DR PATRICIA BENITEZ University of Nebrija - ucd.ie · 1708 Portor y Castro Martínez de Aranda...

09.05DR PATRICIA BENITEZ

University of Nebrija

The late Gothic helical staircase:Geometry & widespread use

Colegio Mayor Arzobispo Fonseca. Salamanca.

HELICAL STAIRCASE

wide variety of geometrical designs

Colegio Mayor Arzobispo Fonseca. Salamanca.

THE LATE GOTHIC HELICAL STAIRCASE

GEOMETRY &WIDESPREAD USE

INTRODUCTION OVERVIEW EARLY TREATISES REAL HELICAL STAIRS COMPARATIVE ANALISIS RESULTS CONCLUSIONS FUTURE RESEARCH DISSEMINATION

On the basis of the following objective criteria:

COMFORT, SAFETY AND WORK ECONOMY(ease of construction and financial cost)

OBJECTIVE

HOW THE GEOMETRICAL DESIGN

used to solve the inner aperture

COULD IMPACT ON THEIR WIDESPREAD




HELICAL STAIRCASE OVERVIEW

DefinitionTerminology

Origin and evolution

Structural aspects

Comfort/safety

Constructive aspects




Palacio Real de Olite (Navarra)Fuente: Tripadvisor

HELICAL STAIRCASE

wide variety of geometrical designs

Santa María de Bonaval (Guadalajara)Fuente: P. Benítez

Helical staircaseevolution of the

spiral staircase




Castle of the Cabrera island. (Mallorca)Fuente: repasosayer.com

• Natural light to illuminate the space

• Improve the movement of people

BENEFITS




FUNDAMENTALS GOTHIC ARCHITECTURE

• Standarized techniques

• Ease of construction

• Search for space-saving designs

Monastery in Tomar (Portugal) Fuente: santillan3.blogspot.ie

Chambord Castle (France)Architect: Leonardo da Vinci?

Fuente: sunsurfer




Caernarfon castle (Wales)Fuente: Flickr

Castle Nuovo (Italy)Fuente: i.pinimg.com

Catedral de SalamancaFuente: P.Benítez

STEP

PED

SO

FFIT

SMO

OTH

HEL

ICAL

SO

FFIT

FLU

TED

HEL

ICAL

SO

FFIT




Louvre Museum (France) Architect: Ieoh Ming 1989 Fuente: dreamstime.com

Vatican Museum (Italy). Architect: Giuseppe Momo 1932

Fuente: civitavecchia.portmobility.it




SEGOVIA

Villacastín

Martín MiguelParadinas

Martín Muñoz de las Posadas

Valverde del Majano

SEGOVIAVillacastín

THEORETICAL FRAME WORK

Time PeriodLate Gothics.XV-s.XVI

MorphologyOne-piece stepCircular case

Geographical areaCiudad y Tierra de Segovia

Segovia Cathedral Salamanca Cathedral Gothic expansion




1708Portor y Castro

Martínez de Arandac.1600

Vandelvira c.1580

1639San Nicolás

Gelabert1653

Tosca1712

1678Caramuel

1747García Berruguilla

Bails1783Gil de Hontañón

c.1580

Guardiac.1600

EARLY SPANISH TREATISES ANALISED




EARLY SPANISH TREATISESData sheets




Church Ntra. Sra. De la AsunciónValverde del Majano

Church San BartoloméMartín Miguel

Cathedral Ntra. Sra. De la Asunción y de S. FrutosSegovia

Monastery Santa Cruz la RealSegovia

Church S. SebastiánVillacastín

REAL HELICAL STAIRCASES ANALYSEDSacred buildings

Villacastín

Valverde del Majano

Martín Miguel




REAL HELICAL STAIRCASESData sheets




REPRESENTATIVE APPROACHES

Caracol de mallorcaA. Vandelvira

Caracol de “gradas torcidas”San Nicolás

Caracol de Santa Cruz




GENERAL CLASSIFICATION

ACCORDING THE GEOMETRICAL DESIGN

EMPLOYED TO SOLVE THE CENTRAL APERTURE

RADIAL NON RADIAL TANGENT

NON RADIALMiddle-way solutionRiser crosses the hollow

RADIALCircular-sector stepRiser = staircase radius

TANGENT Fan-shaped stepRiser tangent to the hollowRiser length > case radius




RADIAL SOLUTION

Caracol de mallorcaA. Vandelvira

First helical staircase in the Iberian PeninsulaPere Compte (1482-1498)

The most commonly used layout




TANGENT SOLUTION

Monastery of Santa Cruz la Real (Segovia)Juan Guas (1484-1492)

Fuente: P. Benítez

• Quite unusual design

• Not included in any spanish stonemasonrytexts




NON RADIAL SOLUTION

• Quite unusual design

• Included in Arte y vso de Architectvra

(Fray Lorenzo de San Nicolás, 1639)




COMPARATIVE ANALYSIS

MAIN PARAMETERS OF THE TREAD

Staircase diameter 180cm Number of steps per rotation 14Turning direction anticlockwise

Central aperture diameter20cm / 25cm / 30cm / 35cm / 40cm

Fixed parameters




COMPARATIVE ANALYSISMEASUREMENT

Geometrical parameters affected bythe soluction adopted which impact

the movement and economy:

Tread- area (nominal & effective)

Tread- length (nominal & effective)Tread- depth (nominal)

Volume- of the smallest square block




CASES DEPENDING OF THE LOCATION OF THE WALKING LINE

AuIII

radio

AuIV

radio25.00

AuI

radio

AuII

radio25.00 15.00 15.00

radio radio

AuI

25.00radio radio

25.00

AuIII AuIVAuII

15.00 15.00

AREA ÚTIL I

HU

ELL

AR

AD

IAL

HU

ELL

ATA

NG

EN

CIA

L

10.00 10.00

10.00 10.00

AREA ÚTIL II AREA ÚTIL III AREA ÚTIL IV

HU

ELL

AN

O R

AD

IAL

AuI

radio

AuII

radio

AuIII

radio

AuIV

radio

10.00 10.00

25.00 15.00 15.00 25.00

At

radio

AREA TOTAL

At

At

RAD

IAL

TAN

GEN

TN

ON

RAD

IAL

TOTAL AREA EFFECTIVE AREA I EFFECTIVE AREA II EFFECTIVE AREA III

EFFECTIVE ARE IV




1680%1700%1720%1740%1760%1780%1800%1820%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%

Diámetro%ojo%interior%(cm)%

Variación%Área%total%%

solución%radial%

solución%no%radial%

solución%tangencial%

Nominal Area

Central hollow (cm)




760,00%

780,00%

800,00%

820,00%

840,00%

860,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%II%%

solución%radial%



1620%1640%1660%1680%1700%1720%1740%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%I%%

solución%radial%



0,00%

200,00%

400,00%

600,00%

800,00%

1000,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%IV%%

solución%radial%



1450,00%

1500,00%

1550,00%

1600,00%

1650,00%

1700,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%III%%

solución%radial%



760,00%

780,00%

800,00%

820,00%

840,00%

860,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%II%%

solución%radial%



1620%1640%1660%1680%1700%1720%1740%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%I%%

solución%radial%



0,00%

200,00%

400,00%

600,00%

800,00%

1000,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%IV%%

solución%radial%



1450,00%

1500,00%

1550,00%

1600,00%

1650,00%

1700,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Área%%(cm

2)%


Variación%Área%ú5l%III%%

solución%radial%



Effective Area I

Inner apperture diameter (cm)

Effective Area II

Effective Area III

Effective Area IV

Central hollow (cm)

Central hollow (cm)

Central hollow(cm)

Central hollow (cm)




0,00#

20,00#

40,00#

60,00#

80,00#

100,00#

20,00# 25,00# 30,00# 35,00# 40,00#

Longitu

d)(cm))

Diámetro)ojo)interior)(cm))

Variación)Longitud)total)))

solución#radial#

solución#no#radial#

solución#tangencial#

Nominal length

Central hollow (cm)

Leng

th(c

m)




64,00%66,00%68,00%70,00%72,00%74,00%76,00%78,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)I))

solución%radial%



42,00%43,00%44,00%45,00%46,00%47,00%48,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)II))

solución%radial%



0,00%

20,00%

40,00%

60,00%

80,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)III))

solución%radial%



0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)IV))

solución%radial%



64,00%66,00%68,00%70,00%72,00%74,00%76,00%78,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)I))

solución%radial%



42,00%43,00%44,00%45,00%46,00%47,00%48,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)II))

solución%radial%



0,00%

20,00%

40,00%

60,00%

80,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)III))

solución%radial%



0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

20,00% 25,00% 30,00% 35,00% 40,00%

Longitu

d)(cm))


Variación)Longitud)ú7l)IV))

solución%radial%



Effective length I

Effective length II

Effective length III

Effective length IV

Central hollow (cm)

Central hollow (cm)

Central hollow (cm)

Central hollow (cm)

Leng

th(c

m)

Leng

th(c

m)

Leng

th(c

m)

Leng

th(c

m)




0,00#

50,00#

100,00#

150,00#

200,00#

250,00#

20,00# 25,00# 30,00# 35,00# 40,00#

Perím

etro((cm)(

Diámetro(ojo(interior((cm)(

Variación(Perímetro(total((

solución#radial#

solución#no#radial#

solución#tangencial#

Nominal perimeter

Central hollow (cm)

Perim

eter

(cm

)




175,00&180,00&185,00&190,00&195,00&200,00&205,00&210,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(I((

solución&radial&

solución&no&radial&

solución&tangencial&

120,00&

125,00&

130,00&

135,00&

140,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(II((

solución&radial&



150,00&

160,00&

170,00&

180,00&

190,00&

200,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(III((

solución&radial&



0,00&20,00&40,00&60,00&80,00&

100,00&120,00&140,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(IV((

solución&radial&



175,00&180,00&185,00&190,00&195,00&200,00&205,00&210,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(I((

solución&radial&



120,00&

125,00&

130,00&

135,00&

140,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(II((

solución&radial&



150,00&

160,00&

170,00&

180,00&

190,00&

200,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(III((

solución&radial&



0,00&20,00&40,00&60,00&80,00&

100,00&120,00&140,00&

20,00& 25,00& 30,00& 35,00& 40,00&

Perím

etro((cm)(


Variación(Perímetro(ú5l(IV((

solución&radial&



Effective perimeter I

Central hollow (cm)

Perim

eter

(cm

)

Central hollow (cm)

Perim

eter

(cm

)

Central hollow (cm)

Perim

eter

(cm

)

Central hollow (cm)

Perim

eter

(cm

)

Effective perimeter III

Effective perimeter II Effective perimeter IV




Ø"20cm Ø"40cm Ø"20cm Ø"40cm≈ ≈ Nominal"tread"area ≈ ≈≈ 37% Effective"tread"area ≈ 36%

10% 21% Tread"perimeter 7% 13%10% 25% Nominal"width"of"run 15% 14%7% 10320% Effective"width"of"run" 233% 3310%12% 28% Minimum"stone"block 35% 52%

Central"hollow Central"hollow

NON RADIAL in relation to

RADIAL

TANGENTin relation to

RADIAL

COMPARATIVE ANALYSISresults




Ø"20cm Ø"40cmNominal"tread"area ≈ ≈Effective"tread"area ≈ ≈Tread"perimeter 3% 7%

Nominal"width"of"run >5% 13%Effective"width"of"run" 5% 11%Minimum"stone"block >18% >16%

Central"hollow

TANGENT-NON RADIAL

COMPARATIVE ANALYSISresults




REASON OF UNEVEN WIDESPREAD OF DIFFERENT LAYOUTS

WORK ECONOMY(ease of construction and financial cost)

RADIAL SOLUTION = MOST FRECUENT.




FUTURE REASEARCH

ü IDENTIFICATION & ANALYSIS OF WIDESPREAD PATHS Extend the research to other geografical areas

ü IDENTIFICATION & ANALYSIS OF THE DIFFERENT STAGES OF EVOLUTIONExtend the research to other time periods

ü CLASIFICATION IN SUBGROUPSThe research extension would confirm the broad types classification

as well as determine possible subgroups

ü IDENTIFICATION OF SCHOOL / MASTERStudy of the different features in order to attribute to certain school/master




FUTURE RESEARCHResearch tools

ü CREATION OF A DATABASE OPEN TO GENERAL PUBLIC PARTICIPATIONEasy location & identificaction of different samples

ü CRETATION OF A STAIRCASES INVENTORYFill in a data-sheet for every stair analyzed




CAMDEM FORT

Fuente:/www.camdenfortmeagher.ie




BIRR CASTLE

Fuente: pinterest.com.au




BALLYHANNON CASTLE (1490)

Fuente: pinterest.ie




NEXUS NETWORK JOURNALPeer-reviewed journal indexed in Journal Citation Reports (JCR) & other databases

The tangent solution to the late gothic helical staircase: a justified oblivion

INDEXED JOURNAL




VIII CONGRESO NACIONAL DE HISTORIA DE LA CONSTRUCCIÓNMadrid (Spain), october 2013Diseño y construcción del caracol de mallorca de la iglesia delmonasterio de Santa Cruz la Real (Segovia)

INTERNACIONAL CONFERENCE ON PRESERVATION, MAINTENANCEAND REHABILITATION OF HISTORIC BUILDINGS

Tomar (Portugal), march 2014From spiral to helical stairs: Santa Cruz la Real and Santiago Apóstolapproaches

CONGRESSES




I CONGRESO INTERNACIONAL HISPANOAMERICANO yIX CONGRESO NACIONAL DE HISTORIA DE LA CONSTRUCCIÓN

Segovia (Spain), october 2015Diseño y construcción del caracol de mallorca de la iglesia delmonasterio de Santa Cruz la Real (Segovia)

II CONGRESO INTERNACIONAL HISPANOAMERICANO yX CONGRESO NACIONAL DE HISTORIA DE LA CONSTRUCCIÓN

San Sebastián (Spain), october 2017From spiral to helical stairs: Santa Cruz la Real and Santiago Apóstolapproaches

CONGRESSES




Thank youDR PATRICIA BENITEZ

University of Nebrija

DR PATRICIA BENITEZ University of Nebrija - ucd.ie · 1708 Portor y Castro Martínez de Aranda...

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