APL104
APL 104: Solid Mechanics (Fall semester 2022)
Course Info
Credit: 4 units (3-1-0)
Instructors: Prof. Ajeet Kumar (ajeetk@am.iitd.ac.in) and Prof. Rajdip Nayek (rajdipn@am.iitd.ac.in)
TA 1: Intaf Alam (amz198096@am.iitd.ac.in)
TA 2: Roushan Kumar (amz208472@am.iitd.ac.in)
TA 3: Vinayak (amz218561@am.iitd.ac.in)
Class timings: Tue, Wed & Fri (9:00 to 10:00 AM) at LHC108
Tutorial Session A: Tue (2:00 to 3:00 PM) at LHC 606
Tutorial Session B: Wed (2:00 to 3:00 PM) at LHC 606
Tutorial Session C: Thu (2:00 to 3:00 PM) at LHC 606
Tutorial Session D: Fri (2:00 to 3:00 PM) at LHC 606
List of students in particular tutorial sessions can be accessed here: Tutorial group list
Office hours (TA): By email appointment
Office hours (Instructor): Prof. Ajeet Kumar (Wed 5-6pm) Office Block IV-340 and Prof. Rajdip Nayek (Thu 5-6pm) Office Block V-418D
Intended audience: BTech students in Applied Mechanics, Materials, and Mechanical Engineering disciplines.
NOTE-For all course related emails, please put APL104 in the subject line
Lecture Schedule
| Module | Topics | Lecture Notes | Handwritten Classroom Notes |
|---|---|---|---|
| Module 00 | Mathematical Preliminaries | Lecture 1 | Class 1 Class 2 Class 3 |
| Module 01 | Traction vector | Lecture 2 | Class 4 Class 5 |
| Module 02 | Stress Tensor and its representation | Lecture 3 | Class 6 |
| Module 03 | Transformation of Stress matrix | Lecture 4 | Class 6 |
| Module 04 | Stress Equilibrium equations | Lecture 5 | Class 7 |
| Module 05 | Balance of Angular momentum | Lecture 6 | Class 8 |
| Module 06 | Principal Stress and planes Maximizing Shear component of traction |
Lecture 7 Lecture 8 |
Class 9 Class 10 |
| Module 07 | Mohr’s circle Stress invariants Decomposition of stress tensor |
Lecture 9 Lecture 10 |
Class 11 Class 12 Class 13 |
| Module 08 | Concept of Strain Longitudinal and Shear strains Volumetric and infinitesimal strain tensors Similarity in Properties of Stress and Strain Tensors |
Lecture 11 Lecture 12 Lecture 13 Lecture 14 |
Class 14 Class 15 Class 16 Class 17 |
| Module 09 | Stress-strain relation Stress-strain relation for isotropic materials |
Lecture 15 Lecture 16 |
Class 18 Class 19 Class 20 |
| Module 10 | LMB in cylindrical coordinates Strain matrix in cylindrical coordinates Extension-Torsion-Inflation of cylinders |
Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 |
Class 21 Class 22 Class 23 Class 24 Class 25 Class 26 |
| Module 11 | Uniform Bending of Beams Non-uniform Bending of Beams Bending of Unsymmetrical Beams Shear Center |
Lecture 23 Lecture 24 Lecture 25 Lecture 26 |
Class 27 Class 28 Class 29 Class30 |
| Module 12 | Euler-Bernoulli beam theory Timoshenko beam theory |
Lecture 27 Lecture 28 |
Class 31 Class 32 |
| Module 13 | Energy Methods | Lecture 29 Lecture 30 |
Class 33 Class 34 Class 35 Class 36 |
| Module 14 | Failure Theories | Lecture 31 Lecture 32 |
Class 37 Class 38 |
Tutorial Schedule
| Topics | Tutorial Questions | Tutorial Solutions |
|---|---|---|
| Mathematical Preliminaries | Tutorial 1 | Solution |
| Traction vector | Tutorial 2 | Solution |
| Stress tensor and its transformation | Tutorial 3 | Solution |
| Stress equilibrium and principal stresses | Tutorial 4 | Solution |
| Mohr’s circle | Tutorial 5 | Solution |
| Strain | Tutorial 6 | Solution |
| Stress-Strain relation | Tutorial 7 | Solution |
| Cylindrical coordinates | Tutorial 8 | Solution |
| Symmetrical Beam bending | Tutorial 9 | Solution |
| Bending and shear stresses and shear center | Tutorial 10 | Solution |
| Beam Theory (EBT and TBT) | Tutorial 11 | Solution |
| Energy methods | Tutorial 12 | Solution |
Table of Contents
Course Outline
This is the first course where deformation of solid bodies and the underlying concepts are introduced to undergraduate students. The course begins by building foundation of the concepts of stress and strain in three-dimensional deformable bodies. It further uses these concepts to study extension, torsion and bending of beams. The one-dimensional theory of beams are also introduced. Various theories of failure that are critical for design of machine elements in industry will also be discussed.
Course Layout
- Mathematical preliminaries and notation; Concept of Traction vector; Concept of Stress tensor
- 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 cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system
- Axisymmetric deformations: combined extension-torsion-inflation of a cylinder
- Bending of beams having symmetrical and non-symmetrical cross-section
- Shear center, Shear flow in thin and open cross-section beams; Euler Bernouli and Timoshenko beam theories; beam buckling
- Energy methods, Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
- Various theories of failure and their application
Course References
This course is not based on any particular textbook. However, the course materials have been prepared using the following four references:
- Solid Mechanics (NPTEL) by Prof. Ajeet Kumar [video link]
- Srinath, L.S., “Advanced Solid Mechanics”, Elsevier, 2018.
- Timoshenko, S.P. and Goodier, J.N., “Theory of Elasticity”, McGraw Hill, 2017.
- Sadd, M.H., “Elasticity: Theory, Applications and Numerics”, Elsevier, 2005
Grading
| Component | Scores | Solutions |
|---|---|---|
| Attendance | 10 | |
| Quiz #1 | 10 | Solution |
| Minor | 30 | Solution |
| Quiz #2 | 10 | Solution |
| Major | 40 | Solution |
| Total | 100 |
Course Attendance
Students are highly encouraged to attend all classes. They have to attend the classes and tutorials to receive 10 point attendance scores. Class attendance will be taken via Timble. Please mark yourself in and out for each class. In case of unavoidable absence, such as illness, please send an appropriate email within a week after absence with email subject specifying the subject code APL 104.
A minimum of 80% attendance is required for passing the course.
Quiz
Quiz 1 (syllabus will be everything upto principal stress and principal planes). DATE: 09/09/22
Policy for Cheating
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.