DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8 - PART 3 PROVISIONS

Transcription

1 DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8 - PART 3 PROVISIONS Konstantinos CHRISTIDIS 1, Emmanouil VOUGIOUKAS 2 and Konstantinos TREZOS 3 ABSTRACT A series of six reinforced concrete shear walls was tested under cycling static loading and is presented within this paper. The specimens represent shear walls designed according to older seismic codes, characterized by the absence of confined (column like) boundary elements and by the low ratio of shear reinforcement. The experimental behaviour of these specimens was evaluated in chord rotation and shear strength terms and it was compared with the values given by the application of Eurocode 8 - Part 3 (EC8-3) provisions, which refer to the assessment of reinforced concrete members. INTRODUCTION It is widely accepted that reinforced concrete shear walls play an important role in modern seismic design, as they constitute a bracing system capable of contributing to the lateral seismic resistance of the structure. However, it is well-known that in a lot of countries with high seismic exposure, there is a significant number of existing buildings designed according to older seismic codes, which include shear walls non-compliant with modern seismic provisions. These shear walls do not include confined (column like) boundary elements and they are characterized by low ratios of shear reinforcement. Theoretically, the lacking of confining stirrups leads to lower values of ultimate concrete strains, therefore lowering ductility values, and in addition the sparse shear reinforcement does not ensure that the shear strength exceeds the flexural one, leading to a prior shear (brittle) failure, often even before flexural yielding. In addition, the absence of stirrups makes the walls vulnerable to buckling of the compressive longitudinal rebars. A lot of scientific researches have been conducted over the last years regarding the assessment of existing reinforced concrete buildings. Several models have been developed, trying to predict the deformation capacity and the degradation of the shear strength with the inelastic cyclic displacements of existing reinforced concrete members (e.g. Priestley et al., 1994; Kowalsky and Priestley, 2; Panagiotakos and Fardis, 21; Biskinis et al., 24; Biskinis and Fardis, 21a; Biskinis and Fardis, 21b; Krolicki et al., 211). Some of these models are adopted, with some modifications, from modern seismic codes, such as EC8-3 (CEN, 25; CEN, 21) which includes a series of expressions which focus on the assessment of existing reinforced concrete members. The main aim of the present paper is to compare the experimental values which characterize the behaviour of the specimens with the values given by the application of EC8-3 (CEN, 25; CEN, 21) provisions. 1 Ph.D. Candidate, National Technical University of Athens, Athens, christidis@central.ntua.gr 2 Lecturer, National Technical University of Athens, Athens, manolis@central.ntua.gr 3 Assistant Professor, National Technical University of Athens, Athens, ctrezos@central.ntua.gr 1

2 EUROCODE 8 - PART 3 PROVISIONS EC8-3 (CEN, 25; CEN, 21) in Annex A proposes models for the performance assessment of reinforced concrete members that refer to their deformation capacity and their shear strength. The deformation capacity of reinforced concrete members is defined in terms of the chord rotation, θ, i.e. the angle between the tangent to the axis at the yielding end and the chord connecting that end with the end of the shear span (L V = M/V = moment/shear at the end section). The chord rotation is, simultaneously, equal to the element drift ratio, i.e. the deflection at the end of the shear span with respect to the tangent to the axis at the yielding end divided by the shear span. EC8-3 (CEN, 25; CEN, 21) defines three different limit states, indicating the state of damage of the concrete member Damage Limitation (DL), Significant Damage (SD) and Near Collapse (NC). The value of the chord rotation, θ y, in the limit state of Damage Limitation (DL) for rectangular walls is given in Eq.(1) and it corresponds to the yielding moment capacity, M y. L V +α V z d bl f y θ y =φ y +.13+φ 3 y (1) 8 f c where: φ y is the yield curvature of the end section, α V z is the tension shift of the bending moment diagram (Eurocode 2 - Part 1-1 (CEN, 24) with, z the length of internal lever arm, taken equal to.8h in walls with rectangular section (h is the depth of cross-section), α V =1 if shear cracking is expected to precede flexural yielding at the end section (i.e. if M y >L V V R,c ); otherwise (i.e. if M y <L V V R,c ) α V =, where V R,c is the shear resistance of the member considered without shear reinforcement according to Eurocode 2 - Part 1-1 (CEN, 24), f y and f c are the steel yield stress and the concrete compressive strength, respectively, in MPa, ε y is equal to f y /E s (E s is the reinforcement modulus of elasticity), d bl is the (mean) diameter of the tension reinforcement. The value of the ultimate (total) chord rotation, θ um, in the limit state of Near Collapse (NC) is given in Eq.(2) and it corresponds to the ultimate moment capacity, M u. θ um = 1.16*.3 ν max.1;ω'.225 γ el max.1;ω f c min 9; L.35 V h 25 αρ f yw sx f c (1.25 1ρ d ) (2) where: γ el is equal to 1.5 for primary seismic elements and to 1. for secondary seismic elements ν = N / bhf c (b is the width of compression zone, N is the axial force positive for compression), ω, ω are the mechanical reinforcement ratios of the tension (including the web reinforcement) and compression, respectively, longitudinal reinforcement, f yw is the stirrup yield strength (MPa), ρ sx = A sx /bs h = ratio of transverse steel parallel to the direction x of loading (A sx =stirrup reinforcement area and s h =stirrup spacing), ρ d is the steel ratio of diagonal reinforcement (if any), in each diagonal direction, α is the confinement effectiveness factor. Note that in shear walls the above value must be multiplied by.58 and for members without seismic detailing it must be also divided by 1.2. The intermediate value of the chord rotation, θ SD, in the limit state of Significant Damage (SD) may be taken as the.75θ um. The above deformation capacity can be attained provided that the structural member has not previously reached its shear strength capacity which is assumed to be degraded with the inelastic cyclic displacements. EC8-3 (CEN, 25; CEN, 21) suggests that both the shear strength as controlled by the stirrups, V R, and the shear strength as controlled by the web crushing, V R,max, should be decreased with the plastic part of ductility demand, expressed in terms of ductility factor of the 2

3 K. Christidis, E. Vougioukas and K. Trezos 3 transverse deflection of the shear span or of the chord rotation at member end: μ Δ pl = μ Δ -1. This ductility can be calculated as the ratio of the plastic part of the chord rotation, θ um pl =θ um -θ y, normalized to the chord rotation at yielding, θ y. The shear strength as controlled by the stirrups, V R, can be derived by Eq.(3) (with units: MN and meters). V R = 1 γ el h-x 2L V min N;.55A c f c min 5;μ Δ pl.16max.5;1ρ tot 1-.16min 5; L V h f c A c +V w (3) where: γ el is equal to 1.15 for primary seismic elements and 1. for secondary seismic elements, x is the compression zone depth, N is the compressive axial force (positive, taken as being zero for tension), A c is the cross-section area, equal to b w d for a cross-section with a rectangular web of width (thickness) b w and structural depth d ρ tot is the total longitudinal reinforcement ratio, V w is the contribution of transverse reinforcement to shear resistance, equal to: V w = ρ w b w zf yw (ρ w is the transverse reinforcement ratio) The shear strength as controlled by the web crushing, V R,max, can be derived by Eq.(4) (with units: MN and meters). V R,max = min 5;μ pl Δ N 1+1.8min.15; γ el A c f c 1+.25max 1.75;1ρ tot 1-.2min 2; L V h f c b w z (4) where: γ el is equal to 1.15 for primary seismic elements and 1. for secondary seismic elements and the other variables as previously defined. According to the above provisions the final deformation capacity could be predicted using a common diagram which includes both flexural and shear strength capacities expressed in Load- Rotation terms (P-θ) (Fig.1). Failure point Pum P u,sd (SD) (NC) Load P fail P y (DL) Flexural behaviour Shear behaviour θ y θ fail Chord rotation θ u,sd θum Figure 1. Definition of failure point according to EC8-3 (CEN, 25; CEN, 21)

4 CHARACTERISTICS OF SPECIMENS The experimental process included the testing of a series of six older reinforced concrete shear walls. Four of these specimens were previously presented in Christidis et al. (213), while the last two are first presented within this paper. The dimensions and the reinforcement configuration of all specimens are shown in Fig.2 and Fig.3 and they are summarized in Table.1. L 1 L 2 L 3 L 4 L 5 L 6 h bw Lw W 2 -FRP W 4 -FRP W 5 -FRP W 6 -FRP W W L 1 L 3 L 2 L 2 Lw Lw h bw L 5 L 5 L 4 L 6 Figure 2. Dimensions of specimens (in m) It is noted that, as it was mentioned before, in older reinforced concrete shear walls one of the most important causes of the loss of their bearing capacity is the buckling of the compressive rebars, which reduce the bearing capacity of the reinforcement not only in compression but in tension too. In addition, the loss of the bearing capacity due to buckling often occurs quite prematurely, making the wall unable to develop its plastic characteristics. Thus, many times, even in walls with low shear strength, the buckling phenomenon appears to be the cause of the loss of their capacity. However, the specific series of tests focuses, mainly, on the influence that shear reinforcement has at the behaviour of each specimen. For this purpose two layers of Glass Fiber Reinforced Polymers (GFRP) were placed in specimens W 2 -FRP, and W 4 -FRP while in specimens W 5,W 6,W 9,W 11 a configuration of open stirrups was added. With these two different interventions the buckling phenomenon of compressive reinforcement rebars was avoided. Table 1. Reinforcement ratios and material properties of specimens Concrete compression strength f c (MPa) Reinforcement yield/failure f y /f u (MPa) Longitudinal Reinforcement Stirrups Longitudinal reinforcement ratio (uniform) ρ tot ( ) Transverse (shear) reinforcement ratio ρ w ( ) Wall W 2 -FRP /67 622/ Wall W 4 -FRP /67 622/ Wall W /699 55/ Wall W / / Wall W /67 588/ Wall W /67 568/ ρ tot =Area sum of longitudinal reinforcement/cross section area=σa s,l /(b w *h) ρ w =Area sum of stirrup/(wall width*stirrups distance)=σα s,w /(b w *s) 4

5 K. Christidis, E. Vougioukas and K. Trezos 5 3x2 3x D8/3 stirrups D8/3 open stirrups D6/3 stirrups A 4 GFRP A' A A' D8/3 D8/3 D6/3 Section A-A' 4x175 Section A-A' 4x175 Walls W 2 -FRP,W 4 -FRP Walls W 5,W 6 3x2 3x D8/1 open stirrups D8/4 stirrups D8/1 open stirrups D6/4 stirrups A A' A A' D8/1 D8/4 D8/1 D6/4 Section A-A' 4x173 Section A-A' 4x173 Wall W 9 Wall W 11 Figure 3. Reinforcement configuration of specimens (in mm) APPLICATION OF EUROCODE 8 - PART 3 PROVISIONS The first step of this paper was to apply EC8-3 (CEN, 25; CEN, 21) provisions in order to predict the deformation capacity of each specimen. The application of Eq.(1) requires the calculation of the yield curvature, φ y. However, the fact that there are several layers of reinforcement does not lead to a clear yield point. Thus, and since EC8-3 (CEN, 25; CEN, 21) does not give specific instructions for that case, some assumptions had to be made in order to proceed the application. Finally, it was decided to search for a conventional yield point coming from the bilinearization of the Moment- Curvature diagram, M-φ, using an equivalent bilinear curve (elastic-plastic with hardening) where the elastic stiffness is defined from the first yield point (P y1, φ y1 ). The conventional yield point (P y, φ y ) is

6 derived by equating the area (energy) of the two curves, as shown in Fig.4. The most characteristic values of the diagrams shown in Fig.4 are summarized in Table Moment (knm) Analytical Moment-Curvature curve Curvature (1/m) Moment (knm) Analytical Moment-Curvature curve Curvature (1/m) (a) Wall W 2 -FRP (b) Wall W 4 -FRP Moment (knm) Analytical Moment-Curvature curve Curvature (1/m) Moment (knm) Analytical Moment-Curvature curve Curvature (1/m) (c) Wall W 5 (d) Wall W Moment (knm) Analytical Moment-Curvature curve Curvature (1/m) Moment (knm) Analytical Moment-Curvature curve Curvature (1/m) (e) Wall W 9 (f) Wall W 11 Figure 4. Analytical Moment-Curvature curve and bilinearization of specimens Table 2. Theoretical chord rotation ductility according to EC8-3 (CEN, 25; CEN, 21) M y1 (knm) 1 st Yield Conventional Yield Ultimate P y1 =M y1 /L V φ y1 M y P y =M y /L V φ y M u P u =M u /L V (kn) (1/m) (knm) (kn) (1/m) (knm) (kn) φ u (1/m) Wall W 2 -FRP Wall W 4 -FRP Wall W Wall W Wall W Wall W The diagrams of Fig.5 are derived from the application of Eq.(1), Eq.(2) and Eq.(3) where the safety factor γ el is taken equal to 1. It is noted that in these diagrams only the shear strength as controlled by the stirrups, V R, is included as the shear strength as controlled by the web crushing, V R,max, is in all cases higher than the flexural strength. As shown in this figure for walls W 5, W 6 and W 11, EC8-3 (CEN, 25; CEN, 21) predicts a prior brittle failure which, in one case (W 11 ), occurs even before the yielding of the wall. The ductility values calculated according to the previous methodology are included in Table.3. 6

7 K. Christidis, E. Vougioukas and K. Trezos Shear capacity (a) Wall W 2 -FRP 2 18 Failure Point θ fail =.11 Shear capacity Shear capacity (b) Wall W 4 -FRP Failure Point 2 18 ν= θ fail =.115 Shear capacity (c) Wall W 5 (d) Wall W Shear capacity Failure Point θ fail =.66 Shear capacity (e) Wall W 9 (f) Wall W 11 Figure 5. Deformation capacity of specimens according to EC8-3 (CEN, 25; CEN, 21) Table 3. Theoretical chord rotation ductility according to EC8-3 (CEN, 25; CEN, 21) Conventional Yield Ultimate (failure) Ductility P y P θ u (or P fail ) μ=θ um /θ y (kn) y θ (kn) um (or θ fail ) Wall W 2 -FRP Wall W 4 -FRP Wall W Wall W Wall W Wall W Note that in Walls W 5, W 6 and W 11 the failure point (P fail, θ fail ) is derived from the intersection of curves of flexural and shear capacity and it is prior to ultimate point (P u, θ u ). In addition, in wall W 11 where the failure rotation, θ fail, is lower than the yielding chord rotation, θ y, the ductility value is taken equal to 1. EXPERIMENTAL PROCESS The specimens were tested as cantilevers, under static cyclic loading. During the testing procedure, the displacement control method was adopted, including an initial displacement of ±1 mm with steps of

8 1 mm until failure. Three cycles of each displacement group were applied. Time - history of the loading is shown in Fig.6. Axial load was also applied to wall W6. The axial load had an initial value of ν=.7 and during the experiment had a variation as pointed in Fig.7d. Displacement (mm) Displacement LV time Figure 6. Time history of loading of specimens EXPERIMENTAL RESULTS The experimental results are presented in Fig.7 as a Load-Displacement diagram, P-δtop, where δtop is the displacement at the top of each specimen ν= (d) Wall W ν=.6 Displacement (mm) (c) Wall W5-4 ν=.85-1 ν=.85 ν=.1-15 Displacement (mm) -5 ν= ν= (b) Wall W4-FRP Displacement(mm) (a) Wall W2-FRP Displacement (mm) Displacement (mm) Displacement (mm) (e) Wall W9 (f) Wall W11 Figure 7. Lateral load - Top displacement curves of specimens 8

9 K. Christidis, E. Vougioukas and K. Trezos 9 In Fig.8 the experimental envelopes of all specimens are presented in a common Load-Chord rotation (or drift) diagram, P-θ, where θ is defined as the experimental top displacement normalized to the shear span (θ=δ top / L V ) W 4 -FRP 1 W 5 W 6 W 2 -FRP W 9 W Chord rotation Figure 8. Experimental envelopes, P-θ, of specimens In order to compare experimental and theoretical values, the experimental envelopes had first to be edited so as to define an experimental conventional yield and failure point. The experimental ductility, in chord rotation terms, is derived from the bilinearization of the experimental envelope of each specimen (P-θ), assuming an equivalent bilinear curve (elastic-plastic with hardening). The initial stiffness of the bilinear curve is obtained from the point where the theoretical first yield load, P y1, (Table.2) intersects the experimental curve and the ultimate rotation θ um,exp corresponds to.8p max,exp, where it is assumed that failure occurs. Finally, the conventional experimental yielding (P y,exp, θ y,exp ) point is arrived at by equating the area (energy) of the two curves (Fig.9). P max,exp P y,exp.8p max,exp Load P y1 P-θ envelope Equivalent bilinear curve θ y ' θ y,exp Chord rotation θ um,exp Figure 9. of experimental envelope, P-θ Applying the above procedure to the experimental envelopes of all specimens the curves of Fig.1 are derived. The theoretical values and experimental values obtained from Fig.1 are compared in Table.4.

10 Experimental envelope Experimental envelope (a) Wall W 2 -FRP (b) Wall W 4 -FRP Experimental envelope Experimental envelope (c) Wall W 5 (d) Wall W Experimental envelope Experimental envelope θ y,exp (e) Wall W 9 (f) Wall W 11 Figure 1. Experimental envelope and bilinearization of specimens Table 4. Experimental and theoretical chord rotation ductility Experimental θ um,exp Ductility μ exp EC8-3 (from Table.3) θ y θ um (or θ fail ) Ductility μ Load Experimental EC8-3 (from Table.3) P max,exp P u (or P fail ) (kn) (kn) Wall W 2 -FRP Wall W 4 -FRP Wall W Wall W Wall W Wall W DISCUSSION OF RESULTS As concluded from the experimental results, the different ratios of shear reinforcement do not seem to affect the load capacity of shear walls. This was clearly demonstrated by the fact that all specimens exhibited a level of lateral load capacity close to their flexural strength, not affected by the amount of shear reinforcement. As for the post yield behaviour, namely the deformation capacity, the results of walls W 5 to W 11 lead to conflicting conclusions. Walls W 5 and W 6 exhibited a post yield behaviour 1

11 K. Christidis, E. Vougioukas and K. Trezos 11 with a descending branch, whilst walls W 9 and W 11, with the same or even less shear reinforcement, exhibited a clear flexural behaviour. The different behaviour of walls W 5 and W 6 compared to walls W 9 and W 11 may be due to the difference in wall thickness (1 cm and 12.5 cm respectively) and the influence of accidental eccentricities. However, all four specimens (wall W 5 to W 11 ) exhibited a similar cracking mode, being characterized by the formation of significant inclined cracks (in contrast to W 2 -FRP and W 4 -FRP with higher amount of shear reinforcement - Table.1) which were, in one case (Wall W 11 ), followed by the failure of one of the stirrups located approximately at the middle height of the wall web. The deformation capacity of shear walls is directly connected to the shear strength. As concluded from the comparison of theoretical and experimental results, EC8-3 (CEN, 25; CEN, 21) provisions (Eq. (3)) seem to underestimate the shear strength of walls as in two cases (walls W 5 and W 6 ) the calculated shear strength intersects the flexural strength curve before the ultimate chord rotation, θ um, and in one case (wall W 11 ) the calculated shear strength is lower even than the yield flexural strength, predicting values of ductility lower than the experimental ones (μ exp is 87%, 7% and 4%, respectively, higher). At this point, some comments have to be made. The first one concerns the method of bilineazisation of the M-φ diagram. Within this paper the calculations were made assuming an equivalent elastic-plastic with hardening diagram. However, the use of an elastic-perfectly plastic diagram may lead, in some cases, to different theoretical values. For example, assuming an elasticperfectly plastic M-φ diagram for wall W 6 (Fig.11a) a theoretical ductility value μ=1.81 is calculated (13% higher than μ=1.6 with elastic-plastic with hardening diagram). The second comment concerns the value of z=.8h which in EC8-3 (CEN, 25; CEN, 21) is defined as the lever arm of internal forces. This value is quite accurate for beams, but not for walls, especially when the longitudinal reinforcement is distributed uniformly. Applying the value z=.57h as derived from the cross-section analysis in wall W 9 (Fig.11b) a theoretical ductility μ=1.29 is calculated (73% lower than μ=2.23 with z=.8h) Shear capacity Failure Point θ fail =.85 Shear capacity (a) Wall W 6 (b) Wall W 9 Figure 11. Deformation capacity of specimens (a) W 6 assuming an equivalent elastic- perfectly plastic M-φ curve and (b) W 9 for z=.57h from cross-section analysis, according to EC8-3 (CEN, 25; CEN, 21) Finally, in walls W 2 -FRP, W 4 -FRP and W 9 where the calculated shear strength is always higher than the flexural one, the experimental ductility is 7%, 117% and 53%, respectively, higher than the theoretical one. As shown in Table.4, while there is a good convergence between experimental and theoretical values of θ y, the experimental values of θ um are approximately twice the theoretical ones. This remark leads to the conclusion that Eq.(2) underestimates the ultimate chord rotation, θ um. CONCLUSIONS Six reinforced concrete shear walls, representing shear walls of existing buildings designed according to older codes, were tested under static cyclic loading. As concluded from the experimental results, low ratios of shear reinforcement seem to affect neither the bearing capacity nor the deformation capacity of walls. All the specimens reached their flexural bearing capacity, while in most cases they exhibited a flexural post yield behaviour followed by significant values of ductility. Low ratios of

12 shear reinforcement seem to determine the crack mode of walls which was characterized by the formation of significant inclined cracks. However, it is noted that these cracks were not followed by loss of bearing capacity. The experimental results were compared with the provisions included in EC8-3 (CEN, 25; CEN, 21), which refer to the assessment of reinforced concrete members. EC8-3 (CEN, 25; CEN, 21) seems, in some cases, to underestimate the shear strength of the walls indicating a prior brittle failure mode, therefore poor deformation capacity, not confirmed by the experimental results obtained in the present research. In addition, EC8-3 (CEN, 25; CEN, 21) underestimates the ultimate chord rotation, θ um. However, in general, all the above provisions underestimate the behaviour of shear walls, thus they are on the safe side. REFERENCES Biskinis DE, Roupakias GK and Fardis MN (24) Degradation of shear strength of reinforced concrete members with inelastic cyclic displacements, ACI Structural Journal, 11(6): Biskinis D and Fardis MN (21a) Deformations at flexural yielding of members with continuous or lap-spliced bars, Structural Concrete, 11(3): Biskinis D and Fardis MN (21b) Flexure-controlled ultimate deformations of members with continuous or lap-spliced bars, Structural Concrete, 11(2): Christidis K, Vougioukas E and Trezos KG (213) Seismic assessment of existing RC shear walls noncompliant with current code provisions, Magazine of Concrete Research, 65(17): CEN (24) Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings (EN ), European Committee for Standardization, Brussels, Belgium CEN (25) Eurocode 8: Design of Structures for Earthquake Resistance - Part 3: Assessment and Retrofitting of Buildings (EN ), European Committee for Standardization, Brussels, Belgium CEN (21) Eurocode 8: Design of Structures for Earthquake Resistance - Part 3: Assessment and Retrofitting of Buildings (EN : 25/AC), European Committee for Standardization, Brussels, Belgium Kowalsky MJ and Priestley MJN (2) Improved analytical model for shear strength of circular reinforced concrete columns in seismic regions, ACI Structural Journal, 97(3): Krolicki J, Maffei J and Calvi GM (211) Shear strength of reinforced concrete walls subjected to cyclic loading, Journal of Earthquake Engineering, 15(S1): 3-71 Panagiotakos TB and Fardis MN (21) Deformations of reinforced concrete members at yielding and ultimate, ACI Structural Journal, 98(2): Priestley MJN, Verma R and Xiao Y (1994) Seismic shear strength of reinforced concrete columns, Journal of Structural Engineering ASCE, 12(8):