principal stress and strain ppt

Stress-Strain Curve. Ductile Material: Ductile materials are materials that can be plastically twisted with no crack. Maximum Principal Strain theory (M.P.St.T) Condition for failure, Maximum Principal strain (ε The graphs show that σθ has a maximum and minimum value and a mean value not usually zero. Transformation of Stresses and Strains David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 Stress and Strain Curves or Diagram: This curve is a behavior of the material when it is subjected to load. Part Number . Principal planes carry only normal stresses 5. Planes that have no shear stress are called as principal planes. Max. x y P x y P/2 P/2 xy y x xy y x Stresses Approximately Equal Strain Energy dx u dz dy x y z Strain Energy = Energy Stored Inside an Elastic Solid Due to the Applied Loadings One-Dimensional Case Three-Dimensional Case Principle of Virtual Work Change in Potential Energy (UT-W) During a Virtual Displacement from Equilibrium is Zero. if the length in the x-direction changes from 1 m to 0.99 m, the strain is xx = 0.01. If you continue browsing the site, you agree to the use of cookies on this website. Ô 1 > Ô 3; Ô 2 = 0 Right side figure represents Bi-axial state of stress. Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor.. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. Plane stress is a type of load that is applied to a material. The values of these six components at the given point will change with OF TECHNOLOGY • Strain is also a symmetric second-order tensor, identical to the stress. A. Principal planes the planes on which the principal stresses act 8 Principal Stresses Shear stress on the principal planes 9 Principal Stresses Example 2 Find principal stresses of an element which is in pure shear. The resulting stresses on these planes are normal stresses and are called principal stresses (Eigen values) and The principal stresses are defined as those normal components of stress that act on planes that have shear stress components with zero magnitude ! three normal and three shear components, with respect to an arbitrary coordinate system. stress and biaxial state of stress when principal stresses are like in nature. Principal stresses and strains. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. The maximum shear stress is about 112 MPa on a plane at angle 77o. On the other hand, the three quantities S 1 ≥ S 2 ≥ S 3 are the principal stresses of S, so that the quantities indicate the magnitudes of tensile stress. See our User Agreement and Privacy Policy. These general results are the same what ever the values of the applied stresses. These are called the PRINCIPAL STRESSES. xBi-axial stress: one principal stress equals zero, two do not, i.e. If you continue browsing the site, you agree to the use of cookies on this website. Lecture 3 mohr’s circle and theory of failure, Lecture 13 torsion in solid and hollow shafts 1, Lecture 9 shear force and bending moment in beams, Lecture 4 3 d stress tensor and equilibrium equations, No public clipboards found for this slide. Stresses and strains In last lecture we looked at stresses were acting in a plane that was at right angles/parallel to the action of force. Mechanical type, 2. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. How much force material experience can be measured using stress units. In this region, the material obeys the Hooke’s Proportional limit law. Determine the normal, tangential and resultant stresses on a plane inclined at 30deg to the minor stress. simple stress is defined as the internal resistance force that opposes the external force per unit area.Tensile Stresses, Compressive Stresses, Shear Stresses, Bending Stresses, Torsion Stresses. Principal Stress and Strain Theory at a Glance (for IES, GATE, PSU) 2.1 States of stress xUni-axial stress: only one non-zero principal stress, i.e. Procedure for constructing Mohr’s circle. Clipping is a handy way to collect important slides you want to go back to later. P4 Stress and Strain Dr. A.B. Introduction to the stress tensor. A simple Stress and strain are produced due to any of the following type of actions done on the machine parts. The effect of stress on a body is named as strain. Stresses on an inclined element. Note that these principal stresses indicate the magnitudes of compressional stress. principal rd_mech@yahoo.co.in Ramadas Chennamsetti 22 strain theory Y = τy + υτy = τy (1 + υ) Relation between yield stress in tension and shear τy = Y/ (1 + υ) for υ= 0.25 Example 1 (FEIM) The principal stresses (σ2, σ1) are most nearly (A)–62 400 kPa and 14 400 kPa (B)84 000 kPa and 28 000 kPa (C)70 000 kPa and 14 000 kPa (D)112 000 kPa and –28 000 kPa SEMINAR Stress and Strain Transformation 2.1 INTRODUCTION In Chapter 1 we defined stress and strain states at any point within the solid body as having six distinctive components, i.e. 1. Stress can deform the body. 2. The operation, including the Mohr’s strain … 1 Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load " = P / A torsional load in circular shaft $ = T!/ Ip bending moment and shear force in beam In physics, stress is the force acting on the unit area of a material. Therefore, there are 6 independent variables in the strain matrix, instead of 9. The stress-strain curve depends on two types of material.. 1. Plane stress deals solely with the loads that occur in parallel to the plane being considered. Here, the fully three dimensional stress state is examined. 1 m 0.99 m Lecture 3 mohr’s circle and theory of failure. 19. Principal Stresses Principal stresses maximum and minimum normal stresses. See our Privacy Policy and User Agreement for details. • The principal stresses are labelled 1, 2 and 3 with 1 being the largest and 3 the smallest principal stress. 3.This theory is suitable for ductile materials and gives oversafe design i.e. In the most general form can be thought of as a 3 dimensional surface. Example #1 Q. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. See our Privacy Policy and User Agreement for details. 3. Principal stresses and maximum shear stresses. For the most part, the discussion was confined to two-dimensional states of stress. Looks like you’ve clipped this slide to already. 152 Stress Transformations Principal Stresses and Maximum Shear Stresses 153 18 Example 6.2 The state of plane stress at a point on a body is shown on the element in the figure given. Measuring Strain and Displacement Accurately. Two Dimensional State of Stress and Strain: Principal stresses, principal strains and principal axes, calculation of principal stresses from principal strains.Stresses in thin cylinder and thin spherical shells under internal pressure , wire winding of thin cylinders. Stress can be categorized into three categories depending upon the direction of the deforming forces acting on the body. Stress and Strain For examples 1 and 2, use the following illustration. Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. STRESS ANALYSIS 2.1 Cauchy Stress Principle 2.2 State of Stress at a Point 2.3 State of Stress on an Inclined Plane 2.4 Force and Moment Equilibrium 2.5 Stress Transformation Law 2.6 Normal and Shear Stresses on an Inclined Plane 2.7 Principal Stresses 2.8 Stress Decomposition 2.9 Octahedral Stresses 2.10 References 3. refers to the angle between the x-axis and the axis of the maximum principal strain ε1, and θ2, which is the angle between the x-axis and the axis of the minimum principal strain ε2. There will … The concept of traction and stress was introduced and discussed in Book I, §3. The stress-strain-time relationship, or constitutive law, can be determined by loading a polymer specimen with constant stress (creep) or constant strain (stress relaxation or isometric). The point where this line intersects the stress-strain curve is the offset yield point. If you continue browsing the site, you agree to the use of cookies on this website. 1. Plane stress does not involve any forces that are applied perpendicular to the plane. 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- 3-D stress and strain, Equilibrium equations and impact loading  Lecture -5 - Generalized Hooks law and Castiglionos. It is found by drawing a line that crosses the X (strain) axis at 0.002 and runs parallel to the stress-strain line (slope = E). Now customize the name of a clipboard to store your clips. 3. Stress-strain curves are useful to understand the tensile strength of a given material. Zavatsky HT08 Lecture 6 Mohr’s Circle for Plane Stress Transformation equations for plane stress. Ô 1 Right side figure represents Uni-axial state of stress. M.S.S.T is not suitable under hydrostatic stress condition. 10 Maximum Shear Stresses 11 Plane Stress Principal stresses and strains PROBLEM- A rectangular block of material is subjected to a tensile stress of 110 N/mm2 on one plane and a tensile stress of 47 N/mm2 on the plane at right angles to the former. Principal stresses and strains What are principal stresses. Strain can be measured using various types of devices classified depending upon their principle of operation. You can change your ad preferences anytime. 2. AHEMEDABAD INSTITUTE The principal stresses can then be calculated from the principal strains by utilizing … 4. This seminar is about Principal stresses and strains. Geodynamics3.ppt 19 Geodynamics3.ppt 20 Normal Strain • Normal strain measures the fractional change in length. Understanding plane stress is important to avoid material failure. Pneumatic type 4. Looks like you’ve clipped this slide to already. etc. Experimental Principal Strains. Clipping is a handy way to collect important slides you want to go back to later. Represent this stress in terms of the : (a) principal stresses. The main purpose of a strain gauge is to indirectly determine stress and its variation with time, quantitatively. The various engineering and true stress-strain properties obtainable from a tension test are summarized by the categorized listing of Table 1.1. presentations for free. You can change your ad preferences anytime. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. STRAIN ANALYSIS Now customize the name of a clipboard to store your clips. principal strain theory Pure shear Principal stresses corresponding to τy shear yield stress σ1 = + τy , σ2 = -τy For onset of yielding – max. Principal stresses and stress invariants. If you continue browsing the site, you agree to the use of cookies on this website. The principal stresses occur on planes 90o apart. Hint: Solve the problem graphically using a Mohr’s circle plot. Strain Gauges are an important geotechnical tools that measure strain in underground cavities, tunnels, buildings, concrete, masonry dams, bridges, embedment in soil/concrete. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Offset yield strength is the stress that will cause a specified amount of permanent strain (typically 0.2 percent). Some of them are as follows: 1. See our User Agreement and Privacy Policy. • Strain can also be “rotated” to find its principal strain, principal strain direction, and maximum shear strain. For any general state of stress at a point P, there exists 3 mutually perpendicular planes on which the shear stresses. The curve from O to A is linear. Strain Gauge A Strain Gauge is a device used to measure the strain of an object. The given figure shows a stress-strain curve of a given metal. Vanish. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. safe and uneconomic design. Results. Add the following 2-D stress states, and find the principal stresses and directions of the resultant stress state. Characterisation of salmonella abortusequi strains harbouring defined mutatio... No public clipboards found for this slide. – e.g. 7.2 Analysis of Three Dimensional Stress and Strain . Optical type 3. Diagram of Rosette. The stress and strain induced when a load is applied are a function of time.