International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
188
Effect of high strength concrete intersecting beam on bond
behaviour at the joint
Kafeel Ahmed 1, Ahmed El Ragi2, Ayesha Mahmood3, Uzma Kausar3
Civil Engineering Department, University of Engineering and Technology Lahore, Pakistan. Kafeel91@gmail.com
Civil Engineering Department, College of Engineering, Qassim University Saudi Arabia
3
Global Engineering Associates, Pakistan
1
2
ABSTRACT
At the joint of intersecting beams, bending of one beam, affects the bond strength of the intersecting beam. The bond strength of
intersecting beams decreases due to magnification of tangential/circumferential tensile bond stress. Experimentation was carried out to study the bond behaviour at the joint of high strength concrete intersecting beams. High strength concrete beams
were casted for this purpose. These were divided into different sets. Each set consisted of three beams, two intersecting and one
control. All the beams were instrumented with steel and concrete strain gauges and linear variable displacement transducers.
The results of the experimentation showed that at the joint of intersecting beams, bond strength of primary beam reduced as
compared to control beam due to flexural action of secondary beam. This reduction in bond strength of primary beam was 11 to
20% as compared to control beam. It necessitates the provision of bond improving measures at the joint of high strength concrete intersecting beams.
Keywords : Intersecting beam, Conrol beam, Slip of steel, Bond stress magnification, Fracture process zone.
1 INTRODUCTION
T
IJOART
he bond behaviour of concrete and embedded reinforcing
steel is essential for composite action in reinforced concrete construction [1,2,3,4]. Generally the pullout test is
performed to determine the bond strength, however, the results do not represent the actual stress as the bond stress distribution in pullout test, is different from that present in flexural members. Lateral confinement is also different in pullout
tests. This affects the tangential stress developed around the
steel bar in the pull out samples [5,6,7].
However, in reinforced concrete flexural members, the
joints of the intersecting beams are important as there are
chances of bond failure and subsequent slip of steel relative
concrete. Therefore, it is necessary to study their bond performance. At such locations, reinforcement of column and beam
is passing, leaving little openings for concrete to be poured.
Concrete may not be properly compacted at such locations.
This honey combed concrete may have reduced adhesion and
friction bond [2].
The provision of micro silica in high strength concrete,
may increase the adhesion and friction bond [8]. However this
may not be enough to overcome the problem of poor compaction at the congested joints of the flexural members.
Moreover the mechanical bond may also be weak due to
weak concrete keys that may split as a result of tangential
bond splitting stress. This may cause slip of steel relative to
concrete. Therefore decrease in bond stiffness at the joint may
result in joint rotation and mid span deflection more than the
limits given by the code of practice [2, 13].
In order to study this complex stress state at the joints of
high strength concrete intersecting beams, bond beam tests
with models of intersecting beams were designed and preCopyright © 2013 SciResPub.
pared to study the bond behaviour. The development length
was kept constant in bond beams tests and models of intersecting beams. The compressive strength of concrete was also
same. Bond beam acted as control beams and beams of intersecting model were named as primary and secondary beams.
All these beams and models were tested and data was recoded. This data was processed and relationships were developed.
In all the samples, bond strength of primary beam reduced
as compared to control beam. Taking into account the mechanics of joint of intersecting beams, the flexural stress of one
beam acts in the same direction as the tangential/circumferential tensile bond stress developed around the
steel bars of the other beam [13]. This tangential stress developed due to slip of the concrete keys at the rib of the reinforcing steel. Concrete crushed infront of the rib, forms a wedge
on which concrete present between two ribs (concrete key)
slips [9,10]. The flexural stress of the intersecting beam, magnified the tangential bond stress and when, it exceeded the tensile strength of the concrete, longitudinal splitting cracks were
initiated [13]. Mathematical model was developed to calculate
the magnified bond splitting stress responsible for the initiation of the splitting cracks around the steel bar in high
strength concrete beams.
2. BOND FRACTURE MECHANICS
Strain softening and stress redistribution of the bond, adjoining the reinforcing steel bar, do not occur in high strength concrete. There is a small fracture process zone in front of primary
and longitudinal splitting bond cracks. The zone of perfect
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
plasticity is insignificant or very small [13,14,15,16] as shown
in Fig.1. Little energy is used in plastic cracking in high
strength concrete. All the bond fracture energy consists of surface energy. The stored strain energy is large and crack propagation suddenly take place in a brittle manner [1, 2, 13, 15].
The high strength concrete samples exhibit an initial stiff linear bond behaviour. Cracks initiate at much higher load level,
typically 70 to 80% of the ultimate load [17]. Therefore in high
strength concrete bond beam tests and models of intersecting
beam tests, interface de bonding cracks and longitudinal splitting cracks initiate at higher magnitudes of bond stress. The
bond strain energy accumulates in high strength concrete
keys, present between the ribs of the steel reinforcing bars. As
soon as a crack initiates at the interface due to slip between
steel and concrete, all the accumulated bond strain energy is
poured in to this crack where it is dissipated in the form of
surface energy. Since small cracking occurs therefore whole
energy is used in immediate crack propagation in highly abrupt manner [13].
σ ys =
rp =
rp α
k
i
2πr
p
189
deformed steel bars according to ASTM C 36 were used. Since
the tangential bond stress is a function of rib height and rib
spacing, therefore geometric properties of the steel bar were
measured and these are shown in Table 1. Four control beams
were casted. In each set, the strength of the concrete was same
and different in defferent sets. In order to keep only one variable, all other factors were kept constant. This variable was the
flexural tensile stress of the intersecting beam. The embedded
length of 5.0 d b was provided in all the beams. The objective
was to study the bond behaviour at the required embedded
lengths. PVC pipes were used to break the bond between steel
and concrete in the remaining part of the beam as shown in
Fig.2. The cross section is shown in Fig.3. This was done on the
basis of research findings of pull out and bond beam tests of
researchers [8, 9].
Uni-axial strain gauges with 7.0 mm gauge length, were
used to determine the strain developed during the testing of
the specimens as shown in Fig.4. The surface of the steel bar
was made smooth and level, for the installation of strain
gauge. Degreasing, conditioning and neutralization of the
steel bar was done as per guidelines provided by the strain
gauge manufacturer. The concrete stain gauge embedded in
polymer concrete, was used to determine concrete strain as
shown in Fig.5. Polymer concrete was provided to have a perfect bond between polymer concrete and adjoining concrete of
the beam. This arrangement ensured the determination of the
concrete strain accurately
IJOART
Ki 2
2πσys 2
Ki 2
σys 2
(1)
(2)
(3)
σ ys = Yield strength of material
r p = Size of fracture process zone
K I = Stress intensity factor
This bond fracture behaviour of high strength concrete can be
explained by linear elastic fracture mechanics (LEFM). All the
grains of the fracture path of longitudinal splitting bond
cracks, rupture due to de-cohesion of bonds between grains.
However, the remaining material shows elastic response.
Mathematical relationships mentioned below is for high
strength materials and developed by David and Broeks that
support the fracture behavior of high strength concrete
[14,15,16].
3. EXPERIMENTATION
In this experimentation, cementitious materials, micro fillers,
mineral admixtures and superplasticizers were used to fully
pack the constituents of high strength concrete. Hot rolled
Copyright © 2013 SciResPub.
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
190
through the data logger of the universal testing machine.
Fig. 5 Concrete strain gauge
Table 1
Properties of steel bar used
Bar
Dia
meter
Rib
Height
'a'
mm
13
mm
1.21
13
1.35
1.85
19
1.47
1.80
19
1.52
1.84
Table. 2
Results of compressive strength tests with age
IJOART
Avg.
Rib
Width
'b'
mm
Avg.
c/c Rib
spacing
'c'
mm
Clear
distance
between
ribs
mm
a/c
1.91
7.38
4.945
0.16
7.96
5.03
0.17
7.97
4.945
0.18
8.01
5.574
0.19
During pouring, concrete and steel strain gauges and their
wires were properly protected. The process of pouring is
shown in Fig.6. Immediately after pouring, the curing of the
beams was started to stop the loss of water due to evaporation
as shown in Fig.7. Since water/cement ratio was kept low
therefore water loss may lead to desiccation of cement. The
compressive strength of the concrete was determined by testing 150.0mm diameter and 300.0 mm heigh cylinders at 7, 14
and 28 days as per ASTM C-39. The results are shown in Fig.8
and Table.2.
The bond beams were tested at 28 days. The marking on
the beams was carried out according to the testing scheme of
data logger. All channels were reserved for the selected outputs. Testing was done in strain controlled universal testing
machine (UTM) as shown in Fig.9. Linear variable displacement transducers (LVDTs) were used to determine the slip of
steel and concrete as shown in Fig.10. Load cells, attached
with the data logger, were used to confirm the load values
obtained from the UTM. Similarly strain gauges were also attached with the data acquisition system. Two points loading
was applied through the load cells. Deflection was measured
Copyright © 2013 SciResPub.
Compressive Strength
Age
Sample
1st
Set
2nd
Set
3rd
Set
4th
Set
Days
Cylinder
MPa
MPa
MPa
MPa
7
100.0 mmX 200.0 mm
20.0
32.0
43.0
60.0
14
100.0 mmX 200.0 mm
23.0
36.0
56.0
72.0
28
100.0 mmX 200.0 mm
42.0
50.0
75.0
100.0
In the first set of the beams, the strength of the concrete used,
was 42.0 MPa. The size of the beam was 150.0 x 200.0 x1080.0
mm. Its behaviour is explained below. First, steel and concrete
experienced expansive strain monolithically as recorded by
strain gauges and LVDTs. However, when the adhesion and
friction bond failed, slip occurred. As the slip increased, steel
strain decreased and concrete strain increased.
Fig.8 Compressive strength of concrete
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
The stress was transferred through the mechanical bond.
When mechanical bond failed, steel bar relaxed and returned
back. Failure started by the initiation of flexural cracks present
at locations of PVC pipes. These cracks propagated and multiplied as the load increased. Then they converted to horizontal
bond cracks as shown in Fig.11. Finally a “v” notch bond failure was observed. The concrete strain gauge failed quite earlier. However steel strain gauge recoded the data even when
steel bar was compressed.
191
beam. The whole testing arrangement is shown in Fig. 16. In
the next 2nd , 3rd and 4th set of beams and intersecting models, the strength of the concrete was increased to 50.0, 75.0 and
100.0 MPa respectively. The model of intersecting beams before testing is shown in Fig.15. Testing was done in the same
way as that of 1st set as shown in Fig.16. The results were obtained, processed and relationships were plotted. They are
shown in Fig.17 to Fig.20 and all bond strengths are compared
in Fig.21 and Table.6.
Fig. 13 Tied steel and pouring in progress
Fig.9 Testing of beam in progress
Two point loading
IJOART
Primary
beam
Secondary
beam
Fig.10 Testing of beam in progress
Fig. 14 Loading of intersecting beams
Fig.15 Model of intersecting beams before test
Fig.11 Failure in progress
Similarly 1st model of intersecting beams was casted from 42.0
MPa concrete. Its plan and arrangement were same as that of
1st beam of bond beam test. The arrangement of steel in the
form and during concreting is shown in Fig.13. The gird marking and instrumentation was done in the same way as it was
that of beams. The load was applied through a special testing
assembly. This assembly had same shape as that of X-section
to be tested as shown in Fig.14. Two point load could be applied simultaneously on both the beams. Load cell was attached with the data logger. One beam having more effective
depth was named as primary beam and other as secondary
Copyright © 2013 SciResPub.
Fig.16 Testing of the model
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
192
Fig.17 The Bond behaviour of Set_1
Fig.21 Comparison of Bond behaviour of all the beams
Table.3
Comparison of the bond strengths
Type of beam
Secondary Beam
Primary Beam
Control Beam
Bond Strength in MPa
Set-1
Set-2
Set-3
Set-4
14.0
18.0
22.0
22.0
24.0
30.0
23.0
29.0
35.4
26.0
33.0
37.0
IJOART
Fig.18 The Bond behaviour of Set_2
4. ANALYSIS OF THE RESULTS AND
DISCUSSION
The bond strength was calculated by using the formula as given below. The strain was measured from the steel strain
gauge. Then using the modulus of elasticity of steel, stress
present in steel was calculated, from the stress by using the
area of steel, force present in steel was calculated. Then this
force was divided by the bonded area of the steel bar present
over the development length or embedded length.
Fig.19 The Bond behaviour of Set_3
(4)
(5)
f s = Steel Stress
A b = Area of steel bar
ε s = Steel Strain
d b = Bar Diameter
E s = Modulus of elasticity of steel
l d = Development length
Fig.20 The Bond behaviour of Set_4
Copyright © 2013 SciResPub.
The results of the experimentation show that in 1st set of experimentation the bond strength of primary beam reduced by
about 18.0%, in 2nd set by about 20.0%, in 3rd set by about
18.0% and in 4th set by about 11.0% as compared to control
beam. Following equation was developed for the separate
control beam and primary beam of the model of intersecting
beam. The co-efficient of correlations of these result varied
from 0.97 to 0.98.
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
(6) For Control Beam
(7) For Primary Beam
u p = Bond stress of primary beam
u c = Bond Stress of Control Beam
s = Slip of the steel
α , β = Coefficients
This reduction may be due to the reason that when two intersecting beams are loaded then steel has the tendency to slip
relative to the concrete due to difference in stiffness of both the
materials. During this conical compression struts are formed
around the reinforcing bar ribs and tangential bond stresses
generated in the surrounding concrete [2,13]. This stress is
responsible for the formation of longitudinal bond splitting
cracks around the steel bar as shown in Fig.22. This stress is
magnified by the tensile component of the flexural stress of
intersecting beam. Hence stress magnification reduces the
bond strength of the beam. Brittle behaviour was observed in
high strength concrete The mechanics of intersecting model is
shown in Fig.23[18]. The mechanism for stress magnification is
shown in Fig.24 [2, 13]. In order to calculate the magnitude of
the bond splitting stress,
193
Tepfer et al, used the thick walled cylinder analogue to the
expanding concrete key over the ribs in the anchorage zone.
The inner radius of the cylinder is taken as bar size and out
radius as the concrete cover. The radial pressure “pi” is equal
to tangential tensile stress as shown in Fig.25. In the plane of
the steel bar, the radial pressure is a function of concrete bond
stress by the assumption of Mohr-Columb failure criterion,
these two parameters are defined as “τ” and “pi” [10,19]. In
the model, steel of radius “Ro” is embedded in concrete of
radius “Ri”, Where as “Ri” defines the crack front as shown in
Fig. 26 [10, 11, 12, 19]. At the crack front tangential bond stress
is equal to the tensile strength of the concrete fct.
IJOART
Fig.25 Radial component of the bond stress
Fig. 22 Longitudinal splitting crack formation [19]
Fig.26 Model for partly cracked concrete [10,19]
Fig. 23 Mechanics of model [16]
Fig.27 Stress magnification at the joint
Boundary condition is used to calculate “pi” in the elastic outer part. The radial and tangential stresses are given by the
classic theory of elasticity [2,10,11,12].
Fig. 24 Stress magnification at intersecting beam [10]
Copyright © 2013 SciResPub.
p i = τ tanα
Assume α = 45o
pi = τ
(8)
(9)
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
194
For Ascending part of the curve (14)
For descending part of the curve (15)
(10)
At the crack front σ t = f ct r= R i
6. CONCLUSIONS
(11)
The flexural stress of the secondary beam of the intersecting
beam model is given by the bending stress theory and shown
in Fig.28. At the joint of the intersecting beams these two
stresses add up and magnify the total stress that is responsible
for the splitting of the concrete keys in the anchorage zone of
the ribs of the steel bar as given by the author in following
equations
(12)
6.1 When bond behaviour of high strength concrete primary
beam is compared with control beam of the model of intersecting beams, then it is clear that bond strength of primary beam
reduced as compared to control beam. This result is present
incase of all the sets of the beams.
6.2 The bond strength of primary beam of intersecting model
reduced for 42, 50, 75 and 100 MPa concrete. The magnitude of
the reduction varies from 11.0% to 20.0%.
6.3 This may be attributed to the flexural action of secondary
beam that magnified the circumferential tensile bond stresses
of primary beam, leading to longitudinal splitting crack initiation and propagations. This reduced the bond strength of primary beam as compared to control beam.
IJOART
(13)
5. COMPARISON WITH LOCAL BOND
CONSTITUTIVE MODEL
When the bond behavior of the control beam and primary
beam of the intersecting model is compared with bond constitutive model given by Eligehausen et al (1983), (ascending part
adopted by Comite- International du Beton- Federation International de la Precontrainte Model Code 1990), then it shows
that the response of the beam is close to splitting bond failure
and not to pull out bond failure as shown in Fig.28. The reason
for this behavior is the splitting of the concrete due to circumferential tensile bond stress. This local bond model is shown in
Fig.28. This ascending part is mathematically given by Eligehausen et al (1983) and shown below. The descending part
could not be determined in this set of experimentation
[11,12,13].
Monotonic
Envelope
u1
umax
α
Splitting
βumax
failure
Smax
S1
S2
S3
Fig. 28 Bond constitutive model by Eligehausen et al [11]
Copyright © 2013 SciResPub.
6.4 Mathematical model is developed to calculate the bond
splitting stress responsible for failure at the joint of intersecting beams.
6.5 The results showed the splitting failure which is having
same shape as that of bonds splitting failure given by ComiteInternational du Beton- Federation International de la Precontrainte Model Code 1990
ACKNOWLEDGMENT
The author wish to thank University of Engineering and Technology Lahore Pakistan, to provide support for this work.
REFERENCES
Journal
[1] Ahmed, K. Mahmood. A, El Rajy, A. Goraya, R. A., “ Effect of cover on bond behaviour of fiber reinforced high
strength concrete” International Journal of Scientific and
Engineering Research, Vol 5, No. 1, 2014, ISSN: 2229-5518,
Accepted for publication.
[2] Ahmed K., El Raji A., Kausar U., Goraya, R. A., “ Mechanics of bond behaviour at the joint of normal strength concrete intersecting beams” Life Science Journal 2014,
ISSN:1097-8135, Accepted for publication.
[3] Ahmed, K. Siddiqi, Z.A. and Ghaffar, A (2008), “Comparison of bond behaviour of hot rolled and cold twisted steel
reinforcement in high strength concrete”, Mehran University Research Journal of Engineering and Technology,
ISSN 0254-7821, Volume 27, pp365-377.
IJOART
International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013
ISSN 2278-7763
[4] Ahmed, K. Siddiqi, Z.A. and Ashraf, M. (2009), “Effect of
cover and development length of twisted steel on bond
stress and slip relationship for High Strength Concrete”,
Pakistan Journal of Engineering and Applied Sciences,
Vol.2, pp79-88.
[5] Ahmed, K. Siddiqi, Z.A. Ghaffar, A and M. Saleem,
(2007), “Bond behavior of twisted steel in High Strength
Concrete”, Proceedings of International Conference on
Cement Based Materials ACBM-ACI Lahore, 11-14 September 2007, ISBN No:978-969-546-016-0, Vol. 2, pp10111022.
[6] Ahmed, K. Siddiqi, Z.A, Z. A. and Yousaf, M (2007),
“Slippage of steel in high and normal strength concrete”,
Pakistan Journal of Engineering and Applied Sciences,
Vol.1, 2007, pp31-40.
[7] Tastani S. P, Pantazopoulou S. J, “Experimental evaluation
of the direct tension pullout bond test”, Bond in Concrete
from Research to Standards 2002, Budapest, Hungary.
[8] Weisse, D and Holschemacher, K (2003) “Some aspects
about the bond of reinforcement in UHSC” LACER, No8,
pp 251-261.
[9] Abrishami H H, Mitchell D, “Analysis of bond stress distributions in pullout specimens” Journal of Structural Engineering ASCE, Vol 122, No 3, Paper No 10368, 1996, pp
255-261.
[10] Wang, X and liu, X (2003) “A strain softening model for
steel-concrete bond” Cement and Concrete Research, Vol.
33, pp 1669–1673
[11] Harajli M. H, “Comparison of bond strength of steel bars
in normal and high strength concrete”, Journal of Materials in Civil Engineering, Vol. 16, No 4, 2004, pp 365-374.
[12] Harajli M H, “Comparison of bond strength of steel bars
in normal and high strength concrete” Journal of materials in Civil Engineering, Vol 16, No 4, 2004, pp 365-374.
195
[19] Tepfer, R, “ A theory of bond applied to overlapped tensile reinforcement splices of deformed bars” Report 73-2,
Chalmers University of Technology, Goteborg, 1970.
IJOART
Book
[13] Ahmed, K. (2009) “Bond strength of ultra high strength
concrete at intersection of beams” PhD Thesis, University
of Engineering and Technology Lahore, Pakistan. ,pp 2193
[14] D. Broek. “Elementary engineering fracture mechanics”,
1st edition, ISBN: 90 286 0304 2, Noordhoff International
Publishing Lyden, 1974.
[15] ACI 446.1 R-91 (1991), “Fracture mechanics of concrete:
concepts, models and determination of material properties”, Reported by ACI Committee 446, Fracture Mechanics, (Re approved 1999).
[16] ACI 408R-03 (2003), “Bond and development of straight
reinforcing bars in tension”, Reported by ACI Committee
408, 2003,pp 4-7.
[17] Newman, J. Choo, B. S (2004), “Advanced concrete technology”, 1st edition, ISBN 07506 5104 0, ELSEVIER, Butterworth Heinemann, Vol.3, pp3/1-3/16.
[18] Nilson, A, H. Winter, G (1991) “Design of concrete structures”, 11th edition, ISBN 0-07100844-6, McGraw-Hill, pp
177-215.
Copyright © 2013 SciResPub.
IJOART