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Proceedings of the IASS Annual Symposium 2016
“Spatial Structures in the 21st Century”
26–30 September, 2016, Tokyo, Japan
K. Kawaguchi, M. Ohsaki, T. Takeuchi (eds.)
Copyright © 2016 by Pierluigi D’Acunto, Lukas Ingold
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
The Approach of Sergio Musmeci to Structural Folding
Pierluigi D’ACUNTO1*, Lukas INGOLD1
1* ETH Zürich, Institute of Technology in Architecture, Chair of Structural Design
Stefano-Franscini-Platz 5, 8093 Zürich (CH)
dacunto@arch.ethz.ch
Abstract
Thanks to the experimental nature of his work, Sergio Musmeci (1926-1981) holds an exceptional
position within the Italian School of Engineering of the postwar period. Musmeci’s peculiar view on
structural design is supported by the search for novel structural forms, which is initiated by his
exploration on structural folding. In particular, during the 1950s, folded plates are applied by the
engineer in place of the conventional beam and slab typology for the design of various roofs in
reinforced concrete. In this paper, the approach of Musmeci to structural folding is discussed. The
investigation is focused on the folded plate roof of Stabilimento Raffo in Pietrasanta, which is here
regarded as a fundamental moment in the research of the engineer in the field of structural folding. The
design method used by Musmeci for the development of the project is examined in details.
Keywords: Sergio Musmeci, folded plate structures, reinforced concrete, parametric design, postwar Italy
1. Introduction
The development of architecture and engineering in Italy after World War II originates from very
specific conditions. While the rapid economic, technological and social changes trigger the prosperity
of the building industry, resources are still limited. Under these constraints, structural engineering is
strongly affected by the exploration of new typologies, particularly for reinforced concrete (Iori [7]).
The search for structural efficiency leads to the production of various examples of innovative buildings.
This is achieved with the introduction of new construction technologies, like prefabrication and
prestressing, and a plurality of design approaches working according to the principle of resistance
through form (Poretti [16]).
The employment of structural folding, like in the work of Sergio Musmeci, is a result of this process.
One of the most peculiar properties of folded structures is their ability to resist the external applied load
through their form. A folded system has a clear structural logic, which relies on the relationship between
the flow of the forces within the system and its overall geometry. It is because of its inherent potential
that structural folding has been investigated during the 1950s, especially in Italy.
The use of structural folding can be traced in the works of several engineers in postwar Italy. A very
early example is represented by Pier Luigi Nervi’s Padiglione della Magliana in Roma (1945), which is
built using ferrocemento elements with a corrugated shape. A decade later, the folded structure of
Nervi’s Assembly Hall for the UNESCO Headquarters in Paris (1953-58, with Marcel Breuer and
Bernard Zehrfuss), receives significant international attention (Nervi [14]). Structural folding is
subsequently applied by other renowned Italian engineers for the design of churches: Riccardo Morandi
in the Chiesa San Luca in via Gattamelata in Roma (1956, with Studio Passarelli) (Pedio [15]), Aldo
Favini in the Chiesa Sacro Cuore in Ivrea, (1958, with Mario Oliveri and Marcello Nizzoli) (Barazzetta
and Favini [2]) and Michele Pagano in the Chiesa Madre di San Pietro Apostolo in Satriano di Lucania
(1956, with Giulio De Luca) (Gigliotti [4]).
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
2
In this context, one of most consistent explorations on the structural properties of folded plate systems
is due to Sergio Musmeci. His work is encompassed within the theory of minimal structures based on
his life-long research on structural design involving the optimum use of materials (Musmeci [11]).
Folding represents an important topic of investigation for Musmeci, who has employed it on an extended
series of projects, mostly developed at the end of the 1950s (Ingold and Rinke [6]). In fact, these projects
bear witness to the evolution in the concept of structural folding within the design approach of Musmeci.
In the present paper, the analysis is specifically focused on the folded plate roof of Stabilimento Raffo
in Pietrasanta (1956), which is regarded here as an exemplary project that reveals Musmeci’s
understanding of structural folding. The peculiar method used by the engineer for the design of the roof
is discussed in details. In particular, the models employed for the definition of the geometry of the roof
in plan and in elevation are presented.
2. Sergio Musmeci and his Research on Structural Folding
During his early career as a structural engineer, Musmeci applies structural folding in place of the
conventional beam and slab structural typology for the design of several roofs in reinforced concrete.
The series of folded plate roofs by Musmeci includes eight projects (Figure 1), which have been
designed in a time span of twelve years (1954-1966). The evolution of the projects shows an increasing
competence and desire for experimentation by the engineer. In this research on structural folding, three
main phases can be distinguished.
1954 Formia
Scuola Nazionale di Atletica Leggera
1955 Roma
Cinema Araldo (Project)
1956 Pietrasanta
Stabilimento Raffo
1957 Montecchio Maggiore
Cinema San Pietro
1957 Vicenza
Cappella dei Ferrovieri (Project)
1958 Frosinone
Palestra CONI
1959 Roma
Ristorante Stadio del Nuoto
1966 Torino
Teatro Regio
Figure 1: Chronology of the folded plate roofs designed by Sergio Musmeci.
The first phase includes the early design experiments by Musmeci on the structural properties of folding.
The design of the roof of the gymnastic hall of Scuola di Atletica in Formia (1954, with Annibale
Vitellozzi) is the first occasion in which the engineer employs a folded plate structure (Vaccaro [17]).
In order to minimize the use of material on the roof slab and achieve the required static height, the
engineer proposes a solution consisting on a typical accordion-like corrugated slab on a regular
rectangular plan; the fold lines are parallel and oriented along the short side of the rectangle. One year
later, while working on the project of Cinema Araldo in Roma (1955, with Carlo Ammannati), Musmeci
designs a roof composed of a network of equally compressed polygonal arches spanning over a non-
regular dodecagonal plan (Musmeci [9]). Folded plates are used here to fill the fields in-between the
arches and not as the main elements of the load-bearing system of the roof. As a result, the segmented
vault is based on a hierarchical structure made of main struts and secondary panels.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
3
In the second phase, Musmeci introduces a design approach to relate the form of the folded structure to
its static behaviour. The roofs of Stabilimento Raffo in Pietrasanta (1956, with Leo Calini and Eugenio
Montuori) (Musmeci [10]) and of Cinema San Pietro in Montecchio Maggiore (1957, with Sergio
Ortolani) (Morgan [8]) are designed in relation to the distribution of the bending moments within the
structures. This leads to the definition of non-standard geometries, based on polygonal folded patterns.
For the project of Cappella dei Ferrovieri in Vicenza (1957, with Sergio Ortolani and Antonio Cattaneo),
Musmeci proposes a three-dimensional folded plate structure that is equivalent to a three-hinged frame.
In this case, structural folding is not limited only to the roof, but it is applied to the entire load-bearing
structure of the building.
In the third phase, which is associated to the roof of Palestra CONI in Frosinone (1958), the ceiling of
Ristorante del Nuoto in Roma (1959) and the foyer ceiling of Teatro Regio in Torino (1966, with Carlo
Mollino), Musmeci explores the possibility to work with hollowed folded geometries. This is usually
achieved by incorporating the horizontal slab into the folded plate structure. These examples can be
considered as hybrids between folded plate systems and spatial trusses, and directly influence the later
work of the engineer on antiprismatic systems (Musmeci [13]).
3. The Design of the Roof of Stabilimento Raffo in Pietrasanta
The folded plate roof of the marble workshop Raffo in Pietrasanta (1956) is a self-supporting slab on a
rectangular plan of around 1000m2 with a uniform thickness of 10cm (Figure 2). The slab consists of a
folded plate module that is repeated five times along the longitudinal axis of the roof. It is supported by
two rows of six V-shaped pillars each with a maximum span of 12.40m. From a geometric point of view,
the roof of Stabilimento Raffo achieves a higher level of complexity in comparison to the conventional
solution adopted for the Scuola di Atletica a couple of years before. At the same time, the roof is entirely
self-supporting, unlike the one previously designed for Cinema Araldo, which relies on an underlying
network of load-bearing polygonal arches.
Figure 2: Stabilimento Raffo in Pietrasanta (1956), inner view – Source: Musmeci [10], p. 712.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
4
The roof of Stabilimento Raffo has been conceived by Musmeci in line with his belief that in the process
of structural design the form and not the inner stresses should be regarded as the unknown (Musmeci
[12]). As pointed out by the engineer himself, it is not because of its dimensions or any construction
principle adopted that the roof stands out from other contemporary examples of folded plate structures.
On the contrary, the uniqueness of the design solution relies on the ability of the form to express its
static behaviour in an explicit, nearly diagrammatic way. “The roof of Stabilimento Raffo had to be built
quite quickly and above all with a low budget. It had to comply with nothing else but the static
requirements, defined by the free spans that had to be realized. Therefore, it was a good occasion to
make a kind of experiment […]: to see to which extent a thin vault is able to express its statics through
its own form” (Musmeci [10]). The aim of Musmeci is to reach a true integration between structure and
architecture, where the form predominantly argues for its expressiveness through the statics; a form
whose load-bearing behaviour is explicitly communicated to the observer (Brodini [3]). In fact, the roof
has been designed in such a way that the form follows directly the inner forces. As such, the engineer
proposes a specific design interpretation of the common principle of resistance through form and
develops an explicit methodology how to apply it to structural design. Considering the relevance given
by Musmeci to this project, which reflects his peculiar approach to structural design, Stabilimento Raffo
in Pietrasanta marks a fundamental moment in his research in the topic of structural folding.
As already observed in relation to the development of other projects (Adriaenssens [1]), also in the case
of Stabilimento Raffo the engineer makes use of diverse tools and models, both analytical and physical.
Based on the analysis of the documents available at Archivio MAXXI Musmeci e Zanini in Roma, an
overview on the methodology followed by Musmeci for the design of the roof of the marble workshop
is presented in the following sections.
3.1 The Geometry of the Roof in Plan
Of particular interest is the topological study of the folded plate pattern of the roof of Stabilimento Raffo
in plan, developed by Musmeci as a hand sketch (Figure 3). This drawing shows a series of design
variations that share the same support conditions. By changing the position of the nodes as well as the
number and connectivity of the folded edges, the engineer investigates diverse geometric configurations,
which imply different structural behaviours for the distribution of the forces within the roof.
Figure 3: Stabilimento Raffo in Pietrasanta (1956), sketch of design variations of the roof plan by Musmeci
Source: Archivio MAXXI Musmeci e Zanini.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
5
One of the ideas followed by Musmeci for the definition of the general topology of the folded plate
module was to activate in the roof an explicit load-bearing mechanism equivalent to a rigid truss where
the folded edges represent the bars of the truss, loaded either in tension or compression. “In reinforced
concrete the tensile stresses are channelled into the main reinforcement bars, and considering that these
stresses tend to be confined to specific edges, it is natural to try to keep them as straight and continuous
as possible. These edges are the ones that should connect geometrically the different parts of the
structure, likewise a rigid truss. The intuition that along them tensile stresses run contributes to fix the
form of the vault, moving away from any sense of arbitrariness. Compressive stresses have always been
kept in large sections of the slab in order to facilitate their diffusion and, again, with the intention of
expressing this characteristic structural behaviour in the form” (Musmeci [10]).
Among the various tools used by Musmeci, remarkable is the parametric model developed by the
engineer to refine the geometry of the folded plate module, presumably in the mid-stage of the design
process (Figure 4). Grounded on a series of geometric relationship expressed in an analytical form, the
parametric model is analogous to the one set up by the engineer for the design of the roof of Cinema
Araldo (Musmeci [9]). The model is based on a grid, whose nodes are located at the intersection of three
main vertical gridlines parallel to the transversal axis of the roof, and four main horizontal gridlines
parallel to the longitudinal axis. The main vertical gridlines are located at the transversal axes of the V-
shaped pillars and their distances are represented by the constant i, which is set to 10.00m. Secondary
vertical lines whose distances from the main gridlines are i/2 and i/4 are also present. Here various offset
distances from the main and secondary vertical lines are defined with the variables x, y, z and t. In
particular, the values 2y and 2x are used to describe the distances between the two branches of the V-
shaped pillars, at the points where the roof is connected to the supports. The main horizontal gridlines
consist of the two longitudinal axes of the V-shaped pillars and the projections on the ground of the two
overhanging roof edges. The distance between the axes of the V-shaped pillars is described by the
parameter b, which in this parametric model was set to vary between 12.55m and 12.72m. The two
overhang lengths, which are asymmetric, are designated with the variables a and c respectively. An
additional variable u is used to define the distance of two secondary horizontal lines offset from one of
the pillar’ axis and the variable v represents the distance of another secondary horizontal line that is
offset from the other pillar’s axis.
Figure 4: Stabilimento Raffo in Pietrasanta (1956), diagram representing the parameters used by Musmeci to
describe the geometry of the folded plate module of the roof – Source: Archivio MAXXI Musmeci e Zanini.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
6
References to the golden ratio φ, which had been already used by Musmeci in the analytical model of
Cinema Araldo (Musmeci [9]), can be detected in the model. The value of the ratio and its root are noted
by the engineer on the side of the document and they are used to define the upper extreme of the domain
of the parameter b, being 10.00m1.618 12.72m.
Grounded on this set-up, each edge of the folded plate module of the roof is represented by a segment
that connects two nodes of the grid. Based on the constant i, its divisors i/2 and i/4, the eight variables
x, y, z, t, u, v, a and c and the parameter b, a series of relationships on the slopes of the segments have
been established by Musmeci in an analytical form. This has led to the definition of a system of eight
independent equations in eight variables and one parameter (Figure 5). By conveniently reworking the
equations, the variables x, y, z, t can be expressed as functions of u, v, a, b, c and i; by allowing the
parameter b to vary within its domain, the space of the solutions of the system can be explored.
Figure 5: Stabilimento Raffo in Pietrasanta (1956), system of equation used by Musmeci to describe the
geometry of the roof – Source: Archivio MAXXI Musmeci e Zanini.
3.2 The Geometry of the Roof in Space
The diagram of the distribution of the bending moments on the transversal section of the roof (Figure 6)
has been used as a guideline to arrange the folded edges in elevation (Musmeci [10]), with the aim to
achieve a uniform distribution of the bending stresses within the structure. In the diagram, the transversal
section of the roof is represented as a continuous beam on two pin-jointed supports with asymmetric
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
7
overhangs. The position of the supports and the length of the overhangs are related to the previously
described parametric model of the roof in plan.
Figure 6: Stabilimento Raffo in Pietrasanta (1956), Diagram of the maximum bending moments on the
transversal section of the roof – Source: Musmeci [10], p. 710.
The diagram shows the envelope of the bending moments generated by a series of uniformly distributed
vertical loads; in particular, three extrema can be identified, at the supports and nearby the mid-span.
Giving a design interpretation to the principle of resistance through form, the engineer has adjusted the
elevation of the nodes of the folded plate module in relation to the variation of the bending moments
(Figure 7). That is, the distance between the portion of the folded plates under tension and the one under
compression due to bending has been adapted by Musmeci to relate to the magnitude of the bending
moments along the transversal axis of the roof. The cross-section of the folded plate module is higher
at the supports and nearby the mid-span. As a result, the distribution of bending stresses within the
folded plate structure is kept uniform, allowing the engineer to overall minimize the cross-section of the
folded plates and to adopt a slab with the same thickness all over the roof. In fact, this approach could
be regarded as an early example of form-finding based on mathematical models (Ingold and Rinke [5]).
Figure 7: Stabilimento Raffo in Pietrasanta (1956), construction of the transversal section of the roof
Source: Archivio MAXXI Musmeci e Zanini.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
8
Grounded on the geometry of the folded plate module of the roof in plan and the one in elevation
developed through the parametric model, the geometry of the roof in three-dimensions can be derived
(Figure 8). To visualize and control the complex geometry of the roof in space and to test its global
structural behaviour, Musmeci made use of physical models (Figure 9).
Figure 8: Stabilimento Raffo in Pietrasanta (1956), axonometric diagram of the roof constructed from the
parametric models of the roof in plan and elevation.
Figure 9: Stabilimento Raffo in Pietrasanta (1956), physical model of the roof – Source: Musmeci [10], p. 711.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
9
3.3 The Final Geometry of the Roof
By comparing the final plan of the roof of Stabilimento Raffo (Figure 10) to the parametric models
previously described, some minor modifications can be detected. A few design constraints set in the
analytical model have been removed and the reference to the golden ratio has been eventually neglected.
Nevertheless, it can be observed that the layout of the main reinforcement bars of the slab directly
follows the tensile stress lines in the folded plate module. That is, according to the design intentions of
Musmeci, the main tensile stresses of the structure are confined to specific edges of the folded plate
while the main compressive stresses along the other edges are allowed to spread on wide sections of the
slab. Thus, the the form of the roof expresses its static behaviour explicitly.
Figure 10: Stabilimento Raffo in Pietrasanta (1956), final plan of the roof with main reinforcement layout
Source: Musmeci [10], p. 711.
4. A Design Method for Structural Folding
With the project of the roof of Stabilimento Raffo, Musmeci establishes a methodology for the design
of folded plate structures based on the use of analytical and physical models. In his approach, the folded
plate geometry does not follow predefined conventional patterns but it is generated starting from specific
structural considerations, such as the relationship between the section of the structure and the diagram
of the bending moments. In fact, the same method is applied by the engineer to the following projects
related to folded plate structures (Figure 1) and the effects are particularly evident in the case of Cinema
San Pietro in Montecchio Maggiore (1957) and Cappella dei Ferrovieri in Vicenza (1957).
The reinforced concrete structure of the roof of Cinema San Pietro consists of a folded plate module that
is uniformly scaled and arrayed four times along the longitudinal axis of the roof. The module is laterally
supported on a concrete frame structure and its geometry has been constructed in relation to the variation
of the bending moments along the transversal axis. “The choice of the form follows as much as possible
the internal stress pattern; the folds are then deeper at the mid axis of the cinema, where the stiffness
required to resist the global bending moments is maximum” (Morgan [8]). Consequently, as already
observed in the case of Stabilimento Raffo, the main reinforcement bars are located along specific folded
edges and it has not been necessary to disrupt or bend them within the plates to resist shear forces.
Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
10
The structure of Cappella dei Ferrovieri is based on a folded plate module, which works as a three-
hinged frame and is repeated five times along the longitudinal axis of the building to generate an overall
corrugated surface. The geometry of the folded plate module evidently reflects the distribution of the
bending moments along the section of the frame. In fact, the distance between the portion of the folded
plates under tension and the one under compression due to bending reaches its highest value at the frame
corners and it is reduced to the minimum at the mid-span and at the supports.
These three projects are representatives of an exceptional approach on structural folding, which
distinguishes Musmeci among the other engineers of his time. This is especially evident in relation to
the resulting geometries of the folded plate modules emerging out of structural considerations.
5. Conclusions
Following the concept that in the process of structural design the form is the unknown and not the inner
stresses, Sergio Musmeci investigates the properties of structural folding in a series of eight projects
during his early career. Among these, particularly relevant is the roof of Stabilimento Raffo in
Pietrasanta, where the engineer for the first time tries to attain a precise relationship between the form
of the structure and its static behaviour. The analysis of the tools used by Musmeci to define the
geometry of the roof clarifies his methodology, which is based on a parametric design process. At the
same time, it outlines his specific approach to structural folding, which directly influences the
subsequent folded plates projects as well as his lifelong research for new structural forms.
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