A basic element in frame construction is the beam–column joint. Despite numerous studies, there is still no uniform procedure for designing shear force in different countries. We are still witnessing serious problems and even the destruction of buildings under seismic effects caused by failures in the frame beam–column connection. Over the past six decades, a huge number of experimental studies have been carried out on frame assemblies, where various parameters and their compatibility under cyclic impacts have been tracked. What continues to remain incompletely understood is the magnitude and distribution of the forces passing through the joint. The creation of a new mathematical model of the beam and column that transmit their forces in the frame joint contributes significantly to clarifying the flow of forces. For this purpose, the full dimensions of the beam, as well as its material properties, are taken into account. All research was performed for a stage before the opening of a crack and after its appearance and growth on the face of the column separating it from the beam. In the present paper, the loading of two transverse, uniformly distributed loads, remaining symmetrical on the beam, is considered. The position of the loads for which there is an extremum of the forces contributing to the shear force is investigated. Numerical results are demonstrated for the influence on the magnitudes of the support reactions from different concrete strengths of the beam. The obtained results are compared with those specified in Eurocode for shear force design. It was established that at the appearance of the crack, the shear force determined with the proposed new model exceeds the magnitude of the force calculated by Eurocode.