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Behavior of microconcrete hyperbolic-paraboloid shell

Experimental and analytical results of a clamped hyperbolic-paraboloid shell subjected to uniformly distributed load are presented. The model behavior at ultimate load is also discussed

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Abstract

The paper presents the results of an experimental as well as analytical investigation on the behavior of square hyperbolic-paraboloid (hypar) shell, subjected to uniformly distributed load and clamped all along the boundaries. The experimental investigation involves casting and testing of a microconcrete model of size 1000 mm×1000 mm, rise 222 mm and shell thickness 15 mm, clamped along all the four edges. The experimental results within elastic limit are compared with the results of a finite-element analysis using a doubly curved triangular shell element. The model was tested to destruction to study the behavior of the shell at ultimate load stage.

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Abbreviations

A :

size of the finite element (250 mm)

M xy :

twisting moment (Kg-cm/cm)

N xy :

inplane shear force (Kg/m)

U :

strain energy

X :

global X-direction

Y :

global Y-direction

a′ :

size of the finite element in x-direction in the general case

b′ :

size of the finite element in y-direction in the general case

c′ :

size of the finite element in z-direction in the general case

m i, ni :

coefficients for the power of the coordinates (transformation matrix)

p i, qi :

coefficients for the power of the coordinates (transformation matrix)

r i, si :

coefficients for the power of the coordinates (transformation matrix)

u :

displacement in X-direction (mm)

u X :

first derivative ofu (ϖu/ϖX) in X-direction

u Y :

first derivative ofu (ϖu/ϖY) in Y-direction

v :

displacement in Y-direction (mm)

v X :

first derivative ofv (ϖv/ϖX) in X-direction

v Y :

first derivative ofv (ϖv/ϖY) in Y-direction

w :

vertical deflection (mm)

w X :

slope in X-direction

w Y :

slope in Y-direction

w XX :

curvature in X-direction

w XY :

twist

w YY :

curvature in Y-direction

x :

local x-direction

y :

local y-direction

∈y :

strain along Y-direction (micron/meter)

B :

orientation of element with respect to global axis

References

  1. Cowper, G.R., Lind Berg, G.M. andOlson, M.D., “A Shallow Shell Finite Element of Triangular Shape,”Intern. J. of Solids and Structures,6,1133 (1970).

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  2. Singa Rao, K. andVenkateswara Rao, G., “A Note of Cylindrical Shell Finite Element,”Intern. J. for Numerical Methods in Engrg.,9,245 (1975).

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  3. Gnana Sambanthan, T., Aravindan, P.K. and Srinivasa Rao, P., “Analysis of All Round Clamped Rectangular Hypar Shell,” presented at the Oct. 23–25, 1979, International Conference on Computer Applications in Civil Engineering, held at Roorkes, India.

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Authors and Affiliations

  1. Structural Engineering Laboratory, Department of Civil Engineering, Indian Institute of Technology, 600 036, Madras, India

    T. G. Sambanthan (Senior Research Fellow), P. K. Aravindan (Assistant Professor) & P. S. Rao (Professor and Head)

Authors
  1. T. G. Sambanthan
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  2. P. K. Aravindan
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  3. P. S. Rao
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Sambanthan, T.G., Aravindan, P.K. & Rao, P.S. Behavior of microconcrete hyperbolic-paraboloid shell. Experimental Mechanics 21, 240–244 (1981). https://doi.org/10.1007/BF02326847

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  • DOI: https://doi.org/10.1007/BF02326847

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