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@ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2367
CONCLUSIONS:
The observations of the study are as follows:
The effect of rise: By increasing the rise stresses are
minimum for 2.25m rise, for shallow and deep shell
the loads are resisted by stresses as compare to
intermediate rise. Shells with intermediate rise
moment plays major role. Transverse normal shear is
played negligible part in loads resistance.
The effect of thickness: longitudinal stresses plays
major role in resisting the loads compare to other two
stresses, the transverse normal stress is negligible
with thickness. Moments are increasing with
thickness. Transverse moment increases more in
comparison of longitudinal moments.
The effect of skew angle: The longitudinal stress
decrease as the skew angle increase, transverse stress
increase as the skew angle increases. The in plane
shear stress almost remain constraint there for it can
be concluded that the role of resistance to load shift
from longitudinal stress to transverse as skew angle
increases.
Longitudinal Moment does not varies much the
transverse moment increases for skew angle in 30, 45
but more increases in 30.Further the transverse
moment has more than double in all cases which
shows transverse moment plays the major role in
resisting the load.
REFRENCES
Books
[1] Ramaswamy, G. S. “Design and construction of
concrete shell roofs”. Cbs Publishers &
Distributors Pvt. Ltd., New Delhi, , India.
[2] Timoshenko, S. and Krieger, S. “Theory of
plates and shells”. Tata McGraw Hill
Education Pvt ltd., New Delhi, India, 429-575.
[3] Agrawal P. and shrikhande M. “Earthquake
resistant design of structures”. PHI learning
pvt. ltd. New Delhi-110001, India.
Thesis and dissertation
[1] Kandasamy, S. and Singh, A. V., (2010). “Free
Vibration Analysis of Cylindrical Shells
Supported on Parts of the Edges”. Journal of
aerospace engineering, ASCE, 33-43.
[2] Rao, G. (1983). “A study of funicular shell”. M.
E. dissertation, Shree Govindram Seksaria
Institute of Technology and Science Indore.
[3] Reddy, E. S. (1978). “Optimum design of
stiffened cylindrical and conical shells”. M.
Tech., department of mechanical engg., Indian
Institute of technology, Kanpur.
[4] Rode, V. (1984). “Bending analysis of conoidal
shell panels for hydrostatic loads”. M. E.
dissertation, Shree Govindram Seksaria
Institute of Technology and Science Indore.
[5] Singh, L. (1971). “Experimental and analytical
study of the design of reinforcement in folded
plates and cylindrical shell structure”. M. Tech.,
department of civil engg., Indian Institute of
technology, Kanpur.
Papers
[1] Arciniega, R. A. and Reddy, J. N. (2006).
“Large deformation analysis of functionally
graded shells”. International Journal of Solids
and Structures, 44, 2036–2052.
[2] Haldar s. Majumdar A. Manna M. C. “Bending
of Skewed Cylindrical Shell Panels” (2010)
International Journal of Computer Applications
(0975 – 8887)Volume1 – No. 8
[3] Halder, S. (2008). “Free vibration of composite
skewed cylindrical shell panel by finite element
method”. Journal of Sound and Vibration, 311,
9–19.
[4] Wang C. and Lai J. C. S. (1999) “Prediction of
natural frequencies of finite length circular
cylindrical shells “Elsevier Applied Acoustics
59 385±400
[5] Bathe, K. J. and E. N. Dvorkin. 1986. "A
Formulation of Genera l Shell Elements --
The Use of Mixed Interpolation of Tonsorial
Components". Int. Journal for Numerical
Methods in Engineering, Vo l. 22, No. 3. pp.
697- 722.
[6] Zienkiewicz, O. C. 1977. The Finite Element
Method. McGraw-Hill Book Company.
[7] N. Krishna Raju “ Advanced Reinforced
Concrete Design “ based on IS-456-2000
(2nd Edition ).
[8] “Membrane theory of cylindrical shells”, K.
C. Roy, Indian concrete journal, Vol. 23,
1949.
[9] “An Analytical and Experimental
Investigation of the Behavior of thin
Cylindrical Shell Roof Structures” –M.
Smolira, University of London Ph. D. Thesis
Part 1 and 2, 1949.
[10] “Theory and Design of Cylindrical Shell
Structures” by R. S. Jenkins, Lund and
Humphries and Co. Ltd. London 1947.
[11] Timoshenko, S. P., Woinowsky-Krieger, S.
1959. “Theory of Plates and Shells” 2d ed.,](https://image.slidesharecdn.com/341analysisofparabolicshellbydifferentmodelsusingsoftwaresap2000-210927060505/85/Analysis-of-Parabolic-Shell-by-Different-Models-Using-Software-SAP-2000-7-320.jpg)
![International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2368
McGraw-Hill Book Company, New York.
[12] Dr. Umesh Pendharkar, Ravindra Rai, 2012.
“Computer Aided Analysis of Multiple
Cylindrical Shell Structure Using Different
Parameters”. (IJERT) Vol. 1 Issue 3, May -
2012 ISSN: 2278- 0181
[13] Srinivasan Chandrasekaran1*, S. K. Gupta2,
FedericoCarannante3, 2009. “Design aids for
fixed support reinforced concrete cylindrical
shells under uniformly distributed loads”.
International Journal of Engineering, Science
and Technology Vol. 1, No. 1, 2009, pp. 148-
171
[14] Varghese P. C. 2014. “Design of Reinforced
Concrete Shells and Folded Plates” First
Edition, PHI Learning Private Limited, Delhi.
[15] IS-2210-1988, “Criteria for Design of
Reinforced Concrete Shell Structures and
Folded Plates”, B. I. S., New Delhi.
[16] Bandyopadhyay J. N., 1998. “Thin Shell
Structures Classical and Modern Analysis”,
New Age International Publishers, New Delhi.
[17] Chandrashekara K., 1986. “Analysis of Thin
Concrete Shells”, Tata McGraw Hill, New
Delhi.
[18] “Design of Cylindrical Concrete Shell Roof”,
Manual No. 31, ASCE, New York, 1952
[19] Chandrasekaran S., Ashutosh Srivastava,
Parijat Naha. 2005. “Computational tools for
shell structures” Proc. of Intl. conf. on
structures and road transport (START-2005),
IIT-Kharagpur, India, pp. 167-175.
[20] Ramaswamy G. S. 1968. “Design and
construction of concrete shell roof” First
Edition, Mc-Graw Hill.
[21] “Distribution method for Circular
Cylindrical Shell Roofs” by Yit zhaki North
Holland Publishing Co., A msterdam, Holland
[22] Cylindrical Thin Concrete Shells Jose
Antonio Lozano Ga lant May 2009, TRITA-
BKN. Master Thesis 277, 2009 ISSN 1103-
4297, ISRN KTH/BKN/EX-277-SE.
[23] Design aids for fixed support reinforced
concrete cylindrical shells under uniformly
distributed loads Dept. of Ocean
Engineering, Indian Institute of Technology
Madras, Chennai 600 036, India.
[24] “Design of cylindrical concrete shell roofs”
prepared by the committee masonry and
reinforced concrete of the structural division
through its subcommittee on thin shell
design. R. F. Bleich, Mario G. salvadori.,
Alfred l Prame.
[25] Thin Shell Concrete Structure Design and
Construction, Jessica Mandrick, E90 Project
Proposal Swarthmore College, Department of
Engineering.
[26] Integrated Modeling, Finite -Element Analysis,
and Engineering Design for Thin-Shell
Structures using Subdivision Fehmi Cirak,
[27] Michael J. Scott, Erik K. Antonsson, Michael
Ortiz and Peter Schr¨oder.
[28] “Practical design of cylindrical shell roofs”
V. K. Chavan.
[29] Rohit Sahu, Barun Kumar, Deeksha
Shrotriya “Dynamic Study of Parabolic
Cylindrical Shell: A Parametric Study”
Volume 5 Issue 4, May-June 2021 Available
Online: www. ijtsrd. com e-ISSN: 2456 –
6470
[30] Dr. Umesh Pendharkar, Ravindra Rai, 2012.
“Computer Aided Analysis of Multiple
Cylindrical Shell Structure Using Different
Parameters”. (IJERT) Vol. 1 Issue 3, May -
2012 ISSN: 2278- 0181
[31] Srinivasan Chandrasekaran1*, S. K. Gupta2,
Federico Carannante3, 2009. “Design aids for
fixed support reinforced concrete cylindrical
shells under uniformly distributed loads”.
International Journal of Engineering, Science
and Technology Vol. 1, No. 1, 2009, pp. 148-
171
[32] Varghese P. C. 2014. “Design of Reinforced
Concrete Shells and Folded Plates” First
Edition, PHI Learning Private Limited, Delhi.
[33] IS-2210-1988, “Criteria for Design of
Reinforced Concrete Shell Structures and
Folded Plates”, B. I. S., New Delhi.
[34] Bandyopadhyay J. N., 1998. “Thin Shell
Structures Classical and Modern Analysis”,
New Age International Publishers, New Delhi.
[35] Chandrashekara K., 1986. “Analysis of Thin
Concrete Shells”, Tata McGraw Hill, New
Delhi.](https://image.slidesharecdn.com/341analysisofparabolicshellbydifferentmodelsusingsoftwaresap2000-210927060505/85/Analysis-of-Parabolic-Shell-by-Different-Models-Using-Software-SAP-2000-8-320.jpg)
Analysis of Parabolic Shell by Different Models Using Software SAP 2000
- 1. International Journal of Trend in Scientific Research and Development (IJTSRD) Volume 5 Issue 5, July-August 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2361 Analysis of Parabolic Shell by Different Models Using Software: SAP 2000 Rohit Sahu1 , Barun Kumar2 , A. K. Jha3 1 PG Student, 2 Assistant Professor, 3 Associate Professor, 1,2,3 Department of Civil Engineering, Lakshmi Narain College of Technology, Bhopal, Madhya Pradesh, India ABSTRACT The shell structure consists of a thin reinforced concrete shell without the use of internal columns to create an internal opening., parabolic or spherical cross section. On the other hand, warehouses and playgrounds are conventional concrete frame structures, on the other hand, they can be difficult to design as the exact shape required for the stability of the structure depends on the material used, the dimensions of the enclosure, external or internal loads and other chamfers.. .. Thus, by changing the shell parameter, the performance of the shell will also change. The main goal of this work is to parametrically analyze different designs of cylindrical shells of different lengths in order to analyze two different lengths of taken cylindrical shells, and then change two parameters, first the radius and then the thickness, based on the radii. and the difference in thickness for the same width, length and material of the frame, we will evaluate the behavior of the frame for different models. KEYWORDS: Multiple cylindrical shells, Analysis, Different Parameter, shell structures, parametric analysis Transient dynamics analysis, Time-History Analysis, modeling, analysis, design, and reporting How to cite this paper: Rohit Sahu | Barun Kumar | A. K. Jha "Analysis of Parabolic Shell by Different Models Using Software: SAP 2000" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456- 6470, Volume-5 | Issue-5, August 2021, pp.2361- 2368, URL: www.ijtsrd.com/papers/ijtsrd46337.pdf Copyright © 2021 by author (s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0) INTRODUCTION Concrete circular cylindrical shells have been widely used for roofing large column-free areas and have been constructed in various countries for almost half a century. From architectural and functional points of view, shells have their applicability as roofing units in many of the public buildings. These roofs are used where full-size floor areas are required to be covered without obstruction from columns. There are many situations where skew shells are required to cover rather than the plot area having unsymmetrical plot size, inclined corridors verandas, etc. connecting the straight areas are such common situations. Due to architectural and structural point of view it is required to use skew shell in so many situations. some time it is essential to used in ships, sub marines, etc. The objectives of the present work are: To study the behavior of the parabolic cylindrical shell subjected to Dynamic loading conditions. Comparison between the behaviors of straight parabolic cylindrical shell vs. skewed parabolic cylindrical shell. To conduct parametric studies on such parabolic cylindrical shell roofs having different rises, thicknesses and Skew Angle of shells. Plotting the graphs and tables on the behavior of shell (moment, stress, strain, deflection), which will provide the ready to use data for practicing engineers planning to use such type of shells. SOFTWARE USED Among the features introduced by the analysis of SAP2000 are modal examination, static and dynamic analysis, linear and nonlinear analysis, and easy analysis. The investigative modeling used in this software is the member type model which means that beams or columns are model using single fundamentals. The layered shell modeling can be possible in SAP2000 which permit any number of layers to be defined in the thickness direction, each with an independent position, thickness, behavior, and material. Material behavior may be non linear. The hysteretic response of the concentrated plasticity at IJTSRD46337
- 2. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2362 ends of a member can be described by a moment curvature association. SAP2000 can specify for each material one or more stress-strain curves that are used to produce nonlinear hinge properties in frame elements. The different curves can be used for different parts of a frame cross section. For steel and other metal materials, SAP2000 usually only specify one stress-strain curve. A multiplicityof cross sections are available in SAP2000 element library. These sections include rectangular sections as used for modeling the beams and columns of the Reinforced concrete (RC) buildings. SAP2000 provides the tools required for easy target analysis as material nonlinearity at discrete, user-defined hinges in frame elements. The hinge properties are created based on easy target analysis regulations found in performance- based procedure. Default hinge properties are provided based on FEMA- 356 criteria. Display capabilities in the graphical user interface to generate and plot easy target curves, including demand and capacity curves in spectral ordinates. Capabilities in the graphical user interface to plot and get information regarding the state of every hinge formed at each step in the easy target analysis. PROPOSED METHODOLOGY: For this proposed work single bay cylindrical shell roof having Span 10 m, Length 18 m (i.e. plan area 10m X 18m), rise are 1.5, 2.25 & 3m and Thickness 200,150 & 100 mm with Edge beam 0.300m X. 8m taken. Different Models are studied (for dead load, live load and time history analyses) with variation in rise, thickness & skew angle by using SAP-2000. The results of shells are presented in the form of tables and graphs. METHODOLOGY: Finite element method has been used for the numerical analysis. Shell is discretised by 9 noded Quadrilateral elements. Sap software has been used for analysis. Study of Variation in skew angle has been done keeping rise & thickness constant. Study of Variation in rise has been done keeping skew angle & thickness constant. Study of Variation in thickness has been done keeping skew angle & rise constant. MODELING For the analysis of multiple cylindrical shell following dimension are considered which is tabulated in table In the current study main goal is parametric analysis of the shell structure. Following results are formed and compare the results for different models. Fig 1.1 Isometric view of skewed parabolic cylindrical shell structure Fig 1.2 Top view of skewed parabolic cylindrical shell structure Fig.1.3- model of multi-bay cylindrical shell Structure Fig.1.4 Front perspective view of modeled multiple shell structure
- 3. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2363 PROPERTY AND DIMENSIONS OFMODELS Span in X direction 11 m Span in Y direction 11 m Live load 0.6 kN/m2 Grade of Concrete M-25 Type of Steel HYSD bars Column Height 5.0 m Column Size 0.3 m X 1.0 m Column Support condition Fixed Beam Size 0.30 m x 0.50 m Varying Thicknesses for Radius = 0.08m, 0.12m Number of bay 3 bay Semi central angle (Type-A) 40o Semi central angle (Type-B) 310 Semi central angle (Type-C) 570 Radius of model (Type-A) 10.83m Radius of model (Type-B) 8.56m Radius of model (Type-C) 6.53m ANALYSIS RESULT As mentioned in the objective of the study, the behavior of skewed parabolic cylindrical shells under dynamic loading have been analyzed with varying parameters. The results obtain from the analysis are represent bytables and graphs. Comparison between various Skewed parabolic cylindrical shell and non-skewed parabolic cylindrical shell has been done for different rise, thickness and skew angles in tables and graphs.The linear static analysis is adopted for analysis of various cylindrical shell using structural engineering software SAP-2000 due to static load only. the following analysis result, stresses and force contour are obtain from the analysis for changing thickness and radius for fixed length and chord width of the model which are presented below Stresses in longitudinal direction S11 (Nx) Table No. 4.7 Rise3 m & Thickness 200mm S11 (N/mm²) Model skew angle Mode 1 2 3 4 7 0 0.385 1.605 25.842 33.972 16 30 0.844 1.636 26.809 34.431 25 45 0.774 1.4 26.031 36.038 Table No. 4.8 Rise3 m & Thickness 150mm S11 (N/mm²) Model skew angle Mode 1 2 3 4 8 0 0.672 1.774 21.412 39.757 17 30 1.321 1.979 22.607 35.431 26 45 1.216 1.736 23.138 33.878 Table No.4.9 Rise3 m & Thickness 100mm S11 (N/mm²) Model skew angle Mode 1 2 3 4 9 0 1.516 2.412 16.706 51.011 18 30 2.095 2.538 17.552 37.342 27 45 1.991 2.29 18.384 29.569
- 4. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2364 Stresses in Transverse direction S22 (Nɵ) Table No. 4.16 Rise3 m & Thickness 200mm S22 (N/mm²) Model skew angle Mode 1 2 3 4 7 0 0.31 1.184 1.044 25.068 16 30 1.284 1.77 3.061 36.322 25 45 2.352 2.311 7.842 57.52 Table No. 4.17 Rise3 m & Thickness 150mm S22 (N/mm²) Model skew angle Mode 1 2 3 4 8 0 0.366 1.564 1.184 24.961 17 30 1.519 2.306 3.073 33.482 26 45 3.077 2.98 8.312 49.954 Table No. 4.18 Rise3 m & Thickness 100mm S22 (N/mm²) Model skew angle Mode 1 2 3 4 9 0 0.626 2.396 1.283 19.271 18 30 1.559 3.296 2.782 26.545 27 45 3.767 4.09 9.223 48.011 In plane shear stress S12 (Nxɵ) Table No. 4.25 Rise3 m & Thickness 200mm S12 (N/mm²) Model skew angle Mode 1 2 3 4 7 0 0.266 0.689 10.097 12.504 16 30 0.773 1.286 16.22 18.862 25 45 0.874 1.56 19.899 26.247 Table No. 4.26 Rise3 m & Thickness 150mm S12 (N/mm²) Model skew angle Mode 1 2 3 4 8 0 0.476 0.969 9.058 13.547 17 30 1.108 1.635 14.995 18.248 26 45 0.378 1.063 7.303 10.516 Table No. 4.27 Rise3 m & Thickness 100mm S12 (N/mm²) Model skew angle Mode 1 2 3 4 9 0 0.899 1.389 8.549 15.203 18 30 1.668 2.202 14.089 18.87 27 45 1.819 2.745 19.646 18.963
- 5. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2365 Graphs for the stresses Fig. 4.15 Fig. 4.16 Fig. 4.17 Longitudinal moment M11 (Mx) Table No. 4.34 Rise3 m & Thickness 200mm M11 (KN/m) Model skew angle Mode 1 2 3 4 7 0 14.0883 27.7392 104.1938 432.981 16 30 18.9146 26.8797 102.9506 420.7515 25 45 19.1589 24.3558 99.2122 389.0721 Table No. 4.35 Rise3 m & Thickness 150mm M11 (KN/m) Model skew angle Mode 1 2 3 4 8 0 11.4395 16.1881 57.9523 219.0174 17 30 13.297 15.6892 58.0957 213.9864 26 45 13.0929 14.3925 56.7519 201.1809 Table No. 4.36 Rise3 m & Thickness 100mm M11 (KN/m) Model skew angle Mode 1 2 3 4 9 0 7.2557 7.3388 25.6174 84.6964 18 30 6.9833 7.0818 25.9891 78.3767 27 45 7.0291 6.6433 26.0607 86.6395
- 6. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2366 Graphs for Moments Fig. 4.34 Fig. 4.35 Result for rise variation Tables No4.52. Skew angle 45' & Thickness 200mm Model Rise Stress N/mm² S11 S22 S12 19 1.5 18.645 9.489 14.352 22 2.25 24.786 9.538 18.666 25 3 26.031 7.842 19.899 Tables No.4.54 Skew angle 45' & Thickness 100mm Model Rise Stress N/mm² S11 S22 S12 21 1.5 16.414 13.457 19.337 24 2.25 8.701 14.252 7.381 27 3 18.384 9.223 19.646 Tables No4.53. Skew angle 45' & Thickness 150mm Model Rise Stress N/mm² S11 S22 S12 20 1.5 18.223 10.903 16.419 23 2.25 7.712 16.503 7.648 26 3 23.138 8.312 -2.336 Graphs for stresses Fig. 4.48 Fig. 4.49 Fig.4.50
- 7. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2367 CONCLUSIONS: The observations of the study are as follows: The effect of rise: By increasing the rise stresses are minimum for 2.25m rise, for shallow and deep shell the loads are resisted by stresses as compare to intermediate rise. Shells with intermediate rise moment plays major role. Transverse normal shear is played negligible part in loads resistance. The effect of thickness: longitudinal stresses plays major role in resisting the loads compare to other two stresses, the transverse normal stress is negligible with thickness. Moments are increasing with thickness. Transverse moment increases more in comparison of longitudinal moments. The effect of skew angle: The longitudinal stress decrease as the skew angle increase, transverse stress increase as the skew angle increases. The in plane shear stress almost remain constraint there for it can be concluded that the role of resistance to load shift from longitudinal stress to transverse as skew angle increases. Longitudinal Moment does not varies much the transverse moment increases for skew angle in 30, 45 but more increases in 30.Further the transverse moment has more than double in all cases which shows transverse moment plays the major role in resisting the load. REFRENCES Books [1] Ramaswamy, G. S. “Design and construction of concrete shell roofs”. Cbs Publishers & Distributors Pvt. Ltd., New Delhi, , India. [2] Timoshenko, S. and Krieger, S. “Theory of plates and shells”. Tata McGraw Hill Education Pvt ltd., New Delhi, India, 429-575. [3] Agrawal P. and shrikhande M. “Earthquake resistant design of structures”. PHI learning pvt. ltd. New Delhi-110001, India. Thesis and dissertation [1] Kandasamy, S. and Singh, A. V., (2010). “Free Vibration Analysis of Cylindrical Shells Supported on Parts of the Edges”. Journal of aerospace engineering, ASCE, 33-43. [2] Rao, G. (1983). “A study of funicular shell”. M. E. dissertation, Shree Govindram Seksaria Institute of Technology and Science Indore. [3] Reddy, E. S. (1978). “Optimum design of stiffened cylindrical and conical shells”. M. Tech., department of mechanical engg., Indian Institute of technology, Kanpur. [4] Rode, V. (1984). “Bending analysis of conoidal shell panels for hydrostatic loads”. M. E. dissertation, Shree Govindram Seksaria Institute of Technology and Science Indore. [5] Singh, L. (1971). “Experimental and analytical study of the design of reinforcement in folded plates and cylindrical shell structure”. M. Tech., department of civil engg., Indian Institute of technology, Kanpur. Papers [1] Arciniega, R. A. and Reddy, J. N. (2006). “Large deformation analysis of functionally graded shells”. International Journal of Solids and Structures, 44, 2036–2052. [2] Haldar s. Majumdar A. Manna M. C. “Bending of Skewed Cylindrical Shell Panels” (2010) International Journal of Computer Applications (0975 – 8887)Volume1 – No. 8 [3] Halder, S. (2008). “Free vibration of composite skewed cylindrical shell panel by finite element method”. Journal of Sound and Vibration, 311, 9–19. [4] Wang C. and Lai J. C. S. (1999) “Prediction of natural frequencies of finite length circular cylindrical shells “Elsevier Applied Acoustics 59 385±400 [5] Bathe, K. J. and E. N. Dvorkin. 1986. "A Formulation of Genera l Shell Elements -- The Use of Mixed Interpolation of Tonsorial Components". Int. Journal for Numerical Methods in Engineering, Vo l. 22, No. 3. pp. 697- 722. [6] Zienkiewicz, O. C. 1977. The Finite Element Method. McGraw-Hill Book Company. [7] N. Krishna Raju “ Advanced Reinforced Concrete Design “ based on IS-456-2000 (2nd Edition ). [8] “Membrane theory of cylindrical shells”, K. C. Roy, Indian concrete journal, Vol. 23, 1949. [9] “An Analytical and Experimental Investigation of the Behavior of thin Cylindrical Shell Roof Structures” –M. Smolira, University of London Ph. D. Thesis Part 1 and 2, 1949. [10] “Theory and Design of Cylindrical Shell Structures” by R. S. Jenkins, Lund and Humphries and Co. Ltd. London 1947. [11] Timoshenko, S. P., Woinowsky-Krieger, S. 1959. “Theory of Plates and Shells” 2d ed.,
- 8. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD46337 | Volume – 5 | Issue – 5 | Jul-Aug 2021 Page 2368 McGraw-Hill Book Company, New York. [12] Dr. Umesh Pendharkar, Ravindra Rai, 2012. “Computer Aided Analysis of Multiple Cylindrical Shell Structure Using Different Parameters”. (IJERT) Vol. 1 Issue 3, May - 2012 ISSN: 2278- 0181 [13] Srinivasan Chandrasekaran1*, S. K. Gupta2, FedericoCarannante3, 2009. “Design aids for fixed support reinforced concrete cylindrical shells under uniformly distributed loads”. International Journal of Engineering, Science and Technology Vol. 1, No. 1, 2009, pp. 148- 171 [14] Varghese P. C. 2014. “Design of Reinforced Concrete Shells and Folded Plates” First Edition, PHI Learning Private Limited, Delhi. [15] IS-2210-1988, “Criteria for Design of Reinforced Concrete Shell Structures and Folded Plates”, B. I. S., New Delhi. [16] Bandyopadhyay J. N., 1998. “Thin Shell Structures Classical and Modern Analysis”, New Age International Publishers, New Delhi. [17] Chandrashekara K., 1986. “Analysis of Thin Concrete Shells”, Tata McGraw Hill, New Delhi. [18] “Design of Cylindrical Concrete Shell Roof”, Manual No. 31, ASCE, New York, 1952 [19] Chandrasekaran S., Ashutosh Srivastava, Parijat Naha. 2005. “Computational tools for shell structures” Proc. of Intl. conf. on structures and road transport (START-2005), IIT-Kharagpur, India, pp. 167-175. [20] Ramaswamy G. S. 1968. “Design and construction of concrete shell roof” First Edition, Mc-Graw Hill. [21] “Distribution method for Circular Cylindrical Shell Roofs” by Yit zhaki North Holland Publishing Co., A msterdam, Holland [22] Cylindrical Thin Concrete Shells Jose Antonio Lozano Ga lant May 2009, TRITA- BKN. Master Thesis 277, 2009 ISSN 1103- 4297, ISRN KTH/BKN/EX-277-SE. [23] Design aids for fixed support reinforced concrete cylindrical shells under uniformly distributed loads Dept. of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600 036, India. [24] “Design of cylindrical concrete shell roofs” prepared by the committee masonry and reinforced concrete of the structural division through its subcommittee on thin shell design. R. F. Bleich, Mario G. salvadori., Alfred l Prame. [25] Thin Shell Concrete Structure Design and Construction, Jessica Mandrick, E90 Project Proposal Swarthmore College, Department of Engineering. [26] Integrated Modeling, Finite -Element Analysis, and Engineering Design for Thin-Shell Structures using Subdivision Fehmi Cirak, [27] Michael J. Scott, Erik K. Antonsson, Michael Ortiz and Peter Schr¨oder. [28] “Practical design of cylindrical shell roofs” V. K. Chavan. [29] Rohit Sahu, Barun Kumar, Deeksha Shrotriya “Dynamic Study of Parabolic Cylindrical Shell: A Parametric Study” Volume 5 Issue 4, May-June 2021 Available Online: www. ijtsrd. com e-ISSN: 2456 – 6470 [30] Dr. Umesh Pendharkar, Ravindra Rai, 2012. “Computer Aided Analysis of Multiple Cylindrical Shell Structure Using Different Parameters”. (IJERT) Vol. 1 Issue 3, May - 2012 ISSN: 2278- 0181 [31] Srinivasan Chandrasekaran1*, S. K. Gupta2, Federico Carannante3, 2009. “Design aids for fixed support reinforced concrete cylindrical shells under uniformly distributed loads”. International Journal of Engineering, Science and Technology Vol. 1, No. 1, 2009, pp. 148- 171 [32] Varghese P. C. 2014. “Design of Reinforced Concrete Shells and Folded Plates” First Edition, PHI Learning Private Limited, Delhi. [33] IS-2210-1988, “Criteria for Design of Reinforced Concrete Shell Structures and Folded Plates”, B. I. S., New Delhi. [34] Bandyopadhyay J. N., 1998. “Thin Shell Structures Classical and Modern Analysis”, New Age International Publishers, New Delhi. [35] Chandrashekara K., 1986. “Analysis of Thin Concrete Shells”, Tata McGraw Hill, New Delhi.