APL104F23

APL 104: Solid Mechanics (Fall semester 2023)

Course Info

Credit: 4 units (3-1-0)

Instructors: Prof. Rajdip Nayek (rajdipn@am.iitd.ac.in)

Class timings: Tue, Wed & Fri (9:00 to 10:00 AM) at Block VI 301

Tutorial Session 1: Tue (2:00 to 3:00 PM) at LHC 313.3
Tutorial Session 2: Fri (2:00 to 3:00 PM) at LHC 313.3

A list of students in particular tutorial sessions can be accessed here: Excel sheet

Office hours (TA): Wed 4:00-5:00 pm (in Block 4 Room B-24)

Intended audience: BTech students in Applied Mechanics and Materials

NOTE-For all course related emails, please put APL104 in the subject line

Lecture Schedule

Module	Topics	Handwritten Lecture Notes
Module 01	Analysis of Mechanical System	Study of forces Equilibrium conditions Additional requirements for deformable bodies
Module 02	Traction	Traction vector Traction decomposition
Module 03	Stress	State of Stress at a point Stress equilibrium equation
Module 04	Principal Stresses and Planes	Stress eigenvalue problem Maximum Normal and shear stress
Module 05	Mohr’s Circle Decomposition of Stress Tensor	2D Mohr’s circle 2D & 3D Mohr’s circle Stress Invariants, Octahedral Stresses, etc.
Module 06	Concept of Strain	Normal and Shear Strain Strain-displacement relation Strain compatibility Similarity of properties of stress and strain tensors
Module 07	Stress-strain-temperature relations	General stress-strain curves Isotropic linear elastic material and thermal strain
Module 08	Complete equations of linear elasticity	Equations and boundary conditions for unique solution
Module 09	Application to extension-torsion-inflation in cylindrical coordinates	Elasticity Equations in cylindrical coordinates Simplified equations Solving simplified equations
Module 10	Bending of beams	Uniform bending Non-uniform bending Uniform bending of unsymmentrical beams Non-uniform bending and Shear flow Deflection of beams and buckling
Module 11	Energy methods	External work and strain energy Castigliano’s theorem

Tutorial Schedule

Topics	Tutorial Questions	Tutorial Solutions
Study of forces	Tutorial 1	Solution
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 elasticity	Tutorial 7	Solution
Extension-torsion-inflation	Tutorial 8	Solution
Uniform beam bending	Tutorial 9	Solution
Non-Uniform beam bending	Tutorial 10	Solution
Euler-Bernoulli beams & Energy Methods	Tutorial 11	Solution

Table of Contents

• Course Outline
• Course Layout
• Course References
• Grading
• Course Attendance
• Quiz
• Policy for Cheating

Course Outline

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.

Course Layout

• Fundamental Principles of Mechanics; Introduction of 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 the symmetrical and non-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

Course References

This course is based on three textbooks:

• Archer, Cook, Crandall, Dahl, Lardner, McClintock, Rabinowicz, Reichenbach, “An Introduction To The Mechanics Of Solids”, Tata Mcgraw Hill, 2012
• Hibbeler, R. C., “Mechanics of Materials”, Prentice Hall, 2014
• Srinath, L.S., “Advanced Solid Mechanics”, Elsevier, 2018.

Other references

• Solid Mechanics (NPTEL) by Prof. Ajeet Kumar [video link]
• 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
Quiz #1	15	Solution
Minor	30	Solution
Quiz #2	15	Solution
Major	40	Solution
Total	100

Course Attendance

Students are highly encouraged to attend all classes. If any student has less than 80% class-plus-tutorial attendance, he/she will get one grade less than would have been awarded. 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 an email subject specifying the subject code APL 104.

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.