# Mechanics of Solids - IITG

- Institution: IIT Guwahati
- Department: Civil Engineering
- Teacher: Prof. Arunasis Chakarborty
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/105103684)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/105103684)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

The course introduces the fundamental concept of stress-strain behavior of ductile and brittle material, yield stress, and ultimate stress. Then, the participants are introduced to the state of stress in 2D and 3D space, stress transformation, eigen analysis for principal stress, and principal plane. It is followed by the definition of strain tensor, compatibility conditions, and their role in strain-displacement relation, principal strain, and different elastic constants for homogeneous, isotropic, and elastic material. Once the 3D stress and strain fields are explained, plane stress and plane strain problems are discussed along with the construction of Mohr's circle with numerical examples. With this background of 3D stress and strain field, different failure theories are explained with examples. Then, the bending and shear stress distribution across different cross-sections are explained, followed by the Euler-Bernoulli theory for beams undergoing bending deformation. A series of examples are presented at this stage to correlate the theory developed for different engineering problems. Then, the concepts of pure torsion and torsional rigidity are introduced, followed by energy formulation, i.e., the principle of virtual work and Castigliano's theorem for determinate and indeterminate structures. Finally, the column buckling theory, Euler's critical buckling load for different boundary conditions, and the beam-column problem formulation are covered.

Intended audience: UG Students

## Lectures

1. [Lecture 1: Introduction to Stress and Strain.](https://invisiblenetwork.ai/learn/nptel/105103684/fffb2e3b331b) (YouTube)
2. [Lecture 2: Stress-Strain behaviour.](https://invisiblenetwork.ai/learn/nptel/105103684/57bb78157d22) (YouTube)
3. [Lecture 3: Problems on Stress and Strain](https://invisiblenetwork.ai/learn/nptel/105103684/1458333f2e06) (YouTube)
4. [Lecture 4: Normal & Shear Stress](https://invisiblenetwork.ai/learn/nptel/105103684/51cd0f339702) (YouTube)
5. [Lecture 5: 2D Stress Field](https://invisiblenetwork.ai/learn/nptel/105103684/8b53e49d837e) (YouTube)
6. [Lecture 6: Principal Stresses](https://invisiblenetwork.ai/learn/nptel/105103684/59cfeeaf35e9) (YouTube)
7. [Lecture 7: 2D Mohr Circle](https://invisiblenetwork.ai/learn/nptel/105103684/33314e0ac062) (YouTube)
8. [Lecture 8: 3D Stress Analysis](https://invisiblenetwork.ai/learn/nptel/105103684/bc6607ed580a) (YouTube)
9. [Lecture 9: 3D Stress Analysis contd.](https://invisiblenetwork.ai/learn/nptel/105103684/0e7b4ba5f785) (YouTube)
10. [Lecture 10: 3D Principal Stresses and Planes](https://invisiblenetwork.ai/learn/nptel/105103684/131653a7deb1) (YouTube)
11. [Lecture 11: 3D Mohr Circle](https://invisiblenetwork.ai/learn/nptel/105103684/5bcd985f6406) (YouTube)
12. [Lecture 12: Mohr Circle numerical examples](https://invisiblenetwork.ai/learn/nptel/105103684/8ec18457ab01) (YouTube)
13. [Lecture 13: Octahedral Stresses](https://invisiblenetwork.ai/learn/nptel/105103684/3366d757204b) (YouTube)
14. [Lecture 14: Plane Stress](https://invisiblenetwork.ai/learn/nptel/105103684/367169b29777) (YouTube)
15. [Lecture 15: Plane Stress Example](https://invisiblenetwork.ai/learn/nptel/105103684/1665d8b33e72) (YouTube)
16. [Lecture 16: 3-D Strain Analysis](https://invisiblenetwork.ai/learn/nptel/105103684/ea327d2e1145) (YouTube)
17. [Lecture 17: Principal strains](https://invisiblenetwork.ai/learn/nptel/105103684/ad59beede02b) (YouTube)
18. [Lecture 18: 3-D Strain numerical example](https://invisiblenetwork.ai/learn/nptel/105103684/67daf388c0dc) (YouTube)
19. [Lecture 19: Strain Compatibility](https://invisiblenetwork.ai/learn/nptel/105103684/9f990d0b2f1e) (YouTube)
20. [Lecture 20: Strain Compatibility numerical example](https://invisiblenetwork.ai/learn/nptel/105103684/9e10d9d691d6) (YouTube)
21. [Lecture 21: Stress-Strain relation](https://invisiblenetwork.ai/learn/nptel/105103684/bb10dc9dd4a2) (YouTube)
22. [Lecture 22: Stress-Strain relation contd.](https://invisiblenetwork.ai/learn/nptel/105103684/f431ec6709e4) (YouTube)
23. [Lecture 23: Failure theories](https://invisiblenetwork.ai/learn/nptel/105103684/5af5aea1964b) (YouTube)
24. [Lecture 24: Simple beam bending theory](https://invisiblenetwork.ai/learn/nptel/105103684/f78348c6e1a7) (YouTube)
25. [Lecture 25: Bending stress in standard sections](https://invisiblenetwork.ai/learn/nptel/105103684/d863df632e22) (YouTube)
26. [Lecture 26: Bending stress in built-up sections](https://invisiblenetwork.ai/learn/nptel/105103684/c757c8e18bb8) (YouTube)
27. [Lecture 27: Shear stress distribution](https://invisiblenetwork.ai/learn/nptel/105103684/7e4afc7f5d3a) (YouTube)
28. [Lecture 28: Shear stress distribution Example](https://invisiblenetwork.ai/learn/nptel/105103684/3d2d862e563a) (YouTube)
29. [Lecture 29: Shear center](https://invisiblenetwork.ai/learn/nptel/105103684/699b9eeb848b) (YouTube)
30. [Lecture 30: Shear center contd.](https://invisiblenetwork.ai/learn/nptel/105103684/9b85e0c37e11) (YouTube)
31. [Lecture 31: Double integration method](https://invisiblenetwork.ai/learn/nptel/105103684/d94c536ae254) (YouTube)
32. [Lecture 32: Double integration with Macaulay's bracke](https://invisiblenetwork.ai/learn/nptel/105103684/1943398692aa) (YouTube)
33. [Lecture 33: Beam deflection example](https://invisiblenetwork.ai/learn/nptel/105103684/eec30246b780) (YouTube)
34. [Lecture 34: Beam deflection example contd.](https://invisiblenetwork.ai/learn/nptel/105103684/432508b0a5bd) (YouTube)
35. [Lecture 35: Pure Torsion](https://invisiblenetwork.ai/learn/nptel/105103684/7ce0a3f267df) (YouTube)
36. [Lecture 36: Shear Stress Distribution](https://invisiblenetwork.ai/learn/nptel/105103684/5fd9cb541b06) (YouTube)
37. [Lecture 37: Power Transmission & Composite shaft](https://invisiblenetwork.ai/learn/nptel/105103684/0c3186021ae7) (YouTube)
38. [Lecture 38: Torsion with Warping](https://invisiblenetwork.ai/learn/nptel/105103684/75fca1e02b75) (YouTube)
39. [Lecture 39: Strain Energy](https://invisiblenetwork.ai/learn/nptel/105103684/6d46a124c980) (YouTube)
40. [Lecture 40: Castigliano's theorems](https://invisiblenetwork.ai/learn/nptel/105103684/bfb4d7649fbb) (YouTube)
41. [Lecture 41: Castigliano's theorem example](https://invisiblenetwork.ai/learn/nptel/105103684/34f6fee0dbb9) (YouTube)
42. [Lecture 42: Castigliano's theorem for Indeterminate structure](https://invisiblenetwork.ai/learn/nptel/105103684/d96974940bae) (YouTube)
43. [Lecture 43: Castigliano's theorem for Indeterminate structure contd.](https://invisiblenetwork.ai/learn/nptel/105103684/20999f4d37ab) (YouTube)
44. [Lecture 44:Column Buckling Theory](https://invisiblenetwork.ai/learn/nptel/105103684/b2ac47117a30) (YouTube)
45. [Lecture 45: Euler Buckling Load](https://invisiblenetwork.ai/learn/nptel/105103684/6f45bb95f923) (YouTube)
46. [Lecture 46:Column Buckling Example](https://invisiblenetwork.ai/learn/nptel/105103684/ad14dba346aa) (YouTube)
47. [Lecture 47: Rankine's Theory](https://invisiblenetwork.ai/learn/nptel/105103684/779f80581239) (YouTube)
48. [Lecture 48: Column with Eccentric Load](https://invisiblenetwork.ai/learn/nptel/105103684/60b0b97a5e63) (YouTube)
49. [Lecture 49: Beam-Column Concept](https://invisiblenetwork.ai/learn/nptel/105103684/9387f293c415) (YouTube)