Summary: We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are locally free stable sheaves investigated earlier in [S. K. Donaldson and R. P. Thomas, in: The geometric universe: science, geometry, and the work of Roger Penrose. Proceedings of the symposium on geometric issues in the foundations of science, Oxford, UK, 1996 in honour of Roger Penrose in his 65th year. 31–47 (1998; Zbl 0926.58003); the authors, Int. J. Math. 14, No. 10, 1097–1120 (2003; Zbl 1083.14520); R. P. Thomas, J. Differ. Geom. 54, No. 2, 367–438 (2000; Zbl 1034.14015)]. We show that these Gieseker moduli spaces are isomorphic to some Quot-schemes. We prove a formula for Behrend’s \(\nu\)-functions when torus actions are present with positive dimensional fixed point sets, and use it to obtain the generating series of the relevant Donaldson-Thomas invariants in terms of the McMahon function.