“Bond in Concrete – from research to standards” 2002, Budapest EXPERIMENTAL RESPONSE AND BEHAVIORAL MODELLING OF ANCHORED SMOOTH BARS IN EXISTING RC FRAMES Giovanni Fabbrocino, Gerardo M. Verderame, Gaetano Manfredi, Edoardo Cosenza Department of Structural Analysis and Design, University of Naples Federico II Via Claudio 21, 80125, Napoli, Italy SUMMARY Assessment of structural behaviour of existing reinforced concrete constructions under gravity loads and seismic actions has a high social and economical impact in planning risk reduction activities; presently in many European countries and especially in Italy, most of the buildings date back to 60’s and 70’s and are basically underdesigned, since many areas have been later classified as seismic or old codes were used in design. These structures are reinforced with smooth bars that show poor bond and need specific anchoring end details. In the present paper, the force-slip response of typical circular hooks is analysed. The results of pull-out tests are presented pointing out some aspects of the response under service and ultimate loads. Experimental data are then used to develop an analytical relation able to fit the relation between force and slip of 180° hooks commonly used for smooth rebars. 1. INTRODUCTION A large number of existing reinforced concrete buildings in Europe, located in seismic areas, has been designed according to old seismic codes or even only for gravity loads, resulting in low available ductility and lack of appropriate strength hierarchy. Seismic assessment of existing buildings requires a reliable evaluation of the displacement capacity of framed structures, that can be obtained only using refined non-linear models. Capacity is commonly expressed in terms of interstorey drift ratio, which depends on the development of the deformation contributions of different components, i.e. beams, columns and beam to column joints (Bonacci and Wight, 1996). The latter is generally divided in two components related to shear deformation of the panel zone and to the fixed-end rotation that is dependent on bond properties of reinforcement and anchoring devices, as sketched in Figure 1.a. The fixed end rotation largely influences the drift capacity as confirmed by theoreticalexperimental comparisons (Cosenza et al., 2002) and as observed in Figure 1.b that shows the push-over curves of an existing building located in Catania (South Italy), designed only for gravity load in the 70’s (Cosenza et al. 1999). The results, expressed in terms of base coefficient versus drift ratio, refer to smooth reinforcement and point out the strong influence of fixed-end rotation, up to 30-40%, on the drift capacity of the building. As a consequence, a reliable modelling of the phenomenon is needed, mainly when smooth bars are considered, since end details of reinforcing bars are essential for development of strength and deformation of the anchorage, but on this subject the experimental background is definitively poor. The main aspects related to response and modelling of member end sections are summarised in Fig. 2 that reports in detail the force transfer governing the behaviour of the reinforcing bar under tension. The anchored bar is divided into two components, the straight region and the anchorage, represented by a circular hook. From a mechanical point of view, the end anchorage results in a restraint for the straight rebar inner end, as shown in Figure 2.a. 0.07 Base shear coefficient, Cb without fixed end rotation 0.06 0.05 with fixed end rotation 0.04 32 5 0.03 32 5 27 5 0.02 a) 400 220 360 405 200 350 530 0.01 drift ratio, D/H 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 b) Fig. 1: Fixed-end rotation mechanism (a) and its influence on overall frame drift capacity (b). The drawing schematically highlights two boundary conditions for the straight region: - end detail ideally rigid, in this case at the unloaded end the slip is zero, while the bar stress is not zero, since high ratios between applied force and anchorage reaction (even 50-60% of the tensile force applied at the loaded end); - end detail ideally free, in this case a slippage develops at the unloaded end, but the rebar stress is zero, resulting in poor pull-out strength. τ (bond) hooked end rigid end ds/dx ≠ 0 ; s = 0 ds/dx ≠ 0 ; s ≠ 0 free end slip ds/dx = 0 ; s ≠ 0 F = σs⋅As F = σs⋅As σh (hook) a) slip b) Fig. 2: The anchored smooth bar idealization. Common anchorage devices have a stress-slip response that lays between the above boundaries, so that both slip and its derivative are not zero and are dependent upon device response, as sketched in Fig. 2.b and influence the strength and deformation capacity of the member end sections. In fact, pull-out of smooth bars without anchors leads to the premature failure of the member end section, conversely rigid anchorage allows the full development of flexural strength and does not give any contribution to the slip at the loaded end (Fabbrocino et al., 2002a). Thus, an experimental evaluation of the relationship between the axial force applied on the anchorage and the slippage of its loaded end is necessary to develop a behavioural model of the anchored bar. A specific force-slip relation for anchorage allows to model the anchored bar on the analogy of a smooth bar embedded in a concrete matrix, taking the end detail into account using an appropriate non-linear stress-slip relationship for the anchored end (Fig. 2b); as a result, traditional analytical procedure to evaluate development length can be easily extended to anchored bars using appropriate mechanical force (stress)/slip relationships for end details. In the following, an analytical formulation able to represent from a global point of view the response of the end detail is proposed, pointing out a good level of accuracy. 2. PULL-OUT TESTS: SETUP AND MAIN RESULTS A comprehensive critical review of former Italian codes, design manuals (Santarella, 1937) and design drawings referring to existing buildings has been carried out in order to identify typical anchors for smooth bars in existing buildings. It has been found that hooks with 180° opening angle can be addressed as the most common anchoring device when smooth bars are concerned. Therefore, pull-out tests have been carried to experimentally evaluate the forceslip relation of such anchors. The reinforcement used in the experimental program consists of smooth rebars that are still available for secondary purposes in r.c. structures; their mechanical properties are similar to steel classified as Aq42 according to former Italian design codes (Fabbrocino et al., 2002b); yielding stress is about 320 MPa, ultimate stress is equal to 430 MPa and ultimate uniform strain is about 20%. All the specimens are characterised by a cubic mean strength of about 30 MPa with a mix design based on type and size of aggregates commonly used in existing buildings; cubes 150 mm wide are used to define mean concrete strength. The main investigated parameters are the bar diameter, the concrete cover, the cast direction and position of circular branch respect to the top surface of the specimen, the type of loading (monotonic or cyclic). In particular, two bar diameters, 12 mm and 16 mm, have been selected on the basis of a review of available data concerning reinforcement details in existing r.c. buildings. Plastic pipe Steel spacer F Steel rebar Concrete specimen Concrete specimen F 300 mm Steel rebar 300 mm 300 mm Plastic pipe F F a) 300 mm b) Fig. 3: The modified pull-out specimens; FULL specimens (a), END specimens (b). Two types of specimens have been designed in order to modify the hook concrete cover in compliance with the reinforcement detailing in base column/internal beam to column joint and external joint respectively. Therefore, two test set-up have been considered: FULL type specimens, shown in Figure 3a, that consist of a concrete cube 300 mm wide and the rebar centered in the cross section; this leads to a relevant concrete cover that can be representative of the above mentioned base column or internal beam to column condition; END type specimens that are representative of the typical location of rebars in external beam to column joint regions. In this case, the concrete cover is 22 mm or greater depending on the bar diameter; the concrete block has a 180 mm thick by 300 mm wide cross section. A third group of specimens is called FULL-H; it is characterised by the same geometry of FULL type specimens, but the cast direction is perpendicular to the rebar and the location of circular branch respect to the block top surface is changed. In all cases, the load is applied to the free end of the rebar and the reaction force is given by an external steel box restrained to the concrete block using bolts embedded in the concrete. This specific set-up has been chosen in order to avoid compressive stresses on the top surface of the concrete and fit the real conditions of rebars under tension in cracked sections. The bolts used as shear connectors are the only reinforcement present in the concrete blocks and do not transfer any compressive stress to concrete. The main aspect of the test set-up is the direct measure of the slip at the end section of the anchorage; in fact, interaction of the straight branch is prevented using a plastic pipe, as shown in Figure 3, and the slippage at the end of the circular branch is measured using a high performance draw-wire displacement sensor. In addition an extensometer is also used during all the load process in order to evaluate the stress-strain relationship of each tested bar. The tests have been carried out using a uniaxial testing system able to apply the load under displacement control and measuring slip of anchorage inside the concrete block. A total number of 14 tests are here reported. σhook (MPa) 500 500 400 400 300 300 200 200 100 100 σhook (MPa) yielding εrebar (mm/mm) shook σhook shook (mm) 0 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 0.0 1.0 2.0 3.0 4.0 5.0 a) b) 0.30 0.25 0.20 0.15 0.10 0.05 0.00 shook (mm) Steel rebar Plastic pipe 300 mm εrebar (mm/mm) F 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Concrete specimen F c) 300 mm d) Fig. 4: Summary of experimental results of pull-out tests, full type specimens. The results of the modified pull/out tests are collected referring to the 12 mm bars. The tests have been carried out up to failure identified as the achievement of bar ultimate strain or of severe hook pull-out. The plots given in Fig. 4 are able to completely describe the response of hooks under monotonic pull-out test. In fact, the stress-hook slip relation (b), the rebar strain vs. hook slip relation (c) and finally the rebar stress/strain law (a) are shown. It is worth noting that yielding and ultimate stress are not scattered, mean values of yielding stress is 320 MPa, while mean ultimate stress in 440 MPa. The stress-hook slip relation is characterised by a very steep initial branch, with a zero slip stress range, and a strongly non-linear behaviour up to failure. The direct measure of the hook end slip enable to observe that the yielding spreading in the circular branch of the anchorage is negligible, since hook slip does not change as the bar strain develops on the plastic plateau. This circumstance is much more clear if the bar strain-hook slip curves are considered and the constant branch in the strain range between yielding and strain hardening is analysed. Fig. 5 gives a full overview of experimental results and shows that the concrete cover plays a relevant role in the development of deformation mechanisms. 500 400 σhook [MPa] #4 #5 #1 #2 #3 300 200 100 hook slip, shook [mm] 0 a) 0.0 500 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 σhook [MPa] #1 400 #5 300 #2 200 #3 #4 100 hook slip, shook [mm] 0 b) 0.0 1.0 2.0 500 σhook [MPa] 400 #1 down 3.0 4.0 5.0 6.0 7.0 8.0 #2 down #2-up #1-up 300 200 100 hook slip, shook [mm] 0 c) 0.0 1.0 Fig. 5: Summary of experimental results. 2.0 3.0 4.0 5.0 6.0 7.0 8.0 b) a) Fig. 6: Stress-slip relation for 180° hooks, END specimens (a), FULL specimens (b). Plot of Fig. 5.b (END specimens) clearly show a loss of load at high rebar strain due to longitudinal splitting failure of concrete cover, resulting in a large increase of slip. This circumstance is confirmed by the comparison of pictures 6.a and 6.b, that show the longitudinal cross section of the specimens after the test. It is easy to recognise that ultimate slips of FULL specimens are negligible respect to END one. 3. THEORETICAL STRESS-SLIP FORMULATION OF 180° CIRCULAR HOOKS In the present section, the definition of a theoretical stress-slip relationship is analysed with specific reference to FULL type specimens. In order to fit experimental data, a review of experimental curve shapes and plot of functions commonly used in literature to fit similar phenomena, i.e. bond (Eligehausen et al. 1983; CEB, 1993), shear connectors in composite constructions (Ollgaard et al., 1971) has been carried out, and a comparison with the main aspects of the experimental behaviour previously discussed has been done. The basic requirements of a theoretical formulation of stress-slip relationship for circular hooks can be summarised as follows: experimental curves are basically continuous, thus a single curve formulation is reliable. Ultimate stress and slip at bar failure can be used as basic parameters of the theoretical formulation; the first one is an exogenous parameter, depending upon the steel grade, the second one can be evaluated using a statistical analysis of available test results. The first branch of the well-known constitutive law for bond by Eligehausen et al. (1983) fulfils the above requirements. σhook/fu 1.0 0.8 α s  σ hook (s ) = fu ⋅  hook   su  0.6 0.4 α ∈ [0,1] 0.2 shook/su 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Fig. 7: Stress-slip relation for 180° hooks, FULL specimens. In Fig. 7 the above mentioned constitutive laws has been rewritten and plotted depending on the shape exponent α; shook is the hook slip, su is the hook slip at bar failure, fu is the bar ultimate stress and α is a dimensionless positive exponent that is generally lower than 1. Characterization of theoretical formulation requires the definition of two parameters, the ultimate hook slip su and the exponent α, able to minimize the error function ∑ (siexp − sinum ) (n − 1) , where s iexp is the experimental value of hooks slip at a given stress 2 i =1, n level, σiexp ; s inum is the hook slip calculated at the σiexp stress level and finally n is the number exp of experimental data ( s exp ). In Fig. 8, the comparison between the experimental curves i , σi and the optimal constitutive law is reported for all the type of pull-out specimens (FULL and FULL-H). It is worth noting that the adopted constitutive law is really able to fit the experimental behaviour. The results of the parameter optimisation is reported in Table 1, where the values of α and of the slip, su, at the steel failure are given. 1.2 steel stress, σhook / fu #5 1.0 #4 1.2 a) #1 #3 #2 steel stress, σhook / fu b) 1.0 #1 0.8 0.8 0.6 0.6 0.4 #2 α = 0.25 su = 3.1 mm 0.4 α = 0.30 su = 4.1 mm 0.2 0.2 slip, shook [mm] slip, shook [mm] 0.0 0.0 0.0 1.2 1.0 2.0 3.0 4.0 5.0 6.0 7.0 steel stress, σhook / fu 0.0 8.0 c) 1.2 1.0 2.0 3.0 4.0 5.0 6.0 7.0 steel stress, σhook / fu 8.0 d) 1.0 1.0 #2 #1 0.8 0.8 0.6 0.6 α = 0.37 su = 4.0 mm 0.4 0.4 0.2 α = 0.30 su = 3.9 mm 0.2 slip, shook [mm] 0.0 slip, shook [mm] 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 1.0 2.0 3.0 4.0 Fig. 8: Stress-slip relation for 180° hooks, FULL specimens. Reference test groups (a) (b) (c) All α su (mm) 0.30 4.10 0.25 3.10 0.37 4.00 0.30 3.90 Tab. 1: Summary of optimised parameters of the theoretical stress-slip law. 5.0 6.0 7.0 8.0 4. CONCLUSIONS The present paper reported an overview of a research program on the structural behaviour and modelling of anchored smooth rebars used in existing buildings. In particular, the attention has been focussed on the local response of GLD r.c. frames under seismic actions and on the influence of anchored smooth rebars on the development of fixed end rotations. The results of pull-out tests on 180° circular hooks has been discussed and a formulation able to express from a global point of view the response of the end detail has been proposed. The comparison of hook performances depending on concrete cover, cast direction and hook location have shown that only the concrete cover has a relevant role in development of failure mechanism and deformation of the system. The extension of a well know formula for bond interaction, made of a single continuous branch has been presented. The formulation requires the knowledge of three parameters: the steel ultimate stress, the hook slip at bar failure and finally a shape coefficient α. Since the first parameter depends only on the steel grade, an optimisation of two remaining parameters has been carried out, using α = 0.30 and su= 3.90 mm the theoretical curve is able to fit the experimental data with a satisfactory level of accuracy. This is a very useful result in view of the development of an effective theoretical model able to simulate the structural response of r.c. beam to column joint ensuring both equilibrium and compatibility between anchored rebars and concrete panel. 5. REFERENCES Bonacci, J.F. and Wight, J.K., (1996) "Displacement-based assessment of reinforced concrete frames in earthquake" – Mete A. Sozen Symposium, ACI publication SP 162, pp. 117-133. CEB (1993), Bulletin d’Information n° 213/214, "Model Code 90", Georgi Publ. Co., SaintSaphorin, Switzerland. Cosenza, E., Manfredi, G., Verderame, G. (1999) "Seismic assessment of R.C. structures: case studies in Catania in The Catania Project: earthquake damage scenarios for high risk area in the Mediterranean", CNR – Gruppo Nazionale per la Difesa dei Terremoti Publication, (E.Faccioli and V. Pessina Eds.), Roma. Cosenza, E., Manfredi, G., Verderame, G.M. (2002), "Seismic assessment of gravity load designed r.c. frames: critical issues in structural modeling", Journal of Earthquake Engineering, Vol. 6, n.2, April, pp. 101-122. Eligehausen, R., Popov, E.P., Bertero, V.V. (1983), "Local bond-stress relationships of deformed bars under generalised excitations", UCB/EERC 83, 23. Fabbrocino, G., Verderame, G., Manfredi, G. (2002a), "Experimental behaviour of straight and hooked smooth bars in existing R.C. buildings", Proceedings of Twelfth European Conference on Earthquake Engineering, London, September, paper # 393. Fabbrocino, G., Verderame, G., Manfredi, G., Cosenza, E. (2002b), "Experimental behaviour of smooth bars anchorages in existing r.c. buildings", fib 2002 Osaka Congress, Osaka, Japan, paper W-463. Ollgaard J.G., Slutter R.G., Fisher J.W. (1971), "Shear Strength of Stud Connectors in Lightweight and Normal Weight Concrete" - AISC Engineering Journal, pp. 55-64. Santarella, L. (1937), "Il cemento armato – La tecnica e la statica", Hoepli - Milano, (in Italian).