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

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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.

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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.


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Intensive flexural cracking and remaining deflection of the first test specimen.

Elongations of transverse reinforcement of the under net flexure strained central section.

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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.



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