Design of Machine Members Subjected to Direct Stress

1. Introduction

Machine members subjected to direct stress experience forces acting perpendicular (normal) or parallel (shear) to the cross-sectional area.

• Direct Stress = Force applied uniformly over a cross-section
• Common in structural and machine components like rods, bolts, columns, plates

2. Types of Direct Stress

(A) Tensile Stress

• Caused by pulling forces
• Tends to elongate the member

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(B) Compressive Stress

• Caused by pushing forces
• Tends to shorten the member

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(C) Shear Stress

• Force acts parallel to the cross-section
• Causes sliding between layers

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3. Basic Stress Formula

$\sigma = \frac{F}{A}$σ=AF​

Where:

• $\sigma$σ = Normal stress
• $F$F = Applied force
• $A$A = Cross-sectional area

For shear stress:$$\tau = \frac{F}{A}$$τ=AF​

4. Strain and Hooke’s Law

$$\text{Strain} = \frac{\text{Change in length}}{\text{Original length}}$$Strain=Original lengthChange in length​ $$\sigma = E \cdot \varepsilon$$σ=E⋅ε

Where:

• $E$E = Young’s modulus

5. Design Considerations

(A) Factor of Safety (FOS)

$$\text{FOS} = \frac{\text{Ultimate stress}}{\text{Working stress}}$$FOS=Working stressUltimate stress​

• Ensures safe design
• Depends on material and loading conditions

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(B) Working Stress

$$\sigma_{working} = \frac{\sigma_{ultimate}}{\text{FOS}}$$σworking​=FOSσultimate​​

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6. Design of Members in Tension

Examples

• Tie rods
• Bolts
• Chains

Design Condition

$$A = \frac{F}{\sigma_{allowable}}$$

Failure Modes

• Yielding
• Fracture

7. Design of Members in Compression

Examples

• Columns
• Struts

Short Columns

• Fail by crushing

$$\sigma = \frac{F}{A}$$σ=AF​

Long Columns

• Fail by buckling (Euler’s theory)

8. Design of Bolts and Fasteners

Bolt in Tension

$$\sigma_t = \frac{F}{A_t}$$σt​=At​F​

Bolt in Shear

$$\tau = \frac{F}{A_s}$$τ=As​F​

Types of Loading

• Direct tensile load
• Shear load
• Combined loading

9. Design of Cotter and Knuckle Joints

Cotter Joint

• Used for axial loads
• Failure modes:
  • Shear of cotter
  • Crushing

Knuckle Joint

• Used for tensile loads
• Failure modes:
  • Shear
  • Bending
  • Crushing

10. Stress Concentration

• Occurs near:
  • Holes
  • Notches
  • Sudden changes in section

Reduction Methods

• Fillets
• Smooth transitions

11. Materials for Direct Stress Members

• Mild steel
• Alloy steel
• Aluminum alloys

12. Key Design Steps

1. Determine applied load
2. Select material
3. Choose factor of safety
4. Calculate allowable stress
5. Determine required cross-section
6. Check for failure modes

13. Applications

• Structural members
• Machine frames
• Fasteners and joints
• Pressure vessels

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