繰返し載荷を受けるコンクリートの応力-ひずみ曲線の表示式について : 要素分布モデルを用いたコンクリートの応カ-ひずみ曲線の解析 その2

Abstract

The purpose of this investigation is to propose the analystical expression of stress-strain curve for concrete under cyclic loadings through a stochstic process theory it is necessary to make clear five item, which are envelope curve, elastic modulus, residual strain reloading curve and unloading curve, in order to expression analytical stress-strain curve of concrete under cyclic loadings. Brief of the analytical expressin of this investigation was follows. (1) Envelope curve S=E(X×X_y・αX^β)e^<-αx^β> Where S=relative stress X = relative strain X_y=relative yield strain E=elastic modulus=e^α/(1+X_y・α) α=(1-1/X_y)+√<(1-1/X_y)^2+4/βX_y>/2 Parameter β and X_y is defined by experiment. This is agreement with the expression of stress-strain curve of concrete for uniaxial compression. (2) Elastic modulus When 0<X<X_y, E_<dN>=Ee^<αx^βγ(N-1)^σ>)=m(E-E_<dN>) When N=number of cyclic loadings m=harden coefficient Parameter γ, δ is defined by experiment. This is changing with number of cyclic loadings and shows the extent of fatigue damage under cyclic loadings. (3) Residual strain X_<pN>=X_0(1-e^<-αx^β_0γ(N-1)^σ) Where X_0=starting point of unloading strain. This shows the extent of fatique damage under cyclic loading in the same as elastic modulus. (4) Reloading curve. As for analytical expression, S=E_<dN>X_se^αx^β_x+m[(E-E_<dN>)X_s-(E-(m+1)/mE_<dN>X_y)αX^β_se^<αX^β_s> Where X_s=X-X_p(N-1). As for practical expression, S=S_0-E(X_0-X)e^<-αX_α-X]^β This shows to change the shape of reloading curve from upside curve to straight line and downside curve with increasing number of cyclic loadings. (5) Unloading curve S=S_0(1-X_Re^<-1/β(x^β_R-1)> Where X_R=(X_0-X)/(X_0-X_<p(N-1)>) So=starting point of unloading stress. As seen from this expression, unloading curve shows dowonside curve regardless of Number of cyclic loadings.