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We construct a new infinite series of irreducible components of theGieseker-Maruyama moduli scheme $\mathcal{M}(k), ~ k \geq 3$ of coherentsemistable rank 2 sheaves with Chern classes $c_1=0,~ c_2=k,~ c_3=0$ on$\mathbb{P}^3$ whose general points are sheaves with singularities of mixeddimension. These sheaves are constructed by elementary transformations ofstable and properly $\mu$-semistable reflexive sheaves along disjoint union ofcollections of points and smooth irreducible curves which are rational orcomplete intersection curves. As a special member of this series we obtain anew component of $\mathcal{M}(3)$.

New series of moduli components of rank 2 semistable sheaves on $\mathbb{P}^{3}$ with singularities of mixed dimension