Simple stresses and strains strength of materials ce 241. Stresses and strains compressive load failure in shearstresses are acting normal to the surface yet the material failed in a different plane. 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. A surface force is of the concentrated type when it acts at a point. Stress required for forming, yield or flow stress therefore depends on several factors, such as strain, strain rate, temperature etc. To derive the constant strain triangle cst element stiffness matrix and equations. 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. Search ebooks dynamics statics mechanics fluids thermodynamics math. Points a and b are rotated to the point of maximum. Stress strain temperature relationships and thinwalled pressure vessels.
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. Stress is the external force per area in an object, and strain is the deformation of the object caused by that stress. The above geometrical data the strains will be multiplied by material properties to define a new physical. 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 tensor relates a unitlength direction vector n to the traction. All equations and diagrams of structural properties are presented in an easytouse, thumb, through format. View notes simple stresses and strains from cee 321 at university of south dakota. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 3 of. A pressure vessel crosssectional view because of i,ii, the isotropic linear elastic model is used. Mild steel bars have yield strength of 250 nmm2 and hence it. Strainbased formulas for stresses in profiled centerwound rolls article pdf available in tappi journal 827.
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. The engineering tension test is commonly used to provide basic design. For most practical purposes it can often be assumed that points a and b are coincident. The finite volume method is used in the calculation. Shear stress in fillet weld of length l subjected to load p fv 0. Tensile and compressive stress and strain equations. If the stresses are normal to the areas concerned, then these are termed as normal stresses. One of the simplest tests for determining mechanical properties of a material is the. Columns appendix basic math units basic equations sections material properties structural shapes beam equations. Gate academy plus is an effort to initiate free online digital resources.
Lecture 1 stresses and strains linkedin slideshare. 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. Apr 02, 2018 stress when we apply some forces on an object, it undergoes some deformation. Find materials for this course in the pages linked along the left. 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. However, it does so by a mathematically equivalent method by minimizing the total potential energy of the system a scalar quantity. 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. The success and failure of the process depends on how perfectly stress and strain are considered. Multiple choice questions and answers on stress management. Torsional stress, as encountered in twisting of a shaft is a shearing stress. Strength of materials for gate civil engineering 38 lessons 8 h 47 m.
This paper presents numerical analysis of stress and strain conditions of a threedimensional furniture skeleton construction and its joints. Called principal planes and the normal stresses acting on these planes are principal stresses denoted as s1, s2 and s3. Let us define the normal stresses and shear stresses in the following sections. 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. Presents simple formulas, organized by type of member, to permit more complex members to be solved. Relation between elastic constants and strain energy densities recap of lectures 1 to 11. These properties relate the stresses to the strains and can only be determined by experiment. Strength and deformability of jointed rock mass, stability of rock slopes, foundation on rocks. 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. Limit state of collapse, limit state of serviceability. Each of these stresses can be calculated from static equilibrium equations.
Modulus of elasticity e elastic materials always spring back into shape when released. Introduction to composite materials asm international. Stress life curves, sn continued common terms used with the sndiagram are fatigue life, n f. Compound stress and strain part 1 materials engineering. Here, the fully three dimensional stress state is examined. To demonstrate how to determine the stiffness matrix and stresses for a constant strain. Piping stress analysis is the most important activity in piping design. Download roarks formulas for stress and strain esm. The relationship of stress and strain for steel can be observed in.
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. Stress and strain are synonyms, and both mean an internal force per unit area. Bhattacharyya, department of civil engineering, iit kharagpur. Displacement method, stress method, airys stress functions for plane stress and strain problems, uniaxial tension, thickwalled annular cylinder subjected to. 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. 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. 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. For the most part, the discussion was confined to twodimensional states of stress.
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. As deformation starts, an internal resisting force develops to resist the. Hookes law holds up to a maximum stress called the proportional limit. This notes are best for strength of material subject. The eigenvectors of the stress matrix are the principal directions. The limiting point b for this condition is termed the elastic limit. 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. Principal stress convention ordered principal stresses in 3d. 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. Basic material properties stress and strain tensor. 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.
An alternative approach is to ignore the displacements and attempt to solve for the stresses and strains only. Approximation to the stress arising in a pressure vessel. Topic simple stress and strain lecture 1 faculty venugopal sharma. Strength of materials ce 241 course content in brief 1. Shear stress shear stress stress induced when body is subjected to equal and opposite forces that are acting parallel to resisting dl p surface. Stress calculations example 1 from statics we can determine. The joints and connections are then carefully developed. 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. What is the change in volume, if stresses in x, y and z direction are 100 mpa, 150 mpa and 160 mpa respectively. Using a cst element we have constant strains and stresses everywhere in the element domain.
Chapter 6, is expanded, presenting more coverage on electrical strain gages and providing tables of equations. Pdf numerical analysis of stress and strain in a wooden chair. Thereafter came the so called rigorous elastic theory where the levels of stresses in concrete and steel are. The basic structural unit of matter is which one of the following. Stress analysis summary from online notes chapter 3. The eigenvalues of the stress matrix are the principal stresses. However, stresses are not always induced along a direction normal to the axis, but also along inclined planes, in the form of shear stress. Stresses, strains, displacements chapter 4, members subject to bending and extension problem 4. 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.
Modulus of elasticity, poisons ratio, shear modulus etc. Stress strain relationships tensile testing one basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. Simple stress and strain strength of materials in hindi. Stress when we apply some forces on an object, it undergoes some deformation.
The modules of elasticity e for these steel is 2x105 nmn2. Basic concepts of stress and strain mechanics of materials describes how solid materials will deform. Kinematic boundary conditions exist at all three node points of the single element. Basic caepipe, pipe stress analysis software piping. Materials are subjected to complex states of stresses during forming. 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. Mechanical design of equipment addresses the stress and strain produced in di. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. Working stress method is used for the design of reinforced concrete, steel and timber structures. 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.
Piping stress analysis is also termed as piping flexibility analysis. Pdf strainbased formulas for stresses in profiled center. Simple stresses and strains mechanical engineering mcq. Nonlinear finite elementsstress and strain in one and two dimension. Stress and strain theory at a glance for ies, gate, psu 1. Definitionof prameters related to material properties. The number of cycles of stress or strain that a specimen sustains before failure occurs. Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. Lecture 2 principal stress and strain linkedin slideshare.
Strain also known as unit deformation, strain is the ratio of the change in dimension caused by the applied force, to the original dimension. As deformation starts, an internal resisting force develops to resist the deformation. Other stresses either are similar to these basic stresses or are a combination of this e. For any state of stress, we can find a set of planes on which only normal stresses act and the shearing stresses are zero. 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. Lecture notes mechanics and materials ii mechanical. Engineering stressstrain curve and true stressstrain curve are equal up. External forces acting on a body may be classified as surface forcesand body forces. Soil exploration lecture notes, notes, pdf free download, engineering notes, university notes, best pdf notes, semester, sem, year, for all, study material. Aug 08, 2011 types of stresses and strains stress strain tensile stress tensile strain compressive compressive stress strain shear stress shear strain. Oct 03, 2014 tortional stress the stresses and deformations induced in a circular shaft by a twisting moment. Strength of materials module 2 principal stress and. 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.
Wallace bending moment in curved beam insideoutside stresses. No shear stresses act on these faces because of the symmetry of the vessel and its loading. Presently he is the deputy director of iit kharagpur. 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. It is based on the elastic theory and assumes that both steel and concrete and elastic and obey.
The same method to calculate principle stresses is used to find maximum shear stress. F bc 50 kn 11,240 lb f tension f ab 40 kn 8992 lb f compression specifications. Basic concepts of stress and strain since compliant mechanisms are used for mems devices, there. Because of iii, it will be assumed that there is negligible variation in the stress field across the thickness of the vessel, fig. Module 3 constitutive equations learning objectives understand basic stress strain response of engineering materials. This article will explain the basic points for piping stress analysis. Methods to improve rock mass responses, numerical modeling of rock and rock masses. Jun 27, 2008 lecture series on strength of materials by prof. 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. Mechanical engineering strength of materials nptel. Mechanical engineering advanced strength of materials nptel. Mechanics of materials analysis is based on several basic concepts such as.
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