Building the Octagon Pt.72 Boxing clever?

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It occurred to be that a dome could be built from shallow boxes, placed on edge, in rings. The four sides of the boxes would become vertical and horizontal ribs of twice the thickness where they joined. Somewhere in my mind I remembered seeing an inside view of a building or structure with a similar arrangement of ribs. The idea seemed so logical I thought I'd better see what could be accomplished. Thin [marine?] plywood is strong for its thickness. As a box it gains stiffness from the sides and base. Now stick lots of them together with glue and the strength is multiplied by the sheer number of self-reinforcing surfaces and huge number of stiffening ribs. 

Geodesic domes are sometimes built from folded cardboard. The joining edge flaps may be turned in or out to taste and can provide extra stiffness. It may be this which I am vaguely remembering from my earlier interest in geodesic domes and structures.

 IGLOO | MUT architecture | Archinect

Here is an image I found online of a spiral built, shelter igloo for hot and cool days on a Manhattan rooftop. These boxes have been deliberately spaced for air movement. Or simply to cater for the fixed geometry of the boxes.

Now imagine if they were all tightly snuggled up against each other. [Assuming that was possible] If the boxes were placed directly over each other they ought to get smaller as each ring of boxes rises up the dome. Now imagine each box was made to a precise size but kept shallow. Almost like a tray with raised edges. The sides will need a slight taper and be angled to bring the edges flat against each other. So that they are able to have a firm bond between adjacent boxes as they are stacked tightly together. To keep the weight down it is suggested that 3mm [1/8"] plywood would be a suitable building material. 

Such material needs rather unorthodox means of joining box edges to edges. Kayaks and boats are sometimes made of similarly thin, wood-based material and shaped panels are sewn together with copper wire. The joint is then filled with epoxy resin before the stitches are later removed after curing. The finished shape is then usually glassed over with glass mat or thin glass cloth and coated with resin. Requiring lots of patient sanding to obtain a high gloss finish.

Assuming a dome is to be constructed from similarly sized boxes stacked side by side and one above the other: The number of gores gives the inward angle required of the vertical surfaces. The number of vertical segments fixes the angle of the horizontal surfaces. The observation slit may "use up" two gores but this will not affect the inward angles of the box sides. The central rib of the slit area is simply removed.

A full circle has 360° so dividing by the number of gores [sectors] gives the angle of the ribs.

360/16 = 22.5° per sector in the horizontal plane.

Let's move onto the vertical plane which must be divided by the chosen number of vertical sectors. A quarter radius of a circle = 90 degrees.  Assuming four flat surfaces are desired then 90/4 = 22.5°. A happy coincidence where multiple components have to be cut.

These angles would only be correct if we were dealing with arcs but we are placing a straight line across each sector. The flat bottoms of the boxes will lie across the sectors and these become segments. Which means that the angle of the sector is shared between the two sides. 22.5/2 = 11.25°. This is the inward angle to be applied to all four sides of the box to make them fit snugly together. Though I doubt the 1/4 of a degree will matter much even if it could be measured, marked and then cut with a high degree of accuracy. Now I have to work out how to build a series of boxes with rather thin sides and bottoms. Preferably without adding reinforcement or using epoxy resin. 

But why build lots of boxes and then glue them together? The ribs are far more substantial once they are doubled in joining adjacent sides. Thick ribs provide thicker glue surfaces when the bottoms are added to form the outer skin of the dome. So why not cut the angles on the ribs out of double the thickness of the original assembled boxes? Why make lots of boxes when only the edges really matter for strength? Now join the vertical edges of all the uprights into strips. Or all the horizontal edges? Maintaining the strength of multiple ribs, in a grid pattern spread evenly over the dome, suggests the arcs are joined using halving joints. Basically you cut a deep slot to half the width of the rib in each piece at the joint and then glue them together. This joint is commonly used for making partitions in drawers. Accuracy of cutting the slots an their exact spacing is obviously desirable to avoid misaligned joints. Now I have a table saw I can cut such joints.   

The area of a hemisphere [dome] is 2 x Pi x r² 
1.5m x 1.5m = 2.25 x 6.284 = ~14.14m².
5'x5' = 25 = 6.284 x 25 = ~157' ²

Assuming a 3m or 10' diameter dome [hemisphere] has a surface area of 14m² or 157' ². 

4mm ply weighs ~15lbs per 5'x5' sheet. So ~160/25 = 6.4 x 15 = 100lbs for the covering alone without any skeleton.

Click on any image for an enlargement.    

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