【正文】 bility putation it is convenient to transform x into the standard normal space y＝ y(x) such that the elements of y are statistically independent and have a standard normal distribution. An iteration algorithm is used to locate the design point (the most likely failure point)on the limitstate function using firstorder approximation. During each iteration, the structural response and the response gradient vectors are calculated using finiteelement models. The following iteration scheme can be used for finding the coordinates of the design point: where To implement the algorithm and assuming the limitstate equation has a general form of g(x,u,s)=0, the gradient of the limitstate function in the standard normal space can be derived as where =Jacobians of transformation (., ). Once the coordinates of the design point y* are evaluated with a preselected convergence criterion, the reliability index b can be evaluated as The evaluation of Eq. (11) will depend on the problem underconsideration and the performance functions used. The essential numerical aspects of SFEM were just discussed in the evaluation of the three partial derivatives and four Jacobians in Eq. (11). They are evaluated in the following sections in the context of a frame and RC shear wall structural system. Performance Functions The safety or reliability of a structural system is always estimatedwith respect to predetermined performance criteria. The performance criteria are usually expressed in the form of limitstate functions. Two types of limitstate functions are monly used in the engineering profession: strength and serviceability. Strength Performance Functions According to the American Institute of Steel Construction’s (AISO) Load and Resistance Factor Design (LRFD) Design guidelines, the strength performance criteria for 2D steel frame members can be defined as and where =required tensile and pressive strength。 and r=governing radius of gyration about the plane of buckling (inch). Not all the members in the frame are connected to the shear walls. The shear walls are expected to prevent local and lateral torsional buckling of steel members, thus improving their strength. To consider the strength failure probability of the weakest steel members, this study considers the failure of steel members where shear walls are mnot present. Serviceability Performance Functions For the serviceability criterion, the limitstate function is represented as wherδ＝ calculated displacement ponent and δlimit＝ prescribed maximum value of the displacement ponent. As will be elaborated later, the vertical deflection at the midspan of beams and the lateral displacements at the top of the frame are considered to be the two serviceability performance functions in this study. Implementation of Proposed SFEM to the Combined System To implement the concept, the three partial derivatives and four Jacobians in Eq. (11) need to be evaluated in terms of random variables x, u, and s for all the performance functions to be considered. Evaluation of Partial Derivatives The three partial derivatives in Eq. (11), namely, and for the strength limit states are evaluated first. Neither g function in Eqs. (13) and (14) contains any explicit displacement ponent, therefore ＝ 0. In order to evaluate the basic random variables in the limitstate functions need to be defined. The Young’s modulus E, area A, yield stress Fy , plastic modulus Zx , and the moment of inertia of a crosssection I along with the external force F are considered to be basic random variables. Therefore, it can be shown that Thus, substituting Eqs. (15)and (16)into Eqs. (13) and (14), each term of Eq.(21) can be evaluated. can also be derived by taking the partial derivatives withrespect to Pu and Mu as As discussed earlier, only steel members where RC shear walls are not present are checked for the strength limit states. The steel members are expected to be weaker in strength in this case. Thus, although the parameters in Eqs. (13) and (14) are expected to be influenced by the presence of shear walls, the partial derivatives with respect to the random variables related to shear walls, namely, Ec and ν, need not be evaluated. For the serviceability limit state represented by Eq. (20), for the steel frame elements it can be shown that and where . For the serviceability limit state, the partial derivatives with respect to Ec and ν of the RC shear walls are zero. Therefore, the partial derivatives need not be calculated. Evaluation of Jacobians As discussed previously, the four Jacobians in Eq. (11)need to be puted. Jy,x and its inverse are easy to pute due to the triangular nature of the transformation. Since s is not an explicit function of x, Js,x=0. However, the other two Jacobians of the transformation, ., Js,D and JD,x, are not easy to pute since s, D, and x are implicit functions of each other. The adjoint variable method (Arora and Haug 1979。 k=effective length factor。 The SFEM algorithm for frame structures has been developed by several researchers. However, the main drawback of frame structures is their inability to transfer horizontal loads (., wind, earthquake, and ocean waves) effectively. They are relatively flexible. To increase their lateral stiffness, bracing systems or shear walls are needed. Haldar and Gao (1997) Attempted to consider bracing systems in a steel frame structure. They used truss elements in their model. However, there has not been an attempt to consider shear walls, represented by two dimensional plate elements, in a frame in the context of SFEM. Shear walls have been used for a long time to increase the lateral stiffness of steel frames. The use of concrete shear walls is specifically addressed in this paper. It is not simple to capture the realistic behavior