Magazine of Concrete Research, 2013, 65(12), 757–764 http://dx.doi.org/10.1680/macr.12.00215 Paper 1200215 Received 19/11/2012; revised 23/01/2013; accepted 15/02/2013 Published online ahead of print 21/05/2013 ICE Publishing: All rights reserved Magazine of Concrete Research Volume 65 Issue 12 Flexural fatigue behaviour of concrete under uniaxial and biaxial stress Kim, Yi, Lee and Zi Flexural fatigue behaviour of concrete under uniaxial and biaxial stress Jihwan Kim Doctoral Candidate, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea Chongku Yi Assistant Professor, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea Seung-Jung Lee Doctoral Candidate, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea Goangseup Zi Associate Professor, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea The main objective of this investigation was to study the effect of stress states on the flexural fatigue behaviour of concrete. The fatigue behaviours obtained from different test methods were compared, including the recently developed biaxial flexure test, ASTM C 1550 and four-point bending test. Fourteen specimens were cast and tested for each test method, under both monotonic and repeated loadings. The fatigue strength was compared with those recommended by existing design codes. Test results showed that there were no significant differences in the flexural fatigue behaviours under different stress states (i.e. uniaxial and biaxial). These results suggest that the uniaxial flexural tensile fatigue strength of concrete may be adopted for the design of concrete components subjected to biaxial flexural tensile fatigue loading. Notation a radius of the support ring or circle b radius of the loading ring b 0 radius of the loaded area f 9 c compressive strength of concrete f d design strength of concrete f max maximum stress of the sinusoidal load wave in each load cycle f min minimum stress of the sinusoidal load wave in each load cycle f r modulus of rupture of concrete f rd design fatigue strength for concrete h thickness of specimen K constants determined from the relative humidity and density of concrete k 1 f constants determined from the types of applied loads N number of load cycle R stress ratio (R ¼ f min = f max ) R 0 radius of the circular panel S min minimum stress ratio to static strength S max maximum stress ratio to static strength Æ ratio of the tensile strength to the square root of the compressive strength ó p permanent load Introduction Many structures, for example offshore structures, concrete bridges, road and airfield pavements, and slab tracks in railway systems, and so on, are subjected to repeated loadings in service. The repeated loading results in the initiation and growth of microcracks in concrete, which lead to a reduction in the stiffness, durability and aesthetic quality of the concrete mem- bers. For structural design consideration, various models to predict the fatigue strength of concrete in compression, tension and flexure have been suggested, such as ACI Committee 215 (ACI, 1992), Japan Society of Civil Engineers (JSCE) (JSCE, 2007), CEB-FIP Model code 1990 (CEB-FIP, 1993) and a comprehensive review on fatigue phenomena of concrete struc- tures reported by RILEM (1984). ACI Committee 215 provides a simple way to estimate the stress range compared with the static strength at which plain concrete can withstand a million repetitions, using a modified Goodman diagram (ACI, 1992). The JSCE (JSCE, 2007) has suggested that the design fatigue strength f rd for concrete, as a function of number of load cycle N under permanent loads ó p , is as follows f rd ¼ k 1f f d (1  ó p = f d ) 1  log N K   1: where N < 2 3 10 6 , f d is the design strength of concrete, K and k 1f are constants determined from the relative humidity and density of concrete, types of applied loads respectively. ó p is the stress due to permanent loads. Alternatively, JSCE allows con- struction of an S  N curve, using Equation 2 757