Conventional fragility is defined as probability of failure. Based on concise mathematics, it is found that if fragility is probability of collapse then the design curve is probability of survive. The sum of these two is equal to 1. Consequently, if a member (structure) is designed based on a give curve, then its fragility of collapse is also known!.
Scale the horizontal axes of a fragility curve (s) of a structure, between 0 and 1. Then:
what is the probability of collapse at s=0.5 ?
what is the probability of survive at s=0.5
Don you agree with the above findings? Why ?
Semantically collapse and survival do look like mutually exclusive events, thus indeed their probabilities should add up to one (complementarity). Unless of course there were alternative ways of interpreting "collapse" and/or "survival", but if they are both in the same context, I don't see how.
It should be taken into account the fragility number which depends on structural hierarchy and width of cracks or collapsed element within the structure itself.
As shown the Design curve and the Fragility curve are always complement of each other. For a given system with an upper bound of capacity ( km= area * maximum stress) the Survive function (SR) times km is capacity, and the fragility function (FR) times km is fragility, where SR+FR=1. These relations apply at any state of the system before failure.
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