Aug 08, 2011 types of stresses and strains stress strain tensile stress tensile strain compressive compressive stress strain shear stress shear strain. Stress and strain are synonyms, and both mean an internal force per unit area. Module 3 constitutive equations learning objectives understand basic stress strain response of engineering materials. Tensile and compressive stress and strain equations. Lecture 2 principal stress and strain linkedin slideshare. Stress when we apply some forces on an object, it undergoes some deformation. For most practical purposes it can often be assumed that points a and b are coincident. Stress life curves, sn continued common terms used with the sndiagram are fatigue life, n f. The engineering tension test is commonly used to provide basic design. Modulus of elasticity e elastic materials always spring back into shape when released. Working stress method is used for the design of reinforced concrete, steel and timber structures. Shear stress in fillet weld of length l subjected to load p fv 0.
The limiting point b for this condition is termed the elastic limit. As deformation starts, an internal resisting force develops to resist the. However, stresses are not always induced along a direction normal to the axis, but also along inclined planes, in the form of shear stress. Mild steel bars have yield strength of 250 nmm2 and hence it. The same method to calculate principle stresses is used to find maximum shear stress. This paper presents numerical analysis of stress and strain conditions of a threedimensional furniture skeleton construction and its joints. View notes simple stresses and strains from cee 321 at university of south dakota. Bhattacharyya, department of civil engineering, iit kharagpur. All equations and diagrams of structural properties are presented in an easytouse, thumb, through format. Basic concepts of stress and strain since compliant mechanisms are used for mems devices, there. Oct 03, 2014 tortional stress the stresses and deformations induced in a circular shaft by a twisting moment. Kinematic boundary conditions exist at all three node points of the single element.
Because of iii, it will be assumed that there is negligible variation in the stress field across the thickness of the vessel, fig. Pdf numerical analysis of stress and strain in a wooden chair. Once, pipes are routed following design guidelines, those needs to be verified by piping stress analysis to ensure those will work smoothly throughout its design life. Piping stress analysis is also termed as piping flexibility analysis. Definitionof prameters related to material properties. The main assumption in the wsm is that the behaviour of structural material is restricted with in linearelastic region and the safety of it is ensured by restricting the stresses coming on the members by working loads. Apr 02, 2018 stress when we apply some forces on an object, it undergoes some deformation. Hookes law holds up to a maximum stress called the proportional limit. Called principal planes and the normal stresses acting on these planes are principal stresses denoted as s1, s2 and s3. Basic caepipe, pipe stress analysis software piping.
In this case, the application of a tensile stress produces elongation in the xdirection and contraction in the ydirection, and the distorted element remains rectangular. Basic concepts of stress and strain mechanics of materials describes how solid materials will deform. Relation between elastic constants and strain energy densities recap of lectures 1 to 11. Since thermal stresses generated are directly dependent on how stiff or flexible the layout is, in order to reduce thermal stresses, it may be necessary to make the layout flexible by including bends, offsets, loops etc. Soil exploration lecture notes, notes, pdf free download, engineering notes, university notes, best pdf notes, semester, sem, year, for all, study material. Stress strain temperature relationships and thinwalled pressure vessels. Let us define the normal stresses and shear stresses in the following sections. Nonlinear finite elementsstress and strain in one and two. Stress is the external force per area in an object, and strain is the deformation of the object caused by that stress. Gate academy plus is an effort to initiate free online digital resources.
Nptel syllabus experimental stress analysis video course course outline the course covers the basic aspects of experimental stress analysis that includes exhaustive treatment of the most versatile techniques like photoelasticity and strain gauges and also a brief introduction to the emerging techniques like digital image correlation. As deformation starts, an internal resisting force develops to resist the deformation. In any loaded member,there exists a three mutually perpendicular planes on which the shear stress vanishes zero,the three planes are called principal planes and the normal force acting acting on that principal plane are called principal stresses. To derive the constant strain triangle cst element stiffness matrix and equations. Lecture notes mechanics and materials ii mechanical. Lecture 1 stresses and strains linkedin slideshare. External forces acting on a body may be classified as surface forcesand body forces. Stress required for forming, yield or flow stress therefore depends on several factors, such as strain, strain rate, temperature etc. Stress strain relationships tensile testing one basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. Stress and strain theory at a glance for ies, gate, psu 1. Engineering stressstrain curve and true stressstrain curve are equal up. Presents simple formulas, organized by type of member, to permit more complex members to be solved.
What is the change in volume, if stresses in x, y and z direction are 100 mpa, 150 mpa and 160 mpa respectively. Search ebooks dynamics statics mechanics fluids thermodynamics math. The joints and connections are then carefully developed. Stress, strain and displacement fields stress, strain and displacement fields for various problems, beam under pure bending, analytical solution, fringe contours from various experimental methods, disc under diametral compression analytical solution, fringe contours from various experimental techniques, clamped circular plate. Useful constants that you will need to know are in a table below. Materials are subjected to complex states of stresses during forming. Topic simple stress and strain lecture 1 faculty venugopal sharma. Simple stress and strain strength of materials in hindi. Stresses and strains compressive load failure in shearstresses are acting normal to the surface yet the material failed in a different plane. Torsional stress, as encountered in twisting of a shaft is a shearing stress. The eigenvalues of the stress matrix are the principal stresses. Find materials for this course in the pages linked along the left.
To demonstrate how to determine the stiffness matrix and stresses for a constant strain. One of the simplest tests for determining mechanical properties of a material is the. The relationship of stress and strain for steel can be observed in. Columns appendix basic math units basic equations sections material properties structural shapes beam equations. Mechanical engineering strength of materials nptel. Stress analysis summary from online notes chapter 3 introduction finite element static stress analysis satisfies the differential equations for force and moment equilibrium newtons laws. Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. A surface force is of the concentrated type when it acts at a point. It is very common therefore, to find that both direct stress and shear stress occur at the same time, and as a result, the stress across any section will be neither normal nor tangential to the plane of. The most comprehensive book in its field, formulas for stress, strain, and structural matrices, second edition is a source of formulas for the analysis and design of structural members and mechanical elements. Stresses for the inside and outside fibers of a curved beam in pure bending can be approximated from the straight beam equation as modified by an appropriate curvature factor as determined from the graph below i refers to the inside, and o. Jun 27, 2008 lecture series on strength of materials by prof.
Wallace bending moment in curved beam insideoutside stresses. Strength and deformability of jointed rock mass, stability of rock slopes, foundation on rocks. For the love of physics walter lewin may 16, 2011 duration. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. Methods to improve rock mass responses, numerical modeling of rock and rock masses. Presently he is the deputy director of iit kharagpur. Thereafter came the so called rigorous elastic theory where the levels of stresses in concrete and steel are. Stresses and strains in last lecture we looked at stresses were acting in a plane that was at right anglesparallel to the action of force. The success and failure of the process depends on how perfectly stress and strain are considered. Limit state of collapse, limit state of serviceability. The number of cycles of stress or strain that a specimen sustains before failure occurs.
However, it does so by a mathematically equivalent method by minimizing the total potential energy of the system a scalar quantity. Download roarks formulas for stress and strain esm. Joints are single and double shear connections frictionless the distance from the center of the hole of joint c to the end of the member is 25mm determine. For any state of stress, we can find a set of planes on which only normal stresses act and the shearing stresses are zero. Strength of materials module 2 principal stress and. The tensor relates a unitlength direction vector n to the traction. A pressure vessel crosssectional view because of i,ii, the isotropic linear elastic model is used. Quantify the linear elastic stress strain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law.
Strain also known as unit deformation, strain is the ratio of the change in dimension caused by the applied force, to the original dimension. Introduction to composite materials asm international. Multiple choice questions and answers on stress management. Points a and b are rotated to the point of maximum.
Mechanical design of equipment addresses the stress and strain produced in di. For the most part, the discussion was confined to twodimensional states of stress. Piping stress analysis is the most important activity in piping design. Modulus of elasticity, poisons ratio, shear modulus etc. Mechanical engineering advanced strength of materials nptel. Basic concepts of stress and strain mechanics of materials describes how solid materials will deform change shape and how they will fail break when subjected to applied forces. The above geometrical data the strains will be multiplied by material properties to define a new physical. The finite volume method is used in the calculation. Approximation to the stress arising in a pressure vessel. The basic structural unit of matter is which one of the following.
Stress calculations example 1 from statics we can determine. F bc 50 kn 11,240 lb f tension f ab 40 kn 8992 lb f compression specifications. The modules of elasticity e for these steel is 2x105 nmn2. If the stresses are normal to the areas concerned, then these are termed as normal stresses. This article will explain the basic points for piping stress analysis. Stress analysis summary from online notes chapter 3. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 3 of. In continuum mechanics, the cauchy stress tensor, true stress tensor, or simply called the stress tensor is a second order tensor named after augustinlouis cauchy. Principal stress convention ordered principal stresses in 3d. An alternative approach is to ignore the displacements and attempt to solve for the stresses and strains only. Boundary value problems for elasticplastic materials 9. Simple stresses and strains mechanical engineering mcq. Using a cst element we have constant strains and stresses everywhere in the element domain. Stresses, strains, displacements chapter 4, members subject to bending and extension problem 4.
Called principal planes and the normal stresses acting on these planes are principal stresses denoted as s1, s2 and s3 convention, s1 s2 s3 the principal directions are orthogonal to. Hookes law in terms of stress and strain is stress strain in terms of the definitions l l y a f the constant of proportionality is called the elastic modulus or youngs modulus. These properties relate the stresses to the strains and can only be determined by experiment. The questions and answers on stress management have been designed in such a way that you will learn the subject in the process of answering the questions. A hypothetical value of stress at failure for exactly n f cycles as. Simple stresses and strains strength of materials ce 241. If the radius of wire stretched by a load is doubled, then its youngs modulus will be a doubled b halved c become four times. Compound stress and strain part 1 materials engineering. Pdf strainbased formulas for stresses in profiled center. Chapter 6, is expanded, presenting more coverage on electrical strain gages and providing tables of equations. Principal stresses for any state of stress, we can find a set of planes on which only normal stresses act and the shearing stresses are zero.
Nptel syllabus rock mechanics web course course outline the objective of the course is to provide basic knowledge of rock mechanics and will help to understand the design aspects of various structures inon rock like tunnels and other underground openings, slopes etc. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. Basic material properties stress and strain tensor. Each of these stresses can be calculated from static equilibrium equations. Mechanics of materials analysis is based on several basic concepts such as. Other stresses either are similar to these basic stresses or are a combination of this e. Here, the fully three dimensional stress state is examined. The eigenvectors of the stress matrix are the principal directions. No shear stresses act on these faces because of the symmetry of the vessel and its loading. Nonlinear finite elementsstress and strain in one and two dimension. Subject strength of materials topic module 2 principal stress and strain lecture 18 faculty venugopal sharma gate academy plus is an effort to initiate free online digital resources. Shear stress shear stress stress induced when body is subjected to equal and opposite forces that are acting parallel to resisting dl p surface. Strainbased formulas for stresses in profiled centerwound rolls article pdf available in tappi journal 827. Roarks formulas for stress and strain book provides tabulated formulations that can be applied to the stress analysis of a comprehensive range of structural components.
It is based on the elastic theory and assumes that both steel and concrete and elastic and obey. Displacement method, stress method, airys stress functions for plane stress and strain problems, uniaxial tension, thickwalled annular cylinder subjected to. Formulas for stress, strain, and structural matrices walter. Stressstrain analysis or stress analysis is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces.
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