Abstract:
Water towers are prerequisite for providing the hydraulic head and partial storage to
meet the fluctuating demands. Among different type of tanks used for water towers
'Intze' tank is an economical tank for reinforced concrete, because its ability to carry
part of the water load by direct compressive forces. Stress analysis of 'Intze' tank is
extremely complicated due to many degrees of redundancy. However, the elastic
theory of thin shell with certain approximation may be used to analyze these tanks
with sufficient accuracy.
The principle stress system is obtained using membrane theory of shells. The
deformations due to membrane forces are found to be incompatible at the junction
where the different shells forming the tank meet and the continuity of the structure
gives rise to edge restoring forces. The edge restoring forces and the perturbation or
the membrane stress system due to edge forces are obtained by using compatibility
equations and bending theory of shells.
Along with the assumptions made in electric theory of thin shells, the following are
included,
1 ) . The effect of edge restraining forces in the shell is predominant in the border
zone, and diminishes away from the edge point. The restraining forces at one
edge have only a small effect on stresses on deformation at the other edge,
when the linear dimension is large compared to the thickness. Therefore it is
assumed that the effect of restraining forces at one edge is independent to
the end condition at the other edge. This assumption is satisfactory for the
usual proportion of shells forming an 'Intze' tank.
2). Thomson's functions are approximated to the first term of the asymptotic
expansion when the variable is greater than ten.
The analysis of shell structures involves a two step procedure similar to the
one used for statically indeterminate frames. In shell structures membrane
analogy is used to obtain the principal stress system. Membranes theory
assumes that a thin shell structure, because of its low flexural rigidity
carries the loads by direct shearing forces in the plane of its surface. This
assumption necessitates specific support conditions for the different families
of shell and loading conditions.
