Asymptotic Matching Analysis of Scaling of Structural Failure Due to Softening Hinges. II: Implications

The asymptotic matching analysis in the preceding Part I has established a new kind of size effect, caused by postpeak softening of inelastic hinges in beams and frames. The present Part II analyzes various implications, particularly the size effects on the maximum loads under load control or displacement control, the design loads, and the energy absorption of the structure. DOI: 10.1061/~ASCE!0733-9399~2003!129:6~651! CE Database subject headings: Hinges; Structural failures; Size effect; Softening; Fracture mechanics; Frames; Beams. JO Wi5 Pi 2 S 1 Ki11 1 KiD ~Pi2Pi8! (1) Continuing from point A to point B, the structure decelerates, and at B its kinetic energy is Wi2Wi8 , where Wi8 is the area of the triangle ABPi11A , representing the energy stored in the structure upon moving from A to B; Wi85 ~Pi112Pi! 2 2 F 1 Ki11 1 Pi112Pi11 8 S Pi11 Ki11 Pi11 8 Ki12D G (2) If Wi2Wi8.0, as shown in Fig. 1~a!, and if the damping is not negligible, the kinetic energy has not been fully absorbed by the structure. So the structure continues to increase its load-point displacement w, i.e., the snapthrough continues, and the peak Pi11 8 can never be reached. In that case, the maximum load attainable under load control is Pi . If finite damping is taken into account, then the condition of continuing snapthrough at load Pi may be written as