ENGR 220 Section 10.1 - 10.3.

Slides:

Advertisements

Similar presentations

Mechanics of Materials – MAE 243 (Section 002) Spring 2008

Advertisements

Principle Stresses Under a Given Loading

A bar is shown in (a) in pure shear due to torsion

Strengths Torsion of Circular Shafts Chapter 12. Introduction A member subjected to twisting moments (torques) is called a shaft Only solid and hollow.

Hamrock Fundamentals of Machine Elements Chapter 2: Load, Stress and Strain The careful text-books measure (Let all who build beware!) The load, the shock,

MAE 314 – Solid Mechanics Yun Jing

PLANE STRAIN TRANSFORMATION

PLANE STRESS TRANSFORMATION

CHAPTER OBJECTIVES Apply the stress transformation methods derived in Chapter 9 to similarly transform strain Discuss various ways of measuring strain.

Copyright © 2011 Pearson Education South Asia Pte Ltd

Principle and Maximum Shearing Stresses ( )

ENGR 220 Section Statically Indeterminate Torque-Loaded Members Same method of analysis as for axial loaded members Sum of the moments Compatibility.

Analysis of Stress and Strain

Mechanics of Materials – MAE 243 (Section 002) Spring 2008 Dr. Konstantinos A. Sierros.

Analysis of Stress and Strain Review: - Axially loaded Bar - Torsional shaft Questions: (1) Is there any general method to determine stresses on any arbitrary.

Mohr's Circle - Application

Experimental stress Analysis Introduction. Main Course Topics Review of Concepts Failure Theories Generalized Hook’s law – Elasticity Stress-Strain Response.

ENGR 225 Section 2.1. Review ~ Force per Area Normal Stress –The average normal stress can be determined from σ = P / A, where P is the internal axial.

Stress Transformation

THEORIES OF FAILURE THEORIES OF FAILURE FOR DUCTILE MATERIALS

Copyright © 2011 Pearson Education South Asia Pte Ltd

PROBLEM-1 State of stress at a point is represented by the element shown. Determine the state of stress at the point on another element orientated 30

Mechanics of Materials Goal:Load Deformation Factors that affect deformation of a structure P PPP Stress: intensity of internal force.

CHAPTER OBJECTIVES Define concept of normal strain

Theories of Stress and Strain

Content Stress Transformation A Mini Quiz Strain Transformation

Transformations of Stress and Strain

APPLICATIONS/ MOHR’S CIRCLE

8 Principle Stresses Under a Given Loading. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston.

MECHANICS OF MATERIALS Third Edition Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University CHAPTER.

If A and B are on the same side of the origin (i. e

In general stress in a material can be defined by three normal stresses and three shear stresses. For many cases we can simplify to three stress components.

CHAPTER OBJECTIVES To show how to transform the stress components that are associated with a particular coordinate system into components associated with.

 2005 Pearson Education South Asia Pte Ltd 2. Strain 1 CHAPTER OBJECTIVES Define concept of normal strain Define concept of shear strain Determine normal.

BFC (Mechanics of Materials) Chapter 1: Stress & Strain Shahrul Niza Mokhatar

Triaxial State of Stress at any Critical Point in a Loaded Body

Transformations of Stress and Strain

 2005 Pearson Education South Asia Pte Ltd 2. Strain EXAMPLE 2.1 Rod below is subjected to temperature increase along its axis, creating a normal strain.

 2005 Pearson Education South Asia Pte Ltd 2. Strain 1 CHAPTER OBJECTIVES Define concept of normal strain Define concept of shear strain Determine normal.

CHAPTER OBJECTIVES Derive equations for transforming stress components between coordinate systems of different orientation Use derived equations to.

Transformation methods - Examples

Copyright ©2011 by Pearson Education, Inc. All rights reserved. Mechanics of Materials, Eighth Edition Russell C. Hibbeler General Plane-Strain Transformation.

Principal Stresses and Strain and Theories of Failure

CHAPTER OBJECTIVES Define concept of normal strain Define concept of shear strain Determine normal and shear strain in engineering applications 1.

 2005 Pearson Education South Asia Pte Ltd 2. Strain 1 CHAPTER OBJECTIVES Define concept of normal strain Define concept of shear strain Determine normal.

Mechanics of Materials Instructor: Dr. Botao Lin & Dr. Wei Liu Page 1 Chapter 10 Strain Transformation 2015 Mechanics of Materials Foil gauge LVDT.

1. PLANE–STRESS TRANSFORMATION

Chapter 7 Transformations of Stress and Strain.

Mohr’s circle for plane stress

If A and B are on the same side of the origin (i. e

Transformations of Stress and Strain

Transformations of Stress and Strain

EXAMPLE 2.1 Rod below is subjected to temperature increase along its axis, creating a normal strain of z = 40(10−3)z1/2, where z is given in meters.

BDA30303 Solid Mechanics II.

Example 7.01 SOLUTION: Find the element orientation for the principal stresses from Determine the principal stresses from Fig For the state of plane.

Concepts of stress and strain

Chapter 2 Strain.

Strain Transformation

Mechanics of Materials Engr Lecture 20 More Mohr’s Circles

CHAPTER OBJECTIVES Define concept of normal strain

Compound Normal & Shear Stresses

Copyright ©2014 Pearson Education, All Rights Reserved

Copyright ©2014 Pearson Education, All Rights Reserved

Presentation transcript:

ENGR 220 Section 10.1 - 10.3

Plane Strain Review of Strain Deformation due to a stress is specified using the concept of normal and shear strain.

Normal Strain Elongation or contraction of a line segment per unit of length.

Shear Strain The change in angle the occurs between two line segments that were originally perpendicular.

Volume and shape deformations

Plane Strain

Strain Gauges

Strain Gauge

Strain Gauge http://www.youtube.com/watch?v=YBm_j232yUU&feature=related http://www.youtube.com/watch?v=TjY48vYMPxw

Strain Rosette

Generic Solution Strain measured along three axes at angles a b c Transform along x-y coordinates Stain Transformation Equations.

45˚ Strain Rosette

60˚ Strain Rosette

Principal Strains

Maximum In-Plane Shear Strain

Mohr’s Circle

Mohr’s Circle

Problem 10-2: Determine the in-plane strains of an element orientated at θ=20° counter-clockwise from the original position.

10.12 (10.3 8e) A strain gauge is mounted on the 1 inch diameter A-36 steel shaft as shown below. When the shaft is rotating with an angular velocity of 1760 rpm, the reading on the strain gauge is 800 (10-6). Determine the power output of the motor. Assume the shaft is subjected only to a torque.