Nptel video lectures, iit video lectures online, nptel youtube lectures, free video lectures, nptel online courses. Concepts of stress and strain one of our principal concerns in this course is material behavior strength. Introduction free body diagram revisited normal, shear and bearing stress stress on inclined planes under axial loading strain mechanical properties of materials true. The stress can be measured and has a unit of measure while strain. Unit 1 stress and straintopics covered lecture 1 introduction, state of plane stress lecture 2 principle stresses and strains lecture 3 mohrs stress circle and theory of failure lecture 4 3d stress and strain, equilibrium equations and impact loading lecture 5 generalized hooks law and.
Nptel video lectures, iit video lectures online, nptel youtube lectures. Mechanics of solids simple stress and strain part 1. For any state of stress, we can find a set of planes on which only normal stresses act and the shearing stresses are zero. Stress required for forming, yield or flow stress therefore depends on several factors, such as strain, strain rate, temperature etc. Mechanics of solids simple stress and strain simple stress and strain part 1.
Stress strain relation considering thermal effects. Strain energy elastic strain energy, u energy spent by the external forces in deforming an elastic body du0. The stress can occur without strain, but strain cannot occur with the absence of stress. Stress and strain study notes for mechanical engineering. Stressstrain curve for this material is plotted by elongating the sample and recording the stress variation with strain until the sample fractures.
Lecture notes mechanics and materials ii mechanical. The three invariants are given by the roots of the following equation. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 4. Modulus of elasticity, poisons ratio, shear modulus etc. The firm line denotes engineering stress strain plot where as the dotted line is the true stress strain plot. Lecture 6 numerical problems on shear strain, modulus of rigidity lecture 7 stressstrain diagram for uniaxial loading of ductile and brittle materials. Stressstrain relationship, hookes law, poissons ratio, shear stress, shear strain, modulus of rigidity. Civl 78117 chapter 6 plane stressplane strain stiffness equations part 1.
Strain approximationin terms of straindisplacement matrix stress approximation summary. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 3 of 9 further analysis and extrusion defects 1. Engineering stress true stress engineering strain true strain. Lecture 1 stresses and strains linkedin slideshare. This notes are best for strength of material subject. Consider a crystal with acrosssectionalareaa 0 being deformed in tension by an applied force f along the axis of the cylindrical crystal. The fe solution was based on the approximate linear displacement. Mechanical engineering advanced strength of materials nptel. The mechanical properties that we look for the selection of metals and alloys for a given application are the yield strength or the tensile strength. Strain,% stress,mpa toughness,mjm 3kgm jkg ancientiron 0. If the material is subjected to torsion, it results in torsional strain. Relationship between material properties of isotropic materials.
This expression is identical in form with the equation defining the direct stress on any inclined plane q with ix and iy replacing sx and sy and. 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 stress tensor the secondorder tensor which we will be examining has. Definition of stress, stress tensor, normal and shear stresses in axially loaded members. 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. In most crystals, slip occurs with equal ease forward or backward, so a characteristic shear stress is required for slip. But strength models are often intimately related to stress. Apr 08, 2018 engineering stress true stress engineering strain true strain. Bhattacharyya, department of civil engineering, iit kharagpur. We are satisfied with engineering stress strain diagrams since this is good enough to estimate these. There will be some repetition of the earlier analyses.
Unit 1 stress and straintopics covered lecture 1 introduction, state of plane stress lecture 2 principle stresses and strains lecture 3 mohrs stress circle and theory of failure lecture 4 3d stress and strain, equilibrium equations and impact loading lecture 5 generalized hooks law and castiglionos. The above geometrical data the strains will be multiplied by material properties to define a new physical. Strength of material som notes free pdf download strength of material notes by prof. Mechanical engineering strength of materials nptel. Here, the fully three dimensional stress state is examined. There is no relationship exists in between stress and strain of the. The true stress is defined as the ratio of the load to the crosssection area at any instant. Examples on calculation of strains and tractions, principal stresses and. However for metal working we need to know the true stress versus true strain plots.
Modulus of elasticity e elastic materials always spring back into shape when released. As the engineering design of different components, structures etc. Stresses, however, cannot be directly measured, but stain is measurable and can be directly related to stress. Ppt stress and strain powerpoint presentation free to. Stress and straindefinition, curve or diagram, formula, pdf.
Hookes law, poissons ratio, shear stress lecture 5 shear strain, modulus of rigidity, bulk modulus. Imagine an arbitrary solid body oriented in a cartesian coordinate system. Both mathematical and engineering mi stakes are easily made if this crucial difference is not recognized and understood. Aug 08, 2011 unit 1 stress and straintopics covered lecture 1 introduction, state of plane stress lecture 2 principle stresses and strains lecture 3 mohrs stress circle and theory of failure lecture 4 3d stress and strain, equilibrium equations and impact loading lecture 5 generalized hooks law and castiglionos. By convention, the strain is set to the horizontal axis and stress is set to vertical axis. Shear strain is the complement of the angle between two initially perpendicular line segments. Stress is defined as a force that can cause a change in an object or a physical body while a strain is a change in the form or shape of the object or physical body on which stress is applied. We can recover any stressstrain information using the given the node displacements, including.
Lecture 2 principal stress and strain linkedin slideshare. Basic concepts of stress and strain since compliant mechanisms are used for mems devices, there is a significant need to understand the mechanics of materials. Strain effects on flow stress and hence on extrusion pressure are predominant for hot extrusion. Straindisplacement, stressstraintemperature, and stressequilibrium. Stresses in terms of the original xy reference frame used to form the element equations and the n and b matrices. Stress strain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029 august 23, 2001. For the most part, the discussion was confined to twodimensional states of stress. Stressstrain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029. Stressstrain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029 august 23, 2001. This lecture includes following topics what is stress. They have the tendency to hold the deformation that occurs in the plastic region.
Above this point, stress is no longer linearly proportional to strain. Materials are subjected to complex states of stresses during forming. Stress is a directed force distributed over an area. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 4 of. The relationship of stress and strain for steel can be observed in the following movie. The subsequent part indicates the increase in yield stress with strain or work hardening. An assessment of the true stresstrue strain curve provides a realistic characteristic of the material. Strain life continued the apparent poor fit of the coffinmanson relationship in figure 1 is due to the narrow strain range of the gathered data, demonstrating a caveat of the strainlife method. The truestresstruestrain curves are obtained by converting the tensile stress and its corresponding strain into true values and extending the curve.
For each element element stiffness matrix element nodal load vector u n d. To determine the shear stain in the direction om consider the displacement of point p at the foot of the. This number is a function of many variables, including stress level, stress state, cy. Normal strain is the change in length in a given direction divided by the initial length in that direction. Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials. The stressstrain curve depends on two types of material. Strength of materials is a fundamental subject needed primarily for the students of mechanical sciences. Ghosh, dept of metallurgical and materials engineering be divided into elastic and plastic parts. Definitionof prameters related to material properties.
This curve is a behavior of the material when it is subjected to load. Stress strain curve of mild steel bar in tension created by aman. Mar 23, 2020 stress is defined as a force that can cause a change in an object or a physical body while a strain is a change in the form or shape of the object or physical body on which stress is applied. Stressstrain testing tension tests engineering stress engineering strain compression tests a0. A free powerpoint ppt presentation displayed as a flash slide show on id. Ductile materials are materials that can be plastically twisted with no crack. Second invariant, i2, is the sum of principal minors third invariant, i3, is the determinant of the matrix. On stress strain curve, proportional limit is shown by p. Aug 08, 2011 lecture 2 principal stress and strain 1. Civl 78117 chapter 6 plane stress plane strain stiffness equations part 1 1181. 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. Constant strain triangle cst recommendations for use.
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