Over the life of a structure, the smaller but more frequent earthquakes contribute more to the cumulative damage than the larger earthquakes on which structural design is traditionally based. This is a quantitative argument in favour of designing structures beyond what the codes require for life-safety. This book presents a computational method to evaluate the damage sustained by a building over its lifetime in a seismic environment. The ability to estimate future damage is relevant to a pair of current trends in earthquake engineering: a growing interest for preventing damage on top of protecting the public, and development of performance-based design. The proposed method combines probabilistic principles with traditional structural analysis, which makes it readily applicable to evaluation of planned structures in an engineering office. The analytical models, computational steps and supporting data used to produce an estimate of damage are discussed, and variants of the method with different run time and accuracy are considered.As an example of application to structural design, the book proposes a method to optimise placement of viscous dampers in buildings by minimising a life-cycle cost that includes the investment in damping and the losses due to future damage. Along with the results obtained in the course of other examples, the optimal solutions support a shift toward more resilient structures designed to mitigate structural and nonstructural damage beyond the traditional life-safety requirements.

Table of Contents:
Table of contents 1 Damage assessment method Introduction; Performance-based earthquake engineering; Earthquake damage assessment; Life-cycle cost minimization; Probabilistic framework; PEER equation; Fragility and damage functions; Procedure; Incremental response analysis; Damage calculation; Hazard consideration; Summary: Strategy for validation and application; Outline of chapters; Standard method parameters; Benchmark structures 2 Method properties 2.1 Ground motion; Earthquake events and records; Record set size; Record set composition; Fragility; Hazus model and data; Damage systems; Fragility functions; Fragility parameters; Damage calculation; Floor specificity; Calculation rule; Collapse scenarios; Hazard; Hazard functions; Measures of earthquake intensity; Location comparison; Summary and conclusions 3 Incremental response analysis Introduction; Elementary response analysis methods; Linear and nonlinear methods; Static and dynamic methods; Chapter objectives and organization; Assumptions; FE model; Simulated time in dynamic methods; Nonlinear direct integration; Procedure; Intensity range reduction; Lower bound; Upper bound; Modified procedure; Reference damage estimates and run times; Linear direct integration; Procedure, Procedure, Performance evaluation, Error propagation, Error propagation, Procedure, Mode filtering, Performance evaluation, Applicability to nonproportional damping; Spectral combination; Introduction; Variants; Framework; Combination rules; Spectral quantities; Loading directions; Response directions; Example; Performance evaluation; 3.6 Summary and conclusions 4 Nonlinearities Introduction; Chapter objectives; Two-dimensional models; Generic nonlinear model; Nonlinear effect on damage assessment; Chapter organization; Sources and propagation; Propagation to floors and systems; Negligible sources; Counteracting sources; Sensitivity to model parameters; Member capacity; Member post-capacity stiffness; Member failure; Damper capacity; Damper failure; Sensitivity to structural properties; Stiffness; Local damping, Proportional damping; Other parameters; Summary and conclusions 5 Application to damping optimization Viscous damping design; Practical importance; Existing optimization examples; Problem formulation; Solution strategy; Inner-outer formulation; Outer objective function evaluation; Inner problem initialization; Outer design space and algorithm; Cost and constraints modelling; Continuous formulation; Binary formulation; Mixed-integer formulation; Illustration; Inner problem; First inner iteration; Multiple modes consideration; Summary and conclusions