Lesson 4.1: Design for Static & Dynamic Loading

Machine Design is focused on creating components that can safely withstand applied loads. GATE and PSU exams often test strength of materials, factor of safety, and fatigue concepts.

🔹 1. Introduction

• Definition: Machine design involves selection of dimensions, materials, and safety factors to ensure components work reliably under static or dynamic loads.

• Applications: Shafts, gears, bolts, levers, springs

• Types of Loads:

  1. Static Load: Constant or slowly varying load → no fluctuation

  2. Dynamic Load: Varying load → causes fatigue, vibrations, impact

🔹 2. Design for Static Loading

• Stress Calculation:

σ=FA\sigma = \frac{F}{A}σ=AF​

Where:

• $\sigma$ = stress

• $F$ = applied force

• $A$ = cross-sectional area

• Factor of Safety (FoS):

FoS=Failure stressWorking stress\text{FoS} = \frac{\text{Failure stress}}{\text{Working stress}}FoS=Working stressFailure stress​

• Typical values: 1.5–3 (depends on material & application)

• Design Steps:

  1. Identify load type (tensile, compressive, shear, bending)

  2. Compute allowable stress using FoS

  3. Select dimensions & material to satisfy stress limits

• Example:
  A shaft subjected to tensile load 10 kN, allowable stress 80 MPa. Minimum diameter:

d=4Fπσ=4∗100003.1416∗80∗106≈12.6 mmd = \sqrt{\frac{4F}{\pi \sigma}} = \sqrt{\frac{4*10000}{3.1416*80*10^6}} ≈ 12.6 \text{ mm} d=πσ4F​​=3.1416∗80∗1064∗10000​​≈12.6 mm

🔹 3. Design for Dynamic Loading

• Fatigue Loading: Repeated or fluctuating stress can cause failure below yield strength

• Endurance Limit (σeσ_eσe​): Maximum stress a material can withstand for infinite cycles

• Stress Concentration Factor (K_t): Amplifies stress at notches or grooves

• Modified Goodman Diagram: Checks factor of safety under fluctuating stress

σaSe+σmSu≤1FoS\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_u} \le \frac{1}{\text{FoS}}Se​σa​​+Su​σm​​≤FoS1​

Where:

• σa\sigma_aσa​ = alternating stress

• σm\sigma_mσm​ = mean stress

• SeS_eSe​ = endurance limit

• SuS_uSu​ = ultimate tensile strength

• Example:
  Shaft subjected to alternating stress 50 MPa, mean stress 70 MPa. Material Se=120MPaS_e = 120 MPaSe​=120MPa, Su=400MPaS_u = 400 MPaSu​=400MPa, FoS = 2. Check safety:

50120+70400=0.416+0.175=0.591<0.5? Not safe → redesign required\frac{50}{120} + \frac{70}{400} = 0.416 + 0.175 = 0.591 < 0.5? \text{ Not safe → redesign required}12050​+40070​=0.416+0.175=0.591<0.5? Not safe → redesign required

🔹 4. Design Considerations

• Material Selection: High strength-to-weight ratio, toughness, corrosion resistance

• Shape & Cross-Section: Circular, I-section, rectangular → based on bending & torsion

• Key Design Rules:

  1. Avoid sharp corners → reduce stress concentration

  2. Provide fillets, shoulders, and proper tolerances

  3. Account for safety factors & dynamic effects

🔹 5. Solved Examples (PYQ Style)

Example 1 (GATE ME 2019):
Design a circular shaft to transmit 10 kW at 200 rpm. Material allowable shear stress = 60 MPa. Find diameter.

• Step 1: Torque $T=P/\omega =10000/(2\pi \ast 200/60)\approx 477N\cdot m$

• Step 2: Torsion formula: τ=16T/πd3→d≈25mmτ = 16 T / π d^3 → d ≈ 25 mmτ=16T/πd3→d≈25mm

Example 2 (PSU Exam):
Bolt subjected to fluctuating tensile load: 20 kN max, 10 kN min. Material σe=150MPaσ_e = 150 MPaσe​=150MPa, σu=400MPaσ_u = 400 MPaσu​=400MPa, FoS = 2. Determine minimum bolt diameter.

🔹 6. Practice Exercises

1. Determine minimum shaft diameter for given static and torsional loads.

2. Compute factor of safety for fluctuating load using Modified Goodman Diagram.

3. Calculate torque and diameter for power transmission shaft.

4. Identify stress concentration points in machine components.

5. Select suitable material for a high-speed rotating shaft.

🔹 7. Summary

• Static Loading: Stress = F/A, design using FoS

• Dynamic Loading: Fatigue, alternating stress, endurance limit, Modified Goodman diagram

• Material & Shape: Key to safe, efficient design

• Applications: Shafts, bolts, gears, machine elements