Statics of Historic Masonry Constructions by Mario Como

Author:Mario Como
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.4)

where r o is the radius of curvature of the profile at the crown. When n = 0, Eq. (6.4) represents an arc of the circle; when n = 1, an arc of a cycloid; when n = –3 an arc of a parabola; and when n = –2, an arc of catenary.

Catenary profile

In this case the profile equation is

(6.5)

Thus, from the second equation in (6.2), we have

(6.6)

and consequently

(6.7)

The barrel vault is uniformly supported on its lateral walls, as shown in Fig. 6.4. The central section, defined by x = 0, belongs to a plane of symmetry and therefore there N xϕ = 0. Consequently, the first of Eq. (6.2) yields A(ϕ) = 0 and the shear force N xϕ in the vault cancels perfectly.

Fig. 6.4Scheme of a barrel vault

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