Earthquake-resistant design of indeterminate reinforced-concrete slender column elements

Engineering Structures 29 (2007) 163 175 www.elsevier.com/locate/engstruct Earthquake-resistant design of indeterminate reinforced-concrete slender column elements Gerasimos M. Kotsovos a, Christos Zeris a, Milija N. Pavlović b, a Department of Civil Engineering, National Technical University of Athens, Athens 15780, Greece b Department of Civil and Environmental Engineering, Imperial College, London SW7 2AZ, UK Received 28 January 2005; received in revised form 15 November 2005; accepted 20 April 2006 Available online 27 June 2006 Abstract The work extends the range of application of previous work, which had been concerned with the earthquake-resistant design of reinforced concrete short column elements (elements with a shear span-to-depth ratio smaller than 2), by means of an experimental investigation into the behaviour of slender column elements (elements with a shear span-to-depth ratio larger than 2). As for the previous study, the present investigation of slender column elements is based on the use of indeterminate specimens (which represent more realistically elements in a building than their determinate counterparts) designed by using two different methods: the truss analogy method, as applied by current codes of practice, and the compressive-force path method. The results obtained indicated that the unexpected, premature brittle mode of failure observed in short column elements in the region of the point of inflection also characterises slender column elements when designed to current code provisions. In contrast, those elements designed to the compressive-force path method are found to satisfy the performance requirements of current codes for both strength and ductility. c 2006 Elsevier Ltd. All rights reserved. Keywords: Columns; Concrete; Design; Earthquake-resistant design; Reinforced concrete 1. Introduction The results obtained from tests on indeterminate reinforcedconcrete (RC) column elements with a shear span-to-depth ratio (a v /d) smaller than 2 (henceforth referred to as short column elements) have shown that current code methods for earthquake-resistant design do not always safeguard against brittle types of failure [1,2]. On the other hand, tests on similar specimens designed to the compressive-force path (CFP) method were found to exhibit strength and ductility characteristics that satisfy the performance requirements imposed by current codes [3]. However, these tests on CFPdesigned members only covered part of the a v /d range encountered in real structures. Hence, although the resulting experimental information may be considered sufficient for disproving an established design method, it can only form part of the evidence required in order to validate a new one. Corresponding author. Fax: +44 171 594 5989. E-mail address: m.pavlovic@ic.ac.uk (M.N. Pavlović). To this end, the aim of the present work is to complement the results obtained from the tests on the short column elements with experimental information on the behaviour of RC columns with a v /d > 2 (henceforth referred to as slender column elements) designed to the CFP method. For comparison purposes, similar tests are carried out on specimens designed to the truss analogy (TA) as this is applied by the seismic provisions of current codes such as ACI-318 [4] and EC2&8 [5,6]. The tests are carried out on indeterminate structural elements, similar to those used to investigate the behaviour of the short column elements [1 3], since experimental information on the behaviour of such specimens is sparse when compared with that obtained from tests on determinate structural elements. Moreover, the testing of indeterminate structural elements provides a more severe test of the validity of a design method, since it allows the investigation of features of the structural element behaviour such as, for example, sequential plastic-hinge formation and their strength and ductility characteristics, the structural modelling of points of inflection, etc. features found in real 0141-0296/$ - see front matter c 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2006.04.019

164 G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 Fig. 1. Structural forms investigated: (a) applied forces; (b) bending-moment diagram; (c) shear-force diagram. (Faint lines and P 1 indicate first-hinge formation, solid lines and P 2 denote second-hinge formation, while M p is the flexural capacity of the cross-section.) structures, such as buildings which cannot be investigated by testing determinate structural elements. 2. Experimental details The validity of the design methods for achieving flexural capacity and desirable ductility ratio values for medium class ductility column RC elements was investigated experimentally by testing two-span linear structural elements such as that shown in Fig. 1, containing the load arrangement and the corresponding bending-moment and shear-force diagrams for one- and two-hinge formation. It is interesting to note in the figure that portion BC of the structural element is subjected to internal actions similar to those of a column in a building. Similarly, portions AB and CD are subjected to internal actions similar to those of the portion of a column between its point of inflection and one of its ends. From the lengths of the above portions, and the cross-section depths adopted (see later), the values of a v /d for portions AB, BC and CD are in the range of 6.5 7, 2.6 2.9, and 5.2 5.8, respectively. 2.1. Loading path The specimens were subjected to sequential loading comprising axial (N) and transverse ( P) components, as indicated in Fig. 1. The loading histories adopted are shown in Fig. 2. From the figure, it can be seen that N was applied first. It increased to a predefined value equal to N 0.2N u = 0.2 f c bh (N u is the maximum value of N that can be sustained by the specimen in pure compression, f c is the uniaxial cylinder compressive strength of concrete, and b, h are the crosssectional dimensions of the specimen), where it was maintained constant during the subsequent application of P. The latter force (applied at the middle of the larger span) increased to failure either monotonically (refer to Fig. 2(a)), or in a cyclic manner inducing progressively increasing displacements in opposite directions as shown in Fig. 2(b). 2.2. Experimental set-up The experimental arrangement used for the tests comprised three identical steel portal frames, with double-t cross-section, bolted in parallel onto the laboratory strong floor at distances equal to the element spans. As shown in Fig. 3, the element was supported using two rollers and one pin support that were positioned underneath the bottom flange of the frame beams so that the reactions could act either upwards or downwards depending on the sense of the transverse point load. The transverse load was applied through a double-stroke 500 kn hydraulic actuator (MTS) fixed to the laboratory strong floor. The axial-compressive force was applied concentrically using an external prestressing force by means of two high-yield steel rods symmetrically arranged about the longitudinal axis of the element and acting on the horizontal plane. The rods were anchored at each end with two steel plates, one of them being attached at one end face of the element through a load-platen

G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 165 other end face of the specimen. The actuator was capable of maintaining the axial force constant with an accuracy of ±1 kn. The transverse load was displacement-controlled. It was interrupted at regular intervals, corresponding to displacement increments of approximately 5 mm, during which the load was maintained constant for at least 1 min in order to mark cracks and take photographs of the specimen s crack pattern. The load and two of the three support reactions were measured by using load cells, while the deformation response was measured by linear variable displacement transducers (LVDTs) measuring the specimen deflection at the location of the transverse load point. The forces and deflections were recorded by using a computer-based data-acquisition system. Since measuring one support reaction was sufficient for the calculation of the remaining two reactions from the equilibrium conditions, the measured values of the two additional reactions were used for assessing the accuracy of the obtained force measurements. This assessment was based on the comparison between the measured values and their calculated counterparts, which showed that the difference between any two such values did not exceed 2 kn. 2.3. Specimen design Fig. 2. Loading histories of structural elements tested: (a) monotonic loading; (b) cyclic loading. (δ y = displacement at yield.) arrangement ensuring concentric loading, while the other was attached at the end face of a 900 kn hydraulic actuator acting against another steel load-platen arrangement attached to the The elements were designed from first principles by using methods based on two contrasting concepts: the TA, as applied by ACI [4] and EC2&8 [5,6], and the CFP method, as described in [7] and complemented for the case of earthquake-resistant design in [3]. The physical models underlying the design methods are shown in Fig. 4. It is interesting to note that, unlike the TA, the CFP method recognises the locations in the structural element where the development of transverse tension is most likely to cause a non-flexural type of failure [3, 6], and these are denoted in Fig. 4(b) by the numbers 1 to 7. For the structural forms investigated in the present work, the CFP concept predicts the region of location 3 (i.e. point Fig. 3. Experimental set-up.

166 G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 Fig. 4. Models underlying the methods used for designing the structural forms tested: (a) truss analogy (TA); (b) compressive-force path (CFP). Table 1 Mean yield stress and strength values of the longitudinal bars and stirrups used for the specimens Diameter of steel bar D14 D16 D8 D6 D6 for D16 specimens for D14 specimens f y (MPa) 618.71 541.03 471.1 361.64 317.89 f u (MPa) 724.35 638.06 684.4 403.38 395.14 Table 2 Mean compressive strength values of the concrete employed for the specimens Compressive strength ACI- D14 EC- D14 CFP- D14 ACI- D16 EC- D14 f C (MPa) 35 39 36 32 37 37 CFP-D14 of inflection) as the region most likely to fail in transverse tension, with the remainder of the element requiring only nominal transverse reinforcement. It must be noted that, for load reversals, additional stirrups are needed in the region where the compressive force path changes direction, when this change occurs at a distance less or equal to 2d from the section undergoing peak values of combined action of shear force and moment bending. Also, hoop stirrups are required both in the region of the compressive and tension zone (becoming compressive when load reverses) (Fig. 5(c) and 6(c)) within the region extending 2d from the point load to the right and 2d from the middle support to the left (Fig. 4(b), regions 6 and 7). The above additional transverse reinforcement (to the one calculated by CFP for monotonic loading [7], both hoops and stirrups) is required in order to compensate for the weakening of concrete due to load reversals [3]. On the other hand, both ACI and EC2 specify denser stirrup spacing in regions where a large shear force combines with a large bending moment. Such regions, referred to in codes as critical lengths, are marked with l cr in Figs. 1 and 4(a). In all cases, the specimens were designed assuming that their load-carrying capacity is reached when the cross-sections through support B and the transverse-load point C (see Fig. 1) Table 3 Design values of specimens to be tested (assuming second hinge is formed) Specimen M B,d M C,d V AB,d V BC,d V CD,d N ACI-D14-M ACI-D14-C EC-D14-M EC-D14-C CFP-D14-M CFP-D14-C ACI-D16-M ACI-D16-C EC-D16-M EC-D16-C CFP-D16-M CFP-D16-C 54.8 54.8 45.5 112.3 55.9 280 55.2 55.2 45.8 113.1 56.3 280 58.0 58.0 48.1 118.9 59.1 320 54.0 54.0 44.8 110.7 55.1 300 51.3 51.3 42.6 105.2 52.3 240 49.7 49.7 41.2 101.8 50.7 300 M B,d, M C,d : bending moments (in kn m) at support B and point load C respectively; V AB,d, V BC,d and V CD,d : shear forces (in kn) within portions AB, BC and CD, respectively; N axial force (in kn). (Locations of B, C, AB, BC and CD as shown in Fig. 1). attain their flexural capacity, the latter condition being referred to henceforth as plastic-hinge formation. Using the crosssectional and material characteristics of the specimens, together with a rectangular compressive-stress block with a depth equal to the neutral-axis depth and a stress intensity equal to f c, as recommended by the CFP method [6], the flexural capacity of the element was calculated as M p (for a value of N equal to N 0.2bh f c ).

G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 167 Fig. 5. Design details of specimens with 14 mm diameter longitudinal bars: (a) design to TA (ACI); (b) design to TA (EC); (c) design to CFP. Assuming that, at the ultimate-limit state, the bending moments at cross-sections through support B and load point C are equal to M B = M c = M p, the indeterminate specimen becomes determinate (just prior to the development of the collapse mechanism) and the shear forces within the portions AB, BC, and CD are easily calculated as V AB = 0.51M p, V BC = 2.05M p, and V CD = 1.02M p, as indicated in Fig. 1 (which also shows the corresponding values resulting from elastic analysis just prior to the formation of the first hinge). These values were used as design values for safeguarding against shear failure, in line with current code thinking where critical cross-sections are checked for shear but the member is not considered as a whole (as in the CFP method). The values of bending moment, shear force and axial force used to design the specimens (these are covered in the next section) are given in Table 3. It should be noted that, for the calculation of both

168 G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 Fig. 6. Design details of specimens with 16 mm diameter longitudinal bars: (a) design to TA (ACI); (b) design to TA (EC); (c) design to CFP. flexural and shear capacities of the elements, all safety factors were taken equal to 1. 2.4. Specimens All structural elements were simply supported with a large span of 1950 mm and a small span of 1200 mm. Their total length was 3350 mm, with a square cross-section of 200 mm size. Henceforth, these structural elements are referred to by using a three-part denomination, arranged in sequence to denote: method employed for the design of the specimens, diameter of the longitudinal steel reinforcement, and loading history adopted (see Section 2.1). As mentioned earlier, two methods were employed for designing the specimens: the TA method as applied by ACI and EC2, and the CFP method. These methods are indicated in the structural-element name by the abbreviations ACI, EC and CFP respectively.

G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 169 (a) ACI-D14-M. (b) EC-D14-M. (c) CFP-D14-M. Fig. 7. Load displacement curves for D14 specimens tested under monotonic loading: (a) ACI-D14-M; (b) EC-D14-M; (c) CFP-D14-M. (The triangular symbols represent (moving upwards) the points at first yield, first plastic hinge and second plastic hinge, respectively.) Fig. 8. Modes of failure and associated crack patterns for D14 specimens tested under monotonic loading: (a) ACI-D14-M; (b) EC-D14-M; (c) CFP-D14-M. Two different types of longitudinal reinforcement were used for the specimens: 14 mm, diameter bars denoted as D14, and 16 mm diameter bars denoted as D16. The above steel characteristics are indicated in the structural-element name by D14 and D16, respectively. The yield stress and strength mean values of the steel bars, which were obtained from tension tests, are indicated in Table 1. The concrete employed for the specimens tested was cast in batches, their values of mean strength f c are indicated in Table 2. These values were determined by crushing tests on at least six cylinders per batch performed during the testing of the structural elements (approximately two months after casting). The specimens (both cylinders and structural members) were cured under wet hessian for one month, after which they were stored under laboratory ambient conditions (with a temperature of approximately 20 C and a relative humidity of approximately 50%). Finally, the loading regime used in the programme was broadly classified as monotonic loading and cyclic loading. The type of loading regime is indicated in the structural-element name by M and C, respectively. The design details of the specimens are shown in Figs. 5 and 6. As discussed earlier, it is interesting to note in the figures the different transverse-reinforcement arrangements which, for the specimens designed to the codes, is characterised by a denser stirrup spacing within the critical lengths, whereas, for the specimens designed to the CFP methodology, the stirrup spacing is denser within the region of the point of inflection. Another important difference in the transverse-reinforcement arrangement is the stirrup arrangement within the compressive

170 G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 Table 4 Experimentally established and calculated values of the transverse force (in kn) and corresponding displacement (in mm) at various load levels for the specimens tested Specimen Experimental Calculated P max δ Pmax δ 0.85max δ sust δ fail P y P ny = P 1P P 2P P max /P 2P δ ny µ sust µ fail ACI-D14-M 178 40.3 60.2 110 146 168 1.06 11.6 5.2 EC-D14-M 170 28.9 60.1 114 147 169 1.01 12.6 4.8 CFP-D14-M 196 33.1 60 119 155 178 1.10 12.5 4.8 ACI-D16-M 178 29.0 61.2 109 144 166 1.07 10.9 5.6 EC-D16-M 164 34.2 61.6 101 137 157 1.04 11.6 5.3 CFP-D16-M 154 29.7 55.8 97 133 152 1.01 9.5 5.9 ACI-D14-C 169 33.7 39 52 110 146 168 1.01 11.6 3.4 4.5 EC-D14-C 173 25.8 30 45 114 147 169 1.02 12.6 2.4 3.6 CFP-D14-C 196 28.1 34 50 119 155 178 1.10 12.5 2.7 4 ACI-D16-C 171 28.3 45.8 109 144 166 1.03 11.0 4.2 EC-D16-C 167 31.1 17 34 101 137 157 1.06 11.6 1.5 2.9 CFP-D16-C 164 30.7 41.4 51.5 97 133 152 1.08 9.5 4.4 5.4 P y, P 1P, P 2P and P max : the values of transverse force at first (beginning of) yield, 1st plastic hinge, 2nd plastic hinge (predicted load-carrying capacity) and experimentally established peak level, respectively; δ ny, δ Pmax, δ 0.85Pmax, δ sust, and δ fail : the values of transverse displacement at P y, P max, the post-peak value of P = 0.85P max, the maximum sustained loading cycle and loading cycle that caused failure, respectively; µ sust = δ 0.85Pmax /δ ny or µ sust = δ sust /δ ny for the cases of monotonic and cyclic, respectively, loading, and µ fail = δ fail /δ ny for the case of cyclic loading, δ 1P = δ ny. Table 5 Experimental values of bending moment (in kn m) at support B (M B,e ) and point load point C (M C,e ) and their comparison with the design values (M B,d and M C,d ), shear force (in kn) within portions AB (V AB,e ), BC (V BC,e ) and CD (V C D,e ), and mode of failure (and its location) for all specimens (values in bold indicate locations of shear failure) Experimental values Specimen M B,e M B,e /M B,d M C,e M C,e /M C,d V AB,e V BC,e V C D,e Mode of failure Location of failure ACI-D14-M 63.9 1.16 66.1 1.20 53 122 56 Flexural Load point C EC-D14-M 62.4 1.13 59.8 1.09 52 117 53 Flexural Load point C CFP-D14-M 64.5 1.11 73.4 1.27 54 131 64 Flexural Load point C ACI-D16-M 63 1.17 64 1.18 53 121 57 Flexural Load point C EC-D16-M 54.8 1.07 60.7 1.19 46 110 54 Flexural Load point C CFP-D16-M 51.1 1.02 57.9 1.16 43 103 50 Flexural Load point C ACI-D14-C 57.1 1.04 63.3 1.15 48 114 55 Web horizontal cracking Middle of BC EC-D14-C 59.1 1.07 62.0 1.13 49 117 56 Web horizontal cracking Middle of BC CFP-D14-C 61.7 1.06 73.7 1.27 51 130 66 Stirrup snapping BC left of C ACI-D16-C 57.2 1.06 63.3 1.17 48 115 56 Flexural Load point C EC-D16-C 55.8 1.09 61.0 1.20 47 112 55 Web horizontal cracking Middle of BC CFP-D16-C 54.2 1.08 61.1 1.22 45.0 109 53 Comp. zone failure & inclined cracking CD right of C Locations of B, C, AB, BC and CD as in Fig. 1. Table 6 Shear capacities (in kn) predicted by EC2 and ACI for the various portions of the specimens tested (values in bold indicate locations of shear failure) Specimen Specimen portion AB left side AB right side BC both ends BC middle CD left side CD right side EC2 ACI EC2 ACI EC2 ACI EC2 ACI EC2 ACI EC2 ACI ACI-D14-M 125 149 257 307 257 307 125 149 257 307 125 149 EC-D14-M 123 133 181 224 181 224 123 150 181 224 123 181 CFP-D14-M 122 159 118 159 118 159 170 206 118 159 122 159 ACI-D16-M 175 202 262 308 262 308 175 202 262 308 175 202 EC-D16-M 131 145 252 289 252 289 131 145 252 289 131 145 CFP-D16-M 114 133 105 133 105 133 158 182 105 133 114 133 ACI-D14-C 125 149 257 307 257 307 125 149 257 307 125 149 EC-D14-C 123 133 181 224 181 224 123 150 181 224 123 181 CFP-D14-C 122 159 118 159 118 159 170 206 118 159 122 159 ACI-D16-C 175 202 262 308 262 308 175 202 262 308 175 202 EC-D16-C 131 145 252 289 252 289 131 145 252 289 131 145 CFP-D16-C 114 133 105 133 105 133 158 182 105 133 114 133 Element portions AB, BC, CD as in Fig. 1.

G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 171 (a) ACI-D16-M. (b) EC-D16-M. (c) CFP-D16-M. Fig. 9. Load displacement curves for D16 specimens tested under monotonic loading: (a) ACI-D16-M; (b) EC-D16-M; (c) CFP-D16-M. (The triangular symbols represent (moving upwards) the points at first yield, first plastic hinge and second plastic hinge, respectively.) Table 7 Ratios of shear capacities predicted by EC2 and ACI to measured shear forces for the various portions of the specimens tested (values in bold indicate locations of shear failure) Specimen Specimen portion AB left side AB right side BC both ends BC middle CD left side CD right side EC2 ACI EC2 ACI EC2 ACI EC2 ACI EC2 ACI EC2 ACI ACI-D14-M 2.35 2.80 4.83 5.77 2.11 2.52 1.03 1.22 4.57 5.46 2.22 2.65 EC-D14-M 2.37 2.56 3.48 4.31 1.55 1.91 1.05 1.28 3.42 4.23 2.32 3.42 CFP-D14-M 2.27 2.96 2.19 2.96 0.90 1.22 1.30 1.58 1.83 2.47 1.89 2.47 ACI-D16-M 3.33 3.85 4.99 5.86 2.16 2.54 1.44 1.66 4.62 5.43 3.09 3.56 EC-D16-M 2.87 3.17 5.52 6.33 2.29 2.62 1.19 1.32 4.68 5.36 2.43 2.69 CFP-D16-M 2.67 3.12 2.46 3.12 1.02 1.29 1.54 1.77 2.09 2.65 2.27 2.65 ACI-D14-C 2.63 3.13 5.40 6.45 2.26 2.70 1.10 1.31 4.65 5.56 2.26 2.70 EC-D14-C 2.50 2.70 3.68 4.55 1.55 1.92 1.05 1.28 3.22 3.98 2.19 3.22 CFP-D14-C 2.37 3.09 2.30 3.09 0.91 1.23 1.31 1.59 1.78 2.40 1.84 2.40 ACI-D16-C 3.67 4.24 5.50 6.47 2.28 2.68 1.52 1.76 4.66 5.48 3.11 3.60 EC-D16-C 2.82 3.12 5.42 6.21 2.25 2.58 1.17 1.29 4.59 5.27 2.39 2.64 CFP-D16-C 2.53 2.95 2.33 2.95 0.97 1.22 1.45 1.67 1.97 2.50 2.14 2.50 Element portions AB, BC, CD as in Fig. 1. zone which characterises the specimens designed to the CFP methodology. The values of yield stress and strength of the transverse reinforcement are indicated in Table 1. 3. Results of tests The test results are presented in Tables 4 7 and Figs. 7 14. Table 4 shows the experimental and calculated values of the transverse load and corresponding displacement at various load stages for all the specimens tested. Table 5 lists the experimentally obtained values of the internal actions (bending moments and shear forces), describes the failure mode, and indicates the location of failure for all specimens tested in the programme. Table 6 shows the code predictions of shear capacity of characteristic portions of the specimens, whereas Table 7 contains the ratios of these values to their experimental counterparts. The figures show both the load displacement curves and the mode of failure and associated crack pattern of the specimens tested. Although the work focuses primarily on structural behaviour under cyclic loading, testing under monotonic loading was

172 G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 considered essential for purposes of comparison. Moreover, the results obtained under monotonic loading were used to define a nominal value of the yield point, which formed the basis for the assessment of the ductility ratio of all specimens subsequently tested cyclically in the programme. 4. Discussion of results 4.1. Monotonic loading Fig. 10. Modes of failure and associated crack patterns for D16 specimens tested under monotonic loading: (a) ACI-D16-M; (b) EC-D16-M; (c) CFP-D16- M. Figs. 7 and 9 show the load displacement curves obtained for the specimens tested under monotonic loading. On these figures, the location of the nominal yield point used for assessing the specimen ductility ratio is also indicated. The location of this point was determined as follows: (a) The section bending moment at first yield, M ty (assessed by assuming that yielding occurs when either the concrete strain at the extreme compressive fibre attains a value of 0.002 or the tension reinforcement yields), and the section flexural capacity, M p, are first calculated. (b) Using the values of M ty and M P derived in (a), the corresponding values of the transverse load at first yield, P ty = 2.67M ty, and at the formation of the first plastic hinge, P 1P = 2.67M P, are obtained from Fig. 1. (c) In Figs. 7 and 9, lines are drawn through the points of the load displacement curves at P = 0 and P = P y. These lines are extended to the load level P 1P, which is considered to define the nominal yield point, and to the corresponding value of the displacement δ ny, which are given in Table 4. (a) ACI-D14-C. (b) EC-D14-C. (c) CFP-D14-C. Fig. 11. Load displacement curves for D14 specimens tested under cyclic loading: (a) ACI-D14-C; (b) EC-D14-C; (c) CFP-D14-C. (The triangular symbols represent (moving upwards) the points at first yield, first plastic hinge and second plastic hinge, respectively.)

G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 173 the stirrup spacing is smaller than 50 mm, the deviation between the above values is of the order of 20%. The explanation lies in the unavoidable triaxial behaviour of concrete, at a local material level, just prior to failure [7,8]. Finally, it can be seen from the load displacement characteristics (Figs. 7 and 9) that testing was stopped at a relatively large ductility, before significant loss of load-carrying capacity. In all cases, the crack pattern was characterised by flexural cracking. 4.2. Cyclic loading Fig. 12. Modes of failure and associated crack patterns for D14 specimens tested under cyclic loading: (a) specimen ACI-D14-C; (b) specimen EC-D14-C; (c) specimen CFP-D14-C. It is evident that all monotonically loaded specimens exhibited ductile behaviour. In fact, Table 4 indicates that the average value of the ductility ratio (µ) of the specimens, defined as the ratio of the displacement at a post-peak load of 85% the load-carrying capacity (δ 0.85Pmax ) to the displacement at nominal yield (δ ny ), i.e. µ = δ 0.85Pmax /δ ny, is over 5. Moreover, the table shows that, for all specimens the experimental values of load-carrying capacity either equalled or exceeded their calculated design counterparts. It is interesting to note in Table 5 that the experimentally established values of the section flexural capacity can be significantly larger than their calculated counterparts. In fact, the deviation of the experimental from the calculated values can be as large as 30% at the cross-section when the first plastic hinge forms (point C), whereas at the cross-section of the second plastic hinge (point B), it can be as high as 20%. Such high values of flexural capacity cannot be entirely attributed to the confinement provided within the critical lengths by the dense stirrup spacing specified by the methods employed to design the specimens, since flexural capacity appears to be independent of stirrup spacing. For example, specimen CFP-D14-M, with stirrup spacing of 100 mm, exhibited an experimental value of flexural capacity 28% larger than the calculated value, whereas for most other specimens, for which Figs. 11 and 13 show that the behaviour of the specimens tested under cyclic loading was not as ductile as that of the specimens subjected to monotonic loading. In fact, Table 4 indicates that, for the loading cycle that induced the maximum sustained displacement (δ sust ), the ductility ratio (µ sust = δ sust /δ ny ) varied from 1.5 to 4.4, while the ductility ratio at failure (µ fail = δ fail /δ ny, where δ fail is the displacement at which failure occurred) only once exceeded 5. It is interesting to note in Table 4 that a significantly lower ductility was exhibited by all specimens designed to EC2. Fig. 12(b), 14(b) show that such low ductility is characterised by a brittle type of failure due to near horizontal splitting of the portion of the specimen between the point load and the middle support (portion BC in Fig. 1), i.e. in the region of the point of inflection. A similar mode of failure was exhibited by specimen ACI-D14-C (see Fig. 12(a)), but, in this case, horizontal splitting occurred at a higher ductility (see Table 4). This can also be seen from Table 7, where failure in the middle (BC) portion of the specimen (indicated by bold numbers) occurred despite the apparent margins of safety against shear failure in both ACI (31%) and EC2 (10%). However, for specimen ACI- D16-C, an increase of the safety margin to the level specified by the CFP method safeguarded against horizontal splitting in the region of the point of inflection of portion BC. Naturally, such horizontal splitting did not occur in the specimens designed to the CFP method (see Fig. 12(c), 14(c)). However, one of the latter specimens, specimen CFP-D14-C, failed prematurely due to snapping of one of the stirrups located at a distance of approximately 2d (d = effective cross-section depth) from the load point within portion BC of the specimen (see Fig. 12(c)): the reason for this is given in [3], where it is pointed out that, in the case of load reversals, the concrete strength decreases in areas extending 2d from point loads (areas with a combination of high-shear force and bending-moment values), which weakens this region of change in the compressive-force path (not the case for monotonic loading) additional vertical stirrups are needed to prevent this [3], but these were not the provided in the present test series. As for the case of testing under monotonic loading, testing under cyclic loading revealed that the values of flexural capacity at the cross-sections of the plastic hinges were significantly larger than their calculated counterparts (see Table 5). Once again, such an increase can only occur if the concrete stresses developing within the compressive zone are significantly larger than the uniaxial cylinder compressive strength of concrete, f c,

174 G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 (a) ACI-D16-C. (b) EC-D16-C. (c) CFP-D16-C. Fig. 13. Load displacement curves for D16 specimens tested under cyclic loading: (a) ACI-D16-C; (b) EC-D16-C; (c) CFP-D16-C. (The triangular symbols represent (moving upwards) the points at first yield, first plastic hinge and second plastic hinge, respectively.) i.e. only triaxial behaviour can account for such high concrete stresses, as fully described elsewhere [7,8]. As discussed earlier, these high stresses are mainly caused by the dilation of concrete and much less (if at all) by stirrup confinement. For example, the flexural capacity of specimen CFP-D14-C with 100 mm stirrup spacing was 27% larger than the calculated value (see Table 5), whereas the flexural capacity of specimen ACI-D14-C with 17 mm stirrup spacing was only 22% larger than the calculated value (Table 5). 5. Conclusions 1. For all the specimens tested, the experimentally established load-carrying capacity was found to be larger than the calculated design value by an amount that approached 10% in certain cases. 2. Similarly, the experimentally established flexural capacity at the locations of plastic hinges was found to be significantly larger than its calculated value by an amount that ranged between 17% and 28% at the location of the first plastic hinge, and up to 17% at the location of the second plastic hinge. 3. The above significant increase in flexural capacity cannot be attributed to the confinement provided by the dense stirrup arrangement specified by current code methods, since it was found that flexural capacity was independent of stirrup spacing. It is the natural confinement of the concrete material itself (trying to dilate) which accounts for this effect. 4. Under cyclic loading, the specimens (with the exception of the ACI-D16 specimen) designed to current code provisions suffered premature failure due to near-horizontal web cracking in the region of the point of inflection. Fig. 14. Modes of failure and associated crack patterns for D16 specimens tested under cyclic loading: (a) ACI-D16-C; (b) EC-D16-C; (c) CFP-D16-C. 5. The above mode of failure was found to be prevented (case of specimen ACI-D16-C) by increasing the amount of stirrups

G.M. Kotsovos et al. / Engineering Structures 29 (2007) 163 175 175 in the region of the point of inflection to the levels specified by the CFP method. 6. The specimens designed to the CFP method seem more likely to satisfy the performance requirements of current codes for strength and ductility. Acknowledgement The present work forms part of a research programme financed by MacBeton (Hellas). References [1] Kotsovos MD, Baka A, Vougioukas E. Earthquake-resistant design of reinforced-concrete structures: Shortcomings of current methods. ACI Structural Journal 2003;100(1):11 8. [2] Vougioukas E, Zeris C, Kotsovos MD. Towards a safe and efficient use of FRP for the repair and strengthening of reinforced concrete structures. ACI Structural Journal 2003;102(4):525 34. [3] Kotsovos GM, Zeris C, Pavlovic MN. Improving RC seismic design through the CFP method. Structures & Buildings, Proc. ICE 2005; 158(SB5):291 302. [4] American Concrete Institute. Building Code requirements for reinforced concrete (ACI 318-99) and commentary ACI 318R-99. 1999. [5] Commité Européen de Normalisation, ENV-1992-1. Eurocode No. 2. Design of concrete structures. Part 1: General rules and rules of building. Brussels; October, 1991. [6] Commité Européen de Normalisation, ENV-1998-1. Eurocode No. 8. Structures in seismic regions. Part 1: General rules and rules of building. Brussels; October, 1991. [7] Kotsovos MD, Pavlovic MN. Ultimate limit-state design of concrete structures: A new approach. London: Thomas Telford; 1999. p. 164. [8] Kotsovos MD, Pavlovic MN. Structural Concrete: Finite-element analysis and design. London: Thomas Telford; 1995.