Abstract
In order to analyze the whole process of fatigue behaviours of reinforced concrete beams, an equivalent static analysis method is proposed in this paper. Firstly, the constitutive models based on the degradation of stiffness and strength and the accumulation of residual strain of concrete and reinforcement subjected to fatigue loadings are deduced and established by coupling the uniaxial constitutive model of concrete and the ideal elastic-plastic model of reinforcement under static load. Secondly, based on the similarity of concrete failure under static load and fatigue load, the equivalent relationship between fatigue and static analysis can be constructed by using the concrete residual strain as the equivalent parameter. On this basis, an equivalent static method for the analysis of fatigue behavior of reinforced concrete beam is proposed. At last, three reinforced concrete beams with rectangular section are tested, and the fatigue behaviours are analyzed by the method proposed in this paper. The numerical simulation results are compared with the field test data. The result shows that the numerical simulation results are in good agreement with the experimental results, which verifies the reliability and practicability of the method.
Highlights
The research shows that the elastic modulus of concrete changes in three stages with the fatigue times:In the first stage, it decays rapidly; in the second stage, it shows stable linear degradation, which accounts for 75% ~ 80% of the fatigue life; in the third stage, it decays rapidly and unsteadily until the fatigue failure [1]
The compressive constitutive models based on the degradation of stiffness and strength and the accumulation of residual strain of concrete subjected to fatigue loadings is established by coupling the uniaxial constitutive model under static load [11]
Is the strain after N times of fatigue; kc and kt are damage evolution parameters under compression and tension fatigue; c and t are the shape factor of the descend phase in stress-strain curve, which can be taken from table C.2.4 in reference [6]; f,r (N ) is the residual strain after the N times loading and unloading; EN is the elastic modulus after N times of fatigue; fcN and ftN are the residual compressive and tensile strength after N times of fatigue; cr and tr are the peak compressive strain and the peak tensile strain under the Nth time loading
Summary
According to the research results in reference [5], the relationship between the fatigue times N and the upper limit of compressive stress c,max (i.e. residual fatigue compressive strength fcN ) and the lower limit of compressive stress c,min is as follows: lg. The compressive constitutive models based on the degradation of stiffness and strength and the accumulation of residual strain of concrete subjected to fatigue loadings is established by coupling the uniaxial constitutive model under static load [11]. In this process, the hysteresis between unloading and reloading curves is ignored. In formula (6) ~ (14): r,c ( N ) and r,t ( N ) are the compressive and tensile stresses after N times of fatigue; is the strain after N times of fatigue; kc and kt are damage evolution parameters under compression and tension fatigue; c and t are the shape factor of the descend phase in stress-strain curve, which can be taken from table C.2.4 in reference [6]; f ,r (N ) is the residual strain after the N times loading and unloading; EN is the elastic modulus after N times of fatigue; fcN and ftN are the residual compressive and tensile strength after N times of fatigue; cr and tr are the peak compressive strain and the peak tensile strain under the Nth time loading
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