1. The document discusses various theories of failure including maximum shear stress theory, maximum principal stress theory, maximum distortion energy theory, maximum strain theory, and maximum total strain energy theory. 2. It also covers topics like stress tensors, principal stresses, combined stresses, and design for strength under static loads. 3. Examples, equations, and references are provided to explain concepts related to stress analysis and failure theories.

1. Dr. Mathew John
Assistant Professor
Department of Mechanical Engineering
Government Engineering College Barton Hill
S7 ME401: DESIGN OF MACHINE ELEMENTS - I
1
Module 2 (Part A)
(KTU Syllabus)
Date of commencement of KTU odd semester classes: 17Aug 2020
Online Classes GEC-BH - Sep 2020

2. Introduction
2

3. 3

4. Stress Tensor- stress state at a point
The stress tensor components
(the elements of the matrix)
depend on the coordinate
system chosen
By a special rotation of the coordinate system, it is possible to reduce a
general stress tensor to one with only the three normal components.
Principal Stresses
4

5. Principal Stresses- 2D (Plane stress)
5

6. 6
Ref.Machine Design- R.L Norton

7. Theories of Failure (Static)
7
Dr. Mathew John S7 ME – DME-1 GEC Barton Hill
1. Maximum Shear StressTheory (Tresca/ Guest’s
Theory)
2. Maximum Principal StressTheory (Rankine’s
Theory)
3. Maximum Distortion EnergyTheory (von Mises -
HenckyTheory)
4. Maximum StrainTheory (St.Venant’sTheory)
5. Maximum total strain energy theory (Haigh’s
Theory)
Ref.Machine Design- R.L Norton

8. 1. Maximum Shear Stress Theory
(Tresca- Guest’s Theory)
8
Dr. Mathew John S7 ME – DME-1 GEC Barton Hill
Also known as Coulomb theory
MSST states that, failure occurs when maximum
shear stress in a part exceeds the shear stress
in a tensile specimen at yield (one half of the
tensile Yield Strength)

9. Maximum Shear Stress Criterion contd….
9

10. 10
Failure surface in case of
TrescaYield criterion.

11. 2. Maximum Principal Stress Theory
(Rankine’s Theory)
Ref.Machine Design- R.L Norton
Failure occurs when,
11
Dr. Mathew John S7 ME – DME-1 GEC Barton Hill

12. 12

13. 13

14. 14

15. 15
3. Maximum Distortion Energy Theory
(von Mises - Hencky Theory)
Dr. Mathew John Govt. Engg. College Barton Hill
According to this theory the failure or yielding occurs at a
point when the distortion strain energy per unit volume in
a stress system reaches the limiting distortion strain energy
per unit volume (ie. at yield point) as determined from a
simple tension test.

16. 16
Dr. Mathew John S7 ME – DME-1 GEC Barton Hill
Ref:Design of Machine Elements-V B Bhandari

17. 17Dr. Mathew John Govt. Engg. College Barton Hill

18. 18Ref.Machine Design- R.L Norton

19. ForThree dimensional stress state the failure occurs when,
…Eq. (1)
19

20. 20

21. 21

22. Comparison-
Tresca theory vs. von Mises theory
22

23. 23Ref:Design of Machine Elements-V B Bhandari

24. 24
4. Maximum Strain Theory (St. Venant’s
Theory)
Maximum value of the
principal strains is considered
According to this theory, The failure of a component
occurs when the maximum strain under actual loading
exceeds the maximum strain in tension bar subjected to
yield point stress
Dr. Mathew John Govt. Engg. College Barton Hill

25. 5. Maximum Total Strain Energy Theory
(Haigh’s Theory)
According to this theory, Failure of a component occurs
when the total strain energy per unit volume under actual
condition of loading exceeds the total strain energy per
unit volume of tension test bar at the yield point stress.
25

26. 26Dr. Mathew John Govt. Engg. College Barton Hill

27. Please refer: (1) Design Data book by K. Mahadevan (4e)- Page Nos. 21, 22
Theories of Failure
27Dr. Mathew John Govt. Engg. College Barton Hill

28. Please refer: (1) Design Data book by K. Mahadevan (4e)- Page Nos. 21, 22 28

29. Design for Strength- Static loads
29Dr. Mathew John Govt. Engg. College Barton Hill

30. Module 1 – Part A (Summary)
30Dr. Mathew John Govt. Engg. College Barton Hill

31. Plane stress (2D)
Ref: Text book Mechanics of Materials by Gere and Goodno 31
Appendix

32. 32
Combined Stresses- Plane stress (2D) ..contd/..
Dr. Mathew John Govt. Engg. College Barton Hill

33. 33Ref: Text book Mechanics of Materials by Gere and Goodno

34. 34Dr. Mathew John Govt. Engg. College Barton Hill

35. 35

36. 36Dr. Mathew John Govt. Engg. College Barton Hill

37. 37
Combined Stresses- Plane stress (2D) ..contd/..
Ref:Mechanics of Solids by Egor P.Popov

38. 38
Dr. Mathew John S7 ME – DME-1 GEC Barton Hill