APL108

APL 108: Mechanics of Solids for Civil Engineers (Fall semester 2025)

Course Info

Credit: 4 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

Lecture Schedule

Module	Topics	Lecture Notes
Mod 01	Recap of Engineering Mechanics & Motivation for Solid Mechanics	Recap Additional requirements for deformable bodies
Mod 02	Traction Vector and Stress Tensor	Traction vector Stress Tensor
Mod 03	Stress Equilibrium Eqns and Traction BC	Stress Equilibrium & Traction BC
Mod 04	Principal stress, Principal planes Planes of max/min shear stress	Principal Stress and Max/Min Shear Stress
Mod 05	2D and 3D Stress Mohr’s circles	Stress Mohr’s Circle
Mod 06	Stress Invariants, Octahedral Stresses Hydrostatic and Deviatoric Stress	Addn. topics on Stress tensor
Mod 07	Concept of Normal and Shear Strain Strain displacement relation Strain compatibility	Normal and Shear Strain Strain displacement relation and Strain Tensor Strain-Compatibility Other topics on strain tensor
Mod 08	Constitutive relations	Material Behavior and Modeling Response of real materials and idealizations Linear elastic isotropic model
Mod 09	Applications of elasticity	Axial loading and deformation Torsion of circular members Uniform bending of beams Non-uniform bending of beams Uniform beam bending with unsymmetrical C/S and/or loading Transverse deflections of beams using Euler-Bernoulli theory

Tutorial Schedule

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

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 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

Course References

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

Grading

Component	Scores	Solutions
Quizzes	20
Minor	20	MinorSol
Practical	20
Major	35
Tutorial Attd	5
Total	100

Course Attendance

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.

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.