Structural Folding as a Source of Research for Sergio Musmeci

Abstract

At the beginning of his career, the Italian engineer Sergio Musmeci (1926-1981) experimented widely with folded plate structures. Through the design of a series of reinforce concrete roofs, developed within a short time span (1954-1959), Musmeci exemplified his peculiar approach to structural folding by interpreting the principle of resistance through form in an exceptional manner. In his different folded plate designs, he aimed to embody the very nature of the structure by expressing directly its static behaviour through the form. In this way, his experiments and structural conceptions represented a unique position in the context of the Italian architecture and engineering in the postwar period. The work of Musmeci on structural folding led the way to his further search for novel structural forms, which eventually branched out into two independent lines of investigation. On the one hand, his research on the potential of double-curved surfaces for large-span halls and bridge designs; on the other hand, the exploration on spatial lattices, based on the organization of prismatic and anti-prismatic elements in space. As suggested in this paper, the elementary principles at the base of both research branches can be traced already in his folded plate projects.

Full text

Proceedings of the IASS Annual Symposium 2017
“Interfaces: architecture.engineering.science”
25 - 28th September, 2017, Hamburg, Germany
Annette Bögle, Manfred Grohmann (eds.)
Copyright © 2017 by Lukas Ingold and Pierluigi D’Acunto
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Structural Folding as a Source of Research for Sergio Musmeci
Lukas INGOLD*, Pierluigi D’ACUNTOa
*ETH Zürich, Chair of Structural Design
Stefano-Franscini-Platz 1, 8093 Zürich, Switzerland
ingold@arch.ethz.ch
a ETH Zürich, Chair of Structural Design
Abstract
At the beginning of his career, the Italian engineer Sergio Musmeci (1926-1981) experimented widely
with folded plate structures. Through the design of a series of reinforce concrete roofs, developed
within a short time span (1954-1959), Musmeci exemplified his peculiar approach to structural folding
by interpreting the principle of resistance through form in an exceptional manner. In his different
folded plate designs, he aimed to embody the very nature of the structure by expressing directly its
static behaviour through the form. In this way, his experiments and structural conceptions represented
a unique position in the context of the Italian architecture and engineering in the postwar period. The
work of Musmeci on structural folding led the way to his further search for novel structural forms,
which eventually branched out into two independent lines of investigation. On the one hand, his
research on the potential of double-curved surfaces for large-span halls and bridge designs; on the
other hand, the exploration on spatial lattices, based on the organization of prismatic and anti-
prismatic elements in space. As suggested in this paper, the elementary principles at the base of both
research branches can be traced already in his folded plate projects.
Keywords: Construction history, Sergio Musmeci, postwar Italy, reinforced concrete, folded plate structures, shells, double-
curved surfaces, spatial lattice structures, polyhedra
1. Introduction
The interests of Sergio Musmeci (1926-1981) in mathematical sciences and his broad understanding in
building mechanics originated already from his education. Musmeci graduated in civil engineering in
1948 and aeronautic engineering in 1953 (Capanna [2]). Furthermore, in his early professional career
he had the opportunity to collaborate with the most influential protagonists in the structural
engineering and architecture scene of the postwar period in Italy. He worked for the prominent
engineers Pier Luigi Nervi (1891-1979) and Riccardo Morandi (1902-1989) and collaborated on
numerous occasions with some of the most celebrated Italian architects at that time, like Adalberto
Libera (1903-1963), Giuseppe Vaccaro (1896-1970), Carlo Mollino (1905-1973), Leo Calini (1903-
1985) and Eugenio Montuori (1907-1982) (Capanna [2]). Even though the postwar years in Italy were
characterized by economic and cultural prosperity, which led to a boom of real estate developments
and the initiation of several new infrastructural projects, the building industry was still heavily
affected by the limitation of technological and material resources of the interwar time (Poretti [13]).
These strict constraints on the one hand and the inspiring professional environment on the other hand,
strongly influenced Musmeci’s early projects. A variety of new structural concepts emerged from his
experimental approach to structural design, most of them following the principle of resistance through
form. From this perspective, particularly interesting are his folded plate roofs in reinforced concrete of
the 1950s. With these projects, Musmeci explored the potentials of structural folding in a radically
new way, grounded on a peculiar understanding of these structural systems (D’Acunto and Ingold [3]).

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The wide diversity of conceptual approaches and the richness in the results make a categorization of
Musmeci’s work difficult. A reading of his work through the identification of clear typologies seems
to be impractical, as the engineer himself aimed to develop completely new structural forms, which go
beyond the well-known conventional typologies. A novel reading of the work of Musmeci is proposed
here. The idea is to show the relation between some of the design principles investigated by the
engineer in his folded plate structures of the 1950s and the structural concepts applied by the engineer
in his later projects of the 1960s and 70s. Two main branches can be traced: The first one represents
the stepwise transition from folded plate structures based on polyhedral surfaces towards shell
structures based on smooth surfaces with curvature continuity; the second one the transition from
folded plate structures made of on polyhedral cells towards spatial lattice structures made of nodes and
bars. This connection between the early folded plate designs of Musmeci and his later projects
highlights the relevance of structural folding as a source of research for the engineer.
2. Genealogy of Folded Plate Structures
Structural folding represented the first major field of research in Musmeci’s career as a structural
engineer. Seven out of eight projects in which Musmeci employed the principle of structural folding
have been designed and constructed in a time span of only five years (1954-1959). Nevertheless, these
folded plate designs show a variety of approaches on the same structural topic, which bears witness to
Musmeci’s desire for experimentation. This series of projects defines a clear line of development in
three main phases (D’Acunto and Ingold 2016 [3]) and appears as part of a genealogy (Figure 3). The
first phase includes Musmeci’s early implementations of structural folding, while in the second phase
the folded plate structures begin to define a direct correlation between the form and the flow of the
inner forces in the structure. In the third phase, structural folding is used to generate spatial structural
systems as combination of polyhedral cells.
2.1 Early Implementations of Structural Folding
By questioning the general typologies for roof structures, Musmeci intended «to change the simple
slab and beam typology towards a folded structure which is resistant through its form» (Musmeci [8]).
This approach was directly connected to challenges in the use of reinforced concrete as a construction
material: «The separation of the load bearing function between beams and slab, which is the residual
of a mentality that was built upon timber and iron constructions, is certainly unnatural since they
actually form a single structure and it is anyway unrelated to the logic of reinforced concrete. On the
contrary, it is natural to try to provide the ceiling with an intrinsic capacity for load-bearing, by
corrugating it and thereby abolishing the beams» (Musmeci [8]). With this development, Musmeci
took advantage of the opportunities of reinforced concrete as a plastic material that can be moulded
into one single folded surface (Ingold and Rinke [4]). As observed by the engineer, in folded plate
structures the edges are crucial for the accumulation and distribution of the inner stresses: «In […] the
simplest case of a corrugated slab […] it can be assumed that tensile stresses are localized in the lower
edges and compressive stresses in the upper edges» (Musmeci [8]).
An early reflection of the engineer on this topic relates to the roof of Scuola di Atletica in Formia
(1954, with Annibale Vitellozzi), where inclined plates shape a 10cm-thin corrugated slab in
reinforced concrete, which spans almost 20m (Vaccaro [14]). In this project, Musmeci realized «that
the layout of the reinforcement bars of the roof of the gym hall was particularly beautiful. The bars
were following the stress lines making explicit the structural behaviour of the system once the
formwork would have been removed. […] Reflecting on the fact that the layout of the reinforcement
bars would have disappeared after the concrete was cast and, with it, every chance to read the static
behaviour, I understood that the form of the thin vault was not following enough the nature of the
structure to express it directly» (Musmeci [9]).

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2.2 Correlation between Form and Inner Forces
One of the main goals of Musmeci as a structural engineer has been to design structures that could
manifest their inner static behaviour through their form (Musmeci [7]). The design of the roof of
Stabilimento Raffo in Pietrasanta (1956, with Leo Calini and Eugenio Montuori) was his first attempt
to correlate the form of the structure to the flow of the inner forces in a direct way (Figure 1).
Therefore, it marks the transition between the first and second phase in the genealogy. The reinforced
concrete roof is based on the repetition of a folded plate module, whose geometry follows the
distribution of the bending moments in the transversal section of the roof. To derive the geometry of
the folded plate module, Musmeci developed a parametric model where a set of equations defined the
projections of the folded edges of the roof in plan (D’Acunto and Ingold [3]).
As a result, contrary to the roof of Scuola di Atletica in Formia, the static behaviour of the structure
was made visible in an almost diagrammatic way. «[…] This time the main reinforcement bars were
placed straight along the edges, while the full expressiveness inherent to the static behaviour remained
visible in the form» (Musmeci [9]). Particularly relevant was the standpoint of the engineer on the
distribution of tensile and compressive forces: «If the slab is in reinforced concrete, it is correct that
the tension is concentrated in a point, which becomes a nucleus of tensile reinforcement, but it is not
appropriate the presence of a compressed edge because in there a peak of compressive stresses occurs,
while the rest of the concrete cannot fully contribute to the resistance» (Musmeci [8]). In the case of
Stabilimento Raffo «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 [7]).
Figure 1: Stabilimento Raffo in Pietrasanta: The geometry of the roof follows in a diagrammatic way the
distribution of the bending moments along the transversal section of the structure [MAXXI Rome]

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2.3 Integration of Spatial Structural Systems
In a subsequent step, Musmeci’s folded plate geometries started to converge towards a spatial
structural organization. The roof of Palestra CONI in Frosinone (1958, with Uga de Plaisant) denotes
the transition between the second and third phase of the genealogy. The plates are larger than in the
other projects, so that the occurrence of local bending could become critical. In addition, the angles
between the plates are very shallow and the slightly pronounced edges let the roof appear as an almost
smooth surface. This implies that the geometry is approximating a funicular shape in space (Figure 4).
At the same time, the border of the roof of the gymnastic hall is embedded into a rigid truss.
Therefore, the folded plate structure works as a combination of modular polyhedral cells that are
repeated along the longitudinal axis of the roof.
A further development on this approach is marked by the Ristorante Stadio del Nuoto in Rome (1959,
with Annibale Vitellozzi and Enrico Del Debbio). The pavilion is placed next to the main swimming
pool for the 1960 Olympic Games and its rooftop worked as an open terrace. The modular folded plate
structure of the ceiling of the restaurant, which is supported by a series of columns, is covered by a
horizontal slab and the roof enclosed a hollow space (Figure 2). In this cases, «[…] by introducing
horizontal connections between the upper edges an additional constant compression force can be
activated» (Musmeci [8]). Hence, also in this case the folded plate roof is ultimately based on
polyhedral cells repeated along the longitudinal axis of the structure. From an architectural and
construction point of view, particularly relevant in this project is the solution adopted for the columns
supporting the folded plate ceiling. Geometrically, they can be regarded as anti-prisms whose lateral
faces match at the node the plates in the ceiling. The columns do not appear as independent elements,
but rather as integrated members of the overall system (Brodini [1]).
One of the most prominent and refined examples of Musmeci’s folded plate structures, the Teatro
Regio in Turin (1963-1973, with Carlo Mollino and Felice Bertone), was designed and constructed
several years later than the initial folded plate projects. The ceiling and the flying bridges of the foyer
of the theatre are made of polyhedral cells. The structural principle is very similar to the one adopted
for the roof of the Ristorante Stadio del Nuoto and represents the peak in the evolution of folded plate
structures by Musmeci. Thanks to the fruitful collaboration with the architect Mollino, the structure
plays a crucial role in the overall perception of the architectural space.
Figure 2: Ristorante Stadio del Nuoto in Rome: The roof, formed by the addition of polyhedral cells, was
supported by columns with an anti-prismatic shape [CONI Archive Rome]

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2.4 Structural Folding Reveals New Lines of Research
A peculiarity of structural folding is the possibility to correlate the form of a structure to its load-
bearing behaviour. A significant advantage of folded plate structures is the ease and economy of
construction. Since these structures are made of planar elements connected along straight edges, the
formwork for the concrete is relatively easy to fabricate and the use of reinforcement steel can be
reduced to the minimum. The disadvantages in the use of structural folding start to emerge mainly
when a certain scale is exceeded. If individual plates are used to cover large spans, their local
structural behaviour may become a governing factor. In this case, the correlation between form and
inner forces is not only relevant at the level of the global structure, but also at the local one.
The experience with the folded plate projects, including the advantages and the limitations connected
to that structural system, revealed to Musmeci further lines of investigation. Influenced by the studies
on structural folding, his research branched out into two different directions: towards shell and
membrane structures, based on smooth surfaces, and towards spatial lattice structures. Musmeci
himself observed: «There are two typical approaches to structural invention. The first one is the
synthesis of forms that coincide with the forces located in space, showing their equilibrium and
allowing their organic flow (shells, membranes, tensile structures), while the second one is the
creation of constructive systems, in which identical elements are ordered according to spatial systems
(spatial truss structures and geodesic domes)» (Musmeci [10]). The development of a genealogy of
Musmeci’s work is therefore not constricted to the folded plate projects, but can be extended to these
two branches of further research (Figure 3).
Figure 3: Genealogy of Musmeci’s folded plate structures. The arrows illustrate the influence of specific projects
on later works by the engineer

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3. Transition towards the Geometry of the Continuum
Already in the late 1950s, Musmeci tried to go beyond the principle of structural folding in his search
for novel structural forms. Specifically, the experience gained in the design of folded plate structures,
which were based on polyhedral surfaces, suggested to the engineer the possibility to explore the
potentials of surfaces with double-curvature. «[This] way to compose structures leads towards the
geometry of the continuum; the proprieties vary gradually from one point to another and they manifest
themselves as curvatures or torsions of surfaces or lines. Statics is the protagonist of the spatial
phenomenon and from the way it is controlled and explicated the result is largely dependent»
(Musmeci [10]). This line of investigation, which tried to develop the relationship between form and
inner forces on a more radical way than in the folded plate projects, neglected progressively the given
constraints of constructability.
The transition of Musmeci from folded plate surfaces towards smooth surfaces with curvature
continuity can be articulated into two steps (Ingold and Rinke [4]). In the first one, the structures
designed by the engineer were still based on the combination of modular elements. However, due to
the aforementioned limitations of structural folding, the individual plates were locally curved and were
transformed into shell-like components to follow the local distribution of the inner stresses. These
elements were then combined together along folded edges. In the second step, following the principle
that compressive stresses in reinforced concrete should diffuse gradually within the structure, the
folded edges were completely dissolved. Hence, the structure was turned into one single smooth
surface, where there was no distinction anymore between the local and the global structural behaviour.
3.1 Parallel Development of Structural Folding and Smooth Surfaces
The research on the possibilities of double-curved surfaces was developed by Musmeci for projects in
larger scales (spans more than 25m), in particular for bridge designs and large-span halls. In the
competition proposal for Ponte sull’Astico in Caltrano (1956, with Sergio Ortolani and Antonio
Cattaneo), instead of using proven conventional structural typologies, the engineer suggested a
combination of shell-like elements for the main structure of the bridge. The geometry of the bridge is
therefore based on the hierarchical assembly of double-curved modular components (Ingold and Rinke
[4]). A further interesting example of the first step of Musmeci’s investigation into the continuum was
represented by the Distributore Aquila in Bologna (1958, with Giuseppe Vaccaro).
Figure 4: Palestra CONI in Frosinone (left) and Distributore Aquila in Bologna (right): The projects show the
conceptual affinity between structural folding and smooth surfaces [Musmeci [9]-[10] and Mulazzini [6] ]

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The design of the gas station consisted in the combination of double-curved surfaces, which intersect
along transversal folded edges. The same shell module was used four times for the widely
cantilevering roof. While the border of the roof appears quite flat-angled, the section rises towards the
main supports in the middle. The gas station was built at the same time of the Palestra CONI in
Frosinone. Considering the roof geometry of the gymnastic hall, which approximates a funicular
shape, a clear conceptual connection between the two projects becomes obvious, even when the
support condition and the use of the buildings were completely different (Figure 4).
3.2 The Disappearance of the Folded Edges
While the combination of components represented an intermediate step in the convergence towards the
geometry of the continuum, all indications of folded edges are dissolved in Musmeci’s further
approach to bridge designs and large-span halls. A relevant example at the transition point is
represented by the proposal for the Mercato del Pesce and the Mercati Generali in Rome (1960, with
Annibale Vitellozzi, Massimo Castellazzi and Guilio Dall‘Anese). The roof of the Mercato del Pesce
was planned to span 35m and consisted in an undulating, double-curved surface, where still certain
curved edges were present. This basic layout can be related to the folded plate structure for the
Cappella dei Ferrovieri in Vicenza (1957, with Sergio Ortolani). Both roof designs followed the
principle of a spatial frame developed along the transversal axis of the structure. Contrary to the roof
of Mercato del Pesce, the design for the roof of the nearby Mercati Generali had no edges (Figure 5).
The roof was intended to span 68m and the entire structure should have been formed in one single
smooth surface with curvature continuity.
Similar strategies were used by Musmeci for several bridge designs, like Ponte a Tor di Quinto in
Rome (1959, with Ugo Luccichenti) and Ponte sul Basento in Potenza (1967-1976, with Aldo
Livadiotti and Zenaide Zanini). Also in these cases, the component-based approach was replaced by
an integral design, where the whole structure was turned into a continuous and smooth surface, which
allowed the engineer to achieve a direct dependency between the form and the inner forces (Ingold and
Rinke [4]). To derive these novel structural forms, various studies with physical and mathematical
models were used. As a result, forms that involved the minimum amount of construction material
could be obtained. However, the spatial complexity of these geometries implicated a series of
disadvantages in terms of constructability. This aspect has been particularly relevant for the
construction of the Ponte sul Basento in Potenza (Iori and Poretti [5]). Exemplarily, it represents the
change from the economic and pragmatic construction principles of the folded plate structures towards
the novel geometries of the continuum.
Figure 5: Mercato del Pesce (left) and Mercati Generali in Rome (right): The comparison shows the gradual
disappearance of edges and the emergence of the geometry of the continuum [MAXXI Rome]

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4. Transition towards Discrete Geometry
The second branch of research in Musmeci’s work relates to the transition from folded plate structures
based on polyhedral cells, towards novel spatial lattice structures. The investigation reached its peak
during the late 1970s. Musmeci illustrated that «the second way [of structural design] leads instead
towards the geometry of the discrete; the elements that compose the structure are identical and
numerable» (Musmeci [10]). The clear order of these structures was explained by the following
guiding principle: «What counts are the nodes and the bars that define them, the ratios between
distances and angles, the manifestation ultimately of organizational laws that allow to read the space.
In this case, geometry has a more direct role, because a bar is not perceived as a force line, but rather
as a geometric vector» (Musmeci [10]).
From his in depth studies on polyhedra and modular geometries, Musmeci derived spatial structural
systems made of bars and nodes. Starting from basic geometric elements like the tetrahedron, the cube
and the octahedron, Musmeci explored extensively the parameters that control the assembly of these
polyhedra in space. The regularity and irregularity of angles and faces were taken into consideration to
define different polyhedral configurations. Further, the structural behaviours of the different spatial
lattices were investigated, specifically in relation to the degree of static indeterminacy. The basic order
of such structures refers to the concept of the crystal lattice: «These systems of bars are directly related
to regular systems of points according to which the atoms in a crystal are organized; the points
correspond to the nodes where the bars are connected» (Musmeci [10]).
4.1 Nodal Geometry Defines the Spatial Order
The first step in Musmeci’s convergence towards spatial structural systems can be found in his works
on folded plate structures involving polyhedral cells, in particular in the designs of Ristorante Stadio
del Nuoto in Rome (1959) and Teatro Regio in Turin (1963-1973). Considering that the edges of these
cellular systems define a sort of rigid truss (Musmeci [7]), the transition from the folded plate
structures to the spatial lattice structures becomes evident (Figure 6). The edges of the polyhedral cells
were replaced by bars and the vertices of the cells turned into spatial nodes. In this transition, the node
becomes a crucial element, because all information about the structure are bundled in this point: the
amount of bars, their angles of arrangement, the degree of static indeterminacy and the assembly
method for construction.
Figure 6: Physical model in the exhibition of Padiglione InArch: The concept for a large-span spatial lattice
structure was based on a rhombic dodecahedron module [MAXXI Rome]

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The particular importance of the nodal geometry can be already detected in the detail of the folded
plate structure of the Ristorante Stadio del Nuoto (Brodini [1]) where the folded plate ceiling is
connected to the anti-prismatic columns. The tapered shape of the column changes its section from a
rectangle at base to a hexagon below the roof, where it merges together with the folded plate structure.
The node principle, the anti-prismatic shape of the column as well as the overall polyhedral cell order
have a clear correlation to the later projects of the engineer based on spatial lattice structures.
4.2 The Components Act in an Organized Spatial System
Musmeci’s intense studies on the assembly principles of bars and node connections have been
exemplarily represented in the exhibition for the Architecture Week in Rome in 1979. Musmeci
presented in his Padiglione InArch (1979, with Zenaide Zanini and Carlo La Torre) several full-scale
prototypes (Figure 6) and physical models of large-span structures (Figure 7). Each proposal was
derived from studies of various combinations of prisms and anti-prisms. The most significant
structures in the exhibition were the ones based on a rhombic dodecahedron module with 12 prismatic
bars per node, a hexahedral structure with 6 anti-prismatic bars per node and a tetrahedral structure
with 4 anti-prismatic bars per node. These examples went beyond the known typologies of spatial
trusses, in both their geometrical order and the use of construction materials. Indeed, an innovative
polymer-impregnated lightweight concrete has been specifically manufactured for that occasion
(Musmeci and Rio [11]).
The principles for structures with spans up to 100m (Brodini [1]) were further applied for the project
of the Copertura della Regia in Rome (1980-1981, with Zenaide Zanini and Carlo La Torre). This
unbuilt shelter for the protection of the Roman remains in the Area della Regia of the Forum
Romanum consisted in a spatial lattice structure based on a rhombic dodecahedron module. As
explained by Musmeci, if the node of the structure is designed as a rhombic dodecahedron itself, this
can be eliminated by designing bars with a cross section equal to the rhombic faces of the node. In this
way, the whole system can be generated by just one element: the bar. The spatial lattice structure can
be assembled out of the same prefabricated element, while the node physically dissolves and exist
only in its geometrical order (Musmeci [12]). Whit this repetitive application, the local order of
components and connections determines the global order of the overall spatial system. At the same
time, the components act in an organized spatial system. Peculiar to these structural systems is the
overcoming of the conventional hierarchy between supporting and supported elements, both in their
structural function and their architectural connotation (Musmeci [12]).
Figure 7: Full-scale prototypes at Padiglione InArch: Rhombic dodecahedron module (left) with 12 prismatic
bars per node and tetrahedral structure (right) with 4 anti-prismatic bars per node [MAXXI Rome]

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5. Conclusion
The multifaceted investigations of Sergio Musmeci in the field of structural folding during the 1950s
constitute the base for his further research as a structural designer. In the series of folded plate
structures, it is possible to trace crucial characteristics that influence the later work of the engineer.
During the 1960s and 70s, mainly two lines of investigation are followed by Musmeci: the first relates
to the geometry of the continuum, the second one to discrete geometry. While in the first branch, the
global form becomes more and more relevant and all folded edges dissolve, in the second branch, the
local order of the nodal geometry determines the rule of the whole system. In this sense, both lines in
Musmeci’s work converge towards a complementary understanding of structural design. In both
developments, structural folding has been an initiating source of research that eventually revealed
novel structural conceptions.
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Translations of the quotation from Italian to English by the authors.