# Probabilistic Seismic Risk For Buildings And Other Structures Essay

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5. Risk AnalysisEquation Chapter 5 Section 1
Probabilistic seismic risk (of damage) assessment is becoming the basis for longer-term approaches for buildings and other structures.
According to N.Luco[2011], the latest edition of the American Society of Civil Engineers (ASCE) standard entitled “Minimum Design Loads for Buildings and Other Structures” (ASCE 2010) defines Risk-Targeted Maximum Considered Earthquake ground motion maps for the United States (US) by explicitly targeting a probabilistic 1% risk of collapse in 50 years, an approximation of the lifespan of a building. These probabilistic risk-based maps have since been adopted for inclusion in the 2012 International Building Code ( International Code Council 2012). Moreover, the next generation of performance-based seismic design procedures for new and existing buildings being developed by the Applied Technology Council use probabilistic risk of earthquake-caused deaths, dollars (repair costs), and downtime (repair duration) as metrics for seismic performance assessment of buildings.
The Advanced Seismic Assessment Guidelines developed by Bazzurro et al (2006) use the probability that an aftershock ground motion will exceed the capacity of a damaged building after a main-shock (treated deterministically for simplicity) as a rational criterion for deciding whether and when to permit re-occupancy of the building.
This chapter introduces the methodology for post-main-shock probabilistic risk assessment that we propose in order to develop a computational tool for automatic assessment.
The core of this methodology is that the risk integral couples (1) ground motion hazard results for the location of a structure of interest with (2) k...

... middle of paper ...

...x)=∫_S▒〖f_(x│r) (x│r) 〗 f_r (r)dr=1/(σ_lnPGA∙x) ∫_S▒〖∫_(m_min)^(m_m)▒φ((lnx-Ψ(r,m))/σ_lnPGA ) f_m (m)f_r (r)drdm〗 (5.7)

Then we can substitute this in the aftershock risk equation.
However, the risk of equation 5.5 cannot be directly compared with the time-independent risk in equation 5.1 because the latter is the annual data.
So we shock transfer equation 5.5 to an equivalent annual risk which is shown below

(λ_(i,3)^a ) ̃(t,M_min,M_m )=T_1y/(T-t) ∫_t^T▒〖λ_(i,3)^a (τ)dτ〗=[T_1y/(T-t) ∫_t^T▒〖α_a (τ,M_min,M_m )dτ〗]*P_(i,n)=(α_a ) ̃(t,M_min,M_m )*P_(i,n) (5.8)

(λ_(i,3)^a ) ̃(t,M_min,M_m ) is the annual rate of transitions from the i-th damage state to structural collapse, or risk. T_1y =365 is the length of one year in units of days. t is the elapsed time from the main-shock event. T is the estimated duration of the aftershock sequence.

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