Bearing Capacity near Support Areas of Continuous Reinforced Concrete Beams and High Grillages

This work presents a proposed engineering method for calculating the bearing capacity of the supporting sections of continuous monolithic reinforced concrete tape beams, which combine pressed or driven reinforced concrete piles into a single foundation design. According to the mechanics of reinforced concrete, it is recommended to consider the grillage to be a continuous reinforced concrete beam, which, as a rule, collapses according to the punching scheme above the middle support (pile caps), with the possible formation of a plastic hinge above it. The justification for the proposed method included the results of experimental studies, comparisons of the experimental tensile shear force with the results of calculations according to the design standards of developed countries, and modeling of the stress-strain state of the continuous beam grillage in the extreme span and above the middle support-pile adverse transverse load in the form of concentrated forces. The work is important, as it reveals the physical essence of the phenomenon and significantly clarifies the physical model of the operation of inclined sections over the middle support. The authors assessed the influence of design factors in continuous research elements, and on the basis of this, the work of the investigated elements under a transverse load was simulated in the Lira-Sapr PC to clarify the stress-strain state and confirm the scheme of their destruction adopted in the physical model by the finite element method in nonlinear formulation. Based on the analysis and comparison of the experimental and simulation results, a design model was proposed for bearing capacity near the supporting sections of continuous reinforced concrete beams and high grillages that is capable of adequately determining their strength.

Evaluation of crack resistance of welded joints with soft interlayers

Introduction. Welded joints in large-sized metal structures (e.g., in the structures of ship hulls) subject to low-cycle fatigue are considered. The characteristic appearance of soft interlayers, which are significantly plastically deformed under working loads, was noted. Deformation of the metal structure with damage, especially in the form of cracks, reduces the strength and reliability of structural elements and joints. Pre-deformation negatively affects plasticity; therefore, much depends on the residual plasticity of the cracking material. At the same time, with a decrease in residual plasticity, such an important reliability indicator as the resistance of the material to crack propagation — the fracture toughness – decreases. The paper is devoted to the development of a model that includes analytical dependences for assessing the crack resistance of metal structures and their welded joints with soft interlayers according to the crack resistance limit for all crack sizes.Materials and Methods. The theory and methods of linear mechanics of materials destruction, structural-mechanical approach are used. The calculation results were analyzed and compared to the experimental data and other analytical solutions. The numerical experiment was performed for the ferrite-perlite steel grades of 10, 50, 22K, St3sp, etc., widely used in industry, as well as for alloy steels hardened to medium and high strength of 30KhGSA, 37KhN3A, etc. Results. Analytical dependences are obtained for calculating the relative crack resistance limit according to three main known mechanical characteristics of the state of the material of the soft interlayer of the welded joint.Discussion and Conclusions. The results obtained can be used to assess the crack resistance of pre-deformed structural elements and welded joints (including those with soft interlayers) operating under a transverse load. The results of experimental data and analytical calculations are shown in dimensionless form, which enables to obtain invariant results with respect to the fracture toughness limit.

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

APPLICATION OF ANALYTICAL SOLUTIONS FOR BENDING BEAMS IN THE METHOD OF MOVEMENT

Introduction: Usually, to analyze statically indeterminate rod systems, the classical displacement method and preprepared tables for two types of rods of the main system are used. A mathematically correct representation of local loads with the use of generalized functions makes it possible to find an accurate solution of the differential equation for the equilibrium of a beam exposed to an arbitrary transverse load. Purpose of the study: We aimed to obtain analytical expressions for functions of deflection, rotation angles, transverse forces, and bending moments depending on four types of local loads for beams with different boundary conditions, so as to apply accurate solutions in the displacement method. Methods: We propose an analytical form of the displacement method to analyze rod structural models. For beams exposed to different types of transverse load (uniformly distributed force, concentrated force, or a couple of forces), accurate analytical solutions were obtained for functions of deflection, bending moments, and transverse forces at different types of beam ends’ restraint. This is possible due to the fact that concentrated load and load in the form of the moment of force can be specified by using unit column functions. By transforming Mohr’s integrals, using integration by parts, we show that the system of canonical equations of the displacement method was obtained based on the Lagrange principle. Results: Based on the analysis of a statically indeterminate frame, the effectiveness of the proposed analytical method is shown as compared with the classical displacement method.

Novel 2D strain-rate-dependent lamina-based and RVE/phase-based progressive fatigue damage criteria for randomly loaded multi-layer fiber-reinforced composites

Two implicit progressive fatigue damage models that rely on new equivalent-damage and equivalent-stress criteria are presented for the prediction of various failure modes of the composites. The criteria are coupled with lamina-based and representative-volume-element-based damage progression approaches. The common concepts of residual strength and residual stiffness are revisited and modified. A fatigue life assessment algorithm that incorporates the strain-rate-dependence of the fatigue strengths and stiffnesses, and random and asynchronous changes of the stress components, distinct mean values, and phase shifts of the stress components is employed. New ideas and new post-processing procedures are employed in the current research. It is the first time that the significant impacts of the strain-rate-dependence of the properties of the composites on stress and fatigue life analyses are investigated. Results of the proposed fatigue criteria are first implemented to a composite plate with a complex lamination scheme under a random transverse load and the predicted fatigue lives are verified by the experimental results. Then, these criteria are implemented to a composite chassis frame of an SUV car under realistic random road inputs and the theoretical results are verified by the experimental results. Results confirm the significant role of the strain-rate-dependence effects on the fatigue lives.

Bending of a ship's skin panel loaded along the axis of symmetry

Задача изгиба прямоугольной панели обшивки от действия распределенной по оси симметрии поперечной нагрузки не имеет точного решения в конечном виде в виду сложности краевых условий и вида нагрузки. Использование другими авторами различных приближенных методов оставляет открытым вопрос о точности полученных результатов. Целью исследования является получение точного решения с помощью гиперболо-тригонометрических рядов по двум координатам. Для этого используется метод бесконечной суперпозиции указанных рядов, которые в отдельности удовлетворят лишь части граничных условий. Порождаемые ими невязки взаимно компенсируются в ходе итерационного процесса и стремятся к нулю. Частное решения представлено двойным рядом Фурье. Точное решение достигается увеличением количества членов в рядах и числа итераций. При достижении заданной точности процесс прекращается. Получены численные результаты для прогибов и изгибающих моментов для квадратной пластины при различной длине загруженной части оси пластины. Представлены 3D-формы изогнутой поверхности пластины и эпюры изгибающих моментов. The problem of bending a rectangular skin panel from the action of a transverse load distributed along the axis of symmetry does not have an exact solution in the final form due to the complexity of the boundary conditions and the type of load. The use of various approximate methods by other authors leaves open the question of the accuracy of the results obtained. The aim of the study is to obtain an exact solution using hyperbolo-trigonometric series in two coordinates. To do this, we use the method of infinite superposition of these series, which individually satisfy only part of the boundary conditions. The residuals generated by them are mutually compensated during the iterative process and tend to zero. The quotient of the solution is represented by a double Fourier series. The exact solution is achieved by increasing the number of terms in the series and the number of iterations. When the specified accuracy is reached, the process stops. Numerical results are obtained for deflections and bending moments for a square plate with different lengths of the loaded part of the plate axis. 3D shapes of the curved surface of the plate and diagrams of bending moments are presented.

A mechanical model to determine upheaval buckling of buried submarine pipelines

Thermal loads in submarine pipelines generate an axial compressive load that can force the pipeline to buckle, leading to failure if these loads are not considered in the design. Buried pipes are constraint to displacements in all directions, which leads to a high compressive load in the longitudinal axis and makes the pipes more vulnerable to buckling. If buried pipes under thermal loads do not buckle, a high-stresses state takes place when it is combined with high-pressure conditions. In this work, a simple mechanical model to determine the axial buckling load of a buried pipeline is proposed. The model is based on a simply supported beam subjected to a distributed transverse load representing the soil uplift resistance obtained from a referenced model, and an axial compressive load that represents the effective axial force and is computed according to the DNV-RP-F110. Additionally, the pipe–soil system is analyzed through a non-linear finite element model to compare the results with the analytical solution. The proposed simple mechanical model can capture the upheaval buckling behavior and provides results that are consistent with the numerical analysis, specifically for the two main parameters evaluated, namely, the initial pipe curvature and the magnitude of the transverse load.