The plastic node method previously developed by the authors is very effective one for elastic-plastic analyses of the framed structures. In this method, the new mechanism of plastic hinge based on the plastic flow theory is introduced to the fully yielded nodal point of one dimensional finite element. Therfore, the elastic-plastic behavior of the framed structures subjected only to the concentrated loads can be exactly evaluated using the discrete model where nodal points are placed on the loading points and joints. On the other hand, when the distributed loads act on the framed structures, possible yielded zones cannot be estimated in advance. Inappropriate discrete models lead to overestimation of the collapse load. In this paper, applying the plastic collocation method developed newly by the authors, the advanced theory for elastic-plastic analyses of the framed structures subjected either to concentrated or to distributed mid-span loads is proposed. In this new theory, the exact collapse load, collapse mechanism, and mid-span deformation of such structures can be obtained by the discrete model where nodal points are placed only on the joints.