THEOREM FOR THE CALCULATION OF BUILDING STRUCTURES

Abstract

The well-known calculation provisions of construction practice are analyzed. It is noted that the invention of new approaches and theorems for the calculation of structures is one of the ways of progress in construction. The introduction of new theorems into design practice opens a way to reliability in design and efficiency of the construction sector of the economy. Based on the basic physics concept of the rotational effect of forces, we prove that it is possible to find deformations and stresses in the cross-section of a beam structure. The force moment, in contrast to the bending moment, takes into account the rotational effect of all forces relative to the design point of the section. This approach to calculation is basic, physically sound, easy to use, and reliable for design engineering practice. The author proposes to build a diagram of force moments not along the longitudinal axis of the beam, as is customary for the bending moment, but along the height of the section. The moments of forces acting on each of the points belonging to the section line in their aggregate create a diagram of the rotational moment in the section. This approach has no restrictions and such a section can be oriented freely in any direction with respect to the longitudinal axis of the building structure. In the further implementation of a three-dimensional model it is possible to determine the torques for all conditional points of the array that make up the design volume or the entire structure. The characteristic provisions concerning the rules for constructing diagrams of torque moments of rotational forces are formulated. The author proposes a theorem for determining the differential of the function of the rotational force moment by the height of the section. Since in the proposed calculation the force moment embodies two factors – force and moment – both stresses and strains in the section can be determined using it. Based on the results of our research, we obtained a somewhat simplified expression for determining linear relative deformations and stresses in the section. Summarizing, we conclude that the proposed theorem for the calculation of building structures in the form of a differential dependence of the moment of rotational force by the height of the section to determine the longitudinal force in the section is effective. Based on the consequences of the theorem, the dependencies for stresses and strains are determined. The application of the theorem makes it possible to verify existing calculations and perform the calculation part for a new construction project.