Explicit solutions for the response probability density function of linear systems subjected to random static loads

•A new version of the probabilistic transformation method is proposed.•The probability density functions of single response quantity are evaluated.•Some exact results for the response of linear systems to generic random loads are given.•Strongly non-Gaussian responses are considered.

In the present work a new version of the Probabilistic Transformation Method (PTM) has been reported for the study of linear systems subjected to static random loads. Even if this application could appear trivial, it allows to find some exact results, difficulty obtainable by other approaches. In particular, some interesting results have been obtained in the case of uniformly distributed random loads. For a generic vector of random loads this version of the PTM has allowed to obtain the characteristic function (cf) of any response elements in a very simple and effective way.