Bearing Capacity of Structures Made of Materials with Different Tensile and Compression Strengths

2019 ◽  
Vol 968 ◽  
pp. 200-208
Author(s):  
Mykola Soroka
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Limit State ◽  
Analytical Calculation ◽  
Bending Moment ◽  
Maximum Load ◽  
Longitudinal Force ◽  
Plastic State ◽  
Limiting State ◽  
Tension And Compression

The paper considers the problem of the ultimate load finding for structures made of a material with different limits of tensile strength and compression. The modulus of elasticity under tension and compression is the same. It is assumed that upon reaching the ultimate strength, the material is deformed indefinitely. The calculations use a simplified material deformation diagram — Prandtl diagrams. The limiting state of a solid rectangular section under the action of a longitudinal force and a bending moment is considered. The dependences describing the boundary of the strength of a rectangular cross section are obtained. Formulas allowing the calculation of the values of the limit forces and under the action of which the cross section passes into the plastic state are derived. Examples of the analytical calculation of the maximum load for the frame and two-hinged arch are given. An algorithm is proposed and a program for calculating arbitrary flat rod systems according to the limit state using the finite element method is compiled. The proposed algorithm does not involve the use of iterative processes, which leads to an exact calculation of the maximum load within the accepted assumptions.

Plastic Flexure of Mild Steel Beams of Rectangular Cross-section

1952 ◽  
Vol 166 (1) ◽  
pp. 112-122 ◽  
Author(s):  
K. K. Shackell ◽  
J. H. Welsh
Keyword(s):  
Yield Stress ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Strain Curve ◽  
Bending Moment ◽  
Steel Beams ◽  
Stress Tests ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Tension And Compression

The paper describes tests on a 0–28 per cent carbon steel in tension and compression, and in flexure of beams of rectangular cross-section, to a maximum strain about three times that at the initial yield. The object of these tests-was to investigate the shape of the stress-strain curve immediately after the initial yielding, and to determine whether in a case such as flexure the upper yield stress could be relied upon as a criterion of design. The results from this material indicate that the stress-strain curve falls rapidly but not immediately from the upper to the lower yield value, and that a beam is capable of withstanding a slightly greater bending moment than would be predicted by calculations based on the direct stress tests including the upper yield stress.

scholarly journals CALCULATING THE STRENGTH OF AN EXCENTRALLY COMPRESSED REINFORCED CONCRETE ELEMENT OF RECTANGULAR SECTION

2020 ◽  
Vol 10 (1) ◽  
pp. 4-8
Author(s):  
Nikolay A. ILYIN ◽  
Sergey S. MORDOVSKY ◽  
Vera A. MALGINA ◽  
Nadezhda A. KIREEVA
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Structural Parameters ◽  
Bending Moment ◽  
Longitudinal Force ◽  
Quality Parameters ◽  
Labor Costs ◽  
Concrete Element ◽  
Structural Indicators

One of the main tasks in the calculation of reinforced concrete elements is the determination of strength. This problem is relevant for structures in various stress-strain states - bending, eccentrically-compressed, eccentrically-stretched, eccentrically-compressed with torsion, etc. This article discusses the solution of the strength problem in the design of an eccentrically compressed reinforced concrete element of rectangular cross section with symmetrical reinforcement. The improvement relates to taking into account the infl uence of structural parameters of the quality of reinforcement and concrete on the value of the design loads and the ultimate tensile strength of an eccentrically compressed reinforced concrete element, taking into account its deflection. By simplifying the mathematical description of the influence of structural indicators and quality parameters of reinforcement and concrete on the calculated value of the bending moment and on the strength of an eccentrically compressed reinforced concrete element, as well as simplifying the calculation of the coefficient of increase in the initial eccentricity of the longitudinal force taking into account the deflection of the compressed reinforced concrete element, this improvement is obtained. Using the proposed formulas in calculating the strength of an eccentrically compressed reinforced concrete element of rectangular cross section allows us to ensure the convergence of the result with the classical version of the calculation with a reduction in labor costs due to the simplicity of the formulas.

Elastic-plastic bending of the pipeline under combined loading

2021 ◽  
pp. 372-377
Author(s):  
Виктор Миронович Варшицкий ◽  
Евгений Павлович Студёнов ◽  
Олег Александрович Козырев ◽  
Эльдар Намикович Фигаров
Keyword(s):  
Internal Pressure ◽  
Limit State ◽  
Bending Moment ◽  
Axial Direction ◽  
Longitudinal Force ◽  
Combined Loading ◽  
Dimensional Problem ◽  
Elastic Plastic ◽  
Pipeline Section ◽  
Thin Walled Pipe

Рассмотрена задача упругопластического деформирования тонкостенной трубы при комбинированном нагружении изгибающим моментом, осевой силой и внутренним давлением. Решение задачи осуществлено по разработанной методике с помощью математического пакета Matcad численным методом, основанным на деформационной теории пластичности и безмоментной теории оболочек. Для упрощения решения предложено сведение двумерной задачи к одномерной задаче о деформировании балки, материал которой имеет различные диаграммы деформирования при сжатии и растяжении в осевом направлении. Проведено сравнение с результатами численного решения двумерной задачи методом конечных элементов в упругопластической постановке. Результаты расчета по инженерной методике совпадают с точным решением с точностью, необходимой для практического применения. Полученные результаты упругопластического решения для изгибающего момента в сечении трубопровода при комбинированном нагружении позволяют уточнить известное критериальное соотношение прочности сечения трубопровода с кольцевым дефектом в сторону снижения перебраковки. Применение разработанной методики позволяет ранжировать участки трубопровода с непроектным изгибом по степени близости к предельному состоянию при комбинированном нагружении изгибающим моментом, продольным усилием и внутренним давлением. The problem of elastic plastic deformation of a thin-walled pipe under co-binned loading by bending moment, axial force and internal pressure is considered. The problem is solved by the developed method using the Matcad mathematical package by a numerical method based on the deformation theory of plasticity and the momentless theory of shells. To simplify the solution of the problem, it is proposed to reduce a twodimensional problem to a one-dimensional problem about beam deformation, the material of which has different deformation diagrams under compression and tension in the axial direction. Comparison with the results of numerical solution of the two-dimensional problem with the finite element method in the elastic plastic formulation is carried out. The obtained results of the elastic-plastic solution for the bending moment in the pipeline section under combined loading make it possible to clarify criterion ratio of the strength of the pipeline section with an annular defect in the direction of reducing the rejection. Application of the developed approach allows to rank pipeline sections with non-design bending in the steppe close to the limit state under combined loading of the pipeline with bending moment, longitudinal force and internal pressure.

scholarly journals NUMERICAL INVESTIGATION OF THE ELASTIC-PLASTIC LINEAR HARDENING STRESS-STRAIN STATE OF THE FRAME ELEMENT CROSS-SECTION

2016 ◽  
Vol 8 (3) ◽  
pp. 94-100
Author(s):  
Andrius Grigusevičius ◽  
Gediminas Blaževičius
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Software Environment ◽  
Stress Strain ◽  
Hardening Material ◽  
Frame Element ◽  
Nonlinear Stress

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments.

scholarly journals PLASTIC DEFORMATIONS OF STEEL FRAME: STATICS AND DYNAMICS

2010 ◽  
Vol 2 (3) ◽  
pp. 101-105 ◽  
Author(s):  
Vytautas Kargaudas ◽  
Nerijus Adamukaitis
Keyword(s):  
Dynamic Analysis ◽  
Cross Section ◽  
Axial Force ◽  
Bending Moment ◽  
Transverse Force ◽  
Steel Frame ◽  
Plastic State ◽  
Strain Diagram ◽  
Plastic Deformations ◽  
Elastic Plastic

When all deformations of a column are elastic, transverse deflections of the column depend on transverse force and axial displacements depend on axial force only. These classical dependences are unsuitable for elastic-plastic deformations. Plastic deformations develop in columns when steel frame is influenced by extreme action. When a steel column is in the elastic-plastic state, the distribution of elastic and plastic deformations in the cross-section depends on both the bending moment and compressing force. The ideal elastic-plastic material is assumed in this investigation (Prandtl stress – strain diagram). If the shape of the column section is double tee, flange width is neglected with respect to web height, but the area of the flange cross-section is assumed a constant. Single-sided or double-sided yield depends on the moment and force, and therefore curvature and the axial strain of the column can be calculated when yielding dependences are determined. Transverse and axial displacements of the highest point of the column are deduced by integration and depend on two arguments: bending force and axial force. These dependences are essentially non-linear, so linear approximations can be assessed for some vicinity of axial force and bending moment values. When axial force is a constant and transverse force increases, both axial and transverse displacements tend to increase. If transverse force is a constant and axial force increases, both displacements increases but dependence lines remain different and depend on cross-section shape parameter equal to the ratio of the flange area and the area of the whole cross-section. A distinguished feature of plastic deformations is dependence on the history of loading a frame of which can be selected in an arbitrary way by an investigator if a quasi-static solution is under examination. The loading of a frame and inertia forces have to be deduced if dynamic analysis is studied. Not only the ultimate result but also the way of approaching a plastic piston – plastic hinge is important. The bended and compressed column is the structure when inelastic dynamic analysis is really important.

scholarly journals Cross-Sectional Analysis of the Resistance of Rc Members Subjected to Bending With/without Axial Force

2021 ◽  
Author(s):  
Marek Lechman
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Nonlinear Stress ◽  
The Cross ◽  
Sectional Analysis

The paper presents section models for analysis of the resistance of RC members subjected to bending moment with or without axial force. To determine the section resistance the nonlinear stress-strain relationship for concrete in compression is assumed, taking into account the concrete softening. It adequately describes the behavior of RC members up to failure. For the reinforcing steel linear elastic-ideal plastic model is applied. For the ring cross-section subjected to bending with axial force the normalized resistances are derived in the analytical form by integrating the cross-sectional equilibrium equations. They are presented in the form of interaction diagrams and compared with the results obtained by testing conducted on RC columns under eccentric compression. Furthermore, the ultimate normalized bending moment has been derived for the rectangular cross-section subjected to bending without axial force. It was applied in the cross-sectional analysis of steel and concrete composite beams, named BH beams, consisting of the RC rectangular core placed inside a reversed TT welded profile. The comparisons made indicated good agreements between the proposed section models and experimental results.

Generating Interaction Curve Graph Based on the Rotation Angle of Strain Diagram, According to EN 1992

2015 ◽  
Vol 797 ◽  
pp. 61-68
Author(s):  
Juliusz Lechniak ◽  
Krzysztof Kamiński
Keyword(s):  
Cross Section ◽  
Rotation Angle ◽  
Bending Moment ◽  
Longitudinal Force ◽  
Strain Diagram ◽  
Interaction Graph ◽  
Easy Calculation ◽  
Strain Limit ◽  
Complete State ◽  
Material Interaction

The most comfortable way to present capacity is M-N interaction curve diagram (bending moment and longitudinal force). Graph of M-N most commonly appears as a function, where an axial force is the argument and the bending moment is the value. This work introduce a formation of the curve way, where the the rotation angle of the strain diagram is the argument, and the full strain diagram is the value. Using the complete state of the strain of the cross section, enables easy calculation the M-N forces using stress-strain diagram for a given material. Interaction graph is based on parabola-rectangle diagram for concrete and the graph with inclined top branch with strain limit for reinforcing steel. The method has no restrictions due to the concrete class.

scholarly journals STRESS-STRAIN STATE OF REINFORCED CONCRETE BEAMS STRENGTHENED WITH A NEW EXTERNAL STEEL STRUCTURE

2017 ◽  
Vol 1 (48) ◽  
pp. 90-99
Author(s):  
V. P. Zhyrakhivskyi ◽  
М. G. Chekanovych ◽  
О. М. Chekanovych
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Concrete Beams ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Steel Structure ◽  
Research Data ◽  
Reinforced Concrete Beams ◽  
Reinforced Beams ◽  
Steel Bars

The study presents a new structure for strengthening of one-span reinforced concrete beams in rectangular cross-section using external steel bars. The specific feature of the proposed strengthening is the unloading of the compressed upper zone of a beam with simultaneous compression of its lower stretched zone. The article considers some variants of making the strengthening structure with rigid and flexible reinforcement elements for faster tension of external bars, and the variant including only flexible elements. It provides a design scheme and method for such reinforced beams. The study provides experimental research data on the series of beams with different parameters of the strengthening structure in the form of «bending moment – deflection» and «bending moment - deformation of concrete» dependencies.

Combined Bending and Compression of a Pressurized Circular Cylindrical Membrane Column

1965 ◽  
Vol 87 (3) ◽  
pp. 372-378
Author(s):  
W. E. Jahsman
Keyword(s):  
Compressive Strength ◽  
Cross Section ◽  
Compressive Load ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Maximum Load ◽  
Bending Moments ◽  
Lateral Deflection ◽  
The Cross

Load-lateral deflection curves are developed for a pressurized tube of circular cross section under combined bending and compression. The tube walls are assumed to have negligible compressive strength so that wrinkling develops if the stress tends to become negative. It is found that for a given bending moment, the load increases monotonically with deflection until a maximum is reached beyond which the load decreases with increasing deflection. An interaction curve of the maximum load versus bending moment shows that the presence of only a small amount of bending significantly decreases the maximum compressive load below the classical Euler load. Conversely, for bending moments which produce almost complete wrinkling of the cross section, only very small amounts of compressive load can be supported.

Analysis of Helical Torsion Spring for Epicyclic Traction Drive

2017 ◽  
Vol 261 ◽  
pp. 408-415
Author(s):  
Geza Nemeth
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Initial Shape ◽  
Traction Drive ◽  
Torsion Spring ◽  
Spring Wire ◽  
Tangential Forces ◽  
Radial Forces ◽  
Proper Operation

Let us consider a simple epicyclic traction drive containing a sun wheel, an annular wheel, planetary wheels and a planet carrier. The annular wheel is substituted by a helical torsion spring with rectangular cross section. The spring has initial tensioning, tightened to the planetary wheels. When the number of coils is z and the number of planet wheels is N, there are zN piece of concentrated forces acting to the spring from inside towards outside. The main load of the spring is bending, it is computable along the spring wire. The bending moment is limited by the spring material and the cross section of spring. The radial forces acting to the spring are governed by the constraint of stress equality, the deflections of the contacting parts are determined by the radial (and slightly the tangential) forces. An initial shape of the spring that assures the proper operation of the drive after the assembly, is calculated by elementary mechanical calculation methods. The main goal is the developing of a traction drive in which the clamping force is proportional to the torque which should be transmitted, for the sake of the favourable life rating and the efficiency.

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