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 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.

On the Experimental Analysis of Temperature Influence on Stiffness of Reinforced Concrete Beams

2015 ◽  
Vol 6 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Robert Kowalski ◽  
Michal Glowacki ◽  
Marian Abramowicz
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Cross Sections ◽  
Concrete Beams ◽  
Rectangular Cross Section ◽  
Thermal Strain ◽  
Bending Moment ◽  
Reinforced Concrete Beams ◽  
Stiffness Reduction ◽  
Tensile Zone

The paper presents results of experimental research whose main topic was determination of stiffness reduction in bent reinforced concrete beams in two cases: when only tensioned or only compressed zone was exposed to high temperature. Twenty four reinforced concrete beams with rectangular cross-section were prepared for the experiment. Eight groups of beams were prepared in total: 2 with reinforcement ratio - 0.44 and 1.13% x 2 levels of load - 50 or 70% of destructive force ensuring the constant value of bending moment in the centre part of heated beams x 2 static schemes. Three beams were used in each group. Significant cross-section stiffness reduction was observed in beams where the tensile zone was heated. This was due to considerable elongation of the bars where the steel load elongation summed up with the free thermal strain. In beams where the compressed zone was heated the stiffness reduction was observed only after the time where the tensile zone heated cross-sections were already destroyed.

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 Theory of “dissolution” and “condensation” of the physical geometric characteristics of an arbitrary cross-section under the action of torsion with bending

2019 ◽  
Vol 15 (4) ◽  
pp. 261-270
Author(s):  
Vladimir I. Kolchunov ◽  
Aleksej I. Demyanov ◽  
Nikolay V. Naumov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Large Circle ◽  
Stress Strain ◽  
Cross Sectional ◽  
Tangential Stresses ◽  
Stress Strain State

Aim of research - to continue the development of methods for determining the stress-strain state of rods during torsion using materials resistance methods. Methods. A new approach for determining tangential torsional stresses for arbitrary cross sectional rods, based on simplified assumptions of material resistance, is proposed. The main feature of this approach is the approximation of rectangular or any complex cross section of reinforced concrete structures by describing a large circle around the cross section and splitting it into small squares with circles inscribed into them. Results. Three theorems have been formulated, the first of which relates the accumulation of tangential stresses (increments) from the edges of a rectangle to the middle of a rectangular section with the formula for determining tangent stresses for round sections. The second theorem allows to establish a connection between the tangential stresses calculated for each of the small squares-circles and the tangent stresses of the large circle through their increments. The third theorem makes it possible to find tangential stresses for each of the small square circles. The proposed approach allows to remove the need to use special tables for the calculation and not only in the elastic stage. It also makes it possible to separate the stress-strain state in the whole set of round cross-sections from the additional field caused by the deplanation of the rectangular cross-section. In addition, the proposed approach makes it possible to take into account the concentration of angular deformations in the incoming angles and other places with changing geometric parameters.

Unsymmetrical Bending and Bending Combined with Axial Loading of a Beam of Rectangular Cross Section into the Plastic Range

1953 ◽  
Vol 57 (512) ◽  
pp. 503-509 ◽  
Author(s):  
Anthony J. Barrett
Keyword(s):  
Cross Section ◽  
Axial Load ◽  
Rectangular Cross Section ◽  
Form Factors ◽  
Strain Curve ◽  
Bending Moment ◽  
Theoretical Work ◽  
Mathematical Form ◽  
Stress Strain Curve ◽  
Stress Strain

SummaryThis note considers two cases of bending beyond the limit of proportionality which have not received a great measure of attention in the past. These are Case(i). A beam subjected to a pure bending moment acting in a plane other than one of symmetry. Case(ii). A beam subjected to a bending moment and an axial load.A mathematical form is used for the stress–strain curve in order that the results shall be applicable to a large number of materials and to avoid the tedious arithmetical summations which would be necessary if actual stress-strain curves were used. All the results are presented in terms of form factors since this notation is convenient for design purposes and is consistent with current British practice. Although the method adopted in the analysis is applicable to a number of different types of beam cross section, only rectangular cross sections are considered in detail at the present time.Curves are presented showing the variation of the form factor with respect to the angle of the plane of loading, for Case(i), and with respect to the ratio of bending moment to axial load for Case(ii). These curves are based upon a standardised form of the stress–strain curve which may be taken as representative of a range of aircraft materials. Consideration is given to the automatic satisfaction of present military proof loading requirements when these form factors are used for the estimation of maximum permissible bending moments and axial loads under ultimate loading conditions.The recommendations of F. P. Cozzone, for dealing with these two problems are examined and comparison is made between the theoretical work of this note and a limited number of test results available for Case(i).

Closed-form moment-curvature relations for reinforced concrete cross sections under bending moment and axial force

2016 ◽  
Vol 129 ◽  
pp. 67-80 ◽  
Author(s):  
Pedro Dias Simão ◽  
Helena Barros ◽  
Carla Costa Ferreira ◽  
Tatiana Marques
Keyword(s):  
Reinforced Concrete ◽  
Closed Form ◽  
Axial Force ◽  
Cross Sections ◽  
Bending Moment

scholarly journals Particle separation of a modified feed nozzle hydrocyclone under different operating parameters

2021 ◽  
Vol 11 (5) ◽  
pp. 159-170
Author(s):  
Zsolt Hegyes ◽  
Máté Petrik ◽  
L. Gábor Szepesi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Particle Separation ◽  
Baffle Plate ◽  
Important Data ◽  
Preliminary Research ◽  
All Speeds ◽  
Plate Solution

During the operation of the hydrocyclone the cut size diameter is the most important data. This is connected to feed rate, which is closely related to the feed cross section. Preliminary research has revealed that square cross-section is more effective than circular cross-section. The research compared 2 types of feed cross sections at 5 different feed rates. One is a standard rectangular cross-section and the other is a square cross-section that narrows with a baffle plate. Preliminary calculations for cut size diameter have shown that better particle separation at all speeds can be achieved with the baffle plate solution. In both types, the increased velocity created decreased cut size diameter. During the simulation, the baffle plate did not cause any abnormalities in the internal pressure and velocity distributions. The simulation revealed that the particles did not behave as previously calculated.

The movement investigation of an axisymmetric rotation body under the action of electromagnetic fields

2020 ◽  
Vol 2 (103) ◽  
pp. 67-77
Author(s):  
O. Hrevtsev ◽  
N. Selivanova ◽  
P. Popovych ◽  
L. Poberezhny ◽  
O. Shevchuk ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Cross Section ◽  
Variable Thickness ◽  
Structural Damage ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Stress Strain ◽  
Coordinate Time ◽  
Stress Strain State ◽  
Natural Time

Purpose: To ensure an adequate level of accuracy, it is rational to study the ponderomotor forces of the ring, which drive a hollow disk of variable thickness, hung on the ring. Design/methodology/approach: The solution of the motion problem of a hollow disk of variable thickness suspended on a force ring of rectangular cross section is based on the method of solving the equations of the theory of thermoelasticity. The stress-strain state, as well as the motion of the specified body of rotation, the disk, in studies in a cylindrical coordinate system, under the action of ponderomotor forces. Findings: The motion equation of a hollow disk hung on a force ring-torus is made, exact solutions of the motion equations of a ring in the torus form of rectangular cross section are found. New component expressions of ponderomotor forces, which appear from the action of the ring's own electromagnetic field and cause the motion of a hollow disk, have been found on the basis of Maxwell's equations. It is proved that at high speeds and low natural accelerations the stress - strain state of the disk material does not cause the destruction of the structure. Research limitations/implications: Calculations of ponderomorphic forces are valid for the ring, which drives a hollow disk of variable thickness, hung on the ring. Practical implications: It is proved that at high velocities and small natural accelerations the stress-strain state of the disk medium does not cause structural damage. It is determined that the rotation in the direction of movement at an angle of 90 degrees changes only the direction of the acceleration vector without increasing its value. Originality/value: The dependences between own time and coordinate time are formulated. It is proved that a small change in the natural time for the studied disk can significantly change the coordinate time, and the pulsed electromagnetic field provides the ability to cover infinitely large distances over finite periods of time.

A shear center demonstration model using 3D-printing

2021 ◽  
pp. 030641902110574
Author(s):  
Lawrence N Virgin
Keyword(s):  
3D Printing ◽  
Cross Section ◽  
Cross Sections ◽  
Principal Axis ◽  
Practical Importance ◽  
Bending Moment ◽  
Shear Center ◽  
Cross Sectional ◽  
Thin Walls ◽  
Section Profile

Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment about a principal axis, results in uni-directional deflection, and no twisting. For example, in aerospace structures it is particularly important to assess the propensity of an airfoil section profile to resist bending and torsion under the action of aerodynamic forces. Cross-sections made of thin-walls, whether of open or closed form are of special practical importance and form the basis of the material in this paper. The advent of 3D-printing allows the development of tactile demonstration models based on non-trivial geometry and direct observation.

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.

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