Subject: Equation for the bending in a beam w/ a constriction?

I am a graduate student studying the ecology of a Caribbean soft 
coral.
This coral reproduces asexually by breaking off fragments; these 
fragments
then start new colonies. In some branches, there is a constriction 
which
facilitates breaking. I have tried to find an explanation and/or an
equation to explain the stresses and strains that occur. So far I have 
only been able to find equations for beams with a constant cross-
section.

Is there an equation that takes into account the failure of a beam 
with 
a constriction near the base?

Re: Equation for the bending in a beam w/ a constriction?