Interpretation of Goodman Diagram in Machine design 
In the Goodman diagram, the max and min stresses are plotted as a function of midrange stress. If I understand correctly, these are the upper and lower stress limits that can be applied in a repeated loading for infinite life. But the criteria for infinite life is that the endurance limit cannot be exceeded. How is it that if the midrange stress is greater than or less than 0 the Goodman diagram indicates that a material subjected to stresses greater than the endurance limit can still have an infinite life?
 A: You are correct. The reason is that endurance $S_e$ is tested in a uniaxial test machine with alternating stress (zero midrange stress). This defines points B and B' below. Also in static uniaxial stress test point A is defined with median stress = actual stress. Or with zero stress amplitude. So a constant load defines point A and the purely alternating loads (from - to + in equal amounts) defines B and B'.

The Goodman theory states that for all the in-between cases you draw lines from A to B and from A to B' to define the endurance limits in the presence of non-zero average stress (midrange stress).
This hypothesis is supported from testing (in some other page in Shigley book) and from the elastic theory of solids.
In looking at the diagram, the 45° line is the line of constant loading, and the breadth up and down is the amount of the oscillating load allowed. The "modified" endurance limit is the values $\sigma_a$ shown above which are $<S_e$ when $\sigma_m>0$. So to read this diagram you understand that endurance decreases as steady loading increases.
