# Modal Failure Probability and System Performance

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*by*Wei Wang,

Ross B. Corotis,

Martin R. Ramirez,

**Document Type:**Proceeding Paper

**Part of:**Structural Engineering in Natural Hazards Mitigation:

**Abstract:**It is pointed out that the modal failure probability, i.e., the probability that a structure fails in a particular mode, cannot be uniquely defined under the time-invariant framework. In addition to the popular β-definition, two alternative definitions that have straightforward physical justification are introduced. Not only the magnitudes but also the rank of the modal failure probabilities computed using these definitions are shown to be quite different from each other and from the true ones. Consequently, the results of dominant mode identification and reliability-based design code calibration are likely to depend on which definition is adopted.

**Subject Headings:**Failure analysis | Probability | Structural reliability | Structural analysis | Terminology and definition | Structural failures | Frames |

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