The design calculations for members subject to fluctuating loads with the same factor of safety, yield the most conservative estimates when using

Answer: Option B

When designing machine components under fluctuating or alternating loads, it is essential to account for fatigue failure.

Different failure theories or criteria are used to estimate the safety of such components, with varying levels of conservativeness.

Gerber relation uses a parabolic curve and is less conservative, allowing for higher allowable stresses.

Goodman relation is linear and more conservative than Gerber but less than Soderberg.

Soderberg relation is the most conservative. It uses the yield strength instead of the ultimate strength for comparison and assumes a linear relation. This provides the lowest permissible stress, making it the safest design for fluctuating loads when using the same factor of safety.

Therefore, using the Soderberg relation yields the most conservative estimates for fluctuating loads.

Correct Answer: Option B: Soderberg relation