The purpose of this study is to learn if it is possible and safe to treat persons with severe sickle cell disease (SCD) by bone marrow transplant (BMT) from human leukocyte antigen (HLA) half-matched related donors. Preparation before transplant includes the chemotherapy drugs hydroxyurea, fludarabine, thiotepa, anti-thymocyte globulin, and cyclophosphamide. It also includes radiation.