Line Geometry for Lightweight Structures

International Summer School 2018 at the TU Dresden September 10 – 28

The main objective of LGLS is to design lightweight structures using ruled surfaces. Ruled surfaces play a major role in architecture and civil engineering like in the works of Vladimir Shukhov, Antoni Gaudí, Felix Candela, Santiago Calatrava and many others. A good reason for using ruled surfaces is that they can be generated quite easily by moving a straight line. This fact already leads to strategies of fabrication like hotwire cutting of extruded polystyrene for the formwork of concrete shells. On the other hand, ruled surfaces are statically efficient, especially in the case of skewed ruled surfaces, which are very stable due to a generally negative Gaussian curvature. Last not least, most shapes using ruled surfaces are characterized by extraordinary elegance. LGLS is both a summer school to enhance your knowledge and abilities and a design space exploration of ruled surfaces, especially in lightweight construction applications.


pic Pekka Sipila
pic Pekka Sipila

The front side of the building is shaped like an oak leaf following a ruled surface geometry. It is also the key architectural feature. The oak wall is fixed to a 100 metre long steel structure with a 40 metre overhang. It is produced with CNC mills out of 20.000 different pieces using local timber from the southern norwegian forests. The material is a reference to Kristiansand‘s founding in the 17th century as a harbor to export wood to Europe for shipbuilding.

Location Kristiansand, Norway
Architect ALA Architects Helsinki & SMS Arkitekter, Kristiansand
Construction Time 2007 – 2011
Materials Wood, Glas
Geometric Shape Konoid


pic Juan Díaz Bernardo

The building covers a bus terminal with complex engineering and superb slenderness. The
most characteristic element is the curved white concrete tape, folded over itself, which
serves as a culmination and home to travelers and vehicles. A laminar structure with a
vocation for sculpture, which in its form not only seeks the aesthetic pleasure, but the
functionality: to expel the pollution coming from the exhaust pipes of the buses, separating it
from the schools that flank the station. The result recalls, without a doubt, the soft
architecture that other architects like Óscar Niemeyer or Félix Candela worked with.

Location Casar de Cáceres – Spain
Architect Justo García Rubio
Construction Time 2003
Materials Concrete
Geometric Shape Freeform


Architect Miguel Fisac

The tower was made up of five floors, with a base of three floors below. The tower’s five
octagonal floor plans shift 45 degrees as they rise, creating the shape that recalls a
traditional pagoda. Within the building, steel columns and the central core with circulation
unite the twisting floors. On the exterior, Fisac’s spectacular concrete panels also unite the
floors, which are topped with a pinnacle. The surface of the concrete is marked with the lines
of the wooden formwork. The lines repeat and enhance Fisac’s hyperbolic helicoid curves,
which wrap the tower’s shifting floor plans. These concrete hyperbolic paraboloids are shells
of concrete which curve in two directions. The panels are rectangular, and vary in size to
connect the floors.

Location Madrid – Spain
Architect Miguel Fisac
Construction Time 1965 – 1967
Materials Concrete
Geometric Shape Helicoid


pic Felipe Gabaldón

The geometry of the concrete shell structure designed for the entrance of the
L’Oceanogràphic comes from the intersection of three lobes that describe the shape of a
hypar. The shell is based on the hand-drawn sketches by Candela, which inspired the
subsequent building project. It is interesting to note the scaffolding that supports the
formwork, especially the perpendicular layout of the ledgers. If the hypar were not equilateral,
these ledgers would form an angle of 90º. This angle would correspond with the director axes
of the paraboloid.

Location Valencia – Spain
Architect Félic Candela – Alberto Domongo – Carlos Lázaro
Construction Time 1996
Materials Concrete Shell
Geometric Shape Hyperbolic Paraboloid


pic Toshiko Mori

The building is constructed using local materials and builders who shared their sophisticated
knowledge of working with bamboo, brick, and thatch. These traditional techniques are
combined with design innovations by Mori. The customary pitched roof is inverted and will be
capable of collecting approximately 40% of the villagers’ domestic water usage in fresh

Location Sinthian – Senegal
Architect Toshiko Mori
Construction Time 2015
Materials Bamboo
Geometric Shape Freeform


pic Pizzigoni photo archive

The church spans over 900 square meters, for 18 meters top height. It is conceived as a
double-reflectional symmetrical room made of four identical quarters. Each quarter is made
of 5 reinforced concrete hypar shells and a beam frame. Figures 1 and 2 show, respectively,
an external and an internal view of the church. Geometrically speaking, four hypar-surfaces
are joined together in the shape of a ring and then topologically transformed into a Möbius
strip. A fifth hypar is placed between the other ones in order to give strength to the overall
configuration. The use of hypar shells offers several spatial configurations for the proposed
frame. Moreover, the topology through which the hypars are arranged, allowed the architect
to put to practice the concept of Möbius ring as well.

Location Bergamo – Italy
Architect Pino Pizzigiono
Construction Time 1961-1960
Materials Concrete Shell
Geometric Shape Different Hyperbolic Paraboloids

Line Geometry for Lightweight Structures
International Summer School 2018

Organizer Prof. Dr.-Ing. Daniel Lordick
Research Group Geometric Modeling and Visualization

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