I was privileged to meet Buckminster Fuller in my grad school career at Dartmouth’s Thayer School of Engineering and listened to his random musings and wisdom. I still recall his dicta when it came to structural engineering: no structural engineer was ever sued because a bridge or building was too heavy, but mechanical engineers have do design airplanes that will actually fly; and, if you want structural analysis, give some shapes to a three year old and watch them manipulate them, they will get to know that anchored triangles are the simplest self supporting structure– then build on the triangles!
- Indians knew their tepees and lodges would work with posts in the ground and connected at the ridge or apex. We westerners adopted that in the A-Frame and the Cape. The Cape roof is a marvelous triangle, anchored at the eaves to the second floor joists, and compressed along a ridge board at the peak. Then came the bad old days, which I attribute to carpenters who knew the rules being killed in the Civil War. The builders forgot the triangle and tried to get more headroom in the second story. Knee walls. Unreinforced with strongbacks or hammer braces were lofted above carriage sheds in the Victorian era. Every one of them is swaybacked on the ridge because those knee walls are pushed outward.
- Collar ties. So we want to triangulate those rafters and are sure “a collar tie or two on four or eight foot centers will pull the walls back in”. First of all you are trying to resist a moment at the short end of a lever, and second, you are applying a bending moment to a point where the rafter is already at designed maximum bending. Not a pretty sight. Ridge beams to eliminate the bending or designing the knee wall studs to cantilever and the top plate to act as a beam will do. Better think about it and ask for help.
- Cantilevers: when we carry a beam over multiple supports, or to float a load in space we are cantilevering (horizontally, usually in the case of pop out closets and windows; vertically in the case of the above mentioned knee walls). This bending moment becomes obvious through failure when we see an old mill building with beautiful first growth southern yellow pine beams (Pinus palustris, long leaf yellow pine, used for ship’s masts and warehouse buildings. I salvaged hundreds of thousands of these timbers for recycled post and beam “Yankee Barn Homes”. A truly magnificent material, we would see 30 growth rings per inch where a modern yellow pine has 3 or 4, and they would still smell of turpentine when resawn; drive a nail in and it would break before it could be pulled), which are coming apart halfway between top and bottom: excessive moment from cantilever bending shears the top and bottom halves.