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.

Load Regime Diagram of a Pipe With Cyclically Plastic Bending

2002 ◽  
Author(s):  
Yanping Yao ◽  
Ming-Wan Lu
Keyword(s):  
Axial Force ◽  
Bending Moment ◽  
Boundary Curve ◽  
Plastic Behavior ◽  
Cyclic Bending ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Load Regime ◽  
Reversed Cyclic ◽  
Cyclic Bending Moment

The criteria of piping seismic design based on linear elastic analysis has been proved to be conservative, which is mainly because the influence of plastic deformation on piping dynamic response is neglected. In the present paper, a pipe under seismic excitation is simplified as an beam with tubular cross section subjected to steady axial force and fully reversed cyclic bending moment, and the elastic-plastic behavior of the pipe is studied. Various behavior of the pipe under different combinations of axial force and cyclic bending moment is discussed and the boundary curve equations between them are obtained. Also the load regime diagram for a pipe which is formed by the boundary curve equations in the loading plane is given, from which the elastic-plastic behavior of the pipe can be determined directly.

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.

Elastic-Plastic Stress Analysis in a Thermoplastic Composite Cantilever Beam Loaded by Bending Moment

2002 ◽  
Vol 21 (2) ◽  
pp. 175-176
Author(s):  
Onur Sayman ◽  
Mesut Uyaner ◽  
Necmeitin Tarakçioglu
Keyword(s):  
Stress Analysis ◽  
Cantilever Beam ◽  
Yield Criterion ◽  
Stress Component ◽  
Bending Moment ◽  
Thermoplastic Composite ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Governing Differential Equation ◽  
Plastic Stress

In this study, an elastic-plastic stress analysis is carried out in a thermoplastic composite cantilever beam loaded by a bending moment at the free end. The composite beam is reinforced unidirectionally by steel fibers at 0, 30. 45, 60, and 90° orientation angles. An analytical solution is performed for satisfying both the governing differential equation in the plane stress case and boundary conditions for small plastic deformations. The solution is carried out under the assumption of the Bernoulli-Navier hypotheses. It is found that the intensity of the residual stress component of σ x is maximum at the upper and lower surfaces or at the boundary of the elastic and plastic regions. The composite material is assumed to be as hardening linearly. The Tsai-Hill theory is used as a yield criterion.

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.

Elastic-Plastic Stress Analysis in a Thermoplastic Composite Cantilever Beam Loaded by Bending Moment

2002 ◽  
Vol 21 (2) ◽  
pp. 175-192
Author(s):  
Onur Sayman ◽  
Mesut Uyaner ◽  
Necmettin Tarakçioglu
Keyword(s):  
Stress Analysis ◽  
Cantilever Beam ◽  
Yield Criterion ◽  
Stress Component ◽  
Bending Moment ◽  
Thermoplastic Composite ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Governing Differential Equation ◽  
Plastic Stress

In this study, an elastic-plastic stress analysis is carried out in a thermoplastic composite cantilever beam loaded by a bending moment at the free end. The composite beam is reinforced unidirectionally by steel fibers at 0, 30, 45, 60, and 90° orientation angles. An analytical solution is performed for satisfying both the governing differential equation in the plane stress case and boundary conditions for small plastic deformations. The solution is carried out under the assumption of the Bernoulli-Navier hypotheses. It is found that the intensity of the residual stress component of σ x is maximum at the upper and lower surfaces or at the boundary of the elastic and plastic regions. The composite material is assumed to be as hardening linearly. The Tsai-Hill theory is used as a yield criterion.

scholarly journals Stretching of a cylindrical rod of variable cross-section in the theory of small elastic-plastic

2020 ◽  
pp. 78-81
Author(s):  
Николай Ильич Петров
Keyword(s):  
Cross Section ◽  
Axisymmetric Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Initial State ◽  
Plastic Deformations ◽  
Linearized Equations ◽  
Elastic Plastic

В работе рассматривается растяжение бесконечно длинного цилиндрического стержня переменного сечения. Используются результаты решения линеаризированных уравнений теории малых упругопластических деформаций [1-7] в случае осесимметричной задачи. Предполагается, что в начальном состоянии имеет место простое растяжение. We considers the stretching of an infinitely long cylindrical rod of variable cross-section. The results of solving the linearized equations of the theory of small elastic-plastic deformations [1-7] in the case of an axisymmetric problem are used. It is assumed that a simple stretch occurs in the initial state.

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.

scholarly journals Non-linear Analysis of Slender High Strength Concrete Column

2019 ◽  
Vol 5 (7) ◽  
pp. 1440-1451
Author(s):  
Ernesto Fenollosa ◽  
Iván Cabrera ◽  
Verónica Llopis ◽  
Adolfo Alonso
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Axial Force ◽  
High Strength Concrete ◽  
Bending Moment ◽  
High Strength ◽  
Concrete Columns ◽  
Strength Concrete ◽  
The Moment ◽  
High Strength Concrete Columns

This article shows the influence of axial force eccentricity on high strength concrete columns design. The behavior of columns made of normal, middle and high strength concrete with slenderness values between 20 and 60 under an eccentric axial force has been studied. Structural analysis has been developed by means of software which considers both geometrical and mechanical non-linearity. The sequence of points defined by increasing values of axial force and bending moment produced by eccentricity has been represented on the cross-section interaction diagram until failure for each tested column. Then, diagrams depicting the relationship between failure axial force and column's slenderness have been drawn. The loss of bearing capacity of the member for normal and middle strength columns when compared with the bearing capacity of their cross-section is more noticeable as axial force eccentricity assumes higher values. However, this situation reverses for high strength columns with high slenderness values. On the basis of results obtained, the accuracy level for the moment magnifier method was checked. Despite the good concordance in most of the cases, it was verified that the moment magnifier method leads to excessively tight results for high strength concrete columns with high slenderness values. In these specific cases, a coefficient which amends the column rigidity is proposed so as to obtain safer values.

Buckling Analysis of the Tube Compression-Bending Member in Elastic-Plastic State with ANSYS

2011 ◽  
Vol 327 ◽  
pp. 143-148
Author(s):  
Zhi Cai Jiang ◽  
Wei Lian Qu
Keyword(s):  
Axial Compression ◽  
Bending Moment ◽  
Steel Structure ◽  
Plastic Instability ◽  
Plastic State ◽  
Axial Pressure ◽  
Nonlinear Buckling ◽  
Elastic Plastic ◽  
Compression Stiffness ◽  
The Relationship

Stability is an important issue in steel structure design.When the steel member is subjected to elastic-plastic instability, the axial compression stiffness reduces with the increasing axial pressure and bending moment at end. Therefore, the authors analyze the process of steel member that is instable in elastic-plastic state in this paper by studying the degradation laws of axial compression stiffness. The eigenvalue buckling and nonlinear buckling analyses of axially compressed member and compression-bending member are carried out by using commercial package ANSYS in this study. The relationship curve between the axial force at end and the axial compression stiffness and the relationship surface among the axial pressure at end, bending moment at end and the axial compression stiffness are determined respectively. The made observations indicate that it is feasible to analyze the process of the steel member that is instable in elastic-plastic state by investigating the degradation properties of axial compression stiffness, which becomes lower with axial pressure at end and bending moment at end.

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.

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