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Figure 8: (left) Baltimore Cathedral early project;(center) Baltimore cathedral as built (plans redrawn by Na- thanial Martin after Kimball 1918, Hamlin 1955); (right) Baltimore Cathedral inverted arch in undercroft to sup- port the dome; (Photo: John G. Waite Associates Architects)

Figure 8 (left) Baltimore Cathedral early project;(center) Baltimore cathedral as built (plans redrawn by Na- thanial Martin after Kimball 1918, Hamlin 1955); (right) Baltimore Cathedral inverted arch in undercroft to sup- port the dome; (Photo: John G. Waite Associates Architects)

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Figure 1: (left) Curéié 1992; (center) St.-Sulpice, Note fanning voussoirs; (right) Note labels “a”, “b” ; (Armi 2000) his contemporaries and his Baroque successors, believed that arches can also have the function of ‘tying’ the structure together” (Bellini 2004, p. 46). To talk of tying —legare in Italian — a wall together through serial arches is to Our Modern way of thinking a curious expression, since we refer to tensile members such as steel “tie” rods as serving the function designated by their name. These Italian architects of the sixteenth and seventeenth centuries were speaking metaphorically when they wrote about tying a wall together, much the way we would use the verb “to consolidate.” We must recall that walls and vaults were often, if not generally, compos- ite constructions, consisting of a primary armature or ligature and then
Figure 1: (left) Curéié 1992; (center) St.-Sulpice, Note fanning voussoirs; (right) Note labels “a”, “b” ; (Armi 2000) his contemporaries and his Baroque successors, believed that arches can also have the function of ‘tying’ the structure together” (Bellini 2004, p. 46). To talk of tying —legare in Italian — a wall together through serial arches is to Our Modern way of thinking a curious expression, since we refer to tensile members such as steel “tie” rods as serving the function designated by their name. These Italian architects of the sixteenth and seventeenth centuries were speaking metaphorically when they wrote about tying a wall together, much the way we would use the verb “to consolidate.” We must recall that walls and vaults were often, if not generally, compos- ite constructions, consisting of a primary armature or ligature and then
Figure 2: (left)Mark 1982; (center) Hagia Sophia (Torroja 1967); (right) Algeciras Market; (Torroja 1967)
Figure 2: (left)Mark 1982; (center) Hagia Sophia (Torroja 1967); (right) Algeciras Market; (Torroja 1967)
Figure 3: (left) City Hall, Arles; (center) Tamboréro and Sakarovitch 2003; (right); (Archives Municipales, Arles) J. Chambareau and the master mason D. Pilleporte on the adequacy of the building’s foundations for the stereotomic vault by Jules Hardouin-Mansart over the vestibule of the City Hall of Arles (Fig. 3 left). This vault, in effect, is actually composed of two vaults braced by an intermediary tangential arch (Fig. 3 center). The re- port explains that the largely hidden walls R-O and P-a (Fig. 3 right) were considered as “buttressing” walls to be erected at either side of this anticipated “large arch” (ACA, DD 42, folios 75v, 76v). The massive size of these walls reveals the contemporary understanding about the magnitude of the force being redirected from the vaults into the tangential arch.
Figure 3: (left) City Hall, Arles; (center) Tamboréro and Sakarovitch 2003; (right); (Archives Municipales, Arles) J. Chambareau and the master mason D. Pilleporte on the adequacy of the building’s foundations for the stereotomic vault by Jules Hardouin-Mansart over the vestibule of the City Hall of Arles (Fig. 3 left). This vault, in effect, is actually composed of two vaults braced by an intermediary tangential arch (Fig. 3 center). The re- port explains that the largely hidden walls R-O and P-a (Fig. 3 right) were considered as “buttressing” walls to be erected at either side of this anticipated “large arch” (ACA, DD 42, folios 75v, 76v). The massive size of these walls reveals the contemporary understanding about the magnitude of the force being redirected from the vaults into the tangential arch.
Figure 4: (left and center) Noyon Cathedral apses with “girdle” of barrel vaults; (right); (Lancaster 2005 delicate” (Seymour 1939, p. 121, see also p. 131). All of these types of structural behavior appear to belong to the category that Felix Candela has termed a: active structures. Candela explains that external loads can be transmitted in two ways: “passive sfructure: conduct loads directly without changing their course, like bearing walls and columns which are merely ele- ments interposed between the loads and the ground; active structures are those capable of changing the di rection of loads and forcing them to move throughout the structure enclosing a certain space” (Candelc 1954, p. 84, his emphasis). The embedded serial arches at Thessaloniki and the “corbel tables” in the First Ro: manesque now permit us to ask whether architects in other historical periods were using such structural form: as active structural elements for similar purposes? It is time to address more fully Jean-Pierre Adam's passing observation that the serial arches around the perimeter of the Pantheon “stiffen the construction” (Adam 1984 p. 200) (Fig. 4 right). William Addis has recently emphasized the ingenuity of tangential barrel vaults “to carry the horizontal thrust from the dome” in the Pantheon and then Hagia Sophia (Addis 2007, pp. 55, 66).
Figure 4: (left and center) Noyon Cathedral apses with “girdle” of barrel vaults; (right); (Lancaster 2005 delicate” (Seymour 1939, p. 121, see also p. 131). All of these types of structural behavior appear to belong to the category that Felix Candela has termed a: active structures. Candela explains that external loads can be transmitted in two ways: “passive sfructure: conduct loads directly without changing their course, like bearing walls and columns which are merely ele- ments interposed between the loads and the ground; active structures are those capable of changing the di rection of loads and forcing them to move throughout the structure enclosing a certain space” (Candelc 1954, p. 84, his emphasis). The embedded serial arches at Thessaloniki and the “corbel tables” in the First Ro: manesque now permit us to ask whether architects in other historical periods were using such structural form: as active structural elements for similar purposes? It is time to address more fully Jean-Pierre Adam's passing observation that the serial arches around the perimeter of the Pantheon “stiffen the construction” (Adam 1984 p. 200) (Fig. 4 right). William Addis has recently emphasized the ingenuity of tangential barrel vaults “to carry the horizontal thrust from the dome” in the Pantheon and then Hagia Sophia (Addis 2007, pp. 55, 66).
Figure 5: (left) Polonceau 1839; (center, right) Flying buttress and rose window; (Viollet-le-Duc 1854-1868) the larger arch, with the area below left hollow and merely covered with a protective front wall, Turriano em- phasized that the smaller arch makes the bridge stronger: “this small arch is of strong force for the two large! arches” (Turriano 1984, p. 506; see also p. 502). Turriano also believed that the link between the larger arches made by the smaller arch benefited from the weight of the stone above the smaller arch: “this will put to work what appears to be of no use; because the smaller arch...is of great value in that location with the use of those materials” that sit upon it (Turriano 1984, p. 506, fol. 376r.). From this account, it would appear that Turri- ano considered such an arrangement, like the rounded cutwater, as “self-strengthening.” Note that similar di- minutive connecting arches can be found in eighteenth-century bridge design, as over voids in the repair of Westminster Bridge in 1748 (Ruddock 1979, pp. 16-17). Robert Mylne’s explanation of his design of 1759 fol Blackfriars Bridge articulates the need for such bracing elements, which he provided in the form of a connect- ing flat arch. Mylne understood the small connecting arches as relieving the thrust from the main arches against their haunches and the piers: “the weakness is, that the middle part of the [large] arch makes a latera pressure against the haunches of it.” Ted Ruddock explains, “the horizontal course of hewn stone from haunck to haunch would certainly have performed this function [i.e., “carrying the horizontal thrust from haunch te haunch”] and thus relieved the piers of nearly all horizontal thrust...."" Jonn Rennie “always made an invertec arch of hewn stone to carry the thrust from one main arch to the next” in his multi-arch bridges (RUddock 1979. pp. 67-68, 147, 183). It would seem that the weighted connecting arch in Turriano’s design was intended tc serve the same purpose. As for the hollowing under the small arches. Turriano appears to utilize the advantage of providing a clear path for loads according to consistent stresses, a principle exemplified by the engineel Curt Siegel’s account of Pier Luigi Nervi’s design for the Municipal Stadium (Florence, 1929-1932) where Nerv created a hollow frame in a V-support so that “the bending moment is then resolved into a couple and the structure is resolved into clearly defined tension and compression members” (Siegel 1962, p. 134).
Figure 5: (left) Polonceau 1839; (center, right) Flying buttress and rose window; (Viollet-le-Duc 1854-1868) the larger arch, with the area below left hollow and merely covered with a protective front wall, Turriano em- phasized that the smaller arch makes the bridge stronger: “this small arch is of strong force for the two large! arches” (Turriano 1984, p. 506; see also p. 502). Turriano also believed that the link between the larger arches made by the smaller arch benefited from the weight of the stone above the smaller arch: “this will put to work what appears to be of no use; because the smaller arch...is of great value in that location with the use of those materials” that sit upon it (Turriano 1984, p. 506, fol. 376r.). From this account, it would appear that Turri- ano considered such an arrangement, like the rounded cutwater, as “self-strengthening.” Note that similar di- minutive connecting arches can be found in eighteenth-century bridge design, as over voids in the repair of Westminster Bridge in 1748 (Ruddock 1979, pp. 16-17). Robert Mylne’s explanation of his design of 1759 fol Blackfriars Bridge articulates the need for such bracing elements, which he provided in the form of a connect- ing flat arch. Mylne understood the small connecting arches as relieving the thrust from the main arches against their haunches and the piers: “the weakness is, that the middle part of the [large] arch makes a latera pressure against the haunches of it.” Ted Ruddock explains, “the horizontal course of hewn stone from haunck to haunch would certainly have performed this function [i.e., “carrying the horizontal thrust from haunch te haunch”] and thus relieved the piers of nearly all horizontal thrust...."" Jonn Rennie “always made an invertec arch of hewn stone to carry the thrust from one main arch to the next” in his multi-arch bridges (RUddock 1979. pp. 67-68, 147, 183). It would seem that the weighted connecting arch in Turriano’s design was intended tc serve the same purpose. As for the hollowing under the small arches. Turriano appears to utilize the advantage of providing a clear path for loads according to consistent stresses, a principle exemplified by the engineel Curt Siegel’s account of Pier Luigi Nervi’s design for the Municipal Stadium (Florence, 1929-1932) where Nerv created a hollow frame in a V-support so that “the bending moment is then resolved into a couple and the structure is resolved into clearly defined tension and compression members” (Siegel 1962, p. 134).
Figure 6: (left) bridge design (Turriano 1984); (right) inverted arches as interpreted by J. Martin; (Alberti 1553)
Figure 6: (left) bridge design (Turriano 1984); (right) inverted arches as interpreted by J. Martin; (Alberti 1553)
Figure 7: (left) Adam 1984; (center) Pompeii, detail (Photo: Raffaella Somma); (right) (Photo: Robert Loversidge) erti 1966, p. 47 [Ill.5]). The English translation by Rykwert et al., as well as the French version by Choay, spe of “loads that converge on a single point” (Alberti 1989, p. 68; see also Alberti 2004, p. 150). Ine can imagine various ways of configuring these arches. Jean Martin’s French edition of 1553 (Fig. 6 right) strates piles for each column connected by inverted jack arches. Jacques-Germain Soufflot applied t Sonfiguration in the foundations of the Eglise Sainte-Geneviéve (Rondelet 1797, p. 31). A second approa [an be found at Pompeii (VIII.3.14) where serial inverted arches have been constructed along a bound vall, with many under a line of putlog holes (Fig. 7 left and center). The arches are composed of stone bloc Iternating at times with thin bricks and seated on a thin inverted arch of bricks, the latter extending throu he entire depth of the wall. In addition to consolidating the wall, these serial inverted aches seem to ha yeen intended to support a wooden superstructure. Hence, these inverted arches seem intended to avoic otentially disastrous point-load on the weak rubble surface, since each side of the arch, according to ,erti’s explanation, captures the load from its timber and redirects it into a self-bracing semicircle. The Ol tate Capitol (1838-1861) features a similar configuration of serial semicircular brick arches embedded in tone wall under the heavy stone columns of the central portico (Fig. 7 right). These inverted arches exte hrough the entire, massive wall.
Figure 7: (left) Adam 1984; (center) Pompeii, detail (Photo: Raffaella Somma); (right) (Photo: Robert Loversidge) erti 1966, p. 47 [Ill.5]). The English translation by Rykwert et al., as well as the French version by Choay, spe of “loads that converge on a single point” (Alberti 1989, p. 68; see also Alberti 2004, p. 150). Ine can imagine various ways of configuring these arches. Jean Martin’s French edition of 1553 (Fig. 6 right) strates piles for each column connected by inverted jack arches. Jacques-Germain Soufflot applied t Sonfiguration in the foundations of the Eglise Sainte-Geneviéve (Rondelet 1797, p. 31). A second approa [an be found at Pompeii (VIII.3.14) where serial inverted arches have been constructed along a bound vall, with many under a line of putlog holes (Fig. 7 left and center). The arches are composed of stone bloc Iternating at times with thin bricks and seated on a thin inverted arch of bricks, the latter extending throu he entire depth of the wall. In addition to consolidating the wall, these serial inverted aches seem to ha yeen intended to support a wooden superstructure. Hence, these inverted arches seem intended to avoic otentially disastrous point-load on the weak rubble surface, since each side of the arch, according to ,erti’s explanation, captures the load from its timber and redirects it into a self-bracing semicircle. The Ol tate Capitol (1838-1861) features a similar configuration of serial semicircular brick arches embedded in tone wall under the heavy stone columns of the central portico (Fig. 7 right). These inverted arches exte hrough the entire, massive wall.
Figure 9: (left) Inverted arch, Baltimore Cathedral undercroft (Photo: John G. Waite Associates Architects); (right) elliptical barrel vault with mirrored inversion, Ohio State Capitol; (Photo: Robert Loversidge) One of the most important uses of inverted arches has occurred within the stereotomic tradition of vaulting whereby the architect or mason chooses an arrangement of stones or bricks (apparecchiatura, appareil) fo the erection of a vault that creates a succession of stacked, shallow, inverted arches, each self-sustaining a every level of construction, thereby avoiding the need for full wooden centering, as in the traditional Lecce star vault (Fig. 10 left) (Fallacara 2008). Herein lies the genius of Brunelleschi at the Florentine Cathedral. In 197¢ Salvatore Di Pasquale recognized that the festooning profile of bricks apparent on the outer surface of the cupola, whose roofing tiles had been removed for repair, revealed that Brunelleschi had conceived his desigr as the intersection of an inverted cone and a modified octagonal cloister vault, a cutting of geometric solid: that necessarily yields such a profile of inverted arches at each level of construction, as can also be seen by computer modeling (Fig. 10 center) and contemporary reconstructions (Di Pasquale 2002; Sakarovitch 2006 BBC/OU 2004).
Figure 9: (left) Inverted arch, Baltimore Cathedral undercroft (Photo: John G. Waite Associates Architects); (right) elliptical barrel vault with mirrored inversion, Ohio State Capitol; (Photo: Robert Loversidge) One of the most important uses of inverted arches has occurred within the stereotomic tradition of vaulting whereby the architect or mason chooses an arrangement of stones or bricks (apparecchiatura, appareil) fo the erection of a vault that creates a succession of stacked, shallow, inverted arches, each self-sustaining a every level of construction, thereby avoiding the need for full wooden centering, as in the traditional Lecce star vault (Fig. 10 left) (Fallacara 2008). Herein lies the genius of Brunelleschi at the Florentine Cathedral. In 197¢ Salvatore Di Pasquale recognized that the festooning profile of bricks apparent on the outer surface of the cupola, whose roofing tiles had been removed for repair, revealed that Brunelleschi had conceived his desigr as the intersection of an inverted cone and a modified octagonal cloister vault, a cutting of geometric solid: that necessarily yields such a profile of inverted arches at each level of construction, as can also be seen by computer modeling (Fig. 10 center) and contemporary reconstructions (Di Pasquale 2002; Sakarovitch 2006 BBC/OU 2004).
Fig. 10: (left) Giuseppe Fallacara, Lecce star vault (Fallacara 2008); (center) Florentine Cathedral (Drawing: Farzam Yazdanseta); (right) Frézier 1737: stereotomy as “the theory of the sections of geometric solids.”
Fig. 10: (left) Giuseppe Fallacara, Lecce star vault (Fallacara 2008); (center) Florentine Cathedral (Drawing: Farzam Yazdanseta); (right) Frézier 1737: stereotomy as “the theory of the sections of geometric solids.”
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