The stress values at the crack tip in bending reinforced concrete beams are considered. The stress state is analytically determined with an initial and propagating crack. Equations of the equilibrium of a part of the beam cut along the crack line are compiled. These equations are reduced to a system of two nonlinear algebraic equations using the plane-sections hypothesis. The equations determine the stress zone’s height and the nominal stress at the crack tip for a beam with an initial crack and the crack length. The rest of the stress state parameters are expressed regarding the zone stress height and the nominal stress or crack length. The same equation system determines the external moment starting from which the crack length increases. The analytical method for determining the stress intensity factor (SIF) with an initial and growing crack in bent reinforced concrete beams is proposed. The method is based on the assumption that the size of the stress concentration zone at the crack tip is determined by the equality of the nominal and local stresses at the end of this zone. The method determines the value of the external moment starting from which the crack length increases. The stress zone’s size is determined by the coincidence of the local stress with the nominal stress. The same problem is solved in a three-dimensional formulation by the FE method, considering the stress field’s peculiarities at the crack tip. The calculation results coincide with the analytical solutions.

In this paper, the bending of cantilever triangular plates at the same angles of inclination of the side edges to the base is investigated. Due to the complexity of the boundary conditions, a numerical finite difference method is applied using a grid of scalene triangles that fits well into the contour of the plate. To solve the problem of an acute angle at the top of the plate, the method of combining the results of calculating a cantilever bar of variable bending stiffness with similar results of calculating a triangular plate supported along the contour using a reduction factor is applied. The results of deflections of the cantilever triangular plate at different angles of inclination of the side edges to the base are given. The theoretical provisions and applied results of this study can be used both in scientific research and in engineering design.

The work is devoted to determining the stress parameters of flexible reinforced concrete beams with cracks. The problem is solved using LIRA-SAPR using beam finite elements, taking into account the nonlinear relationship between deformation and stress in concrete. In the course of solution, a step-by-step loading method is used with the use of an iterative process at each step. To obtain the dependence of the stress parameters on varied factors, a rational planning matrix for a multifactor computer simulation was compiled to determine the stress parameters in bent rectangular reinforced concrete beams with a crack. According to this plan, computer simulations were conducted for concrete beams of C20/25 and B32/40 class. The obtained dependences enable to evaluate the operability of the considered structural elements for both groups of limiting states. They can be used to determine the parameters of fracture mechanics and evaluate the crack resistance of a beam.

In this paper, there are studied the dynamic processes (free and forced oscillations) of isotropiccantilever plates in the form of an isosceles (wedge-shaped) triangle. In the study, the finitedifference method has been applied using a regular one-dimensional (linear) grid. The finite-difference equations developed by the authors for point-distributed masses along the length ofthe wedge are presented, taking into account the linearly variable bending stiffness. On this basis,the results of studies in the form of amplitude-frequency characteristics (frequencies, dynamicforces and deflections) in the resonant and near-resonant regions have been obtained. The contentof theoretical provisions and applied results can be widely used in the scientific and engineeringfields and in the field of mechanics of structures.

In this work there has been studied the rod system operation dependence on the action ofexternal force effects. The system presents a multi-span continuous beam with elastic yieldingsupports. To identify the stress-strain state of the object under study, a precise analytical methodof forces is used. The method of five moments is used as the resolving (canonical) equations. Thefinal results are the parameters of the stress-strain state for a five-span continuous beam withvariable compliance coefficients on 5 intermediate supports and an absolutely rigid left extremesupport, deflections, bending moments, shear forces, and support reactions.Theoretical provisionsand practical results can be used in the design of load-bearing beam structures in buildings andvarious engineering structures.