Solution of a class of load combination problems by directional simulation

Abstract The load combination problem of Ferry Borges-Castanheta may be effectively handled by the Rackwitz-Fiessler algorithm provided the load pulses have absolutely continuous distribution function. However, realistic modelling of extraordinary actions requires the load pulse distributions to have a concentrated probability at zero. In principle this discontinuity may be handled by conditioning such that the combination problem reduces to several problems with absolutely continuous distribution functions. With just some few extraordinary actions taking part in the combination problem this method of conditioning becomes quite cumbersome and even impracticable. If it is assumed that the single load pulses are clipped normal random variables, i.e. of the form max{0, X} where X is normal, then a combination of the RF-algorithm and directional Monte Carlo simulation technique turns out to be useful. At any given argument the directional simulation method gives not only a confidence interval for the value of the distribution function but also a confidence interval for the value of the density function of a random variable defined as a sum of clipped dependent or independent normal variables. This is just what is needed in the RF-algorithm in order to apply the principle of normal tail approximation on the distribution of the sum.