A support structure for an offshore device is provided, including a vertical guide sleeve and three elongated guide sleeves positioned around the vertical guide sleeve, and various braces connecting the elongated sleeves and the vertical guide sleeve. The support structure also includes a transition joint including a cylindrical portion for connection to an offshore device, such as a support tower of a wind turbine assembly, and a conical portion connected to the vertical guide sleeve. To provide resistance to thrust, bending, and torsional fatigue, at least one set of braces is formed in an oval, racetrack, obround, or stadium configuration, and one or more horizontal stiffeners are positioned in the transition joint to maximize the strength of the support structure.