Bond of deformed bars in steel fibre reinforced concrete under cyclic loading

The Intemational Journal of Cement Composites and Lightweight Concrete, Volume 8, Number 4

November 1986

Bond of d e f o r m e d bars in steel fibre reinforced concrete under cyclic loading A. K. Panda*, R. A. Spencer-/-and S. Mindesst

Synopsis The bond between reinforcing steel and steel fibre reinforced concrete under reversed cyclic loading was studied. This loading simulates the conditions that may occur at an interior beam-column joint of a concrete frame structure during an earthquake. An analytical study was carried out, which included an assessment of the stresses and deformations in both the concrete and the steel. The results of an extensive experimental programme indicated that the behaviour of specimens under reversed cyclic loading was quite different from that under monotonic loading. In addition, under reversed cyclic loading, specimens containing steel fibres exhibited much better anchorage bond characteristics and a decreased rate of crack development as compared to specimens without fibres. Keywords Bond stress, beams (supports), reinforced concrete, reinforcing steels, fibre concrete, steel fibres, cyclic loads, numerical analysis, finite elements, anchorage bond, cracking (fracturing), structural members, earthquake resistant structures, ductility.

INTRODUCTION During an earthquake, alternate yielding of the reinforcing steel in tension and in compression can occur at the interior beam-column joints of high-rise moment resisting reinforced concrete frame structures. This may cause penetration of the yielding into the anchorage zone, thereby reducing the effective length available to develop the yield strength of the reinforcing steel. Indeed, anchorage bond failure in the beam-column joints has been the cause of severe local damage and even collapse of some structures during eathquakes [1 ]. ACI-ASCE Committee 352 has pointed out the need for research in making recommendations for the anchorage of continuous beam bars passing through beam-column joints of ductile moment resisting reinforced concrete frames subjected to reversals in the inelastic range such as might occur during earthquakes [2]. ACI Committee 544 has, in addition, suggested the need for research on fibre reinforced concrete for seismic resistance, to allow development of design procedures for structural elements such as ductile joints [3]. This research was undertaken to investigate whether the use of steel fibre reinforcement might lead to an improvement in bond * Steel AuthorityoflndiaLtd RourkelaSteeIPlant, Rourkela, Orissa, India. t Department of Civil Engineering, Universityof British Columbia, Vancouver, British Columbia, Canada © Longman Group UK Ltd 1986 0262-5075/86/08404239/$02.00

which could be significant in the beam-column joints of ductile moment resistant frames under earthquake loading conditions. ©ther possible improvements in the behaviour of earthquake resistant buildings as a result of using steel fibre reinforced concrete were not investigated. Even with modern techniques, major difficulties exist in measuring the mechanical behaviour of concrete surrounding a reinforcing bar. The bond between steel and concrete is a complex, nonlinear process. Therefore, in the present work, an analytical study was first carried out. An elastic, axisymmetric finite element program was developed that could take into account slip and separation between the reinforcing bar and the concrete, as well as cracking in the concrete itself. To complement the analytical study, an experimental programme was carried out on the bond behaviour of reinforcing steel in steel fibre reinforced concrete (sfrc) under conditions of loading simulating seismic motions. The main objectives of the experimental work were to study the bond behaviour of specimens representing an idealised model of a beam reinforcing bar passing through a beamcolumn joint, and to explore the desirability of using sfrc in these joints.

ANALYTICAL STUDY Finite element model The model considered was that of a smooth round bar embedded in a concrete cylinder having a diameter

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Figure1 Idealised finite element model seven times the bar diameter, and held fixed at the outer longitudinal surface. An idealisation of the problem is shown in Figure 1. It was assumed that with a ratio of cylinder diameter to bar diameter of 7.0, the boundary conditions at the support would not significantly affect the results obtained for local stresses around the reinforcing bar, at the steel-concrete interface. The elements considered were rings of triangular cross-section, as shown also in Figure 1. The application of a push-in pull-out load to the reinforcing bar was effected by applying suitable equal displacements to the nodal points on the outer surface of the bar. The finite element mesh consisted of 422 elements and 274 nodes, with the provision of dual nodes at the steel-concrete interface. It should be noted that the exact shape of the ribs on a reinforcing bar was not simulated in the mesh, because of their small size compared to the overall size of the model. Had the ribs been considered in detail, the computational effort would have been prohibitive. Although the effect of different types of rib was not considered, the model did use a relationship between bond stress and slip which was derived experimentally for the ribbed reinforcing bars used in this study. The criteria used for crushing of the concrete were those of Hannant [4}.

Element stiffnesses were suitably modified in the case of cracking or crushing of the concrete, and the structural stiffness matrices reformed. Slip at the interface nodes was calculated from the computed bond stresses, using the stress vs. slip relationship obtained from the experimental data and given in Equation 5. The slip values obtained were incorporated as input in the computation of stresses in the subsequent step, and so on. The mechanical properties of the steel and of the concrete were assumed to be: modulus of elasticity Poisson's ratio tensile strength

240

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In the absence of experimental data from the present investigation for the evaluation of the local bond stress vs. slip relationship, some previously published data obtained in other investigations [5-1 2] were used in the analytical study. There is, however, considerable variability in these published results, as may be seen from the different empirical equations for monotonic pull-out loading that these researchers derived from their

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Method of analysis Two different cases were considered in the finite element analysis. In the first case, perfect bond between the reinforcing bar and the concrete was assumed all along the length of the bar; the push-in pull-out load was applied to the outside nodes of the protruding ends of the bar. In the second case, an incremental step-by-step loading procedure was adopted, to account for nonlinear behaviour due to cracking of the concrete, and due to slip between the steel and the concrete at the interface

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Further, other studies [13, 14} have shown that the slip resulting from monotonic pull-out loading depends upon variables such as concrete strength, bar diameter, deformation pattern of the bar, bar spacing, amount of confining reinforcement, transverse pressure, rate of pull-out, and so on. Therefore, it was considered to be inappropriate simply to use a formula from the literature without verification. Instead, using a trial and error procedure, a formula similar in form to that used by Nilson [5], but with a different constant, was found to give reasonably good agreement with the experimental results. U = 1.425S V (f--/~.)(d+ 26.67)

(5)

where f~, the average crushing strength of the concrete, was found from tests on 150ram x 300mm cylinders. The different constant reflects the fact that the relationship between bond stress and slip is influenced by factors, such as the shape of the ribs on the reinforcing bars, the presence of steel fibres and the method of load application, which are not taken into account in the formula. The constant used by Nilson was multiplied by 2.5, indicating less slip at a given bond stress in these tests.

Analytical results Case I: No slip, perfect bond A push-in pull-out load of _+6.7 MPa was applied to the protruding ends of the bar. The four component stresses, m, cr~, o-z, "rrz(Figure 2) and the principal stresses were computed in both the steel and the concrete, as shown in Figure 3. The salient features of Figure 3 are described below: 1. Large circumferential and longitudinal tensile stresses exist in the concrete at the pull-out end. The presence of large tensile adhesion stresses in the concrete indicates that separation should occur with a further increase in the load. 2. High stress concentrations in the bar exist at the loaded ends of the cylinder. 3. There are indications that internal diagonal cracks would form at an applied stress level of 48 MPa.

Case I1: Slip and separation It is clear that if slip occurs, then the adhesion will be destroyed. Therefore, radial separation between the steel and the concrete was permitted to occur. The following results were obtained from the analytical study: 1. internal diagonal cracks developed at an applied stress level of 40 MPa in the concrete surrounding the reinforcing bar at the pull-out end. With a further increase in load, more and more diagonal cracks developed. Some crushing was predicted at the push-in end at a stress level of about 80 MPa. 2. The bond stress and the steel stress distribution at the steel-concrete interface at various stress levels, along the length of the cylinder, are shown in Figures 4 a n d 5, respectively A comparison of these results with those obtained experimentally I151 indicates

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satisfactory agreement at the ends of the specimen. The lack of agreement in the central region illustrates the limitations of a method of analysis that does not include factors such as the shape of the ribs, splitting cracks and the effect of steel fibres acting as closing forces. The increase in the lack of agreement as the stress increases is due to the fact that nonlinear behaviour of the concrete in front of the ribs due to crushing is not accounted for. . There is some indication of the formation of a conical crack at a distance of about 6 0 m m from the pull-out end at an applied stress of about 300 MPa. In the experimental study [15}, such cracks were observed only at an applied stress of about 500 MPa.

EXPERIMENTAL I N V E S T I G A T I O N The experimental phase of this investigation consisted of testing 24 concrete specimens with a single, centrally placed reinforcing bar subjected to simultaneous push-in and pull-out loading applied at the protruding ends. This model may be considered as a very simplified representation of a beam-column joint. The experimental procedures are detailed elsewhere [15]. They may be summarised as follows:

Materials CSA Type 30 (corresponding to ASTM Type III) high early strength portland cement, 10mm pea gravel, and ordinary river sand were used for the concrete. Two types of steel fibres, 3 0 m m and 50mm long, with crimped ends * and aspect ratios of 60 and 100, respectively, were used. The mix proportions are given in Table 1. The deformed steel reinforcing bars used had a nominal yield stress of 414 MPa and a nominal diameter of 25mm. Produced byN V Bekaert, Belgium

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Test specimens

All but two of the specimens had the dimensions 250 x 250 x 90@mm; the other two specimens had the dimensions 250 x 375 x 900mm. A threaded connector was welded to each protruding end of the reinforcing bar, in order to facilitate attachment to the loading system. Strain recordings along the test reinforcing bar were carried out by using electric resistance strain gauges spaced at 38ram on centres, mounted in grooves (5.1 mm wide x 2.5mm deep) machined on opposite sides of the bar. Displacements were measured relative to the centerline of the specimen, using linear variable differential transformers (LVDT's).

specimens were subjected to four basic types of loading histories: 1. Reversed cyclic loading, in which, for each incremental increase in the peak loading, one cycle was applied. 2. Reversed multiple cyclic loading, in which multiple cycles were applied for each incremental increase in loading. 3. Repeated loading, in either tension or compression only. 4. Monotonic loading.

TEST RESULTS

The test results are given in detail elsewhere [15]. The most significant findings are described below.

Test procedure

The test frame, and the method of mounting the specimens for testing, have previously been described [16]. The loading conditions are shown schematically in Figure 6. A servo-controlled hydraulic system was used to apply the loads, and the data were recorded using a data acquisition system and a mini-computer. The test

Strain distribution in the reinforcing bar

The strain distribution diagram for a typical specimen subjected to reversed multiple cyclic loading is shown in Figure 7. The general trend of the strain distribution

Table 1 Concrete mix proportions Specimen Type Plain concrete Steel fibre reinforced concrete

Steel fibre (kg,'m3) Nil 62.3 (0.79% by volume)

Cement (kg/m 3) 417.0 443.7

Gravel Sand 10 mm Water (kg/m 3) (kg/m 3) (kg/m 3) 878.0 840.6

878.0 840.6

192.2 205.8

Water reducer (ml/m 3)

Air entrainment (ml/m 3)

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258 310

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Panda, Spencer and Mindess

diagrams for the push-in pull-out loading indicated a greater bond resistance at the push-in end than at the pull-out end. This was primarily due to cracking and separation of the concrete around the bar at the pull-out end. A few loading cycles at a relatively high load amplitude, especially beyond yielding of the bar, caused an increase in strain values at any particular location in the reinforcing bar, indicating deterioration in the stress transfer capacity. An increase in the peak amplitude of loading increased the length of the tensile strain zone as compared to the length of the compressive strain zone by about 10 to 35%. This implied that the push-in force could be transmitted within a much smaller length than could the pull-out force. Further, an increase in the peak amplitude of loading caused bond deterioration at a lower stress level in the subsequent cycle. This is shown by curves 2 and 3 in Figure 7, which are for the same force applied in the third and seventh cycles, respectively.

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The bond stress distribution curves at various stress levels for a typical specimen subjected to monotonic loading are shown in Figure 8. It may be seen that, at low applied stress levels, the peak bond stress occurs at both

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ends of the specimen. However, when the applied stress level is increased, the peak bond stress shifts towards the centre of the specimen, with the largest values generally ocCurring at the push-in end. This suggests that there is greater bond resistance at the push-in end.

Cracking and failure mode For all specimens, the first radial splitting crack occurred at approximately the same applied stress level (300-400 MPa). With an increase in the peak load, more radial splitting cracks emerged, some of which propagated further as longitudinal cracks. The emergence of a

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Applied stress vs. displacement relationship In order to explain the overall response of the specimens to reversed cyclic loading, the hysteretic behaviour of the specimens must be examined. The definition of terms pertaining to the hysteretic curves for an applied stress less than the yield stress in the steel is given in Figure 9. The experimental results indicate a severe reduction in stiffness and resistance capacity of the specimens under reversed cyclic loading. A specimen subjected to monotonic loading could sustain a push-in pull-out load up to a stress level in the steel of greater than 700 MPa, while a companion specimen subjected to only a few cycles of reversed loading failed at a stress level of 540 MPa, indicating a decrease in load resisting capacity of more than 24%. This loss is mainly due to deterioration in the stress transfer mechanism, because of inelastic deformation, cracking in the concrete, a n d the Bauschinger effect in the reinforc!ng steel. A few cycles of reversed loading even at stress levels as low as 200-300 MPa caused a noticeable reduction in the loading stiffnesses, though no significant changes in stiffness KTi and KCI (Figure 9) were observed. However, an increase in the load beyond the yield stress level in the steel caused a severe reduction in the stiffness, and an increase in the displacement.

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Bond o f deformed bars in steel fibre reinforced concrete under cychc loading

circumferential conical crack on the pull-out end of the specimen indicated the onset of pull-out bond failure. After the formation of a conical crack, the anchorage capacity of the specimen depended on the remaining length of embedment, corrected for any cracking that might have occurred at the outer end. The diameter and the depth of the cone were observed to be smaller for specimens containing steel fibres than for those made of plain concrete. For plain concrete specimens, only a few wide, radial and longitudinal cracks occurred, whereas for fibre reinforced specimens many narrow radial and longitudinal cracks developed under identical loading conditions.

E f f e c t of s t e e l f i b r e s

The steel fibre reinforced concrete specimens exhibited better anchorage bond characteristics than did specimens without any fibres, particularly under reversed cyclic loading. This may be seen from a comparison of the hysteretic behaviour of the sfrc specimens and the plain concrete specimens, under identical loading conditions. Beyond the yield stress level in the steel, the displacements on the pull-out side were higher for the plain concrete specimens than for the sfrc specimens. Moreover, the sfrc specimens could sustain many more cycles before failure than could the plain concrete specimens. This is shown in Figure 10, which compares the hysteretic behaviour of typical plain concrete and sfrc specimens. It can be seen that the displacement of the bar in the sfrc specimen after 17 cycles was approximately equal to that of the bar in the plain concrete specimen after only 9 cycles.

Panda, Spencer and Minde'ss

During the tests, it was observed that longitudinal splitting in the concrete due to circumferential tension was quite common. The development of such splitting cracks relaxes the pressure between the concrete and the steel, leading to bond degradation. It may be hypothesised that the presence of the steel fibres inhibits both crack propagation and crack opening. The fibres would thus enable some stress to be transferred across cracked sections, allowing the affected parts of the composite to retain some post-cracking strength, and to withstand greater deformation [17]. Both the 30mm and 50mm long fibres (volume fraction = 0.79%) had essentialy the same effect on anchorage bond performance, as is evident from the applied stress vs. displacement curves. However, it shoud be noted that during casting, the concrete containing the 50mm fibres was found to be less workable than the concrete containing the 30mm fibres. Bond effectiveness

The improvement in bond capacity of an sfrc specimen compared to a plain concrete (pc) specimen can be expressed in terms of a bond effectiveness parameter, defined as bond effectiveness = [1 - Asfr,;] x 100 Apc

where

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A smaller area indicates more effective bond. For example, in Figure 11, the strain distribution diagrams for both a plain concrete specimen and a sfrc specimen are superimposed. Based on the area calculations, the sfrc specimens generally have smaller areas under the strain distribution diagrams. For the two specimens shown in Figure 11, the improvement in bond effectiveness for the sfrc was 20-26%.

Bond degradation ratio While it is very difficult to get a quantitative measure of the extent of bond degradation, one possible approach is to correlate bond degradation with respect to displacement at different numbers of loading cycles. The bond degradation ratio (BDR) at a particular stress level may then be defined as BDR =

displacement in the Nth cycle displacement in the 1st cycle

The BDR values for specimens subjected to identical loading at peak stress levels of 536 MPa are plotted in Figure 12. This indicates a much higher rate of bond degradation for a plain concrete specimen compared to sfrc specimens. This suggests that steel fibres are effective in retarding the rate of bond degradation.

CONCLUSIONS 1. The axisymmetric finite element analysis which was carried out to predict the bond between sfrc and a reinforcing bar produced reasonable results. However, the model would be improved if the effect of the steel

248

fibres in restraining crack growth, bearing stresses at the ribs of the reinforcing bar, and the failure mode of concrete under a triaxial state of stress could be included in the analysis. 2. Reversed cyclic loading causes a much greater reduction in stiffness and load resistance capacity than does monotonic loading. 3. The loading history has a significant effect on bond deterioration. An increase in the peak amplitude of loading causes bond deterioration at a lower stress level in subsequent cycles. 4. Specimens containing steel fibres exhibit better anchorage bond characteristics, improved deformational characteristics, and greater damage resistance than do specimens without fibres. Steel fibres are effective in retarding the rate of bond degradation under mutiple cycles of reversed loading. 5. The improvement in bond characteristics found in these tests due to the use of steel fibres suggests that their use in the joint regions of earthquake resistant ductile concrete frames should be investigated further.

ACKNOWLEDGEMENTS This work is based on the Ph.D. thesis of DrA. K. Panda. It was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada. REFERENCES 1. Bertero, V. V. and Popov, E. P. 'Seismic behaviour of ductile moment resisting reinforced concrete frames', Reinforced Concrete Structures in Seismic

Bond of deformed bars in steel fibre reinforced concrete under cyclic loading

2.

3. 4. 5.

6.

7.

.

9.

10.

Zones, SP-53, American Concrete Institute Detroit, 1977, pp. 247-92. ACI-ASCE Committee 352 'Recommendations for design of beam-column joints in monolithic reinforced concrete structures', Journal of the American Concrete Institute, Vol. 73, No. 7, July 1976, pp. 375-93. ACt Committee 544 'State of the art on fibre reinforced concrete', Concrete international, Vol. 4, No. 5, May 1982, pp. 9-25. Hannant, D. J. 'Failure criteria for concrete in compression', Magazine of Concrete Research, Vol. 20, No. 64, September 1968, pp. 137-44. Niison, A. H. 'Bond stress slip relations in reinforced concrete', Report No. 345, Department of Structural Engineering, Cornell University, Ithaca, New York, 1971. Houde, J. 'Study of force-displacement relationships for the finite element analysis of reinforced concrete', Ph.D. Thesis, McGill University, Montreal, Quebec, 1974. Houde, J. and Mirza, S. M. 'Finite element analysis of shear strength of reinforced concrete', Shear in Reinforced Concrete, SP-42, American Concrete Institute, Detroit, Michigan, 1974, pp. 103-28. Mirza, S. M. and Houde, J. 'Study of bond stressslip relationships in reinforced concrete', Journal of the American Concrete Institute, Vol. 76, No. 1, January 1979, pp. 19-46. Hungspreug, S. 'Local bond between a reinforcing bar and concrete under high intensity cyclic load', Ph.D. Thesis, Cornell University, Ithaca, New York, 1981. Lutz, L. A. 'The mechanics of bond and slip of

Panda, Spencer and Mindess

deformed reinforcing bars in concrete', Ph.D. Thesis, Cornell University, ithaca, New York, 1966. 11. Lutz, L. A. and Gergely, P. 'The mechanics of bond and slip of deformed bars in concrete', Journal of the American Concrete Institute, Vol. 64, No. 11, November 1967, pp. 711-21. 12. Lutz, L. A. 'Analysis of stresses in concrete near a reinforcing bar due to bond and transverse cracking', Journal of the American Concrete Institute, Vol. 67, No. 10, October 1970, pp. 778-87. 13. Ciami, V., Eligehausen, R., Bertero, V. V. and Popov, E. P. 'Analytical model for concrete anchorage of reinforcing bars under generalised excitations', Report No. UBC/EERC-82-83, University of California, Berkeley, California, 1982. 14. Morita, S. and Kaku, T. 'Local bond stress-slip relationship under repeated loading', International Association of Bridge and Structural Engineering, Symposium, Vol. 13, Lisbon, 1973, pp. 221-6. 15. Panda, A. K. 'Bond of deformed bars in steel fibre reinforced concrete under cyclic loading', Ph.D. Thesis, University of British Columbia, Vancouver, British Columbia, 1984. 16. Spencer, R. A., Panda, A. K. and Mindess, S. 'Bond of deformed bars in plain and fibre reinforced concrete under reversed cyclic loading', international Journal of Cement Composites and Lightweight Concrete, Vol. 4, No. t, February 1982, pp. 3-17. 17. Johnston, C. D. 'Steel fibre reinforced mortar and concrete - a review of mechanical properties', Fibre Reinforced Concrete, SP-44, American Concrete Institute, Detroit, Michigan, 1974, pp. 127-42.

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