I received a book of "Porte e Portali in Fermo" written by Marco, whom I met last May, in cooperation with a photographer.
The photographs are superb and show the great variety of doors and portals in Fermo with the different architecturals styles down the ages. Fermo was an important city in Roman times in Marche. Marche from the "marks" were the boundary of the Roman Empire. The city occupies an obvious position of advantage in the ascoli piceno parte of Marche.
Anyway, Marco makes a serious point that the door portal is the basis of architecture of buidings and the design of the portal ensures that the door is supported. However the portal also hold the construction above the portal. Look at the number of balconies that were designed to be directly above the door.

In its simple form the force system is a simply supported beam supporting a UDL. Think about the reaction forces in the supports and how the cross beam is subjected to a combination of compressive and tensile stresses.
Also, consider the importance of a keystone in an arched portal and how this suited the materials chosen.

i think that it would be worth looking at local buildings, old and new and considering the force system about the doors and portals. remember that architects nowadays have a greater range of materials to select from.