On the equilibrium of the flat arch with joints that have neither friction nor cohesion

Coulomb's essay of 1773 is universally known for the fundamental contribution it gave to examine the different static problems in architecture. One of the issues tackled by the French scholar is the equilibrium of the flat arch (or "plate-bande") introduced as an example of the third corollary to the equilibrium of arches free of friction or cohesion. The problem is addressed by searching the inclination to be assigned to arch joints, once the intrados and extrados curves are known. The problem of the flat arch with horizontal intrados and extrados - studied and solved by Coulomb - is suitable for further applicative developments to determine the inclination of the joints in a flat arch with "en châpe" intrados and extrados and in a circular arch.