Simplified Derivation of a Damage Curve for Seismically Induced Beam Fractures in Steel Moment-Resisting Frames

Abstract

This paper presents a simplified method of deriving a novel damage curve to quantify the damage extent of seismically induced beam fractures in steel moment-resisting frames. The damage curve expresses a damage index as a function of reduction in bending stiffness at the fractured section, where the damage index is obtained by comparing strain responses measured on steel beams under ambient vibrations before and after earthquakes. A closed-form expression of the damage curve was formulated from a two-story two-bay frame model based on a parametric analysis conducted to examine relationships between the damage curve and various structural parameters. The notable finding from the parametric analysis was that the damage curve was primarily affected by the span-depth ratio of the monitored beam. Thus, the closed-form expression was demonstrated to be applicable to the construction of damage curves for common multi-story multi-bay steel moment-resisting frames. The effectiveness of the closed-form expression was verified numerically using a nine-story steel moment-resisting frame model and experimentally using a one-quarter-scale five-story steel frame testbed.