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 compression, 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 homogenized based on the methods of mechanics 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 members is particularly challenging for complex 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 masonry structure are dependent on the Mechanical Properties of the used in Guastavino construction have physical characteristics and configura- Masonry Assembly been studied far less in the literature. Lane, tion of members, as well as on the physi- in studying the chemical constitution of The elder Guastavino's writings about cal properties of masonry, rather than mortar specimens extracted from numer- the tests conducted on tile and mortar on intentionally designed pins or points ous Guastavino vaults, has shown that specimens reveal that maintaining consis- of fixity, as in a steel structure. there is not one particular composition tency in tile and mortar manufacturing The verification of the support condi- used by the Guastavino Company; in- was difficult in the late-nineteenth and tions of a structural model is particu- stead, each building has a case-specific early-twentieth centuries.f In addition to larly challenging whet). dealing with recipe for mortar.'! the inconsistent materials, it is apparent large-scale masonry vaults, since the Specimens of loose tile and mortar that the R. Guastavino Company under- nondestructive means of obtaining were collected from the debris above the went a continuous process of experirnen- empirical data from such systems is State Education Building vaults. The tarion." As a result, it is desirable today limited. Investigating the full-scale be- elastic properties of these specimens to obtain properties of the specific mate- havior of a masonry vault under artifi- rials that were used in construction. were examined by static compressive cial static loading is infeasible, due to The fundamental material-stiffness tests in laboratory conditions, and the the risk and the difficulty of placing a material characteristics of mortar and property used in this analysis is an effec- large static load and in loading the tive modulus of elasticity representing the tile were identified both as individuals structure sufficiently to obtain a measur- and as a homogenized assembly. The combined effect of tile units, mortar joints, able response. Visual methods, such as and voids. If the properties of both mortar comparing the crack locations on the and tile are known, a simple formula can existing structure to the tension zones in be used to average the two materials, the FE model, are susceptible to error, based on the ratios of tile-unit and mortar- especially in structures with support joint dimensions, Saliklis studied the movements. Laboratory tests conducted material characteristics of Guastavino tile on scaled vault samples, which may be by conducting a survey on numerous small successful in determining the stress tile samples and found that the terra-cotta distribution within the system caused by tile has significant orthotropic properties various loading conditions, often over- over the transverse and longitudinal direc- look the actual elastic boundary conditions of the unit. Noting that the tiles are tions, which are influenced by the adja- f oriented in both directions to break the cent elements within the system. I( joints, the study suggested an average In the early stages of this study a Fig. 5. Steel truss system and interaction with elastic-modulus value of about 16.5 GPa domes, New York State Education Building. The form of nondestructive vibration testing (2390 ksi).IOSaliklis's study provides a connection between the dome and the bottom called experimental modal analysis general guideline for the mechanics of the chord of the truss is evident. This connection (EMA) was used to obtain natural fre- tile unit; however, the mechanics of mortar had to be included in the boundary conditions of quencies and modes of vibration of the the dome. Photograph by Sezer Atamturktur. , ! ; 24 APT BULLETIN: JOURNAL OF PRESERVATION TECHNOLOGY I 384,2007

vaults. Using EMA the natural frequen- Table 1, Individual Mechanical Values for lile and Mortar Specimens cies and associated mode shapes of the system can be determined and compared Tile Longitudinal Young's Modulus (E) 1.91 X 106 lbs/irr' to those calculated by FE analysis. Since Tile Transverse Young's Modulus (E) 2.23 x 106 lbs/irr' the dynamic parameters are intrinsic to Tile Longitudinal Poisson's ratio (v) each structure and are directly related to Tile Transverse Poisson's ratio (v) the spatial distribution of mass and Tile Density (d) 110 lbs/fr' 5 stiffness in the system, modal testing Mortar Young's Modulus (E) 4.30 X 10 lbs/irr' provides an opportunity to verify the Mortar Longitudinal Poisson's ratio (v) uncertain model variables. The procedure used in this study is the manual refinement of the uncertain Table 2. Effective Material Properties Entered into the FE Model boundary conditions and is based on the comparisons of dynamic parameters Young's Modulus (E) estimated by the FE model to those Poisson's Ratio (v) determined by modal testing. In this Density (d) 110 lbs/fr' iterative procedure, the FE model is accepted as valid when overall agreement between the model and the dy- Young's modulus of 430 ksi (2.97 CPa) tests, which are directly entered into the namic parameters (mode shapes and was obtained. initial FE models. natural frequencies) is achieved by While Saliklis's results display a 1:1.8 Due to the lack of original tile or means of numeric comparisons. The ratio in orthotropic directions, the find- mortar specimens, laboratory test data adjustments in material properties and ings of this study show an almost for the material properties was not boundary conditions of the model are isotropic behavior. Such a difference obtained for the City-County Building. made based on observable conditions, between Saliklis's findings and those of Noting that both the State Education such as measured material properties or this study is possibly due to the inconsis- Building and the City-County Building the contribution of visible elements to tency in tile manufacturing or to the were constructed in the same decade, the the boundary conditions, The results difference in measurement techniques, as material-property values of the State obtained through the analytical model, Saliklis's results are based on wave- Education Building specimens were along with the established literature on propagation velocity. entered into the preliminary FE model of Guastavino's construction technique, Given the individual properties of tile the City-County Building. support the discussion presented here on and mortar (Table 1), the effective val- Cuastavino vaults. 12 ues that incorporate the combined effect Application of Finite-Element Method of the two materials can be obtained by and Updating by Experimental Experimental Methodology: a homogenization procedure, based on a Modal Analysis Static (Compression) Test rule of mixtures The domes of both buildings were During the site visits to the State Educa- (Ee((ective x Ltota,) = modeled in the commercially available tion Building, a loose tile sample mea- finite-element software ANSYS v. 8.0. (Emortar x Lmorta) + (E'ayer x L'nye) suring 6 inches (15.8 cm) by 8 inches The physical dimensions of the systems (20 cm) and an irregular mortar speci- through the z-axis. Generally speaking, were determined based on construction men measuring 4 inches (10 cm) by 5.5 the tile units are 0.8 inches by 6 inches drawings of the City-County Building inches (14 ern), believed to be left from by 12 inches (2 em by 15 ern by 30 cm) and the architectural drawings of the the construction, were obtained from in size, and the typical mortar joint is State Education Building; on-site survey the rubble behind the domes. The speci- 0.8 inches (2 cm) in all directions. data was used to assure the geometric 1 mens were subjected to longitudinal and Consequently, an effective Young's accuracy of the drawings. The domes transverse static compressive testing modulus value of 1,100 ksi (7.6 CPa) is were modeled as symmetric spherical closely following the compressive- obtained. When repeated for Poisson's segments with square plans, meshed strength-testing procedure of ASTM ratio, the same procedure yields a value with thin, elastic shell elements C67 (2000).13 The tiles were cut into 6- of 0.26. The effective density of the (SHELL93 in ANSYS) of an approxi- inch-by-e-inch (15 cm) squares, ground, assembly is obtained from a simple mate mesh size of 8 inches to 12 inches and capped with plaster of paris. The computation of the weight and volume (20 to 30 cm). Using the impact-echo tests yielded a linearly elastic stress- of the specimens. Assuming an equal technique on the dome of the State strain curve whose slope determined the contribution of tile and mortar to the Education Building, this study deter- Young's modulus of the tile: 1910 ksi total volume, one can linearly average mined an approximate thickness of 5.4 (13.2 CPa) in the longitudinal direction the densities of both materials and inches (13.5 Cm).14The dome of the and 2230 ksi (15.4 CPa) in the trans- obtain the effective density of the as- State Education Building is modeled as verse direction. When the mortar speci- semblyas 112 lbs/ft- (1,800 kg/rn-). a constant thickness of three tile layers, men was tested, an approximate Table 2 presents the findings of these and the dome of City-County Building ----~-==:;===~~~

FINITE-ELEMENT MODELS AND THE HORIZONTAL THRUST OF GUASTAVINO DOMES 25

DRIVING POINT FRF & COHERENCE @ POINT #15

0.009 - - 1.2

0.008 1 ~ 0.007 :§ 0.006 ~ 0.005 ~ 0.004 - ;, 0.003 , E 0.002 j 0.001 4 o ,.--~~------~------~------~O o ro ID ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ g ~ ~ ~ ~ ~ N frequency (hz) -+ Accelerometer * Hammer I - magnitude - coherence I

Fig. 6. Accelerometer array for modal-analysis Fig. 7. Typical frequency response and coherence function. New York State Education Building. testing of a single dome. New York State Education Building. All drawings by the authors.

is modeled as a constant thickness of other, and the symmetries of the vibra- translation perpendicular to the plane of five tile layers. In the initial phases of tion mode can be determined and com- symmetry but are generally allowed to the analysis, the modal-analysis feature pared to the analytically determined translate vertically and to rotate. At the of the finite-element program was used. vibration modes. base line, where the dome webbing meets The natural frequencies, as well as the The results of the procedure led to the supports, translation in all three axes mode shapes of the vibrations of the conclusions about the elastic support is restrained; the tile buttresses between dome, were determined subject to the restraints (Fig. 9). The peripheral edges of the adjacent domes provide vertical re- material properties outlined above and the dome are restrained from a horizontal straint while the diagonal buttresses allow boundary conditions based on visual inspection of the structure. DRIVING POINT FRF of RING #1 The techniques of experimental (imaginary) mpdal analysis were used to investigate thf structural interaction of an interior 3 r------, tile dome at the State Education Build- :c 2 in~ with the adjacent domes, as well as ~~ ~t-----~~~~~~~~~n~~~~~~~~,k~~7~~~~~~ wth the steel trusses and tile buttresses .,; -1 0) thft rest:ain and partially support the E -2 1 do es. ) In this procedure, an array of - -3· ac elerometers was placed on the back 4+-----~--~L-~----~------~----~------__---_-_----~ of the dome, and the dome is excited o ~ ~ ~ ~ ~ ~ ~ g ~ ~ ~ ~ ~ ~ E ~ ~ ~ ~ ~ ~ ~ G ~ ~ ~ usrEg a measured impact force at vari- I frequency(hz) oUppoints within the array (Fig. 6). The i--point3 -::.: p~lnt4 --pOintS --POlnl.6--:- pOlntY-pOintS -P;;I~i9---PomttOJ typ.~icaol utput from a single accelerometer consists of a frequency response fu Iction (Fig. 7). This graph shows the 2 ~~~~---:;;:::-~ ratfo of output acceleration to input 15 aCgeleration as a function of frequency; 1 0.5· pe,ks in the graph represent natural frequencies of the system. By investigat- -0.5o~~~. ~====~~~ ing\the output of multiple accelerome- -1 -1.5 ter~, the natural frequencies of vibration of ripestructure and associated mode ·2+------~ ~'" ~ ~ ~ shapes can be determined. An example '"rreq~ncy".(tu:1 , r----:------,- of the determination of a mode shape is point 3 point4 -POintS -pOlol6 quadrature response analysis (Fig. 8). L-J?O~ =_po{rXa -polr(9 ~~_1~ In this figure the frequency-response functions for accelerometers placed in Fig. 8. Quadrature response analysis of a lower vibration mode, New York State Education Building 'our separate quadrants of the vault are domes. Two diametrically opposed points are moving 180 degrees out of phase with the two points either in phase or out of phase with each located at right angles. This vibration mode has also been identified in the analytical model. 26 APT BULLETIN' JOURNAL OF PRESERVATION TECHNOLOGY / 384,2007

boundary arch restrained by V all directions horizontal translation adjacent dom restrained at rastralned at buttress ... ~-- -./ /. -\~II/~''''''''- / ~~r\: ijlU~ ~ a~ all dirUtions restrained a pier top

Fig, 9, Final summary of the support conditions, New York State Education Fig, 10. Final summary of the support conditions, City-County Building, The Building, The domes are supported vertically only by a very slender arch at domes are supported vertically by massive arches at the boundary, while their boundary, while symmetry prohibits horizontal displacement at the symmetry prohibits horizontal displacement at the boundary Insignificant boundary, Based on the observed mode shapes, it became necessary to vertical load is transmitted directly to the supporting piers after first being consider the additional restraint at the connection between the trusses and transferred to the boundary arches. The tile buttresses at the diagonals the domes, The results for horizontal and vertical reactions are shown in assist marginally in resisting horizontal thrust; their need is questionable, Table 4, The results for horizontal and vertical reactions are shown in Table 4,

vertical movements; the truss members, from restrained expansion of the dome at solutions to experimental results differ which contact the dome surface along the the buttresses. They have no measurable from the preliminary boundary condi- pendentive edges at four corners, restrict influence on the global behavior of the tions only in the fixity of the support of rotation in all directions. Although the dome. Moreover, the need is shown later the dome and in the addition of the boundary conditions determined by the to include the buttresses in the boundary effect of the tile buttresses (Fig. 10). The initial inspection had to be modified in the conditions to replicate the experimental stone arches provide translational and FE model on the basis of the dynamic mode shapes. The significance of the rotational fixity along the periphery; the results, the changes all reflect observable restraint provided by the tile buttress tile buttresses, extending between the conditions: the arches between vaults are shown in Figure 2 implies that the shear dome webbing and the steel columns, sufficiently slender to permit rotation, and across the crack is sufficient to transfer restrain lateral translation. the tile buttresses are directly connected to the restraint of the buttress to the dome. a very solid system of steel trusses. A final The final boundary conditions ob- FE Models in SAP 9.0 Nonlinear detailed comparison of the experimental tained through the comparisons of FE and analytical frequencies and mode The availability of frame-analysis soft- shapes leads to the comparison between ware to practicing structural engineers results shown in Table 3. Table 3. Comparison of the Sequence of makes it necessary to discuss the model In City-County Building, three tile Analytically and Experimentally creation and analysis of Guastavino domes rest on massive brick arches: Determined Natural Frequencies domes in SAP 9,0 nonlinear software. preliminary dynamic testing determined for the New York State Education Generally speaking, the solid modeling that these arches prevent dynamic inter- Building Domes features in SAP 9.0 have far fewer op- action between adjacent domes. This tions compared to general-purpose FE observation leads to the modeling of a Experimental Finite-Element software, such as ANSYS. Therefore, it is Modal Analysis Method single dome on fixed supports, Although convenient to develop the geometric not measured, the surcharge volume is 1 41.0 Hz 40.91 Hz model in a CAD platform, especially observed to have a low rise, and its 2 x 41.47 Hz when the physical geometry of the sys- influence on the structural behavior is 3 48.33 Hz 50.19 Hz tem is nonstandard. In SAP 9,0, three or therefore excluded from the analysis. The 4 , 52.04 Hz 51.47 Hz four node shell elements are suitable for cracks at the intersection of the tile but- 5 58.50 Hz 53.53 Hz the modeling of the dome webbing. In tresses and the dome, previously de- 6 x 57.35 Hz this study the solid model is created and scribed, are not modeled because they are 7 64.50 Hz 60.19 Hz meshed in AutoCAD v. 2004. Due to the local in character, appearing to result 8 73.00 Hz 64,6 Hz lack of curved shell elements in SAP 9,0," . the curved dome surface is divided into FINITE-ELEMENT MODELS AND THE HORIZONTAL THRUST OF GUASTAVINO DOMES 27

nizable as fallacious. The gravity-loading Table 4. Horizontal and Vertical Reaction Results for the New York State Education behavior of the domes, assessed by static Building and the City-County Building analysis from the FE model, also leads to Reaction (Vertical) Reaction (Horizontal) the same conclusion. Feature Building single all single all Engineering perspective on thrust in State boundary arches 0 0 4.62 k 18.5 k Guastavino domes. The investigation of Education )0.7 kN 82.8 kN Building reaction forces for the City-County ! top of pier 6.14 k 24.6 k 0 0 Building under gravity loading reveals ir.s kN 110 kN i that a horizontal thrust of 54.7 kN is steel truss framework 14.0 k 0 3.51 k transferred to the massive arches, while 15.7 kN I 62.8 kN I the buttresses contribute little in hori- surcharge 0 I 0 0.76 k 3.0 k I 3.4 kN 13.6 kN zontal support (Table ~ It is also ob- I served that the tile arches carry the I City-County boundary arches 16.2 k 64.S k 12.2 k 48.9 k entire vertical load, 72.6 kN, and ulti- Building 7?6 kN 290 kN 54.7 kN 219 kN mately transfer it to the piers. Almost top of pier 0 0 0 0 no vertical load is resisted at the base, tile buttresses 0 0 1.50 k 5.99 k where the vault web meets the sur- 6.7 kN 26.8 kN charge volume. Similarly, reaction forces are obtained under gravity loading for the State multiple straight lines and represented by Discussion: Presence of Horizontal Education Building. The results show plate elements. At this stage, creating the Thrust and Elastic Thin-Shell Behavior that the steel girders contribute signifi- solid model and meshing is somewhat Guastavino and later scholars research- cantly to the vertical load transfer of the interrelated. Manual meshing of the ing his work often argued that a cohe- total dome weight. Approximately 15.7 model gives control to the analyst on the sive dome does not exert any horizontal kN is carried by each steel truss at the element aspect ratio and size refinement. thrust on its supports due to its rigid buttress locations between the domes, Providing an acceptable aspect ratio for nature. Guasravino (the father) illus- each element is crucial to achieve accu- while approximately 27.5 kN is trans- trated his claim on the absence of hori- rate results. Keeping the aspect ratio as ferred through each surcharge volume. zontal thrust in domes with the follow- close as possible to unity gives the most The horizontal reaction force counter- ing sraremenr." accurate results; however, for actual balanced by the adjacent domes is calcu- geometries, the limitation on the aspect Suppose we take a big block of stone, say ten lated to be 20.7 kN in total along one feet long and ten feet wide, and one foot or one ratio may be relaxed up to four. side of the pendentive dome, and the foot 6 inches thick; if we support that on the horizontal reaction forces where the Once the CAD model is successfully four sides, just as a lintel, we have practically imported into the SAP 9.0 software, the no thrust, and if we make a caviry on the dome web meets the surcharge is ob- modeling procedure continues with the under side, making a curve like dome, we 17 served to be limited to 3.4 kN. will have a dome arch but WIll have no thrust. entry of the material-property and the The FE solutions reveal the signifi- Interestingly, in the same essay, he cor- boundary-condition input. SAP 9.0 cance of the lateral thrust in this con- rects the misunderstanding on the absence requires unit mass, Young's modulus, struction system. For both the City- of horizontal thrust for tile arches: 18 and Poisson's ratio input entries to County Building and the State define a material type. The boundary It is frequently seen that the greatest friends of the Education Building, the magnitude of system sometimes go too far in their enthusiasm conditions can be defined as translation the horizontal load supported by the and favor of the new idea ... [Flor instance it is stone arches is equal to 75% of the or rotation restraints at joints. In this said that arches under system have no thrust. .. part of the study, the material properties [Tlhe barrel arch has some thrust, and requires vertical load transferred to one pier. and boundary conditions, refined and some material to counterbalance this, that is rods. These findings point out that the hori- That is one of the causes, which makes the barrel zontal thrust is unavoidable for this type verified earlier within the ANSYS soft- construction more expensive than the dome. ware, are adapted in the SAP 9.0 model. of structure. Contrary to Guastavino's assertion, a The static state of the domes under thin-shell dome, including a Guastavino Historical perspective on thrust in Guas- gravity loading is investigated with both dome, is not perfectly rigid, nor is it free tavino domes. A review of Guastavino's ANSYS and SAP 9.0 models and found from bending moment. Therefore, the writing also reveals another remarkable to be in good agreement for the force tendency of the dome to bend down- point on the issue. Despite his passionate solutions. For instance, the vertical wards forces the peripheral abutments to claims, horizontal thrust is in fact taken reaction force transferred to one pier is spread; hence, there is a need for a hori- into account in Guastavino's calculations estimated as 27.4 kN (6.12 k) by SAP zontal-force component at the supports and erections of domes. 19 His formula 9.0 model. This value deviates only to balance this internal moment. The for cohesive arches is based on the sim- 0.3 % from that of the ANSYS model monolithic block argument could be ple statics of the voussoir arch, which is (27.5 kN)(6.14 k). made similarly for an arch carved from a widely known to exert a lateral thrust. stone lintel and would be instantly recog- Guastavino's equations for domes are 28 APT BULLETIN JOURNAL OF PRESERVATION TECHNOLOGY / 38:4,2007

strengthening of domes is indicated clearly an average value was found to yield Un.lormtydi$U'Ibo.JlediQadw(!ctalloadlzwS I I 1 1 1 1 1 1 to account for the tension zones occurring adequate results. in the webbing. The patent specification One of the difficulties associated with of the reinforcement permits an interest- analyzing such structures with the tools ing inference from the following sentence: of the FE method is the uncertain elastic "As the greatest outward thrust of a boundary conditions caused by the semicircular dome is near the base, I place complex functioning of the elements of a the metal rod extending around the dome monumental vaulted structure (ribs, closer near the bottom. ,,20 web, piers, buttresses, etc.). The bound- This statement reveals that in 1908 the ary conditions of the FE models de- younger Guastavino was aware of the scribed herein were refined in the earlier existence of a lateral thrust in his domes. stages of the study through a process of On January 18,1910, he was granted the comparing the modal-parameter (natu- patent on reinforced masonry domes. A ral frequencies and mode shapes) esti- . Fig. 11. Guastavino's analysis of the forces in an arch. Horizontal forces in a dome are halved. carefully researched historical perspective mates of the FE model to those delivered' C represents the compressive strength of the on this discussion is provided by Santiago by experiments. The updated boundary tile, which is multiplied by the area (12 inches/It Huerta. He considers the elder Guas- conditions for the domes in considera- and the thickness) to obtain the strength as a tavino to be of two minds on the question tion yielded the following inferences: function of the crown thrust. of horizontal thrust in domes: on the one • While massive arches supporting the side arguing that the horizontal thrust domes provide complete fixity (trans- extensions of the arches, assuming that does not exist, and on the other side lational and rotational) to the dome one-half of the loads are carried in each inserting metal reinforcement strategically webbing, slender supporting arches do direction: longitudinal and transverse. in the domes to counteract this horizontal not restrain the periphery of the dome, Hence, he calculates the center thickness thrust. The younger Guastavino is much • The symmetric configuration of the of a dome with the formula for the arch more single-minded in his understanding system results in horizontal restraint and divides by two. In all cases, the of this issue, using very refined methods of perpendicular to the plane of symmetry.. existence of the lateral thrust at the graphical analysis to determine the magni- support is considered (Fig. 11). The tude of the horizontal thrust and to design • Tile buttresses, when present, restrain formula used by Guastavino implies a reinforcement to resist it.2l horizontal movement in the direction, horizontal thrust equal to L5116r, where of their main axis. L is the total load, 5 is the span of the Conclusions • The base, where the dome shell rests dome, and r is the rise of the dome. on the piers, can be simplified as fixed: Noting that the vertical support reaction To place the question of lateral thrust in in translation. is L512, the ratio of horizontal/vertical Guastavino domes in perspective, a When masonry structures are analyzed' reaction reduces to 118 the span/rise comprehensive investigation of the with the FE method, another challenge is ratio. For the State Education Building, structural behavior of the vestibule the identification of the material proper- with a span of 29.2 feet (8.90 m) and a domes of the City-County Building and ties. To determine the mechanical behaviof rise above the pendentives of 5.9 feet of the Reading Room domes of the State of Guastavino tile and mortar, static (1.8 m), there is an estimated horizontal Education Building was completed. For compressive tests were conducted sepa- thrust of 62 % of the weight of the dome. these purposes the computerized tools of rately on samples obtained from the State For the City-County Building, with a FE method were used extensively. Al- \ Education Building. The test results wer~ span of 32.8 feet (10 m) and a rise of 7.2 though it has long been known that the homogenized according to the special '~. feet (2.2 m), there is an estimated hori- computerized FE tools have the ability constitution of cohesive construction. zontal thrust of 56% of the weight of the to provide accurate results for given Through the homogenization routine, an dome. These values are comparable to inputs, care must be exercised to enter effective Young's modulus of 7.6 GPa '. the ratios of total horizontal thrust to physically sound and appropriate input (1100 ksi), effective Poisson's ratio of o.i, weight determined in this study to be values and conditions into the program. and effective density 1,800 kg/rrr' were;"~ 57% for the State Education Building In this study, the vault webbing is obtained. Although the tile and mortal' and 85% for the City-County Building. modeled with thin-shell elements of manufactured by the Guastavino Com-, Although the elder Guastavino confi- approximately 7.9-to-11.8-inch (20-30 pany is known to have undergone con: dently argued that his domes do not have em) mesh size. Although the site survey uous experimentation and have inconsi thrust due to their monolithic nature, the revealed slight deviations from symme- tent nature, these values can be adapted' younger Guastavino apparently did not try, the simplified symmetrical geometric the initial FE modeling of Guastavino fully trust the tensile capacity of the cohe- model revealed satisfactory correlation domes and vaults in future studies. sivesystem. On July 31,1908, four with the experimental data. Typically in The FE models are employed to months after his father's death, the a Guastavino dome the tile layers de- analyze the structures under [he forc younger Guastavino filed an application crease from spring point up to the apex. of gravity. This static analysis enables for a patent on reinforcement of the tile Approximation of the dome thickness to one to identify the support reactions arches and domes with steel bars. The FINITE-ELEMENT MODELS AND THE HORIZONTAL THRUST OF GUASTAVINO DOMES 29 exerted by the dome to the unmodeled with the cohesive-construction technique, one 9. Guastavino, 144-145. Guastavino the elder calls for the assistance of architects and manu- adjacent members. The findings of this can build domes that do not exert horizontal thrust to their supports (pp. 78-79). In "The facturers ro perfect the building materials and study illustrate the existence and, more Transfer of Thin Masonry Vaulting from Spain in particular notes the necessity ro manufacture importantly, the significance of the to America," George Collins supports Guasta- lighter tiles. . horizontal thrust in a Guastavino dome. vine's rationale and states that due to the monolithic nature of cohesive construction the 10. E. Saliklis, S. Kurtz, and S. Furnbach, "Finite Element Modeling of Guastavino Tiled Arches," domes exert very little rhrust to their supports Proceedings of the Eighth International Confer- SEZER ATAMTURKTUR is a doctoral candi- (p. 180). The language that Guastavino used to support his stone-block argument - rigid ence on Structural Studies, Repairs and Mainte- date in the Department of Architectural Engi- nance of Heritage Architecture (Southampton, membrane, monolithic nature of domes - is neering at Pennsylvania State University. She Mass.: WIT Press, 2003), 257-266. recently completed a master's degree on the also unchallenged and repeated extensively in assessment of Guastavino domes. the literature. In her master's thesis, "Guas- 11. Daniel Lane, "Putting Guastavino in tavino Tile Construction" (University of Penn- Context: A Scientific and Hisroric Analysis of THOMAS E. BOOTHBY, PhD, is a professor sylvania, 1992), K. Ann Milkovich, in common His Materials, Method, and Technology" of architectural engineering at Pennsylvania with orher architectural hisrorians, perpetuates (master's thesis, Columbia University, 2001). State University. He was appointed to the the claims of Guastavino uncritically (po29). Lane investigates the chemical composition of faculty in 1992. He has more than 15 years of Dietrich Neumann in "The Guastavino System mortar specimens collected from several struc- experience in the assessment of historic unrein- in Context: History and Dissemination of a tures built by two Guastavinos. The findings of forced-masonry structures. Revolutionary Vaulting Method," APT Bulletin his study reveal differences in the mortar 30, no. 4 (1999): 7-13, mentions that the constitution that are not justified by technical Guastavino vaults exert minimal lateral thrust advancement; instead, Lane considers that to their supports (p. 8). Cuastavino was experimenting on cement or Acknowledgements 4. Santiago Huerta, "Mechanics of Timbrel simply using any available material that he could come up with (p. 104). Lane also nores This research was funded by National Center for Vaults: A Historical Outline," in Essays on the History of Mechanics, ed. Becchier al. (Basel: the association of Guastavino with Jose Fran- Preservation Technology and Training. The cisco Navarro, an established cement producer, authors are also grateful to Bruce Padolf of the Birkhauser Verlag, 2003),88-133. Huerta argues forcefully that a "cohesive" vault exhibits funda- and stresses Guastavino's dedication to make City of Pittsburgh and George Webb of the New his products better. York State Education Department for the oppor- mentally the same behavior as any other masonry i tunity to test the City-County Building vestibule vault and that the advantage of the Guastavino 12. SezerAtarnrurkrur, "Structural Assessment of !. vaults and the State Education BuildingReading system is more due to its extreme thinness, Guastavino Domes" (master's thesis, Pennsylva- Room domes. Also, the editorial help of Corinna carefully positioned reinforcement, and conse- nia State University,2006), 119-121, 132-133. Fisher and Lori Smith and the assistance of Sally quently reduced loads (and horizontal thrust). Gimbert in the material tests are greatly appreci- 13. American Society for Testing and Materials, 5. Section drawing, Reading Room, Albany "Standard Test Methods for Sampling and ated. The authors also wish to express their State Education Building. Drawing A156A.l thanks to the peer reviewersof this manuscript for Testing Brick and Structural Clay Tile," ASTM #01959, Guastavino Collection, Avery Library, C67-05, in Annual Book of ASTM Standards, their thoughtful and thought-provoking com- Columbia University. ments, and the editors and staff of Mount Ida vol. 4.05, Chemical-Resistant Nonmetallic Press for their indispensibleeditorial assistance. 6. Janet Parks and A. G. Neumann, "The Old Materials; Vitrified Clay Pipe; Concrete Pipe; World Builds the New: The Guastavino Com- FIber-Reinforced Cement Products; Mortars pany and the Technology of the Catalan Vault, and Grouts; Masonry; Precast Concrete (Con- 1885-1962," catalog of an exhibition at Avery shohocken, Penn.: ASTM, 2005), 43-44. Notes Architectural and Fine Arts Library and the 14. Atarnturktur, 35-38 and 60-61. It is Miriam and Ira D. Wallach Art Gallery (New 1. Salvador Tarrago, ed., Guastauino Co. noteworthy that the impact-echo study that York: Columbia University, 1996), 12 and 51. determined the thickness of this vault was done (1885-1962) Catalogue of Works in Catalonia This exhibition catalog has a comprehensive and America (Barcelona: Collegi d' Arquitectes before the authors were made aware that the list of available documentation on Guastavino's thickness of the vault is three tiles, or approxi- de Catalunya, 2002). Taraggo's introductory method of vaulting. essay, "Considerations on Guastavino's Work mately 12-13 em (5 in) (see note 5). in Catalonia" (pp. 7-15), evaluates work of 7. Thomas E. Boothby, Sezer Ararnturktur, and 15. R. J. Allemang, D. L. Brown, and A. S. Guastavino in Spain and provides a general E. Erdogmus, "Manual for the Assessment of Kobayashi, "Chapter 16-Experimental Modal overview of timbrel vaulting. In the essay Load Bearing Unreinforced Masonry Struc- Analysis," in Handbook of Experimental Tarrago states that the use of portland cement tures," http://www.arche.psu.edulmasonry- Mechanics, 2nd ed. (Bethel, Ct.: Society for enabled Guastavino to widen the distance assessment, accessed October 15,2007. Experimental Mechanics, 1993), 635-750. This between pillars up to 26 feet (8 m), significantly standard reference provides a good introduc- greater than the standards of the time. 8. Guastavino, 58. In this 1892 article the elder Guastavino indicates a series of tests conducted tion to the techniques and applications of 2. George Collins, "The Transfer of Thin Masonry with engineer A. V. Abbort at the Fairbanks EMA. The Atarnturktur supra furnishes de- Vaulting from Spain to America," Journal of the Scale Company in May 1887. Although no tailed descriptions of the applications and Society of Architectural Historians 27 (Oct. 1968): detailed information is provided regarding the results of the method for masonry domes and 176-201. Collins'sarticle provides an overviewof test setup or methodology, obtained values for provides further general references on the the background of Guasravino and history of his four different sets of compression tests are method. construction technique. The prestigethat the presented as 15.60 MPa (2260 psi), 11.19 MPa 16. Guastavino, 78-79. Guastavino Company gained is evident in statistics (1620 psi), 9.86 MPa (1430 psi) and 20.07 of the work the company has performed. Collins MPa (2910 psi). For future calculations Guas- 17. Huerta traces the origins of this argument to emphasizes that the high visibilityof their projects tavino used the mean of these significantly the 1754 writings of the Cornte d'Espie, 93-95. is far more impressivethan the number of the vatying results. The inconsistency in the projects with which the company was involved. strength capacity of rhe rile samples is evident 18. Guastavino, 136, 140. even in laboratory environments. 19. Guastavino, 66-67. 3. Rafael Guastavino, Essay on the Theory and History of Cohesive Construction, 2nd ed. 20. R. Guastavino, Masonry Structure, 2-3. (Boston: Ticknor and Company, 1892). In this U.S. Patent 947,177, issued Jan. 18, 1910. article Rafael Guastavino the elder claims that 21. Muerta, 107-119.