A turbine airfoil (31) with an end portion (42) that tapers (44) toward the end (43) of the airfoil. A ridge (46) extends around the end portion. It has proximal (66) and distal (67) sides. A shroud platform (50) is bi-cast onto the end portion around the ridge without bonding. Cooling shrinks the platform into compression (62) on the end portion (42) of the airfoil. Gaps between the airfoil and platform are formed using a fugitive material (56) in the bi-casting stage. These gaps are designed in combination with the taper angle (44) to accommodate differential thermal expansion while maintaining a gas seal along the contact surfaces. The taper angle (44) may vary from lesser on the pressure side (36) to greater on the suction side (38) of the airfoil. A collar portion (52) of the platform provides sufficient contact area for connection stability.