Structural System Reliability with Application to Light Steel-Framed Buildings

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Virginia Tech


A general framework to design structural systems for a system-reliability goal is proposed. Component-based structural design proceeds on a member to member basis, insuring acceptable failure probabilities for every single structural member without explicitly assessing the overall system safety, whereas structural failure consequences are related to the whole system performance (the cost of a building or a bridge destroyed by an earthquake) rather than a single beam or column failure. Engineering intuition tells us that the system is safer than each individual component due to the likelihood of load redistribution and al- ternate load paths, however such conservatism cannot be guaranteed without an explicit system-level safety check. As a result, component-based structural designs can lead to both over-conservative components and a less-than-anticipated system reliability.

System performance depends on component properties as well as the load-sharing network, which can possess a wide range of behaviors varying from a dense redundant system with scope for load redistribution after failure initiates, to a weakest-link type network that fails as soon as the first member exceeds its capacity. The load-sharing network is characterized by its overall system reliability and the system-reliability sensitivity, which quantifies the change in system safety due to component reliability modifications. A general algorithm is proposed to calculate modified component reliabilities using the sensitivity vector for the load-sharing network. The modifications represent an improvement on the structural properties of more critical components (more capacity, better ductility), and provide savings on less important members which do not play a significant role.

The general methodology is applied to light steel-framed buildings under seismic loads. The building is modeled with non-linear spring elements representing its subsystems. The stochastic response of this model under seismic ground motions provides load-sharing, system reliability and sensitivity information, which are used to propose target diaphragm and shear wall reliability to meet a building reliability goal. Finally, diaphragm target reliability is used to propose modified component designs using stochastic simulations on geometric and materially non-linear finite-element models including every individual component.

This material is based upon work supported by the National Science Foundation under Grant Nos. 1301001 (Virginia Tech), 1301033 (University of Massachusetts, Amherst) and 1300484 (Johns Hopkins University). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily re ect the views of the National Science Foundation. The author is grateful to the industry partner, the American Iron and Steel Institute, for their cooperation.



System reliability, Probability, Finite-Element Modeling, Cold-Formed Steel, Seismic, Incremental Dynamic Analysis, Diaphragms, Shear Walls, LRFD