SIMPLIFIED SHAKING TABLE TEST METHODOLOGY USING EXTREMELY SMALL SCALED MODELS

Transcription

1 13 th World Conference on Earthquake Engineering Vancouver,.C., Canada Augut 1-6, 2004 Paper No. 662 SIMPLIFIED SHAKING TALE TEST METHODOLOGY USING EXTREMELY SMALL SCALED MODELS Noriko TOKUI 1, Yuki SAKAI 2, Yauhi SANADA 3, Naruhito YAMAUCHI 4, Yohiaki NAKANO 5, Haruhiko SUWADA 6, and Hirohi FUKUYAMA 7 SUMMARY To etablih a imple and cot effective teting technique to invetigate eimic behavior of RC tructure, extremel mall caled model tructure coniting of high performance fiber reinforced cement compoite (HPFRCC) material reinforced onl with longitudinal reinforcement are fabricated, and their dnamic behavior are experimentall and analticall invetigated. INTRODUCTION Shaking table tet have been widel applied to invetigate dnamic behavior of tructure under earthquake excitation. In the haking table tet of reinforced concrete (R/C) tructure, relativel large pecimen are generall teted to eliminate difficultie in fabricating pecimen. However, the number of haking table that have enough capacit to carr out large-cale tet are limited, and much cot and time are generall required. Even when haking table tet uing relativel mall pecimen are carried out, it ma be difficult to provide lateral reinforcement in uch a caled pecimen. Therefore another methodolog i needed to carr out haking table tet within limited cot. Recent invetigation on high performance fiber reinforced cement compoite (HPFRCC) material indicate that tenion tiffening a well a multiple cracking effect of HPFRCC ma reult in ductile behavior. To etablih a imple and cot effective teting technique to invetigate eimic behavior of R/C tructure, extremel mall-caled column pecimen coniting of HPFRCC material reinforced onl 1 Graduate Student, Graduate School of Engineering, Univerit of Toko, tokui@ii.u-toko.ac.jp 2 Aociate Profeor, Intitute of Engineering Mechanic and Stem, Univerit of Tukuba, Dr. Eng. 3 Reearch Aociate, Earthquake Reearch Intitute, Univerit of Toko, Dr. Eng. 4 Technical Aociate, Intitute of Indutrial Science, Univerit of Toko 5 Aociate Profeor, Intitute of Indutrial Science, Univerit of Toko, Dr. Eng. 6 Reearcher, National Intitute for Land and Infratructure Management, Minitr of Land, Infratructure and Tranport 7 Chief Reearcher, uilding Reearch Intitute, Dr. Eng.

2 with longitudinal reinforcement are fabricated, and their dnamic behavior are experimentall and analticall invetigated. TEST SPECIMENS The extremel mall-caled column pecimen invetigated in thi tud are not the impl izereduced model of exiting full-cale R/C member but thoe coniting of longitudinal teel reinforcement and HPFRCC material without lateral reinforcement. The HPFRCC ued in pecimen i mortar matrix (water-cement ratio: 45%, and-cement ratio: 40%) mixed with % volume ratio of polethlene fiber (fiber length: 15mm, the diameter of a fiber: 12 µm). Two tpe of pecimen are deigned a follow: Tpe-S (tub) pecimen with a tub at each end and Tpe-P (plate) pecimen with a plate at each end. The dimenion of pecimen i hown in Figure 1. Each pecimen ha a cro ection of 30 x 30 mm and the height h of 180 mm. The hear-pan-to-depth ratio of each pecimen i 3.0, and the tenile reinforcement ratio i 2.19%. For haking table tet and tatic loading tet, three Tpe-S pecimen and ix Tpe-P pecimen are made. Photo 1 how a cloe-up view of cating HPFRCC Welding Nut M4 unbonded unbonded 4.5 Section A-A' 150 cloe-up view Plate Shear ke 180 h A A' Rebar:M4 HPFRCC h A A' Excitation direction Tpe-S pecimen Tpe-P pecimen Figure1. Dimenion of pecimen

3 Cating HPFRCC Form Rebar (3) (2) (1) Steel plate (1) After cating HPFRCC (2) Under cating HPFRCC (3) efore cating HPFRCC Photo 1. Cating HPFRCC SHAKING TALE TEST Tet Setup The loading tem i hown in Figure 2. Each pecimen i placed on and fixed to component (c). Thi tem ha horizontal and vertical lider, which enable pecimen to deform in the lateral and axial direction when the are ubjected to anti-mmetric bending during excitation. The relative diplacement between point (a) and component (c) i meaured in the direction of excitation. Accelerometer are intalled at point (a), (d), and the haking table. Load cell (1) and (2) are intalled at both end of the component (c), which i placed on horizontal lider, to directl evaluate the inertia force acting on the pecimen. The inertia force Q of each pecimen i calculated from Eq. (1) and (2) baed on the meaured force hown in Figure 3. ( P P P ) 0 Q PI + L1 L2 DS = (1) Auming P 0 DS ( PL + PL ) PI Q (2) = m a P I where P L1 and P L2 are the force meaured with load cell (1) and (2), repectivel, P I i the inertia force acting on lower tub and component (c), and m and a are their ma and abolute acceleration, repectivel. To oberve the effect of different deign detail at pecimen end, i.e., tub end and plate end, the rotation angle θ h' at 10mm above the column bae i meaured a hown in Figure 4. The data are recorded with a ampling interval of 1/500 ec.

4 Tet Program In thi experiment, the gro weight W of a pecimen including elf-weight and equipment weight i 3234N. The calculated initial period of the pecimen i 74 econd. The ine wave of which amplitude increae graduall a hown in Figure 5 i ued to excite pecimen. The period of the ine wave i 0.20 econd, which i about 3 time of the calculated period of pecimen. (ii) Static loading equipment attached at point (e) Figure2. Loading tem (i) Excitation Stem To negative direction Reaction wall PC rod Attached at point (e) To poitive direction Point (e) Point (d) Load cell (1) Load cell (2) Horizontal lider Point (a) Specimen Horizontal lider Component (c) Shaking table Excitation direction Vertical lider Poitive direction

5 Poitive ign Specimen Stub + Component (c) Q P L1 P I P L2 P DS Q: inertia force of pecimen (retoring and damping force) P L1 : force obtained from load cell (1) P L2 : force obtained from load cell (2) P I : inertia force of tub and component (c) P DS : damping force from lider Figure3. Inertia force of pecimen and meaured force R h θ h 10 Figure 4.Rotation angle meaurement Acceleration (m/ 2 ) Time () Figure5. Input ine wave

6 Tet Reult Figure 6 how the relationhip of repone hear coefficient C (= Q / W) and drift angle R (= / h) of each pecimen. oth pecimen how ductile behavior with pindle haped hteretic loop. To compare the fundamental characteritic of extremel mall-caled pecimen propoed herein to thoe of regular R/C member, the following three parameter α, β, and h eq are calculated and ummarized in Table 1 and Figure7. The are defined a: (1) α : the ratio of ecant tiffne at ielding to the initial tiffne. (2) β: the ratio of pot-peak tiffne to the initial tiffne (3) h eq : equivalent damping factor The ielding of the pecimen i defined a the point where it intant tiffne i lower than 10% of the initial tiffne. A can be found in Table1, thee value uccefull imulate thoe of R/C member. Figure 8 how the θ h' - R relationhip of both pecimen. Thi figure how that the ratio of θ h' of Tpe-P pecimen to that of Tpe-S pecimen lie in the range of 1.5 to 2.0, and the deformation i more ignificantl concentrated over the end region for Tpe-P pecimen. Table 2 how the maximum Q value (Q MAX ) of pecimen during haking table tet, together with thoe of tatic loading tet decribed later. Thi Table how that Q MAX of Tpe-S pecimen i 20% larger than that of Tpe-P pecimen although the have the ame ectional and material propertie. To undertand the reaon of different Q MAX value, tatic loading tet of both pecimen are carried out and their fundamental behavior are carefull invetigated. Shear coefficient C - Shear coefficient C Tpe-S Figure6. Shaking table tet reult Tpe-P Table 1. Degradation in tiffne α β Tpe-S pecimen Tpe-P pecimen

7 h eq (%) Tpe-S Tpe-P Rotation angle θ h' ( 10-3 rad.) Tpe-P Tpe-S Figure7. Equivalent damping factor Figure8. θ h' - R relationhip Table2. Comparion of maximum Q value Q MAX (N) [C MAX ] (Shaking Table Tet) Shaking Table Tet Static Tet / (Static Tet) Tpe-S pecimen 2285 [0.707] 2122 [0.656] 8 Tpe-P pecimen 1897 [87] 1911 [91] 0.99 (Tpe-S) / (Tpe-P) Specimen and Tet Setup STATIC LOADING TEST The pecimen ued in tatic loading tet are the ame a thoe of haking table tet. For the tatic tet, the equipment hown in Figure 2 (ii) i attached at the point (e) indicated in Figure 2(i). The diplacement obtained in the haking table tet are applied to each pecimen b puhing and pulling point (e). The diplacement are impoed with a PC rod b tightening and looening a nut placed at the reaction wall. After the maximum diplacement ccle experienced during the haking table tet i impoed, each pecimen i monotonicall loaded to collape. Tet Reult Figure 9 how the C - R relationhip of each pecimen. Figure 9 and Table 2 how that the maximum value of C of Tpe-S pecimen i 11% larger than that of Tpe-P pecimen. The higher trength in Tpe-S pecimen ma be attributed to the different deign detail at pecimen end the Tpe-S pecimen ha tub end where fiber reinforced cement i monolithicall cat together with it mid-column part, and the critical ection at both end can therefore reit tenile action to ome extent even in the pot-crack tage, while the Tpe-P pecimen ha teel plate end which do not contribute to the reitance of cracked ection. A can be found in comparion between haking table tet and tatic loading tet hown in Table 2, Q MAX during the haking table tet i 8% higher for Tpe-S pecimen while it i almot ame for Tpe-P pecimen. Thi reult implie that the effect of train rate ma be different in Tpe-S and Tpe-P pecimen.

8 Shear coefficient C - Shear coefficient C Tpe-S Figure9. Static loading tet reult Tpe-P FIER MODEL ANALYSIS CONSIDERING STRAIN RATE EFFECTS To invetigate the difference in Q MAX due to deign detail at pecimen end and train rate effect, fiber model anale are carried out. Aumption in computation Curvature ditribution Figure 10 how the curvature ditribution aumed in the anali. A can be found in the figure, a triangular curvature ditribution i aumed for Tpe-S pecimen, while a combined profile of rectangular and triangular ditribution i aumed for Tpe-P pecimen ince the longitudinal reinforcement i unbonded to HPFRCC over the length of h p in the end plate a hown in Figure 1. The curvature φ 0 at the critical ection of Tpe-S pecimen at a given diplacement, and the rotation angle θ h at h (=10 mm) above the column bae, i determined b Eq. (3) and (4), repectivel, auming the curvature ditribution hown in Figure 10(a). 3 φ 0 = 2 h (3) 1 h 3 h h θ h = φ 0 h 2 = 2 h 2 h h h (4) 2 The curvature at the critical ection of Tpe - P pecimen, p φ 0, i determined a follow. aed on the curvature ditribution of Tpe-P pecimen hown in Figure 10(b), the drift p and the rotation angle p θ h at a ditance of h (=10 mm) from the bottom tub are obtained a Eq. (5) and (6).

9 P P 1 2 hp = pφ 0h + pφhp hp h (5) 1 h θh = pφ0 h 2 + pφhp hp 2 h (6) Where p φ 0 and p φ hp are curvature at critical ection and at h p below the end plate, repectivel. Conidering the experimental reult hown in Figure 8, the relation of p θ h and θ h i aumed a Eq. (7). P θ = θ (7) ' 2 h S h ' Setting p of Eq.(5) equal to of Eq.(3), the curvature p φ 0 at critical ection at a given diplacement p (= ) i obtained from Eq. (4) to (7). The location of the neutral axi and the train of each fiber egment are then determined baed on the curvature at critical ection φ 0 (or p φ 0 ) obtained above, the equilibrium condition of axial force of a ection and the plane ection aumption. φ h' φ 0 (a) Tpe-S pφ h' φ p 0 pφ h p (b) Tpe-P h h p h Fig.10 Curvature ditribution Material characteritic To conider train rate effect on the σ - ε relationhip on material characteritic bai, the train rate i calculated b Eq. (8). k ε& = ε / t (8) k Where k ε and t are the train increment of element k and the time increment, repectivel. Table 3 and 4 how the mechanical propertie of HPFRCC and longitudinal reinforcement obtained b the tatic material tet. Figure 11 how material propertie model for HPFRCC and longitudinal reinforcement. ε& k

10 In compreion, the σ - ε relation of HPFRCC i repreented with (1) a linear line having a lope of initial Young modulu E c, (2) a parabola curve that pae through the origin (0, 0) and the peak (ε Β, σ Β ), (3) a linearl falling branch and (4) a reidual trength plateau with σ Β. In tenion, a tenile trength of σ Β /20 after ielding i aumed up to 2% for Tpe-S pecimen, while the trength contribution i neglected for Tpe-P pecimen. The Young modulu E c and trength σ Β hown in Table 3 i factored in accordance with train rate, a hown in Eq. (9) through (12). In both tenion and compreion, the σ - ε relation of longitudinal reinforcement i repreented with (1) a linear line having initial Young modulu E and (2) a linear line with 1/100 E. The ield trength σ how in Table 4 i factored in accordance with train rate, a hown in Eq. (13). HPFRCC Young modulu & ε > 10 1 µ / ec d E & ε 10 1 µ / ec d c E = c ( 2 log ε& + 0. ) Ec = 98 E c Where, d E c : Young modulu of HPFRCC (dnamic) E : Young modulu of HPFRCC (tatic) Compreive trength & ε > 10 1 µ / ec d σ & ε 10 1 µ / ec d σ = c ( 0.06 log & ε + 0. ) σ = 94 σ Where, dσ : Compreive trength of HPFRCC (dnamic) σ : Compreive trength of HPFRCC (tatic) (9) (10) Tenile trength Tpe-S σ t = σ / 20 ( σ = σ or dσ ) (11) Tpe-P σ = 0 (12) t Longitudinal reinforcement Yield trength of longitudinal reinforcement & ε > 10 2 µ / ec d f & ε 10 2 µ / ec d f = ( 5 log ε& + 0. ) f = 90 f Where, d f : Yield trength of longitudinal reinforcement (dnamic) f : Yield trength of longitudinal reinforcement (tatic) (13)

11 Dnamic d σ σ Dnamic d σ σ Static -2% d σ σ Linear Ec Parabola Static 1E E ε ε d ε 1.5ε σ = 47( N / mm ), ε E c 4 = ( N / mm 2 HPFRCC 2 ) = 0.4(%) σ = 450( N / mm E = ( N / mm Longitudinal Reinforcement 5 2 ) 2 ) Figure11. Model of material propertie Loading pattern Dnamic Static Table3. Mechanical Propertie of HPFRCC (obtained from tatic material tet) Specimen Young Compreive Strain at Tenile Age modulu *1 trength compreive trength (da) E c (N/mm 2 ) σ (N/mm 2 ) trength ε (%) σ t (N/mm 2 ) S10M (Tpe-S) P10M (Tpe-P) S10M (Tpe-S) *3 P10M (Tpe-P) *1 ecant modulu at 1/3 σ *2 average of 3 clinder *3 not meaured Table4. Mechanical Propertie of Longitudinal reinforcement (obtained from tatic material tet) Section area (mm 2 ) Young Modulu E (N/mm 2 ) Yield trength *1 σ (N/mm 2 ) Yield train ε (%) M *1 0.2% off-et value *2 average of 3 tet piece

12 Reult and Dicuion Computed reult are compared with tatic loading tet reult in Figure 12 and haking table tet reult in Figure 13, repectivel. Figure 14 how the train rate and it correponding magnification factor of tenile reinforcement at the critical ection of each pecimen obtained in the computation. A i found in Figure 12, Q MAX can be predicted conidering the contribution of fiber reinforced cement compoite material to tenion reitance in Tpe-S pecimen and neglecting uch contribution in Tpe-P pecimen. The computed Q MAX of Tpe-S pecimen ubjected to dnamic loading agree well with the tet reult conidering the train rate effect. The train rate and correponding magnification factor of material trength i, a hown in Figure 14, generall lower in Tpe-P pecimen, which i attributed to a curvature profile different from that aumed for Tpe-S pecimen. Although the computed Q MAX of Tpe-P pecimen i accordingl lower than that of Tpe-S pecimen, it i till higher b 15% than experimental reult. Shear coefficient C Shear Coefficient C Conputed Experiment Tpe-S Tpe-P Figure12. Comparion of computed reult with tatic tet reult Strain rate (µ/) Computed Experiment Shear coefficient C Shear coeficient C Tpe-P Figure13. Comparion of computed reult with dnamic tet reult Drift angle R( 10-3 rad.) Figure14. Computed train rate of tenile reinforcement Tpe-S Tpe-P d f / f Computed Experiment Computed Experiment Tpe-S

13 CONCLUSION To etablih a imple and cot effective teting technique to imulate eimic behavior of R/C tructure, extremel mall-caled model tructure coniting of high performance fiber reinforced cement compoite (HPFRCC) material reinforced onl with longitudinal reinforcement are fabricated, and their behavior are experimentall and analticall invetigated. 1) The pecimen of fabricated and invetigated in thi tud can imulate the behavior of actual R/C member. 2) Q MAX under tatic loading can be predicted conidering the contribution of fiber reinforced cement compoite material to tenion reitance in Tpe-S pecimen and neglecting uch contribution in Tpe-P pecimen. 3) The computed Q MAX of Tpe-S pecimen ubjected to dnamic loading agree well with the tet reult conidering the train rate effect. Although the computed Q MAX of Tpe-P pecimen i lower than that of Tpe-S pecimen, it i till higher b 15% than experimental reult. REFERENCES 1. High Performance Fiber Reinforced Cement Compoite (HPFRCC 2), A. E. Naaman and H. W. Reinhardt Ed., RILEM Proceeding 31, Kanda, T.: Material Deign Technolog for High Performance Fiber Reinforced Cementitiou Compoite, Concrete Journal, Vol. 38, No. 6, pp. 9-16, Jun., Sato, Y. Fukuama, H. Suwada, H.: A Propoal of Tenion-Compreion Cclic Loading Tet Method for Ductile Cementitiou Compoite Material, Journal of Structural and Contruction Engineering, No.539, pp. 7-12, Jan., Hirohi, H. Tuneo, O. Yohikazu, K. Yohiaki, N. Fumitohi, K.: Fiber Model Anali of Reinforced Concrete Member with Conideration of The Strain Rate Effect, Journal of Structural and Contruction Engineering, No.482, pp , Apr., 1996 ACKNOWLEDGEMENTS The author gratefull acknowledge Dr. K. Fujii, Potdoctoral Reearch Fellow at the Intitute of Indutrial Science, the univerit of Too, for hi enthuiatic contribution to preparing thi report. The Central Workhop at the Intitute of Indutrial Science i alo greatl appreciated for it technical upport in fabricating pecimen.