【正文】 thod [6,7].Based on the classical probability theory,this conventional RBDO method describes uncertainties in structural systems as stochastic variables or random fields with certain probability distribution and thus provides an effective tool for determining the best design solution while explicitly considering the unavoidable effects of parameter variations[8].As the most mature nondeterministic design approach,the RBDO has been successfully used in many reallife engineering applications[9,10].However,the primary challenge to apply the conventional RBDO in practical applications is the availability of the precise statistical characteristics,which are crucial for a successful probabilistic reliability analysis and ,these accurate data usually cannot be obtained in some practical applications where only a limited number of samples are available. The early treatment [11,12] for insufficient uncertainties is to construction a closest uniform probabilistic distribution by using the principle of maximum 1990s,Elishakoff [13,14] explored that a small error in constructing the probabilistic density function for input uncertainties may lead to misleading assessment of the probabilistic reliability in particular conclusion illuminates that using the traditional probabilistic approach to deal with those problems involving in plete the information might be inconvincible. Consequently, an alternative category,namely the nonprobabilistic approach [15],has been rapid developed for describing uncertainty with inplete statistical information by a fuzzy set or a convexset. In the fuzzy set method[16,17] ,the fuzzy failure probability of structures is assessed based on membership function representation of the observed/measured the convex set method [1820], all possible values of the uncertainties are bounded within a hyperbox or hyperellipsoid without assuming any inner probability models have been regarded as attractive supplements 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 nume