1. Course No.: MEBF ZC342 MACHINE DESIGN
Prof. D. Datta
L1: Stress Analysis Principles, Prof. D. Datta

2. L1: Stress Analysis Principles, Prof. D. Datta
An Overview of the Subject
The Essence of Engineering is the Utilization of resources and the Laws
of Nature for the benefit of Mankind
Engineering is an applied science in the sense that it is concerned with
understanding scientific principles and applying them to achieve a
designated goal.
Mechanical Engineering Design is a major segment of Engineering.
Machine Design is a segment of the Mechanical Engineering Design in
which decisions regarding shape and size of Machines or Machine
components are taken for their satisfactory intended performance.
L1: Stress Analysis Principles, Prof. D. Datta

3. L1: Stress Analysis Principles, Prof. D. Datta
Phases in Design
Design is a highly Iterative Process
Identification of Need
Definition of Problem
Synthesis
Analysis and Optimization
Evaluation
Presentation
L1: Stress Analysis Principles, Prof. D. Datta

4. L1: Stress Analysis Principles, Prof. D. Datta
Steps in Design
Idntify the Need
Collect Data to Describe the System
Estimate Initial Design
Analyze the System
Check Performance Criteria
Is Design Satisfactory?
Yes
Stop No
Change the Design based on Experience/Calculation

5. L1: Stress Analysis Principles, Prof. D. Datta
Design Considerations
Functionality
Strength
Stiffness / Distortion
Wear
Corrosion
Safety
Reliability
Manufacturability
Utility
Cost
Friction
Weight
Life
14. Noise
15. Styling
16. Shape
17. Size
18. Control
19. Thermal Properties
20. Surface
21. Lubrication
22. Marketability
23. Maintenance
24. Volume
25. Liability
26. Remanufacturing
L1: Stress Analysis Principles, Prof. D. Datta

6. L1: Stress Analysis Principles, Prof. D. Datta
Loads and Equilibrium
Restraints
L1: Stress Analysis Principles, Prof. D. Datta

7. L1: Stress Analysis Principles, Prof. D. Datta
Stresses X
Uni-axial Stress X A
Normal Stress
Shear Stress
L1: Stress Analysis Principles, Prof. D. Datta

8. Torsional Shear Stress L1: Stress Analysis Principles, Prof. D. Datta
τmax
J = Polar Moment of Inertia =
Angle of Twist
Torsion formula with slowly varying area may be used as long as they are circular
L1: Stress Analysis Principles, Prof. D. Datta

9. L1: Stress Analysis Principles, Prof. D. Datta
Torsional Shear Stress (cont’d)
Here, τxz is negative as it acts opposite to the +z-axis
but τxy is positive as it acts along the +y-axis
L1: Stress Analysis Principles, Prof. D. Datta

10. L1: Stress Analysis Principles, Prof. D. Datta
Normal Stresses due to Bending X
M = Bending Moment
y = Distance of the layer from
Neutral Axis
I = Moment of Inertia of the cross
section about the axis of bending
L1: Stress Analysis Principles, Prof. D. Datta

11. L1: Stress Analysis Principles, Prof. D. Datta
A Problem: Get the Shear Force and BM Distribution
L1: Stress Analysis Principles, Prof. D. Datta

12. Getting Maximum Normal and Shear Stressesy X
Combining the above two equations
Equation of a circle
Remember this

13. Ductile Materials
Material exhibits sufficient elongation and necking before fracture
Yield point is distinct in stress strain curve
Ultimate tensile and compressive strength are nearly same
Primarily fails by shear

14. Engineering Stress Strain Curve
(MPa)

15. Engineering Stress Strain Curve (cont’d)

16. Cup and Cone Fracture
Necking in a Tensile Specimen

17. Brittle Materials
Material does not exhibit sufficient elongation and necking before fracture.
Yield point is not distinct in the stress strain curve, an equivalent Proof
Stress is used in place of the Yield Stress.
Ultimate tensile and compressive strength are not same, compressive
strength could be as high as three times of the tensile strength.
Primarily fails by tension.

18. Proof Stress

19. Theories of failure for Ductile Materials
Maximum Principal Stress Theory: Rankine
Maximum Shear Stress Theory: Tresca
Maximum Principal Strain Theory: St. Venant
Maximum Strain Energy Theory: Beltrami and Haigh
Maximum Distortion Energy Theory: von Mises

20. Maximum Shear Stress Theory: Tresca’s Theory
Statement
Failure will occur in a material if the maximum shear stress at a
point due to a given set of load exceeds the maximum shear
Stress induced due to a uniaxial load at the Yield Point.
For failure not to occur
With factor of safety
For failure not to occur

21. Maximum Distortion Energy Theory: von Mises Theory
Statement
Failure will occur in a material if the maximum distortion energy at a
point due to a given set of load exceeds the maximum distortion
Energy induced due to a uniaxial load at the Yield Point.
For failure not to occur
With factor of safety
For failure not to occur

22. Theories of failure for Brittle Materials
Maximum Principal Stress Theory: Rankine
Mohr’s Theory
Coulomb Mohr Theory
Modified Mohr Theory

23. Maximum Normal Stress Theory for Brittle Materials
The maximum stress criterion states that failure occurs when
the maximum principal stress reaches either the uniaxial tension
strength σt or the uniaxial compression strength σc .
For failure not to occur

24. Coulomb Mohr’s Theory of Failure for Brittle Materials
All intermediate stress states fall into one of the four categories in the following table. Each case defines the maximum allowable values for the two principal stresses to avoid failure.
Case
Principal Stresses
Criterion Requirements
1. Both in tension
1 > 0, 2 > 0
1 < t, 2 < t
2. Both in Compression
1 < 0, 2 < 0
1 < c, 2 < c
3. One in T and other in C
1 > 0, 2 < 0
4. One in T and other in C
1 < 0, 2 > 0

25. Variable Loading or Fatigue Loading

26. S-N Diagram

27. Failure Criteria for Variable Loading or Fatigue Loading
Gerber (Germany, 1874):
Goodman (England, 1899):
Soderberg (USA, 1930):
Morrow (USA, 1960s):

28. Failure Lines for Different Fatigue Failure Criteria

29. · Stress Concentration · Notch Sensitivity · Size · Environment
Factors Affecting Endurance Limit
· Surface Finish
· Temperature
· Stress Concentration
· Notch Sensitivity
· Size
· Environment
· Reliability