This work proposes a chance-constrained formulation for shakedown analysis under non-Gaussian uncertainty in structural strength. A Gaussian distrubition used in [1] seems to be not a suitable stochastic model for strength data which can assume only finite positive values. Therefore, a lognormal model has been proposed in [2] which still has infinite values. Alternatively it is suggested to truncate the Gaussian distribution to positive data or twosided truncation to allowable and possible strengths within a unified optimization framework. The formulation is developed for truss structures [3] and expressed as a linear programming problem with probabilistic constraints, which is subsequently transformed into an equivalent deterministic optimization problem. This transformation enables efficient computation while incorporating reliability requirements into shakedown analysis. Numerical examples on truss systems demonstrate that truncation has a strong effect on the reliable load capacity of engineering structures. This can guide reliability based decissions in quality control in structural engineering and maintenace.