APPROXIMATIONS OF THE TORQUE-CURVITY DIAGRAM RECTANGULAR CROSS-SECTION WOODEN REINFORCED AND NONREINFORCED BEAMS

The sequence of approximation of the "torque-curvature" diagram to the function is described for a reinforced and unreinforced bending wooden element of rectangular cross-section. It has been established that for the approximation it is necessary to go through the following sequence: 1) using the hypothesis of flat sections, determine the stress-strain state of the section, taking into account the current models of the work of the materials included in the structure under consideration; 2) build a graph "torque-curvature" according to the previously given algorithms; 3) for a given section, establish the main points of the diagram; 4) to carry out the apromaximization of the diagram to the function using mathematical methods; 5) confirm the convergence of functions to determine the accuracy of their approximation, over the entire diagram and at specific points of the diagram. An example of diagram approximation is given. An example of an approximated function for theoretical and experimental data is given. The sequence of approximation of the diagram to the function is described. The main points of the diagram are established for their reliable description. The possibility of using the function to simulate the work of wood is indicated. A comparison is made between the diagram and the function that describe the "torque-curvature" graph. It was found that this technique can simplify the "torque-curvature" diagram to an elementary power function (in this example, two-degree). It was found that the diagram and the function have an average deviation in the diagram in size , and the total deviation in percentage was less than 1.28%. In this regard, we can conclude that the function has sufficient similarity to use it in further calculations.