I am looking at a an early 1900's Guastavino vaulted floor and arch ribs. Guastavino wrote in his treatise that arch thrusts were calculated for the crown as H = LS/8r where L was the distributed uniform load, S was the arch span, and r was the rise from the arch spring to the crown. Kidder has the same formula in his construction handbook for that era. I'm puzzled on the derivation of this formula. If I take a freebody of half an arch, I come up with the thrust as H = LS^2/8r.
does anyone know how Guastavino and Kidder derived their formulas?
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