ESO202A: Mechanics of Solids
Instructor: Anurag Gupta (ag@)
Office hours: Please email me to seek an appointment
Schedule: Lectures MThF 8-9 am, L16; Tutorial W 8-9 am
Teaching assistants: Animesh Pandey (animesh.pandey1991@gmail.com), Manish Singh (manishsn@), Saptarshi Paul (sapaul@), Arnav Gupta (arnavg@)
Grading policy: Tutorial attendance (5%), Quizzes (30%), Midterm (25%), Final (40%)
Texts
Primary text: (readings and problems assigned from this text)
[1] S. H. Crandall, N. C. Dahl, and T. J. Lardner, An Introduction to the Mechanics of Solids, McGraw Hill, Second Ed., 1978.
Additional texts:
[2] E. P. Popov, Engineering Mechanics of Solids, PrenticeHall, Second Ed., 1998.[3] S. Govindjee, Engineering Mechanics of Deformable Solids, Oxford, 2013.
General readings:
[4] Structures or Why Things Don’t Fall Down, by J. E. Gordon: This immensely entertaining book can be read like a novel without bothering about the dry technicalities of the subject. It successfully attempts at bringing both curiosity and personal experience to our interesting subject. [5] Biomechanics, by R. M. Alexander. This and other books by the same author presents a very readable introduction to application of simple concepts from mechanics of solids to biological world.
History of Mechanics and Strength of Materials:
[6] History of Strength of Materials, by S. Timoshenko[7] Essays in the History of Mechanics, by C. A. Truesdell[8] Mechanics of Pre-industrial Technology, by B. Cotterell and J. Kamminga[9] A good summary can be found in the two-part article by Truesdell: [Part 1] [Part 2]
Further readings:
[10] Applied Mechanics of Solids by Allan Bower. The complete book is available at http://solidmechanics.org[11] The Linearized Theory of Elasticity, by W. S. Slaughter [12] Theory of Elasticity, by L. D. Landau and E. M. Lifshitz [13] Elasticity, J. R. Barber
Notes, Assignments,...
{Note: 'T' referes to tutorial problems, 'P' to practice problems, and 'R' to reading, all prescribed from Crandall and Dahl}
Week 1: The concept of force; traction; moment due to force; couple; equilibrium equations; [Lecture notes] [R: 1.1-1.9]
Week 2: Consequences of equilibrium equations; 3D simple solid; the concept of stress; stress equilibrium equations; slender structures and their equilibrium; [Lecture notes] [T:1.9, 1.23, 1.30][P:1.8, 1.11, 1.15, 1.22, 1.31, 1.34, 1.36; Solution]
Week 3: Stress equilibrium; plane stress; stress transformation; normal force; shear force; [Lecture notes] [T:4.3, 4.10, 4.15] [P:4.4, 4.7(d), 4.8, 4.14, 4.27, 4.28 Solution][R:4.2-4.6, 4.15]
Week 4: Quiz 1, Thin-walled pressure vessels, the concept of strain; [Lecture notes][Quiz Solution] [T:4.30, 4.32] [P: 4.12, 4.18, 4.19, 4.25, 4.29 Solution][R:4.8-4.11]
Week 5: Deformation; Strain-deformation relations; nonlinear and linear strain; Elasticity; [Lecture notes] [T: 4.17, 5.1, 5.12][P: 5.7, 5.8, 5.10, 5.11 Solution][R:5.1-5.4]
Week 6: The complete BVP of linear isotropic elasticity; boundary conditions; uniqueness of solution; pressurized thick-walled cylinder; thermoelasticity [Lecture notes] [T:5.26,5.48][P:5.13,5.20,5.21,5.40,5.41 Solution][R:5.5-5.7]
Week 7: The stress determination in thermoelasticity; some illustrative problems; [Quiz 2 Solution]
Week 8: Mid-term Exam; Tension-compression bars; [MT Solution] [T: 2.17, 2.26][P: 2.10, 2.11, 2.12, 2.20, 2.22, 2.24, 2.38][R:2.2-2.4]
Week 9: Torsion of circular shafts; shear force and bending moment diagrams; curved beam [Lecture notes][Quiz 3 Solution][T: 6.12, 6.24][P: 6.6,6.9, 6.10, 6.11, 6.16][R:6.1-6.7 ]
[[Readings for the break: We will discuss these (at a faster pace) once classes resume. You are encouraged to read the relevant portions in the book, understand the solved examples, and solve the prescribed problems]]
1. Symmetric beam bending [Lecture notes] [P:7.8, 7.14, 7.22, 7.24][R:7.2-7.5]2. Shear stress in beam bending; Combined stresses; Deflection during beam bending [Lecture notes] [P:7.38, 7.44,8.5, 8.10, 8.13][R:7.6,7.7,8.2-8.5]3. Energy methods; Castigliano's theorems: [Lecture notes] [P:8.22, 8.25, 8.36][R:2.6,8.6]4. Geometric instability; Bucling of mechanisms; Euler buckling of columns [Lecture notes (These are from the book [3]] [P:9.4, 9.6, 9.10][R:9.2-9.4]
Problems for the final Exam: The final exam, whenever it happens, will contain problems taken from either the practice problems assigned throughout the course (marked P above) and the set of 52 problems collected in this pdf document.