Compurers & Slrucrures Vol. 43. No. 3, pp. 41’+430, 1992 Printed in Greet Britain. 0045-1949~92 S5.00 + 0.00 Q 1992 Pergamon Press Ltd STRUCTURAL RELIABILITY USING MONTE-CARLO SIMULATION WITH VARIANCE REDUCTION TECHNIQUES ON ELASTIC-PLASTIC STRUCTURES J. E. PULIDO,~ T. L. JAcoBst and E. C. PRATESDE LIMA$ tDepartment of Civil and Environmental Engineering, Duke University, Durham, NC 27706, U.S.A. SCOPPE-Department of Civil Engineering, Federal University of Rio de Janeiro, CX.P. 68506, Rio de Janeiro 21945, Brazil (Received 12 April 1991) Abstract-A structure is subjected throughout its lifetime to loadings that may cause damage, deterio- ration and possibly failure. The objective of this paper is to present a method of assessing a structure’s reliability and collapse mechanism using Monte-Carlo simulation and variance reduction techniques. The objective of this methodology is to accurately assess the reliability and collapse mechanism for a structure while significantly reducing the number of analyses completed. Structural failure for this methodology may be defined in different ways including: maximum permissible stress or deflection, plastic mechanism, buckling, punching-shear or any other serviceability characteristic. For the procedure proposed here, the failure function is interpolated from values obtained in structural analysis. The advantage of this methodology over classical Monte-Carlo simulation is that no prior knowledge of the failure mechanism is required. Two example structures are presented to obtain the failure probability using the Monte-Carlo method. 1. INTRODUCTION AND SCOPE 1.1. Reliability The relative uncertainty of parameters involved in structural analysis and design is known to be an important factor influencing structural safety. Mayer [ 11, Basler [2], and Cornell [3] proposed safety measures early in this century but their work was largely ignored and had little influence on the design practices of that time. Forsel[4] investi- gated the optimization of structural designs in 1924 to minimize the total expected cost of the structure. Others have proposed design strategies based on the mean and variance of critical design parameters [ 1, 51. The first comprehensive presen- tation of the structural reliability theory and econ- omical design was presented by Johnson[6] and included the statistical theories of strength developed by Weibull[7]. The reliability of a structure is defined as the complement of the probability of failure and represents the probability that the structure will not fail L = 1 -p/. (1) The fundamental concept of structural reliability was first proposed by Freudenthal[8] and focused on determining the probability of failure. Brown [9], Freudenthal [lo] and others have shown that the probability of failure can be determined using the relationships P[R <S] =p,= s m f-,(s)L&) ds. (2) 0 Equation (2) illustrates that structural reliability refers to the probability that the structural loads do not exceed the structure’s ability to resist the loads. Both the loading (S) and the structure’s resistance (R) are random in nature and described by known probability density functionsf&) and fR(r), respect- ively. Alternatively, the probability of failure of a structural element can be defined as P/ = P[G(R, S) < 01, (3) where G(.) is the known performance function. In the case of structural systems which include loading and design parameters, analysis becomes complicated due to the combination of events that can lead to a system failure. Past research in structural reliability has focused on fatigue, design, analysis and optimal design under loading conditions and damage assess- ment [l l-131. Several investigations have considered the limit state failure of structural systems and a great number of approximate solutions techniques have been developed for this problem. Stevenson and Moses [14] reported that solutions are determined more efficiently when the mathematical expression is 419