Abstract
Base-isolation may be looked upon as state-of-the-art technique as it is being adopted now successfully in design of some seismic resistant buildings. In this technique, superstructure of the buildings are kept separated from substructure and which floats horizontally with limit barriers, safely over number of Circular Base Slabs attached with seismic bearings which are inserted underneath each columns of the framed super structure of such buildings. These circular base slabs need be so designed as to resist the entire static downward gravity loads of the superstructure resting over them and also these must safely respond to any dynamic loads that may get imposed onto the buildings. In the present study conducted here on these circular slabs attached to the seismic bearings provided with several shear layers of viso-elastic materials, all have been modelled as slabs that appear as resting on Winkler-Pasternack type foundations. In order to understand the static and dynamic behaviours, such base slabs are analysed then, using Chebyshev Polynomials since reported earlier as a rapidly converging and one of the best suited analytical technique. This study is another appendage to those several studies already conducted and published in the literature on circular elastic plates, resting on elastic foundations. Several of the numerical results so generated on the design parameters were then plotted graphically and are found to have offered certain interesting observations that are believed to be the useful inputs for deigning such circular base slabs for attaching them to seismic bearings systems that may safely be deployed in base-isolation process for buildings.
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Abbreviations
- D :
-
Eh3/ 12(1 − υ2)
- E, υ:
-
Young’s Modulus & Poisson’s ratio of the material
- q :
-
Distributed load per unit area, positive load downwards
- γ :
-
Mass density of the slab material
- τ :
-
Time variable √(D/ha4).t
- a :
-
Radius of circular slab
- h :
-
Thickness of circular slab
- r, θ :
-
Polar coordinate
- g :
-
Gravitational acceleration
- N, M :
-
Number of terms in Chebyshev series
- Mr :
-
Radial bending moment
- Q :
-
qa 4 /Eh 4
- P :
-
Non dimensional load q · a3/D
- T :
-
Time in seconds
- ∇2:
-
\(\left\{\frac{\partial^2 }{\partial r^2}+\frac{1}{r}\frac{\partial }{\partial r}\right\}\)
- ∇4:
-
∇2 ∙ ∇2
- W :
-
Displacement in transverse direction
- \(\overline{w}\) :
-
W/a
- W r :
-
Coefficient of Chebyshev series for W
-
: -
r/a Non dimensional radius
-
: -
The rth Chebyshev polynomial in the range
- G :
-
Pesternack Foundation coefficient
- K :
-
Winkler foundation modulus
- Z :
-
Wnikler foundation factor Ka4/D
- V :
-
Pesternack Foundation Factor −Ga2/D
- f(z),
: -
Arbitrary functions in the range
- Superscript ‘:
-
First term of expansion to be halved
- Subscript J:
-
Step of marching variable
- Superscript (k):
-
Order of derivative
:
:
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Kamal, K. (2021). Dynamic Response of Circular Base Slabs (CBS) Attached to the Seismic Bearing Systems, Inserted for Base-Isolation Underneath the Buildings. In: Sitharam, T., Pallepati, R.R., Kolathayar, S. (eds) Seismic Design and Performance. Lecture Notes in Civil Engineering, vol 120. Springer, Singapore. https://doi.org/10.1007/978-981-33-4005-3_26
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DOI: https://doi.org/10.1007/978-981-33-4005-3_26
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