Lecture_Stress_Strain_Displacement

# Lecture_Stress_Strain_Displacement - Class Workbook and...

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -3- Advanced Mechanics of Materials Advancing the concepts of “Mechanics of Materials” (MME 312), in order to provide the future engineer tools, for analyzing and designing various load bearing structural components, mainly the determination of stresses and deformations Review elementary mechanics of materials 2D and 3D Stress and Strain Plane Elasticity Problems (Bi-Harmonic Equations) Failure theories Torsion and bending of structural elements Curved beams Pressure Vessels and Rotating disks Energy methods Buckling and Stability Introduction to Finite Element Methods Fracture and Stress concentration Most engineering structures are treated as continuous media or a distributed parameter system. Analysis of such structures and structural components/members that are made of different materials are studied in the field of “Continuum Mechanics” Two different approach Mechanics of Materials or Elementary Theory Concentrate on approximate solutions Deformation is known or assumed Exact/Approximate solution from deformation Constitutive stress-strain relationship Load – Equilibrium equations Energy method (displacement field) Theory of Elasticity Exact stress strain distribution Differential equations (Boundary value problems) Equilibrium and compatibility equations Basic Terminology and Review of MME 312 Self Study: Chapter 1 - “Advanced Mechanics of Materials”, by Robert D. Cook and Warren C. Young, 2 nd Ed., Prentice Hall, 1999. (Available in Bb) Read Section 1.1 and 1.2 of the Textbook Read Appendix B, Appendix C and Appendix I of the textbook Review your knowledge of Statics, Calculus and Differential Equations

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -4- What is Stress: It is a measure of intensity of internal distribution of forces on an imaginary cut surface of a body. It is also a measure of materials’ strength subjected to various loading. It is an internal quantity which can only be inferred but cannot be measured directly. Force : Surface force (in plane, out of plane, concentrated, distributed) Body force - Act on the volume of the element (magnetic, gravity etc.) General body with external applied force Cut the body at some arbitrary plane An infinitesimal elemental area with forces Figure 1.3-4 [1] Figure 1.3-5 [1] Stress is point function hence once we know the average stress (average distribution of forces per unit area) we can calculate the exact stress at a point.
Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -5- Normal Stress Shear Stress Shear Stress Figure 1.3-6 [1] Figure 1.3-7 [1] The average stress in each direction can be illustrated as short notation called index notation, The first subscript defines the direction (normal to the plane) on which the stress is acting The second subscript defines its direction on that plane In order to uniquely define the stress at a point the stress must be defined on the mutually perpendicular planes.

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## This document was uploaded on 11/04/2011 for the course MME 512 at Miami University.

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Lecture_Stress_Strain_Displacement - Class Workbook and...

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