Buckling Loads of Two-Layer Composite Columns with Interlayer Slip and Stochastic Material Properties Simon Schnabl 1 ; Igor Planinc 2 ; and Goran Turk 3 Abstract: This paper presents an efficient stochastic buckling model for studying the structural reliability of layered composite columns with interlayer slip between the layers and random material and loading parameters. The model is based on the exact buckling model, re- sponse surface method, and Monte Carlo simulations. The probability of failure is investigated for a different number of random variables, sample points, and various degrees of response surfaces. The results show that the probability of failure is considerably affected by the type (deterministic or probabilistic) of the loading and its distribution. DOI: 10.1061/(ASCE)EM.1943-7889.0000478. © 2013 American Society of Civil Engineers. CE Database subject headings: Buckling; Composite columns; Structural reliability; Slip; Probability; Monte Carlo method; Material properties. Author keywords: Buckling; Composite columns; Structural reliability; Slip; Probability; Response surface method; Monte Carlo method. Introduction Currently, the application of composite layered systems is in- creasing tremendously in various engineering industries, such as mechanical and structural engineering. This is because composite layered structures have many advantages compared with the con- ventional structures. The benefits of using layered composite materials are high strength-to-weight and stiffness-to-weight ratios, corrosion resistance, design flexibility, durability, and so on. Despite their many attractive qualities, one of the main disadvantages of using layered composites is that it is almost impossible to manu- facture an absolutely stiff connection between the layers. Conse- quently, an interlayer slip between the layers develops that can significantly affect the mechanical behavior of the composite structure. As a result, to model the mechanical behavior of such structures adequately, an interlayer slip has to be taken into con- sideration. A large number of papers on this very interesting topic can be found in the literature (Al-deen et al. 2011; Challamel and Girhammar 2011a; Erkmen and Attard 2011; Foraboschi 2009; Krofli  c et al. 2010; Miller and Bulleit 2011; Nguyen et al. 2011a, b; Ranzi et al. 2010; Schnabl et al. 2006; Schnabl et al. 2007a, b; da Silva and Sousa 2009; Zona et al. 2011). A survey of the type and form of engineering structures de- veloped over the last few decades reveals a continuing significant trend toward high-strength, slender, and lightweight composite structures. Therefore, buckling is an important design consider- ation, especially when such structures are subjected to axial compressive loading. A considerable amount of research has been conducted on the stability of composite structures, and a number of papers on this subject have recently been published (Amadio and Bedon 2011; Challamel and Girhammar 2011b; Chen and Qiao 2011; Girhammar and Pan 2007; Kry zanowski et al. 2009; Schnabl and Planinc 2010; Schnabl and Planinc 2011; Xu and Wu 2007). All of the aforementioned papers have analyzed the behavior of composite structures considering the material properties, geometric properties, loading, and boundary conditions as fully determined. Composite materials display significant and unavoidable variability in their properties, and the axial loading also has random variations. As a result, the behavior of composite structures with interlayer slip becomes stochastic. Therefore, in the analysis of such structures, these variations have to be taken into account. Recently, a few researchers considered the cases of stochastic behavior of composite beams with incomplete interaction between the layers (Zona et al. 2010, 2012). However, it seems that there is no analysis in the open literature for stochastic buckling analysis of composite structures with interlayer slip. Thus, the primary ob- jective of this paper is to simulate and investigate the stochastic buckling behavior of composite columns with interlayer slip and random material properties, random contact parameters, and loading. Although the first-order reliability method (FORM) (Melchers 1999) and second-order reliability method (FOSM) are difficult to apply because the true limit state function (LSF) is hard to obtain explicitly, and the computational times are long, the critical buckling loads and probabilities of failure in this paper have been obtained using the exact structural model, response surface method, and crude Monte Carlo method. In the numerical examples, the reliability assessment is carried out to obtain the probability of failure for layered composite col- umns with interlayer slip and stochastic material and loading parameters. A parametric study is conducted in which the combined effect of the degree of response surface and the number of sample points is analyzed. 1 Assistant Professor, Chair of Hydrology and Hydraulic Engineering, Faculty of Civil and Geodetic Engineering, Univ. of Ljubljana, Hajdrihova 28, 1000 Ljubljana, Slovenia (corresponding author). E-mail: simon .schnabl@fgg.uni-lj.si 2 Professor, Chair of Mechanics, Faculty of Civil and Geodetic Engi- neering, Univ. of Ljubljana, Jamova 2, 1000 Ljubljana, Slovenia. 3 Professor, Chair of Mechanics, Faculty of Civil and Geodetic Engi- neering, Univ. of Ljubljana, Jamova 2, 1000 Ljubljana, Slovenia. Note. This manuscript was submitted on November 15, 2011; approved on May 23, 2012; published online on May 25, 2012. Discussion period open until January 1, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Engineering Mechanics, Vol. 139, No. 8, August 1, 2013. ©ASCE, ISSN 0733-9399/ 2013/8-961–966/$25.00. JOURNAL OF ENGINEERING MECHANICS © ASCE / AUGUST 2013 / 961 J. Eng. Mech. 2013.139:961-966. Downloaded from ascelibrary.org by Fakulteta Za Gradbenistvo on 04/16/15. Copyright ASCE. For personal use only; all rights reserved.