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The Journal of Preservation Techn~-~Og~ I INTERNATIONAL BULLETIN Vol. XXXVIIII, No.4 2007 ~~~ JiM Ii THE JOURNAL OF PRESERVATION TECHN~-~OG~ The Association '0' Preservation Technology • Association poue I, preservation et ses leclmiqu"" INTERNATIONAL The Development of Finite-Element lYIodels and the Horizontal Thrust of Guastavino Domes SEZER ATAMTURKTUR AND THOMAS E. BOOTHBY Modern engineering tools applied to Introduction testing, cannot be obtained for every building under investigation; conse- structural analysis of two existing The Guastavino vaulting system, ini- quently the mechanical properties that tially promoted by Rafael Guastavino Guastavino tile domes prove the were calibrated based on the nonde- Moreno and continued by his son, existence of horizontal thrust, in structive dynamic tests were compared Rafael Guastavino Esposito, has in- to the results of direct measurement on spite of the elder Rafael Guastavino's spired numerous studies in architectural specimens in laboratories and found to claims to the contrary. history and historic preservation. It is be in good agreement. Once the appro- the intention of this article to further the priate boundary conditions and material understanding and appreciation of properties were obtained through the Guastavino domes and to present means ANSYS model, the domes were then of investigating their structural behavior modeled in the frame-analysis program with modern engineering tools. For SAP 9.0 nonlinear, a program widely these purposes the finite-element (FE) used by engineers in practice. method is extensively employed through the computerized package ANSYS. The findings of these studies are used to Overview: Rafael Guastavino and assess the characteristics of Guastavino Cohesive Construction vaulting, specifically focusing on the Rafael Guastavino transferred a thou- question of horizontal thrust in domes. sand-year-old system of Catalan vault- The results presented are supported by ing from Spain to the United States, analytical models and field and labora- with the additional refinement of re- tory tests conducted on the City-County placing the traditional mortar with Building entrance-vestibule domes in rapidly hardening portland cement. Pittsburgh and the New York State Using this version of Catalan vaulting, Education Building Reading Room he achieved spans of three to five times domes in Albany, both of which were the typical span of a traditional Catalan designed by Henry Hornbostel. vault.' The capabilities of Cuastavino Because the FE modeling of a historic vaulting, or, in the elder Guastavino's masonry structure poses two major words, "cohesive construction," con- challenges - the identification of the tributed to the structure of many impor- boundary conditions and the effective tant buildings between the 1890s and material properties - two separate 1940s and resulted in more than 1,000 model-refinement efforts were under- examples in North America.' taken to achieve an acceptably accurate During his career the elder Guasta- representation of a structural system. In vino, a successful marketer, developed a the early stages of this research, a form number of rationales to promote his of dynamic-vibration testing was used novel technique. One argument pro- for the verification and updating of the moted by Guastavino, which appears to boundary conditions. To obtain effective be widely accepted by historians, is that mechanical characteristics of the assem- cohesive domes exert no thrust on their bly, static compressive tests on tile and supports.' A dome without a lateral mortar specimens obtained from the thrust does not require thick walls; hence, State Education Building were con- lower building costs give it a great advan- ducted, and the combined elastic con- tage over other systems. This argument Fig 1. View of the underside of the loggia straints of tile and mortar were homoge- surely contributed to Guastavino's domes, City-County Building, Pittsburgh, Penn- nized. These results, although more reputation for inexpensive and quickly sylvania. Photograph by Sezer Atamturktur. reliable than nondestructive dynamic 21 22 APT BULLETIN: JOURNAL OF PRESERVATION TECHNOLOGY / 38:4.2007 Fig. 2. Detail of the domes at the City-County Building. Photograph by John Fig. 3. Tile buttresses above the loggia domes. City-County Building. G. Waite. Photograph by Thomas E. Boothby. erected vaulting in the early 1900s. This The cracks are confined to a small zone 40 inches (150 em) connect the truss assertion, largely unquestioned for 100 around the intersection between the tile chords to the dome shell (Fig. 5). The years, has only recently been challenged buttresses and the back of the dome. domes are non bearing, as they are by a historian of technology, Santiago The dome thickness varies from three fully detached from the upper floor. Huerta." Huerta's critique is comprehen- to seven layers. The interior surface is The tile vaults have a thickness of three sive and thorough in identifying the finished with decorative tiles that create courses.' No apparent cracks on the nature and origins of the widespread a highly ornamented and colorful finish. back of the tile domes were observed fallacies concerning the behavior of this The intrados of the vestibule domes are during the visual site survey. 6 structural system. In addition to describ- exposed to the weather, whereas the ing a procedure for the detailed analyti- extrados are less susceptible to climatic Analytical Methodology: cal modeling of this type of structure, changes. The upper balcony floor, Finite-Element. Method the present article supplements Huerta's mainly carried by concrete beams, is in arguments by using contemporary engi- contact with the apex of each dome. In general, analytical modeling of neering tools to estimate the horizontal Although the structural effect of this masonry structures is a particularly thrust of a working Guastavino dome. connection and the extent of the support challenging task. The true behavior of of the domes to the balcony floor are masonry, both in tension and in com- pression, is nonlinear; however, the Description: Structures of Interest unclear, this study assumed the domes to be non bearing and independent from needed stress-strain law is seldom avail.•. City-County Building (1916). The City- the balcony. able, Due to the orientation of the mors County Building has three side-by-side tar joints, the material is anisotropic an·' New Vork State Education Building spherical segmental domes of 22-foot inhomogeneous. On the other hand, 0$ (1911). In the State Education Building, (6.7 m) radius that span the entrance significant progress in the assessment of twelve identical rib-and-dome units are vestibule (Figs. 1 and 2). Through the a masonry structure can be made assunz arranged in a three-by-four grid: a use of pendentives and stone masonry ing masonry as a linearly elastic repetitive circular system. The spherical arches, the tile domes are inserted into a isotropic and homogenous material; __. domes are truncated from a 21-foot 33-foot-by-33-foot (10 m) square bay thus avoiding the complications in the' radius (6.3 m) over 29-foot-by-29-foot and supported by stone piers. At the constitutive law, as well as the conver- (8.9 m) bays with 6-foot (1.8 m) rise. core of each pier a steel lattice column gence issues associated with nonlinear The transformation from a circular plan continues towards the back of the analysis," In the present paper, these domes and supports the balcony floor. to a square bay is accomplished by uncertainties are mitigated by obtainio means of pendentives and slender Between these steel columns and the material properties experimentally fro,:. ribbed arches (Fig. 4). The domes are dome webbing, at the four pendentive specimens of the material used in con supported by slender iron columns that corners, tile burrresses were added to struction and by experimentally veri continue past the vaults and join the bolster the back of the domes (Fig. 3). ing the assumed boundary conditions trusses that carry the upper floor loads. The conditions survey on the back of used in modeling the structure. The truss members contact the dome the domes revealed the development of shell at every 45 degrees in plan, where approximately O.l-inch (2 mm) cracks small tile blocks 16 inches (40 em) by at all four corners towards the apex. FINITE-ELEMENT MODELS AND THE HORIZONTAL THRUST OF GUASTAVINO DOMES 23 compressive tests obtained the Young's modulus (E) and Poisson's ratio (v). Subsequently, these values are homoge- nized based on the methods of mechan- ics of materials to obtain the effective values to be entered into the FE model. Boundary conditions for Guastavino domes. In addition to the difficulty in assessing the material properties, the assessment of the physical definition of the connections between adjacent mem- bers is particularly challenging for com- plex masonry systems. Because none of the theoretical fixed or free boundary conditions available on analysis pro- grams exist in real structures, their use introduces approximation; the choice of one or the other depends on an accurate understanding of both the behavior of the structure and the technology and Fig. 4. View of the New York State Library Reading Room domes, New York State Education Building, Albany, New York. Guastavino Company catalog, 1920. capacity of the FE software. Addition- ally the elastic joint restraints in a ma- sonry structure are dependent on the Mechanical Properties of the used in Guastavino construction have
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