CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND CONFINEMENT

http://www.iaeme.com/IJCIET/index.asp 109 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 1, January 2017, pp. 109–122, Article ID: IJCIET_08_01_012
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
CROSS-CORRELATION OF STRESSES IN THE
TRANSVERSE REINFORCEMENT UNDER SHEAR
LOAD AND CONFINEMENT
I. Tegos
Civil Engineering Department,
Aristotle University of Thessaloniki, Thessaloniki, Greece
N. Giannakas
T. Chrysanidis
ABSTRACT
The main aim of the present study is to give an answer to the question whether the transverse
reinforcement, which is required for the shear resistance of columns, must be added to the one
required for the cross section confinement, or it is possible for one to substitute the other. The
superposition of these reinforcements is defended by the fact that the shear reinforcement results
from the shear action, while the transverse reinforcement, required by the confinement, results
from the axial compression of the section. The present study is experimental and uses strain
gauges, in order to check the stresses of the transverse reinforcement. Useful conclusions are
drawn.
Key words: Transverse reinforcement, shear load, confinement, superposition, columns, shear
reinforcement, stresses.
Cite this Article: I. Tegos, N. Giannakas and T. Chrysanidis. Cross-Correlation of Stresses in the
Transverse Reinforcement under Shear Load and Confinement. International Journal of Civil
Engineering and Technology, 8(1), 2017, pp. 109–122.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1
1. INTRODUCTION
The problem of complex stresses of structural concrete elements is known and normally always present.
The pure strain is a more rare condition compared to the complex strain, which nevertheless exists.
Addressing at the design stage complex stresses is a rather commonly accepted practice [1-10]. Perhaps the
thorniest case is the coexistence of bending and shear, where due to their separate treatment, a diagram
known as diagram of shifted forces of tension flange was invented. In other cases the solution is clear: (a)
Bending and axial forces are treated together. (b) The shear and torsion, in contrast, are treated separately
and their results are superimposed. (c) Bending and torsion are superimposed since torsion implies a

I. Tegos, N. Giannakas and T. Chrysanidis
charge of the tension zone and a relief of the compression zone. (d) Bending and puncture are subject to
interaction and (e) Shear and puncture are separated by appropriate criteria.
Another example of interaction is the case of behavior factor q, which according to the Seismic Code of
bridges is considered as a function of both the value of the shear span and the value of the normalized axial
load. It is known that in the case of values below 3.5 for the shear span, value of q equates to these values
for the shear span and then is further reduced depending on the value of the normalized axial load.
It remains, at least for the authors of this paper, the question; what happens, or rather what must be true
in the case of coexistence of normal stresses with shear when inelastic response of structures is examined:
is it enough in this case the shifted diagram of the forces of tension flange?
The trigger, which led to the preparation of this work, can be stated very simply with the following
question: is it possible two cases of columns, one strained with a large shear and the other strained with a
low shear, to be treated versus transverse reinforcement as equally demanding cases? Because equal
treatment is employed by the practice established to earthquake resistant design of structures. And this
practice is, of course, the independent requirements of shear and confinement, so that the required
reinforcement for one of them is assumed to complement the required reinforcement for the other. For
example, in the case of a problem that consists a complex load with M, N and V, if the required
confinement reinforcement due to axial N load is greater than the required reinforcement due to shear V
load, then the reinforcement due to N load is considered enough to meet the smaller requirements of the
second reinforcement, although each reinforcement heals different needs and satisfies a different
mechanism. Of course, it should be noted the fact that usual computer programs, coming from countries
that do not face the problem of earthquakes, calculate merely the reputable against shear checks and then
let the consulting engineer to choose by his/her own judgment about meeting the requirements having to do
with confinement.
At this point, it should be noted the peculiar role of compressive force N, which both through the
increased concrete share attributes and through the disregard of the drastic reduction (because of N) of
lever arm z (Figure 1) contributes to the drastic reduction of the resulting transverse reinforcement required
against shear.
As mentioned above, the defiance of this established concept about the fact that the requirements of
shear and confinement are dealt together, was the main motivation of this research. The foremost part of
the present paper is the experimental part. And there is no doubt that the safest way to document on
complex and complicated matters is the experimental route. This route was followed in this case.
Historically, it is known that Professor Leonhard reversed used experimental results in the early 60’ the
established, until then, theory of Mörsch about shear. He has done so using strain gauges, through which it
was made possible to measure the elongation of the transverse reinforcement. At that time, it was
established the existence of, what is known today as, "concrete share" in resistance against shear.
One issue, which also occupied the present investigation, is whether the same answer applies to both
ductile (calculated with q>1) constructions and to non-ductile (where applicable q=1) since the hitherto
perceptions about the activation of confinement mechanism assume that is activated when concrete reaches
its ultimate resistance. Main argument of this opinion is based on the assumption that the ascending
branches of the unconfined and confined concrete curves are identical [11-16].
It is known that, in nowadays practice, the transverse reinforcement of cross sections, which are
stressed by combined shear and torsion actions, is determined by the superposition of the required, in each
loading, reinforcement. However, the combination of shear and confinement leads to a substitution of the
corresponding reinforcement. In the present experimental study, circular cross section specimens having
longitudinal and transverse spiral reinforcement are examined against different type of loadings: a) Axial
compression, b) bending, c) bending combined with shear force and d) almost only shear force. By means
of strain gauges, the stresses of the transverse reinforcement are checked and conclusions are drawn.

Cross-Correlation of Stresses in the Transverse Reinforcement Under Shear Load and Confinement
2. EXPERIMENTAL RESEARCH
2.1. Test Specimens
The work includes three specimens of circular cross section and is targeting an initial answer to the
question raised. The geometric characteristics, the reinforcement and the qualities of the materials are
shown in Table 1 and Figures 2, 3 and 4.
Table 1 Characteristics of test specimens.
Test
specimen
L
(mm)
D
(mm)
Longitudinal
reinforcement
Transverse
reinforcement
fc
(MPa)
fy
(MPa)
fyw
(MPa)
1 1500 200 16Ø10 Ø4.2/2.0 cm 41 520 760
2 1500 300 2x16Ø10 Ø4.2/2.0 cm 58 520 760
3 300 150 Montage Ø4.2/1.5 cm 41 760 760
The geometry, the reinforcement and the concrete quality of test specimens were selected in such a
way so that the first specimen will be led to flexural failure (and by extension to inelastic behavior), while
the second specimen will be led to shear failure (having roughly equal strength in flexure and shear). The
third, finally, specimen was designed in such a way so that the failure comes from uniaxial compression.
In the first two specimens, dense spiral reinforcement with fixed step 2 cm was placed along their
whole length. In the case of the third test specimen, in order to achieve a constant step of the spiral
reinforcement, thin bars of negligible axial strength were placed. Upon these bars, spiral reinforcement was
bind. At the end base regions, spiral reinforcement was thickened in order to avoid secondary splitting
effects.

Figure 1 Caption of a typical figure.

Figure 2 Geometry, loading and strain gauges’ positions of first test specimen.
Figure 3 Geometry, loading and strain gauges’ positions of second test specimen.
Figure 4 Geometry, loading and strain gauges’ positions of third test specimen.

2.2. Load Test setup
The test specimens 1 and 2 were loaded under an appropriate load setup as simply supported beams having
a static span of 1.35m. Loading consisted of two equal point loads which were applied symmetrically to
the specimen, with an in-between space of 35cm for the first and 30cm for the second specimen. The
relevant shear opening (active) for the first specimen was α = 0.50/(0.75x0.20) = 3.3 and for the second
specimen was α = 0.525/(0.75x0.30) = 2.3. Figures 5 and 6 show the test load setups. As can be seen, in
order to avoid localized failure at the loading point, the loads spread over a wider area through suitable
cylindrical metallic inserts. For specimens 1 and 2, deflections were measured in the middle of both
specimens, while for specimen 3, axial shortenings were measured with the help of a dial indicator.
The locations of the strain gauges were, towards the goal of research, adjudged as the most suitable and
sought to determine the activation of the transverse spiral reinforcement in interesting places that strain
takes place, such as: (a) compression, (b) flexure, (c) shear, and (d) flexure and shear together. Certainly, it
has to be noted the fact that the state of absolutely net shear is considered generally not to be present as a
type of strain of structural elements.
Figure 5 Load test setup of second test specimen.

Figure 6 Load test setup of third test specimen.
3. RESULTS
3.1. Test Specimen 1
The first specimen, as it was expected, showed intensive flexural cracking, whose launch was diagnosed
through readings of the dial indicator. With the progress of loading, vertical flexural cracks appeared
initially in the central region of the specimen, while diagonal shear cracks were few in number, almost
unnoticeable and of minimum width. The flexural response of the specimen was extremely ductile,
resulting to a large remaining deflection for the specimen, which is clearly visible in Figure 7. Concrete
spalling took place in compressed fiber and along the whole length of the area of net flexure.
From the load – normalized strains diagrams obtained from measurements of strain gauges, it was
observed that swelling of the compression zone took part in the central region of net flexure. Transverse
reinforcement was significantly activated and entered deep into the yield region surpassing the
conventional ey = 2.175‰ in the top fiber of the effective cross-section of the specimen, where there was a
record of εS = 4.79‰, while in the location of the same helix of the spiral reinforcement which is 45o to
the vertical, there was a decrease in the value of elongation at 3.17‰. Finally, in the position which is 90o
to the vertical, a value of elongation equal to 1.75‰ was recorded (Figures 8, 9 and 10). The fact that the
depletion of the transverse reinforcement has taken place in the area where axial compression and shear are
absent, which are considered as the only reasons for the existence of such a reinforcement, suggests the
possible existence of a gap in the estimation of transverse reinforcement.
In the area of strain by the coexistence of flexure and shear, transverse reinforcement activated to a
lesser extent than the respective reinforcement of the central region, displaying values about ey = 2.175‰.
The stress difference in the two critical (as far as the shear is concerned) sections between external load
and support, which were strained under the same shear, suggests the quasi smouldering superposition
between requirements on one hand of normal stresses (in this case, the only representative is flexure) and
on the other hand of shear.

http://www.iaeme.com/IJCIET
Figure 7 Intensive flexural cracking and remaining deflection of the first test specimen.
Figure 8 Elongations of transverse reinforcement of the under net flexure strained central section.
IJCIET/index.asp 116
Intensive flexural cracking and remaining deflection of the first test specimen.
Elongations of transverse reinforcement of the under net flexure strained central section.
editor@iaeme.com
Intensive flexural cracking and remaining deflection of the first test specimen.
Elongations of transverse reinforcement of the under net flexure strained central section.

Figure 9 Load – normalized strain diagrams of strain gauges of the first test specimen.

Figure 10 Maximum values of normalized deformation [‰] of transverse reinforcement of the
first test specimen.
While the first specimen can be considered as representative of ductile components, since the resistance to
shear outweighed the corresponding flexural strength, specimen 2 was designed as a representative of
elastically responding, during the earthquake, components, for which capacity design criteria are not
applicable.
The second specimen showed inconspicuous flexural cracking, which was detected first by the values
of the dial indicator. Afterwards, diagonal cracks occurred rapidly. With increasing load, shear cracking
was widened and ultimately the failure occurred explosively, with fracture of the transverse reinforcement
and extensive concrete spalling in the area that flexure and shear act together (Figure 11). Figures 12 and
13 show the locations of the strain gauges and the obtained values of normalized elongation at the point of
time of the specimen’s shear failure. In this case because of the existing correlation between strength
against flexure and against shear, as shown by the small values of elongation of the middle section, it may
be assumed that the burden brought on the critical, against shear, section, was rather limited.
Strain gauges confirmed the criticalness of the region strained under combination of flexure and shear
which has a small shear span. Transverse spiral reinforcement entered deep into the yield region in the
critical section under complex stress of both shear and bending, although transverse reinforcement was not
fully activated in the central region of net bending, which was expected, given that early (because of shear)
failure did not allow the full development of the flexural strength and the entry in flexural yield in that
area. It has to be noted the fact that in the extreme to the support section, the lower tensile reinforcement
showed elongation 10.79‰; significantly superior to the computational ey.

Figure 11 Failure mode of the second test specimen.
Figure 12 Maximum values of normalized deformation [‰] of transverse reinforcement of second
test specimen.

Figure 13 Load – normalized deformation diagrams of strain gauges of second test specimen.

The third specimen, who was strained under axial compression, has experienced severe transverse
deflection and transverse reinforcement in the middle of specimen was elongated up to 9.0‰ (Figure 14).
Figure 14 Load – normalized deformation diagrams of strain gauges of third test specimen.
4. CONCLUSIONS
It was attempted in this paper to give an answer to a key question regarding the design of components and
particularly the piers of earthquake-resistant bridges: Is it right to complement transverse reinforcement
aiming to meet requirements against normal stresses and shear or is it more prudent the emerging needs,
such as in the case of coexistence of shear and torsion, to be super positioned? The answers that are given,
coarsely documented experimentally in this paper, are:
• It is more accurate to associate confinement with normal stresses and not only with the axial compressive
load.
• The design of ductile structural elements shows that the results of requirements for confinement
reinforcement and shear reinforcement at the locations of plastic hinges must be superpositioned. It is
understood that the minimum requirement fixed by the regulation against confinement should be taken into
consideration only when the result of superposition is lower than this minimum requirement. In other words,
the requirement of confinement based on the value of normalized axial ν is taken into account through the
resulting value even when this is lower than the specified minimum value by the Regulation. Regarding
shear, it is understood that meeting its capacity requirement using transverse reinforcement admits no effect,
as proposed for the confinement.
• As far as the cases of elastically behaved under Stage II vertical structural elements, superposition should
take into consideration the full shear requirements plus a premium of about 20%.
Certainly, it is not overlooked the fact that conclusions having a quasi-subversive character are based
on results, which resulted from only two test specimens. However, we must not ignore the fact that
sometimes small causes raise serious issues and stimulate interest in their review. The authors of this report
have the intention to broaden the investigation conducted by examining in greater depth the influence of
the involved parameters, to fully substantiate the view stated in the present work, which concerns a very
common problem in the applications.

REFERENCES
[1] European Committee for Standardization, "EN 1998-1:2004, Eurocode 8: Design of structures for
earthquake resistance - Part 1: General rules, seismic actions and rules for buildings", Brussels, Belgium,
2004.
[2] Standards New Zealand, "NZS 3101:2006, Concrete structures standard: Part 1 – The design of concrete
structures", Wellington, New Zealand, 2006.
[3] Canadian Standards Association, "CAN/CSA-A23.3-04, Design of Concrete Structures (Update No. 2 -
July 2007)", Mississauga, Ontario, Canada, 2004 (Originally published).
[4] International Conference of Building Officials, "Uniform Building Code – Volume 2: Structural
Engineering Design Provisions", Whittier, California, USA, 1997.
[5] Ministry of Environment, Planning and Public Works, "Greek Code for the Design and Construction of
Concrete Works", Athens, Greece, 2000. (In Greek).
[6] European Committee for Standardization, "EN 1992-1-1:2004, Eurocode 2: Design of concrete
structures - Part 1.1: General rules and rules for buildings", Brussels, Belgium, 2004.
[7] European Committee for Standardization, "EN 1993-1-1:1992, Eurocode 3: Design of steel structures -
Part 1.1: General rules and rules for buildings", Brussels, Belgium, 1992.
[8] European Committee for Standardization, "EN 1994-1-1:1992, Eurocode 4: Design of composite steel
and concrete structures - Part 1.1: General rules and rules for buildings", Brussels, Belgium, 1992.
[9] British Standards Institute, "BS 6399-2:1997, Loading for buildings - Part 2: Code of practice for wind
loads", London, UK, 2002.
[10] British Standards Institute, "BS 6399-3:1988, Loading for buildings - Part 3: Code of practice for
imposed roof loads", London, UK, 1997.
[11] CEB/FIP Model Code 1990, Bulletin d’ Information CEB, No 203, Lausanne, 1991.
[12] Schindler S., Bender M., Mark P., "Erweiterung der klassischen M-N-Interaktiondiagramme", Beton-
und Stahlbetonbau, Vol. 102, No. 8, 2007, pp. 539-547.
[13] Tegos I., "Columns with spiral reinforcements under concentric compression", Proceedings of the 12th
Greek Concrete Conference, ΤΕΕ, Lemesos, Cyprus, 1996.
[14] Tegos I., Mantziaris P., "Circular cross section columns under seismic loading", Proceedings of the 12th
Greek Concrete Conference, ΤΕΕ, Lemesos, Cyprus, 1996.
[15] Tegos I., "Rectangular columns with complex spirals", Proceedings of the 12th
Greek Concrete
Conference, ΤΕΕ, Lemesos, Cyprus, 1996.
[16] Tegos I., "Shear design of circular cross section columns and beams", Proceedings of the 12th
Greek
Concrete Conference, ΤΕΕ, Lemesos, Cyprus, 1996.
[17] P. Saravanakumar and A. Govindaraj, Influence of Vertical and Inclined Shear Reinforcement on Shear
Cracking Behavior in Reinforced Concrete Beams. International Journal of Civil Engineering and
Technology (IJCIET), 7(6), 2016, pp.602–610.
[18] Kadhim Naief Kadhim and Ahmed Hameed Rustum Al - Rufaye , The Effects of Uniform Transverse
Magnetic Field on Local Flow and Velocity Profile , International Journal of Civil Engineering and
Technology (IJCIET), 7(2), 2016, pp. 140–151.

CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND CONFINEMENT

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (11)

Similar to CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND CONFINEMENT

Similar to CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND CONFINEMENT (20)

More from IAEME Publication

More from IAEME Publication (20)

Recently uploaded

Recently uploaded (20)

CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND CONFINEMENT