PARAMETRICAL ANALYSIS OF STRUCTURAL DOME

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 13, Issue 6, June 2022, pp. 35-45, Article ID: IJCIET_13_06_004
Available online at https://iaeme.com/Home/issue/IJCIET?Volume=13&Issue=6
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
DOI: https://doi.org/10.17605/OSF.IO/YU5
© IAEME Publication
PARAMETRICAL ANALYSIS OF STRUCTURAL
DOME
Mohamed Imran.S1, Dr. R. Thiyagarajan2, Dr. K. Soundaranayaki3, and Dr. K.P. Jaya4
1
Department of Civil Engineering, College of Engineering Guindy,
Anna University, Chennai, Tamil Nadu, India
2
Teaching Fellow, Project Guide, Structural Engineering, Department of Civil Engineering,
3
Assistant Professor, Project Coordinator, Central for Environmental Studies,
Department of Civil Engineering, Anna University, Chennai, Tamil Nadu, India
4
Professor and Head, Department of Civil Engineering,
ABSTRACT
Dome is an element of architecture that resembles a hollow upper half of a sphere.
Dome structures made of various materials have a long architectural lineage extending
into prehistory. It may be defined as a thin shell generated by the revolution of a regular
curve about one of its axis. The shape of the dome depends upon the type of the curve
and the direction of the axis of revolution. When the segment of a regular curve revolves
about its vertical diameter, a spherical dome is obtained. Domes are used in variety of
structures such as roof of circular areas, circular tanks, exhibition halls, auditorium,
bottom of tanks and bunkers. With the introduction of monolithic dome structures find
wide applications in many branches of technology. From the point of view of
architecture, the development of dome structure offers unexpected possibilities and
opportunities for the combined realization of functional, economic and aesthetic
aspects. Energy efficiency of building designs should be considered and is high in
monolithic domes. A monolithic dome is a structure cast in a one-piece form. The form
may be permanent or temporary and may or may not remain part of the finished
structure. Monolithic is dedicated to improving people’s lives worldwide by introducing
and constructing Monolithic Domes, for personal and public use, that are disaster
resistant, energy-efficient and cost-effective.
Key words: Monolithic Domes, Structural Dome, dome structures.
Cite this Article: Mohamed Imran.S, R. Thiyagarajan, K. Soundaranayaki and
K.P. Jaya, Parametrical Analysis of Structural Dome, International Journal of Civil
Engineering and Technology (IJCIET). 13(6), 2022. pp. 35-45.
https://iaeme.com/Home/issue/IJCIET?Volume=13&Issue=6

Parametrical Analysis of Structural Dome
1. INTRODUCTION
1.1. General
The monolithic dome, for a number of reasons, is very energy efficient. The spherical sections
of the dome offer minimal surface area for the volume they contain, so there is less surface for
heat transfer with the outside air. The construction of monolithic dome with proper earth
sheltering will withstand bomb blasts more effectively than conventional structures. The
strength and stability of domes make them virtually immune to climatic catastrophe, or
earthquakes, as well as to fire, or corrosion hazards. Monolithic Domes are the most energy
efficient and safest buildings that can be built and that can be designed for many uses. Many
schools now conduct their classes in Monolithic Domes. Some are designated as tornado
shelter.
Others have Monolithic Dome gymnasiums, auditoriums, multipurpose centers, libraries,
cafeterias, etc. Three brothers- David, Barry, and Randy south- built and patented the first
monolithic dome in 1975. It was 105 feet (32m) in diameter, and 35 feet (1m) high, and is still
used today. Now there are monolithic domes throughout the United States and the world- built
north of the Artic Circle in Murmansk, Russia, to the Equator in Indonesia. Churches, schools,
storage buildings, homes, and recreational centers all use monolithic domes. Sizes range from
very small 8 foot (2.5m) to very large 260 foot (80m) diameter domes.
1.2. Advantages of Structural Dome
• Strong And Durable
• Energy Efficient
• Minimum Maintenance
• Cost Effective
• Resist Natural Element
• Fire Proof
• Aesthetics And Comfort
• Economy In Construction
• Security
1.3. Need for Study
Dome structures are advantageous due to their structural integrity, rapid construction,
inexpensive materials in construction and aesthetic appeal.
• The ribbed dome does not have diagonal elements and is not structurally stable;
therefore, this type has to be designed as a rigidly jointed system for stability.
• It is observed that parametric study is the key to determine optimum configuration by
overall. This provides direction for practical application for deciding domes with and
without openings during construction.

Mohamed Imran.S, R. Thiyagarajan, K. Soundaranayaki and K.P. Jaya
1.4. Objective of Study
• Analyse the various parameters and their effects on ribbed dome and schwedler dome.
• To examine the percentage of steel required by performing cost analysis.
2. REVIEW OF LITERATURE
Neil Parkyn (2002) Broadening of the knowledge on the major domes in the world, identifying
their key features. M. Mihailescu and R. Sundaram (2009) It discusses the importance of quality
control during construction and once fully completed; waterproofing and insulation. It also
recognises the extensive formwork required during construction, emphasising the advantages
of pre-cast concrete domes. I.Mungan and J.Abel (2011) Identifies milestones for the
construction of concrete shells and arch bridges, displaying the advantages of using concrete as
a construction material; large spans with limited thickness, (Centennial Dome and Carl Zeiss
Planetarium). Will Mclean (2005) Given the architectural review explaining the design
concepts and construction methods behind the ‘inflatable dome’. Due to the nature of the Bini
shell the construction process, although independent of formwork required precision in order
to ensure the stability of the dome once erected.
Carl Hubben (2005) Bini failure’s were covered which stipulates why two Bini shell high
schools collapsed in Australia. S.G. Morkhade, M. Kshirsagar, R. Dange, A. Patil (2019)
Analytical study of effect of web opening on flexural behaviour of hybrid beams. D. Chao, Y.
Guo, Y. Pi, S. Zhao (2014) Flexural-torsional buckling and ultimate resistance of parabolic steel
arches subjected to uniformly distributed vertical load. J. Struct. Eng. S. Kato, N. Yoshida, S.
Nakazawa (2012) Buckling strength of two-way single-layer lattice domes stiffened by
diagonal braces. J. Struct. Constr. Eng
2.1. Summary of Literature Review
• The expected stresses in the domes if erected incorrectly would be distributed unevenly
resulting in dome failure.
• Buckling strength stiffened by diagonal braces.
• Need for precision in order to ensure the stability of the dome once erected.
• Importance of quality control during construction.
3. METHODOLOGY
3.1. General
The aim is to develop understanding through the use of analytical research. The analysis section
of this project requires the use of ANSYS Software.

3.2. Flow Chart of Methodology
Figure 1
3.3. Detailed Methodology
Gaussian Curvature
Gaussian curvatures are usually used for classifying shell surfaces. Gaussian curvature for a
three-dimensional surface is found out by the product of maximum and minimum principal
curvatures. It can be established at any point by intersecting infinite planes with the shell surface
as they are orthogonal to each other.
In this research work, primarily domes are considered with one center of curvature and
positive Synclastic Gaussian curvature.
Behaviour of Dome Roofs
The major components of half-arches are ribs of the dome. They all are connected to the circlet,
but habitually, to evade cramped joint with several members converging around; the ribs are
terminated at a small diameter compression ring circumscribing the circlet.
For the horizontal ribs at the supports, rings are made sufficiently taut
To get maximum compression about the crown or tension just about the base of the ring of
the ribbed and hooped dome, it should be fully loaded with the dead and live load. If the live
load is present from the ring to the base, compression is maximum.An economical rise-to-span
ratio for the spherical type of dome achieved is 0.13 if the radius of the dome is equivalent to
the diameter of the base.

Figure 2 Shows behaviour of the dome
Geometric Parameters of Dome and Modelling
The spans (D) of the ribbed dome and schwedler dome are considered 20 m and 30 m, while
the thickness of the dome is considered to be 10 cm. Three numbers of rings are selected and
equally spaced. From Eq. 1, total angle subtended (Ø) by the dome is found out and this angle
depends on the rise (H)-to-span ratio [29]. The geometry of dome can be clearly defined by
using Fig. 2
……………… (1)
Stresses in dome are maximum at crown and are minimum at bottom of dome. At bottom
of dome tensile stresses called as hoop stresses are acting which are less as compared to stresses
at top. By observation of such kind of behaviour of dome after application of load,it is preferred
to provide opening at bottom of dome. Opening provided at bottom allows us to provide more
opening than that of opening at crown. Surface area of a dome can be calculated using formula
= 2 9 p r 9 h square units. Here, h is the dome height, r is radius of dome. Formula for defining
area of opening provided is as Eq. 2. It depends on diameter of dome at second ring, Area of
opening provided ¼ total area of dome area of dome after opening
where r1 = radius of dome at second ring. h1 = height of dome at second ring. r = radius of
dome at bottom ring. h = height of dome from bottom ring. For this research work, analysis of
dome is carried out by ANSYS software to know the structural behaviour of the structure due
to various loading conditions. Modelling of the dome is carried out using SHELL 63 element
for analysis of the curved surface of the dome. Each node is having six degrees of freedom.
Figure 3 indicates models prepared in ANSYS software of ribbed spherical dome and schwedler
dome with their diagrams, respectively. Steps involved in the analysis of dome are described as
follows:
• First total angle subtended by the dome is calculated using Eq. 1, and then the radius of
the spherical dome for the respective rise-to-span ratio is defined using geometry.

• Key points are generated in ANSYS to draw an arc of specified radius. Arc is divided
in a required number of ribs of a dome.
• The dome surface is then formed using commands extrude lines about the axis.
• A SHELL 63 element is created and material properties, as well as section sizes are
assigned.
• A meshing of size 0.9 mm is provided to complete structure and fixed supports are
provided at the bottom of the dome.
• Loading conditions are applied, and structure is analysed using ANSYS software for
buckling
Figure 3
Material Properties and Loading Conditions
The moment of inertia (I) and area (A) of the section are constant for all members with different
load conditions. The modulus of elasticity (E) of the member is taken as 210 kN/mm2 , yield
stress (fy) as 250 MPa and Poisson’s ratio is 0.3. Member properties of the dome are as shown
in Table . The joints are considered to be rigidly connected and all the supports as fixed
supports. The members are exposed to both axial stresses and bending moments. By varying
rise-to-span ratio, i.e., 0.10–0.50 with an increment of 0.05 is considered for analysis. To know
the behaviour of the dome, a vertical load of 500 kN is considered in the downward direction.
The concentrated load is applied at the apex of the dome for calculating buckling load by
varying rise-to-span ratio. For effective rise-to-span ratio, various parameters were calculated
such as maximum axial stresses in rib and ring members, the maximum moment in the members
and maximum deflection of dome structure by using ANSYS software. The meshing of dome
and the variations in stresses of dome with and without opening are shown in Figs. 4 and 5,
respectively. Short forms are used to represent dome without opening (WO*) and dome with
opening (WO), also stresses are represented as vertical compressive stress without opening
(WO* VC), vertical tensile stress without opening (WO* VT), compressive stress with opening
(WO VC), vertical tensile stress with opening (WO VT). The behaviour of the dome for same
loading conditions with specific changes in geometry is to be defined for an optimum solution.
To carry out analysis, four different cases are defined for above-specified loading conditions
according to the type of dome. These cases are as specified below: • Case I: Analysis of ribbed
dome without opening. • Case II: Analysis of ribbed dome with opening. • Case III: Analysis
of schwedler dome without opening. • Case IV: Analysis of schwedler dome with opening.

(a) Ribbed dome with opening (b) Ribbed dome without opening
(c) Shwedler dome with opening (d) Shwedler dome without opening
Figure 4
Table 1 Comparison of Axial Stresses of Ribbed Dome with and Without Opening

Figure 5
Table 2 Comparison of Axial Stresses on Shwedler Dome with and Without Opening
Figure 6

4. RESULTS
4.1. Ribbed Dome with and without Opening
The percentage decrease in steel for the different rise-to span ratios of the ribbed dome with an
opening as compared to without opening as shown in Fig. 16. It is observed that we can reduce
cost up to 32.24% by providing an opening in the dome.
Figure 7 Percentage Decrease in Ribbed Dome with and Without Opening
4.2. Shwedler Dome without Opening
There is a percentage increase in steel for the different rise-to-span ratios of schwedler dome
without opening as compared to ribbed dome without opening. Schwedler dome costs only 7%
more than ribbed dome but gives excellent performance against loading as compared to the
ribbed dome.
Figure 8 Percentage Increase of Steel in Shwedler Dome without Opening

4.3. Shwedler Dome with Opening
It is observed that we can reduce cost up to 23.05 by providing an opening in the dome.
Figure 9 Percentage Decrease of Steel in Shwedler Dome with Opening
5. CONCLUSIONS
Based on the analysis results, the following conclusions and recommendations are drawn.
• The heavy stress is observed near the surface. For better performance, against lateral
loading, height of dome should be the minimum. Stresses are distributed more evenly
for H/D ratio of 0.25. Therefore H/D ratio should be maintained above 0.25.
• For H/D ratio of 0.3 variations are less in moments. Therefore H/D ratio should be
maintained from 0.25 to 0.4 for dome if moments on members are considered.
• For H/D ratio between 0.1 and 0.3 covers above 80% of the maximum buckling load.
Therefore H/D ratio should be maintained above 0.3.
• Since rigid joints are provided chances of local instabilities are less. There is not much
deflection for the dome structure. For providing lateral stiffness to the dome, diagonal
elements should be provided.
• If axial stress and moments are deciding factors for the dome, then schwedler dome are
preferred, since a considerable decrease in stresses and moments.
• Schwedler dome offers more even distribution of the dead load and reduces the
unbraced length of the ribs.
• Providing an opening, the structure becomes more economical and buckling load on the
dome was also reduced. Because of openings, there was failure observed in the vicinity
of openings. It is recommended that strengthening should be done near openings.
Due to the addition of a diagonal element, the stiffness of schwedler dome is increased. The
cost of schwedler dome is also increased, but the reduction in stresses is observed.

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