The
shell
s uc u es
o
he
Ba oque
F.
~sc i~',
V.
~o n~h',
J.
~jnchez'
&
J.
P.
~alc i cel~
Uni e si y o Se ille, Spain
2
P o esso o S uc u es
o
he Uni e si y
o
LaCo uiia, Spain
Abs ac
The Ba oque has been adi ionally a s yle minimized by i s endency o
deco a ion and i s lack o he sys ema ic. G adually i has le demons a ing ha
his was a p ejudice and ha he a chi ec u al alues we e o i s magni ude,
compa able o he bigges landma ks o classic s yles. As o he s uc u al
aspec s we wan o demons a e ha hey o e come o as much as i was made
p e iously by hei space weal h, hei economy o means and he in elligence o
hei solu ions. Somehow hey ep esen an an eceden o he shell a chi ec u e
ha so much i would make an exhibi ion wi h he Rein o ced Conc e e and he
analy ic echniques o dimensioning. Wi h less means bu wi h g ea in ui ion,
he Ba oque, in en ed o ms o a complexi y ha oday
is
s ill di icul o
unde s and, a leas geome ically. Pa adoxically he e a e no in es iga ions ha
help us o cla i y he s uc u al mi acle o he Ba oque since up o now i has
been in his o ians' hands and no hose o a chi ec s o enginee s. This a icle
ies o open he oad in his unexplo ed ield.
1.
In oduc ion
To speak o shell s uc u es in he ma hema ical and modem sense o he e m, in
designs p e ious o
1900
and in ma e ials di e en o he ein o ced conc e e i
seems an excessi e license.
Howe e , since in he
XIX
cen u y he b ick aul s al eady demons a ed a
good capaci y o adop cap icious o ms in absence o lexions and wi h he b ick
and he mo a like only ma e ials. I is logical o hink ha he cons uc ion o
his shells is p e ious o hei analy ic ools, so p e ious jus i ica ion ha i can
be ex apola ed o he Byzan ine cons uc ion in ha chu ches like Se lio and
Bacchus o S a. So ia, hey ha e been able o be designed like memb anes, wi h
g ea p ecision i we compa e hem wi h he esul s ob ained by Fini e Elemen s.
Howe e he i s p ope ly shells a e no ound un il he Ba oque a chi ec u e,
and no in ac in he I alian whe e a chi ec s like B unelleschi, Miguel ~n~el o
Palladio did g ea achie emen s o o e come he s uc u al challenges o he
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66
S cc al S udi ~, R pam a d Ma n o anc
o
H i ag Aldzi c uw V111
an iqui y. I is la e , when he economy o means ha he XVIII Cen u y
imposed o he cons uc ion, when a g ea quan i y o app en ices, ha we e
o med in
San
Ped o's ac o y, we e dissemina ed by Eu ope o c ea e some
na ional s yles, ich in way, splendid o concep and good s uc u ally.
2.
The
Ba oque
s uc u es
The new gene a ion ha was in I aly, ollowing Miguel Angelo and Bo omini
guidelines, p e e ed o ma e ialize hei s uc u es
in
ne es and complex laces
e y o he medie al s yle. Gua ini (Fig.
1)
o Vi one (Fig. 2) hey go in his
line.
Fig.
l.
S . Lau ence
in
Tu in
by
Gua ino Gua ini
Fig.2. S . Be na dino in Chie i by Vi one
Fig.3. S . Cha les in Vienna Fische on E lach.
Who mo ed o he no h hey p e e ed o s ill use con inuous o ms mo e
complex han he men ioned ne es, al hough masked unde
a
dense o namen al
laye o s uccos and pain ings. Fische on E lach, pa ia ch o all hem, in
Aus ia, he amily Dien zenho e in P ague and Neuman in Ge many a e some
ew ones o among he dozens o a ch ec s ha we could men ion ha , wi h i s
di e ences hey dehca ed o c ea e sugges i e and complex spaces wi h
minimum s uc u es.
Fig.
4.
Selec ion pa s o a sphe e o build he aul s by Geo ge Dien zenho e .
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While Fische was de o ed o explo e he ellip ic spaces (Fig.3) and he
Dien zenho e amily he in e sec ed geome ies
(Fig.
4),
Neuman manages wi h
ease he mos di icul spaces, mix u e o ellipsoids and cylinde s on punc ual
suppo s (Fig.
5).
Zimme man ge s geome ies ha don' ha e ecognisable o ms
(Fig, 6).
Fig.
5.
Type o Neuman Cons uc ion. Fig.6. Zimme man's S einhausen Chu ch.
When we begun he s udy on he s uc u es o he Ba oque, we we e su p ised
by he lack o bibliog aphy and o speci ic s udies.
I
is accen ua ed i in he case
o he Cen al Eu opean Ba oque, in he which, apa analysis made o
consolida ion wo ks and epai o econs uc ion, doesn' exis p ac ically any
esea ch. We excep Jage and C oci al hough hey ha e no in e ened in
pa icula aspec s o shells. I is o i ha we con ibu e he da a ha con inue
wi h in en ion o o open he oad and o demons a e he g ea s uc u al in e es
ha has a ecen ly alued s yle.
The wo k is wide and i will emb ace he di e en ypes o Ba oque
memb ane. Bu a his ime i is logical o begin wi h impo an and e y well-
known monumen s, like hey can be:
Fig.7. Sanc ua y o Kappel. Fig.8.Chu ch o Vie zhenheiling.Fig.
9.
Ne esheim.
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68
S cc al S udi ~, R pam a d Ma n o anc
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H i ag Aldzi c uw V111
1)
Sanc ua y o Kappel nea Waldhsassen o Geo ge Dienzenho e (Fig.
7).
2)
Chu ch o pilg image o S einhausen o Zim ne man (Fig.
6).
3)
F anciscan chu ch o Ve zhenheiling, by Neuman (Fig.
8).
4)
Benedic ine chu ch o Ne esheim, by Neuman (Fig.
9)
In all hese cases we will make he same supposi ions:
a) Fo lack o da a we conside ha he aul s a e buil wi h b icks o h ead
and he e o e wi h a hickness o 0.25
m.
b) The cha ac e is ics o he ab ic a e he ollowing ones:
1.
y=1.7~on/m~
2.
E
=
10
E~
~on/m~ and he ma e ial is elas ic
and
lineal in he
conside ed ange.
3.
U
=
116
c) The aul s a e suppo ed by hinges on he co nices and only he pa upon
hem a e calcula ed s a ing om his le el. I is necessa y o keep in mind ha
he co nices, in he Ba oque, de ine he o m in plan and ha wha he e a e
unde hem is well es ed.
d) The only ac ions ha we will conside hey a e hose o own weigh .
e) The ma hema ical pa e n ha we will use is o conside he medium su ace
o he aul as he geome y o analysis.
)
The me hod used o calcula ion is ha o Fini e Elemen s. The esul ing
g aphics will ep esen he e o s and displacemen s in he conside ed su ace.
3.
Sanc ua y o Kappel in Waldsassen:
by
Geo ge
Dien zenho e
In his case we ha e a es ange unc ional dis ibu ion wi h
a
iangula plan
wi h cu ed sides, acco ding o he geome ic ou line o he Fig.
7.
I has odd
numbe o sides,
wi h
solid walls pe o a ed wi h chapels and s abilizing owe s.
The dome is o med by a sphe e ha in e sec s wi h o he h ee, and he g oup
is suppo ed in all i s con ou . The e a e no mo e pe o a ions han some small
chimneys ha p o ide a so cla i y (Fig. 10).
Fig. 10. In e io o he Sanc ua y o Kappel.
Fig. 1
1.
Scheme o de lec ions.
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I
we calcula e in elas ic condi ion we see:
a) The maximum de lec ions a e, in
h~s
case, o 4.5
mm.
(Fig. 11)
b)
The maximum momen s a e o 0.32 Tonxm in a punc ual case ha is es ed
by he owe s, ha ha e no been conside ed in he calcula ion in
he
p ac ice. In
gene al, in signi ican a eas he maximum momen s a e o 50% o his alue
(Fig. 12).
Fig. 12 Scheme o bending momen s. Fig. 13 P incipal s esses
I
c) The maximum ensions a e, in gene al, smalle han 13 onlm2, al hough,
locally, in a eas ha in ac go ein o ced and ha we ha e no conside ed hey
a i e o
82
~on/m~ (Figs. 13).
This co e , o g ea size and o m, misses i
is
ex ao dina ily e ec i e
whene e hey s ay i s ein o cemen ne es.
4.
Chu ch
o
pilg image
o
S einhausen:
by
Nicholas
Zimme man
The used geome ic pa e n
is
an ellipsoid upon
en
suppo s (Fig. 6). I we
calcula e in elas ic s a e, we ob ain he ollowing conclusions:
a) The maximum de lec ions a e o 0.226 mm. o own weigh
(Fig.
14).
Fig. 14 De lec ions Fig. 15. Bending Momen s.
X
axis.
b)
As o he maximum momen s, excep o due punc ual a eas o he g id o
he ma hema ical pa e n, he maxima a e o 0.13 Tonxm.
in
he a ea
among cylind ical openings
(Fig.
15) o o 0.3 Tonxm. in
he
same
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70
S cc al S udi ~, R pam a d Ma n o anc
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H i ag Aldzi c uw V111
pe o a ions ein o cemen . This is alse in ou case since hey ha e a eas
specially ein o ced by o namen al elemen s. (Fig. 16).
Fig. 16. Dome o he S einhausen chu ch Fig.
l7
and 18 P incipal s esses.
c) As o he ension s esses, you lea e in he Figs.
17
and 18 ha he
9
Ton/m2 doesn' su passed in any poin .
On he whole i means i ha i s ops own weigh and s a ic loads gi e
a
sa e
s a e. This s uc u e canno ha e pa hology and i s design is good.
5.
F anciscan Chu ch
o
Vie zhenheiling:
by
Bal hasa
Neuman
The geome y is ex emely complex and he aul is o med by he in e sec ion
o h ee ellipsoids,
wo
sphe es, wo cylinde s and wen y- wo cylind ical
openings,
in
such a way ha he whole g oup suppo s on wen y- ou poin s
(Fig.
8).
All
he in e sec ions and bo de s a e conside ed mished o by ne es
o 0.5x0.5 m. (Fig.
19
and 20). The analysis e eals beha iou as a shell wi h
e y good esul s ha app oaches o he memb ane s a e, wi h he excep ion o
some poin s.
a)
In
he Fig. 21 a e app ecia ed he displace nen s ha , in he wo s in he
cases, hey don' o e come he
0
.7
mm. in he key
o
he in e sec ion cylinde s.
b)
As o he ension s esses we ha e a widesp ead s a e ha i oscilla es
be ween
3
and
-3
Tonlm2.
In
he in e sec ion ne es we e en ha e 30 ~on/m' o
ac ion s esses (Fig. 22). Fo comp ession s esses, in he kidneys o he domes,
i a i es o 30 Ton/m2 (Fig. 23).
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Fig.
19.
D awing o a longi udinal sec ion.
Fig.
20.
In e nal iew o he shell
Fig
2
1.
Scheme o displacemen s.
c) Fo he bending momen s hey oscilla e among
+/-0.15
Tonxm in he
X
di ec ion (Fig.
24).
Some hing g ea es a e in he ne es in he
Y
di ec ion
(Fig.
25),
al hough inside he accep able ange.
Fig. 22. P incipal Tension s esses
I
Fig. 23. P incipal ension s esses 11.
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72
S cc al S udi ~, R pam a d Ma n o anc
o
H i ag Aldzi c uw V111
Fig. 24. Bending Momen s
X
Fig.
25.
Bending Momen s
Y
6. Benedic ine Chu ch
o
Ne esheim:
by
Bal asa Neuman
The a chi ec u e o his chu ch is ex emely complex and i is one in he mos
complica ed mas e piece in he whole Ba oque (Fig.
9).
He e we ha e he
in e sec ion o se en ellipsoids o di e en size and heigh wi h sphe ical
canyons, in acco dance wi h he geome y o he Fig.
26.
The whole is su p ising
(Fig.
27).
The s uc u al beha iou o he g oup is deduced om he calcula ion
by means o Fini e Elemen s wi h he ollowing esul s:
Fig.
26
Longi udinal sec ion o he Ne esheim Chu ch.
a) In he Fig.
28
a e app ecia ed he displacemen s ha ,
in
he wo s in he
cases, hey don' o e come he 16 mm. in he key o he in e sec ion cylinde s.
b)
As o he ension s esses we ha e a widesp ead s a e ha i oscilla es
be ween
-9
and
3
~onlm~. In he penden i s we e en ha e
60
~on n' o ac ion
s esses (Fig.
29
and 30).
c) Fo he bending momen s hey oscilla e among +/-0.20 Tonxm in he
X
di ec ion (Fig.
3
1).
Some hing g ea es a e in he ne es in he
Y
di ec ion (Fig.
32),
al hough inside he accep able ange. (0.50 Tonxm.).
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Fig.
27
In e nal iew o he Ne esheim
aul s.
NODAL
SOLUI
ON
Fig.
28.
De lec ions scheme.
7.
Conclusions
Al hough i is di icul o es ablish some
conclusions a he p esen s a e o he
esea ch we wan poin on he in e es o his
kind o cons uc ion so li le s udied and so
in e es ing. Ou in e es is o ex end he s udy o all
he
Ba oque p oposals ha
a e so di e en ia ed o o he s yles, de eloped be o e o a e .
Fig.
29.
P incipal es eses
I
Fig.
30.
P incipal es eses
I1
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