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ISSN : 2093-5145(Print)
ISSN : 2288-0232(Online)
Journal of the Korean Society for Advanced Composite Structures Vol.11 No.1 pp.18-24
DOI : https://doi.org/10.11004/kosacs.2020.11.1.018

# Wind Fragility of Steel and Carbon-Fiber Reinforced Plastic Single-Span Greenhouses

Viriyavudh Sim1, WooYoung Jung2
1Ph.D. Candidate, Department of Civil Engineering, Gangneung-Wonju National University, Gangneung, Korea
2Professor, Department of Civil Engineering, Gangneung-Wonju National University, Gangneung, Korea

본 논문에 대한 토의를 2020년 03월 31일까지 학회로 보내주시면 2020년 04월호에 토론결과를 게재하겠습니다.

Corresponding author: Jung, WooYoung Department of Civil Engineering, Gangneung-Wonju National University, 7 Jukheon-gil, Gangneung, Gangwon 25457, Korea. Tel: +82-2-400-2208, Fax: +82-2-400-2268 E-mail: woojung@gwnu.ac.kr
November 11, 2019 December 5, 2019 December 17, 2019

## Abstract

In this study, the probabilistic performances of greenhouses made of steel and carbon-fiber reinforced plastic, when subjected to wind loads, were compared. Wind fragility was used to estimate the failure probability in the case of strong wind. The finite element model of a single-span vinyl greenhouse was developed based on the specifications published by the Rural Research Institute of the Republic of Korea; the failure state could be determined by comparing the structural analysis results with the limit state of the structure. Ten thousand greenhouses under randomly generated wind pressures were simulated via the Monte Carlo method to estimate the failure probability as a function of the wind speed. The global horizontal and vertical deformation limit states were also considered. The steel-frame greenhouse exhibited the best performance and the horizontal deformation limit state was the predominant factor in the single-span greenhouse failure under the investigated loading conditions.

# 강재 및 CFRP 단동비닐하우스의 강풍 취약도 개발 방법

심 비리야붓1, 정 우영2
1강릉원주대학교 토목공학과 박사수료
2강릉원주대학교 토목공학과 교수

## 초록

본 논문에서는 풍하중에 노출된 강재 및 CFRP로 구성된 비닐하우스에 대한 확률론적 성능비교를 하였다. 풍하중에 대한 취약성은 강풍에 노출된 온실의 파괴확률을 추정하기 위해 사용되었으며 단동 비닐하우스의 유한요소 모델링은 한국농촌 경제연구원에서 발간한 설계도를 적용하였다. 해석결과를 구조물의 한계상태와 비교함으로써 비닐하우스의 파괴상태를 결정할 수 있다. 기본적으로 몬테카를로 시뮬레이션은 풍속에 따른 파괴확률을 도출하기 위해 가상의 풍하중에 대하여 적용하지만 본 논문에서는 전체에 대한 수직 및 수평 변형한계상태를 고려하였다. 그 결과, 강재 비닐하우스가 가장 높은 성능을 보였으며 수 평 변형 한계상태가 하중조건에 대한 단동비닐하우스의 파괴원인임을 확인하였다.

Ministry of Interior and Safety
National Research Foundation of Korea
2017R1A2B3008623

## 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 (Akhoondzade-Noghabi and Bargi, 2016). In fact, PRA is a comprehensive and systematic procedure to estimate risks associated with life-cycle 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 disaster-prone 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):

$F r ( V ) = Φ [ ln ( x ) − μ σ ]$
(1)

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 7-10 (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 Cp parameter.

$W = 0.613 K z K z t K d V 2 ( G C p − G C π )$
(2)

in which, Kz = the velocity pressure exposure, Kzt = the topographic factor, Kd = the wind directionality factor, V = the basic wind speed in (m/s), G = gust-effect factor, Cp = external pressure coefficient, Cpi = 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 load-displacement 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 self-weight 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 log-normal 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 self-weight 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 two-counterpart 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 self-weight 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.

## ACKNOWLEDGMENT

This research was supported by a grant (MOIS-DP- 2015-05) of Disaster Prediction and Mitigation Technology Development Program funded by Ministry of Interior and Safety (MOIS, Korea) and was also supported by the National Research Foundation [NRF] grant funded by the Korea government [MEST] [No.2017R1A2B3008623].

## Figure

Vinyl Greenhouse used in South Korea
Finite Element Model of Single Span Greenhouse
Deformation and Load-Displacement Curve of Single Span Greenhouse
Probability of Failure Determination Flowchart
Wind Fragility of Steel Frame Single Span Greenhouse
Wind Fragility of CFRP Frame Single Span Greenhouse
LS2 Wind Fragility of the Three Types of Single Span Greenhouse
All Cases of Wind Fragility of Steel, CFRP and Steel and CFRP Frame Single Span Greenhouse

## Table

Material Properties of Greenhouse Components
Element Type and Element Number of Greenhouse Model in ABAQUS
Wind Fragility Parameters of Single Span Greenhouse

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