Normal Bending Moment Research Articles

Temporary Structural Health Monitoring of Historical Széchenyi Chain Bridge

A temporary monitoring system was installed on the 175-year-old historical Széchenyi Chain Bridge during its reconstruction. The bridge is in the downtown area in the capital city of Hungary and plays a significant role in the city life of Budapest. Six-month-long measurements were conducted during the reconstruction process of the bridge, yielding crucial insights into the structural behaviour of the historical structure. The measurement results were evaluated; the findings encompass the rotation capacity of the pins between the chain elements and the structural response to temperature changes. This information helped the decision-making between 2021 and 2023 by the designers and construction company during the reconstruction. For instance, daily temperature fluctuations resulted in increased bending moments in the chain elements, rising up to 158% compared to the values observed during a proof load test in 2018. Furthermore, the measurements reveal an approximate 42% increase in normal forces compared to the proof load test, which highlights the high sensitivity of chain bridges to temperature fluctuations, where geometric stiffness plays a crucial role. Reconstruction, namely reducing self-weight, notably intensifies the impact on normal forces and bending moments. These outcomes strongly emphasize the dominance of the dead load and self-weight in the case of chain bridges.

Dynamics of elastic lattices with sliding constraints

This study investigates the impact of sliders – constraints acting on elastic rods allowing for a transverse displacement jump while maintaining axial and rotational displacement continuity – on the dynamics of a periodic elastic grid, including the effects of axial preload. The grid is linearly elastic and subject to in-plane incremental deformation, involving normal and shear forces and bending moment. The periodicity of the infinite grid permits a Floquet–Bloch wave analysis and a rigorous dynamic homogenization, leading to an equivalent prestressed elastic solid. The investigation is complemented by ad hoc developed F.E. simulations and perturbations with a pulsating Green’s function. Results show that the sliders create band gaps, flat bands and Dirac cones in the dispersion diagrams and generate macro-instability even for tensile prestress. The latter corresponds to the loss of ellipticity at the parabolic boundary in the equivalent elastic solid and provides a rare example of an almost unexplored form of material instability. Therefore, our results offer design strategies for metamaterials and architected materials showing reversible material instabilities and filtering properties for mechanical signals.

A Fourier‐series numerical approach for the analysis of tubular members

AbstractThis paper provides an efficient and robust numerical solution for the linear buckling analysis of tubular members, such as the supporting tower structures of wind turbines. The method uses Fourier‐series approximations for the displacement functions. Longitudinal discretization can optionally be applied, i.e., the member can be divided into segments. The strain‐displacement relationship directly considers the curved geometry. The implementation allows for arbitrary support conditions. Four pure loading situations are considered, uniform – in each segment – along the length: normal force, bending moment, torque, and shear force; however, they can arbitrarily be combined, as is commonly occurring in wind turbine towers. The applied methodology results in a computational advantage compared to the shell finite element method, while still maintaining much more generality and applicability compared with common analytical solutions. Furthermore, the method is supplemented with features, as spectral analysis and buckling length calculation.

Performance and Loads of a Wing-Offset Compound Helicopter

Analysis of a hingeless rotor with a single wing on the retreating side for lift compounding was conducted. The goals included validation of performance and load predictions with wind tunnel test data, study of the impact of different aerodynamic inflow models, and understanding of benefits by lift compounding with a single wing on the retreating side. The three primary test cases include collective sweeps of the isolated rotor, and the rotor with the wing, at two different incidence angles. The comprehensive analysis was able to accurately predict the performance and blade structural loads of both the isolated rotor and rotor plus wing configurations. Overprediction of propulsive force leads to underprediction of lift-to-drag ratio in several cases. The normal bending moments were well captured for all cases, while the chord bending moment predictions had a phase offset from the test data, but magnitude and harmonics were captured. Comparing inflow models found that dynamic inflow and vortex wake (prescribed and free) models provided similar results. At these advance ratios, prescribed and free wake models showed almost no differences. Additionally, the vortex particle method showed an overprediction of thrust and greater rotorto-wing aerodynamic interference compared to test data. The addition of the wing on the retreating side provided dual benefits of increasing maximum lift-to-drag ratio and reduction of structural loads for a given total thrust. These effects are a result of both lift share between the rotor and wing, and lift offset, the rotor carries a roll moment to balance the wing's roll moment.

Justification of vaulted structures of the Kyiv underground station as design in terms of shallow foundation

Purpose. Analysis of the effectiveness and competitiveness of single-span vaulted structures for shallow-depth underground stations. The following objectives were set to achieve the aim: 1. Technical and economic comparison of the proposed designs for shallow-depth underground stations. 2. Calculation of the load-bearing capacity of the structure. The methods. The following methods were employed to address the stated objectives: Calculation of volumes and costs of major construction works for station construction using different designs (at a depth of 0.75 meters). Determination of normal forces and bending moments at the joints of the structure. Findings. During the research, the stress state of the vault blocks was determined by solving a system of 11 linear equations, taking into account vertical and horizontal loads, as well as stress at the rock interface at the joint level. A technical and economic analysis was also conducted using aggregated indicators, indicating the competitive advantages of the proposed designs among single-span structures for shallow-depth underground stations. The originality. Correlations found lies in substantiating the effectiveness of the designs and implementing various configurations of single-span vaulted stations for shallow-depth metro construction. Practical implementation. Based on the technical and economic analysis of the options presented in Tables 2 and 3, it can be observed that compared to the first variant, the third variant incurs reduced costs of monolithic concrete. Additionally, there is no need to deviate from the planned track route during the construction of support tunnels and, consequently, manipulate the rings of the structure. Furthermore, the structural features of the third variant allow for the passage of a larger-sized mechanized tunneling complex compared to the first and second variants. The obtained results from the calculations, in combination with the conducted technical and economic comparison and justification of the proposed designs, indicate that the proposed single-span vaulted station designs with an island platform type fully satisfy the engineering and geological conditions, possess sufficient load-bearing capacity, and are competitive among single-span structures for shallow-depth underground stations.

Geometry and static analysis of thin shells in the form of a diagonal translation surface of the velaroidal type

The author presents the results of a study of the geometry and stress-strain state of a surface with a frame of three flat curves in coordinate planes, which have found application today mainly in the shipbuilding industry. The purpose of the work is to identify from the point of view of the stress-strain state from the action of a constant uniformly distributed load the most optimal shell of a diagonal transfer of a velaroidal type with the same main frame of three superellipses. The static calculation was performed using the SCAD program based on the finite element method, designed to perform strength calculations of various types and purposes of structures. The influence of parametric equations for defining a surface depending on the generative family of the same type of cross sections on the distribution pattern of normal stresses and bending moments is shown. The results obtained can help architects and designers with choosing the shape of shells for new projects.

Aerodynamic performance of a dual turbine concept characterized by a relatively close distance between rotors

AbstractIn this work, a closely spaced dual turbine concept is studied. The distance between the two side‐by‐side hubs is 1.05 , where is the rotor diameter. This configuration has a potential benefit for offshore wind developments in which power density can be maximized. The main goal is to evaluate the overall aerodynamic performance, blade loads, and wake structure of a reference wind turbine generator operating within this dual turbine configuration and to compare the effects against those for the typical single turbine configuration. For this purpose, an actuator line model has been employed together with the large eddy simulation approach for predicting the turbulence effects. This model was implemented by using the open‐source computational fluid dynamics toolbox OpenFOAM. Results show a better performance for the dual turbine concept. Under same operating conditions, the aerodynamic power of each turbine within the dual concept is higher than the power of the stand alone turbine, particularly at lower operating wind speeds (approximately 2% to 3% of extra power per turbine). Comparison between the two configurations shows similar character of the tangential and normal forces acting on the blades in terms of magnitude and fluctuation, eliminating potential concerns regarding fatigue and blade design. The largest difference in the tangential and normal root bending moments are approximately 3% and 2%, respectively, between single and dual turbine configurations. Finally, wake recovery analysis shows a downwind velocity deficit that is not enhanced streamwise in the dual turbine configuration with no considerable difference after 7 .

Hindered thermal warping triggers tensile cracking in the cores of compressed columns of a fire-loaded tunnel segment structure: Efficiency and accuracy of beam theory prediction, compared to FEM

The nonlinear Finite Element Method (FEM) is the current gold standard for the thermo-mechanical analysis of reinforced concrete structures. As an alternative, this paper is devoted to a model reduction strategy which reduces the CPU time by a factor of 500. This strategy combines Fourier series-based solutions for the thermal conduction problem, and thermo-elastic Timoshenko beam theory. Temperature histories known to be relevant for fire accidents enter series solutions quantifying the conduction of heat into a closed cell frame consisting of slabs, walls, and columns. Corresponding temperature profiles are translated into thermal eigenstrains. The latter are represented as the sum of three portions: (i) their cross-sectional averages (called thermal eigenstretches); (ii) their cross-sectional moments (called thermal eigencurvatures); and (iii) the remaining eigenstrain distributions (called eigenwarping). The latter portion is hindered at the cross-sectional scale, giving rise to non-linearly distributed self-equilibrated thermal stresses. The eigenstretches and eigencurvatures, in turn, are constrained at the scale of the frame structure. Together with external mechanical loads, they enter the exact solutions of thermo-elastic Timoshenko beam theory with equivalent cross-sections accounting for the different material properties of concrete and steel. Axial normal stresses, quantified from beam-theory-related normal forces and bending moments, are superimposed with the hindered-warping-induced stresses. These stresses agree well with corresponding results obtained by the nonlinear FEM. As regards the load carrying behavior of the columns, excessive thermal tensile strains at the periphery of the columns trigger, in the core of the columns, large tensile stresses which even exceed the strength of concrete. Respective cracking events are considered through reduced effective columnar cross-sections. Right after initiation of cracking, around 12min after the start of the heating process, the cracks propagate for some 30sec quite rapidly, and very much slower thereafter. If the initial cross-sections of the columns are increased, more pronounced hindered thermal warping, together with less quickly evolving compressive forces, results in earlier cracking. Overall, it is concluded that tensile cracking is the key material non-linearity, at least during the first 30min of the fire test, with maximum temperatures up to 300°C.

Identification of deformed configurations of segmental tunnel rings based on measured convergences

If convergences grow so large that the serviceability of a tubbing ring is lost, remedial measures must be taken. In this context, it is useful to reconstruct the displacement history of the tunnel ring in order to gain insight into the evolution of the structural behavior that has led to the current configuration. This challenge is tackled with the help of measured convergences and rigid body kinematics. The latter are sufficient, because the deformations of tubbings, resulting from normal forces and bending moments, do not contribute significantly to the displacements of segmental rings. The analysis is focused on convergences measured during a real-scale test of a symmetric tunnel ring. It consists of six tubbings and has three kinematic degrees of freedom. Deformed configurations are reproduced by optimizing the three scalar components of one symmetric and two antisymmetric modes of rigid body displacements. This problem is under-determined, because convergences are routinely measured in two directions only. Its solution is obtained in two steps. At first, the component of the symmetric mode of rigid body displacements is identified such that the measured convergences are reproduced in the best-possible fashion. Thereafter, the remaining differences between measured and modeled convergences are reduced to zero by optimizing the components of the two antisymmetric modes. This kind of structural analysis starts with the most recent set of measured convergences. It proceeds, in a step-by-step manner backwards in time to older sets of monitored data. It is shown that the developed method allows for a satisfactory reproduction of the displacement history of the tested tubbing ring, making use of measured vertical and horizontal convergences. The obtained visualization of the displacement history of the entire tunnel ring provides more insight into the structural behavior than diagrams showing only the evolution of single convergences.

Singularities at interface corners of piezoelectric-brass unimorphs

Abstract In this study, singularity fields at the interface corners of piezoelectric-brass unimorphs are investigated. Two models differing in side surface geometry (step and flat surfaces) are analyzed to study the singularity effect on mechanical (stress–strain) and electrical (electric potential and intensity) behavior. A mixed-mode mechanical boundary condition is applied for analyzing the realistic application of unimorphs, with normal force, shear force, and bending moment as internal forces. The conservative integral together with a three-dimensional finite element analysis is used to determine the intensity of singularity. There are three singularity terms at each vertex and singular line. All singularity terms are investigated in detail. Intensities of the singularities at the vertex and several points located on side surfaces (singular lines) are examined. Results show that the intensities of singularities for mixed-mode conditions differ from that of tensile load conditions. For mixed-mode conditions, the intensity of singularity must be calculated for all singularity terms. In addition, the stress singularity characteristics at the vertex may be described as a function of the singularities along the singular lines. These findings clarify the understanding of singularity at interface corners of piezoelectric-brass unimorphs and may be used as references for developing relevant piezoelectric devices.

Numerical analyses of twin stacked mechanized tunnels in soft grounds – Influence of their position and construction procedure

Twin stacked tunnels become more and more common due to the limited surface area and underground space. Most researchers have already paid attention separately to the influence of the twin stacked tunnels’ position and construction sequence. However, the influence of the lagging distance and pillar depth of twin stacked tunnels has not yet been fully investigated when considering the tunnels construction sequence. The present study aims at analysing the effect of the construction sequence, pillar depth between tunnels, and lagging distance between stacked tunnels’ faces on the structural forces induced in the tunnel linings and on the surface settlements. For this purpose a three-dimensional (3D) numerical model was developed using the finite difference element code FLAC3D. Most of the parameters of the slurry-type shield machine were simulated. The analyses included the influence of the face support pressure, shield conicity, shield weight, grouting pressure, harden grout, jacking forces, the weight of the backup train and jointed segmental lining. The results indicated that the most critical scenario, both in terms of ground settlement and internal forces in the tunnel lining is when the upper tunnel (UT) is excavated first and followed by the lower tunnel (LT) excavation. On the other hand, the following upper tunnel should be excavated at a lagging distance, which is larger by about 4 to 5 times the tunnel diameter behind the preceding lower tunnel. The research results reviled that designing a too small pillar depth between stacked tunnels should be avoided. This concerns pillar depths of about 0.25 to 0.5 times the tunnel diameter, as indicated in this study. It could cause a great increment in the normal displacements, longitudinal forces, and bending moments in the lower tunnel lining.

Buckling failure mechanism of liner pipe in bimetal mechanical clad pipe under complex loading

Bimetal mechanical clad pipe is one of the main measures for anti-corrosion control adopted in oil and gas fields. The liner pipe failure is a key problem that restricting the clad pipe applications. In this paper, a calculation model of clad pipe is established, and the buckling failure of liner pipe under complex loading was investigated. Effects of forming process, working pressure, external environmental loading and structural parameters on the failure mode of liner pipe were studied. The results show that increasing the residual contact pressure in the forming process is helpful to improve the buckling resistance of the liner pipe. The residual stress between liner and outer pipes can make the clad pipes bear a larger bending loads and have a larger critical curvature. Buckling mode “8” of the liner pipe occurs under complex loading. A larger working pressure can reduce the buckling degree and fold amplitude of the liner pipe. The liner pipe is more resistant to buckling in shallow water than in deep water. With the increasing of the wall thickness for liner and outer pipes, buckling resistance of the liner pipe becomes stronger. Finally, prediction formulas for critical curvature and the maximum normalized bending moment of the clad pipe are presented. The research results can provide a theoretical basis for the design, manufacture, and safety evaluation of clad pipe.

Effect of Axial Normal Stress and Bending Moment between Contact and Non-Contact Zone on Forming Accuracy for Flexible Stretch Bending Formation

Flexible 3D stretch bending (FSB) is a technology that uses multi-point molds instead of traditional integral molds to bend and deform profiles. Since the position of a multi-point mold can be adjusted in the horizontal and vertical directions, a set of molds can be used to form profile products with different contour structures. Due to the contact area and non-contact area between the multi-point mold and the surface of the profile, the forming accuracy of different areas is different. Thus, the axial normal stress and bending moment of the contact zone and non-contact zone between the profile and roller dies are studied in this article. By simulating the change in axial normal stress at the same position in the middle of a web along the axial direction, it is found that the axial normal stress shows little difference in the contact zone and non-contact zone. The value of axial normal stress in the non-contact zone is relatively stable, and there is a small increase on the side near the clamp. By simulating the axial normal stress of different cross-sections in the middle areas of three groups of webs, it is found that there is a linear relationship between the axial normal stress and the distance from inner curved surface. The bending moment of the profile in the contact zone is obviously greater than that in the non-contact zone, and the bending moment gradually decreases to near zero from the contact zone to the non-contact zone. The bending deformation of the profile in the contact zone is obviously greater than that in the non-contact zone, which results in the deviation between simulated bending displacement and theoretical bending displacement in the contact zone and non-contact zone.

Shafts with U-shaped circumferential grooves: design charts for stress concentration factors, radial displacement and Poisson’s ratio influence

Shafts with U-shaped circumferential grooves subjected to internal normal force and bending moment are investigated on the basis of finite element analysis. The classical problem of the stress concentration factors (SCFs) identification is addressed. SCF charts are provided, adopting the maximum equivalent von Mises stress in the SCF definition. The discrepancy between the uniaxial SCFs extracted from the standard reference books and the multiaxial SCF obtained by finite element increases from 5% up to 20%. The intersections between the SCF curves are studied, which reveal a non-monotonic profile of the SCFs with respect to the outer and inner diameter ratio of the notched shaft. The radial displacement at the notch root is examined and design charts of ample validity and prompt access are compiled. It is found that the radial displacement sign and magnitude are largely dependent on the geometry of the notch. Furthermore, the strain and stress state of extremely shallow grooves are analysed, and a critical discussion on their SCFs using the von Mises criterion is presented. The influence of Poisson’s ratio is considered. A simplified method for the evaluation of a multiaxial SCF is proposed to account for the Poisson’s ratio effect. Thanks to the employment of few dedicated diagrams, and the present method allows an accurate evaluation of the SCF for U-grooved shafts, when Poisson’s ratio differs from the common 0.3 value.

Cross-Sectional Analysis of the Resistance of RC Members Subjected to Bending with/without Axial Force.

This paper deals with the cross-sectional analysis of the resistance of RC members subjected to a bending moment with or without axial forces. To determine section resistance, the nonlinear material law for concrete in compression is assumed according to Eurocode 2, taking into account the effect of concrete softening. It adequately describes the concrete behavior of RC members up to failure. The idealized stress–strain relation for the reinforcing steel is assumed. For the ring cross-section subjected to bending with axial force and for areas weakened by an opening, normalized resistances have been derived by integrating corresponding equilibrium equations. They are presented in the form of interaction curves and compared with the results of testing conducted on RC eccentrically loaded columns. Furthermore, the ultimate normalized bending moment has been derived for the RC rectangle subjected to bending without axial force. It was applied to the cross-sectional analysis of steel and concrete composite beams consisting of the RC rectangular core located inside a reversed TT-welded profile. Comparative analysis indicated good agreements between the proposed section models and experimental data. The objective of the paper is the dimensioning optimization of the considered cross-sections with the fulfillment of structural safety requirements.

Transverse Wave Propagation in a Thin Isotropic Plate Part I

This article deals with the propagation of a transverse wave in a thin rectangular isotropic plate, which is fixed around the perimeter. The transverse wave is generated by an impact falling on the geometric center of the plate. The solution is performed analytically in the MATLAB software environment for Kirchhoff and Rayleigh geometric models and Hooke’s model. The introduction to the article outlines a very brief history of the solution, followed by a general analytical solution. The basic relations for displacements and velocities in the direction of the x, y, z axes are derived. Under the defined assumptions, the deformations in the individual axes and the rotation of the axes are also solved. Part of the general solution is the derivation of relations for normal and shear stresses, as well as the magnitudes of shear and normal forces and bending moments. Attention is also paid to determining the relationships for different types of excitation loads of the board. The relations for Kirchhoff’s and Rayleigh’s model are derived, as well as the results of the analytical solution at selected points of the plate. A comparison of the results of the solution of both models, i.e., Kirchhoff’s and Rayleigh’s, is performed, both in terms of displacements, velocities, and normal stresses.

On the Formulation of an Elastic-Plastic Beam Model: the Pre-Integration Idea

This paper provides a formulation of an elastic-plastic beam model. The constitutive behaviour of material after elasticity limit is considered perfect plastic. Although this is not a general plastic behaviour, it allows to minimize mathematical difficulties to fulfil the idea: pre-integration trough the thickness extended to material non-linearity. Three types of deformation mechanisms are found: fully elastic, plasticization over only one side or both of sides. The complete kinematic set of equations are obtained, together with the analytical stress trends. Yield stress-continuity equations are used to separate the elastic and plastic domains. These domains define a quasi-state diagram; Allowing to associate the normal force and bending moment acting on the section to the elastic-plastic state within the section. Note that in the case of a rectangular section, the solution is given in a fully analytical form, otherwise the domains are solved numerical solutions. But these last, may be obtained once for all, for any one-symmetrical section.

M-N interaction curves for rectangular concrete-filled steel tube columns subjected to uniaxial bending moments

abstract: In this paper, a computational code was developed to obtain M-N interaction curves for rectangular concrete-filled steel tube columns considering the strain compatibility in the cross-section. Considering the composite section subjected to uniaxial bending moments, expressions were developed to determine normal force, moment resistance, neutral axis depth and components resistance of cross-section. Such expressions were implemented in a computational tool developed to the authors and that allows to obtain the M-N pairs of strength. The steel and concrete ultimate strains were defined with the aid of the Brazilian standard for reinforced concrete structures ABNT NBR 6118. The obtained results were compared to simplified curves defined according to the theoretical models of ABNT NBR 8800, ABNT NBR 16239, EN 1994-1-1 and literature data. The proposed model showed good agreement with literature results and had good precision to estimate the ultimate moment values. To further understand the resistance of composite columns under uniaxial bending moments, parametric study was performed to evaluate the influence of the compressive strength of concrete, yielding strength of steel and steel area ratio on M-N interaction curves. The results indicate that the yielding strength of steel and the steel area ratio were the variables that most influenced the values of composite columns resistance (normal force and bending moment).

ANALYSIS OF THE COMBINED STRUCTURE OF THE SHAFT OF THE DNIPRO METRO BY THE FINITE ELEMENTS METHOD

Purpose. The development of construction of underground excavations of the Dnipro Metro requires analysis and scientific substantiation of design solutions based on technologies that are new for Ukraine. The aim of the scientific article is to analyze the combined design of the shaft of the Dnipro Metro by the finite element method with determination of force factors in the linings of the pile system and shotcrete system with further substantiation based on the results of design solutions to the real situation of Dnipro Metro construction. Methodology. Two finite element models were constructed for the analysis of the shaft № 1 of the Dnipro Metro by the finite element method. They reflect the combined design of the shaft, which consists of two parts. The finite-element model of the pile system, which reflects the shell of bored piles, supported by a cap beam and ring beams, is analyzed separately. The model for the shotcrete system, which is used for the second part of the shaft, which lies in a solid rock mass, is separately modeled and analyzed. Finite-element models of both systems are assigned real deformation and geometric parameters, as well as the load, which became the key to adequate calculations by the finite element method. Findings. During the numerical analysis of the combined structure of the shaft № 1 of Dnipro Metro, the force factors (normal forces and bending moments) for the pile system and the shotcrete system were determined. These results became the basis for the reinforcement of both systems. Originality. A numerical analysis of the shaft structure was performed, which provided a complete picture of the force factors that allow predicting the appearance of normal forces and bending moments in similar engineering and geological conditions. Practical value. The results of the analysis of the combined design of the shaft of the Dnipro Metro by the finite element method allowed to scientifically substantiate the design solutions and ensure high performance of both shaft systems № 1.

JUSTIFICATION OF THE STRESS-STRAIN STATE OF THE PILE FOUNDATION USING SOFTWARE COMPLEXES

Purpose. Bridge supports with a high pile caps require more attention when calculating their strength due to the difficult operating conditions of the piles. The purpose of the scientific article is to substantiate the stress-strain state of the pile foundation of the bridge structure using software computing systems SCAD and LIRA-CAD. Methodology. An analysis of software used to automate the design of foundations was conducted. The main parameters of SCAD and LIRA-CAD software packages are yielded. With their help, finite-element models of the pile foundation of the bridge support with a high pile cap were built. The developed models maximally reflect the properties of the soil base and foundation, its pile cap and piles, geometric characteristics and the influence of the finite elements meshing is considered. Calculations were performed in SCAD and LIRA-CAD software packages with monitoring of the calculation process. Findings. During the numerical analysis of the pile foundation of the bridge structure with a high pile cap, vertical displacements, force factors (normal forces and bending moments) in the piles and stresses in the body of the support and piles were determined. Based on these results, an analysis was performed, which is combined with a comparison of the obtained results. Implementation of SCAD and LIRA-CAD software allows to significantly reduce design time, to reduce project costs, to improve the quality and efficiency of investments. Originality. A comparison of the stress-strain state obtained during the numerical analysis of SCAD and LIRA-CAD software, which proved the difference in the approach to modeling in these complexes, was conducted. Practical value. The results of substantiation of the stress-strain state of the pile foundation with the use of software complexes made it possible to verify the design solution of all elements of the foundation of the bridge structure with a high pile cap.