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Unformatted text preview: FATIGUE O F CONCRETE UNDER RANDOM LOADINGS By Young J. Park, 1 Associate Member, ASCE INTRODUCTION Traditionally, the fatigue of concrete has been analyzed using S-N rela- tionships. T he most recent and frequently cited equation m ay be the one proposed by Aas-Jakobsen and Lenschow (1973) and modified by Tepfers and Kutti (1979) as follows: ^ - x =l - 0 ( l - f ^ ) log* (1) J c \ J max/ in which/ min and/ max = minimum and maximum stress levels;/^ = concrete strength; and p = 0.0685, according to Tepfers and Kutti (1979). This equa- tion w as examined using fatigue test data having various combinations of / min and / m M (Antrim and McLaughlin 1959; Assimacopoulos et al. 1959; Bennett and Muir 1967; El-Jandali 1978; Holmen 1979; Karsan and Jirsa 1969). The results of Fig. 1 appear to indicate a relatively poor correlation, especially at low cycle range. Moreover, a difficulty arises in applying the formulation when loadings are defined in probabilistic terms, such as a power spectrum density function or RMS statistics. In this paper, a fatigue model is presented for a plain concrete subjected to random loadings in compres- sion. The nonlinear hysteretic behavior of concrete is idealized and incor- porated in a mathematical formulation of fatigue progress under random loading condition. NONLINEAR FATIGUE MODEL The large prediction error in Fig. 1 seems to indicate the limitation in the use of S-N relationship for concrete material. Since the fatigue life of con- crete, unlike metallic material, is affected by many loading parameters, such as/ mi // ma x,/mean//max,/n K a n //c,/max//'c, a n d (/ malt-f min )/f' c , e t C , it i s difficult to define a single S-N relationship when all the loading parameters are var- ied. T o reduce the prediction error in fatigue life, especially at low cycle range, it may be more appropriate to incorporate the highly nonlinear char- acteristics of concrete than to manipulate existing S-N relationships. A s the basis for fatigue model development, the stress-strain relationship of con- crete is idealized to trace the hysteretic behavior and stiffness degradation process to a failure point. A dual-coordinate system is used to model the envelope curve in compression and the hysteresis loops within the envelope curve, as shown in Fig. 2. A simplified degradation rule is adopted herein by assuming the centerline of hysteresis loops always passes through the 'Struct. Engr., Dept. of Nuclear Energy, Brookhaven Nat. Lab., Upton, NY 11973. Note. Discussion open until April 1, 1991. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on February 15, 1989. This paper is part of the Journal of Structural Engineering, Vol. 116, N o....
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