Bending Element Research Articles

EXPERIMENTAL AND THEORETICAL STUDIES OF REINFORCED CONCRETE BENDING ELEMENTS MADE OF HIGH-STRENGTH CONCRETE

The use of quality materials is necessary for the manufacture of load-bearing reinforced concrete structures that are subject to heavy loads. To meet such requirements, it is necessary to use high-strength concrete, which has high compressive strength, water and gas tightness, corrosion resistance due to its dense structure. The use of high-strength concrete makes it possible to reduce the cross-sectional dimensions of structures, thereby reducing the weight of structures compared to structures of traditional classes of concrete.The results of experimental and theoretical researches of work of reinforced concrete beams from high-strength and ordinary concrete at crossbending are resulted in work.A program of experimental research has been developed, which includes the manufacture and testing of concrete samples of prisms and cubes todetermine the strength and deformation characteristics of concrete of different composition, the manufacture and testing of experimental reinforcedconcrete beams for transverse loading. Three series of rays were tested, four in each. The composition of the concrete mixture for high-strength concreteusing metakaolin and hyperplasticizer is proposed.The proposed algorithm for calculating the bearing capacity of bending elements, based on the method of deformation, allows obtaining resultswith sufficient accuracy. The calculation is performed according to the developed algorithm, which is implemented in the Mathcad program.The analysis of experimental and theoretical values of bearing capacity of reinforced concrete beams from high-strength and usual concrete attransverse bend.

NONLOCAL IN TIME MODEL OF MATERIAL DAMPING IN COMPOSITE STRUCTURAL ELEMENTS DYNAMIC ANALYSIS

In this paper the problem of numerical simulation of composite bending elements dynamic considering internal (material) damping. For this purpose the nonlocal in time damping model, called damping with memory, is proposed as an alternative to the classic local Kelvin-Voigt model. Damping with memory makes damping forces not only dependent on the instant value of the strain rate, but also on the previous history of the vibration process. Since finite element analysis is the most common method of structural analysis, the nonlocal damping model is integrated into FEA algorithm. The FEA dynamic equilibrium equation is solved using the explicit scheme. The damping matrix was developed using the stationary full energy requirement. One-dimensional nonlocal in time model was implemented in MATLAB software package. The results of three-dimensional numerical simulation of the composite beam vibration obtained in SIMULIA Abaqus were used for model calibration. The obtained results were compared to the results based on classic Kelvin-Voight damping model.

FREE VIBRATION OF SKEW LAMINATES – A BRIEF REVIEW AND SOME BENCHMARK RESULTS

This study investigates and reviews prior research works on skew composite laminates. The equivalent single layer theories are explored and discussed. An exhaustive review on static and dynamic analysis of composite skew laminates is also presented. Subsequently, a nine node isoparametric plate bending element is used for free vibration analysis of laminated composite skew plate with central skew cut out. The effect of shear deformation is incorporated in the formulation considering first order shear deformation theory. Two types of mass lumping schemes are analysed to study the effect of rotary inertia. Certain numerical examples of plates having different skew angles, skew cut out sizes, boundary conditions, thickness ratios (h/a), aspect ratios (a/b), fiber orientations and number of layers are solved which will be useful for benchmarking of future studies.

DYNAMIC ANALYSIS OF PLATES WITH CUT-OUT CARRYING CONCENTRATED AND DISTRIBUTED MASS

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

STRESS DISTRIBUTION IN THE HOLLOW STIFFENED HYBRID LAMINATED COMPOSITE PANELS IN SHIP STRUCTURES UNDER SINUSOIDAL LOADING

A simplified hollow stiffened hybrid laminated plate model has been developed for the marine structures. The detailed stress analysis through the thickness of the stiffened plate based on the higher order shear deformation theory has been carried out under sinusoidal loading. The hybrid laminates are made by wrapping the GFRP laminates with CFRP at the outermost layers of the stiffened panel. This hybridization technique can be an optimum solution from the point of view of cost reduction as well as enhancement of strength properties. The layer-wise stresses for the stiffened plate have been calculated in the present paper. A 3D polynomial curve fitting technique has been used to obtain higher accuracy and consistency in the computation of stresses. The computer code has been developed using MATLAB considering the plates as eight noded isoparametric plate bending element and the stiffener has been modeled as three noded isoparametric beam element. The stiffened panel has also been analysed using the ANSYS14.0 software package considering 2D model. The results obtained from the present formulation have been compared with those available in the published literature to validate the present formulation. The stiffened panels made of GFRP, CFRP and GFRP-CFRP hybrid laminates have been studied here. An extensive parametric study has been carried out with varying fibre content in the laminates.

Enchainment of the Coefficient of Structural Quality of Elements in Compression and Bending by Combined Reinforcement of Concrete with Polymer Composite Bars and Dispersed Fiber.

Polymer composite reinforcement (PCR) and its use to produce high-quality concrete with the right design and technological and formulation solutions can demonstrate the results obtained with the steel rebars. This article discusses the synergistic effect from the combined reinforcement of concrete with traditional polymer rods and dispersed fiber, which, as a result, lead to an increase in strength and deformation characteristics and an improvement in the performance of compressed and bent structural elements. The synergistic effect of the joint work of polymer rods and dispersed reinforcement is considered in the context of relative indicators (structural quality factor CSQ), showing the relationship between strength characteristics and concrete density. The behavior of glass fiber in a cement matrix and the nature of its deformation during fracture were studied by scanning electron microscopy. It is shown that the use of PCR and dispersed reinforcement makes it possible to increase the strength characteristics of concrete in bending. In quantitative terms, the achieved results demonstrated that the CSQ values of a beam reinforced with a PCR frame with the addition of glass fiber were 3.4 times higher compared to the CSQ of a beam reinforced with steel reinforcement frames. In addition, for a beam reinforced with a PCR frame with no fiber addition, the CSQ values were three times higher.

Structure-preserving techniques in accelerator physics

To very good approximation, particularly for hadron machines, charged-particle trajectories in accelerators obey Hamiltonian mechanics. During routine storage times of eight hours or more, such particles execute some revolutions about the machine, oscillations about the design orbit, and passages through various bending and focusing elements. Prior to building, or modifying, such a machine, we seek to identify accurately the long-term behaviour and stability of particle orbits over such large numbers of interactions. This demanding computational effort does not yield easily to traditional methods of symplectic numerical integration, including both explicit Yoshida-type and implicit Runge–Kutta or Gaussian methods. As an alternative, one may compute an approximate one-turn map and then iterate that map. We describe some of the essential considerations and techniques for constructing such maps to high order and for realistic magnetic field models. Particular attention is given to preserving the symplectic condition characteristic of Hamiltonian mechanics.

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.

Layered shock-resistant element parts shape change process selection and modeling

An impact-resistant layered element consisting of two outer layers from highly rigid material and an inner layer from viscoelastic material has been developed. The item reduces the barring effect on the protected object. The design peculiarity is that the outer part has a bend with a deflection arrow within 10… 15 thicknesses, and has a connection of the outer layers from high-stiff material on opposite edges with staples from plastic material, which during plastic deformation flows into the edge holes coaxially in the outer layers, on the inner side of the impact-resistant element is attached a shock-absorbing layer from elastic foamed polymeric material, the back surface of which corresponds to the surface of the protected object. For the parts manufacture it has been developed bending sheet parts method in which the bending the part shelves with a bending element with their subsequent straightening. The aim is to increase the process productivity and the geometric dimensions’ accuracy of the part. Modeling the process of parts spontaneous forming "Impact-resistant element upper sheet" on the reverse and direct schemes is performed by the finite element method in the AnSYS / AutoDYN system. The study purpose is to develop technology and modeling the process of the impact-resistant element sheet parts deformation.

Influence of the percentage of reinforcement by unstressed rebar on the deformability of pre-stressed RC beams

Abstract This article presents the materials of deformability studies of pre-stressed steel-concrete beams reinforced with a package of reinforcement with different ratio of tape and rebar in the pure bending moment zone. The aim of the research was determination of the reinforcement percentage influence, for pre-stressed reinforced concrete beams reinforced with a package of reinforcement on their deformability. Also, the aim was to evaluate the effectiveness of using pre-stressed rebar in combined reinforcement. The practical significance of the experimental research is to study the deformability in pre-stressed bending elements with external tape and rebar reinforcement, taking into account the influence of different ratios of reinforcement areas within the combined reinforcement and development of proposals for such structures` calculation and design. The scientific novelty of the research is in obtaining the deformability characteristics of reinforced concrete beams reinforced with a package of reinforcement (tape and steel bars with periodic profile) with different ratios in the case of static loads` action.

REINFORCEMENT OF REINFORCED CONCRETE STRUCTURES WITH COMPOSITE MATERIALS

Recently, in the Republic of Kazakhstan, as well as in other countries of theAsian region, it is becoming more and more urgent to strengthen the operated reinforcedconcrete structures with external reinforcement systems with carbon materials during thereconstruction of any engineering structures. In order to eliminate the consequences of concretedestruction and reinforcement corrosion as a result of long-term exposure to natural factors andaggressive environments, carbon fiber external reinforcement systems are widely used during the operation of structures designed to repair and strengthen the load-bearing structures of artificialstructures. External reinforcement is used to increase the seismic resistance, strength andreliability of the structures being built, as well as to increase the time between repairs. The repairsystem provides for the use of materials and technologies that ensure stopping and preventingfurther corrosion of reinforcement and concrete, reliable adhesion of repair compounds with oldconcrete, increased water resistance, frost resistance and chemical resistance. This articledescribes FibARM carbon materials that are used to strengthen columns and pylons, broadbandreinforcement of slabs, beams, crossbars and structures with increased requirements forreinforcement joints, covering reinforcement of concrete with large-scale grid cracking.The mainmethods of strengthening the stretched and bent elements of building structures of artificialstructures are considered, and the technology of work on strengthening the structures of artificialstructures is also given.

Iron alloys and structural steels from XIX century until today: Evolution of mechanical properties and proposal of a rapid identification method

Mechanical properties of materials, as provided by current design standards, are the pre-requisites for the proper identification and structural assessment of existing buildings and civil engineering works. For mechanical characterisation, in case of “Limited Knowledge” (KL1) without direct information on the material properties, the usual features according to the standards at the construction time are considered. This is the case, for example, of structural metalworks characterised by historical and artistic interest (bridges, roof galleries, covered markets, railway stations, etc.) or industrial archaeology buildings where, because of the constraints imposed by the National Authorities of Cultural Heritage Preservation, extensive or exhaustive in-situ tests cannot be performed. This paper focuses chronologically, from the XIX century until today, on the evolution process of ferrous alloys, namely cast iron, wrought iron and steel, for structural applications. After a description and classification of the aforementioned materials and their production processes, the main mechanical properties and design stresses for bending and compression elements are briefly analysed and collected in a chronological order. Reference is made to the product specifications and design codes, integrated with data from extensive experimental testing. The resulting database can support realistic assumptions about materials and their properties, used over a range time of over 100 years, once the age of building is known. Finally, a methodology for identifying existing metal carpentry structures, which combines the database with fast non-destructive testing methods, is proposed. Such an approach can be effectively used not only for historical steelworks, but also for the mechanical characterization of structural subsystems or elements (e.g. beams, columns, lintels, tie rods) in common existing buildings made of either steel or steel-rc composite structure.

Features of Evaluation of Fire Resistance of Reinforced Concrete Ribbed Slab under Combined Effect "Explosion-Fire"

Calculations using the example of a reinforced concrete ribbed slab have shown that if, as a result of an explosion, due to cracks that have arisen, a part of the compressed concrete layer is turned off, then even while maintaining the bearing capacity of the slab, its fire resistance is significantly reduced. It is shown that on the basis of the proposed methodology for studying the behavior of bending elements under the combined effect of "explosion-fire", it is possible to take into account the necessary parameters of reinforced concrete ribbed slabs in the design and operation of structures of hazardous operations industrial facilities. Also, the proposed technique makes it possible to predict a relatively safe amount of explosive in the technological process of an hazardous operations industrial facility, without leading to catastrophic consequences.

The numerical parametric study of the stress-strain state of I-beams having versatile corrugated webs

Introduction. The numerical parametric study of the stress-strain state of I-beams, having versatile corrugated walls, was carried out in the ANSYS Mechanical APDL software package. Numerical results are obtained for displacements, equivalent stresses and stability coefficients depending on the change in the inclination angle of web corrugations for trapezoidal, wavy and triangular profiles. The obtained results can help to design and substantiate the design solutions applicable to bending elements.
 Materials and methods. The parametric study involved a series of numerical experiments conducted using the finite element method in the ANSYS Mechanical APDL software package. APDL parametric language was used to develop the software that was built into the software package. It allowed to perform a parametric reconstruction of the numerical model depending on varied parameters of the corrugated wall, and the reconstruction was followed by the numerical solution and post-processing of the calculation results. The calculations were made with the help of the model whose overall dimensions and material were identical to those of a standard I-beam having a solid wall exposed to a uniformly distributed transverse load.
 Results. The parametric study enabled the co-authors to identify the main features of the stress-strain state of the beams that had different types of corrugated walls. A parametric numerical model was compiled to determine maximum displacements, equivalent stresses and stability coefficients for various types of corrugated walls and various parameters of the corrugation angle. Isofields of equivalent stresses and buckling modes are provided for characteristic parameters and types of corrugations. The reliability of the obtained results was confirmed by the verification of the numerical model using the method of the strength of materials and corrugation inclination angle α = 0, which was the initial point of simulation for all types of corrugations.
 Conclusions. The results, obtained in the course of parametric studies, have identified the main features of the stress-strain state of beams having corrugated walls; they allow to substantiate their effectiveness as design solutions applied to bending elements.

Effect of crack location on buckling and dynamic stability in plate frame structures

It is well known that damages affect the dynamic characteristics of the structures in such a way that they may lead those structures to fail. Therefore, it is essential to construct a reliable mathematical model for estimating the effect of the damage in these structures. In this study, the effect of the straight, through-thickness crack and its location on the thin single-bay one-storey, two-bay-one-storey, and single-bay two-storey plate frames is investigated. For this purpose, a four-node quadrilateral plate bending and membrane elements are combined to perform finite element free vibration analysis of the healthy and cracked thin plate frame structures. The Classical Plate Theory is employed to satisfy the strain and stress conditions of these thin structures. A computer code is written using MATLAB to obtain the first three natural frequencies, critical buckling loads, and the first unstable regions of the healthy and cracked thin structures. To ensure the validity of the employed mathematical model, a convergence analysis is performed via ANSYS. The effect of crack location in plate frame structures is investigated by measuring the differences between the healthy and cracked structures’ first three buckling modes and the first unstable region. It is seen that the bending regions of the buckling modes are more affected by the crack than the other zones. Besides, crack occurrence within these regions has more impact on the first unstable regions. Accordingly, it has been revealed that the bending regions are the weakest locations of the frame structures. Therefore, potential cracks occurred within these regions may affect the structural integrity more than those of emerged in other regions.

A Triangular Plate Bending Element Based on Discrete Kirchhoff Theory with Simple Explicit Expression

A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular element, using the compatible trial function for the transverse displacement along the element sides, the construction of the present SDKT element is based on a specially designed trial function for the transverse displacement over the element, which satisfies interpolation conditions for the transverse displacements and the rotations at the three corner nodes. Numerical investigations of thin plate structures were conducted, using the proposed SDKT element. The results were compared with those by other prevalent plate elements, including the analytical solutions. It was shown that the present element has the simplest explicit expression of the nine-DOF (Degree of Freedom) triangular plate bending elements currently available that can pass the patch test. The numerical examples indicate that the present element has a good convergence rate and possesses high precision.

On the formulation and evaluation of old and new efficient low order triangular plate bending elements with shear effects

This paper deals with the presentation of a general, variational principle as theoretical support for the development of simple and efficient triangular elements having only one displacement and two rotations at the corner nodes to model thin to thick plates based on the first order Reissner- Mindlin plate theory. The functional is a modified Hellinger–Reissner mixed expression in terms of the kinematic variables (transverse displacement w and rotations βx and βy), and independent transverse shear strains (γx and γy). The approximations of the five independent variables of the mixed formulation take into account the accumulated knowledge on existing performing 2D Timoshenko beams and triangular elements such as T3γs, MITC3, DKT, DST, DKMT. The present mixed variational support is useful, not only to give a unique theoretical support to the above existing elements, usually based on assumed natural strain formulations, but it allows also to propose new simple and efficient elements, here called BAK1, BAK2 and BAK3. The paper includes a detailed presentation of results of patch tests for very thin and very thick plates, for convergence of displacements, bending moments and shear forces, for clamped circular and simply supported square plates and for s-norm convergence tests considering regular and irregular meshes. Shear force distribution is also considered for situations with boundary layer effects.

Designing bending-active gridshells as falsework for concrete shells through numerical optimization

Shell structures are material efficient structures capable of covering large spans with minimum weight. If concrete is used as the building material for the shell, it must be initially supported by a formwork. These generally rigid formworks, and their supporting falsework structure, are time and material consuming to construct. Recently, researchers have recommended the use of elastic gridshells as falsework system. Unfortunately, the design of such a system is complicated by large deformations of the bending elements. Moreover, since gridshells are inherently flexible, significant displacements generally occur when applying the wet concrete.To overcome these difficulties, this paper presents a design tool to effectively design a gridshell serving as the falsework for a concrete shell. The gridshell is assumed to be constructed from an initially flat grid of straight slender rods, using cables with adjustable lengths to brace the erected gridshell. An optimization algorithm is proposed that fits the shape of the gridshell under the wet concrete loading to a given target shape by manipulating the lengths of the bracing cables. Meanwhile, the optimization algorithm reduces the construction effort by minimizing the number of cables, and the diameter of the grid rods. Moreover, feasibility of the design is ensured by constraining the axial force in the cables and limiting the displacements under increased loading. A gradient-based optimization scheme is adopted, and an implicit dynamic relaxation approach previously developed specifically for the simulation of bending-active structures is used to solve the nonlinear equilibrium equations. Nonlinear effects such as buckling of the grid rods are taken into account by using co-rotational beam elements. The resulting design tool is applied for the design of a scale model, demonstrating the feasibility of the suggested falsework system. The optimized design fits the target better, uses less cables, and is more resistant to additional loading compared to designs from existing design approaches. Comparisons between the numerical and physical models show deviations of up to around 2% of the larger span for the design load and smaller deviations for smaller loads, with differences attributed to small model scaling effects.

Strain-Stress Distribution of Structural Components from Foam Concrete for Monolithic Construction

The problem of use of hi-tech macroporous concrete in load-carrying structures of low-rise buildings is designated and the forthcoming research problems of power resistance and deformation of the compressed and bent elements from foam concrete of natural solidification are formulated. Results of pilot researches of intense state of strain of the compressed and bent elements from foam concrete of average density of 1200-1600 kg/m3 of different structural modification in the conditions of short-term and long action of loading are provided. It is established that foam concrete meet for nonrigid indicators regulatory requirements and take the intermediate place between full-strength cellular and light concrete on expanded aggregates that creates premises for their successful application in the bearing concrete and reinforced concrete constructions. Deformation and strength characteristics of foam concrete of different structural modifications taking into account the impact of the long processes caused by solidification of concrete and external power factors, necessary for calculation and structural design are offered. The received results of researches will allow to project rationally bearing and enclosing structures from foam concrete that leads to increase in technological level of monolithic construction.

Comparative Study of Conventional and Partial RCC Beams and Slabs for Flexural and Shear strength – A review

IS456-2000, Clause 38.1 Assumptions, one of the assumptions is; the tensile strength of concrete is ignored. As per this assumption, Instead of using high grade concrete in tension zone, use of nominal grade concrete or creating vacuum near neutral axis, to develop “Partial RC beam or slab”. Both beam and slab are bending structural elements, hence understanding of flexural and shear strength is very important. Review of research papers gives an insight on difference between conventional and partial bending elements. Ultimate flexural strength will be nearly same in both partial elements and conventional bending elements. Initial crack load is less in partial bending elements compare to conventional elements. But partial elements are the best solution to reduce usage of cement in RC structural elements. Understanding shear strength of partial bending elements is very essential in the shear reinforcement design, but less research work is done on shear strength of partial flexural elements. Use of less cement in partial elements reduces CO2 emission, makes structure economical and it is also the solution for global warming