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Study on Shallow Funicular Concrete Shells over Square Ground Plan Subjected
Post: #1

Study on Shallow Funicular Concrete Shells over Square Ground Plan
Subjected to Ultimate Loads




.pdf  1Study on Shallow.pdf (Size: 583.89 KB / Downloads: 83)


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.
Post: #2
Peels, taut skin structures due to their geometry and small stiffness of skin flexion, tend to carry loads mainly by direct stresses acting on their plane. Surface funicular concrete Rectangular plant shells, double curvature with different rises are loaded to failure with a concentrated central force. Specimens of size 100 cm x 90 cm in plan with edge beam of size 4cm x 4cm are prepared with grade M30 concrete for which the mixing design is carried out by the Indian Standard method. The specimens are prepared in various increments and are cured wet. They are subjected to final loads and the corresponding stains and deflections are measured. Fault patterns are observed for shells with different rises. From the experimental investigations we arrive at a relation between the relation of amplitude to elevation and the final load. It is concluded that the final loads are a function of the increase of the shell.

Structures can be classified in many ways according to their form, their function and the materials from which they are made. A structure or structural element may be a fully three-dimensional solid object such as a monolithic pyramid or may have some dimensions smaller than a ball bearing. The shells belong to the class of structures of stressed skin that, due to their geometry and small stiffness to the flexion of the skin, tend to load loads mainly by direct stresses that act in their plane. Shells impart force through their shape as opposed to force through the mass. Concrete shells are structures that by their shape offer an exceptional load capacity. Concrete shell structures are capable of spanning great distances with a minimum amount of material. Reinforced concrete shell structures are widely used because they provide exceptional performance and architectural beauty. Although it is an elementary structure in nature, much remains to be learned about its application in the construction industry. Ideally, a concrete shell in its membrane state withstands the external loads by pure compression, unaccompanied by shear stresses so that tensile stresses are not developed. It is advantageous to select the shape of the shell in such a way that, under the loading condition, the shell is subjected to pure compression without bending. This can be achieved by forming the wrapper in the form of a catenary whose funicular shape corresponds to the dead weight. Shell's rectangular and square ground plans are very prevalent in modern construction and architectural practice.
 

Marked Categories : project report on concrete shells, project experimental study on shallow funicular concrete shells subjected to ultimate load,

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