# Damage Analysis and Evaluation of Light Steel Structures Exposed to Wind Hazards
## 5 Performance Evaluation of Light Steel Systems Exposed to Wind Hazards  
Fragility analysis methodology was the most common method for implementing the performance-based engineering theory into the evaluation of light steel systems exposed to wind hazards since it is widely applied in the evaluation of the low-rise light-frame wood construction exposed to multi-hazard loads. Its main theory was mentioned as below.  
Fragility can be defined as the conditional probability of failure of a structural member of the system for a given set of input variables. It is expressed as  
\[P[LS]\ =\sum_{all\ D}P[LS|D=x]P[D=x], \tag{1}\]  
in which \(D=a\) random demand on the system (e.g., 3 s gust wind speed); \(P[LS|D=x]\) is the conditional probability of the limit state (LS) at given demand \(x\). The hazard is defined by the probability \(P[D=x]\). The conditional probability, \(P[LS|D=x]\) is the fragility. Equation (2) also can be expressed in convolution integral form if the hazard is a continuous function of demand \(x\):  
\[P[LS]=\int_{0}^{\infty}Fr(x)g_{X}(x)dx \tag{2}\]  
in which \(Fr(x)=\) fragility function of demand \(x\) expressed in the form of a probability density function. The conditional probability \(Fr(x)\) is known as a \"fragility\" [70]. In order to study the fragility of the each level of light-frame structures, several types of research have been conducted. [PERSON] [71] established a probabilistic analysis framework for the vulnerability of typical light steel structures in the United States. [PERSON] [72; 73; 74; 75] proposed a series of fragility analysis methodologies for assessing the response of light-frame wood construction exposed to stipulated extreme windstorms and earthquakes. [PERSON] and [PERSON] [76; 77] proposed a series of vulnerability model for Australian high-set house or metal-clad industrial buildings to extreme wind loading for cyclonic regions. [PERSON] and [PERSON] [78] presents a fragility assessment for roof sheathing in light frame constructions built in high wind regions which considering the influence factor of roof shapes, geographic locations, nail types, and exclosure conditions. The fragility model can be used to develop performance-based design guidelines for wood frame structures as well as tools for condition assessment and loss estimation for use with the existing building inventory. [PERSON] and [PERSON] [79] proposed a method of probabilistic wind vulnerability analysis for typical light-weight steel buildings in China. Based on real damage investigation of light steel industrial buildings, [PERSON] [3] and [PERSON] [80] studied the damage of light steel structures under typhoon loads through the fragility method. [PERSON] and [PERSON] [81] presented a methodology to assess the effect of wind directionality on the vulnerability of rural houses to cyclonic wind speed and also provide a cyclonic risk assessment of coastal regions. [PERSON] and [PERSON] [82] developed fragility curves for localized pull-through failures of thin steel roof battens. The proposed model can be used to evaluate the effects of roof batten span and spacing and levels of enhancement that could be achieved with the strengthening method proposed for roof battens. [PERSON] [83] studied the typhoon-induced wind vulnerability for residential buildings in Japan based on reliability modelling. However, performance-based wind engineering methodologies for cold-formed light-frame steel construction are currently unavailable. Performance goals, vulnerable model, time-dependent theory, and limit states suitable for cold-formed steel structural systems exposed to wind hazard to incorporate different owner and occupant performance expectations still need to be studied.