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A forged steel link with uniform diameter of 30 mm at the centre is subjected to an axial force that varies from 40 kN in compression to 160 kN in tension. The tensile (Su), yield (Sy,) and corrected endurance (Se) strength of the steel material are 600 MPa, 420 MPa and 240 MPa respectively. The factor of safety against fatigue endurance as per Soderberg’s criterion is   
  • a)
    1.26  
  • b)
    1.37  
  • c)
    1.45  
  • d)
    2.00  
Correct answer is option 'A'. Can you explain this answer?
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Given:
- Diameter of the forged steel link: 30 mm
- Axial force in compression: 40 kN
- Axial force in tension: 160 kN
- Tensile strength (Su) of the steel material: 600 MPa
- Yield strength (Sy) of the steel material: 420 MPa
- Corrected endurance strength (Se) of the steel material: 240 MPa

To find:
Factor of safety against fatigue endurance as per Soderbergs criterion

Assumptions:
- The axial force is uniformly distributed along the cross-section of the link.
- The stress concentration factor is neglected.
- The link is subjected to a fully reversed loading condition.

Calculations and Steps:
1. Calculate the maximum compressive stress (σc) and maximum tensile stress (σt) in the link.
- Area of cross-section (A) = (π/4) * (d^2)
- σc = Fc / A
- σt = Ft / A
- Substitute the given values: d = 30 mm, Fc = 40 kN, Ft = 160 kN

2. Check the factor of safety against yielding (FSy).
- FSy = Sy / σc
- If FSy > 1, the link is safe against yielding.

3. Check the factor of safety against fracture (FSu).
- FSu = Su / σt
- If FSu > 1, the link is safe against fracture.

4. Check the factor of safety against fatigue endurance (FSf) as per Soderbergs criterion.
- FSf = Se / σe
- σe = (σc + σt) / 2
- If FSf > 1, the link is safe against fatigue failure.

5. Substitute the given values: Su = 600 MPa, Se = 240 MPa

Answer:
The factor of safety against fatigue endurance as per Soderbergs criterion is 1.26 (option A).
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A forged steel link with uniform diameter of 30 mm at the centre is subjected to an axial force that varies from 40 kN in compression to 160 kN in tension. The tensile (Su), yield (Sy,) and corrected endurance (Se) strength of the steel material are 600 MPa, 420 MPa and 240 MPa respectively. The factor of safety against fatigue endurance as per Soderberg’s criterion is a)1.26 b)1.37 c)1.45 d)2.00 Correct answer is option 'A'. Can you explain this answer?
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