According to one aspect of the invention a turbine shroud engagement arrangement includes an outer shroud and an inner shroud operably connectable to the outer shroud. The outer shroud has at least one of a channel formed in and a protruding member extending from an inner radial surface thereof. The inner shroud has at least one of a protruding member extending from an outer radial surface thereof that is complementary to the at least one channel of the outer shroud or a channel formed in the outer radial surface that is complementary to the at least one protruding member of the outer shroud. The turbine shroud engagement arrangement is primarily axially slidably engagable and configured to radially support the inner shroud relative to the outer shroud.