Stability Degradation and Redundancy in Damaged Structures

The objective of this paper is to assess the promise of a novel tool for structural safety decision-making in severe unforeseen hazards. A straightforward measure is put forth for measuring the intensity of unforeseen hazards: the number of connected members removed from a structure in a brittle fashion. The tool selected for assessing this severe demand is the reduction in the buckling load capacity (stability) of the structure under service loads. Two examples of planar steel frames quantitatively demonstrate how the stability of structures degrade under this severe damage. Degradation of the buckling load, as members are removed, provides an efficient and unique tool for assessing fragility against unforeseen hazards in buildings. Further, a coarse, but efficient measure of progressive collapse is provided by the condition number of the stiffness matrix for the damaged structure. Comparison of a moment frame with and without cross-bracing indicates the beneficial role of redundancy as damage increases. Challenges remain, particularly in determining reasonable distributions for the intensity, improving the computational efficiency of the analysis, and insuring the degrading stability response tracks a buckling mode of interest. A framework for incorporating the analysis into decision-making, similar to that developed in seismic performance-based design, is provided. 1 Assistant Professor, Johns Hopkins University, [email protected] 2 Graduate Research Asst., Johns Hopkins University, [email protected] INTRODUCTION Traditional design methodologies are typified by Figure 1(a): Given a known set of environmental loads estimate the probability of failure (Pf). Current design provides estimates of Pf for each component of the building, with no direct estimate of the system Pf. Next-generation, probabilistic performance-based design methods that aim to assess the system Pf for a given environmental hazard are under development (e.g., see Deierlein 2002). Today, design remains focused on deterministic load cases (e.g., ASCE 7) and component evaluation (e.g., AISC 2001). Each load case is applied to the intact structure. While each case may be slightly different in both magnitude and distribution, the structural analysis generally focuses on the same “weak links” in the building, and these members dominate the failure modes. In the prevailing methodology building sensitivity is not fully explored. service loads (always present) live loads (transient) environmental hazards wind/seismic (transient) Pf? service loads (always present) Pf?