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According to one embodiment, an insulated structure includes a frame comprising a plurality of wall studs coupled together and a plurality of foam boards attached to the frame to form a continuous insulative wall. A plurality of fasteners attaches the foam boards to the frame. Each fastener includes

According to one embodiment, an insulated structure includes a frame comprising a plurality of wall studs coupled together and a plurality of foam boards attached to the frame to form a continuous insulative wall. A plurality of fasteners attaches the foam boards to the frame. Each fastener includes an elongate shaft and a cap. The elongate shaft is configured to penetrate through a foam board and into a wall stud to couple the components together. The cap is configured to be positioned atop a foam board to distribute a load relatively evenly to the foam board. A sealing tape is applied across seams between adjacent foam boards and over the fasteners' caps to seal the wall. A sealing caulk is applied to secondary fasteners and penetrations to seal the wall. In some embodiments, the structure has a fastener density of about 1 fastener per 243 in2 of foam board.

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1. A method for providing a continuously insulated wall, the method comprising: providing a frame comprising a plurality of structural support members coupled together, the frame comprising a plurality of cavities defined by adjacent structural support members;positioning a plurality of insulative f

1. A method for providing a continuously insulated wall, the method comprising: providing a frame comprising a plurality of structural support members coupled together, the frame comprising a plurality of cavities defined by adjacent structural support members;positioning a plurality of insulative foam boards adjacent the frame so as to form a continuous insulative wall or surface over the frame;coupling the plurality of insulative foam boards to the frame with a plurality of fasteners, each fastener having an elongate shaft that penetrates through one of the respective insulative foam boards and into one of the structural support members so as to attach the insulative foam board to the structural support member, the fastener being positioned within a cap such that the elongate shaft is flush or recessed below a top surface of the cap, the cap being positioned on the insulative foam board when the elongate shaft is inserted through the insulative foam board and into the structural support member so as to distribute an applied load to the insulative foam board, wherein a shape of the cap is configured to hinder insertion of the cap into the insulative foam board and over insertion of the elongate shaft into the insulative foam board;applying a sealing tape over seams between adjacent insulative foam boards and over the cap of each and every fastener which penetrates through the plurality of insulative foam boards and into the plurality of structural support members of the continuous insulative wall so as to seal the continuous insulative wall and form an air barrier to restrict airflow through the continuous insulative wall; andfilling the plurality of cavities with insulation. 2. The method of claim 1, wherein the cap is circular and has a diameter of 1-4 inches. 3. The method of claim 1, wherein the fasteners are applied to the plurality of insulative foam boards so as to have a spacing between each adjacent fastener of at least 16 inches. 4. The method of claim 1, wherein the airflow through the continuous insulative wall is less than about 0.2 L/(s-m2) at a pressure of 75 Pa. 5. The method of claim 1, wherein the sealing tape comprises a stretchable plastic film with an acrylic adhesive, the sealing tape being elastic so as to have greater than 100% strain capability in both a machine direction and cross machine direction. 6. The method of claim 1, further comprising coupling cladding to the frame so as to form an exterior wall, the cladding being coupled to the frame via at least the plurality of fasteners and a second plurality of fasteners. 7. The method of claim 1, wherein the cap and the elongate shaft are separate pieces configured to couple together. 8. The method of claim 1, wherein the plurality of fasteners are self-sealing to block or reduce the airflow through the continuous insulative wall. 9. A method for insulating a structure, the method comprising: coupling a plurality of structural support members together to form a frame for a wall or ceiling, the frame comprising a plurality of cavities defined by adjacent structural support members;coupling a plurality of sheathing panels directly to the frame;coupling a plurality of insulative foam boards atop the plurality of sheathing panels and to the frame to form a continuous insulative wall or surface, the plurality of insulative foam boards being coupled to the frame via a plurality of fasteners, each fastener having a respective elongate shaft that is insertable through a respective insulative foam board and sheathing panel and into a respective structural support member so as to attach the respective insulative foam board and sheathing panel to the respective structural support member, wherein the fasteners each include a respective cap that extends radially from the elongate shaft and that is positionable on the respective insulative foam board so as to distribute an applied load about the respective insulative foam board, wherein a shape of the cap is configured to hinder over insertion of the elongate shaft into the respective insulative foam board; andapplying a sealing tape across seams between adjacent insulative foam boards and over the cap of each and every fastener of the continuous insulative wall or surface which penetrates through the plurality of insulative foam boards and into the plurality of structural support members so as to seal the continuous insulative wall or surface so that the continuous insulative wall or surface forms an air barrier to restrict airflow through the wall. 10. The method of claim 9, comprising filling the plurality of cavities with insulation. 11. The method of claim 10, wherein the insulation comprises fiberglass. 12. The method of claim 9, comprising coupling cladding to the frame so as to form an exterior wall, the cladding being coupled to the frame with at least one of the plurality of fasteners and a second plurality of fasteners. 13. The method of claim 12, wherein the cap and the elongate shaft are one-piece. 14. The method of claim 9, wherein the sheathing panels comprise wood based boards or gypsum boards. 15. An insulated structure comprising: a structural base;a plurality of insulative foam boards attached to the structural base to form a continuous insulative wall or surface of the structure;a plurality of fasteners that attach the insulative foam boards to the structural base, wherein each fastener comprises an elongate shaft that penetrates through a respective insulative foam board and into the structural base, wherein each fastener comprises a cap that extends radially from the elongate shaft, the cap having a recess, wherein the elongate shaft does not protrude axially outward from the cap, the cap being positioned atop the respective insulative foam board to distribute an applied load to the respective insulative foam board, wherein a shape of the cap is configured to hinder over insertion of the elongate shaft into the respective insulative foam board; anda sealing tape applied across seams between adjacent insulative foam boards and over the cap of each and every fastener of the insulative structure which penetrates through the plurality of insulative foam boards and into the structural base to seal the continuous insulative wall or surface so that the continuous insulative wall or surface forms an air barrier to restrict airflow through the continuous insulative wall. 16. The structure of claim 15, wherein the cap and the elongate shaft are separate pieces configured to couple together. 17. The structure of claim 15, wherein the plurality of fasteners are self-sealing to block or reduce the airflow through the continuous insulative wall. 18. The structure of claim 15, comprising insulation between the structural base and the continuous insulative wall.