In summary,

Final Answer

Maximum Force: $100,000N$

Minimum Force: $-350,000N$

Mean Force: $-125,000N$

Force Amplitude: $450,000$ N

Required Diameters:

Aluminum Alloy A$356-$T$6$:

$46\mathrm{.}3$ mm

Aluminum Alloy $2014-$T$6$:

$30\mathrm{.}6$ mm

$1045$ Alloy Steel: $37\mathrm{.}6$ mm

The mean stress is not zero. To determine the required diameters for each of the three materials under the cyclic load, you will need to draw three Goodman diagrams. A Goodman diagram has the stress amplitude ${}_A$ on the vertical axis and the mean stress ${}_m$ on the horizontal axis. You will need to draw two lines to create the diagram.

a$.$ The Goodman line has an intercept on the vertical axis at the maximum stress amplitude ${}_A($you found these in part $2)$ and an intercept on the horizontal axis at the ultimate tensile strength ${}_{\text{U}\text{T}\text{S}}$ for the material.

b$.$ The second line connects yield strength ${}_y$ values on the horizontal and vertical axes.

Points $({}_m,{}_A)$ in the area bounded by the two lines $($shaded region$)$ indicate values of ${}_A$ and ${}_m$ that will likely not lead to failure before the desired number of cycles.