Credit: 5 units (3-1-2)
Instructors: Prof. Rajdip Nayek (rajdipn@am.iitd.ac.in)
Class timings: Tue, Thu & Fri (11:00 AM to 12:00 PM) at LHC 408
Tutorial Session: Wed (3:00 to 4:00 PM), LHC 308
Tutorial Attd: An attendance list of students in tutorial sessions can be found here.
Office hours (TA): Fri 4:00-5:00 pm (in Block 4 Room B-24)
Course Policy can be found here.
Intended audience: BTech students in Civil Engineering
NOTE: For all course related emails, please put APL108 in the subject line
| Topics | Tutorial Questions | Tutorial Solutions |
|---|---|---|
| Study of forces | Tutorial 1 | Solution |
| Force-Deformation and Compatibility equations | Tutorial 2 | Solution |
| Traction and Stress Equilibrium | Tutorial 3 | Solution |
| Principal Stresses and Principal Planes | Tutorial 4 | Solution |
| Mohr's Circle | Tutorial 5 | Solution |
| Strain | Tutorial 6 | Solution |
| Complete equations of linear elasticity | Tutorial 7 | Solution |
| Applications of Extension and Torision | Tutorial 8 | Solution |
| Uniform and non-uniform bending of beams with symmetric C/S | Tutorial 9 | Solution |
| Euler-Bernoulli beams & Energy Methods |
Tutorial 10 | Solution |
This is the first course where the deformation of solid bodies and the underlying concepts are introduced to undergraduate students. The course begins by building a foundation of the concepts of stress and strain in three-dimensional deformable bodies. It further uses these concepts to study the extension, torsion, and bending of beams. The one-dimensional theory of beams is also introduced. Various theories of failure that are critical for the design of machine elements in the industry will also be discussed.
- Fundamental Principles of Mechanics; Introduction to mechanics of deformable bodies
- Stress tensor and its representation in Cartesian coordinate system; Transformation of stress matrix; Equations of equilibrium; Symmetry of stress tensor
- State of stress in simple cases; Principal stress components and principal planes; Maximizing shear component of traction; Mohr’s circle
- Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor
- Longitudinal, shear, and volumetric strains; Local infinitesimal rotation; Strain compatibility condition
- Linear stress-strain relation for isotropic bodies; Relation between material constants
- Stress and strain matrices in the cylindrical coordinate system; Equations of equilibrium in the cylindrical coordinate system
- Axisymmetric deformations: combined extension-torsion-inflation of a cylinder
- Bending of beams having symmetrical cross-section
- Shear center, Shear flow in thin and open cross-section beams; Euler-Bernoulli and Timoshenko beam theories; beam buckling
- Energy methods, Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using the energy method
- Various theories of failure and their application
This course is based on two textbooks:
- Archer, Cook, Crandall, Dahl, Lardner, McClintock, Rabinowicz, Reichenbach, "An Introduction To The Mechanics Of Solids", Tata Mcgraw Hill, 2012
- Kumar, Ajeet, "Solid Mechanics for Undergraduates - Using Vectors and Tensors", White Falcon Publishing, 2024.
Other references
- Boresi, Arthur, "Advanced Mechanics of Materials", Wiley, 2019
- Solid Mechanics (NPTEL) by Prof. Ajeet Kumar [video link]
- Srinath, L.S., "Advanced Solid Mechanics", Tata-MgGraw-Hill, 2008.
- Hibbeler, R. C., "Mechanics of Materials", Prentice Hall, 2014
- Timoshenko, S.P. and Goodier, J.N., "Theory of Elasticity", McGraw Hill, 2017.
- Sadd, M.H., "Elasticity: Theory, Applications and Numerics", Elsevier, 2005
| Component | Scores | Solutions |
|---|---|---|
| Quizzes | 20 | |
| Minor | 20 | MinorSol |
| Practical | 20 | |
| Major | 35 | MajorSol |
| Tutorial Attd | 5 | |
| Total | 100 | |
| Grades | Check grades |
Students are highly encouraged to attend all classes. Students who have failed this course were found to have attended less than 60% of the total classes on average. If any student has less than 75% tutorial attendance, he/she will get one grade less than they would have been awarded. In case of unavoidable absence, such as illness, please send an appropriate email within a week before/after the absence with an email subject specifying the subject code APL 104.
Please note that re-quizzes will not be offered for missed quizzes, regardless of the reason.
Retakes will be provided only for Minor and Major exams.
Both copiers and copyees are guilty of cheating and will receive an equal penalty. The penalty includes a zero mark on the corresponding exam. Please do not do anything you might regret.