The spring of the preceding example is made from ASTM A229 oil tempered wire. It is proposed for a non-critical application in which the load varies between a maximum of   F and a minimum of   0.4F. What maximum load can the spring withstand indefinitely ?

Material properties for 4 mm diameter oil tempered wire are, from Table 2 :
      S_ut = ( 2630 + 4 x ( 2180 + 56 x 4))/( 1 + 4 x ( 1.6 + 0.08 x 4)) = 1410 MPa
      S_us = 0.63 S_ut = 888 MPa ;       S_es = 0.13 S_ut = 183 MPa ;       S_ys = 0.48 S_ut = 677 MPa
The solid stress of 625 MPa, evaluated previously, does not exceed this yield, so the spring will not be permanently deformed when solidified during assembly.

Operating stress components from ( 4a) with   F in Newtons :
      F_m = ( F + 0.4F)/2 = 0.7 F ;       τ_m = 1.08 x 8 x 0.7 F x 6.5 / 4²π =   0.782 F MPa
      F_a   = ( F - 0.4F) /2 = 0.3 F ;       τ_a   = 1.22 x 8 x 0.3 F x 6.5 / 4²π =   0.379 F MPa

Inserting these into the Goodman design equation ( 4a) with a safety factor of say 1.1 :
      0.782 F / 888 + 0.379 F / 183   =   1 / 1.1       whence   F   =   310 N   is the maximum load capacity.

The small safety factor should be noted. It is justified because it relates to material properties which have been derived from lower bounds of a great amount of data which has not needed any theoretical correction for size or for surface finish - in other words, there is considerable confidence in the material properties. An additional argument for the small safety factor here is the non-critical application.
This example might have been tackled by first assuming a dummy load and then scaling the result appropriately.