This document is not field policy and has not been subject to field vote. It is a working document provided as a good-faith attempt to describe the current shared viewpoint of the Solids faculty. Per field rules, the exam committee decides the scope of the exam and questions are at the discretion of the committee.
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Q exam name: Solid mechanics
Field(s) to which it applies: AE, ME
Core physical principles covered: the solids Q exam covers topics in ENGRD 2020 and MAE 3270 at the level of being able to teach either course. This includes deriving basic relations and fluency in solving problems with the complexity and broad context appropriate at the graduate level.
The exam committee decides the scope of the exam and questions are at the discretion of the committee; however, this list is provided as a good-faith outline of topics covered as a way to frame students’ broad study of solid mechanics as a discipline.
Recommended textbooks for study:
- Statics and Mechanics of Materials (3rd edition) R.P. Beer, E.R. Johnston, Jr., J.T. DeWolf and D.F. Mazurek, McGraw-Hill (2021).
- Mechanical Behavior of Materials (5th Edition), N.E. Dowling. Mechanics of Materials (e-book available through the library), A. Bedford and K.M. Liechti.
- Materials Selection in Mechanical Design, M.F. Ashby. (e-book available through the library: https://newcatalog.library.cornell.edu/catalog/12111294)
Relevant sections from each book should be identified from the syllabi of ENGRD 2020: Statics and Mechanics of Solids and MAE 3270: Mechanics of Engineering Materials.
Classes required before Q exam: None. Foundational undergraduate training in solid mechanics expected at the level of ENGRD 2020 and MAE 3270.
Classes strongly recommended before Q exam: MAE 6110: Foundation of Solid Mechanics, MAE 6810: Methods of Applied Mathematics I.
Classes deemed helpful: MAE 5700: Finite Element Analysis for Mechanical and Aerospace Design, CEE 6755: Finite Element Method: Theory and Applications in Mechanics and Multiphysics
Reference Readings from ENGRD 2020 and MAE 3270:
ENGRD 2020: Statics and Mechanics of Solids |
Readings |
| Topic | Statics and Mechanics of Materials (3rd edition), Beer, Johnston, Jr., DeWolf and Mazurek |
| Introduction; Forces; Moments | Ch 2.1, 2.2, 2.4, 3.1 |
| FBD, Equilibrium | Ch 2.3, 2.5, 3.1A, 4.1-4.3 |
| Reactions and eqm continued, Couples | Ch 3.3 |
| Centroids, Distributed Loads, Internal Forces and Moments | Ch 5.1, 5.2A, 5.3, 5.4 |
| Trusses: Method of Joints | Ch 6.1 |
| Trusses, Frames | Ch 6.2 |
| Frames | Ch 6.3 |
| Mechanisms | Ch 6.4 |
| Concept of Stress | Ch 8.1 |
| Concept of Strain | Ch 9.1 |
| Yielding and Failure in 1D | Ch 9.9, 8.4 |
| Stress concentration and factor of safety | Ch 9.9, 8.4 |
| Statically indeterminate axial system | Ch 9.2 |
| 1D thermal expansion | Ch 9.3 |
| Multiaxial | Ch 9.4-9.7 |
| Deformation in Torsion | Ch 10.1, 10.2 |
| Stress in Torsion | Ch 10.1, 10.2 |
| Statically Indeterminate Torsion | Ch 10.3 |
| Moment of inertia; stress in pure bending | Ch 7.1A-B, 7.2 |
| Composite Beams | Ch 11.3 |
| VM Diagrams | Ch 12.1, 12.2 |
| Normal Stress in Beams | Ch 12.3 |
| Shear Stress in Beams | Ch 13 |
| Beam Deflection | Ch 15.1 |
| Superposition of Beam Deflection | Ch 15.3 |
| Buckling | Ch 16.1 |
MAE 3270: Mechanics of Engineering Materials |
Reading |
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| Dowling’s Mechanical Behavior of Materials, 5th edition | Bedford and Liechti, Mechanics of Materials | Ashby’s Materials Selection | |
| Course Introduction | Ch 1 | Ch 4.2 and 4.3 | |
| Deformation and stress in rods, shafts, beams and pressure vessels | Ch 5.1-5.3, 6.1, 6.6, 6.7 | ||
| Deformation and stress in rods, shafts, beams and pressure vessels | Ch. 7.6, 9.1, 10.1, 10.2 | ||
| Combined Loading | Ch 7.1, 7.5 | ||
| Stress-strain: linear elastic, plane-stress, isotropic, isothermal | Ch 2.2 | ||
| Transformation of stress | Ch 7.2 | ||
| Mohr’s circle, principal stresses | Ch 7.3 | ||
| Transformations of strain & strain gauge rosettes | Ch 8.1, 8.2 | ||
| Matrix methods for stress transformation and principal stress analysis | Ch 11.1 | ||
| Strain energy | Ch 11.1 | ||
| Energy method for deflection analysis | Ch 2.1, Appendix C | ||
Classes of materials |
Dowling’s Mechanical Behavior of Materials, 5th edition | Bedford and Liechti, Mechanics of Materials | Ashby’s Materials Selection |
| Atomic structure and bonding | Ch 2.2, 2.3 | ||
| Microstructure, materials processing, mechanism of metal deformation | Ch 2.4–2.6 | ||
| Mechanical testing – tension test | Ch 3.1–3.6 | ||
| Mechanical testing – hardness, impact toughness | Ch 4.3, 4.4 | ||
| Stress-strain: thermal strain | Ch 5.3 | ||
| Stress-strain: anisotropic materials | Ch 5.4 | ||
| Stress-strain: time dependence and viscoelasticity | Ch 5.2.2, 5.2.3 | ||
| Brittle failure | Ch 7.1-7.3 | ||
| Ductile failure by yielding | Ch 7.4, 7.5 | ||
Failure analysis under combined loading |
Dowling’s Mechanical Behavior of Materials, 5th edition | Bedford and Liechti, Mechanics of Materials | Ashby’s Materials Selection |
| Fracture mechanics | Ch 8.1-8.4 | ||
| Fracture mechanics: leak before break | Ch 8.4 | ||
| Fracture mechanics: trends in materials | Ch 8.6 – 8.8 | ||
| Fatigue failure | Ch 9.1–9.6 | ||
| Fatigue under multi-axial loading | Ch 9.7 – 9.8 | ||
| Variable amplitude fatigue | Ch 9.9 | ||
| Material selection for mechanical design, material index | Ch 4, 5 | ||
| Material selection for mechanical design, shape factor | Ch 6, 7 | ||