Shear Transfer Strength Evaluation for Ultra-High Performance Fiber Reinforced Concrete

Transcription

1 Shear Transfer Strength Evaluation for Ultra-High Performane Fiber Reinfored Conrete Ji-hyung Lee, and Sung-gul Hong Abstrat Ultra High Performane Fiber Reinfored Conrete (UHPFRC) is distinguished from the normal onrete with reinfored rebar by high strength without aggregates and outstanding tensile behavior of fiber bridging ation. Craked normal onrete has known for resisting shear by aggregate interloking, the mehanism of raked UHPFRC resisting shear remains in the shade. Presents a study of shear transfer in UHPFRC, that is, the transfer of shear aross a plane, suh as at the interfae between a preast beam and a ast-in-plae slab. Twenty-four push-off speimens were tested along the shear plane. The interfae shear transfer design for monolithi onrete are suggested by limit analysis of plastiity and verified by test results. Plasti analysis gives a onservative, but reasonable estimate. The suggested shear frition fator and effetiveness fator of UHPFRC an be applied for interfae shear transfer design of high-strength onrete and fiber reinfored onrete with tensile hardening behavior. Keywords Limit analysis, shear transfer test, UHPFRC H I. INTRODUCTION IGH-strength materials are widely used to build strutures. These materials tend to be brittle, it is important to relieve their brittleness. Ultra High Performane Fiber Reinfored Conrete(UHPFRC) has dutility and durability with its high strength, and these material harateristis are distinguished by tensile hardening behavior. It is well known that raked onrete strutures still have a load arrying apaity is attributable to phenomena as bond slip, tension softening behavior, dowel ation and aggregate interlok. In UHPFRC, tensile softening or hardening behavior is a key issue to analyze the shear transfer between a rak instead of aggregate interloking. The aim of the researh program is to suggest the shear transfer strength for monolithi joint of UHPFRC. The interation between a rak depends on the mehanisms of axial restraint fores due to fiber bridging ation. Experimental study on push-off test gives test results for raked UHPFRC with regards to transverse reinforement ratio and its tensile strength. From limit analysis of plastiity, failure riteria of UHPFRC an be defined. The shear transfer strength for Ji-hyung Lee is with Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul , Korea (orresponding author s phone: ; b415@snu.a.kr). Sung-gul Hong, is with Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul , Korea ( sglhong@snu.a.kr ). UHPFRC is suggested and verified by omparing the push-off test results. II. EXPERIMENTAL INVESTIGATION Twenty four push-off tests were arried out to find out the onstitutive relationship on rak frition. Material tensile strength aording to the fiber volume ratio and transverse reinforement ratio are variables for the experiment. A. Material omposition and properties The basi UHPFRC omposition is shown in Table I. The straight steel fibers are 16.3mm and 19.5mm in diameter, and their tensile strength is 2500 MPa. All speimens are steam ured for 72 hours at 90 degree after 24-hour uring at room temperature. Two kinds of reinforement bar, D10 and D13, are arranged perpendiular to the shear plane with same spaing in Fig.2. The mehanial properties of reinforement bar is shown in Table II. TABLE I UHPFRC COMPOSITION (ALL BY WEIGHT BUT STEEL FIBERS) W/B Cement Zn Sand Filling powder Super plastiizer Reinfore ment Size TABLE II MECHANICAL PROPERTIES OF REINFORCEMENT BAR Modulus of Elastiity (GPa) Yield Strength Yield Strain (X10-6 ) Ultimate Strength Steel fiber (%) 1.5 to 0.0 Ultimate Strain (X10-6 ) D D B. Diret Axial Tensile Strength Test For UHPFRC, tensile strength along the rak due to fiber reinforement is very important mehanial properties. The UHPFRC in this researh has tensile hardening behavior mixing different length of fiber. The tensile stress and rak width relationship is shown in Fig. 1. The tensile strength tends to inrease inreasing fiber volume ratio without V f =0%. Nothed speimens introdued for diret tensile strength is shown in Fig. 1. After high temperature uring wet end, diretly to the tensile speimen width on eah side to introdue a rak in the entre of the entral portion 2mm, is introdued into the 92

2 noth in the depth 12.5mm. The load rate is ± mm/se by a displaement ontrol system. The test result is available only when failure raks are observed within a range of 175mm, between the noth of the speimen and the average of the test values obtained in six test results. Fig. 2 Speimen geometries for tests; (a) test speimen with reinfored bars, (b) speimen dimension and arrangement of bar Fig. 1 Tensile stress and rak width relationship of UHPFRC C. Speimens and Push-off Test proedures The tests were arried out on push-off speimens with internal restraint bars (Fig.2). Three transverse reinforements are arranged with same spaing using different size of the bar. Speimen details are shown in Table III. The speimens were supported on roller bearings and were loaded by a vertial load, applied on top via a knife hinge. With this method of loading, shear without bending moment is produed in the shear plane. The head and the sides of the speimens were reinfored in order to avoid premature failure due to seondary raks. Measurements of the rak width and the shear displaement were performed at the enter of the speimen on the front and rear faes by means of diagonal LVDT. The vertial external load was measured by a load ell. The passive restraint fore normal to the rak plane was determined using strain gauges attahed to the internal bars. During the atual shear test, the speimens were subjeted to a monotonially inreasing load. The shear displaement rate was 0.01 mm/se. The test were stopped when the shear displaement had reahed a value of 2 mm. Speimen Number Steel fiber ratio (%) TABLE III SPECIMEN DETAILS (24EA) Transverse reinforeme nt ratio (%) Compressive strength Tensile strength F15-S00-1, F15-S09-1, F15-S16-1, F10-S00-1, F10-S09-1, F10-S16-1, F05-S00-1, F05-S09-1, F05-S16-1, F00-S00-1, F00-S09-1, F00-S16-1, D. Push-off Test Results Consider a push-off speimen, thikness b, and with a shear plane of length d (Fig. 3). The stresses ating on a small element of onrete lying in the shear plane will be as shown in Fig. 3. Shear stresses τ on all faes, normal stress σ x, due to the restraint provided by the transverse reinforement, and normal stresses σ y. Failure of all speimens our on the shear plane. Typial failure rak pattern is shown in Fig. 4. Higher reinforement ratios, more inlined rak is observed and aompanied by onrete rushing at the nothed edge. Fig. 3 Constrution of relationship between shear strength τ, and the reinforement parameter ρf y Fig. 4 Typial failure rak pattern of push-off test 93

3 Fig. 5 Typial failure rak pattern of push-off test Shear stress τ in Fig. 5 means average value orresponded with Fig. 3. First of all, the maximum shear stress learly inreases aording to inrease of fiber volume ratio regardless of transverse reinforement ratio. However, speimen with transverse reinforement of D10 and D13 makes slight differenes with maximum shear stress. The higher transverse reinforement ratio ontributes inrease of dutility rather than inrease of shear strength. Vertial displaement and horizontal displaement relationship shows dowel ation of transverse reinforement learly. Speimens without transverse reinforement maintain onstant slope until maximum shear strength, but speimens with transverse reinforement have inreasing its slope until ultimate strength point. These behavior an be explained by inlination of final failure rak and onrete rushing, too. ontribution is ohesion, denoted. The other ontribution stems from a kind of internal frition and equals fration μ of the normal stress σ in the setion. The parameter μ is alled the oeffiient of frition. An angle υ given by is alled the angle of frition. Separation failure ours when the tensile stress σ in a setion exeeds the separation resistane f t, when σ= f t. Three material onstants,, μ, and f t must be known for a modified Coulomb material. The material harateristis of UHPFRC oinides with the modified Coulomb material as shown in Fig. 6. The ompression failure will always involve sliding failure and the pure tensile failure will involve separation failure. III. ANALYTICAL INVESTIGATION The first analysis based on the theory of plastiity was performed by B.C. Jensen. A theory of less general harater but rendering similar results is the shear-frition theory developed by Mattok and assoiates. In this researh, the failure riteria of reinfored onrete based on plastiity theory is explained, and then the UHPFRC failure riteria will be presented. Basially the theoretial expetation based on modified Coulomb material is almost same, but the harateristi value for monolithi onrete should be verified by test results. A. Modified Coulomb Material The resulting failure riteria makes it natural distinguish between two failure modes, sliding failure and separation failure. At sliding failure there is motion parallel to the failure surfae, while motion at separation failure is perpendiular to the failure surfae. The ondition for sliding failure is. One Fig. 6 Definition of Modified Coulomb material Fig. 7 Speimen diagram; (a) failure mehanism in disk subjeted to shear, (b) planes and lines of disontinuity 94

4 B. Failure Criteria by Energy Method In most ases, the strength of a joint an be treated as a plane strain problem. Consider a failure mehanism in the form of a yield line along the line of loading. The relative displaement of the right-hand part to left-hand part is, forming the angle to the yield line.(fig. 7) The external work is. The dissipation onsists of two parts, one from the onrete and one from the reinforement. The reinforement bars are perpendiular to the yield line. As before, the dowel effet of the reinforement is negleted, whih means that the dissipation in the reinforement is, where is the reinforement area and the yield stress. From the onrete the ontribution is, where is the length of the yield line, and is given as a funtion of by the formulas, plane stress problems. The load-arrying apaity determined by (1), (2), and (3) is shown in Fig. 8 for virgin material, whih an be applied to UHPFRC at the same time. 1 sin for, tan tan (1) f 2os f 1 sin for 0, tan (1 ) (2) 2os f 1 for 0, f (3) 2 C. Shear Frition Fator of UHPFRC Assumption for the limit analysis inludes negleting dowel effet of reinforement beause shear frition fator indiates the harateristis of UHPFRC itself. As shown in Fig. 7, sliding failure ours on the shear plane of the speimen and relationship of normal and shear displaement along the rak defines the angle. The inlination of the two displaements in Fig. 5. inludes dowel effet of reinforement, so it is not easy to find shear frition fator based on the displaement results diretly. Therefore it is neessary to define the restrited fores lamping the rak preisely assuming fiber reinforement ontribution. Let us fiber reinforement ontribution the hardening region of tensile strength. Fiber bridging ation reveals between maro rak, whih represents. is maximum tensile strength of UHPFRC and is raking strength of UHPFRC. Considering this term, normal stress between the rak defines as. Applying the definition of frition fator, the rate of shear stress to normal stress shown in Fig. 9 an be identified as 1.4 and frition angle υ is 55. Dotted line in Fig. 9 represents failure riteria of UHPFRC material. D. Effetiveness Fator of UHPFRC Effetiveness fator is found fitting the urve to the test results. Solid line in Fig. 9 represents failure riteria of UHPFRC for monolithi onrete onsidering softening and raking. The effetiveness fator of UHPFRC is ν =0.5, whih is muh smaller than normal onrete. The important role of effetiveness fator limits the upper bound for the highly reinfored strutural element. The failure of web rushing is one of the appliation. The effetiveness fator of high strength onrete above 100MPa is hardly known, so this value is important for further researh. Fig. 8 Failure riteria for normal strength onrete As many ases where the strength of the onrete is important, the theoretial results are not in agreement with the experimental results unless effetive strengths are introdued. The weakness of the joints gives rise to a smaller effetiveness fator ν than for the monolithi onrete. The bottom line in Fig. 8 is the results applying ν =0.67 based on Hofbek 's push-off test results. The effetiveness fator reflets softening and raking effet of monolithi onrete. Fig. 9 Failure riteria for UHPFRC 95

5 IV. SHEAR TRANSFER STRENGTH EVALUATION Kahn and Mithell performed push-off tests and suggested the shear frition strength for high-strength onretes based on ACI provision as below. Their test results oinides the test results of UHPFRC in Fig. 10, whih intensifies the assumption of fiber reinforement ontribution and shear transfer mehanism of high-strength onrete without aggregate interloking. For high-strength onrete rak usually pass through aggregates and shear frition strength of high-strength onrete is weakened after raking. v 0.05 f 1.4 f 0.2 f (4) u y ACKNOWLEDGMENT This researh was supported by a grant from Super Struture 2020 funded by Ministry of Land, Infrastruture and Transport of Korea. REFERENCES [1] ACI-ASCE Committee 445, Reent Approahes to Shear Design of Strutural Conrete, Proeedings, ASCE, V. 124, No. 12, De. 1998, pp [2] Ali M.A. and White R.N., Enhaned Conrete Model for Shear Frition of Normal and High-Strength Conrete, ACI Strutural Journal, V. 96 No. 3, May-June, 1999, pp [3] Frenay, J. W., Theory and experiments on the behavior of raks in onrete subjeted to sustained shear loading, HERON, V. 35, No. 1, 1990, pp [4] Hsu, Thomas T. C., Mau, S. T., and Bin Chen, Theory of Shear Transfer Strength of Reinfored Conrete, ACI Strutural Journal, V. 84, No. 2, Mar.-Apr. 1987, pp [5] Hofbek, J. A., Ibrahim, I. 0. and Mattok, Alan H., Shear Transfer in Reinfored Conrete, ACI Journal, Proeedings V. 66, No. 2, Feb. 1969, pp [6] Kahn L.F. and Mithell A.D., Shear Frition Tests with High-Strength Conrete, ACI Strutural Journal, Vol. 99, No.1, 2002, pp [7] Mattok, Alan H., Shear Frition and High-Strength Conrete, ACI Strutural Journal, V. 98, No. 1, Jan.-Feb. 2001, pp [8] Nielsen M.P., Limit Analysis and Conrete Plastiity, 2nd edition. CRC press, [9] Walraven, J. C., Aggregate Interlok: A Theoretial and Experimental Analysis, Delft University Press, 1980, 197 pp. Fig. 10 Comparison with test results of HSC and UHPFRC Shear strength evaluation, dotted line in Fig.10, is aurate and reasonable, but the equation is not simple. The equation (4) suggested by Kahn and Mithell is quite onservative and easily appliable for design. V. CONCLUSION The analytial and experimental investigation of shear transfer strength for UHPFRC an be summarized as follows. (1) The ultimate shear strength of shear transfer is governed by the tensile strength rather than transverse reinforement ratio. The transverse reinforement is muh more effetive to dutility of strutural element. (2) The limit analysis by plastiity theory explains the shear transfer mehanism of UHPFRC well. The assumption for sliding failure defined by modified Coulomb material is appliable for UHPFRC. (3) The fiber reinforement ontribution restrits widening rak width and ats as transverse reinforement. The ontribution of fiber reinforement implies that UHPFRC without transverse reinforement resists shear frition solely. (4) From the push-off test results, ontribution of ohesive, frition fator μ, and effetiveness fator ν is defined and shear transfer strength using the defined variables is represented and verified by test results. 96