# Mechanics of Materials

- Institution: IIT Madras
- Department: Civil Engineering
- Teacher: Prof. Saravanan.U
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/105106172)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/105106172)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Introduction to the course - Why this course?](https://invisiblenetwork.ai/learn/nptel/105106172/bcfa08460c3f) (YouTube)
2. [Introduction to the course - Concepts and equations in this course](https://invisiblenetwork.ai/learn/nptel/105106172/e2dec2d1245d) (YouTube)
3. [Introduction to the course - Objectives and prerequisite](https://invisiblenetwork.ai/learn/nptel/105106172/90e8832bb81a) (YouTube)
4. [Mathematical Preliminaries - Linear Algebra](https://invisiblenetwork.ai/learn/nptel/105106172/235cb07c975d) (YouTube)
5. [Mathematical Preliminaries - Vector Algebra](https://invisiblenetwork.ai/learn/nptel/105106172/419f3953ba94) (YouTube)
6. [Representation of Vector](https://invisiblenetwork.ai/learn/nptel/105106172/1bbc19b79404) (YouTube)
7. [Tutorial 1](https://invisiblenetwork.ai/learn/nptel/105106172/b66a3ba4c42b) (YouTube)
8. [Concept of Force](https://invisiblenetwork.ai/learn/nptel/105106172/50b90d554d97) (YouTube)
9. [Definition of a body](https://invisiblenetwork.ai/learn/nptel/105106172/c1d19b4961b8) (YouTube)
10. [Motion and Displacement field](https://invisiblenetwork.ai/learn/nptel/105106172/fedb28f2cbc9) (YouTube)
11. [Traction](https://invisiblenetwork.ai/learn/nptel/105106172/8388f5b91745) (YouTube)
12. [Properties of traction](https://invisiblenetwork.ai/learn/nptel/105106172/582aafb3e10d) (YouTube)
13. [Defnition of stress tensor and linear function](https://invisiblenetwork.ai/learn/nptel/105106172/2274a20efc9d) (YouTube)
14. [Tensor Algebra](https://invisiblenetwork.ai/learn/nptel/105106172/b14a03695bc8) (YouTube)
15. [Meaning of components of the stress tensor](https://invisiblenetwork.ai/learn/nptel/105106172/040ab1dbf4cc) (YouTube)
16. [Tutorial 2](https://invisiblenetwork.ai/learn/nptel/105106172/f0450caee7c0) (YouTube)
17. [Transformation of stress components](https://invisiblenetwork.ai/learn/nptel/105106172/7873eadce20d) (YouTube)
18. [Mohr's Circle derivation](https://invisiblenetwork.ai/learn/nptel/105106172/8aaa3fedee78) (YouTube)
19. [Example 1: Construction of Mohr's circle](https://invisiblenetwork.ai/learn/nptel/105106172/2064a6e62433) (YouTube)
20. [Example 2: Extremum normal and shear stress](https://invisiblenetwork.ai/learn/nptel/105106172/ad35023a3547) (YouTube)
21. [Example 3: Transformation of stress components](https://invisiblenetwork.ai/learn/nptel/105106172/f17b0d5f239b) (YouTube)
22. [Uniaxial stress](https://invisiblenetwork.ai/learn/nptel/105106172/d906c479af47) (YouTube)
23. [Hydrostatic, pure shear and deviatoric stress](https://invisiblenetwork.ai/learn/nptel/105106172/38e74f58e74e) (YouTube)
24. [Biaxial and Plane state of stress](https://invisiblenetwork.ai/learn/nptel/105106172/a256c19f2f98) (YouTube)
25. [Extreme stress for 3D stresses](https://invisiblenetwork.ai/learn/nptel/105106172/0cc97d6fdb81) (YouTube)
26. [Extremum shear stress](https://invisiblenetwork.ai/learn/nptel/105106172/3e162b1bade3) (YouTube)
27. [Stresses in the Octahedral plane](https://invisiblenetwork.ai/learn/nptel/105106172/42e023428c07) (YouTube)
28. [Tutorial 3](https://invisiblenetwork.ai/learn/nptel/105106172/4ec62da8b9bc) (YouTube)
29. [Stretch ratio and strain](https://invisiblenetwork.ai/learn/nptel/105106172/938bde5a50f7) (YouTube)
30. [Curves and arc Length](https://invisiblenetwork.ai/learn/nptel/105106172/d7efa7d4ceea) (YouTube)
31. [Gradient](https://invisiblenetwork.ai/learn/nptel/105106172/bd1a50026713) (YouTube)
32. [Deformation and displacement Gradient](https://invisiblenetwork.ai/learn/nptel/105106172/44202ccb63ee) (YouTube)
33. [Right Cauchy Green Deformation tensor](https://invisiblenetwork.ai/learn/nptel/105106172/f22abb7b9b20) (YouTube)
34. [Homogeneous deformation](https://invisiblenetwork.ai/learn/nptel/105106172/8c6706ea2362) (YouTube)
35. [Engineering strain](https://invisiblenetwork.ai/learn/nptel/105106172/528a35119e04) (YouTube)
36. [Change in Angle](https://invisiblenetwork.ai/learn/nptel/105106172/f2a02d107526) (YouTube)
37. [Transformation of strain components/ Strain Rosette](https://invisiblenetwork.ai/learn/nptel/105106172/72576ac7349d) (YouTube)
38. [2D Equilibrium equations](https://invisiblenetwork.ai/learn/nptel/105106172/7ad9706ab740) (YouTube)
39. [3D Equilibrium equations](https://invisiblenetwork.ai/learn/nptel/105106172/fba38c8d7bac) (YouTube)
40. [Compatibility condition](https://invisiblenetwork.ai/learn/nptel/105106172/06692f7f3c7c) (YouTube)
41. [Constitutive relation](https://invisiblenetwork.ai/learn/nptel/105106172/e5cc45d364dc) (YouTube)
42. [Young's Modulus and Poisson's Ratio](https://invisiblenetwork.ai/learn/nptel/105106172/3454bc9c8ef6) (YouTube)
43. [Shear Modulus](https://invisiblenetwork.ai/learn/nptel/105106172/cf33ec2836e2) (YouTube)
44. [Bulk Modulus](https://invisiblenetwork.ai/learn/nptel/105106172/3fca938737ec) (YouTube)
45. [Restriction on material parameters](https://invisiblenetwork.ai/learn/nptel/105106172/3e7388d96646) (YouTube)
46. [Strain energy, load potential and total potential](https://invisiblenetwork.ai/learn/nptel/105106172/d831c0525828) (YouTube)
47. [Thermal strain](https://invisiblenetwork.ai/learn/nptel/105106172/e79c12584d30) (YouTube)
48. [Stepped shaft subjected to axial force](https://invisiblenetwork.ai/learn/nptel/105106172/632058a5e6a4) (YouTube)
49. [Inhomogeneous bar subjected to axial force](https://invisiblenetwork.ai/learn/nptel/105106172/e99f4539e0c4) (YouTube)
50. [Stepped shaft subjected to raise in temperature](https://invisiblenetwork.ai/learn/nptel/105106172/13883aa17175) (YouTube)
51. [Traction in member subjected to bending](https://invisiblenetwork.ai/learn/nptel/105106172/e844dc253325) (YouTube)
52. [Governing equilibrium equations](https://invisiblenetwork.ai/learn/nptel/105106172/3e4a45fdb775) (YouTube)
53. [Displacement field](https://invisiblenetwork.ai/learn/nptel/105106172/ff216e5dc945) (YouTube)
54. [Bending equation](https://invisiblenetwork.ai/learn/nptel/105106172/2250c3fc0379) (YouTube)
55. [Radius of curvature](https://invisiblenetwork.ai/learn/nptel/105106172/59fa6857d0bd) (YouTube)
56. [Shear force and bending moment diagram](https://invisiblenetwork.ai/learn/nptel/105106172/867d147af04f) (YouTube)
57. [Variation of axial stress](https://invisiblenetwork.ai/learn/nptel/105106172/cf62e0553894) (YouTube)
58. [Deflected shape and rotation of cross section](https://invisiblenetwork.ai/learn/nptel/105106172/03d2239ee7b7) (YouTube)
59. [Expression to find shear stress](https://invisiblenetwork.ai/learn/nptel/105106172/a23b3ecd43ce) (YouTube)
60. [Finding centroid of a cross section](https://invisiblenetwork.ai/learn/nptel/105106172/4ed710a83933) (YouTube)
61. [Parallel axis theorem and its application](https://invisiblenetwork.ai/learn/nptel/105106172/3795e42247d6) (YouTube)
62. [Vertical shear stress in I section](https://invisiblenetwork.ai/learn/nptel/105106172/2903410646ca) (YouTube)
63. [Horizontal shear stress in I section](https://invisiblenetwork.ai/learn/nptel/105106172/97ac37393ab6) (YouTube)
64. [Connection design](https://invisiblenetwork.ai/learn/nptel/105106172/5fa7925da6cf) (YouTube)
65. [Definition of shear center](https://invisiblenetwork.ai/learn/nptel/105106172/b8565383157c) (YouTube)
66. [Shear center of Channel section](https://invisiblenetwork.ai/learn/nptel/105106172/ff3f00003451) (YouTube)
67. [Expression to find shear center](https://invisiblenetwork.ai/learn/nptel/105106172/f60e25739b69) (YouTube)
68. [Shear force and bending moment diagram](https://invisiblenetwork.ai/learn/nptel/105106172/ba55a8feb38e) (YouTube)
69. [Finding allowable load](https://invisiblenetwork.ai/learn/nptel/105106172/d9b760b69871) (YouTube)
70. [Modified bending equation](https://invisiblenetwork.ai/learn/nptel/105106172/a85ee424759e) (YouTube)
71. [Bending of a composite beam](https://invisiblenetwork.ai/learn/nptel/105106172/065fdf6573d8) (YouTube)
72. [Connection design](https://invisiblenetwork.ai/learn/nptel/105106172/7fdc8005e428) (YouTube)
73. [Moment of Intertia about arbitrarily oriented axis](https://invisiblenetwork.ai/learn/nptel/105106172/acc3d77c92be) (YouTube)
74. [Example: Angle section](https://invisiblenetwork.ai/learn/nptel/105106172/cb8d5696df88) (YouTube)
75. [Bending equation for bending about principal axis](https://invisiblenetwork.ai/learn/nptel/105106172/b5afb435d753) (YouTube)
76. [Bending equation about arbitrary axis](https://invisiblenetwork.ai/learn/nptel/105106172/3aa7326af8dd) (YouTube)
77. [Neutral axis](https://invisiblenetwork.ai/learn/nptel/105106172/f030eefaafd7) (YouTube)
78. [Load not about principal axis](https://invisiblenetwork.ai/learn/nptel/105106172/41db4a333daa) (YouTube)
79. [Load about principal axis](https://invisiblenetwork.ai/learn/nptel/105106172/97c7ae06ff50) (YouTube)
80. [Displacement field](https://invisiblenetwork.ai/learn/nptel/105106172/03f4bc52fc5a) (YouTube)
81. [Torsion equation](https://invisiblenetwork.ai/learn/nptel/105106172/091f06dad88d) (YouTube)
82. [Example problems: Closed sections](https://invisiblenetwork.ai/learn/nptel/105106172/566d0aee6874) (YouTube)
83. [Twisting of open sections](https://invisiblenetwork.ai/learn/nptel/105106172/3ae20366ab6d) (YouTube)
84. [Example problems: Open sections](https://invisiblenetwork.ai/learn/nptel/105106172/bc431e37a576) (YouTube)
85. [Twisting of thin walled closed sections](https://invisiblenetwork.ai/learn/nptel/105106172/8aa010a13d0a) (YouTube)
86. [Example problems: Thin walled sections](https://invisiblenetwork.ai/learn/nptel/105106172/9b79c223e838) (YouTube)
87. [Cylindrical polar coordinate system](https://invisiblenetwork.ai/learn/nptel/105106172/356b86a4459c) (YouTube)
88. [Displacement field](https://invisiblenetwork.ai/learn/nptel/105106172/8bbe80848911) (YouTube)
89. [Governing differential equation and solution](https://invisiblenetwork.ai/learn/nptel/105106172/875f55f94868) (YouTube)
90. [Example problems : Thick walled cylindrical vessel](https://invisiblenetwork.ai/learn/nptel/105106172/5d1e6a628e76) (YouTube)
91. [Thin walled pressure vessels](https://invisiblenetwork.ai/learn/nptel/105106172/78b7ba3d02bc) (YouTube)
92. [General concepts in failure criteria](https://invisiblenetwork.ai/learn/nptel/105106172/8a7790af20b2) (YouTube)
93. [Different failure modes](https://invisiblenetwork.ai/learn/nptel/105106172/ee7e40df27b7) (YouTube)
94. [Tresca Condition](https://invisiblenetwork.ai/learn/nptel/105106172/02554a77bba6) (YouTube)
95. [vonMises condition](https://invisiblenetwork.ai/learn/nptel/105106172/aed23b4eee03) (YouTube)
96. [Maximum normal stress or rankine condition](https://invisiblenetwork.ai/learn/nptel/105106172/fb1415708c83) (YouTube)
97. [Mohr - Columb condition](https://invisiblenetwork.ai/learn/nptel/105106172/e121f939f338) (YouTube)
98. [Drucker-Prager Condition](https://invisiblenetwork.ai/learn/nptel/105106172/4f71eaef7a51) (YouTube)
99. [Numerical Example: Pressure vessel and failure theory](https://invisiblenetwork.ai/learn/nptel/105106172/7aa472bfbb34) (YouTube)
100. [General concepts in buckling](https://invisiblenetwork.ai/learn/nptel/105106172/8561255b5eb3) (YouTube)
101. [Euler critical load for simply supported column](https://invisiblenetwork.ai/learn/nptel/105106172/1e8048cd6c34) (YouTube)
102. [Euler critical load for column with any boundary condition](https://invisiblenetwork.ai/learn/nptel/105106172/ac64f35ca6d2) (YouTube)
103. [Secant formula](https://invisiblenetwork.ai/learn/nptel/105106172/34f1b8947d50) (YouTube)
104. [Determination of maximum load carrying capacity of a simple truss](https://invisiblenetwork.ai/learn/nptel/105106172/2df629afed84) (YouTube)