Deformation Diagrams Research Articles

ЕКСПЕРИМЕНТАЛЬНІ ДОСЛІДЖЕННЯ СУЦІЛЬНОЇ ДЕРЕВИНИ КОНСТРУКЦІЙНИХ РОЗМІРІВ З ВРАХУВАННЯМ ФАКТОРА ВОЛОГОСТІ

2National University of Water and Environmental Engineering, Rivne Materials, elements and structures made of wood can be operated in environments with different humidity. Humidity of wood directly affects its strength and deformable properties. The works of domestic and foreign authors who studied the effect of moisture on the strength and deformability of wood of different species were analyzed in detail. It turned out that there are very few such works. According to these works, it is difficult to detect the effect of moisty on the basic physical and mechanical properties of wood. And they usually concerned the testing of wood under a soft load regime, which does not fully reflect their real stress-strain state. We have developed a method of experimental studies of various deciduous (birch, alder, ash) and coniferous (larch, pine, spruce) compression along the fibers with a single short-term load under a rigid test mode (by increasing the displacement of the press plate) with different moisture (30%, 21% , 12%). The age of all wood samples was 60 years. Section of prisms 30x30x120mm and grades of wood without defects and damages. The total number of tested samples - 126 pcs. After conducting experimental research and processing the results, complete diagrams of deformation of wood σ-u deciduous (birch, alder, ash) and coniferous (larch, pine, spruce) wood species from the beginning of loading and to the point of ultimate deformation, respectively, at a moisty of 30% , 21%, 12%. For the first time, critical deformations of different wood species at the corresponding maximum stress at different moisty were obtained experimentally. It was found that with a decrease in moisty from 30% to 12%, the strength of wood of all species increases. The critical deformations herewith are reduced.

Major Issues of Theory and Practice of Fire Resistance of Reinforced Concrete Structures and Buildings

The basic problems of the theory such as principle of assigning classes of fire resistance, reliability issues, alternative approach to calculation methods, mathematical models of concrete and reinforcement deformation diagram, numerical modelling techniques, temperature analysis and calculation of mechanical work of structural system in fire conditions have been considered. It is revealed that the real practical problem is the lack of professional training of civil engineers in Ukraine and abroad.

To the calculation of reinforced concrete flexible elements with combined pre-stress, taking into account the complete diagrams of material deformation

The formulas for determining losses in pre-compressed high-strength reinforcement are given, as well as the condition for closing the initial technological cracks in bent elements with pre-compressed reinforcement necessary for calculating the reinforced concrete beams with pre-compressed and stretched high-strength reinforcement

Research on the Application of an Information System in Monitoring the Dynamic Deformation of a High-Rise Building

With the acceleration of urbanization, there are increasingly more high-rise buildings in cities. In turn, high-rise building collapse accidents occur frequently. The causes of the danger, in addition to the extremely severe stress, are predominantly due to the long-term role of unstable factors, resulting in an unrecoverable internal structure. Therefore, it is advisable to monitor the dynamic deformation of buildings to prevent accidents. However, there is no particularly mature application system on the market to enable this monitoring, so our research group has carried out a long-term research in this field. This paper introduces the design of a set of practical information systems by using information technology and the principle of close-range photogrammetry. The system used the photographing scale transformation-time baseline parallax (PST-TBP) method to analyse image data collected with a digital camera, implement close-range photogrammetry, and input the image data into a computer. A building deformation diagram is obtained using our own software. The associated deformation curve can clearly reproduce the building deformation trend to monitor the building health. We conducted many laboratory simulation experiments to verify the information system, and the verification results prove that this process is rigorous. To apply this information system to a real-life scenario as soon as possible, we further studied its application to high-rise buildings, improved the system by using data and experience obtained by monitoring the tallest local building, and achieved good results. Finally, combined with the development of current intelligent technology, directions for system improvement are explored.

The effect of eccentricity on the strength characteristics of glued rods made of steel cable reinforcement in solid wood

The article is devoted to the study of the behavior of glued rods made of hot-rolled steel reinforcement and steel cables in a solid wood based on experimental tests of beam elements. The influence of eccentricity on the deformation - strength characteristics is studied with a straight-line gluing of reinforcing rods. The comparative analysis of the deformability indices of the centered and lateral gluing performed by milling with fillet groove U - shaped milling cutters was carried out. The technology of manufacturing samples, which consists of preparing wood, milling and pasting rebar into the groove, were described. The diagrams of deformation - strength characteristics of samples of various types were obtained and correlated. The conclusions were drawn about a local increase in strength in the case of using a steel cable as reinforcement and the negative effect of eccentricity on the strength of the adhesive joint during tensile tests. A visual analysis of the damage occurring during the test showed that in the manufacture of full-scale structures, glued rods should be closed with an array of wood. The conclusions were drawn about the optimal depth of milling of grooves for reinforcement, taking into account the use of adhesive compositions on epoxy resin filled with quartz sand - 1.5 depth of reinforcing bar diameter.

Mechanical Properties of a Basalt-Fiber-Reinforced Plastic Rod Used in Composite High-Voltage Wires in Torsion and Three-Point Bending

Results of experimental investigations into a unidirectional composite of basalt fibers and epoxy resin used as part of high-voltage electric wires are presented. Tensile tests of BFRP specimens previously held wrapped around a transportation drum during 10 h were carried out. The influence of the keeping time of the BFRP core in the composition of a high-voltage electric wire on drums of diameter 385 mm on the elastic, strength and deformation properties of the basalt plastic was evaluated. Tensile, three-point bending and torsion tests on the plastic with different static loads were carried out, and the corresponding deformation diagrams were obtained. The maximum torsion angle of BFRP specimens as a function of the axial load is determined. The results obtained can help one to analyze the operating modes of BFRP core in high-voltage electric wires and to get new data for their strength calculations.

Modified trilinear stress-strain diagram of concrete designed for calculation of beams with fiberglass rebar

An improved technique for determining the strength of reinforced beams with polymer composite reinforcement based on a nonlinear deformation model using a three-line diagram of concrete deformation under uniaxial compression with an elastic, elastic-plastic zone and a concrete softening zone is considered and proposed. The features of the strength analysis of beams with fiberglass reinforcement are revealed. The calculation method presented in this article allows us to minimize the use of empirical coefficients to determine the height of the compressed zone of concrete and at the same time does not lead to labor-intensive calculated dependencies. The method is based on the use of the Euler – Bernoulli beam theory and the use of physical stress-strain relations for concrete. This calculation method allows you to set accurately the height of the compressed zone of concrete, and accordingly the strength of the beam elements in the normal section. Good results of comparison with experimental data were obtained.

Stresses and Strains in a Disk of Physically Nonlinear Material with Stress State Dependent Properties

An analysis properties of the constitutive relations of the theory of deformation for physically nonlinear materials with properties depending on the type of stress state is carried out. These relations take into account two forms of nonlinearity, one of them is associated with the nonlinearity of the deformation diagrams and another one is associated with the change in these diagrams depending on the loading conditions. The distributions of stresses and strains in a rotating disk made of a material with properties sensitive to the type of stress state are investigated and a comparison with the results of calculations for a material with properties invariant to the form of external forces is performed.

TO DETERMINATION OF CRITICAL DEFORMATIONS OF CONIFEROUS AND DECIDUOUS TIMBER SPECIES

The article analyzes in detail the literary sources for determining the critical deformations of various hardwood and coniferous wood species by domestic and foreign scientists. By analyzing the works of different researchers, it was found that the critical deformations of pine wood were experimentally determined by Tuturin S.V. and Varenyk K.A. on samples of structural sizes of different sections in rigid test mode (by increments of displacements). It was also found that the critical deformations of wood were theoretically obtained by Grinkrug N.V. based on the analysis of experimental studies of different scientists. This dependence is empirical and depends only on the boundary stresses.For the first time, we have carried out detailed experimental studies of various conifers (larch, pine, spruce) and hardwood (birch, alder, ash) species of wood for compression along fibers under a single short-term load. Based on these studies, complete wood deformation diagrams were drawn and critical deformations of all the species studied were determined.A universal formula for theoretical determining of the critical deformations of any species of wood was also obtained. The convergence of our dependence and the function proposed by Grinkrug N.V. is carried out on the basis of experimental data of different authors. Our function has been found to have much better convergence. It was found that the main advantages of our dependence are: simplicity and convenience in calculations, it distinguishes two components (elastic and plastic), is not empirical, depends on the maximum tension and the initial modulus of elasticity; can be used for both coniferous and deciduous wood. And in the future it will be used for all kinds of calculations of elements and structures from wood.

Diagram of concrete dynamic deformation confined by CFRP jackets

A review of the current state of the issue of describing the deformation of columns confined by CFRP jackets under of dynamic loading is carried out. The insufficiency of the study of elements under the influence of axial dynamic load is indicated. The dynamic increase factors (DIF) for concrete and CFRP, which are obtained by the results of existing experiments, are substantiated. Using the principle of the invariance of the potential energy of deformation of concrete at the time of its destruction under regime loading, a formula is obtained for determining DIF for ultimate relative strain of unconfined concrete. Based on the assumption of the same law of concrete deformation under static and dynamic loading, was obtained a diagram of concrete dynamic deformation confined by CFRP jackets. The diagram is valid in the range of strain rates 10−3-102 s−1. A comparison is made between a static diagram and a dynamic diagram derived from it. The characteristic of the main sections of the diagram is given. An increase in the strength and ductility of confined concrete at the initial stage of loading is obtained. At stresses equal to the tensile strength of limited concrete, its ductility is somewhat reduced. It was revealed that a significant increase in the bearing capacity of confined concrete begins at strain rates of 10 s−1 or more.

Determination of the area of mechanical hysteresis loop using mathematical models

A method of the hysteresis loop relates to the direct methods for determination of the energy dissipation and studying the inelasticity in the material. The method is based on the direct formation of the mechanical hysteresis loop by static loading and unloading of the sample and measuring of the corresponding deformations. The relative energy dissipation is defined as the ratio of the hysteresis loop area to the elastic energy corresponding to the maximum amplitude of strain. Construction of the hysteresis loop is performed on the installation «torsional pendulum for determination of the mechanical properties of materials» which can work as a device for measuring internal energy dissipation by damped oscillations, and as a precision torsion test machine using a deforming device. The aim of this work is to determine the area of the static hysteresis loop through the choice of the mathematical models of loading and unloading curves with subsequent numerical integration using the ordinate values at equidistant points. The analysis of using polynomials of the second or third degree was carried out according to the criterion of the smallest sum of squared deviations between the empirical and calculated values of the function. The experimentally obtained coordinates of the points of the deformation diagram of the sample during loading and unloading were used as initial data for estimation of regression coefficients in polynomial equations. A distinctive feature of the proposed method is that analytical dependences between stresses and strains obtained by N. N. Davidenkov and containing hard-to-determine geometric parameters of the loop, which must be pre-set from the known values of the logarithmic decrement of oscillations obtained from the experiment are not used in the developed method to calculate the area of the static hysteresis loop. It is shown that a comparative assessment of the relative energy scattering in the ferrite gray iron performed by the direct method of determining the area of the mechanical hysteresis loop at different amplitudes of shear deformation, is in good agreement with the data obtained by the indirect method of damped oscillations on an installation of the similar class.

Effect of a Temperature on the Mechanical Characteristics of ULTEM 9085 Thermoplastic Produced by Additive Technology

Results of experimental investigation of mechanical characteristics of ULTEM 9085 thermoplastic, produced by additive manufacturing, i.e., the method of layer-by-layer application of a molten polymer thread, are presented. Flat specimens were tensile tested within the temperature range of (–40) –150°C. Temperature dependencies of ultimate strength, relative elongation at break, elastic modulus, and Poisson’s ratio are obtained. At a temperature of –40°C, the linear sections of diagrams obtained for various specimens coincide; in the area of elastoplastic deformations, their discrepancy is noted. This caused small variations in elastic characteristics and significant ones in strength and relative elongation at break. Similar features of deformation diagrams were also obtained at a temperature of 50°C. However, at 150°C, tensile diagrams do not coincide even in the area of small elastic deformations; their specific bends are noted. Specimens are fractured by the normal separation mechanism at all temperatures. When the temperature changes from –40 to 150°C, thermoplastic ultimate strength almost linearly decreases; at 150°C it is 26% of the initial value at –40 °C. As temperature increases within the specified range, the relative elongation at break monotonously decreases more than twice (2.9–1.3%). The elastic modulus changes insignificantly within a temperature range of (–40)–20°C; when the temperature rises to 150°C, it decreases to 64% of the value at –40 °C. Poisson’s ratio virtually does not change and is in the range of 0.36–0.37.

Deformation diagram and slip modulus of timber-concrete nailed connection

Problem statement . The common type of ties in hybrid timber-concrete structures are nails (bolts, screws, etc.). In the design of structure the connection work is taken into account through the composite action coefficient, which in its turn depends on the slip modulus. According to the current standards [2], the calculation is based on the assumption of linear elastic behaviour of the connection, while experimental studies have shown that the deformation diagram has a clearly expressed nonlinear character. Besides, the calculated slip modulus differs significantly from the one obtained from test results. Thus, taking into account the actual nature of the operation of the compounds makes it possible to obtain more accurate calculation methods. The purpose of the article is to develop the theoretical relationship for determining the slip modulus of the nailed connection of hybrid wood-concrete structures. Conclusion. Based on the analysis of existing data on the features of the deformation of the nailed connections of hybrid timber-concrete structures, an equation is proposed for the dependence of the slip modulus of the connection on the displacement. It was revealed that the application of linear-elastic behaviour models in the calculation of timber-concrete connections leads to overestimated values of the bearing capacity.The theoretical deformation diagrams obtained correspond to the experimental ones and more accurately reflect the beaviour of the connection under load in comparison with the current design standards. The theoretical values of the slip modulus are 30-35% less than the experimental ones, which is satisfactory taking into account the heterogeneity of the physical and mechanical properties of timber and to ensure the reserve of bearing capacity. The proposed dependence for determining the slip modulus allows taking into account its change during connection operation under load.

INTEGRAL PARAMETERS OF CONCRETE DIAGRAMS FOR CALCULATIONS OF STRENGTH OF REINFORCED CONCRETE ELEMENTS USING THE DEFORMATION MODEL

In accordance with the requirements of regulatory documents, restrictions are introduced on stress levels at the end of the falling branch of the diagrams at the maximum normalized strain values. We have developed mathematical models that establish a uniform sequence for calculating the unambiguous values of deformations at the base points of concrete diagrams, taking into account the accepted functional relationships and the rules for their use according to the tables of normative documents. It was shown that for equal values of deformations and stresses at base points, analytical expressions of diagram recommended by regulatory documents, even if it differs in structure, give identical outlines, diagram branches coincide. The correlation between the calculation models by Russian and foreign regulatory documents was established by comparing the values of the integral parameters of the diagrams and the ultimate forces obtained by calculating the reinforced concrete element according to the deformation model. As integral parameters of concrete deformation diagrams, it was recommended to use areas bounded by diagram branches and diagram completeness coefficients. Analytical modeling of integral parameters allowed us to exclude the procedure for numerically summing stresses along elementary strips in a section and solving nonlinear equations by the method of successive approximations when calculating the strength of an element.

Longitudinal Elastic Modulus and Poisson’s Ratio Computations with Automatic Experimental Data Processing of the Materials

A MEPR Calculator program is described that provides automatic computations of the longitudinal elastic modulus and Poisson’s ratio of structural materials in accordance with operating test standards. The deformation diagram of the material with a clear-cut linear section is examined. The program permits of valuating the agreement between calculated and experimental data with the coefficients of determination r2 and variation V in elastic modulus and Poisson’s ratio computations. The program features the on-line display and visualization of the calculated parameters in establishing the limits of the linear section of the deformation diagram, which makes longitudinal elastic modulus and Poisson’s ratio computations much easier and faster on condition of the best data agreement.

Numerical Modeling of Plastic Deformation of Unidirectionally Reinforced Composites

A technique for the numerical homogenization of plastic deformation of unidirectionally reinforced composites is developed. A modification of Prandtl–Reuss theory that takes into account the influence of the first invariant of stress tensor is used as governing relations for an equivalent orthotropic material. The isotropic hardening is described by a function depending on the work of plastic deformation. A micromechanical analysis is performed on a representative cell by the finite-element method for the general case of triaxial stress state. Deformation diagrams and yield surfaces for carbon fiber plastics with a square packaging scheme of fibers are given.

Experimental studies of the deformation properties of frozen soils under static and dynamic loads

The results of experimental studies of the deformation properties of sand of different water saturation are presented. The studies were conducted for frozen and unfrozen sand in static and dynamic loading conditions. The medium in all cases exhibits nonlinear properties. Dynamic strain diagrams were obtained using the Kolsky method in the split Hopkinson rod system. Static compression tests of sand were carried out in an elastic cage with registration of lateral pressure. The dynamic strain diagrams differ markedly from the static ones for both frozen sand and unfrozen sand. The level of stress in dynamic compression is much higher than in static. The diagrams of static deformation of frozen and unfrozen dry sand practically coincide. With increasing water saturation, the stress level for frozen and unfrozen sand increases.

Indirect Reinforcement of Reinforced Concrete Elements as a Means of Protecting a Constructive System from a Progressive Collapse

A variant of the diagram of static-dynamic deformation of compressed concrete, reinforced by indirect reinforcement of statically indefinable structural systems in bending reinforced concrete elements, is constructed. The characteristic parametric points of the static section of the diagram to the level of the operational load are determined by a three-line diagram using the proposal of A G Tamrazyan. The linear dynamic part of the deformation caused by a sudden structural reorganization of the constructive system is described by the deformation model of G A Geniev. The increments of dynamic forces in an arbitrary cross section of a reinforced concrete element with indirect reinforcement n times of a statically indefinable structural system are determined by a quasistatic method on an energy basis. Numerical analysis of a two-span continuous beam loaded with a given operational load and a special effect in the form of a sudden removal of one of the supports shows the effectiveness of indirect reinforcement to protect the structural system from progressive collapse.

Deformation Models of Concrete Strength Calculation in the Edition of Russian and Foreign Norms

The correlation between the calculation models as amended by Russian and foreign regulatory documents is established by comparing the values of the integral parameters of the diagrams and the ultimate forces obtained by calculating the reinforced concrete element according to the deformation model. As integral parameters of concrete deformation diagrams, it is recommended to use the areas of the areas limited to the branches of diagrams and coefficients of plenitude of diagrams. Mathematical models have been developed that establish a common form for calculating the unambiguous values of deformations at the base points of concrete diagrams, taking into account the accepted functional relationships and the rules for their use according to the tables of normative documents. Analytical modeling of integral parameters allows us to exclude from the calculation of the strength of an element the procedure for numerically summing stresses along elementary strips in a section and solving nonlinear equations by successive approximations.

ВЛИЯНИЕ ВИДА НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ НА ДИНАМИЧЕСКУЮ СЖИМАЕМОСТЬ БЕРЕЗЫ

The results of dynamic tests for compression across the fibers at room temperature of birch samples with air humidity are presented. Dynamic tests were carried out on a setup with a split Hopkinson bar according to the Kolsky method at a strain rate of ~2000 s–1. To assess the effect of the type of stress-strain state on the behavior of the material, in addition to specimens in the form of cylinders with its free expansion during loading (uniaxial stress state condition), specimens were tested in a rigid casing that prevents the radial expansion of the specimen (uniaxial deformation condition), as well as local compressive tests of rectangular board fragments. In the latter case, the material surrounding the loading zone plays the role of a compliant confining casing. In this case, a certain intermediate stress-strain state is realized in the sample. For these three types of stress-strain state, dynamic deformation diagrams were obtained with registration of additional loading cycles. Comparison of obtained deformation diagrams shows a significant effect of the type of stress-strain state on the behavior of the material under study. In the case of free expansion of the specimen in the radial direction, the absence of strain hardening is observed in the first loading cycle. In subsequent cycles, hardening is negligible. The deformation diagrams of specimens in the casing as well as board fragments are characterized by a noticeable increase in the modulus of the hardening branch with increasing deformation. In this case, it can be noted that the behavior of the material in the case of testing a piece of board is intermediate between the cases of uniaxial stress state and uniaxial strain state. Some mechanical characteristics of the material are determined using the diagrams obtained. The obtained experimental results can serve as the basis for the subsequent identification of the model of deformation and destruction of wood.