۱- Introduction

۲- Problem setting

۳- Mechanical model

۴- Dynamic shakedown

۵- A probabilistic collapse estimation framework

۶- Case study

۷- Conclusions

References

Abstract

The modeling and estimation of the inelastic response of wind excited structures is attracting growing interest with the introduction of performance-based wind engineering. While frameworks based on direct integration have been widely adopted in earthquake engineering for estimating inelastic responses, the significantly longer duration of typical windstorms, as compared to seismic events, makes this approach extremely computationally challenging in the case of wind excited systems. This is especially true in the case of modern performance-based wind engineering frameworks, which are based on probabilistic metrics estimated through simulation and therefore repeated evaluation of the system. This paper addresses this challenge through the development of a simulation framework based on dynamic shakedown theory. In particular, an efficient path-following algorithm is proposed for estimating not only the shakedown multipliers, but also the plastic strains and deformations associated with occurrence of the state of shakedown. The efficiency with which this information can be estimated for any given wind load time history enables the development of a simulation-based framework, driven by general stochastic wind load models, for the estimation of the system-level inelastic performance of the structure. The validity and practicality of the proposed framework is illustrated on a large-scale case study.

Introduction

With the introduction of performance-based design (PBD) frameworks in wind engineering, inelastic/non-linear performance assessment is assuming an increasingly important role. Indeed, PBD approaches require the evaluation of building performance under various hazard levels, including structural behavior beyond the elastic limit. In seismic engineering, many methods have been developed for characterizing the inelastic behavior of the structure based on direct stepby-step integration [1], including specialized methods such as incremental dynamic analysis (IDA) [2]. In the field of wind engineering, however, the extremely long duration of typical windstorms effectively prevents the application of such computationally intensive methods, as they require non-linear dynamic integration over the entire load history. This computational hurdle becomes exasperated in applying modern performance-based wind engineering frameworks that are based on propagating uncertainty through the system using simulation methods that require the repeated evaluation of the system [3–۹]. Notwithstanding these issues, a number of studies have been carried out over the years using direct integration methods with the aim of better understanding the inelastic behavior of wind excited systems [10–۱۵]. These studies have provided insight into the inelastic failure mechanisms affecting wind excited structures, e.g. ratcheting in the alongwind direction and low cycle fatigue in the acrosswind direction. In alternative to direct integration, methods have recently been proposed based on nonlinear static pushover analysis [16]. While providing significant computational gains over direct integration, these methods are affected by the inherent difficulty of nonlinear static pushover analysis to capture cumulative damage mechanisms, e.g. ratcheting and low cycle fatigue [17,18]. This has led to the recent development of a computationally efficient approach for determining safety of wind excited systems against these inelastic failure mechanisms within the context of simulation-based wind PBD frameworks.