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Course105106172104 lectures

Mechanics of Materials

Prof. Saravanan.U · IIT Madras

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About

This first course in mechanics of deformable bodies introduces the four concepts - Force, stress, strain, displacement - and the four equations that connect them, namely equilibrium equations, constitutive relation, compatibility condition and strain displacement relation.Systematic procedure to solve problems of engineering interest is outlined. In particular, force and displacement relation of structural elements subjected to uniaxial stress, bending, twisting and inflation is studied. Estimation of possible modes of failure of these structural elements and the failure load is outlined.

INTENDED AUDIENCE : Any Interested learners

PREREQUISITES : Engineering Mechanics, Basic Calculus

Lectures

Week 1 : Introduction and Mathematical Preliminaries

  1. Introduction to the course - Why this course? YouTube
  2. Introduction to the course - Concepts and equations in this course YouTube
  3. Introduction to the course - Objectives and prerequisite YouTube
  4. Mathematical Preliminaries - Linear Algebra YouTube
  5. Mathematical Preliminaries - Vector Algebra YouTube
  6. Representation of Vector YouTube
  7. Tutorial 1 YouTube

Week 2 : Concept of Force, Displacement and stress

  1. Concept of Force YouTube
  2. Definition of a body YouTube
  3. Motion and Displacement field YouTube
  4. Traction YouTube
  5. Properties of traction YouTube
  6. Defnition of stress tensor and linear function YouTube
  7. Tensor Algebra YouTube
  8. Meaning of components of the stress tensor YouTube
  9. Tutorial 2 YouTube

Week 3 : Transformation of stress and equilibrium equation

  1. Transformation of stress components YouTube
  2. Mohr's Circle derivation YouTube
  3. Example 1: Construction of Mohr's circle YouTube
  4. Example 2: Extremum normal and shear stress YouTube
  5. Example 3: Transformation of stress components YouTube
  6. Uniaxial stress YouTube
  7. Hydrostatic, pure shear and deviatoric stress YouTube
  8. Biaxial and Plane state of stress YouTube
  9. Extreme stress for 3D stresses YouTube
  10. Extremum shear stress YouTube
  11. Stresses in the Octahedral plane YouTube
  12. Tutorial 3 YouTube

Week 4 : Concept of strain

  1. Stretch ratio and strain YouTube
  2. Curves and arc Length YouTube
  3. Gradient YouTube
  4. Deformation and displacement Gradient YouTube
  5. Right Cauchy Green Deformation tensor YouTube
  6. Homogeneous deformation YouTube
  7. Engineering strain YouTube
  8. Change in Angle YouTube
  9. Transformation of strain components/ Strain Rosette YouTube

Week 5: Governing equations in mechanics

  1. 2D Equilibrium equations YouTube
  2. 3D Equilibrium equations YouTube
  3. Compatibility condition YouTube
  4. Constitutive relation YouTube
  5. Young's Modulus and Poisson's Ratio YouTube
  6. Shear Modulus YouTube
  7. Bulk Modulus YouTube
  8. Restriction on material parameters YouTube
  9. Strain energy, load potential and total potential YouTube

Week 6 : Displacement due to uniaxial loading, temperature and bending

  1. Thermal strain YouTube
  2. Stepped shaft subjected to axial force YouTube
  3. Inhomogeneous bar subjected to axial force YouTube
  4. Stepped shaft subjected to raise in temperature YouTube
  5. Traction in member subjected to bending YouTube
  6. Governing equilibrium equations YouTube
  7. Displacement field YouTube
  8. Bending equation YouTube
  9. Radius of curvature YouTube

Week 7 : Stresses and deflection in homogeneous beams loaded about one principal axis

  1. Shear force and bending moment diagram YouTube
  2. Variation of axial stress YouTube
  3. Deflected shape and rotation of cross section YouTube
  4. Expression to find shear stress YouTube
  5. Finding centroid of a cross section YouTube
  6. Parallel axis theorem and its application YouTube
  7. Vertical shear stress in I section YouTube
  8. Horizontal shear stress in I section YouTube
  9. Connection design YouTube

Week 8 : Stresses and deflection in beams loaded about one principal axis

  1. Definition of shear center YouTube
  2. Shear center of Channel section YouTube
  3. Expression to find shear center YouTube
  4. Shear force and bending moment diagram YouTube
  5. Finding allowable load YouTube
  6. Modified bending equation YouTube
  7. Bending of a composite beam YouTube
  8. Connection design YouTube

week 9 : Stresses and deflection in beams not loaded about principal axis

  1. Moment of Intertia about arbitrarily oriented axis YouTube
  2. Example: Angle section YouTube
  3. Bending equation for bending about principal axis YouTube
  4. Bending equation about arbitrary axis YouTube
  5. Neutral axis YouTube
  6. Load not about principal axis YouTube
  7. Load about principal axis YouTube

Week 10 : Stresses and displacement due to torsion or inflation

  1. Displacement field YouTube
  2. Torsion equation YouTube
  3. Example problems: Closed sections YouTube
  4. Twisting of open sections YouTube
  5. Example problems: Open sections YouTube
  6. Twisting of thin walled closed sections YouTube
  7. Example problems: Thin walled sections YouTube
  8. Cylindrical polar coordinate system YouTube

Week 11 : Pressure vessels and Failure criteria

  1. Displacement field YouTube
  2. Governing differential equation and solution YouTube
  3. Example problems : Thick walled cylindrical vessel YouTube
  4. Thin walled pressure vessels YouTube
  5. General concepts in failure criteria YouTube
  6. Different failure modes YouTube
  7. Tresca Condition YouTube
  8. vonMises condition YouTube
  9. Maximum normal stress or rankine condition YouTube
  10. Mohr - Columb condition YouTube
  11. Drucker-Prager Condition YouTube
  12. Numerical Example: Pressure vessel and failure theory YouTube

Week 12 : Buckling

  1. General concepts in buckling YouTube
  2. Euler critical load for simply supported column YouTube
  3. Euler critical load for column with any boundary condition YouTube
  4. Secant formula YouTube
  5. Determination of maximum load carrying capacity of a simple truss YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Civil Engineering
Teacher
Prof. Saravanan.U
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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