Strength condition theorems for the elastic structures with a stress error

As is known, the constraints (the strength condi-tions) for the safety factor of elastic structures and the elements of a certain class (i.e. airframes) are set, i.e. the safety factor values of such structures should be within a given range. It should be noted that the con-straints are given for safety factor that correspond to analytical (exact) solutions of the elasticity problems represented for the structures. Developing analytical (exact) solutions for most structures, especially of ir-regular shape ones is of great difficulty. Approximate approaches to solve the elasticity problems, e.g. the technical deformation theories of homogeneous and composite plates, beams and shells, are widely used for a great number of structures. Technical theories based on the hypotheses provide the approximate (technical) solutions with an irreducible error, the exact value being difficult to determine. In the strength calculations of structures at a specified small range for the factor of safety, the application of engineering solutions (by the Theory of Strength of Materials) is to be difficult. How-ever, there are some numerical methods for developing approximate solutions of elasticity problems with arbi-trarily small errors. In this paper two theorems on new (adjusted) strength conditions for elastic structures tak-ing into account the stress error were proposed. It has been shown that to fulfill specified strength conditions for safety factor of given structure corresponding to an exact solution, the adjusted strength conditions for structural safety factor corresponding to approximate solution are required. The stress error estimation being the basis for developing the adjusted strength conditions for the specified strength conditions has been deter-mined. The adjusted strength conditions appear to be given by allowable stresses. Adjusted strength condi-tions make it possible to determine the set of approxi-mate solutions, whereby meeting the specified strength conditions. Some examples of specified strength condi-tions to be satisfied using the technical solutions (the Theory of Strength of Materials) and strength conditions have been given. To meet those, it is necessary for the approximate solutions with a high accuracy to be used.