Advances in Engineering Software 47 (2012) 147–159
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Advances in Engineering Software
journal homepage: www.elsevier.com/locate/advengsoft
Modular Truss-Z system for self-supporting skeletal free-form pedestrian networks
Machi Zawidzki ⇑, Katsuhiro Nishinari
Research Center for Advanced Science and Technology, University of Tokyo, Japan
a r t i c l e
i n f o
Article history:
Received 29 November 2011
Accepted 30 December 2011
Available online 28 January 2012
Keywords:
Truss-Z
Modular skeletal system
Self-supporting structure
Organic design
Discrete structural optimization
Retrofit pedestrian link
Pathfinding with backtracking
a b s t r a c t
This paper presents the concept of Truss-Z (TZ) – a skeletal system for pedestrian traffic which is composed of only two modules and allows the creation of complex three-dimensional self-supporting networks connecting any number of terminals in a given environment. TZ is intended as a universal,
feasible and practical system for newly designed situations and most importantly, for retrofitting, especially where the use of heavy equipment is impossible or uneconomic.
TZ allows automated creation of optimal spatial links where the only required inputs are the coordinates of the terminals and the geometry of the obstacles. As an example a six-terminal network created
with a backtracking based algorithm is shown. An alternative method of aligning consecutive modules to
a given 3D path is also presented.
A preliminary static analysis of the TZ module is carried out – the topological qualities of rigidity and
independence are demonstrated.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Truss-Z (TZ) is a concept of a modular skeletal system for creating free-form transportation links and networks among any number of terminals in space [1]. TZ is intended for pedestrians,
especially ones with strollers or carts, and in particular – persons
on wheelchairs – in other words for ones who have difficulties
using regular stairs. The underlying idea of this system is to create
structurally sound provisional or permanent structures [2] at the
minimal number of types of modular elements. The system
uniquely combines two fundamental qualities that are usually contradictory in such engineering problems, that is universality and
affordability.
Universality – only two types of modules allow the creation of
links between almost any, at least conceptually, two terminals in
space. The system also supports multiple branching, closed loops
and spirals.
Affordability – the modules of TZ system can be prefabricated
and assembled on site, preferably without the necessity for heavy
equipment, or can be made on-site using templates and locally
available materials.
The system can be adjusted in scale and shape for different purposes such as supporting cycle paths or other conveyance tasks,
and ventilation ducts. Most importantly, it allows automated
creation of optimal structural linkages for given terminals and
obstacles [3]. An example of a retrofitting a TZ structure is shown
in Fig. 1.
⇑ Corresponding author. Tel.: +81 3 5452 5286; fax: +81 3 5452 5287.
E-mail address: zawidzki@gmail.com (M. Zawidzki).
0965-9978/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
doi:10.1016/j.advengsoft.2011.12.012
This paper is an updated and revised version of the conference
paper [1]. It provides more insight to the background of the
problem of the creation of free-form shapes in architecture and
engineering contrasted with modularity. It also expounds on some
technical aspects such as the rigidity of the TZ module and the nature of the automated creation of the TZ networks.
2. Modularity vs. free-form
To the best knowledge of the authors, there are no free-form
modular systems for creating linkages similar to TZ. Therefore
the examples illustrating the background of the problem are taken
from the most geometrically advanced field of architecture – the
free-form shells. Since the beginning of the 20th century a number
of systems composed of prefabricated elements and applicable to
different tasks have been developed [4]. The modularity and prefabrication are the common means of reducing the construction
cost. However, they usually also reduce the diversity of possible
shapes of structures. There are a variety of construction modular
systems, where high modularity produces rather simple forms
[5–8]. On the other hand, there is a growing tendency among
designers for creation of free-form shapes in space, which is enabled and encouraged by the ongoing developments of the computer-related tools: computational intelligence, meta-heuristics,
computer aided design (CAD) systems and constantly increasing
computational power. A number of examples of very complicated
geometries, as shown in Fig. 2, have been realized [9].
Such structures, however, require a great deal of customization;
in this example practically every member was custom-made as
shown in Fig. 3.
148
M. Zawidzki, K. Nishinari / Advances in Engineering Software 47 (2012) 147–159
Fig. 1. A visualization of a possible application of Truss-Z system, where the continuity of a pedestrian/cycling path is interrupted by a railway. Since TZ is a lightweight
system, it can be retrofitted as a suspended structure from the existing bridge. Using only two types of modules, and without the necessity of a heavy equipment, TZ can be a
feasible solution for countless situations.
Fig. 2. ‘‘Son-O-House’’ – a small (280 sqm) public pavilion in Son en Breugel, Netherlands, NOX 2000 – 2004. Photograph Ó J.H. Rodriguez.
In the late 19th century Catalan architect Antoni Gaudi initiated
a form-finding method based on physical experimentation with
hanging models [10]. His work is known for the organic, complex
geometry – an extreme example of customization, which is contrary to modularization. Most notably, the completion of his famous Basilica and Expiatory Church of the Holy Family in
Barcelona is presently expected in the late 1920s of this century,
that is nearly 150 years after the commencement. In 1960s Frei
Otto, Heinz Isler and others developed methods of structural optimization of planar structures based on experimentation with soap
bubbles and suspension models. Nearly thirty years later, Joerg
Schlaich and Hans Schrober transferred these findings to a modular
steel-glass system based on a uniform 1 meter strut, which
materialized a shell structure covering the spa in Aquatoll Dome,
Neckarsulm, Germany [11]. Moreover, the connection nodes in this
project were developed so that, independent of the varying angles
of the quadrilateral curved insulated panels, they were manufactured out of identical pieces. In 1989 further development of this
idea was realized in the glass roof of the inner court of the Museum
for Hamburg History [12] as shown in Fig. 4.
In this project, however, although most of the elements where
uniform, the structure required a great deal of adjustments, that
is customization. For example, although each facet of the mesh
has edges of uniform length, the quadrilateral panels filling this
mesh are not uniform as shown in Fig. 5.
Almost always, the complexity of a form comes at the expense
of the modularity of the construction system (Fig. 6). Since the mid
1990s, however, the construction technique has changed as the
ID
566172
Title
ModularTruss-Zsystemforself-supportingskeletalfree-formpedestriannetworks
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