1. INTRODUCTION
Structural damages caused by natural disaster phenomena are reported to be steadily increasing due to recent abnormal climate phenomena and the increased frequency of natural disasters caused by global warming. Lee et al. (2017) estimated that through 2060, the annual damage cost from natural disasters will reach the maximum of US$20.9 billion which is about 1.03% of future Korean Gross Domestic Product (GDP). Specifically, for wind related disaster, Park et al. (2011) reported that the average economic losses resulting from one tropical cyclone landfall increased by three times in the 2000s compare to those in the 1980s. Moreover, the damages due to typhoon not only caused devastating loss on the economy, but also threatened the safety of human life. Therefore, the probability risk assessment (PRA) for structure subjected to strong wind had gained many attentions (AkhoondzadeNoghabi and Bargi, 2016). In fact, PRA is a comprehensive and systematic procedure to estimate risks associated with lifecycle characteristic of the entire structure (Seo and Caracoglia, 2013).
The recent increase of high intensity typhoon in the Pacific Ocean has emphasized the necessity of risk assessment for structure vulnerable to strong wind, especially those located in a disasterprone area (Kim et al., 2017a). Vinyl greenhouse is a lightweight structure and usually located in open terrain with scattered obstruction. Thus, considering the damage characteristics of vinyl greenhouses due to strong winds, Rural Research Institute of Korea (1995) constantly revises and proposes design standards for disaster events (Kim et al., 2017b). Currently, research focused on the safety evaluation through experiments and finite element method (FEM) of the vinyl greenhouse are actively conducted in Korea; however, the research on the development and evaluation of fragility for vinyl greenhouse by mean of probabilistic approach is insufficient. Therefore, in this paper, analytical wind fragility development procedure for single span vinyl greenhouse was shown. This fragility curve can be used to quantify the performance of vinyl greenhouse in function of wind speed. Moreover, with the aim of exploring alternative material to improve the construction of greenhouse, carbon fiber reinforced polymer (CFRP) was used. Three types of greenhouse based on their frame’s material were considered in the development of wind fragility: frame constructed from steel, frame constructed from CFRP, and frame constructed from the combination of steel alternated with CFRP.
2. GREENHOUSE WIND FRAGILITY
2.1 Definition of Wind Fragility
Wind fragility presents a conditional probability of failure of a structural member or system for a given set of input variables in function of wind intensity. It is generally expressed as following (Porter, 2015):
in which Φ(ㆍ) = standard normal cumulative distribution function, μ = logarithmic median of resistance capacity, and σ = logarithmic standard deviation of resistance capacity. This fragility model is an important component for development of risk assessment framework that provides the factual basis for hazard mitigation plan (Vickery et al., 2006;Choi and Jung, 2017;Kim and Jung, 2018).
2.2 FE Model of Single Span Greenhouse
The development of wind fragility in this paper was based on structural analysis of greenhouse with ABAQUS platform. Firstly, a single span greenhouse, shown in Fig. 1(a), was modeled in ABAQUS based on structural drawing and the experimental data of their components. The structural drawing information was published in the guideline of Korean greenhouse design by Rural Research Institute of Korea (1995). The experimental data of greenhouse’s components in Fig. 1(b) were incorporated in the finite element (FE) model. The FE model of a 20 m × 7 m single span greenhouse was shown in Fig. 2. This greenhouse model had a total height of 2.8 m, 1.4 m for the column and 1.4 m for the rise of roof’s arch. Mechanical properties and description of element type were shown in Table 1 and Table 2, respectively.
2.3 Stochastic Wind Loads and Limit States of Single Span Greenhouse
Stochastic wind loads projected on single span greenhouse were determined according to ASCE 710 (2010) standard due to the limit of domestic design standard, which does not include the uncertainty of wind load parameters. Nominal wind loads parameters for wind pressure applied on the greenhouse wall and roof surface were determined with this guideline. However, to employ Monte Carlo Simulation (MCS) method, these nominal wind load parameters were combined with their respective statistical parameters. The statistical wind load parameters were determined based on the work by Ellingwood and Tekie (1999), in which they determined the statistical parameters by mean of Delphi questionnaire. The statistical parameters were determined and summarized as shown in Table 3. With MCS method, ten thousand sets of wind loads were generated and projected on windward wall, windward roof, center roof, leeward roof, and windward roof of the single span greenhouse model. Equation (2) was used to determine the wind load projected on each surface location of the greenhouse based on their respective C_{p} parameter.
in which, K_{z} = the velocity pressure exposure, K_{zt} = the topographic factor, K_{d} = the wind directionality factor, V = the basic wind speed in (m/s), G = gusteffect factor, C_{p} = external pressure coefficient, C_{pi} = internal pressure coefficient.
In Table 3, wind exposure categories were defined based on surface roughness of natural topography, vegetation, and constructed facilities. Exposure B is typical residential subdivision or wooded area, Exposure C is open terrain or hurricane prone shorelines, and Exposure D is flat and unobstructed area within ¼ mile of an inland lake at least one mile across.
The ten thousand greenhouse samples were analyzed in Abaqus. Then, the probability of failure of greenhouse were determined based on the performance of these ten thousand samples. The limit state of vinyl greenhouse considered in this paper were the horizontal and vertical deformation of the main load bearing member in the greenhouse structure. Limit state 1 (LS1), horizontal deformation, was associated with the greenhouse’s column deformation. LS1 was achieved if the deformation at the top of greenhouse’s column was equal to or larger than the column height, in millimeter, divided by 60 which was equal to 23.33 mm. Correspondingly, limit state 2 (LS2), vertical deformation, was associated with the deformation of the greenhouse’s rafter. LS2 was achieved if the deformation at the top of the greenhouse’s rafter was equal to or larger than the greenhouse’s span, in millimeter, divided by 100 which was equal to 70 mm.
The probability of achieving LS1 and LS2 for a given wind speed was obtained by comparing the loaddisplacement curve shown in Fig. 3 with their respective limit state. Since, loading shown in these curves was the function of wind speed and a constant selfweight load, the results of probability of failure were in function of wind speed. These results can be used to quantify the failure of the greenhouse in probabilistic perspective. Furthermore, parameter μ and σ of the lognormal cumulative distribution function were used to present the wind fragility curve for all three types of green house, following Eq. (1). Fig. 4
3. RESULTS AND DISCUSSION
Results of steel frame single span greenhouse wind fragility were presented in Fig. 5. Both limit state cases were presented with their respective wind exposure category. The solid and dash line illustrated LS1 and LS2, respectively. Furthermore, the square (□), circle (○), and triangle (△), symbol presented the wind exposure category B, C, and D, respectively. As expected for greenhouse in exposure category D, the wind load projected on their surface was more than the other two exposure categories at the same wind speed. This higher wind pressure resulted in their higher probability of failure, as can be seen with their logarithmic median of failure μ. This result signified that in wind exposure D at wind speed 28.85 m/s, the steel frame greenhouse had a 50% probability of reaching LS1, i.e. 23.33 mm horizontal displacement. Alternatively, the wind speed required to achieve LS2, 70 mm vertical displacement, for exposure D was 38.59 m/s. Additionally, the highest resistance was the greenhouse in exposure B.
Similar trend could be observed for CFRP frame greenhouse presented in Fig. 6. However, their performances were lower than steel frame greenhouse for their respective limit state and wind exposure category. This result could be due to the suction of wind pressure on the fully enclosed greenhouse. For steel frame greenhouse, their selfweight was higher than their CFRP counterpart.
Further evidence can be seen in Fig. 7 where all three types of single span greenhouse’s wind fragility were plotted for their vertical displacement limit state. The “SteelFRP” curves in Fig. 7 indicated the CFRP frame was place alternatively with the steel frame in the greenhouse model. The ranking of their performance from worst to best were CFRP frame, steel and CFRP frame, and steel frame. Moreover, this figure also shows the order of performance from worst to best of greenhouse based on wind exposure category effect which were exposure D, C, and B.
Lastly, all cases of wind fragility parameters were shown in Table 4 accompanied by Fig. 8. In Fig. 8, all eighteen cases of wind fragility for single span greenhouse were plotted and organized by their respective frame’s material, limit states, and wind exposure category. From this figure, it could be concluded that the horizontal displacement failure was the predominant factor of single span greenhouse failure due to wind load.
4. SUMMARY AND CONCLUSIONS
Structural safety evaluation of greenhouse in strong wind region is a necessity for Korea, where yearly occurrence of typhoon is steadily on the rise. In the current research, to evaluate the performance of greenhouse, wind fragility was constructed and used to estimate the probability of failure of greenhouse when subjected to strong wind. Specifically, this paper demonstrated the development of wind fragility analytically based on structural analysis of greenhouse with ABAQUS finite element analysis software. A model of single span greenhouse was developed based on structural drawing and experimental data of structural components. Subsequently, Monte Carlo Simulation (MCS) method was used to generate thousands sets of random wind loads projected on five different surfaces area, i.e. windward wall, windward roof, center roof, leeward roof and windward roof, of the single span greenhouse. Therefore, ten thousand greenhouse samples were modeled, and their performances were analyzed in function of wind speed. Results from these analyses can be used to determine probability of failure based on specified limited states such as global deformation, frame and connection deformation, frame and connection stress, etc. However, in this paper, only global displacement limit states were considered in the determination of probability of failure, which subsequently used to determine the wind fragility for single span greenhouse.
Results from this study showed that:

The single span greenhouse located in open terrain, exposure category D, experienced the highest wind pressure at the same wind speed compare to their twocounterpart located in exposure B and C. This resulted in the higher probability of failure for both limit states across all three types of greenhouse.

The CFRP frame greenhouse had the highest probability of failure across all three types of greenhouse. This was due to the low selfweight of FRP material to resist the suction pressure of wind load on the fully enclosed single span greenhouse.

In terms of the two limit states, horizontal displacement limit state (LS1) yielded the most critical median failure wind speed, i.e. higher probability of failure at the same wind speed for the same structure at the same location compare to vertical displacement limit state (LS2). Thus, under wind loading, LS1 was the predominant factor of single span greenhouse failure.
This analytical method of fragility analysis can determine the probabilistic performance of single span greenhouse structure without their historical damage data. These fragilities can be used to predict the performance and to improve the design of greenhouse for strong wind resistance.