An offshore structure having a hull, an upper vertical wall, an upper inwardly-tapered wall disposed below the upper vertical wall, a lower outwardly-tapered wall disposed below the upper sloped wall, and a lower vertical wall disposed below the lower sloped wall. The upper and lower sloped walls produce significant heave damping in response to heavy wave action. A heavy slurry of hematite and water ballast is added to the lower and outermost portions of the hull to lower the center of gravity below the center of buoyancy. The offshore structure provides one or more movable hawser connections that allow a tanker vessel to moor directly to the offshore structure during offloading rather than mooring to a separate buoy at some distance from the offshore storage structure. The movable hawser connection includes an arcuate rail with a movable trolley that provides a hawser connection point that allows vessel weathervaning.