【正文】
to the traditional probabilistic model in the reliability design of structural interested readers are referred to research papers . Moens and Vandepitte [21],Moller and Beer [22],Elishakoff and Ohsaki[23]. In a practical engineering problem of adhesive bonded steelconcrete posite beams,the uncertain scatter of structural parameters about their expected values is example,the applied loads may fluctuate dramatically during its service lifecycle,and the parameters defining the structure,such as geometrical dimensions and 3 material properties,are also subject to inaccuracies or these concerned uncertainties,some can be characterized with preciseenough probability distributions,while others need to be treated as bounded ones due to a lack of sufficient sample typical example of such bounded uncertainties is the load magnitude and the geometrical dimensions of a manufactured product,the variation ranges o f which are controlled by specified tolerance bounds. From as early as 1993,attempts have been made to assess and analyze the structural safety in the presence of both stochastic variables and uncertainbutbounded variables by Elishakoff and Colombi [24]. Recently ,many numerical methods,including the multipoint approximation technique[25],the iterative rescaling method [26],the probability bounds (pbox) approach [27],and the interval truncation method [28],have been proposed for estimating the lower and upper bounds of failure probability of structures with a bination of stochastic and interval surveys of both known and new algorithms for this safety assessment problem have also been made by Berleant etal.[29] and Kreinovich etal.[30].However,it is noted that a few studies have considered various uncertainties in the reliabilitybased design optimization .[31] extended the conventional RBDO method to structural design problems under the bination of random and interval their study,a procedure for seeking the worstcase bination of the interval variables is embedded into the probabilistic reliability analysis. As the literature survey shows,the existing studies mainly focus on solving the bination of random/interval variables. Basically,the interval set does not account for the dependencies among the bounded uncertainties,which can be regarded as the simplest instance of the setvalue based convex to the unpredictability of structural parameters and the impossibility of the acquisition of sufficient uncertainty information,problems of structural optimization must be solved in the presence of various types of uncertainties,which remains a challenging problem in realistic systems [32].As a consequence,apractical and efficient reliabilitybased design optimization being capable of quantifying probabilistic and nonprobabilistic uncertainties,as well as associated numerical techniques,should be fully developed and adopted in the professional practice of adhesive bonded steelconcrete posite beam design. In this paper,using the mathematical definition of structural reliability index based on probability and convexsetmixed model [33],a nested optimization formulation with constraints on such mixe