Computational modelling of mechanical response of glulam beams due to moisture inducted delamination

Glued laminated timber beams are nowadays used as load-bearing beams of large-span structures that operate in various humidity conditions. Typical application areas are aqua parks with high humidity as well as market halls with low humidity. It is related to the possibility of the occurrence of cracks typical for the drying of wood, even with such controlled conditions of production technology as glued laminated timber. Cracks visible on the used girders raise doubts as to the safe operation of the structures. The subject of this paper is the computational simulation and the evaluation of the influence of beam delamination on the mechanical response of the structure. The attention was established on a typical two-span beam of constant height with a slight slope to the horizontal. The numerical analysis was carried out for three variants of the location of potential delamination of different scope. The beams were modeled as a problem of the linear theory of elasticity in a plane stress state with orthotropic material properties. The calculations were made in the Abaqus software environment. The results obtained in the paper allow to determine the areas in which the presence of delamination or cracks should be considered dangerous from the point of view of the safety of operation. Computational analysis is helpful in assessing the safety of structures where cracks appear. Theoretical considerations are supplemented by an example from engineering practice.

An Integrated Approach to the Optimization of Plates in Plane Stress State Operated at High Temperatures

Many critical elements of building and machine-building structures during their operation are in difficult operating conditions (high temperature, aggressive environment, etc.). In this case, they can be subject to a double effect: corrosion and material damage. Corrosion leads to a decrease in the cross-section of a structure, resulting in stress increase therein. In turn, damage to the material is accompanied by the appearance of microcracks and voids therein, due to inelastic deformation (creep), leading to a deterioration in its physical properties (for example, the elastic modulus) and a sharp decrease in the stress values at which the structure is destroyed. This article continues the study in the field of the optimal design of structures subject to the aforementioned double effect by the example of the optimization of plates with holes in the plane stress state, exposed to high temperatures (in previous works, the use of this approach was demonstrated in the optimization of the bending elements of rectangular and I-sections). Used as a corrosion equation is the modified Dolinsky mode, which takes into account the (additional) effect of the protective properties of an anticorrosive coating on the corrosion kinetics. Taken as a kinetic equation describing the change in material damage, is Yu. N. Rabotnov’s model, which enables to determine the duration of the incubation period of the beginning of the tangible process of material damage. To study the stress state of a plate, the finite element method is used. With a given contour of the plate, found is the optimal distribution of the thickness of the finite elements into which the given plate is divided. Acting as a constraint of the optimization problem is the parameter of damage to the plate material. The approach proposed in this work can be used to solve similar problems of the optimal design of structures operating under conditions of corrosion and material damage, using both analytical solutions and numerical methods.

Structural Efficiency of Hollow Reinforced Concrete Beams Subjected to Partial Uniformly Distributed Loading

Reinforced concrete (RC) beams containing a longitudinal cavity have become an innovative development and advantage for economic purposes of light-weight members without largely affecting their resistance against the applied loads. This type of openings can also be used for maintenance purposes and usage space of communication lines, pipelines, etc. RC beams are primarily loaded in the plane of the members, which are two-dimensional in a plane stress state and the dominant structural behaviours include bending, shear, or combination of both. In the present study, six numerical models of RC beams with and without openings were simulated by using commercial finite element software ANSYS to evaluate the structural behaviours of those beam models under the partial uniformly distributed load. Different parameters were assessed, including opening dimensions and shear reinforcement ratios. The obtained numerical results were analysed and verified and were found very close to those obtained from the experimental investigations in the literature. The increase of shear reinforcement ratio could enhance the flexural and shear capacities of the RC beams, and the results also showed that some models sustained flexural failure while the others sustained failure of combined bending and shear.

Analytical Solution of the Problem of Symmetric Thermally Stressed State of Thick Plates Based on the 3D Elasticity Theory

An important place among thermoelasticity problems is occupied by the plane elasticity problem obtained from the general three-dimensional problem after using plane stress state hypotheses for thin plates. In the two-dimensional formulation, this problem has become widespread in the study of the effect of temperature loads on the stress state of thin thermosensitive plates. The article proposes a general three-dimensional solution of the static problem of thermoelasticity in a form convenient for practical application. To construct it, a particular solution of the inhomogeneous equation, the thermoelastic displacement potential, was added by us to the general solution of Lamé's equations, the latter solution having been previously found by us in terms of three harmonic functions. It is shown that the use of the proposed solution allows one to satisfy the relation between the static three-dimensional theory of thermoelasticity and boundary conditions, and also to construct a closed system of partial differential equations for the introduced two-dimensional functions without using hypotheses about the plane stress state of a plate. The thermoelastic stress state of a thick or thin plate is divided into two parts. The first part takes into account the thermal effects caused by external heating and internal heat sources, while the second one is determined by a symmetrical force load. The thermoelastic stresses are expressed in terms of deformations and known temperature. A three-dimensional thermoelastic stress-strain state representation is used and the zero boundary conditions on the outer flat surfaces of the plate are precisely satisfied. This allows us to show that the introduced two-dimensional functions will be harmonic. After integrating along the thickness of the plate along the normal to the median surface, normal and shear efforts are expressed in terms of three unknown two-dimensional functions. The three-dimensional stress state of a symmetrically loaded thermosensitive plate was simplified to the two-dimensional state. For this purpose, we used only the hypothesis that the normal stresses perpendicular to the median surface are insignificant in comparison with the longitudinal and transverse ones. Displacements and stresses in the plate are expressed in terms of two two-dimensional harmonic functions and a particular solution, which is determined by a given temperature on the surfaces of the plate. The introduced harmonic functions are determined from the boundary conditions on the side surface of the thick plate. The proposed technique allows the solution of three-dimensional boundary value problems for thick thermosensitive plates to be reduced to a two-dimensional case.

Determination of the Shear Modulus of Pine Wood with the Arcan Test and Digital Image Correlation

Arcan shear tests with digital image correlation were used to evaluate the shear modulus and shear stress–strain diagrams in the plane defined by two principal axes of the material orthotropy. Two different orientation of the grain direction as compared to the direction of the shear force in specimens were considered: perpendicular and parallel shear. Two different ways were used to obtain the elastic properties based on the digital image correlation (DIC) results from the full-field measurement and from the virtual strain gauges with the linear strains: perpendicular to each other and directed at the angle of π/4 to the shearing load. In addition, the own continuum structural model for the failure analysis in the experimental tests was used. Constitutive relationships of the model were established in the framework of the mathematical multi-surface elastoplasticity for the plane stress state. The numerical simulations done by the finite element program after implementation of the model demonstrated the failure mechanisms from the experimental tests.

A Plane Stress Failure Criterion for Inorganically-Bound Core Materials

Inorganically-bound core materials are used in foundries in high quantities. However, there is no validated mechanical failure criterion, which allows performing finite-element calculations on the core geometries, yet. With finite-element simulations, the cores could be optimised for various production processes from robotic core handling to the decoring process after the casting. To identify a failure criterion, we propose testing methods, that enable us to investigate the fracture behaviour of inorganically-bound core materials. These novel testing methods induce multiple bi-axial stress states into the specimens and are developed for cohesive frictional materials in general and for sand cores in particular. This allows validating failure criteria in principal stress space. We found that a Mohr-Coulomb model describes the fracture of inorganic core materials in a plane stress state quite accurately and adapted it to a failure criterion, which combines the Mohr-Coulomb model with the Weakest-Link theory in one consistent mechanical material model. This novel material model has been successfully utilised to predict the fracture force of a Brazilian test. This prediction is based on the stress fields of a finite element method (FEM) calculation.

Calculation of Stress-Strain State and Contact Stresses in the Process of Chip Formation

The reported paper presents a field pattern of sliding lines in a plastic zone of flow chip formation in the process of cutting metals considered for front and rear angles on the cutting blade other than zero. Equations of sliding lines for these conditions are proposed. Using calculation data, plasticity zone border lines are plotted for positive and negative front angles. The paper suggests methods and calculation data on average stress and plane stress state components in nodal points of the plastic zone of chip formation. The study provides data for plotting distribution diagrams of normal and tangential stresses of contact stresses on work surfaces of a cutting blade.

MODERN STRENGTH CRITERIA FOR CONCRETE UNDER TRIAXIAL STRESS STATES

Reliable assessment of the strength and deformations of concrete under multiaxial stress states is important for increasing the accuracy of analysis and design. Classical strength theories do not work for such materials as concrete due to the complex shear-pryout mechanism of its structural failure. Description of the key relations of strength criteria established by G.A. Geniev, G.A. Geniev – N.M. Alikova, E.S. Leites, A.V. Yashin, S.F. Klovanich – D.I. Bezushko, K.J. Willam – E.P. Warnke and N.I. Karpenko is given. Assessment of the compliance of the design strength with the experimental data under uni-, bi- and triaxial stress states is made. Strength criteria that most closely describe the experimental data in the specific areas of the stress state are determined. It has been found out that the most developed strength conditions are the ones developed by S.F. Klovanich – D.I. Bezushko, K.J. Willam – E.P. Warnke and N.I. Karpenko. The criteria introduced by E.S. Leites and A.V. Yashin describe the experimental data under conditions of the plane stress state with sufficient accuracy. The strength conditions established by G.A. Geniev and G.A. Geniev – N.M. Alikova require careful use, taking into account their deviations from the experimental data in certain areas of triaxial stress states. Loading programs in the process of experimental research of concrete strength aimed at identifying the forms of functions of meridional and deviatoric curves more accurately have been determined.