Journal of Sound and Vibration (1989) 129(2), 83-98 A STUDY OF LIN EA R COMBINATION OF LOAD EFFECTS A. NAESS Department of Civil Engineering, The Norwegian Institute of Technology, N-7034 Trondheim, Norway (Received 5 January 1988, and in revised form 11 August 1988) The performance of a combination formula, extensively used in stochastic dynamics for estimating extreme values of linear combination of load effects, is investigated. It is shown that this combination formula is nearly optimal in the case of independent Gaussian load effect components. For non-Gaussian load effects the performance is investigated by studying specific examples, and it is shown that the accuracy deteriorates significantly. 1. INTRODUCTION In the design of, e.g., an offshore structure, one may be faced with the problem of how to estimate in a correct manner the extreme combined load effect due to the environmental forces on the structure during a design situation, for example a loo-year storm. The “best” procedure to use will depend on the specific case at hand; in particular, it will depend on how the individual load effects combine to produce the total load effect. In this paper the main emphasis is on linear combinations of load effects, which from a practical point of view is a very important combination procedure. The possibility to treat more general load effect combinations has been investigated to some extent in reference [l], where it was assumed that the combined load effect X(t) is given by X(r) = h(X,(r), * * * f xl(t)), (1) where jointly stationary Gaussian processes X,(t), . . . , X,(t) are combined according to the deterministic function h. A genera1 method for obtaining the distribution function of the largest value of X(t) during a given interval of time was developed. As one might expect, the practicality of the method depends very much on the nature of the combination function h. Analyses of two specific case studies have been carried out by using this method [2,3]. As stated above, in this paper attention is focused on the particular case of a linear h. Specifically, it is assumed that x(t)=x*(t)+~*~+x”(t), (2) but here the Xj( t)‘S are not restricted to Gaussian processes. This is an important special case of the genera1 load effect combination problem. As an example, to establish a design load for the tendons of a tension leg platform, one would need to consider a linear sum of axial loads, contributed by the various motion modes of the platform. A quantity of particular interest in connection with design is the probability distribution of the largest value of the total load effect X(t) during some specified time interval. If this is known, statistical characteristics of the largest value, or extreme value, can be provided for establishing design loads. However, no general method exists for finding the probability law of the extreme value of the total load effect X(t). Therefore, one usually has to estimate the required statistical characteristics of the extreme value of X(t) 83 0022-460X/89/040083 + 16 %03.00/O 0 1989 Academic Press Limited