Nonlinear Finite Element Analysis on Shear Failure of Structural Elements Using High Performance Fiber Reinforced Cement Composite

Transcription

1 Journal of Advanced Technology Vol. 4, No. 1, 45-57, February 26 / Copyright 26 Japan Institute 45 Scientific paper Nonlinear Finite Element on Shear Failure of Structural Elements Using High Performance Fiber Reinforced Cement Composite Haruhiko Suwada 1 and Hiroshi Fukuyama 2 Received 3 September 25, accepted 1 December 25 Abstract High-performance fiber reinforced cement composites (HPFRCC) are highly ductile and characterized by pseudo strain hardening in tension. High-level in structural performance through the application of HPFRCC is expected. However, many uncertainties remain regarding the influence of the tensile characteristic of HPFRCC on the shear resistance mechanism of structural elements utilizing HPFRCC. Though FEM analysis is an effective engineering tool to analyze the relationship between the material characteristics and the structural performance of elements, a robust constitutive model is indispensable for obtaining accurate results. This paper proposes constitutive models based on basic test results. The proprieties of the model are confirmed based on a comparison between the analytical simulation and the structural test results for shear failure behavior. The analytical results using the proposed model match reasonably well the experimental results of HPFRCC structural elements. 1. Introduction In recent years, a new Fiber Reinforced Cement Composite (FRCC) material called High Performance Fiber Reinforced Cement Composite (HPFRCC) has been newly developed and studied for application to structural members [Li (1993), Naaman and Reinhardt (1995), Fukuyama and Suwada (23), Kesner and Billington (23)]. A property of this material is Pseudo Strain Hardening Behavior (PSH behavior) caused by the distribution of multiple fine cracks (multiple cracking) under tensile stress. It is still uncertain how the tensile characteristics of HPFRCC affect the shear resistance mechanism of structural elements. Therefore, it is essential to implement further investigation in order to establish a rational method for performance evaluation. A non-linear analytical method based on the Finite Element Method (EFM) is an efficient way to analyze the effect of material properties effects on the shear resistance mechanism of structural elements. Additionally, the shape of structural elements and the bar arrangements can be easily investigated with a parametric study. The level of reliability of test results, however, depends on the accuracy of constitutive models. Many FEM analyses on concrete materials have been implemented over a long time with a central focus on two-dimensional analysis using plane stress elements. Greater analytical accuracy of monotonic loading in one direction can be expected along with improved accuracy of constitutive models. 1 Research Engineer, Dept. of Structural Engineering, Building Research Institute, Japan. suwada@kenken.go.jp 2 Chief Research Engineer, Dept. of Structural Engineering, Building Research Institute, Japan. On the other hand, few studies have been conducted on FEM analysis of HPFRCC, particularly basic studies of constitutive models. Kabele et al. (1999) performed FEM analysis of HPFRCC elements and members. Since the most of the constitutive models used in the analysis are not confirmed by tests, further experimental investigation is needed. Han et al. (23) modeled the tensile-compression cyclic stress-strain curve based on the results of the cylinder test and performed cyclic loading analysis on cantilever columns considering the bond characteristics of reinforcements. In this analysis, the simulation of historical characteristics was focused on. A constitutional model considering the shear failure behavior of members was not proposed or investigated. Therefore, the aim of this study is to establish a method of FEM analysis in order to analyze the shear resistance mechanism of HPFRCC structural elements and to investigate the most suitable configurations and bar arrangements of structural element to meet required performance. For HPFRCC investigation and analysis, it is essential to establish a constitutional model of PSH behavior under tensile stress. Because the tensile characteristics of HPFRCC may affect the confinement effect under tension-compression stress, it is also important to adequately model the basic characteristics under tension-compression stress. The compression properties after the development of cracks constitute an important constitutive model in order to reconstruct the failure mode of the compression strut of members with excellent shear strength, and the reliability of test results greatly depends on the accuracy of the model. In this study, a constitutive model is proposed by implementing the basic experiments both on the stress-strain curve under the tensile and compression stress, and on the compression properties after the development of cracks. The basic modeling policy in this

2 46 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, study is to extend the existing models of concrete to the model of HPFRCC. Moreover, a structural experiment that can specify the effects of the constitutive models (analytical verification experiment) is implemented. The applicability of the model and the accuracy of the analysis are defined by comparing the structural test results and the analytical simulation. In this study, the analysis of two-dimensional monotonic loading in one direction is used as FEM analysis. 2. Basic tests on constitutive models 2.1 Uniaxial loading tests of short columns (1) Outline of tests The purpose of this experiment is to implement a uniaxial loading test of a specimen with characteristics similar to those of a real member, and to examine the effects of shape and scale and the influence of the confinement effect. A detailed drawing of the test specimen is shown in Fig. 1, and the instrumentation of the test specimen is described in Table 1. The configuration of the test specimen is a short column ( mm). The central 2 mm section of the specimen is the test section. Variables used in the test are whether or not there are lateral reinforcements and the kind of cement matrix. Four kinds of cement matrix were used. One is the normal concrete used as the control. The others are, and. is mortar matrix (water-cement weight ratio of 45%, sand-cement weight ratio of 4%) which is mixed with PVA fiber (REC 15) with a length of 12 mm, diameter of 37 µm and fiber volume fraction of 1.7%. is mortar matrix which is mixed with polyethylene fiber (dyneema) with a length of 15 mm, diameter of 12 µm and fiber volume fraction of 1.%. is a mortar matrix which is mixed with 1.% of polyethylene fiber with a length of 15 mm, diameter of 12 µm and with steel code (The thing that five piano wire was knit) with a length of 32 mm, diameter of 45 µm and fiber volume fraction of 1.%. A different fiber volume fraction is set for each kind of fiber, which is determined on the basis of workability obtained from the mixing tests. The tensile stress-strain relationship of HPFRCC obtained through the material tests is shown in Fig. 2. A cylinder with a length of 2 mm and a diameter of 1 mm was used in the HPFRCC material test. A tensile test was conducted based on the method proposed by Sato et al (21). A 1MN universal testing machine was used for monotonic loading in the core compressive test. The load was detected through load cells housed in the machine, and the displacement in the test section was an averaged value obtained from four displacement transducers Test area Longitudinal reinforcement 4-D13 (SD295A) Lateral reinforcement 2-D6 (SD295A) 2 (Unit: mm) Fig. 1 Test specimens of uniaxial loading tests (in case of C series). Tensile stress Tensile strain (%) Fig. 2 Tensile stress-tensile strain relationships of HPFRCC. Table 1 List of test specimens. Series of specimen P Series C Series Name of specimen RC-P PVA-P PE-P PS-P RC-C PVA-C PE-C PS-C Cementitious material Lateral reinforcement None (No confinement) -D6@5(SD295A) (Confinement) Longitudinal reinforcement 4-D13 (SD295A) Cross section 15 2 (mm) Length 4 (mm)

3 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, Name of specimens Table 2 Test results of niaxial loading tests. Secant modulus at 1/3σ c E c N/mm 2 Maximum compressive stress σ c Strain at maximum compressive stress ε c N/mm 2 % RC-P ( ) 48.3 (57.9).24 (.28) PVA-P ( ) 48.8 (53.1).41 (.42) PE-P ( ) 41.3 (5.).35 (.39) PS-P ( ) 44.2 (5.4).41 (.41) RC-C ( ) 49.3 (57.9).28 (.28) PVA-C ( ) 49.8 (53.1).56 (.42) PE-C ( ) 45.5 (5.).43 (.39) PS-C ( ) 47.4 (5.4).32 (.41) RC-P RC-C PVA-P PVA-C PE-P PE-C PS-P PS-C Fig. 3 -compressive strain relationships of uniaxial loading tests. (2) Test results and investigation The test results are listed in Table 2 and the compressive stress-strain relationship is shown in Fig. 3. Here, stress is obtained by dividing the load from the load cells by the total cross sectional area of the test specimen without considering the share of longitudinal reinforcements. The obtained results are listed in Table 2. Regarding the 1/3σ c secant stiffness, the value of the C series (with lateral reinforcement) is higher than that of the P series (without lateral reinforcement) for all the materials. The value obtained by the uniaxial loading test is higher than that obtained by the cylindrical test. Regarding the maximum compressive stress, the value of the C series is higher than that of the P series for all the materials. The value obtained by the cylindrical test is higher than that obtained by the uniaxial loading test. Regarding the strain ε c under maximum compressive stress, no clear difference can be observed between the P and C series because

4 48 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, irregular results are obtained for each material. The Maximum compressive strength of the C series restricted by lateral reinforcement is lower than the maximum compressive strength of the cylinder test. The effects of shape and scale may influence the result. 2.2 Biaxial loading tests (1) Outline of tests Vecchio and Collins.(1982) and many other researchers [Miyahara et al. (1987), Okubo et al. (1989), Naganuma and Yamaguchi (1989), Shirai et al. (1989)] experimentally concluded that compressive properties in the direction parallel to cracks in concrete decrease along with strength and stiffness to a greater extent in biaxial loading tests than in cylinder tests. There are four causes of reduction; 1) flexure of cracks, 2) confinement effect of reinforcement and strain stress that occurs in the cracks due to bonding, 3) inner cracks caused by the bond action of deformed reinforcement, 4) scale effect. The same reasons apply by and large to the case of HPFRCC, and further investigations are therefore desirable to demonstrate compressive deterioration properties of cracked HPFRCC. In this study, the authors conducted biaxial loading tests, which are easier to execute than the pure shear loading method employed by Vecchio and Collins (1982). This approach was selected due to the fact that the average tensile strain (ε t ) in the orthogonal direction of cracks is recognized as the main factor of reduction by a relatively large number of researchers. A detailed drawing of the test specimen is shown in Fig. 4. The form and size are the same as those of the specimens used in the test performed by Okubo et al. (1989) and two steel bars with screw ribs are arranged in order to add tensile loading in the horizontal direction. Both ends (25 mm) of the reinforcement are unbonded in order to prevent splitting under tensile loading. The test results vary with the kind of cement matrix and ε t. Four kinds of cement matrix were used. One is normal concrete for comparison purposes. The others are, and. They use the same mixing conditions as those used in the uniaxial loading tests mentioned in the previous chapter, although they are not the same batch. The tensile stress-strain relationship of HPFRCC obtained by the tension test is shown in Fig. 5. A tension test was conducted based on the method proposed by Sato et al. (21). The drawing of the loading machine for the biaxial loading test is shown in Fig. 6. The measurement method is shown in Fig. 7. Two reinforcements horizontally embedded in the specimen are added tensile force though prestressing steel, and when the tensile force reaches a certain level of ε t, compressive force is applied to the specimen by monotonic loading using a 2 kn-testing machine. Two sheets of Teflon were placed between the compressive surface of the specimen and the surface of the loading machine to prevent deformation confinement caused by the friction of the compressive surface of the specimen under compressive loading. ( c σ c ) is obtained by D13 Tensile stress M1 Unbond (Unit: mm) Fig. 4 Test specimens of biaxial loading tests Tensile strain (%) Fig. 5 Tensile stress-tensile strain relationships of HPFRCC. PC rod (? 32) 2kN Servo type testing machine 5 1kN Center hole jack Load cell Spherical support Fig. 6 Test setup of bi-axial loading test. Fig. 7 Measurement method of biaxial loading test.

5 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, dividing the load detected through the load cell housed in the machine by the cross sectional area of the compressive surface of the specimen. ε t and the mean compressive strain in the direction parallel to cracks ( c ε c ) are obtained by dividing the mean value of the data from the four displacement transducers set on both sides of the Cementitious material Name of specimens Table 3 Test results of biaxial loading tests. Average tensile strain Maximum compressive compressive stress stress Strain at at maximum Maximum compressive stress Compressive strength reduction factore at end of tension at compressive cσ cmax c ε cmax c σ cmax / c σ B loading failure ε ti (µ) ε tu (µ) CON CON CON CON CON CON CON CON PVA PVA PVA PVA PVA PVA PVA PVA PVA PE PE PE PE PE PE PE PE PE PS PS PS Measurement became impossible due to cracking at point of attachment displacement transducer. cσ B :Maximum compressive strength of cylinder 2 In the tests of, reinforcements out of the test area were broken when the strain exceeded 5μ.

6 5 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, specimen by the length of the measurement area. (2) Test results and investigation Detailed information of the test specimen and test results are listed in Table 3 and the c σ c - c ε c relationship is shown in Fig. 8. Table 3 shows that ε t is ranges from to about 2 µ. The reduction factor of compressive strength (λ) is defined as the value obtained by dividing the maximum compressive stress ( c σ cmax ) obtained through a biaxial loading test by the compressive strength ( c σ B ) obtained through the cylindrical compressive test. Figure 8 shows that the compressive strength and stiffness of HPFRCC decreases with increases of ε t, as in the case of concrete. Relationship λ and mean tensile strain at the end of tensile loading (ε ti ) is plotted in Fig. 9. This figure shows that along with the increase in ε t, the strength of HPFRCC decreases less than that of concrete when they have the same level of strength. There is no remarkable difference in reduction of compressive properties among, and, and it is therefore, concluded that the tensile properties are not heavily influential. 3. Constitutive models In this study, a two-dimensional analytical program employing plane stress elements is used. As the basic HPFRCC constitutive equation, the orthotropic model based on equivalent axial strain of Darwin and Peckonold (1974) is employed. This model can express the variety of stress conditions based on the failure surface under the multiaxial stress and uniaxial stress-strain relationships. 3.1 Uniaxial compressive stress strain relationship The uniaxial stress-stress relationship can represent the following models proposed by Fafitis and Shah (1985), { 1 ( 1 ε / ε ) } A σ = σ (1) c c c B c A= ε / σ ( ε c ε ) c E c B where c σ B =compressive strength, c E =Young s modulus, and ε =strain at the compressive strength. Figure 1 shows comparative results between models and the test results of a cylindrical test, a uniaxial com CON- CON-4 CON-6 CON PE- PE-5 PE-2 PE-4 PE-6 PE-8 PE-1 PE-15 PE PVA- PVA-5 PVA-2 PVA-4 PVA-6 PVA-8 PVA-1 PVA-15 PVA PS- PS-2 PS Fig. 8 compressive strain relationships of biaxial loading test.

7 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, Compressive strength reduction factor λ ε ti (µ) Tensile stress Model Tensile strain (%) Fig. 9 Relationships between compressive reduction factor (λ) average tensile strain (ε ti) Uniaxial loading test Biaxial loading test(ε t =1.%) Model Fig. 1 Comparison of analytical model with compression tests. pressive test of short columns and a biaxial loading test. Good agreement among these tests can be seen Equation (1) expresses the increasing range of compressive stress-strain relationship normalized by the strain at the maximum strength. For FEM analysis, the strain at the maximum strength in constrains or in 2 axial stresses should be separately defined. In this experiment, however, the strain at the maximum strength is directly applied and calculated in order to verify the reproducibility of the curve. The test result is shown by straight line which is closely related to the softening branch. 3.2 Uniaxial tensile stress strain relationship The uniaxial tensile stress-strain relationship is a trilinear model that approximates the elastic range, pseudo strain hardening behavior and stress softening range by a straight line. Figure 11 shows that the previous tension test of the cylindrical specimen can be well simulated well by the trilinear model. For FEM analysis, an adequate point must be determined based on the tensile test results so that the crack point, maximum tensile strength point and stress become zero. Fig. 11 Comparison of analytical model with tension tests. 3.3 Reduction factor of compressive strength When the members such as short columns, which dominantly failed in the failure of compressive strut are analyzed, it is important to model appropriately the reduction factor of compressive strength(λ) in order to represent the deterioration condition of compressive properties after the development of cracks. In this paper, λ of cracked HPFRCC is modeled based on the results of the biaxial loading test performed by the authors. λ is defined as the value obtained by dividing the maximum compression stress by the compressive strength of a cylinder. Figure 11 shows a comparison of equations (2), (3) and the test results for the relationship between λ and the mean tensile strain of cracks in the orthogonal direction. Here, equation (2) is proposed by Okubo et al. [1] for normal concrete with a compressive strength of 2-3 N/mm 2. Equation (3) is proposed by Enomoto et al. [11] for concrete with various strengths ranging from normal strength concrete to high strength concrete with a compressive strength ranging from 25 N/mm 2 to 1 N/mm 2 (in this study, concrete with a compressive strength of 6 N/mm 2 is used for calculation). 1 λ = ε 1u ε.167 (2) where λ=reduction factor of compressive strength, ε lu =mean tensile strain at the compressive failure, and ε =axial strain under cylindrical compressive strength. 1 λ = ε1 u a + b ε a e e +147 = x x ( ) b = x c =.141x.715 c (3)

8 52 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, Compressive strength reduction factor λ ' 1/ 3 ' x = f c ( f c 2) Eq. (3) Eq. (2) ε tu/ε Fig. 12 Comparison of analytical model with test results for compressive strength reduction factor. where f c =compressive strength of concrete (kgf/cm 2 ). According to Fig. 12, λ of HPRFCC is in good agreement with equation (2) and is less influenced by compressive strength than λ of concrete. Therefore, it is concluded that equation (2) is employed as the equation for λ of HPFRCC. The horizontal axis in Fig. 12 is the normalized value obtained by dividing the strain at the compressive failure (ε tu ) by the strain at the maximum strength of the cylinder test (ε ). 3.4 Other models In this study, models for concrete are employed as other models, because there is not enough basic experimental data to investigate the model at present. A model proposed by Darwin and Pecknold (1974) based on an experiment done by Kupfer and Gerstle (1973) is employed, and for the bond property between steel and HPFRCC, a model proposed by Morita and Kaku (1975) is employed. For cracking, both a discrete crack model and a smeared crack model are employed. As for the crack direction of the smeared crack model, a crack model on rotational displacement is employed because the cracks always develop in the principal stress direction in this model. 4. Investigation of the model applicability 4.1 Test specimens Bar arrangements of test specimens are shown in Fig. 13. The test specimens consist of the DT series, which leads to a shear diagonal tension failure and the SC series, which leads to a shear compressive failure. When a shear failure occurs in these specimens, the difference in failure mode is investigated. In order to ensure shear failure, high strength steel bars with a screw rib are employed as the main reinforcement for both specimens. Additionally, main bars are fastened to endplates by locknuts and those endplates are bolted to a steel stub attached to the loading apparatus for the anti-symmetrical moment condition. Each series has a concrete specimen as a control specimen in order to investigate the effect of the material properties of HPFRCC. Three kinds of HPFRCC (PVA, PE, PE+SC:PS) that have different deformation capacities are employed. The stress-strain relationship of the cement matrix and that of the reinforcement are shown in Fig. 14 and 15, respectively. Wipe back of PVA HPFRCC shown in Fig. 15 is caused by the fracture outside the measuring area of strain by a displacement transducer. Finite element model and boundary conditions are shown in Fig. 16. The part for HPFRCC is expressed as an 8-nodes plane stress element. Shear Rock nut Rock nut PL-36 PL-36 4 Main bar: 6-D13 Hoop 4 Main bar: 6-D13 Shear kye (PL-9) Shear kye (PL-9) (a) SC series (b) DT series (Unit: mm) Fig. 13 Test specimens.

9 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, Tensile stress Tensile strain (%) Fig. 14 Stress-strain relationships of cementitious materials. 12 D13 (Longitudinal reinforcement) 6 D6 (Lateral reinforcement) Tensile stress Tensile stress Tensile strain (%) Tensile strain (%) Fig. 15 Stress-strain relationships of reinforcements. Loading beam Hoop Truss element 2 kn Hydraulic jack Specimen 5 kn Hydraulic jack RC layered element Bond link element Steel stub Pantograph Figure 17 Loading setup. Fig. 17 Loading setup. Crack link element Steel element Fig. 16 Finite element model and boundary condition. reinforcement is expressed by a RC layered element. Longitudinal reinforcement is expressed by a 2-nodes truss element. The bonding of HPFRCC and longitudinal reinforcement is expressed by a bond kink element. A test specimen having steel plates on both ends is expressed by inserting a crack link element with a crack strength of into the interface between the specimen and the steel plate. The joints of the part for the shear key are not detached so that the specimen never causes slippage. A longitudinal reinforcement (D13) is expressed by a trilinear model and a lateral reinforcement (D6) is expressed by a bilinear model. For bond link elements, the bond stress-bond slip relationship obtained from the strain distribution of the longitudinal reinforcement is expressed by a bilinear model. Further, displacement control was used for analysis.

10 54 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, Test method A loading machine is shown in Fig. 17. For loading to the SC series, axial compression force of axial force ratio.4 is applied by using a hydraulic oil jack for axial loading (2kN capacity). At a constant axial compression force, additional horizontal load is applied in one direction by the hydraulic oil jack for horizontal loading (5kN capacity). For loading to the DT series, horizontal load alone is applied in one direction. For both series, the weight of the loading frame on the top end of the specimen is ignored because of the counterweight. The load is detected by the load cell connected to the jack, and the displacement is measured with the method shown in Fig PL-5 PL M22:PC rod Specimen Displacement PL Front view Side view Fig. 18 Measuring method of deformation (Unit: mm) 4.3 s and analytical results The comparison results of analytical data of a shear force-relative displacement relationship and the test results are shown in Fig. 19. The test results of all specimens almost perfectly reflect the analytical data for the maximum strength. For deformation at the maximum strength, the test results of the SC series reflect the analytical data, while those of the DT series, in particular one of the HPFRCC specimens, underestimate the deformation. The DT series doesn t activate a compressive axial force, and therefore a slip occurs on the boundary surface of the steel plates of the specimens during the experiment. However, these phenomena cannot be expressed in analysis. Supposedly, it is the reason of the discrepancy between the test results and analytical data of the DT series. The comparison results for the analytical data of cracking patterns at the maximum strength and the failure mode are shown in Fig. 2. In the DT series, a compressive failure of specimens excluding PS-DT is not observed in either analysis or experiment. Although it can be concluded that shear diagonal tension failure occurs in specimens except for PS-DT, a compressive failure is partly observed in the failure mode of PS-DT. In the SC series, the reduction in strength due to compressive failure occurs both in analysis and experiment. It can be concluded that a shear compressive failure occurs. The correlation of analytical data and test results of shear crack, strength at the yielding of lateral reinforcement, maximum strength and deformation at the maximum strength, are shown in Fig. 21, respectively. This figure shows that for the shear crack strength, analytical results underestimate the test results, but they show good agreement for the strength at the yielding of lateral reinforcements and maximum strength. The investigation of all the test results and analytical data indicates that the analysis in this study achieves sufficient accuracy and can adequately represent the 25 2 RC-DT 25 2 PVA-DT 25 2 PE-DT 25 2 PS-DT RC-SC 3 25 PVA-SC 3 25 PE-SC 3 25 PS-SC Fig. 19 Shear force (Q)-displacement (δ) relationships

11 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, RC-DT PVA-DT PE-DT PS-DT RC-SC PVA-SC PE-SC PS-SC Fig. 2 Final failure patterns. Cracking Crushing (kn) 3 25 RC-SC 2 PVA-SC PE-SC 15 PS-SC 1 RC-DT PVA-DT 5 PE-DT PS-DT (kn) (kn) RC-SC PVA-SC 5 PE-SC PS-SC (kn) (kn) RC-SC PVA-SC PE-SC PS-SC RC-DT PVA-DT PE-DT PS-DT (kn) (mm) 2 15 RC-SC PVA-SC PE-SC 1 PS-SC RC-DT PVA-DT 5 PE-DT PS-DT (mm) (a) Shear crack strength (b) Strength at yielding of lateral reinforcement (c) Maximum strength (d) Deformation at maximum strength Fig. 21 Comparison of analytical results and experimental results. influence of HPFRCC material properties on member performance. 4.4 Parametric analysis of effect of differences in tensile properties on member performance It is possible to control the tensile properties of HPFRCC with the type of fiber, fiber volume fraction, and the mixing conditions. It remains uncertain, however, how member performance changes by controlling the tensile properties. An example of parametric analysis using the level of tensile properties and ultimate tensile strain as variables is introduced here. The tensile stress-strain relationship used for parametric analysis is shown in Fig. 22. The member performance of is employed as each member performance except for the tensile properties. The analytical results are shown in Fig. 23. Accordingly, in the DT series, the ultimate strength of Case 1 and Case2 are on the increase more than that of 2σ t σ t Case2 Case σ t = 2. N/mm 2 ε t =.5% Case1 ε t 4ε t Fig. 22 Stress strain relationship using for parametric analysis.

12 56 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, DT series 25 Shear force (kn) DT-Case DT-Case1 DT-Case Deformation (mm) Shear force (kn) SC series SC-Case SC-Case1 SC-Case Deformation (mm) Fig. 23 Analytical results. Case. In Case 2 with higher strength and unchanged ultimate deformation, the ultimate strength increases more rapidly than in Case 1 with larger ultimate deformation. On the other hand, in the SC series, no remarkable increase in ultimate strength is observed. Each case shows the difference in the deformation capacity. 5. Conclusion Among the constitutive models for HPFRCC, tensile properties, which are regarded as influential on the shear behavior of members, and a reduction in the compressive properties after crack development are picked up in this paper. The analytical accuracy of non-linear FEM analysis is investigated through shear failure experiments on relatively simple members in which the influence of these properties can be easily observed. As a result, it is concluded that the analysis in this study achieves sufficient accuracy and can adequately represent the influence of HPFRCC material properties on member performance. Parametric analysis performed using this analytical tool indicates that the shear performance of structural elements is greatly influenced by both the tensile strength and ductility of HPFRCC. References Darwin, D. and Pecknold, D. A. W. (1974). Inelastic Model for Cyclic Biaxial Loading of Reinforced. SRS No.49, Civil Engineering Studies, University of Illinois, Urbans-Champaign, Illinois. Enomoto, K., Yonezawa, K. and Noguchi, H. (1994). Analytical study on deterioration of compressive characteristics of cracked ultra-high strength concrete. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, C-II, (in Japanese) Fafitis, A. and Shah, S. P. (1985). Lateral reinforcement high-strength concrete columns. ACI Special Publication, No. SP-87, Fukuyama, H. and Suwada, H. (23). al response of HPFRCC dampers for structural control. Journal of Advanced Technology, Japan Institute, 1(3), Han, T-S, Feenstra, P. H. and Billington, S. L. (23). Simulation of highly ductile fiber-reinforced cement-based composite components under cyclic loading. ACI Structural Journal, 1(6), Kupfer, H. B. and Gerstle, K. H. (1973). Behaviour of concrete under biaxial stresses. Journal of Engineering Mechanics Division, ASCE, 99(EC4), Kabele, P., Takeuchi, S., Inaba, K. and Horii, H. (1999). Performance of engineered cementitious composites in repair and retrofit-analytical estimates. High Performance Fiber Reinforced Cement Composite (HPFRCC 3), Proceedings of the Fourth International RILEM Workshop, edited by A. E. Naaman and H. W. Reinhardt, RILEM Publication S.A.R.L Kesner, K. E. and Billington, S. L. (23). al response of precast infill panel connections and panels made with DFRCC. Journal of Advanced Technology, Japan Institute, 1(3), Li, V. C. (1993). From micromechanics to structural engineering The design of cementitious composites for civil engineering applications. Structural Engineering and Earthquake Engineering, Japan Society of Civil Engineers, 1 (2), Morita, S. and Kaku, T. (1975). Study on bond properties between reinforcement and concrete under cyclical loading. Journal of Structural and Construction Engineering, Architectural Institute of Japan, No. 229, (in Japanese) Miyahara, N., Kawakami, Y. and Maekawa, H. (1987). Nonlinear behavior of RC plate elements with cracks under uni-axial compressive stress. Journal of Japan Society of Civil Engineering, No. 378/V.6 (in Japanese). Naganuma, K. and Yamaguchi, T. (1989). Study on the Compressive Properties for with Cracks. JCI Colloquium, Analytical Study on RC Structural

13 H. Suwada and H. Fukuyama / Journal of Advanced Technology Vol. 4, No. 1, Shear Method, (in Japanese) Naaman, A. E. and Reinhardt, H. W. (1995). Characterization of high performance fiber reinforced cement composites HPFRCC. High Performance Fiber Reinforced Cement Composite (HPFRCC 2), Proceedings of the Second International RILEM Workshop, edited by A. E. Naaman, and H. W. Reinhardt, RILEM Proceedings 31, E & FN SPON, Okubo, M., Hamada, S. and Noguchi, H. (1989). Basic study on the reduction of compressive properties for concrete with cracks in Earthquake Motion. JCI Colloquium, Analytical Study on RC Structural Shear Method, (in Japanese) Shirai, N., Matsui, Y. and Sato, T. (1989). The reduction of compressive properties for concrete with cracks. Proceedings of the Japan Institute, 11(2). (in Japanese) Sato, Y., Fukuyama, H. and Suwada, H. (21). A proposal of tension-compression cyclic loading test method for ductile cemntitious composite materials. Journal of Structural and Construction Engineering, Architectural Institute of Japan, (539), (in Japanese) Vecchio, F. and Collins, M. P. (1982). The response of concrete to in-plate shear and normal stresses. Publication No. 82-3, Department of Civil Engineering, University of Toronto.