The diagram below is showing the various criteria of fatigue failure. Which option is the correct representation of these criteria? (Subscripts e, y and u represent endurance, yield and ultimate respectively.)

Correct option is A

1 - Soderberg line, 2 - Goodman line, 3 - Gerber line

​$$\begin{aligned}&\textbf{Goodman Line:} \\&\text{This is the most widely used criterion for fatigue failure under} \\&\text{mean stress } (\sigma_m) \text{ and variable stress } (\sigma_v). \\&\text{It is given by the equation:} \\[0.5em]&\boxed{\frac{\sigma_v}{\sigma_e} + \frac{\sigma_m}{\sigma_u} = 1} \\[1em]&\textbf{Where:} \\&\sigma_v = \text{Variable stress amplitude} \\&\sigma_m = \text{Mean stress} \\&\sigma_e = \text{Endurance limit (fully reversed stress)} \\&\sigma_u = \text{Ultimate tensile strength}\end{aligned}$$

$$\begin{aligned}&\textbf{Soderberg Criterion:} \quad \text{Conservative, uses } \sigma_y \text{ instead of } \sigma_u. \\&\boxed{ \frac{\sigma_v}{\sigma_e} + \frac{\sigma_m}{\sigma_y} = 1 } \\[1em]&\textbf{Gerber Parabola:} \quad \text{More accurate for ductile materials:} \\&\boxed{ \frac{\sigma_v}{\sigma_e} + \left( \frac{\sigma_m}{\sigma_u} \right)^2 = 1 }\end{aligned}$$​​​