A material has $S_{ut}=80\frac{K}{P}SI,S_y=64\frac{K}{P}SI$ and $S_e=40\frac{K}{P}SI.$ The given $S_H$ and $S_y$ have already been adjusted for the factor of safety. The given $S_e$ has already been adjusted by K factor. Sketch a modified Goodman Diagram and show the values at critical points.

Cyclic loading condition for the part of problem $1$ is defined below.

$S_a=40\frac{K}{P}SI$

$S_m=43\frac{K}{P}SI$

Find the $S_a$ and $S_m$ values where yielding on the first cycle takes place for the loading slope. Is this a safe design from a first cycle yielding point of view? $($Fully justify your answer$).$

$3.$ Find the maximum safe combination from the point of view of first cycle yielding point of view for $S_a$ and $S_m$ for the slope of problem $2$ and material properties of problem $1.$

$4.$ By using the factor of safety formulas for Modified Goodman line and Soderberg line $($by reasoning through analogy$),$ define a formula for determining the factor of safety for failure by yielding on the first cycle.

$5.$ A material has the properties of $S_{ut}=80\frac{K}{P}SI,S_y=64\frac{K}{P}SI$ and $S_e=40\frac{K}{P}SI.$ The loading conditions are $S_a=40\frac{K}{P}SI$ and $S_m=43\frac{K}{P}SI.$ Calculate the factor of safety for the ASME$-$elliptic criteria.