Non-integral torsion and 1-dimensional singular sheaves in the Simpson moduli space

In my thesis I am interested in the Simpson moduli spaces $M_{am+b}$ of semi-stable sheaves on $P_2$ with linear Hilbert polynomial $am+b$ where $a,b\in N$. More precisely I want to know which ones and “how many” of them are locally free on their support. I also started a study apart to analyze how torsion of a module behaves in the non-integral case. Apparently this has not been done in detail yet.