Helical masonry vaulted staircase in Palladio and Vignola's ...

310 A. Barbieri, A. Di Tommaso, R. Massarotto
Table 2. Stresses in Pisani Villa staircase, considering fixed round arch and fixed beam static schemes
Palladio' s helical masonry vaulted staircase as fixed beam
x [m m] M[N.mm] J [mm4J (5 [N/mm' ]
0.00 lO' --4.82 105 2.83 10'0 -0.0085
2.90 lO' --4.33 10' 2.59 10'0 -0.0081
11.39 lO' -3.01 lO' 1.97 10'0 -0.0068
24.90 lO' -1.20 lO' 1.2010'0 -0.0038
42.50 lO' 0.60105 5.39 10' 0.0032
63.00 lO' 1.92 105 1.44109 0.0248
85.00 lO' 2.41 105 9.56107 0.1889
(5, stress at extrados.
(5, stress at intrados.
Palladio's helical masonry vaulted staircase as fixed arch
i/J [deg] M [Nmm] N [N] (5/(5; [N/mm']
O 1497 lO' -267.96 lO' -0.118/-0.249
10 232.31 lO' -253.22 lO' 0.034/-0.091
20 --454.67 102 -232.58 10' 0.112/-0.001
30 -690.88 10' -208.41 lO' 0.136/0.034
40 -608.01 lO' -183.08 lO' 0.119/0.030
50 -334.07 lO' -158.83 lO' 0.080/0.002
60 14.27 lO' -137.67 lO' 0.032/-0.036
70 338.57 10' -121.29 lO' -0.012/-0.071
80 564.21 lO' -110.94 lO' -0.042/-0.096
90 644.69 10' -107.40
0° cross section at springing.
90° cross section at crown.
figure] 1, for simulating the parapet influence, as
helical beam.
The ana]ysis of a tri-dimensiona] structure is
reduced to the analysis of many mono-dimensional
ones. Therefore, the parapet works like an he]ical
beam, fixed at the foundation and hinged at the top,
]oaded by dead weight and part of flight weight.
The remaining flight weight is borne by boundary
walls.
Second]y, the flight is evaluated as tri-dimensiona]
element. The structure is schematised as an heJical
] O'
-0.053/-0.105
beam, fixed at the foundation and at the top, which
cross section amounts to masonry vau1t and parapet,
forming a comp]ex cross section. The fixed hinges
a]ong the boundary wall could be neg]ected because
the bricks of each arch are tangent it. The analytical
solution of this static scheme could be found in
bibliography (Belluzzi O. 1994, Pozzati P. ]972); the
difficu1ty consists to define some geometrical
characteristics (torsion inertia moment).
These static schemes are the starting
developing the research on this staircase
point for
typo]ogy.