Straindisplacement, stressstraintemperature, and stressequilibrium. Pdf day 17 simple stress and strain relationship gate. Mechanics of solids simple stress and strain simple stress and strain part 1. Stresses, however, cannot be directly measured, but stain. Stress and strain, stressstrain relationship and elastic constants, mohrs circle for plane stress and plane strain, thin cylinders. This stresscurve is typical for ductile metallic elements.
Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. Hookes law holds up to a maximum stress called the proportional limit. Concepts of stress and strain one of our principal concerns in this course is material behavior strength. But we keep on applying the load it undergoes through the maximum stress and then fails at a lower value. Simple bending theory or theory of flexure for initially straight beams. Syllabus introduction, stress, strain, mechanical properties of materials, linear elasticity, hookes law and poissons ratio, stressstrain relation behaviour in tension for mild steel, cast iron and non ferrous metals. Strength of material study notes hand written free pdf stuff. Unit 1 simple stress and strain linkedin slideshare. Prediction of fatigue life the fatigue life of any specimen or structure is the number of stress strain cycles required to cause failure. 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.
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. Relationship between material properties of isotropic materials. Elasticity and plasticity in building engineering theoretical basement for the theory of structures important for steel, concret, timber structures design to be able design safe structures to resist mechanical load, temperature load statics. Stresslife curves, sn sncurves obtained under torsion or bending loadcontrol test conditions often do not have data at the shorter fatigue lives say 103 or 104 cycles and less due to significant plastic deformation. From the diagram one can see the different mark points on the curve. Stress and straindefinition, curve or diagram, formula, pdf. Bending moment and shear force diagram, bending stresses and deflection of beam.
The above geometrical data the strains will be multiplied by material properties to define a new physical. Flow stress is the stress required to sustain a certain plastic strain on the material. Oct 04, 2018 topic simple stress and strain lecture 1 faculty venugopal sharma. Quantify the linear elastic stressstrain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law. Both mathematical and engineering mi stakes are easily made if this crucial difference is not recognized and understood. The shape of the nominal stressstrain diagram, fig. Hookes law, poissons ratio, shear stress lecture 5 shear strain, modulus of rigidity, bulk modulus.
Topic simple stress and strain lecture 1 faculty venugopal sharma. The hooks law, states that within the elastic limits the stress is proportional to the strain since for most materials it is impossible to describe the entire stress strain curve with simple mathematical expression, in any given problem the behavior of the materials is. Above this point, stress is no longer linearly proportional to strain. Stress strain relation considering thermal effects. If you can remember last time i had demonstrated that the stress strain relationship is of this particular form where this xaxis represents strain and the yaxis represents stress. This lecture includes following topics what is stress. For most practical purposes it can often be assumed that points a and b are coincident. Strength of material study notes hand written free pdf. Lecture 2 principal stress and strain linkedin slideshare.
The true stress is defined as the ratio of the load to the crosssection area at any instant. Book on mechanics of materialssimple stress and strain. Aug 08, 2011 lecture 2 principal stress and strain 1. Strain a point can be displaced by translation, rotation, and deformation. Worked out examples are provided at the end of sections 2. In fluid mechanics, simple shear is a special case of deformation where only. Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials. The stress can occur without strain, but strain cannot occur with the absence of stress. Here, the fully three dimensional stress state is examined. Nptel notes pdf civil engineering 105 courses in pdf format ships within 5 days. In engineering it is more convenient to measured as the force n per square mm. Lecture 9 stress strain relations stress strain relations. Concepts of stress and strain university of arizona.
The stressshown in is an example of a textfigure 6. Mechanical engineering strength of materials nptel. On stress strain curve, proportional limit is shown by p. Exercises simple stresses and strains 1 authorstream.
This number is a function of many variables, including stress level, stress state, cy. Lecture notes mechanics and materials ii mechanical. If we require a 3d analysis of materials, we must use a more. In a first course on mechanics of solids one learns the stress distribution on slender members subjected to simple loading configurations. There will thus be some permanent deformation or permanent set when load is removed.
Herewith we have shared the important gate civil engineering notes pdf. Strength of materials module 1 simple stress and strain. There will be some repetition of the earlier analyses. The stress can be measured and has a unit of measure while strain. Strain is a strain is a change in length per unit original length, while.
Slip results in theformation of steps on the surface of the crystal. Lecture 6 numerical problems on shear strain, modulus of rigidity lecture 7 stressstrain diagram for. The pressure developed may be irregular in the above examples but the. The topics that are covered in this pdf containing strength of materials som previous year gate solved questions are. Conventionally, a shear strain is defined by the shear angle produced in simple shear, below. Flow stress can be determined form simple uniaxial tensile test, homogeneous compression test, plane strain compression test or torsion test. This gives the common engineering unit of stress, mpa. Subject strength of materials topic simple stress and strain lecture 1 faculty venugopal sharma gate academy plus is an effort to initiate free. K bhattacharyya, department of civil engineering, iit kharagpur.
Even great minds in the field of mechanics have committed blunders and it took 200 years to develop an acceptable theory on the deflection of beams. 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. Download pdf, 428kb we will take strict action on publishing above pdf to another website. Kn e stressstrain as per previous calculations strain. Bvs viswanadham, department of civil engineering, iit. Mechanics of solids simple stress and strain part 1. The stress tensor the secondorder tensor which we will be examining has. Mechanics of materials 10me34 compiled by hareesha n g, asst prof, dsce page 2 unit 1. The stress strain curve says that if we apply load gradually up to elastic limit, if we release the load the load the member comes back to its original position.
Ppt stress and strain powerpoint presentation free to. No matter what stresses are imposed on an elastic body, provided the material does not. But strength models are often intimately related to stress. Erich schmiddiscovered that if a crystal is stressed, slip begins when the shear stresson a slip system reaches a critical value, 2 c, often called the. Herewith we have shared the important gate civil engineering notes pdf for the topic of simple stress and strain relationship. It is defined as the ratio of change in dimensionmight be length,dia etc. Stress and strain, stressstrain relationship and elastic constants, mohrs circle for plane stress and plane strain, thin cylinders, shear force and bending moment diagrams. A particular form of elasticity which applies to a large range of engineering. Strain,% stress,mpa toughness,mjm 3kgm jkg ancientiron 0. Stressstrain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029.
Nov 27, 2015 mechanics of materials 10me34 compiled by hareesha n g, asst prof, dsce page 2 unit 1. The stressstrain diagram for a tension test can now be described using the true stressstrain or nominal stressstrain definitions, as in fig. Erich schmiddiscovered that if a crystal is stressed, slip begins when the shear stresson a slip system reaches a. Plane stress and plane strain, simple problems in cartesian and polar coordinates, moduleii hours. For any state of stress, we can find a set of planes on which only normal stresses act and. Stresses, however, cannot be directly measured, but stain is measurable and can be directly related to stress. Sep 01, 2018 the topics that are covered in this pdf containing strength of materials som previous year gate solved questions are. Sep 14, 2014 stress strain curve is a behavior of material when it is subjected to load. Elastic materials hookes law a material is said to be elastic if it returns to its original, unloaded dimensions when load is removed. Materials are prepared, explaining the fundamentals in a simple and lucid manner so that the students can grasp the basics of. Review of stress, linear strain and elastic stressstrain relations 37 relations for small deformation of linearly elastic materials. Stress strain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029 august 23, 2001. The basic unit of stress is the pascal pa which is newton per square metre. Failure criteria for yielding toward indonesia 2020.
Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other. Stress strain curve of mild steel bar in tension created by aman. Stress and strain study notes for mechanical engineering. These are readily detected if the surface is carefully polished beforeplastic deformation. This part we call it as a failure stress and this part, the maximum stress, we call as ultimate stress. Stressstrain diagram for uniaxial loading of ductile and brittle. 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. For the most part, the discussion was confined to twodimensional states of stress. Its a graph which represents stress value against strain value of the given material,when the material is subjected to increasing pull. Pdf strength of materials som gate solved questions. E stressstrain as per previous calculations stress 70. Stress is a directed force distributed over an area. Strain and stress are fundamentally different quantities, which do not share a simple cause and ef fect relationship.
Gate academy plus is an effort to initiate free online digital resources for the first time in india and particularly. Dec 19, 2018 mechanics of solids simple stress and strain simple stress and strain part 1. In this diagram stresses are plotted along the vertical axis and as a result of these stresses, corresponding strains are plotted along the horizontal axis. Stress strain curve is a behavior of material when it is subjected to load. Thus the need for measures of stress and strain based on instantaneous.
Strain energy elastic strain energy, u energy spent by the external forces in deforming an elastic body du0. Definition of stress, stress tensor, normal and shear stresses in axially loaded members. But we keep on applying the load it undergoes through the maximum stress and then fails at a lower. The above equation is a simple linear model for the 1d analysis of materials operating in the elastic region of behavior. Sriman k bhattacharya dept of civil engineering nptel. Stress state, mohrs circle analysis and pole, principal stress space. Finally, the whole chapter is summarized in section 2. The limiting point b for this condition is termed the elastic limit. 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. Strain and stress are fundamentally different quantities, which do not share a simple causeandef fect relationship. Yielding and fracture can be visualized in a typical tensile test as shown in the clipping typical engineering stressstrain relationship from simple tension tests for. Straindisplacement relations, equilibrium equations, compatibility conditions and airys stress function. In reality, not all stressstrain curves perfectly resemble the one shown in strain figure 6.