International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 5, May 2017, pp.60–66,
pp.
Article ID: IJCIET_08_05_008
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DEVELOPMENT AND ANALYSIS
ANALYSIS OF A
PENTAGONAL PRISM TENSEGRITY SYSTEM
SY
IN ROOF STRUCTURE
STRUCTU
Rohith S
P G Student, Department of Civil Engineering, SRM University, Kattankulanthur,
Tamil Nadu, India.
R. Ramasubramani
Assistant Professor, Department of Civil Engineering, SRM University, Kattankulanthur,
Tamil Nadu, India.
ABSTRACT
The deployable tensegrity structures
str
were developed to meet the fast growing
demand for temporary structural systems, that requires
uires a compact storage space
.Though
hough the concept of tensegrity
ten
can be dated
ated to the late 1960’s, only very few
applications exist. This paper focuses on the experimental and analytical study on a
pentagonal configuration tensegrity module.
module The study in this paper confines to a
single pentagonal module.
odule. The behavior of the structure is observed during the
experimental and analytical study based on the nodal displacements and member
forces. The analytical study has been conducted using a FEM package
ckage and the results
are well compared.
Key words: Deployable, Tensegrity, Pentagonal Module, Grid Structure.
Structure
Cite this Article: Rohith S and R. Ramasubramani Development and Analysis of A
Pentagonal Prism Tensegrity System in Roof Structure. International Journal of Civil
Engineering and Technology,
Technology 8(5), 2017, pp. 60–66.
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1. INTRODUCTION
Structures capable of large configuration
configur
changes from the compact-packed
acked state to a largelarge
deployed state is known as deployable structures. Obvious advantage
dvantage of these structures is the
ease in storage and transportation. Hence, they serve great as temporary structures.
Tensegrity structures are comparatively new and developing structural systems, say about
60 years old[1]. Though a lot of study has been conducted in this field, very few practical
p
applications exist. This concept has also received attentions from mathematicians, architects
and biologists etc. A tensegrity system is established when a set of discontinuous compressive
components interacts with a set of continuous tensile components to define
define a stable volume
vo
in
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Development and Analysis of A Pentagonal Prism Tensegrity System in Roof Structure
space [2]. Deployable tensegrity structures have an added advantage since the compressive
elements in the tensegrity systems are disjointed. Hence, this makes it possible to fold the
tensile members and hence the structure can be stored in compact volume and transported
easily after use.
However, the most challenging step is the design of the tensegrity structure, which is
generally known as the form finding process. Though several form finding methods are
available for the design of a tensegrity structure, no single method can be concluded for the
design of tensegrity structures in general. The pentagonal module in this paper has been
designed using the equilibrium equations developed by Ian Stern in 1999[3]. The cables and
the struts have been designed accordingly. This paper reviews the behaviour of the
pentagonal tensegrity module, under the application of various loads. The mechanism of the
structures is studied based on the nodal displacements and member forces, obtained from the
experimental and analytical data.
2. FABRICATION AND TESTING OF MATERIALS
A deployable tensegrity module, of a pentagonal prism configuration has been fabricated in
the structural engineering laboratory, SRM University, Chennai. The structure has been
fabricated, based on cable mode deployability concept [4], [5],[6]. The Mild Steel pipe has
been used for the struts and the MS stranded wires of 6 x 19 strands has been used for the
cables. The cables and pipes were tested in the UTM of 1000 ton capacity as shown in Figure
1 and Figure 2. The key material and section properties are as given in table 1 and table 2.
Figure 1 Testing of MS pipes in UTM
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Figure 2 Testing of cables in UTM
Table 1 Section property
Material
Mild steel pipes
High carbon steel wire
Diameter(mm)
Area(mm2)
Mass(kg/m)
21(external),
15(internal)
169.64
1.2
4
6.53
6.09
Table 2 Material property
Material
Mild steel pipes
High carbon steel wire
Modulus of
elasticity (N/mm2)
Yield stress
(N/mm2)
Poisson’s
ratio
2.06 x 105
0.954 x105
262
1421.335
0.25
0.25
Eye bolts of size M12 are used to connect the cables to the pipes. All measurements has been
taken from centre to centre of the eye bolts.
2.1. FABRICATION AND TESTING OF THE SINGLE TENSEGRITY
MODULE
The structure has been designed as per Sterns equilibrium equations [3], the length of bottom
cables, tie cables and the top cables are 1m, 0.95m and 0.59m respectively. The cables were
connected to the joints using aluminium ferrules by means of hydraulic press to ensure strong
joints with no slip. At first a reticulated cable network was fabricated by connecting cables to
the eye bolts. One turn buckle of size 200mm was connected in one of the tie cables to
provide deployability to the structure. MS pipes of lengths 1.38m were then placed in the
required positions loosening the turn buckle to 15 cm length. In order to perform FEM
analysis, it is essential to determine pre stress levels in the structure at the self-equilibrium
configuration. In order to determine the pre-stress values, 3 strain gauges of 2mm, 120Ω were
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Development and Analysis of A Pentagonal Prism Tensegrity System in
n Roof Structure
connected to one top, one
ne bottom and one tie cable respectively. One 5mm, 120 Ω strain
gauge was connected to one of the struts as well. Once all the strain gauges are then
connected to data logger, the
he turn buckle
buckl is then tightened and the tie cable attains a length of
0.95m. The pre-stress values at this self-equilibrium
self
position were recorded. The structure is
then tested for different
nt loads as shown in Figure 3 for nodal displacement and member
forces.
Figure 3 Testing
esting of the single Tensegrity Modulee under the application loads
3. FEM ANALYSIS
The prototype of the pentagonal tensegrity module as described in the previous section has
been modeled using the FEM package, SAP 2000 v.18. All the cable elements were defined
as cable sections, and the strut members were defined as truss elements. Hence no bending
moments are developed
ed in any of the members.
members. The material was assumed as linearly
linear elastic
and isotropic. All the bottom nodes are restrained against translation in the vertical direction.
The
he values of the Young’s modulus of the strut and the cable elements
eleme
obtained
experimentally has been used. The FEM model of the single pentagonal tensegrity
ten
module is
shown in Figure 4.
Figure
ure 4 3D view of single module in SAP 2000
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The pre-stress forces in the cables were assigned as target forces based on the
experimental analysis performed. Since, initial pre-stress forces were not available for all the
members they were worked out from the equations developed by Stern (1999). For a
pentagonal prism tensegrity module, the member forces are as follows,
=
=
25 − √5
2
25 − √5
2
= Where, Fs, Fa, Fb and Ft are the force in strut, top cable, bottom cable and tie cable
respectively. a, b, Lt, Ls are the length of top cable, bottom cable, tie cable and strut.
Nodal displacement and member forces of the structure have been analyzed for various
loads acting uniformly on each node.
4. RESULTS AND DISCUSSIONS
Nodal displacement (mm)
The comparison of the nodal displacements obtained from the experimental and analytical
studies are shown in Figure 5. Both the deflection curves shows a non-linear variation and the
stiffness of the structure have been observed to increase with loading. The steep increase in
deflection is observed at smaller loads and on further application of loads only small
variations are observed. Despite a variation of 20%, the trend remains same in both the cases.
45
40
35
30
25
20
15
10
5
0
experimental
analytical
0
500
1000
1500
2000
2500
Aplied load(kN)
Figure 5 Comparison of the nodal displacements
Figure 6 represents the comparison of strut forces obtained from the experimental and
analytical study. The experimental values show a non-linear steep variation compared to
analytical result. The experimental value is observed to be lower than analytical value up to
1200 N and on further increase in loading the experimental value shows a slightly higher
deflection than the analytical values.
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Development and Analysis of A Pentagonal Prism Tensegrity System in Roof Structure
7000
Member forces (N)
6000
5000
4000
3000
analytical
2000
experimental
1000
0
0
500
1000
1500
2000
2500
Applied load (N)
Figure 6 Comparison of the strut forces
Comparison of the cable forces in the experimental and analytical study are shown in Figure
7. The top cable shows a higher value than the bottom and tie cables. The plot shows higher
variations (-22%and +32%) between experimental and analytical results. At initial loads, up
to 750 N, the experimental value is observed to be higher than the analytical value. On further
loading, the numerical value is observed to be higher and has a steeper slope.
Member forces (N)
5000
4000
3000
2000
analytical
experimental
1000
0
0
500
1000
1500
2000
2500
Applied load (N)
Figure 7 Comparison of the cable forces
5. CONCLUSION
This paper covers a method of fabrication, instrumentation and testing of a pentagonal prism
tensegrity module. The testing of pentagonal prism module was continuously monitored using
strain gauges and dial gauges. FEM model of tensegrity system was modeled in SAP 2000
and analyzed. Later, the model has been updated based on the experimental findings. The
structural response of FEM model well matched with the experimental model both in terms of
member forces and nodal displacements. Only a variation of 20% has been observed in the
values. Further, studies aim at developing and analyzing tensegrity grids by joining single
pentagonal prisms for roofing purposes. The deployability of the tensegrity structure would
make it suitable for the temporary shelters.
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REFERNCES
[1]
[2]
[3]
[4]
[5]
[6]
Valentin Gomez Jannegui, Tensegrity Structures and Their Applications to Architecture,
Queen’s University, Belfast, 2007.
Gunnar Tibert, Doctoral Thesis on Deployable Tensegrity Structures for Space
Applications: Royal Institute of Technology, Stockholm, 2002
Stern I P, M.S. Thesis on Development of Design Equations for Self-Deployable N- Strut
Tensegrity Systems, University of Florida, USA, 1999.
Apurva Prakash, Project Report on Tensegrity Based Tower Structures: Indian Institute
Of Technology, Delhi, 2007.
Ramankanta Panigrahi, Ashok Gupta and Suresh Bhalla, Dismountable Steel Tensegrity
Grids as Alternate Roof Structures, Steel and Composite Structures, 2009; Vol.9, No.3, pp
239-253.
Ramakanta Panigrahi, Doctoral Thesis on Development, Analysis And Monitoring Of
Dismountable Tensegrity Structure ,Indian Institute Of Technology, Delhi, 2007.
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