Analysis of LRFD factors for a linear limit-state equation with correlated and time-independent random variables: Closed-Form formulation and numerical algorithm

•A general closed-form solution for load and resistance factors in a linear LRFD format is derived for correlated and time-independent normal random variables.•An efficient iteration procedure is proposed for cases with correlated nonnormal random variables•Four numerical examples are provided to demonstrate the feasibility of the proposed algorithm for LRFD calibrations and to illustrate interesting properties of load and resistance factors, safety factors and design point.•The fundamental advantage of the calibrated LRFD over the conventional, but calibrated ASD is explicitly revealed through the numerical example analysis. The calibration of load and resistance factors (LRFs) of multiple loads can be a demanding process, where multiple loads must be considered in a potentially large set of combination scenarios to maintain consistent reliability in structural design. In this study, a set of closed-form formulas of the LRFs are developed with the aid of the coordinates of the design point, under the assumption that the limit-state equation is linear, and the load and resistance variables are mutually correlated and time-independent. These formulas can be used to efficiently calculate LRFs for a combination of multiple loads. Each load ratio is defined in a way that the derived equations can explicitly show the relationship between the LRFs and the conventional safety factor used in the allowable strength design or allowable stress design (ASD). All parameters used in the LRF formulas are dimensionless, making them more general and capable of facilitating comparative observations in a direct and quantitative manner. The closed-form formulas are kept simple by limiting the scope to linear limit-state equations with normally distributed load and resistance variables. For cases where one or more variables are nonnormal, an efficient single-loop iteration algorithm based on the developed formulas and the Rackwitz-Fiessler method is proposed. Four numerical examples are provided to demonstrate the feasibility of the presented formulas and algorithm used for LRFD calibration, followed by discussions of several interesting observations. For example, the fundamental advantage of the calibrated LRFD over the conventional, but calibrated ASD as load ratios change, and the effect of correlation between resistance and loads to the LRFs are illustrated.