Question

Assertion (A): When a component is subjected to fluctuating stresses, Goodman line is more safe from design considerations.
Reason (R): Goodman line is completely inside the Gerber parabola and inside the failure points.

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Goodman line = conservative design; Gerber = more accurate but less safe.

Answer 1

The Correct Option is A

Concept: Fatigue failure criteria:
• Goodman line (linear relation)
• Gerber parabola (parabolic relation)

Step 1: Understand Goodman criterion.
\[ \frac{\sigma_a}{\sigma_e} + \frac{\sigma_m}{\sigma_u} = 1 \]

Step 2: Understand Gerber criterion.
\[ \frac{\sigma_a}{\sigma_e} + \left(\frac{\sigma_m}{\sigma_u}\right)^2 = 1 \]

Step 3: Compare both curves.

• Gerber curve lies above Goodman line
• Goodman line lies below → more conservative

Step 4: Interpretation.
Since Goodman line is inside failure envelope:
• It predicts failure earlier
• Hence safer design

Step 5: Evaluate statements.
Assertion (A): Correct (Goodman is safer)
Reason (R): Correct (lies inside Gerber parabola) Logical relation: Reason correctly explains Assertion. Final Answer: \[ \boxed{\text{Both (A) and (R) are correct and (R) explains (A)}} \]