The article investigates the influence of partial stiffness of the hinge joint of single-span and multi-span freely supported beams with lower structures on their stress-strain state under the action of vertical evenly distributed load. Joints of freely supported beams under the action of external load are opened on supports and mounting bolts interfere with their full opening, that is joints work as partially rigid. Knowing some initial parameters of ideally hinged joints, it is possible to establish what influence their change will have both on the calculation scheme of beams, and on calculation schemes of cross frames of frameworks of buildings and constructions, to which they enter, as a whole. The method of initial parameters was used to determine the influence of the resistance of the mounting bolts on the opening of the support joints on the stress state of the elements. The offered technique allows to define real rigidity of any bolted hinge connection taking into account its actual work and to adjust it stiffnesst by changing the diameter of the bolts, the strength of the material from which they are made, their number, distance between them, as well as use additional material resource by reducing the maximum stresses in the calculated cross sections. This is especially true of elements made of perforated profiles, because the change of stress-strain state in the support zones will cause redistribution of stresses in the calculated points of their cross sections, both on the supports and in the span of the beams. This must be taken into account by including certain coefficients in the calculation formulas, depending on the specific operating conditions.