Stresses in Machine Elements free notes for Diploma / BTech.

1. Introduction

Machine elements such as shafts, gears, bolts, springs, and beams are subjected to different types of forces during operation. These forces produce stresses, which determine the strength, safety, and life of the component.

Key idea:
Stress = Internal resistance offered by a material against external load

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2. Definition of Stress

Stress is defined as:$$\text{Stress} = \frac{\text{Force}}{\text{Area}}$$Stress=AreaForce​

Unit: Pascal (Pa) or N/m²

3. Types of Stresses in Machine Elements

(1) Tensile Stress

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• Occurs when a member is pulled apart
• Causes elongation

$$\sigma_t = \frac{P}{A}$$σt​=AP​

Where:

• $P$P = Tensile force
• $A$A = Cross-sectional area

(2) Compressive Stress

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• Occurs when a member is compressed
• Causes shortening

$$\sigma_c = \frac{P}{A}$$

(3) Shear Stress

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• Acts parallel to the surface
• Causes sliding between layers

$$\tau = \frac{P}{A}$$τ=AP​

(4) Bending Stress

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• Occurs in beams under load
• One side in tension, other in compression

$$\sigma_b = \frac{My}{I}$$σb​=IMy​

Where:

• $M$M = Bending moment
• $y$y = Distance from neutral axis
• $I$I = Moment of inertia

(5) Torsional Stress

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• Occurs due to twisting moment (torque)
• Common in shafts

$$\tau = \frac{Tr}{J}$$

(6) Thermal Stress

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• Caused by temperature changes
• Occurs when expansion/contraction is restricted

(7) Impact Stress

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• Produced by sudden or shock loading
• Higher than static stress

(8) Fatigue Stress

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• Due to repeated or cyclic loading
• Leads to failure even below yield stress

4. Combined Stresses

In real machine elements, multiple stresses act simultaneously.

Examples:

• Shaft → torsion + bending
• Bolts → tension + shear
• Beams → bending + shear

Design must consider combined effect of stresses

5. Principal Stresses and Maximum Shear Stress

• Principal stress: Maximum normal stress at a point
• Maximum shear stress: Maximum shear acting on a plane

Used in design theories:

• Maximum shear stress theory
• Maximum principal stress theory

6. Stress-Strain Relationship

• Stress causes strain (deformation)
• Governed by Hooke’s Law (within elastic limit):

$$\sigma = E \epsilon$$σ=Eϵ

Where:

• $E$E = Young’s modulus
• $\epsilon$ϵ = Strain

7. Stress Concentration

Occurs at:

• Holes
• Keyways
• Sharp corners

Leads to localized high stress

Reduction methods:

• Fillets
• Smooth transitions
• Proper design

8. Failure Theories

Used for safe design:

• Maximum principal stress theory
• Maximum shear stress theory (Guest theory)
• Distortion energy theory (Von Mises)

9. Importance in Machine Design

• Ensures safety
• Prevents failure
• Improves life of components
• Helps in material selection

10. Applications

• Shafts
• Gears
• Springs
• Pressure vessels
• Structural components

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