Bending of Beams with Nonlinear Material Characteristics

1980 ◽  
Vol 102 (4) ◽  
pp. 776-780 ◽  
Author(s):  
G. Szuladzinski
Keyword(s):  
Cross Sections ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Bending Moment ◽  
Nonlinear Material ◽  
Stress Strain ◽  
Slope Change ◽  
Deflection Analysis ◽  
Manual Methods ◽  
Bending Of Beams

When an expression is known for the curvature of a beam as a function of a bending moment, it is a simple matter to determine the deflected shape. It is a bigger problem to obtain such an explicit expression using a realistic stress-strain curve. This paper begins with a Ramberg-Osgood type of stress-strain formula, that is characterized by a continuous slope change typical of metals in elevated temperatures. A moment-curvature equation of a similar form is then developed and its accuracy is verified for several basic cross-sections. The advantage of this approach is to improve the accuracy and efficiency of deflection analysis compared with the existing manual methods.

The Bending of Some Common Beam Sections into the Plastic Range

1953 ◽  
Vol 57 (506) ◽  
pp. 110-115 ◽  
Author(s):  
Anthony J. Barrett
Keyword(s):  
Cross Sections ◽  
Strain Curve ◽  
Bending Moment ◽  
Mathematical Form ◽  
Military Aircraft ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Actual Material ◽  
The Subject ◽  
Axis Of Symmetry

SummaryThere is already in existence a fair volume of work on the subject of bending beyond the limit of proportionality, most of which requires the use of actual material stress-strain curves. This note aims to examine the problem in a more general way by using an accurate mathematical form for the stress-strain curve, strain and bending moments being expressed as functions of the ratios of various properties of the material.The value of maximum permissible fibre stress is considered in relation to current requirements for military aircraft stressing and a guide is presented for the maximum permissible bending moment in some of the more familiar beam cross sections bending about an axis of symmetry.

Influence of FRP-to-Concrete Gap Effect on Axial Strains of FRP-Confined Concrete Columns

2015 ◽  
Vol 1119 ◽  
pp. 760-765
Author(s):  
Thomas Vincent ◽  
Togay Ozbakkloglu
Keyword(s):  
Cross Sections ◽  
Axial Stress ◽  
Axial Strain ◽  
Strain Curve ◽  
Shrinkage Strain ◽  
Confined Concrete ◽  
Gap Effect ◽  
Stress Strain ◽  
Concrete Shrinkage ◽  
Concrete Interface

This paper reports on an experimental investigation on the influence of FRP-to-concrete interface gap, caused by concrete shrinkage, on axial compressive behavior of concrete-filled FRP tube (CFFT) columns. A total of 12 aramid FRP (AFRP)-confined concrete specimens with circular cross-sections were manufactured. 3 of these specimens were instrumented to monitor long term shrinkage strain development and the remaining 9 were tested under monotonic axial compression. The influence of concrete shrinkage was examined by applying a gap of up to 0.06 mm thickness at the FRP-to-concrete interface, simulating 800 microstrain of shrinkage in the radial direction. Axial strain recordings were compared on specimens instrumented with two different measurement methods: full-and mid-height linear variable displacement transformers (LVDTs). Results of the experimental study indicate that the influence of interface gap on stress-strain behavior is significant, with an increase in interface gap resulting in a decrease and increase in the compressive strength and ultimate axial strain, respectively. It was also observed that an increase in interface gap leads to a slight loss in axial stress at the transition region of the stress-strain curve. Finally, it is found that an increase in the interface gap results in a significant decrease in the ratio of the ultimate axial strains obtained from mid-section and full-height LVDTs.

A Modified Johnson–Cook Model to Predict Stress-strain Curves of Boron Steel Sheets at Elevated and Cooling Temperatures

2012 ◽  
Vol 31 (1) ◽  
Author(s):  
Nguyen Duc-Toan ◽  
Banh Tien-Long ◽  
Jung Dong-Won ◽  
Yang Seung-Han ◽  
Kim Young-Suk
Keyword(s):  
Tensile Test ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Boron Steel ◽  
Isotropic Hardening ◽  
Air Cooling ◽  
Stress Strain ◽  
Material Parameters ◽  
Hardening Law ◽  
Simulation Results

AbstractIn order to predict correctly stress-strain curve for tensile tests at elevated and cooling temperatures, a modification of a Johnson–Cook (J-C) model and a new method to determine (J-C) material parameters are proposed. A MATLAB tool is used to determine material parameters by fitting a curve to follow Ludwick and Voce's hardening law at various elevated temperatures. Those hardening law parameters are then utilized to determine modified (J-C) model material parameters. The modified (J-C) model shows the better prediction compared to the conventional one. An FEM tensile test simulation based on the isotropic hardening model for metal sheet at elevated temperatures was carried out via a user-material subroutine, using an explicit finite element code. The simulation results at elevated temperatures were firstly presented and then compared with the measurements. The temperature decrease of all elements due to the air cooling process was then calculated when considering the modified (J-C) model and coded to VUMAT subroutine for tensile test simulation. The modified (J-C) model showed the good comparability between the simulation results and the corresponding experiments.

Buckling of Rectangular Cross-Ply Laminated Plates With Nonlinear Stress-Strain Behavior

1979 ◽  
Vol 46 (3) ◽  
pp. 637-643 ◽  
Author(s):  
Harold S. Morgan ◽  
Robert M. Jones
Keyword(s):  
Strain Curve ◽  
Material Model ◽  
Laminated Plates ◽  
Nonlinear Material ◽  
Stress Strain ◽  
Buckling Loads ◽  
Strain Behavior ◽  
Reinforced Composite ◽  
Nonlinear Stress ◽  
Behavior Characteristic

The Jones-Nelson-Morgan nonlinear material model is used in the derivation of a buckling criterion for laminated plates with nonlinear stress-strain behavior characteristic of many fiber-reinforced composite materials. A search procedure is developed to solve this buckling criterion which is transcendental because of interdependence of the buckling load and the coefficients relating the variations in laminate forces and moments to the variations in strains and curvatures. The effect of stress-strain curve nonlinearities on laminate buckling loads is illustrated by comparing solutions of the buckling criterion to buckling loads for laminates with linear stress-strain behavior.

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 Experimental and Theoretical Investigation on the Thermo-Mechanical Properties of Recycled Aggregate Concrete Containing Recycled Rubber

2021 ◽  
Vol 8 ◽  
Author(s):  
Yunchao Tang ◽  
Wanhui Feng ◽  
Zheng Chen ◽  
Yumei Nong ◽  
Minhui Yao ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Elevated Temperatures ◽  
Microstructural Analysis ◽  
Strain Curve ◽  
Recycled Aggregate Concrete ◽  
Recycled Aggregate ◽  
Recycled Aggregates ◽  
Stress Strain ◽  
Aggregate Concrete ◽  
Recycled Rubber

The utilization of recycled aggregates made from construction wastes and recycled rubber made from waste tires is an effective method to realize the sustainable development. Thus, this study aims to determine the feasibility of using recycled aggregate concrete containing rubber, named rubberized recycled aggregate concrete (RRAC) as a new type of green-building material. The experimental carbon emissions test verified RRAC as a low-carbon material. In addition, the residual mechanical properties of RRAC were investigated under elevated temperatures. After exposure at 200, 400, and 600 C for 60 min, the stress−strain curve, compressive strength, energy absorption capacity, and spalling resistance of RRAC with recycled aggregate replacement ratios of 50 and 100%, rubber contents of 0, 5, 10, and 15% were explored with microstructural analysis. Moreover, empirical models were proposed to describe the effects of heated temperatures and rubber contents on the stress–strain relationship of RRAC. The results indicated that the rubber particles could reduce the spalling of specimens based on the vapor pressure theory. Therefore, this study provided scientific guidance for the design of structures made with RRAC for resisting high temperatures.

Deformational characteristics of thermally treated sandstone from an underground coalmine fire region, India

2021 ◽  
Author(s):  
Adarsh Tripathi ◽  
Noopur Gupta ◽  
Ashok Kumar Singh ◽  
Nachiketa Rai ◽  
Anindya Pain
Keyword(s):  
Large Scale ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Small Scale ◽  
Carbonaceous Shale ◽  
Deformation Pattern ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Thermomechanical Behaviour ◽  
Thermally Treated

<p>The Jharia region of lower Gondwana in India is one of the largest Underground Coalmine Fires (UCF) affected coalfield in the world. The UCF induced small scale as well as large-scale surface fracturing often creates the life-threatening conditions to coal miners and local surroundings. So, there is a need to understand the thermomechanical behaviour of coal measures rocks to predict the land disturbances in thermo-environmental conditions. It will provide an insight into the UCF induced subsidence mechanism and its preventive measures. The Jharia coal field predominantly consists of sandstone (75-80% by volume) and rest is composed of coal, shale and carbonaceous shale. The present study focuses on thermo-mechanical behaviour of Barakar sandstone (BS) under elevated temperatures. The cores of BS sample were prepared according to the ISRM standards. Further, samples were grouped and thermally treated in temperature range of 25°C, 100°C, 150°C, 300°C, 400°C, 500°C, 600 °C, 700°C and 800°C at a heating rate of 5°C/min for 24 hours in furnace.  Then, these thermally treated BS samples were subjected to laboratory test for stress-strain characteristics. In the process of deformational characteristics evaluation, effect of mineralogical changes and mode of fracture pattern were also studied at the mentioned elevated temperature. Based on the obtained results, the deformational behaviour of thermally treated BS specimens can be grouped into three zones, viz., zone 1 (25-300°C), zone 2 (300-500°C) and zone 3 (500-800°C). In zone 1, the characteristics of the stress-strain curve is similar to those under air dried sandstone specimen. However, small increment in stiffness were observed upto 300°C. The stress-strain curves in this zone shows dominantly brittle fracturing. The increment in stiffness may be related to evaporation of pore water that increases the cohesion between the mineral grains resulting higher stiffness value. In zone 2, the deformation pattern again shows brittle fracturing with continuous decrement in stiffness. The reduction in stiffness may be related to thermally induced porosity and increased microcrack density. In zone 3, the stress strain curve is observed to be concave upward. It indicates the pseudo-ductile behaviour of the thermally treated BS specimens. The observed results suggest a typical behaviour of deformation pattern under UCF induced rock fracturing which may be useful in predicting the land subsidence in UCF affected areas. Present research outcome may be used to design the support measures to reduce the associated hazards.</p>

Experimental Setup for the Determination of Mechanical Solder Materials Properties at Elevated Temperatures

2010 ◽  
Vol 638-642 ◽  
pp. 3793-3798
Author(s):  
Wolfgang H. Müller ◽  
Holger Worrack ◽  
Jens Sterthaus
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Elevated Temperatures ◽  
Young's Modulus ◽  
Linear Optimization ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Non Linear

The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young’s modulus, yield stress, and hardness are of great interest. Moreover, a complete stress-strain curve is desirable for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). However, since the amount of matter is so small and it is the intention to describe its behavior as realistic as possible, miniature tests are used for measuring the mechanical properties. In this paper two miniature tests are presented for this purpose, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial load is prescribed and the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and by fitting the corresponding parameters to the experimental data (obtained for various microelectronic solders) by means of a non-linear optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Oliver and Pharr this data can be used to obtain hardness and Young’s modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equations for stress and strain are obtained by means of the inverse method. The stress-strain curves from nanoindentation and tensile tests are compared for two mate-rials (aluminum and steel). Differences are explained in terms of the locality of the measurement. Finally, material properties at elevated temperature are of particular interest in order to characterize the materials even more completely. We describe the setup for hot stage nanoindentation tests in context with first results for selected materials.

Tension-compression stress-strain curves from bending tests

1971 ◽  
Vol 6 (4) ◽  
pp. 286-292 ◽  
Author(s):  
P W J Oldroyd
Keyword(s):  
Strain Curve ◽  
Bending Moment ◽  
Uniaxial Stress ◽  
Bending Test ◽  
Compression Stress ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Bending Tests ◽  
Original Length ◽  
Annealed Copper

A formula—Nadai's bending formula—is derived which enables the tension (or compression) stress-strain curve for a material to be obtained from the curve relating bending moment to curvature for a beam of solid rectangular section. The method is extended to give a formula which covers deformations in which reversals of plastic strain occur. The results obtained from a unidirectional bending test made on annealed copper are compared with those obtained from a tensile test made on the same material and the accuracy of the stress-strain values obtained from the bending test is discussed. The results obtained from a reversed bending test are also compared with those obtained from a tension-compression test in which a specimen was first stretched and then compressed to its original length. The limitations imposed by this method of obtaining the stress-strain curve for a material are examined and the advantages its presents in the study of the behaviour of materials under uniaxial stress are outlined.

Sign in / Sign up

Export Citation Format

Share Document