General Formula of Beams Strengthening

The article proposes one of the approaches to implement the introducing methodology idea for determining strengthening with a general formula. Combining equations recommendations at different parts of beams in the form of a general formula are given. Equations variants for determining strengthening in the form of the general formula have been given by the example of a simple beam calculation under diverse loading schemes. The proposed format distinctive features for the final formulas have been noted in comparison with the traditional ones with writing equations discrete form. The mathematical apparatuses wide usage possibility for general formulas transformation and analysis of the stress–strain state in beams has been shown. Thanks to the elimination of multiple calculations of forces in individual sections used in general problem-solving methods, the use of a joint formula can significantly reduce the number of calculations. The proposed joint record in the form of a single formula, instead of multiple formulas for different sections of the element, simplifies the procedure for adapting the automated calculation methods using simpler algorithms. It is important to state that using the expressions for calculating forces in the form of a joint equation allows us to apply more rational methods of problem-solving, in particular for securing stability and dynamics of structures. It is worth mentioning that the proposed algorithm for formation of a joint equation for beams can be extended to other structures in accordance with proposed methodology.