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What weight will a 2" x 12" board support over a 23' span

I have a garage attic formed by a 12" x 2" board resting on a top plate of the outside walls. Attached to the face of the board by screws or nails are 2" x 6" boards whose opposite ends are supported on a load-bearing wall. The 2" x 6" boards are on 24" centers. I have added some metal strap supports where they connect with the 2" x 12" board. I am making an overhead storage area by placing 3/4" plywood on top of the boards mentioned above. How much weight can these supports and joints safely bear?

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Improving the end connection has not really helped the load bearing of the 2x6 joists over a 23 foot span. You sound like you are describing a roof structure over either the main house or a garage. My suspicion is that the span is not a free length of 23 feet but something affected by other diagonal framing such as found in roof framing. The 3/4 inch plywood is a good idea but it is pretty heavy. When done, I would not store more than casual weight like Christmas decorations and relatively light boxes containing things not any heavier than books or magazines. The highest load bearing areas will be along the edges - generally not at the center.

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