STUDIES OF GAUDI`S "CRIPTA DE LA COLONIA GÜELL"

STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTiONS
p, Roca, J.L González, AR Mari and E. Oi'late (Eds.)
C> CIMNE, Barcelona 1996
STUDIES OF GAUDI'S "CRIPTA DE LA COLONIA GÜELL"
P. Roca
E. T.S. Etlgi flyers de Camills, CaI/ais y Ports
Univers ifaf Politecnica de Catalllllya
08034 BarcelOlla
Spai n
SUMMARY
The Crypt of the Coloni a Güell is only t he existing part of an unfinished
construction imagined and commenced to be erected under Gaudj's direct ion
during the period 1908 to 1915. Once finished , it would have been the
church of the Güell Factory's Village in Santa Colorna de Cervelló, near
Barcelona. A remarkable feature of this building is found in the use made
by Gaudi of a tridimensional funicular model to design the geometry of its
unique structural syste m . The strings in the model were materialized as a
hierarchy of diafragms , arches , and oblique pilars made of brick fabric and
stone. Due to this design, the theoretical stability of th e building should be
largely dependent upon the achievement of a funicular-type balance of forces
among ali the elements of the whole structural system.
A numeric analysis, based on a Generalized Matrix Formulation, was
performed to study in detail the today actual resist ing mechani sm und er
gravity loads for the built part of the st ructure , as a way to measure
the alteration of the funicular equilibrium and relate it to the damage
that is observed. Long term phenomena like mortar shrinkage \Vere also
incorporated in th e stucly and found very singnificative . Through the
comparison between the numeric predictions and the observed in-situ damage
a new undestanding of the real state of the structure and actual resisting
mechanism were obtained. Particularly, the stability of the st ru cture was
demonst rated as a result of the capability of t he building imagined by
Gaudy to aclapt to different states of equilibrium throughout the hypothetic
complete const ruction processo
378
STRUCTURAL ANALYSIS OF HISTORICAL CONSTR UCTIONS
Fig. 1.- The entrance to the Cr ypt under the portico
THE BUILDING AND THE FUNICULAR MODEL
The Crypt af the Colonia Guell is the anly part actually built of what was
to have been the parish church of the madel Village íounded by Eusebi Guell
in 1890. Gaudi was commissioned to design it in 1894, when he was also
working in the Expiatory Temple of the Sagrada Familia. The foundation
stone af the Church was laid in 1908. Gaudí spent fourteen years to lay
out the structure, due to which its construction was not started on until
The works were abandoned in 1914, leaving anIy the crypt and the portico
finished (Figs. 1,2). It is located in Santa Colama de Cervello, just a few
kilometers from Barcelone.
The general form of the fioor pIan is oval, with a star-s haped outline ( Fig. 2)
and it measures 26 by 63 m. The used materiaIs are mainly brick íabric and
stone. The slab rooí is supported by an eskeletaI system which consists oí a
hyerarchy oí ribs, arches and columns. Some oí the columns are oblique. The
externai walls oí the crypt itselí reveal elevations with different inclinations
in such a way that the base oí these configures the star- shaped perimenter;
P. ROCA I Gaudi's "Cripta de l:l Colonin Gücll "
G
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F ig. 2.- Plan and elevati on of the building
the upper part of the walIs are pierced by rhomboidal window s. On the so ut h
facade there is t he portico, its rooí consisting of of hyperboli c paraboloids
made of brick masonry. This was intended as the access to the church, located
to the fia 0 r above.
The central nucleus is delimited by four basalt columns and the arches which
separate it (rom the choi r, ali of them angled in towards th e cent re of the
nucleus , and two peripheral aisles forming a do bule ambulatory, made up
of ten columns arranged in a double semi-circle around the nucleu s ( Figs.
3,4). Colurnl1s and pillars support the main brick arches from which the rib s
spring. These are also of brick, and have bee n treated in two different waySj
t hose which con verge on the two circular bosses - linked by a practically
Rat brick areh- consisting of a brick rowlock arch 15 em thick, supporting
a wali of the same thickness. The remaining ribs are waUs 12 em thick ,
J80
STR UCT URAL ANALYSIS OF I-IJSTORI CA L CONSTR UCTIONS
but raised over brickwork over brickwork arches three courses thick. The
reticulum form ed by the ribs is Hu sh at the same levei and supports the
saleTa ar masanry floor slab (Fig. 5). It consists of a first triple layer of
facing brick) with a suspe nded floor over this) formed by brick partitions,
su pporting the final double layeri pres umably, teh paving of the church was
to have been laid over t hi s.
Fig_ 3.- View of lhe cent ral columns
The limitations of the graphical or numeri cal methods available to Gaudi)
obliged to him work out hi s stereo-fun icula r st ru cture using a physical scale
mo deI. Thus) Gaudí devcloped a tridimen sional funicular model in which
st rings were used to represent actllal brick mason ry arches and oblique brick
or stone columns (Fig. 6). In fact , lhe whole arrangement of colllmns ,
a rches a nd ribs is the materiali zat ion of the funicular model which Gaudi
built and st udied over lhe ten years before ils construction was started on.
There is small doubt that the crypt is th e first large structu re laid out
based on a similar thrce- dimen sional funicular model) were funi cular lin es
illterweave in the t hree spatial dimensions. More details in regard to historie
or constructioTl aspect s may be fOllud in Casais et alo (1990) and Go nzález
et alo (1 993).
P. ROCA I G:wd i's '·Cripta
d~
la Colonia GüdJ"
38 1
Fig. 4.- Section of the hypothet ic complete building
During the Spanish Civil War, the original hanging model wa.s destroyed and
just a few photographs of it survided . However, thank s to the initiative and
the huge task of a graup of Dutch and German admirers af Gaudi , we now
have th e reconst ructed versia ll of it (Tamlow , 1989). Besides, the correlatian
demon st rated by co mparin g phatagraphs af the new model and that hy Gaudi
permits reasonable speculation about the new images af the unbuilt part.
The in cünation of the columns in the crypt was imposed by Gaudi for
composition al reasons, and it was achieved thanks ta the thrust generated by
the arches or ribs which would s upport the Roor of lhe chur ch. Surprinsingly,
the aciual in clination af those column s in th e built structure is high er than
the one observed in the funi cular model.
Thus, the co mparison between t he reconstructed model and t he adual
building arises some doubts. If the structure is in equilibrium at the moment ,
with lines apparently distant from the funicular model, ... would it be in
equilibrium once it was finished?
382
STRUCTURAL ANALY$ I$ OF HI STO RI CA L CONSTR UCTIONS
Fig. 5.- Section af the upper selera
We have herc precisely the great paradox af the crypt. It is a building which
was co ncei ved to be stable Dnce it was fini shed, but nevertheless it is stable
now , in its unfinished statc.
ABOUT THE ACTUAL STATE OF THE BUILDING
However , ane may still t hink that the structure behaves according to
the funicular madel although only partially. This may be dedu ced Crom
all ind icato r which has generally becn overlooked but is af consider able
importance when it comes to checking the possible hypot hesis about hte
behaviour of the building: the intrincate pattern af carcks in the fa cing brick
ceiling a r salera which CQvers t he central nave, and those which affect several
c f the ribs and some a f the arches.
Dc tailed analysis through direct observation and an exhau s- tive photo-graphic survey of over 1000 images has enabled to determine the patterns of
P. ROCA I Gaudi's "Cripta de la Colonia Güell "
183
Fig. 6.- Original picture of the hanging model elaborated by Gaudí
(inverted ).
cracks reproduced in Fig. 8, which is only an overaU view amongst all those
that were detected.
The building has not collapsed , but neither can we say it is undamaged.
The detailed inspection of the structure through dired observation and
photographic survey has enabled to determine the pattern of cracks which
is partially reproduced here (Figs. 7,8) . Those cracks could be seen not
only in the conti nu ous slab of brick masonry over the crypt, but also in the
secondary arches or ribs.
384
STRUCTURAL ANALYSIS OF J-I1 STOR ICA L CONSTRUCTI ONS
Fig. 7.- Example of cracked rib
M ET H OD OF A NALYSI S
The structural analysis of s)'stems composed of curved members such as
the arches, diaphragm s or nervures which may be found in many ancient
structures, is commonI)' carried out usi ng t he finite element method with isoparametric type with di splacements as unknowns. It may be seen that , due
to the deficiencies of the method in the description of the internai equilibrium
of the elements, accurate results of internai forces are only obtained when
a con siderable amount of individual elemeuts are used in thc geomctric
d iscretization. However , for structural system s composed of unidimensional
curved members, it is possible to establish analytical generalizations of
conventional matrix mei hod s based directly on exact equilibrium. Although
the practical use of these matrix formulation s was limited in the past by the
large volume of mat hematical operations required, recent developrnents in
digital compu ters make this poi nt less criticai nowadays , while t he as p ects
of accuracy and versatili ty gain renewed interesL
The analytical model used in the studies presented is directly based on
a Matrix Generalized Formulation specificaU y developed to treat ancient
P. ROCA I G:ludi·s ··Cripl:l de la Colon i:l Gücl l"
385
'-.
Fig. 8 .- Crack pattern in arches and salera
buildings cansistin g af multiple struct ural systems with curved, variable cross
sect ion members. The formulation , initially based on the work of Baron
(196 1) for static linear analysis, has been extended to nonlinear geametric
and modal vibration analyses. Relevant aspects af the resulting method are
the fallowing:
(1) Automatic generatian af complex geometries thraughout the length af the
elemento Three cross sections, having arbitrary shapes, are to be given at
three respective points af the axial curve af each elemenL
(2) Each different cross-sectian is defined as a co mpositian af elementary
trapezoids , where each of them may be associated to a different type of
material.
386
STRU CTURAL ANALYSIS OF HISTORICA L CONST RUCTIONS
(3) Specific devices are included to model load bearing or shear walls as
equivalent systems of linear elements according to the method proposed by
K wan (1991 ).
(4 ) Nonlinear geometric analysis based on an updated Lagrangian formulation ,
thus aUowing the treatment of cases involving instabilty phenomena of arches
ar other curved elements.
(5) Moda! dynamic analysis based ou the formulat ion af a consistent elementary
mass matrix which objectively takes iuta account the distribution of mass
and stiffness throughout the element.
Constitutive equations for brick ar stone masonry at the macro-modeling
levei are now being implemented in the general roodel 50 that an integrated
nonlinear geom etric and material nolinear analysis method will available in
a short time.
Nevertherless, the linear elastic analy sis carried out for the Crvpt, as
described in the following sections, was very informative and revealed itself
suitable to obtaind an interesting understandillg of the adual state of
equilibrium af the building, as well as to investigate the causes of the existing
damage.
Before its systematic use for the study af existing buildings, the madel,
implemented in the computer program CRIPTA , was checked through the
analysis of a series of sim pIe and multi pIe systems af curved members , for
which analytical or experimental res ults were available. The comparisans,
described hy Molin s et alo (1994,1995), showed the very sati sfadory levei af
accuracy and numerical efficiency which are achieved even far geometrically
camplex structures.
NUMERICAL MODELLING AND RESULTS
In arder to reach a better understanding of the presellt state of the structure
and also understand its actual equilibrium , it was decided to carry aut several
comp u ter analyses. The first type of analysis was based in plane stress and
was used to study the individ ual elements like ribs. Due ta time limitatians,
it is not presented here.
The second type af analysis was a global one using the above mentioned
Generalized Matrix Formulation (implemented in computer program
P. ROC A I G:mdi's "Cripta de la Coloni:l Güell "
387
CRlPTA ). The structural members were treated as linear elements with
curved centroidal axes, as well as arbitrary cross sections, thus allowing to
model the arches, ribs, diaphragms and colurnns incorporated in the existing
structure. This allowed to accuratelly take into account their actual stiffness.
Th us, the model show n in Figs. 9,10,11 was constru cted fr om the elevation
and other disposab le inform ation. In addition, solid undeforrnable elements
were introduced to simulate the massive capitab were l:ulumns, arches and
rib s connect.
Fig. 9.- View of the numeri cal mod el
The adopted formulation made it possible to reproduce states of stresses
caused by combined axial, shear , bendin.e; and torsion for ces, and thus to
simulate possible modes of global equilibrium more comp lex to that of a
funic ular model , having also in to account the actual distrubution of stiffn ess
between st ru ctu ral elements.
The lead joints which exists at the juntion between the cent ral columns and
thi r pedestais and capitaIs, were treated alternativelly as perfectly fixed or
rotational free hinges. First, the existing part of the st ructure was studied
subjected to the vertical load produced by the weight of the eskeletaI system
af ribs , arches and columns as well as the weight of the upper slab, which
388
STRUCTURAL ANALYSIS
or 1·IISTORICAL CONSTRUCT10NS
Fig. 10.- View of the numerical model (with stress intensities represented in
chromatic scale )
rests on the firsL By this st udy, the zones subjected to high tension stresses
were recognized.
The tensional stresses obtained in the different elements are mainly caused
by t hei r in dividual behaviour under vertical load, and are hardly infiuenced
by interacting forces due to global effects. Thus, the highest tension zones
appear at the joints between ribs and capitaIs or arches, and lower tension
zones appear at the middle of the s pau af ribs.
Moreover, a correlation was found between the analytical prediction of high
tension leveis and the cracks observed in the structure. However, the first
showed many other poten tially cracked zones whi ch were apparcntly intact in
the building. Thcse are interpreted as parts w hich, although cracked, do not
show an evident structural damage or which, alt hough intact , are subject to
a high leveI of stress and might be easily damaged by overloading ar altering
the present geometry of the structure.
P. ROCA I Gnudi's 'üipta de la Cololli:-t Gücll"
389
Fig. 11.- View of the numerical model (with stress intensities represented in
chromatic scale)
THE RHEOLOGICAL ACTIONS
There are also radial cracks in the upper slab which cannot be explained by
the gravity forces. Having discounted other causes, t he only probable one is
hydraulic shrin kage .
The values shich are habitually handled to dimension the movement due
to hydraulic shinkage in masonry structures range between 1 and 7 yo 8
tenths of a millimetre for each linear rnetre of \VaU. No values have been
found which refer to sheer brickwork elemellts, since this is a constructioll
procedure which is not ordinalrily used, andan which test have not been
gellerally been carried auto However, the values could not be lawer in view
of the larger relative proportion of mortar in the section, as weU as the great
proportion of portland cement in the mortar.
In fact, the R-X difractometric analysis aí some mortar patterns showed that,
surprisingly, it consisted af almast pure Portland cement. This is against the
usual technique for building such a brick rooí ar vault at that time , since
390
STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS
t h e fist skin was always treated with p laster to avoid the use of scafolds and
forms.
Moreover, the measurement of the total wi d th of the cracks amounts very
closely to the shrin kage cont raction that coul d we expected for such a mortar.
Rence we can draw a further conclusion: contraction is the process which
makes visible many cracks oí gravitational origin, ar contribu tes to their
appearance when it is added to the mechanical ten sions in the cases where
tension in the ribs and foreseeable lines of fract u re in t he upper slab coincide.
F ig. 8 represents a plan of the salera which shows the gaps provided to leave
roo m for the columns of the church above, which no doubt is relevant to
the matter of shrinkage. O n this pIan , if we observe the numerical forecasts
and the present evaluations which recommend the provision of walls with
expansion joints every eight metres, and if we look for the areas wh ere,
because of t heir smaLIer cross-section and a geometry which m ight provoke
cr acking, assuming a uniform grid, we reach the conclusion t h at it was to be
expected that tensions would occur along these lines .
To aLI t his should be added the plan showing the areas where, according
to the computer mode!, the upper part of t he ribs is under tension. If
we ass ume complete adherence between the ribs and the sol era , we may
sup p ose that this tension is transmitted to the latter. Hence, in addition
to the tension dyeto hydraulic contraction we must consider the tension
due to mech anical beh aviour under gravity. Due to the fairly con siderable
correlation between the hypothesis an d reality, we may conclude that t he
radial cracks are due to contraction, while the cracks between t he head s of
the columns, the capitais, are due to a combination between contraction and
tension or flexural phenomena due to the gravity loads of the ri b arches.
It its possible to draw a further conclusion: contraction is the proceS5 which
makes vi5ible many cr acks of gravit.ational origin, or contributes to their
appearance when it i5 added to the mechanical tensions in the cases where
ten sion in the ribs and foreseeable lines of fracture in the salera coincide.
CONCLUSIONS
These studies an d considerations aLIows as to present some conclusions upoo
t he actual state of the structure and also about the hypothetical complete
building. F irst, t he b uilding is stable u n der its own weight and the permanent
P. ROCA I Gaudi 's "Cripll de Il Colonia Güell "
39 1
loads at present affecting it. This is 50 in spite of the fact that the present
loads were t he cause, at some time, of the existing damage, The overall
stability is more t han assured, thanks to t he strength of the interior columns
and the perimeter waUs.
Fig. 12,a,- Movement of the central nucleus under today's dead lo ad
Fig. 12,b.- Movement of the central nucleus under the effect of concentrated
loads simulating the completition of the building
The o btained scheme of forces at the leveI of arches and ribs keeps similar
to that of a funicular type of equilibrium , although the geometry does no
correspond to that of he funicular mo de!. It may be seen that, owing to
their much larger sectionaI dimensions , the deformations of columns and the
perimetral wall are very small in any case, 50 that the equilibrium af arches
and ribs is not affected by the fact t hat the devised global structural sys tem
is not campleted .
392
ST RUCT URAL ANA LY SIS OF HI STOR ICA L CONSTR UCTIONS
When lead joints are treated as perfect hinges, a significat ive movcment of the
central columns and upper capitaIs is obtained (Fig. 12,a) which produces
balancing axial and fl exural fo rces in the adjacent rib s. Some real effects
that are observed in t hese zones may also be correlated to such a movement
of the capitais, üke a more extenclecl cra cking in the ribs a nd diagonal cracks
in the upper slab .
The nonexisting part of the structure was simulatecl by th e hypothetic forces
that it would have caused on the existin g parto These forces were knwow
through some labels that were vi sible in the remaining phot ografies of the
original maquet t e. It was establi shed that ab solute funi cular cquilibrium
would not have been obtained for the finished building either. In particular,
t he capitaIs tend to move in ao opposite direction to that produ ced by the
d ead load of the Crypt levei itself (Fig . 12,h ). This suggest s that the theoretic
state of funi cular equilibrium is only reach ed at an intermediat e phase during
the construction of the building.
To overcome the construction difficulties, Gaudi could have im agined a design
in which a t rue funi cular equilibrium was not entirely ob t ain ed eith er for the
fi nal configu rat ion of the structure, or t he const ru ction at t he crypt leveI. The
di sturbing cffccts due to imperfect equilibrium would thus be resis ted thanks
to the confinement action of the very stiff vertical elements. The perfect
funicular equilibrium would have beeo reached at a peculiar intermediate
stage of the construction process , being any previous or laHer alteration of
it counteracted by the enlarged capacity and stiffness given to the resisting
vertical elements. This is just an speculative suggestion t o explain how the
architech could have accounted for the inherent d ifficulties of constructing a
system laid-out through a funicular model.
REFERENCES
BARON , F. , (1961)
Matrix Analysis of Structures Curved
In
Space} Journal of tll e Structural
Division ASCE} VoI. 87} N°. ST3.
TOMLOW, J ., (1989)
T he hanging model oí Gaudí and its reconstruction. New information
for the design of the Church of the Güell Colony. In stitut [ür leichte
Flachentragwerke, Universitat Stuttgard ..
CASALS, A., GONZALEZ J. L., (1990)
P. ROCA I Gaudi's "Cripta de la Colonia Giictt"
393
Gaudí and the my stery of the encarnation (t he m ys t.er ics of the Crypt of the
Colonia GÜell ). Rev. Informes de la Construcción , Vo1.92, no. 408, (written
in Spanish).
KWAN , A.K.H. (1991 )
Analysis fo coup led wallj frame st ructures by frame method with shear
deformation allowed. Proc. Inst. oI Civil Ellg., Part II.
GONZALEZ, A., GONZALEZ, J . L. , ROCA, P., CASALS, A. , (1993)
Studies of Gaudi's Cripta de la Colonia GÜell. Pra c. af lABSE Symposium
on StructuraJ Preservatian af th e Architectural Heritagc, Rome.
MOLINS , C., ROCA, P. , MARJ , A. R., (1994 )
Una farmulación matricial generalizada: (f) análisis es tático. R evista In t. de
lvfét odos Numéricos en In g., VoI. lO ) N° A.
MOLINS C., RO CA P., BARBAT , A. H. (1995)
Una formu!ación matricial generalizada: (II ) anál isis dinámico. Revista Int.
de Métodos' Numéricos en Ing, VoI. lI , N°. !.