An acute problem

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Hello guys, my first post here. This is one of those occasions when it's helpful to set out a problem. If someone has a suggestion, that's a bonus. (The forum software highlighted a previous query about how to cut very acute angles accurately: that's good info but I'm past it already.)

I'm building bookshelves right up the end walls and up to the high, sloping ceiling of a lean-to extension which my wife had built 30 years ago, long before I came on the scene. All the walls are construction block so it's easy to get a strong fix for the lower shelves. The ones under the ceiling are more of a problem. The architect's drawings told me that the ceiling slopes at 22.5deg to the horizontal, so I planned to attach false dados to the joists using coach bolts, cut 22.5deg ends onto the shelves, slide them into the gaps and reinforce the joints with Kreg pocket hole screws.

To this end, I built a vertical fence and sourced a hard-to-find 204mm blade for my old Makita 2708 table saw. Everything went according to plan... until I found that the builders had gone off-spec. I reckon the ceiling angle is actually more like 18deg. The dados are a non-starter.

To my way of thinking a joint of any kind is a non-starter, given that the very sharp angle makes it very difficult to transfer load into supporting members. What are the alternatives? I remember Simpson Strong-Tie making bendable reinforcements that can be set to any required angle. I wouldn't want to use builders ironwork in this context, but I did wonder about buying heavy duty hinges from a flight case company. All suggestions gratefully recd.

NP.
 
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