Proceedings of the First International Congress on Construction History

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00 the origio of some «whiteoess» carpeotry rules
In the greater part 01' Spain during the Middle Ages
the construction 01' wooden roo1' structures used the
system called par y nudillo (principal and collar
beam), system which, with certain variations, was
also used habitually in Northern Europe.
These wooden structures had already come into use
by the 13th century, reaching their high point around
the 15th century, a1'ter which the tradition went into
decline. By the late 17th century, the los s of this
building tradition had become notable, although roo1's
01' this type were still being built in the 18th century.
The carpenters who executed these structures, and
the works themselves, took the name of the light
colour -white- 01' the wood, once peeled and
sawed, and hence the term «whiteness carpentry».
We do not really know why this building tradition
was lost. In reality, in architecture everything is
subject to the changes in society in general, which
ha ve a direct influence on tastes and the adoption 01'
di1'1'erent styles.
In the case 01'Spanish structural carpentry I believe
that two circumstances combined to cause its
progressive disappearance. On one hand, the absence
of texts or manuscripts describing the technique and,
on the other, the appearance 01' successive
architecture treatises whose illustrations 01' roo1'
framing generally ret1ect the ]egacy 01' the Roman
tradition -the truss and purlin system. This system
became prevalent in a short period of time, in the ]7th
century, both in Spain and in other European
countries.
Angel L. Candelas Gutiérrez
There are onJy three known texts about Spanish
«whiteness carpentry», in which the con1'iguration 01'
these 1'rames is described. All three appeared in the
17th century, by which time the tradition was already
in decline; indeed, López de Arenas notes in his
manuscript that his purpose in writing it was to slow
its 1'alling into disuse and make up 1'or the lack 01'
knowledge 01'it among master carpenters.
The a1'oresaid three texts are the manuscript by Diego
López de Arenas Primera y segunda parte de las reglas
de la carpintería, dated 1623; a part 01' the manuscript
written by Fray Andrés de San Miguel, circa 1640; and
the never published manuscript by Rodrigo ÁJvarez
Breve compendio de la carpintería y tratado de lo
blanco ~. . , also 1'rom the mid-17th century.
It must be borne in mind that the knowledge
required to execute majar structures, many 01' them
involving complex tying systems, was transmitted
orally within the guild, and possibly with the
prohibition 01' such knowledge being revealed to
people outside the trade itsel1', as was the case in other
construction guilds. This 1'act, apart 1'rom the possible
illiteracy 01'the majority of the carpenters, may be the
reason behind the inexistence 01' written texts from
the peak period 01'this carpentry.
In executing these structures the carpenters
1'ollowed a series 01' rules which only carne to light
a1'ter the publication in 1633 01' the text by López de
Arenas.
The interpretation 01' this text has entailed serious
difficulties: it was attempted by researchers 1'rom the
Proceedings of the First International Congress on Construction History, Madrid, 20th-24th January 2003,
ed. S. Huerta, Madrid: I. Juan de Herrera, SEdHC, ETSAM, A. E. Benvenuto, COAM, F. Dragados, 2003.

506 A. L. Candelas
field of history, i.e. M. Gómez Moreno, and from the
engineering and mathematical fields, i.e. Prieto
Vives, but it was not truly understood until the 80s,
based on research by E. Nuere.
Now, drawing on E. Nuere's findings, we can
finally interpret with absolute correction the variety
of geometric constructions and the meaning of the
text in the above treatises.
This article is intended to take things a step
further, attempting to understand how the
carpenters could arri ve at so me of the rules that
appear in the treatises, which, while not the fruit of
accident, nor did they correspond, evidently, to the
application of a scientific or mathematical knowledge
that the carpenters of the guild could hardly have
possessed.
Very little is known about the way in which the
rules used in framing carpentry came into being: the
treatises simply explain them, and we still lack
sufficient information regarding the frames built over
the centuries to answer this question. lt would seem
logical that the carpenters arrived at these rules after
a long evolutionary process in which they would have
tried out numerous possibilities; then they would
have stuck with those that combined correct structural
behaviour with easy application.
L/3
Specifically, 1 shall refer to the origin of two of the
many questions that appear in the treatises: on the one
hand, the possible origin of a basic rule in the
structural configuration: the position of the collar
beam and, on the other hand, that of a geometric
construction used to obtain the hip section.
In the first case we shall see, based upon structural
verifications, that the rule results from the
combination of an appropriate structural behaviour
with ease of construction.
In the second case, we shall see that the geometric
solution, in principIe complex, is the result of the
interpretation of certain circumstances that the
carpenters were able to observe in the construction
itself.
HVPOTHESIS ON THE ORIGIN OF THE RULES
FOR DETERMINING THE POSITIONING AND LENGTH
OF THE COLLAR BEAM
In traditional Spanish carpentry the most common
position of the collar beam is at a third of the height,
with which the roof projection generates lengths of a
third of the span of the faces and another third in the
centre ---called the almizate.
t0
""
I
L/3
L
L/3
Figure 1
Most common geometric scheme in Spanish par vnudillo frames, similar to that described in the Treatises

On !he origin of some «whiteness» carpentry rules 507
In the cited treatises, all three authors indicate this
position, although in exceptional circumstances, such
as those related 10 ornamentation, other arrangements
do occur.
On the other hand, the most common roof pitch is
36° -arrived at by dividing the semicircumference
by 5- in keeping with the procedures used for the
execution. Figure l shows schematically the
simplified section of a hypothetical frame designed
according 10 this rule.
First we let us look at questions of structural
performance. In order to simulate the possible
evolutionary process I have analysed the mechanical
behaviour of structures with different placements of
the collar beam, trying out those placements which
most likely would have been used, and which come of
a simple division of the length of the principal. Thus,
1 have taken into account the position of the collar
beam at a third of the height -the most common- at
half height and at the upper fourth of the principal.
Figure 2 shows the diagrams of bending moments
and axial stress associated with these configurations.
Without the need for more exhaustive calculations, any
reader with a mini mal technical background will be
able to understand from these diagrams that the solution
of the collar beam at a third is that which results in the
most appropriate stress distribution. After observing the
real behaviour of other solutions, the carpenters would
have arrived at this very same conclusion.
Figure 2
Diagrams of bending moments and axial stress in par y
nudillo frames with different collar beam lengths (1/2 ]/4
and 1/3 of the width)
Nonetheless, the formal characterisation of most of
the constructions does not lie exclusively in correct
structural behaviour. Without doubt other added
circumstances must have come into play for this
solution to have prevailed. Here is where the need to
attain a regular arrangement comes in, both as an
aesthetic recourse widely used throughout history and
for the introduction of the ornamental/acería. 1
In fact, in the sizing and distribution of the rafters
within the frame the rule of thumb was to separate the
rafters by a distance equivalent two times the
thickness of the principal. On the other hand, that
thickness was obtained precisely by dividing the
width of the bay to be covered by a multiple of 3. The
thickness thus obtained became the unit of measure
used in the construction of the frame.
The plane formed by the collar beams -the
a/mizate- is also where the rich and complex
polygonal pattern of lacería characteristic of the
Mudejar construction was habitually incorporated.
The ¡atter requires the existence of a regular
arrangement that serves as a base for the geometric
development of the ornamentation.
Evidently this regularity can be achieved in many
ways, but the one used in Spanish framing carpentry,
and referred to in the treatises, based on the use of
dimensions multiples or submultiples of 3, has the
advantage of easy application without the need to
make calculations, complex auxiliary constructions,
or even plans.
Indeed, the procedure described in the treatises
combines correct structural behaviour with ease of
construction. The set of the rules cited leads to the
regular lines of the a/mizate, capable, on the other
hand, of absorbing the horizontalloads on the frame,
and providing the basis for laying out the tieso
On the basis of the above, 1 believe that the origin
of the rules for the location of the collar beam and
determination of the thickness of the timbers is
perfectly in accordance with structural and formal
circumstances. Indeed, in Spain, a system was
consolidated in which two highly positive factors
came together: on one hand, the great stability of the
frames and, on the other, having found from a very
early date an ornamentation process which offered
great variety and richness without altering the basic
structural system.2

508 A. L. Candelas
HVPOTHESIS ON THE ORIGIN OF THE GEOMETRIC
CONSTRUCTION USED 'f0 OB'fAIN 'fHE HIP SECTION
The other rule I shall address is that which served to
obtain the cross-section of the «moamar» hips.
By way of introduction I should refer to a feature
that distinguishes Spanish framing carpentry from
that of other countries. The habitual procedure in
almost all cultures for building a roof of various faces
is fit a sloped timber on the edge delimiting one
section from another -the hipo In Spain, in addition
to this procedure another more refined one was
employed, placing a hip on each of the planes that
made up the roofs, thus on the edge there appear two
adjacent hips. This is what is called the «moamar»
hip, and it is associated with the prefabrication of the
roof planes on the ground and the subsequent fitting
of the completely finished spans. Although this is not
the subject of this article, it may be said that it is one
of the first examples of large-scale prefabrication in
the history of construction.
In the definition of the moamar hips, the whiteness
carpenters achieved great subtlety and perfection,
seeking the correct visual effect. In fact, if we build
the hips with rectangular-section timbers, observing
the area between them we see that the inner faces of
the hips are not paralleJ, due to different sJopes of the
spans. Our impression is that they are angled inwards
Figure 3
Spanish «par y nudi11o» roof frame. Note the double
moamar hips in the foreground
with respect to the fictitious plane formed by the inner
edges of the hips. In order to correct this effect, a
trapezoidaJ hip section, known as a campaneo,
emerged. The three writers explain how to obtain this
trapezoidaJ section in moamar hips. The construction
method following is from R. Álvarez:
De como haras la esquadra De limas fairas. . Para
Sacar la esquadra De lineas fairas se a de tomar un
pedazo de madero labrado al marco, que hu viere de Y r
la madera para la tal obra. Y hecharas en tal pedazo De
madero un trazo con la caveza De la Planta Pitagorica,
que los Arquitectos llaman Cartabon de aquatro, en el
ancho o tabla; Y echaras otro trazo con la caveza del
cartabon De Armadura que junte con el de aquatro, Y
luego Daras la Buelta al madero por el canto, y adonde
fenezen los trazos que Y ciste en elaz que fueron a
parar al canto hecharleas Dos trazos con la cola del
alvanecar a que Armaren la tal obra, ora sea cuadrada,
ora ochavada: y el claro o cantidad que ay de cola a
cola del alvanecar la tomaras en un compas, y por la
esquina del madero pondras la tal medida poniendo la
una Punta del conpas en trazo quadrado y con la otra
aras un Punto adonde llegare que sera entre el trazo de
la caveza De la Armadura y el quadrado, y este viage
que haze este trazo Con la esquina Del madero es la
esquadra de lineas fairas como lo Muestra su figura. La
letra A. corte quadrado la B. caveza de armadura la C.
yD. las colas del alvanecar la E. el des vio de las dos
colas la F la horma de la esquadra. (Álvarez, R. 16??,
39v- 40).3
The procedure that Rodrigo Álvarez describes in
this text is similar to that empJoyed by López de
Arenas, although better. Arenas obtains the amount
by which the upper part of the hip must be widened.
Álvarez, empJoying the same procedure, constructs a
special square for this purpose.
The aim here is that, once the structure has been
executed, the inner faces should be parallel, which
can be achieved with a number of systems. But if we
also want symmetry with respect to the diagonaJ of
the building, the only possibility is that the inner
faces, once fitted, should be vertical. That is what is
achieved, with absolute geometric perfection,
following the process described by the three authors.
Rere I will not go into the interpretation of
geometric construction resulting from the cited
paragraph, question which, on the other hand, was
addressed by Nuere (\985), though using the
description by López de Arenas.

On the origin of some «whiteness» carpentry mIes 509
Once this interpretation is known, it is relatively
easy to achieve the arrangement described in the
treatises, but what is not so evident is how the
carpenters arrived at this rule. Researching this
question, I have formulated a hypothesis based on the
geometry that the carpenters could observe in their
first attempts to achieve paral!el inner faces on the
moamar hips.
Figure 4 shows the how a moamar hip joins the
first principal of the structure. The left-hand image
shows a rectangular-section hip and, at the right is the
trapezoidal section sought by the carpenters.
In my opinion, some carpenter must have realised
that in order to achieve vertical inner hip faces he had
draw the lines from the edge of the joint between hip
and principal with a cabeza de la armadura4
With this line, they could then draw on the face of
the principal the sloped section of the hip they wanted
to use, as we can see at the left of figure 4. However,
what they needed was the straight section of such a
hipo Nowadays this question might seem to have a
simple solution; in reality it is no more than the
folding of a section over aplane. But at the time they
did not even work with plans, nar did they have
knowledge of descriptive geometry and, as occurred
in the formulation of other rules, they had to use the
construction elements themselves as a basis for
measurements and work processes.
I imagine that what some clever carpenter would
have observed would be something similar to that
shown in figure 5, where we see a plan view of the
joining of a principal and a hip (next to which is the
projection of the joining of a hip and principal).
Effectively, the carpenter, standing on the trame,
could see that in the sloped section the added distance
A-B could be obtained with «Cartabon de aquatro, en
el ancho o tabla; y echaras otro trazo con la caveza del
cartabon De Armadura que junte con el de aquatro».'
And he might also realise that drawing two lines
paral!el to the face of the hip -achieved with the
angle defined by the set square known as an
albanecar- he could obtain the real dimension of the
upper face of the hipo
Al! that remai ns is to calculate the distance
between the two lines B-D in order to obtain the
thickness of the timber from which he had to start in
order to then cut the sloped face, and hence be able to
prefabricate the hip with absolute precision before
fitting.
On the other hand, Rodrigo Álvarez (l6??)
includes in chapter 43, dedicated to obtaining the
campaneo of the hip, two drawings (fig. 6). The first
Mork with
"cabezo de armadura". See note 4.
/
-------
/" --..
/' '-.
/ '- "- "\\\\I
I
/
I
I
I
I
\\\\\
"- '-
Figure 4
Joining of a moamar hip to the first principal of the structure. using straight-section timhers (left) and with the sought-aftcr
trapezoidal section
(right).

510 A. L. Candelas
A. -"Cabezo de armadura"
.~:Uc
Hip projected section
.!
~-
Figure 5
Plan view of the joint between hip and principal
is the graphic construction of the process he describes
in the text cited above and to which the author himself
refers. The text does not mention the dotted line
which, as a second drawing, appears under the
previous construction. That aroused my curiosity;
convinced that this line must be in some way related
to the campaneo of the hips, 1 did a series of
geometric verifications based on the original
Figure 6
Drawings that appear in chapter 43 of the manuscript by
R. Álvarez
manuscript and found that the angles formed between
the lines in the drawing are precisely the angles, acute
and obtuse, (fig. 7), that Álvarez obtains for the
campaneo of the hip in the first drawing.
Thus, 1 believe that what Álvarez intended with the
dotted line in the drawing in chapter 43 of his
manuscript is a tool, a square, which would be built
for each frame, with objective of facilitating the
Tool
to obtain hip trapezoidal section
"Moamar" hip with trapezoidal section
Figure 7
Interpretation of the lower drawing in figure 6: the dotted line drawn by R. Álvarez in chapter 43 could be a square for
aligning the campaneo of hips. The angles of the dotted line coincide with those which define the bell in the upper figure. Jt
is, therefore, a tool

On the origin of some «whiteness» carpentry rules 511
execution of the hip section. This square wou]d be
p]aced at regular interva]s to verify and obtain the
uniformity of the section throughout the piece.
Perhaps it is to this that Á]varez refers when, at the
margin of the drawing, he writes: «this Zine forms the
square // and here the form».
Or comparative purposes, ]wanted to reproduce
the geometric construction which for the same
objective -obtaining the campaneo of the hip--
López de Arenas includes in his manuscript of ]6] 9
(fig. 8). Expressing himself in different terms and
with a different graphic representation, he obtained
c..] ~.
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'1J..C1~tLS1r
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rf
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it ~J '. ~! ''3./ (
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Figure 8
Construction by López de Arenas (1619) for obtaining the
campaneo 01' the
hipo
Page 7v 01' the manuscript
the same hip dimension as in the cited text
by
Rodrigo
Álvarez.
These differences in expression ]ead me to think
that Álvarez did not come to know this process
through the texts
by
López de Arenas, and that he had
certain experience in the execution of frames with
moamar hips, This fact, a]ong with other similar
verifications, demonstrate the origina]ity of the text
by
Álvarez, a]though it includes fragments of text
copied literally from the treatise
by
López de Arenas.
NOTES
1. The Spanish word for geometrical decoration of straight
lines forming intersecting polygons and star shapes.
Tnherited as a decorative motif from Moorish sources, it
was much used by Mudéjar craftsmen in Spain and
Portuga1.
This situation is rather unique in European carpcntry.
The greater pitch of the roofs in central Europe,
determined by c1imatic conditions, leads to significant
stability problems, and thus the great variety
constructional arrangements that appeared outside
Spain. Spanish carpenters were able lo dedicate their
efforts to perfecting the symbiosis between structure
and ornamentation.
This text is difficult lo understand in Spanish, both for
the terminology and the syntax. Tt is thus practically
untranslatable.
Drafting instrument: set square with an angle equal to
the pitch of the roof.
Which might be translated as: «Mark a 90° line on the
thickness. and another with slope of the trame»: the
resulting triangle is the increase in section of the hip
projected on the principal»,
2.
3.
4.
5.
REFERENCE LIST
Álvarez, Rodrigo. 16'?'?, Breve compendio de la carpinteria
ytratado de lo blanco, con algunas cosas tocantes a la
lometria ypuntas del compás, Salamanca. Manuscrito
n° 557 dc la biblioteca de la fundación Lázaro Galdeano
de Madrid.
Candelas Gutiérrez, A. L. 2000. Carpintería de armar
medieval. La construcciÓn medieval. Sevilla: Universidad
de Sevilla.
Nuere Matauco. E. 1985: La carpil1lería de lo blanco.
Lectura dibujada del primer manuscrito de LÓpez de
Arenas, Madrid: Ministerio de Cultura,
Nuere Matauco, E.
1990:
La carpintería de lazo: lectura

512 A. L. Candelas
dibujada del manuscrito de Fray Andrés de San Miguel.
Málaga: Colegio Oficial de Arquitectos de Andalucía
Oriental.
Nuere Matauco, E. 2000. La carpintería de armar española.
Madrid: Munilla.
Nuere Matauco, E. 200 l. Nuevo tratado de la carpintería de
lo blanco. . . Madrid: Munilla
Segura de la A1cuña, Andrés. (Fray Andrés de San Miguel).
h. 1640: Manuscrito sin título.
López de Arenas, Diego. [1619] 1966. Primera y segunda
parte de las reglas de carpintería, fecho por Diego López
de
Arenas
en
este año de MDCXVJJJ.. Edición facsímil
del primer manuscrito con introducción y glosario técnico
por Manuel Gómez Moreno. Madrid: Instituto de
Valencia de Don Juan.
López de Arenas, Diego. [1633] 1982. Breve Compendio de
la Carpintería de lo Blanco y Tratado de Alarifes, . . . , y
otras cosas tocantes a la ieometria y puntas del compas.
Edición facsímil de 1a primera edición de Sevilla de Luis
Estupiñán, prólogo de Enrique Nuere. Valencia: Albatros.
Yeomans. D. T. (1992): The trussed roof lts history and
development. Hampshire: Scolar Press.