25-08-2017, 09:32 PM
Study on Shallow Funicular Concrete Shells over Square Ground Plan
Subjected to Ultimate Loads
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ABSTRACT:
Shells belong to the class of stressed skin structures which, because of their geometry and small flexural
rigidity of the skin, tend to carry loads primarily by direct stresses acting in their plane. Concrete shallow funicular shells
of square plan, double curvature with various rises are analysed for concentrated central force. Specimens of size 100 cm
x 100 cm in plan with edge beam of 4cm x 4cm are prepared using cement concrete of grade M20 for which the mix
design is carried by IS method. A form consisting of square steel frame and foam leather rexine are used for casting the
shells. The specimens are prepared with various rises of 8 cm, 12 cm and 16 cm. The specimens are moist cured for 28
days before testing. The concentrated force over the centre of the shell specimen is applied and the corresponding
deflections are measured within the elastic range. After the elastic range all the specimens are subjected to failure and
hence the ultimate loads are determined. Finite element models of funicular shells are developed by discretizing the
shell specimens prepared and the coordinates are determined by using Total station. Analysis and computation of
stresses are carried for the modelled shells using standard software. A relation between ultimate loads and span to rise
ratio is arrived. Conclusions are made by comparing the experimental and analytical results.
INTRODUCTION
Shells belong to the class of stressed skin structures
which, because of their geometry and small flexural
rigidity of the skin, tend to carry loads primarily by direct
stresses acting in their plane. In the design of new forms
of concrete shell structures the conventional practise is to
select the geometry of shell first and then making the
stress analysis. In this process no deliberated effort is
taken to ensure the desirable state of stress in the material.
Perhaps it is more logical to reverse this process. Ideally a
concrete shell in its membrane state carries the external
loads by pure compression, unaccompanied by shear
stresses so that no tensile stresses develop and hence the
reinforcement becomes necessary excepting for secondary
effects like bending, shrinkage. It is advantageous to
select the shape of shell in such a way that, under the
condition of loading, the shell is subjected to pure
compression without bending. This can be achieved by
shaping the shell in the form of a catenary which the
funicular shape is corresponding to the dead weight. Shell
of rectangular and square ground plans are very frequent
occurrence in practice.
Methodology
Materials
A study is made to investigate the influence of span/rise
ratio (λ) of shallow funicular concrete shells over square
ground plan on deflections and membrane stresses in
diagonal and longitudinal directions. To determine the
profile and coordinates of shallow funicular shell over
square ground plan with different span/rise ratio (λ),
concrete funicular shell specimens of various rises are
prepared and designated as follows.
RESULTS AND DISCUSSIONS
From the analysis results, it is observed that the membrane
stresses S11 and S22 along the diagonal direction j,
decreases with the increase in rise of the shallow funicular
shell over square ground plans. It is also observed that the
membrane stresses along x and z directions decreases with
the increase in rise of shallow funicular shell over square
ground plans. From the results of displacements due to the
concentrated load applied on shallow funicular shell over
square ground plans of SFS I, SFS II and SFS III for the
same magnitude, the deflections are decreased with the
increase in rise. From the table a plot is made between,
deflection and span / rise ratio (λ). From fig.21 it is
observed that deflection increases with the decrease in
span / rise ratio and the relationship between deflection
(w) and span/ rise ratio (λ) can be approximated by the
equation 1, where λ value lies (5 < λ < 20).
CONCLUSIONS
The following conclusions are drawn from the test results:
The deflection of shallow funicular concrete shell
decreases with increase in rise.
Membrane stresses decreases with the increase in
rise of shallow funicular concrete shell.
It is concluded that a decrement of 20 to 35% of
membrane stresses in SFS II when compared
with SFS I along j direction.
It is concluded that a decrement of 30 to 50% of
membrane stresses in SFS III when compared
with SFS I along j direction.
It is concluded that a decrement of 20 to 30% of
membrane stresses in SFS II when compared
with SFS I along x, z directions.
It is concluded that a decrement of 30 to 50% of
membrane stresses in SFS III when compared
with SFS I along x, z directions.