Vol 20, No 6 (2024)

The problem of strength analysis of a multi-modulus strip, in contradiction to the existing standpoint of essential nonlinearity, may be formulated as a linear problem for a two-layer strip. First order differential equations of the theory of elasticity for the plane strip problem are transformed to dimensionless form and are replaced by integral equations with respect to the transverse coordinate, similar to how it is done in the Picard’s method of simple iterations. In this case, a small parameter appears as a multiplier in the integral equations before the integral sign, which ensures the convergence of solutions in accordance with the contraction mapping principle, also called the Banach fixed point theorem. The original system of equations of elasticity theory is splitted into integratable equations of bending, axial tension-compression and edge effect. The found solutions satisfy all boundary conditions of the elasticity theory problem. The formula determining the position of the neutral axis during bending is written. For a multi-modulus material, such as concrete, the neutral line shifts upward significantly in the compression region during bending, resulting in large displacements at the lower edge in tension and creating conditions for opening of vertical cracks. The occurrence of inclined cracks near supports is explained.

When analyzing building structures in software packages based on the finite element method, incorrect results can be obtained. To justify the correctness of the obtained solution, it is necessary to perform verification studies and engineering assessment of the obtained data. This is required by the national standard of Russian Federation on modeling. The correctness of constructing calculation models can be assessed by comparing the data of the finite element method with the reference value. A numerical experiment was carried out in the SCAD++ version 21 software package for five finite element models of a cantilever beam made of B15 grade concrete, with dimensions of 2.5×0.5×0.5 m: four solid models No. 1-4 and one “reference” model consisting of a dense grid of second-order volumetric finite elements of cubic shape. Based on the calculation results, a comparative analysis of the shear stress distribution pattern from shear force was performed for all models with stresses calculated using the well-known analytical method, according to the Zhuravskii formula. It was found that the shear stress distribution in the sections of four computer models No. 1-4 does not correspond to the theoretical values calculated according to the rules of strength of materials. An accurate solution can be obtained using the “reference” solid model proposed by the authors, consisting of a dense grid of volumetric finite elements of the second order of cubic shape.

The work is devoted to the application of the concept of specific strength for the analysis of the degree of utilization of mechanical properties of beam material under combined loading. The beam is studied and force diagrams are constructed for various types of loads, such as pure bending with tension, pure bending with tension and torsion, pure bending with torsion, and the strength utilization factor of a beam with an arbitrary cross-section is obtained. The research method is based on the superposition of stress states with the determination of the difference between the resistance diagrams. The concept of material resistance to fracture in the form of ultimate stresses distributed over the body volume is introduced. The method of calculating the specific strength for a beam under combined stress, as well as for thick-walled pipes loaded with internal pressure, is given. The relationship between the beam cross-section of the beam and the specific strength is presented, followed by a conclusion for the optimal application of the beam with the cross-section used.

When choosing the shape of a shell, one should strive for the boundary conditions to ensure momentless behavior of the shell. Second-order algebraic surfaces include three degenerate surfaces: parabolic, elliptic, and hyperbolic cylindrical surfaces, and two surfaces derived from them: circular cylindrical surface and cylindrical surface with incomplete ellipse in cross-section. These five surfaces are the objects of this research. For the first time, comparative static analysis of the five shells under a load of self-weight type is performed using the momentless shell theory. The explicit formulae for the determination of three internal membrane forces are obtained. It is shown that the parabolic cylindrical shell and the cylindrical shell with incomplete ellipse in cross-section perform better within the momentless shell theory. The constraints for the application of the momentless theory obtained earlier by other authors are confirmed. For the first time, a system of three partial differential equations with respect to the displacements of middle surfaces of the five cylindrical shells given in previously unused curvilinear coordinates is derived. It is established that no studies dealt with the calculation of hyberbolic cylindrical shells so far. A brief review of publications on the analysis of strength, stability, dynamics, and application of the five considered cylindrical shells is given to clarify the directions of investigation of these five cylindrical shells.

It is shown that the installation of cutoff walls (CW) using various drilling and injection technologies should be considered as the most effective method to protect against the development of karst-suffosion hazard during construction and operation of transportation and other structures. Depending on geotechnical and hydrogeological conditions at the future construction site, it is possible to use various mixtures based on polymers, liquid glass, etc., for CW construction and elimination of karst unconsolidation. It is shown that polymeric impregnation compositions are effective for the accelerated option of increasing the bearing capacity of soils, and the use of compositions based on liquid glass allows to increase biologic resistance. The use of jet grouting technology, collar technology or their combination is also effective. It is reasonable to use mineral-based special injection mixtures for compaction and hardening of karst rocks. These mineral-based special injection mixtures are more technologically advanced, and the soil cement of CW and compacted karst rocks is more durable compared to soil compacted with polymer-based or liquid glass injection mixtures. An effective injection mixture for CW installation for protection against karst-suffosion hazard is the “PFS+” injection mixture, which should be considered as an alternative to injection mixtures based on bentonite, polymers or liquid glass. Taking into account the high probability of sulfate corrosion development during injection of fractured gypsum rocks, the efficiency of application of mineral fine-dispersed binder - “Introcem” slag based microcement in collar technology - is shown. In order to eliminate karst unconsolidation, the most preferable approach is the use of the “ZIS” special injection mixture, which is made on the basis of mineral composite binder. The experience of using the “Super-Jet” technology under different geotechnical conditions and design solutions has shown that the strength of the soil cement body formed by this technology can reach 15 MPa, and the cutoff walls are fully waterproof. It is shown that higher strength of soil bases is achieved when they are injected with powder-activated compositions.

This study presents the results of instrumental observations of the interaction process of an underground structure with the soil environment under explosion-induced seismic impact. During seismic impact, the soil imparts kinetic energy to underground structures, the value of which depends on the contact area of the structure and the soil and the conditions of interaction. In this regard, the energy-based evaluation of the process of joint vibration of the underground structure and the environment under explosive seismic waves is of great significance. The analysis of energy release in terms of frequencies shows that the energy of seismic radiation at different frequencies of the spectrum is not the same, and there is a well-defined maximum in the energy spectrum at small equivalent distances, i.e. at a certain frequency value much more energy is released than at other frequencies. Mathematical expressions are provided for calculating the total energy of ground vibrations, estimated proportion of energy propagating in the soil, and the energy received by the underground structure during their interaction. A formula is proposed for calculating a dimensionless coefficient of the vibration process, indicating the share of energy transmitted through the soil to the underground structures. Three zones are identified that characterize the relationships of the forces of interaction in the contact area. The first is the zone with a linear relationship between the force and the deflection of the structure. Then, in the next zone, the proportionality between the values is violated with the loss of the elastic nature of the interaction. In the third zone, the underground structure slides relative to the ground. Aspects of the interaction of a thin-walled structure with the soil are considered. Calculations show that the obtained relationships can be used with sufficient accuracy to evaluate the seismic intensity of explosive seismic waves.