Smallest cross-sectional area of rod-end?

[samtrix]

i was doing some reading on structural mechanics and i stumbled across this example:

i don't really get the highlighted part. anyone care to explain?

:)

 

[Mapes]

The pin at C exerts a force of 50kN on rod BC. In the middle of the rod, the cross section is circular, and we calculate the stress as $4P/\pi d^2$ (diameter d). At the end of the rod, the cross section is flattened into a rectangle, so the stress is $P/wt$ (width w, thickness t). BUT the width is reduced where material is cut out to fit the pin. At this cross section the stress is higher, $P/(w-d)t$. Does this make sense?