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Course No.: MEBF ZC342 MACHINE DESIGN

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Course No.: MEBF ZC342MACHINE DESIGN

Prof. D. Datta

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

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

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

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

Restraints

L1: Stress Analysis Principles, Prof. D. Datta

X

Uni-axial Stress

X

A

Normal Stress

Shear Stress

L1: Stress Analysis Principles, Prof. D. Datta

Torsional Shear Stress

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

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

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

A Problem: Get the Shear Force and BM Distribution

L1: Stress Analysis Principles, Prof. D. Datta

Getting Maximum Normal and Shear Stresses

y

X

Combining the above two equations

Equation of a circle

Remember this

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

Engineering Stress Strain Curve

(MPa)

Engineering Stress Strain Curve (cont’d)

Cup and Cone Fracture

Necking in a Tensile Specimen

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.

Proof Stress

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

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

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

Theories of failure for Brittle Materials

- Maximum Principal Stress Theory: Rankine
- Mohr’s Theory
- Coulomb Mohr Theory
- Modified Mohr Theory

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

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.

Variable Loading or Fatigue Loading

S-N Diagram

Failure Criteria for Variable Loading or Fatigue Loading

Gerber (Germany, 1874):

Goodman (England, 1899):

Soderberg (USA, 1930):

Morrow (USA, 1960s):

Failure Lines for Different Fatigue Failure Criteria

Factors Affecting Endurance Limit

· Surface Finish

· Temperature

· Stress Concentration

· Notch Sensitivity

· Size

· Environment

· Reliability