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CLASS NOTES Version 5.0 MAE 477/577 - EXPERIMENTAL TECHNIQUES IN SOLID MECHANICS - CLASS NOTES Version 5.0 by John A. Gilbert, Ph.D. Professor of Mechanical Engineering University of Alabama in Huntsville FALL 2013 Table of Contents Table of Contents i Introducing MAE 477/577 iv MAE 477/577 Outline v MAE 477 ABET Syllabus vi MAE 577 SACS Syllabus viii Chapter 1. Stress 1.1 Introduction 1.1 1.2 Types of Forces 1.1 1.3 Traction Vector, Body Forces/Unit Mass, Surface and Body Couples 1.1 1.4 Resolution of the Traction Vector – Stress at a Point 1.3 1.5 Equilibrium Equations – Conservation of Linear Momentum 1.5 1.6 Stress Symmetry – Conservation of Angular Momentum 1.7 1.7 Transformation Equations – Mohr’s Circle 1.7 1.8 General State of Stress 1.16 1.9 Stresses in Thin Walled Pressure Vessels 1.19 1.10 Homework Problems 1.22 Chapter 2. Strain 2.1 Introduction 2.1 2.2 Strain-Displacement Equations 2.1 2.3 Strain Equations of Transformation 2.2 2.4 Compatibility Equations 2.3 2.5 Constitutive Equations 2.3 2.6 Homework Problems 2.5 Chapter 3. Linear Elasticity 3.1 Overview 3.1 3.2 Plane Stress 3.1 3.3 Plane Strain 3.2 3.4 Homework Problems 3.6 i Chapter 4. Light and Electromagnetic Wave Propagation 4.1 Introduction to Light 4.1 4.2 Electromagnetic Spectrum 4.3 4.3 Light Propagation, Phase, and Retardation 4.4 4.4 Polarized Light 4.5 4.5 Optical Interference 4.6 4.6 Complex Notation 4.6 4.7 Intensity 4.7 4.8 Superposition of Wavefronts 4.8 4.9 Reflection and Refraction 4.11 4.10 Double Refraction – Birefringence 4.12 4.11 Homework Problems 4.14 Chapter 5. Photoelasticity 5.1 Introduction 5.1 5.2 Plane Polariscope 5.2 5.3 Circular Polariscope 5.6 5.4 Calibration Methods for Determining the Material Fringe Value 5.10 5.5 Compensation Methods for Determining Partial Fringe Order Numbers 5.12 5.6 Calculation of the σ1 Direction 5.14 5.7 Birefringent Coatings 5.15 5.8 Three-Dimensional Photoelasticity 5.17 5.9 Homework Problems 5.18 5.10 Classroom Demonstration in Photoelasticity 5.24 Chapter 6. Photography 6.1 Introduction 6.1 6.2 Single Lens Reflex Cameras 6.1 6.3 Depth of Field 6.2 6.4 Photographic Processing 6.3 6.5 Polaroid Land Film Cameras 6.5 6.6 Digital Cameras 6.9 Chapter 7. Brittle Coatings 7.1 Introduction 7.1 7.2 Testing Procedures 7.2 7.3 Calibration 7.3 7.4 Measurements 7.8 7.5 Coating Selection 7.9 7.6 Application 7.11 7.7 Crack Patterns 7.11 7.8 Relaxation Techniques 7.11 ii 7.9 Homework Problems 7.12 Chapter 8. Moiré Methods 8.1 Introduction 8.1 8.2 Analysis 8.2 8.3 Optical Filtering 8.4 8.4 Stress Analysis 8.5 8.5 Shadow Moiré 8.6 8.6 Homework Problems 8.8 Chapter 9. Strain Gages 9.1 Introduction 9.1 9.2 Electrical Resistance Strain Gages 9.2 9.3 Length Considerations 9.4 9.4 Transverse Sensitivity Corrections 9.5 9.5 Temperature Considerations 9.5 9.6 Rosettes 9.6 9.7 Gage Selection and Series 9.8 9.8 Dummy Gages and Transducer Design 9.9 9.9 P-3500 Strain Indicator 9.11 9.10 Two-Wire and Three-Wire Strain Gage Circuits 9.13 9.11 Homework Problems 9.15 Appendix I – Review of Statics and Mechanics of Materials A.1.1 2-D Forces in Rectangular Coordinates A1.1 A.1.2 3-D Rectangular Coordinates A1.1 A1.3 Addition of Concurrent Forces in Space/3-D Equilibrium of Particles A1.2 A1.4 Moments and Couples A1.3 A1.5 Equilibrium of Rigid Bodies A1.4 A1.6 Center of Gravity and Centroid A1.4 A1.7 Moments of Inertia A1.6 A1.8 Shear and Moment Diagrams A1.8 A1.9 Deflection of Beams A1.8 A1.10 Synopsis of Mechanics of Materials A1.10 A1.11 Homework Problems A1.13 Appendix II – Basic Formulas for Mechanics of Materials A2.1 iii Introducing MAE 477/577 EXPERIMENTAL TECHNIQUES IN SOLID MECHANICS - 3 hrs. Required Text: Experimental Techniques in Solid Mechanics, Version 4.1 by Gilbert Reference Text: Experimental Stress Analysis, 4th. Edition by Dally and Riley Prerequisite: MAE/CE 370; Junior Standing Overview: When dealing with the majority of real engineering systems, it is not always sufficient, or advisable, to rely on analytical results alone. The experimental determination of stress, strain, and displacement is important in both design and testing applications. MAE 477/577, Experimental Techniques in Solid Mechanics, presents techniques which are valuable complements to the design and analysis process; and, in some difficult or complex situations, provide the only practical approach to a real solution. The bulk of the course constitutes a detailed treatment of the more conventional methods currently used for experimental stress analysis (photoelasticity, brittle coatings, moiré methods, strain gages, etc.); however, more recent developments in the field are also introduced (hybrid methods, speckle metrology, holographic interferometry, moiré interferometry, fiber optics, radial metrology, and STARS). In-class laboratory exercises are included so that students gain some practical experience. The lecture and laboratory exercises are designed to provide enough exposure for participants to secure an entry level position in the field of experimental mechanics. Attendance: Students are required to be present from the beginning to the end of each semester, attend all classes, and take all examinations according to their assigned schedule. In case of absence, students are expected to satisfy the instructor that the absence was for good reason. For excessive cutting of classes (3 or more class periods), or for dropping the course without following the official procedure, students may fail the course. Homework: Homework assignments must be done on only one side of 8 1/2" x 11" paper. Each problem shall begin on a separate page and each page must contain the following (in the upper right hand corner): Your name, the date, and page __ of __. All final answers must be boxed and converted (SI to US or US to SI). Homework is due at the beginning of the class on the date prescribed. Work must be legible and should be done in pencil. Problems shall be restated prior to solution and free-body diagrams (FBDs) shall be drawn for problems requiring such. Loose sheets shall be stapled together in the upper left hand corner. Note: For further information on the course and registration procedure, call Professor Gilbert by telephone at (256) 824-6029, or, contact him by e-mail at [email protected]. iv MAE 477/577 Experimental Techniques in Solid Mechanics Fall 2013 Time/Place: Friday 8:00 a.m. - 10:40 a.m.; TH S117 Instructor: Dr. John A. Gilbert Office: OB 301E Telephone: (256) 824-6029 (direct); (256) 824-5117/5118 (Beth/Cindy) Fax/E-mail: (256) 824-6758; [email protected] Office Hours: To be announced. Grading: 10% Attendance (100% for being in class; 0% for not being there); 30% Homework and Labs; 30% Midterm (10/11/13); 30% Final (11/29/13). Required Text: Gilbert, J.A., Experimental Techniques in Solid Mechanics, Volume 5.0, University of Alabama in Huntsville, 2013. Reference Text: Dally, J.W., Riley, W.F., Experimental Stress Analysis, 4th Edition, College House Enterprises, 2005, ISBN 0-9762413-0-7. Course Outline 1. Overview of Solid Mechanics - Stress, Strain, and Displacement; Equilibrium, Transformation, Strain-Displacement, Compatibility, and Constitutive Equations. 2. Stress Analysis - Method of Attack; Stress Concentration, Failure, Design, and Examples. 3. Light and Electromagnetic Wave Propagation – Amplitude, Phase, Polarization, Coherence, Interference, Reflection, Refraction, Birefringence, and Stress Optic Law. 4. Photoelasticity – Plane and Circular Polariscopes; Calibration and Compensation Methods; Reflection Polariscope, Birefringent Coatings, and 3-D Photoelasticity. 5. Photography – Cameras, Lenses, and Photographic Development; Digital Cameras, Image Acquisition and Processing. 6. Brittle Coatings – Theory, Calibration, Application, and Measurement. 7. Moiré Methods – Geometrical Considerations and In-Plane Displacement Measurement; Diffraction, Optical Filtering, and Stress Analysis; Out-of-Plane Displacement Measurement and Shadow Moiré. 8. Electrical Resistance Strain Gages - Parametrical Studies, Transverse Sensitivity, Rosettes, Circuitry, Installation, and Transducer Design. 9. Advanced Topics – Moiré Interferometry, Speckle Metrology, Holographic Interferometry, Fiber Optics, Digital Image Processing, Hybrid Methods, Panoramic Imaging Systems, Radial Metrology, and STARS. v MAE 477 Experimental Techniques in Solid Mechanics Responsible Department: Mechanical and Aerospace Engineering Catalog Description: 477 Experimental Techniques in Solid Mechanics 3 hrs. Experimental methods to determine stress, strain, displacement, velocity, and acceleration in various media. Theory and laboratory applications of electrical resistance strain gages, brittle coatings, and photoelasticity. Application of transducers and experimental analysis of engineering systems. (Same as CE 477) Prerequisites: MAE/CE 370 and junior standing. Textbook: Required Text: Gilbert, J.A., Experimental Techniques in Solid Mechanics, Volume 5.0, University of Alabama in Huntsville, 2013. Reference Text: Dally, J.W., Riley, W.F., Experimental Stress Analysis, 4th Edition, College House Enterprises, 2005, ISBN 0- 9762413-0-7. Course Objectives: 1. To present techniques that are valuable complements to the design and analysis process; and in some difficult or complex situations, provide the only practical approach to a real solution. 2. The bulk of the course constitutes a detailed treatment of the more conventional methods currently used for experimental stress analysis (photoelasticity, brittle coatings, moiré methods, strain gages, etc.); however, more advanced topics are introduced (hybrid methods, speckle metrology, holographic interferometry, moiré interferometry, fiber optics, radial metrology, and STARS).
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