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A 40 mm diameter bar has been machined from an AISI 1050 cold-drawn bar. This part is to withstand a fluctuating tensile load varying from 0 to 70kN. Because of the ends, and the fillet radius, a fatigue stress-concentration factor Kf is 1.85 for 10⁶ or larger life. Find σ a find σm and the factor of safety guarding against fatigue and first-cycle yielding, using (a) the Gerber fatigue line and (b) the ASME-elliptic fatigue line.

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Final Answer:

(a) Using the Gerber fatigue line, the alternating stress (σ_a) is approximately 94.59 MPa, the mean stress (σ_m) is around 16.99 MPa, and the factor of safety against fatigue and first-cycle yielding is approximately 6.33.

(b) Applying the ASME-elliptic fatigue line, the alternating stress (σ_a) is roughly 76.77 MPa, the mean stress (σ_m) is about 34.81 MPa, and the factor of safety against fatigue and first-cycle yielding is approximately 4.06.

Step-by-step explanation:

Fatigue analysis for the given AISI 1050 cold-drawn bar involves determining the alternating stress (σ_a), mean stress (σ_m), and the factor of safety against fatigue and first-cycle yielding using the Gerber fatigue line and the ASME-elliptic fatigue line.

The Gerber fatigue line is employed to calculate σ_a and σ_m. The formula for σ_a involves the fluctuating tensile load, diameter, and the fatigue stress-concentration factor.

Similarly, σ_m is computed considering the mean stress due to the load. The factor of safety against fatigue and first-cycle yielding is determined by dividing the endurance limit of the material by σ_a.

On the other hand, the ASME-elliptic fatigue line is utilized to find σ_a and σ_m. The equations involve the fluctuating tensile load, diameter, and the fatigue stress-concentration factor.

The factor of safety against fatigue and first-cycle yielding is calculated by dividing the endurance limit of the material by σ_a.

In summary, the Gerber fatigue line and ASME-elliptic fatigue line provide different values for σ_a, σ_m, and the factor of safety, highlighting the importance of selecting an appropriate fatigue analysis method based on design requirements.

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