Report - PEER - University of California, Berkeley

In this study, a two parameter low-cycle fatigue model is used to quantify thedeterioration characteristics of structural systems (Erberik and Sucuoğlu, 2004;Sucuoğlu and Erberik, 2004). The relationship between the energy dissipationcapacity per cycle (normalized with respect to the energy dissipated at the first cycle)and the number of constant amplitude cycles is defined in the form of an exponentialfunctionEh,nβ (1−n)= α + (1 − α)e(1)Here, Ē h,n is the normalized dissipated energy at cycle n, α and β are the twofatigue parameters. The first parameter α is related to the ultimate level ofdeterioration at large values of n and the second parameter β is related to the rate ofdeterioration. A system with α =0 loses all of its energy dissipation capacity as n→∞whereas a system with α =1 always retains its initial energy dissipation capacity(curve-A in Figure 1). An elastic-perfectly plastic system is an example of a nondeterioratingsystem, with α=1. The second parameter β has a wider range between 0and ∞, and it represents the rate of loss in cyclic energy dissipation capacity. In thelimit, β=0 means no deterioration whereas β=∞ defines a system which loses all of itsenergy dissipation capacity after completing the first cycle (curve-C in Figure 1).Curve-B in Figure 1 shows a typical system with realistic fatigue parameters havingvalues between the upper and lower limits.1Normalized dissipated energyper cycle,Ēh,n0(Curve-C)β=∞0 < α < 1(Curve-B)0 < α < 10 < β < ∞Number of cycles, n( )(Curve-A)α=1 OR β=0Figure 1. Energy-based fatigue model with two parameters (α, β).Experimental results obtained from different reinforced concrete specimens areemployed in order to calibrate the low-cycle fatigue parameters and to relate them tothe general behavior of structural systems under cyclic excitations. The experimentaldata used is listed in Table 1 with the characteristic properties of each specimen. Codename of the specimens also indicate the researchers: WS (Wight and Sözen, 1973),SO (Saatçioğlu and Özcebe, 1989), PJ (Pujol, 2002), ES (Erberik and Sucuoğlu,2004). The third column shows the pattern employed in the cyclic loading history:α423