ª Œª Œ 27ƒ 5A Á 2007 9œ pp. 753 ~ 758 gj pœw gj p { x A New Test Method for Pure Isotropic Flexural Tensile Strength of Concretes Ÿ Á y Á x Zi, GoangseupÁOh, HongseobÁChoi, Jinhyek Abstract Proposed is a new test method to measure the biaxial tensile strength of concretes or other quasibrittle materials. One of the most novel features of the method is that only one actuator is used unlike other biaxial tensile test methods. This method is a three dimensional version of the classical modulus of rupture test. The specimen for the test is a circular plate loaded by a circular edge and supported by another circular edge. They have the same center point. The moment within the circular edge on which the applied load is constant in any direction. The biaxial tensile strength of a concrete was measured using the new flexure test method. From the test result, biaxial tensile strength of circular plates is lower than the strength from the traditional theory on the modulus of rupture strength suggested by ACI 318-05. The biaxial tensile strength of concrete is significantly scattered, and its standard deviation is about quadruple of that of uniaxial strength allowed in ACI 318-05. Therefore, to establish on the characteristic of biaxial tensile strength which may be influenced by aggregates, size effect and compressive strength of plain concrete, further experimental and theoretical researches are required. Keywords : Biaxial flexure test (BFT), indirect tensile strength, new test method, modulus of rupture, quasibrittle materials gj pù»k w d w { x w.» w x ƒ»ƒ v w, m { x x wù ƒ» v w. x x r, r ƒ» x w. r, w ew, w w x ü p w w. x w gj p w d w. x ACI318-05 { { ƒ ùkû. x f, x t r w ACI318-05 x wš w x t r 4. { p w yw w w, j»z { w e ƒ x w v w. w : w { x, x, x, { q, 1. gj p t w p wù ƒ 1/8 1/10 w. w j» w, gj p ƒ q. gj p ww» w ³ wš, üw gj pƒ w wš ( m 2003). w, d w ³ w ù ³ s w» w gj p š w wš. z Á Áš w zy lœw (E-mail : g-zi@korea.ac.kr) z Á w m œw (E-mail : hongseob@hotmail.com) w m œw gj p gj p üw sƒw wš. gj p d w» w x, { x, w x ( 2004). x w w ù, x x x» w x ü w x v w. d w ƒ x œe (nominal strength)ƒ. Bazant œ, x d œe 27ƒ 5A 2007 9œ 753
x p j» x w (Bazant 1984, xk j»z Zi (2003) ). x y g w ü ³ w x ww, ¾. w w š w w w, { x w w. { x 4 w { x w» k w r w ¾ x ƒ. { œ l {.»w x ƒ wš w w gj p ü k w k š w w. w k d w» w w e w x ƒ v w (, Muzyka 2002). w w x w w m, e» w 28 w. w w gj pƒ š ù, gj p w» m gj p x k z w w k. w gj p w w q w, ƒ œw, ƒ» w, p, p rwš, w. x w ƒ v w, x p w q ƒ (localization)» w v w. gj p d w x w w, x w.. 1 2 w x w š, 3 ww» w w w w. 4, 5 ƒƒ x w gj p { x w. 6 x w, 7 w. 2. { x { x 1» 4 w x w { x y w. { x w { pƒ w w rw w x. yw 2a š w. x x x ƒ š, x š x q w. wq w x, w q ó g x t x w w. D t x, q, wq ew. q ó wq ó ¾ ƒ w w» wq ü x { p w w ( 2b). w z ew w w. 3 wš 2. (a) { x, (b) { p s 1. { x 3. w w 754 ª Œª Œ
{ x w w. e w x w, e w. w w, w x w w. x x z x s w. x ƒ š, w y. w w wq Á w., { x w w ƒ x, wq ü x w w y. 3. w e» w w w ew w ù, d w w w z. x x w qx x x q yw, e k q l ww. w x { pƒ w ü q( 4b) x, ƒ p w q( 4c) ww. w w Timoshenko Woinowsky-Krieger (1989) k q. w, q w w rƒ w. w q w w t p M ww P ƒ. ( 1 v) 1 ba 2 [ ( )] ( 1 + v)log( ba ) M = ----------------------------------------- ----------------------------------- P 4. w x q w 8π» v=s, a= q, b= wq. x q» (1) 4π (1) 5. wq q j» w p k. w pƒ w w w. σ = ------- 6M h 2» h=q Ì. l ƒw w P σ. σ 3 = ----------- 1 v 4πh 2 ( ) 1 ba 2 { [ ( ) 2( 1+ v)log( ba )]}P q wq j» b/a x w. 5 s 0.18 ƒ wš, ̃ 5 cm 10 cm x w b/a w. w ƒw w (3) w w. š, { x w w w ¼ x. σ 3 = ---- ( aw )[( ba ) 1]P h 2» x 2b š, w w 2a, w= x s. (3) w q ó ¼ w. w ¼ ƒ ¼ w e z w š w w w ƒ w q. 4. x 4.1 x gj p w { x d w» w x w msp p p, w. e ƒƒ 20 mm 2.72 t/m 3, ƒƒ 2.9% 6.6% d. 2.58 t/m 3. (2) (3) (4) 27ƒ 5A 2007 9œ 755
W/C (%) t v (mm) t œ» (%) S/a (%) t 1. gj p wt (kg) SP (CÜwt.%) AE (CÜwt.%) W C S G 35 120 5 39.45 193.9 553.9 642.4 1036.3 0 0 gj p 3.14 msp p p w ww, w 38 MPa, 28 t 30 MPa w. KS L 5108» w wz 3 25 š, KS F 2405 w 28 31.8 MPa d. gj p w t 1 w. { d w» w 75 cm, 12 cm x gj p q x 32 w 28 w. 4.2 x x { y d w» w r x w 6 e w e w, UTM w w ƒ w. xk ƒ 50 cm š, s 2 cmƒ w, ƒ e w x wƒ w 26 cm, s 2 cm xk w. x w e, x ew w x { w š w. w w { d w KS F 2408 ³ w w ƒ 800 kn/min š w q ¾ w x ƒ g d w,» {³ w w» w. ƒ x x d w» w w» x ùkù w UTM ƒ e w. w ƒ x w - ƒ e w. 5. x š x 7 t 2 w, t x w - 7 ùkü. t 2 e d y w.» ³ w 45 kn l 142.9 kn ¾ sw, q w 75 kn l 181 kn s j ùkù» w { x j ƒ y. 6» ³ w s³ w s³ w. x w ³ w w t r ƒƒ 26.30 29.05 7. Biaxial tensile strength distribution of specimens 6. x x x 8. Loads displacement relationship 756 ª Œª Œ
t 2. x. ACI ³ wš gj p x t r 7.0MPa 4 w { w y ƒ { w w, w š ƒ v w ùkü. ƒ x»³ ƒ t 2 w, Kupfer, Hilsdorf Rusch w ùkû, kƒ w q. w ³ w w ³ w w -»»ƒ yw s³ 65 kn q. z x ƒ w ƒ ƒ ƒw ƒ w ƒw xk ùkû.» ³ z ww ³ w ƒw. w ƒ ³ w š ƒw 2-3 w. w z q. (3) w» ³ s³ { 2.34 MPa. gj p w ACI318-05 { 3.5 MPa, š Ahmad Shah (1985) z w { w ƒƒ 4.4 MPa 2.04 MPa. w { ³, ACI318-05 { š z w j w. { ƒ sƒ w š w» { ƒ š ACI» w { 67%» ƒ j ƒ. w Kupfer, Hilsdorf Rusch(1965) w e x ƒ v q. 6. ƒ x w ƒ w x, 1. w, 2. s, 3. ³, 4. ³, 5. FRP p w ƒ 27ƒ 5A 2007 9œ 757
w. p Batdorf Crose (1974) w w w w { ƒw w v w d v w q. 7. 1. { w ƒ» w d w x w. x» { x yw x. 2. w x z w w x k q w w. q wq j» x x. x z ¼ z š w q. 3.» š w, w gj p ³ w dw ùk û, x w ù kü. 4. { x w gj p q { x sƒw, { w w»» x wš j ùkû. 5., gj p, x j» w w» yw { { ³ w» w x, w q. w m» sƒ R&D (05 w D11 and 05 w B01) w w. š x m (2003) gj p». w gj pwz.» t (1964) KS F 2405 gj p x.» t (2000) KS F 2408 gj p { x.» t (2002) KS L 5108 f e w p x., (2004). gj p œw. l. ACI Committee 318 (2005) Building code requirements for reinforced concrete and commentary (ACI 318-2005/ACI 318R- 05), American Concrete Institute, Detroit; 2005. Ahmad, S.H. and Shah, S.P. (1985) Structural properties of high strength concrete and its implications for precast prestressed concrete. PCI Journal, Vol. 30, No. 6, pp. 92-119. Batdorf, S.B. and Crose, J.G.. (1974) A statistical theory for the fracture of brittle structures subjected to nonuniform polyaxial stresses, Journal of Applied Mechanics ASME, Vol. 41, No. 2, pp. 459-464. Bazant, Z.P. (1984) Size effect in blunt fracture: Concrete, rock, metal. Journal of Engineering Mechanics, Vol. 110, pp. 518-535. Kupfer, H., Hilsdorf, H.K., and Rusch, H. (1969) Behaviour of concrete under bi-axial stresses, ACI Vol. J66, No. 8, pp. 656-666. Muzyka, N.R. (2002) Equipment for testing sheet structural materials under biaxial loading. Part 2. Testing by biaxial loading in the plane of the sheet. Strength of Materials, Vol. 34, No. 2, pp. 206-212. Timoshenko, S.P. and Woinowsky-Krieger, S. (1989). Theory of Plates and Shells, Engineering Mechanics Series, McGraw- Hill, Tokyo. Zi, G. and Bazant, Z.P. (2003) Eigenvalue method for computing size effect of cohesive cracks with residual stress, with application to kink-bands in composites. International Journal of Engineering Science, Vol. 41, No. 13-14, pp. 1519-1534. ( : 2007.3.26/ : 2007.6.18/ : 2007.7.18) 758 ª Œª Œ