Geometric Imperfection Distributions of Existing Reticulated Shells: Theoretical and Experimental Analysis
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Online ISSN 2093-6311 Print ISSN 1598-2351
Geometric Imperfection Distributions of Existing Reticulated Shells: Theoretical and Experimental Analysis Jun Wu1 · Yongfeng Luo2 · Lei Wang1 Received: 8 October 2019 / Accepted: 26 August 2020 © Korean Society of Steel Construction 2020
Abstract Geometric imperfection is one of the most disadvantageous factors that impair mechanical behaviors of existing reticulated shell structures. However, the available consistent mode methods and statistical methods which usually applied in designing structures can hardly estimate the actual geometric imperfection distribution for existing structures, because these methods use the assumed imperfections. In this paper, a Markov Random Field (MRF) theoretical model of existing reticulated shells is established by introducing the theory of probabilistic graphical model. The unit of graphic model named node clique are proposed to deduct the geometric state function of reticulated shells, based on the local Markov property. Then the inversion function along with its iterative equation is established to predict geometric imperfection distribution of existing reticulated shells. The MRF method makes the predicted distribution of the numerical model as consistent as possible with its corresponding actual structure, and only a few measurement nodes are needed as known conditions. An experimental structure of K6 single-layer reticulated shell is built to verify the proposed theory by comparing the calculated geometric imperfection distribution results with the actual measured data. Meanwhile, the significance level of the calculated results between MRF and traditional stochastic method is analyzed, which shows MRF method can effectively predict the geometric imperfections of single layer reticulated shells. Keywords Existing reticulated shell · Markov Random Field · Geometric imperfection distribution · Reticulated shell experiment
1 Introduction Over the past few decades, assessment of existing steel structures have attracted much attention from both scientific and engineering communities (Kuehn et al. 2008; Soleimani Amiri et al. 2013; Helmerich et al. 2007; Melchers 2001). Existing reticulated shells (ERSs), as a common form of existing steel structures, are widely used in the construction of complicated large-span structures like theaters and exhibition halls due to aesthetics and lightness. As a result, the safety assessment of ERSs is of great significance for protecting the social property and life safety. Extensive trials and theoretical studies indicate that geometric imperfection * Yongfeng Luo [email protected] 1
Tongen (Shanghai) Engineering Technology Co. Ltd, Shanghai 200433, China
Department of Structural Engineering, Tongji University, Shanghai 200092, China
2
(GI) is one of the main factors adversely affecting mechanical behaviors of reticulated shells (Borri and Spinelli 1988; Gioncu 1995; Yamada et al. 2001; Luo and Shen 1995), because the initial geometric imperfection will significantly reduce the stabi
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