Model study using Levy method Validation using ANSYS FEM model study Levy’s Method and ANSYS 12 will be used Model for known span Analysis for loads under normal condition All kinds of stresses are found out To find the interfacial stresses Load carrying capacity of layered HYPAR Suitability as roofing system

1. Presented by- Naresh Dixit P S
USN-1RV13CSE07
Under the guidance of
Dr. M V Renuka Devi
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2.  Classification of structures (Flugge W)
 What is a Shell?
◦ Surface enclosed by two closely spaced curved lines (Wilhelm
Flugge).
 Application of shells
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3.  Why HYPAR?
◦ Straight line edges
 Advantages of HYPAR
◦ Appearance
◦ Economy
◦ Design simplicity
◦ Construction ease
◦ Promising future
◦ Wide range of structural units
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4. 4
HYPAR roof in test floor civil engineering department

5.  Thermal comfort
 Architectural aspects
 Low cost masonry
 Lean concrete for water proofing
 Cost reduction
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6.  Lack of knowledge on behavior in bending.
 No much research carried out for HYPAR
affordable roofs.
 Wide range of application
 Understand the behavior of layered shells.
 Thermal comfort not taken into
consideration.
 Applications in affordable roofing system.
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7.  To find the interfacial stresses
 Load carrying capacity of layered HYPAR
 Suitability as roofing system
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8.  Model study using Levy method
 Validation using ANSYS
 FEM model study
 Levy’s Method and ANSYS 12 will be used
 Model for known span
 Analysis for loads under normal condition
 All kinds of stresses are found out
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9. 9
Table of
deflections and
errors for 0.5 m
rise and 10cm
thick HYPAR

10. 10
Parameter rise of shell, curvature parameter and Shell parameter

11. 11
0
2
4
6
8
10
12
14
16
0 0.2 0.4 0.6 0.8 1 1.2
χ₁ χ₂
χ₃ μ₃

12. 12
HYPAR model and deflection contour from ANSYS

13. 13
X component
of Moment
Shear stress

14. 14
Layered shell and
Deflection contour

15. 15
Shear Stress
X component of moment

16.  Finding delaminating stresses
 Necessity of shear connectors
 To prove advantages of HYPAR over
conventional slabs.
 Develop it as a affordable roofing system for
commercial buildings.
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17.  ANSYS results have been validated
 Tables for roots of levy method have been
found out which reduces time.
 To solve the levy equations differential
quadrature method is best one.
 Shell-181 element is best type of element to
analyze membrane and bending behavior of
shells.
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18. 1. Ghosh, A., & Chakravorty, D. (2014). Prediction of Progressive Failure
Behaviour of Composite Skewed Hypar Shells Using Finite Element
Method.Journal of Structures, 2014.Banerjee, S.P. (1965), “Numerical method
of analysis of doubly curve shell structures” , the Indian concrete journal,
January 1965. pp. 14-19.
2. Beles, A.A. and Soare, M. (1976), “elliptic and hyperbolic paraboloid shells
used in constructions”, S.P. Christie and partners, London.
3. Bandopadhyay J N (1998), “Thin shell structures”, New age international
publlishers, pp 244-258.
4. Billington, D. P., & Moreyra Garlock, M. E. (2010). Structural Art and the
Example of Félix Candela. Journal of structural engineering, 136(4), 339-342.
5. Chetty, S. M. K., & Tottenham, H. (1964). An investigation into the bending
analysis of hyperbolic paraboloid shells. Indian Concrete Journal, 38(7), 248-
258.
6. Clough, R. W., & Johnson, C. P. (1968). A finite element approximation for the
analysis of thin shells. International Journal of Solids and Structures, 4(1), 43-
60.
7. Flügge, W. (1960). Stresses in shells. 1973.
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19. 7. Shaaban, A., & Ketchum, M. S. (1976). Design of hipped hypar
shells. Journal of the Structural Division, 102(11), 2151-2161.
8. Simmonds, S. H. (1989). Effect of support movement on hyperbolic
paraboloid shells. Journal of Structural Engineering, 115(1), 19-31.
9. Timoshenko, S., & Woinowsky-Krieger, S. (1959). Theory of plates
and shells(Vol. 2, p. 120). New York: McGraw-hill.
10. Ventsel, E., & Krauthammer, T. (2001). Thin plates and shells:
theory: analysis, and applications. CRC press.
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