Those arches

I watched a BBC production the other night, 'How to build a cathedral'. Early construction techniques and the introduction of the gothic arch. I had some bits of beech laying around, nearly square section (grrr, not quite) so I had a go at an arch. Soon learned that I'd left it too slippy. This is just a bit too far! I'm told that if I draw an arc through the top outer (extrados) edge, down to the bottom extrados), it should remain within the wood at the (intrados) mid point. The maximum thrust case is a thrust line, or zone of thrust, which touches the intrados once near the crown and the extrados near each springing (where it's supported at the ground level). Clearly this one doesn't! The next picture in the sequence shows it standing (little wobbly) with just three vertical blocks. This is fun! From (sorry, PDF) this, quote, Upper Bound: When the load path can no longer be contained within the structure, and it is the unique and largest possible load, then it is the collapse load. End quote. Page 3 and 17 show the idea. Intuitively clear, nice to see some science behind it though.

The friction got me. I'd planed the wood and sanded it, so there wasn't much. I'm intrigued now what will happen with rougher timber models! This is next. Could be fun! I'm going to try 45mm square pine though.