Elementary Geometry in Staircases Design. The ‘City House’ of Bernardo Antonio Vittone

La escalera de ojo abierto del Palacio Di Majo en Nápoles entre geometría y equilibrio

“…However, once up the first flight, the unusual spatial design envelope and the bold development of the vaulted system supporting the flights is revealed to the eye. The spatial layout takes shape from a rhombic cage with rounded vertices and convex towards the well (Figure 3) (15).…”

“…These components are also considered as numerical functions of the independent variable The condition of equilibrium along the arc allows us to write: [17] are the Cartesian components of the load transmitted by the arc, and the former represents the derivative with respect to the variable The relationship between the S-component and the V-component of the load as a function of the slope of the compression rays is [19] where in this case indicates the value assumed by the height of the arc (that is The unknowns of the problem are therefore and The simplest way to obtain the numerical solution of this system of first-order differential equations would be to provide some conditions for and However, it is necessary to consider those conditions that impose the passing of the arc the points and defined by [19] (see Figure 15). In order to obtain a solution of ( 19) that satisfies the boundary conditions [13], [14], [15] previously defined, we proceed with a technique called Shooting, imposing the passing through point 0 and iteratively assigning the components of the thrust in , until the passing through point is obtained. This technique consists of solving a first-order differential equation for which initial conditions are assigned to verify the boundary conditions by changing the value of the thrust on the arc .…”