Relationships
Figure 2 shows load-displacement relationships of all the specimens. In the figure, positive directions of
vertical axes were defined that the shear force made the blocks in Photo.! vertically apart from each other. The
shear force loading in the positive direction is also called as tensile loading. In all the specimens, the asymmetry
was observed in the hysteresis loop. This may be lead that concrete cover depth was insufficient in tensile loading,
so that the splitting cracks could develop with obvious opening, while the cracks closed in compressive loading.
Therefore, in tensile loading, the measured relative displacements inevitably included the crack mouth opening
distance. In addition, a pinching effect was so pronounced, that energy absorption could be less than expected,
because the crack development and opening was dominated, and the rebar did not show a plastic behavior up to
the end of the repeated loading.
0.4 0.6 0.8 I
B-30-90
50
40
30
20
10
1 -o,~.~~~-~~~.~oT,"":0.2 0.4 0.6 0.8 1
-20
-30
-40
-50
Displacement [mm]
B-15-90
50
40
30
20
10
'J&~ft,-~. foo 0.4 0.6 0.8
-20
-30
-40
-50
Displacement [mm]
o!
-20 ..-3
-40
-50
Displacement [mm]
z
c;
'0
'"o -1
...J
z
C;
'0
'"
.3 0.4 0.6 0.8
Displacement [mm]
0.4 0.6 0.8 I
o
-30
-40
-50
Displacement [mm]
Fig.2 Load-Displacement Relationships
-70-
3.2.2 Shear Stiffness
Shear stiffness due to the dowel action is defined herein as the slope of the line through points coordinate origin
and maximum load of first cycle for each amplitude (0.5, 1.0, 1.5mm). Figure3 shows the stiffness for each
specimen. Compared with A-0-90 and the specimens, the stiffness of Group B having the interface opening
distance were inferior, because deformability of the rebar was improved by setting up the opening distance. Next,
the stiffness of Group C with the rebar diagonal1y alTanged were superior to that of A-0-90, because a resistance
by axial force in the diagonal rebar was generated.
250
200
~~
E
...... ISOg
(/)
(/)
<l) 100
r.E
<+-
....
r:/J
50
-- tensile loading
- - - compression loading
• A-0-90
it.. 8-15-90
o B-30-90
• C-0-45°
• C-0-30,60
;- - - - - -. -:;-- - - - - - --e
-------- --"-' ...
9 . - - - - . - - 8: .. - - - - - -8
o
0.0 0.5 1.0 1.5
Displacement Amplitude ofTesting machine [mm]
2.0
Fig.3 Stiffness-Displacement Amplitude Relationships
3.2.3 Hysteretic Damping
As shown in Fig.2, the obtained hysteresis loop area, as a useful index of hysteretic damping, was considerably
small in all specimens. The envelope of these loops was regarded as a typical feature of shear-sensitive reinforced
concrete st11lctural elements. It was also recognized from the loops that less energy absorption was due to the
dominate crack and elastic behavior of the rebaI'. The left part of FigA shows equivalent damping factors: heq
calculated by the manner illustrated in the right part of the figure]). The superior factor values were obtained in
diagonally alTanged rebar case, while the inferior values obtained in the group B with the opening distance of the
interface.
12
I
h =~. f,W
eq 4n We
p
... A-a-gO (a)
.8-15-90 }
::I( 8-30-90 (b)
• C-O-45 }
• C-0-30 (c)
1084 6
Total Cycle
2
a)4.1% ~
• c 5.6% •
• • • t.--.~ ~!.~~~.-~=~--.:~.~~ ~r-~i:
.t- ....- .... - • -to -.: .- .. - ..•
... f • ~ \
)K ~
~
~ 10
r::::r
<l)
..c
'-' 8
OJ)
c:
0- 6~
0 4.~
~ 2~
(/)
>-.
:r: 0
0
FigA Hysteretic Damping
-71-
3.3 Shear Transfer Characteristics of Rebar
3.3.1 Dowel Action
In the test specimen of A-O-90, the shear transfer due to the dowel action could be explained by a cantilever
model with linear moment distribution asswnption as shown in FigS This assumption could be verified
satisfactory as shown in Fig.6, where theoretical moment M theo . calculated from Eq. (1) agreed with the obtained
experimental moment at measured point M exp which was calculated from flexural strain (Eq. (2) ).
The shear transfer due to the dowel action in the other specimens could also be explained by the same way.
M theo. =Psinaxx
(2)
where P is applied shear force; x is distance from interface to the measure point; db , Es , Is and eM are diameter,
elastic modulus, moment of inertia and flexural strain of the rebar.
p
Concrete
- Instrumented Strain Gauge
I
I
I
II~
1m
l'tI~
IS
,--,
E
.
~
'--'
~
~ - .8Co)
8
0
~
0.05
-0. I
Displacement [mmJ
0.2 04
Mexp.
- Mtheo
Fig.5 Cantilever Mechanism Fig.6 Rebar Moment-Displacement Relationship (A-O-90)
3.3.2 Shear Transfer Characteristics of Rebar Diagonally Arranges
Figure 8 shows a good agreement of the hysteretic characteristics of C-O-45 between the monitored load and
the calculated one from Eq.(3)~(5) based on the measured strain on the rebar as shown in Fig.7. Moreover
Fig.9 also shows a good agreement between monitored load P and measured shear force Q as shown in Fig.7.
Therefore, in the specimen C-O-45, applied shear force was transferred as flexural force action and axial force
action of rebaI'. In addition, the ratio of flexural force to axial force calculated from Eq. (6) was 15 to 85 as
-72-
shown in Fig.l O. At the SaIne time, calculated for C-0-30,60 in the same way, the ratio was 30 to 70.
Q = QM sin a + QN cosa (3)
M exp . (4)QM=--
x
QN =GNEsAs (5)
QM andQN (6)p p
where QM is calculated as the measured flexurallnoment divided by distance from the interface, QN is calculated
by multiplying axial strain of rebar CN by Esand As (cross section of rebar).
p
Instrumented Strain Gauge
~
CI
...-.8 -0.6
~
40
--30
0.4 0.6 0 8
-40 -- -j-~ :~~
Displacement [mIn]
Fig.7 Definition of Q Fig.8 P , Q -Displacement Relationship (C-0-45)
Fig.9 P-Q Relationship (C-0-45)
0.40.2
~....~-;;-~-- - 0.85
~~W~~-~-~- - 0.15
~.. - QMS ina/Q
.-----------+-9-1 __ Q cosa/Q
- (QMsina+Q cosa)/Q
ca
c
o
.-r./)
c(])
.5
'"d
c
o
Z -0.6
-0.4 -0.2 0
Displacement [rnrn]
Fig.10 The Ratio of Flexural Force to Axial Force(C-0-45)
o10- 20 30
Q[kN]
-30
-40
- -5-
40
30
20
~
~ - 0 -30
-73-
4. Concluding Remarks
Following are concluded.
As for hysteretic characteristics;
I) In all the specimens, the asymmetry was observed in the hysteresis loop because the size of concrete cover
was insufficient in tensile loading.
2) The pinching effect was so pronounced and less energy absorption was expected, because the crack
development and opening was dominated, and the rebar did not show a plastic behavior up to the end of the
repeated loading..
3) Shear stiffness of Group B with some distance were inferior to A, because deformability was improved by
setting up some distance on the interface. On the other hand, that of Group C with the inclined angle were
superior to A because a resistance by axial force was generated by rebar diagonally arranging.
As for shear transfer mechanism ofrebar;
4) Shear transfer of dowel rebar could be explained by a cantilever model with linear moment distribution
assumption.
5) In the specimens with the inclined angle, applied shear force was transferred as flexural force action and axial
force action ofrebar. In addition, the ratio of flexural force to axial force was IS to 85 in C-0-45. On the other
hand, the ratio in C-0-30,60 was 30 to 70.
5. References
1) A. Shibata: Seismic analysis of structures, Morikita Publishing Co., p.49 (2003) (in Japanese)
-74-


Interface Shear Transfer of Diagonally Arranged Reinforcing Bars under Repeated Loading

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Interface Shear Transfer of Diagonally Arranged Reinforcing Bars under Repeated Loading

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