In this study optimum plastic shakedown analysis of framed steel structures with semi-rigid connections (SRC) between beam and columns subjected to multi-parameter static loading presented. Since shakedown analysis does not provide information concerned with the accumulated residual displacements, complementary strain energy of the residual force (CSERF) considered as constrain to evaluate the post yield behavior of framed steel structures. The constraints on the CSERF are modelled using probabilistic and deterministic methods. To evaluate the maximum shakedown load-multipliers a numerical example is introduced, shakedown load-multipliers are calculated and safe loading domains of the framed steel structure are illustrated. The numerical results show that the constraints on CSERF, SRC and probabilistic given constraints can influence on the value of the shakedown load-multipliers.