A.Kubaneishvili
Energyonline #1, 2009
NEW PRESTRESSED REINFORCED CONCRETE STRUCTURES WITH THE
SURFACE OF HYPERBOLOID OF THE SHEET
A.Kubaneishvili
Be received 10.08.2009
New constructions of the prestressed reinforced concerete for power complexes, in particular,
chimney, high voltage bearings, arch dam, water conduit chute with the surfaces delineated
with the hyperboloid of one sheet, are considered. Linearity formed by this surface is utilised
for the orientation of the reinforcement along them by stressing of which volumetrically
reduced constructions with increased rigidity and crack resistance are obtained.
Key words: prestressed reinforced concrete, form, hyperboloid of one sheet, rectilinear
generator, chimney, structure frame, tower, assembling, high voltage shaft bearing, water
conduit chutes, arch dam, tensed reinforcement, supporting structures.
One of the principles of progress in civil engineering is the creation of a new generation of
structures based on the concept of seeking for their new efficient forms differing from
classic ones, which should be chosen for satisfaction of both the aesthetic requirements and
the profile of efforts they are to take up. A structure acquires strength, stability and
rigidity due to its complex and perfect geometric form, and not due to the massiveness.
However, it is not always that the structurally justified forms with the lowest material
consumption are the most judicious ones. The technology of their erection plays a
considerable role, and it may turn out that the developed form of a structure is expensive,
labour-consuming and simply unreal. At the same time, the advance of civil engineering
will allow to erect in future such constructions which were considered for a long time as
unrealistic and unrealizable because of the complexity of their implementationn using the
corresponding construction methods and means.
It is obvious from the above mentioned, that the chosen form should both satisfy aesthetic,
structural and functional requirements and possess technological advantages.
The second order linear surfaces (in particular, hyperboloids of one sheet) formed by the
spatial motion of a straight line take a special place in the civil engineering practice.
The generatrix rectilinearity of a hyperboloid of one sheet is employed in the chimney
structure presented in Fig.1.
The chimney represents two independent structures: reinforced-concrete supporting
structure taking up all principal loads acting upon the whole construction and the shaft
located within the supporting structure serving for gas effluent into the atmosphere.
The reinforced-concrete tower with the middle surface of a hyperboloid of one sheet
represents a spatial frame with prefab elements - posts - oriented along rectilinear surface
generating lines. Horizontal reinforced-concrete belts of circular contour are arranged in
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the intersection sites of inclined posts, as well as between them, in order to reduce their
flexibility. The posts orientated along one family of rectilinear generating lines are located
over one surface, while those possessing the orientation of another family - over the other
surface, i.e. a tower is formed out of two closely positioned surfaces separated by a distance
equal to the sum of the post transverse dimension and the width of horizontal belt.
Fig. 1. General appearance of chimney
The posts are fitted with through channels for the reinforcement ropes to be roved through
after their mounting, as well as with holes for grout injection into the channels and for the
control of their filling. The extension of inclined posts in height is performed by means of
welding of embedded fittings set up on the end faces of prefab elements. The post length is
determined by the following condition: its higher mark should protrude over the horizontal
belt level by the height ensuring convenient performance of erection work.
Gas vent channel transfers horizontal load to the supporting structure through a
diaphragm by means of horizontal belts.
When erecting the chimney of the described structure, a section of 12,0 m long gas vent
channel rigidly fixed in the base in the process of erection was adopted as the main erection
unit. Its vertical position was fixed using geodetic instruments. Four structural channels
serving later on, on the one hand, as erection sites, and on the other - as reference points
for the installation of stiffening ring in the designed position, - were welded to the gas vent
channel section at the level of the horizontal belt.
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The horizontal ring connection with the posts was realized by means of the respective
embedded fittings. After these operations, the lower tier of the chimney represented a
rather rigid part of the supporting structure.
The gas vent channel sections of the next tiers were mounted with structural channels prewelded to them at the building site. Horizontal rigidity rings were also installed at the
building site (Fig.2). The erection of inclined posts was carried out at high altitude. Such a
sequence of the supporting structure assembly has significantly speeded up the erection
process.
Fig. 2. Erection of a chimney
After the prefab elements of the supporting structure are assembled, the reinforcing rope
was passed through the formed channels, and its lower end was anchored in the foundation
recess.
Before tensioning the reinforcing ropes, the connection between the gas vent channel and
the supporting structure realized by means of welded - on structural channels was released
by cutting the latter. The reinforcement tensioning was performed at the tower collar
simultaneously in two posts, which were symmetrically arranged against the vertical tower
axis using a hydraulic jack.
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After tensioning the reinforcement ropes, the grout was injected upwards into the channels
using grout pumps. The channel filling was monitored by the grout outflow from the holes
located higher in the frame posts.
From the structural point of view, the suggested structure predominantly differs from the
adopted ones. The grid-like spatial structure combines all advantages of stressed reinforced
concrete with the rigidity and the stability of spatial systems with the surface of the second
order, which is especially important in case of the structure operation under seismic
conditions. Due to the pre-stressing, the joints between the posts are easy to execute, while
the placement of the main supporting reinforcement in the cross-section centre and the
compression of elements excluding their cracking in the process of operation ensure the
corrosion resistance of the reinforcement and, thus, the increase in the construction
durability as a whole.
The described construction of the supporting structure of the chimney may be successfully
applied, for other tower-type structures, as well, for example, for water, water-cooling and
radio-television towers.
The structure of tower-type supports of high-voltage lines with the surface of a hyperboloid
of one sheet is rather promising.
The practice of the erection of high-voltage line supports shows that they are mainly steel
madeand are characterized by complicated geometry, bends, kinks, etc., which significantly
hinders the execution of reinforced concrete. These disadvantages may be eliminated by
applying the tower-type supports outlined by the surface of a hyperboloid of one sheet.
Similar principle forms the basis of new constructions of supports for high-voltage power
lines. But in this case the smaller diameter of a hyperboloid of one sheet is in the base
(Fig.3).
In order to render functional purpose to the surface, which is characteristic to the
structure of high-voltage power line support, one should draw four vertical conventional
mutually intersecting planes (P1, P2, P3 and P4) passing through symmetrical generating
lines of one family (for instance, the generatrix a1-a2 has only one symmetrical generatrix of
the same family b1-b2, while the generatrix of another family d1-d2 has a symmetrical
generatrix c1-c2). Thus, the term "mutually intersecting" points out the fact that only these
generating lines are employed in the present case. The projections of these generating lines
upon the horizontal plane passing through the neck (e-f) of the hyperboloid of one sheet
represent the second kind of lines defining the spatial orientation of planes.
The structural treatment under consideration makes it possible to fix current-carrying
wires without the additional cross-arm. The lower diameter of the base is chosen according
to the condition of the structure strength and stability, while the upper base diameter is
limited by the structural requirements and judicious arrangement of current-carrying
wires.
Advantage of the suggested structure of prefab pre-stressed tower-type support for highvoltage power line is that it may be assembled of elements of the same standard size. Under
such conditions, the material consumption decreases, the elements become maximally
unified, and their production is industrialized. Linearity of the tower posts allows to carry
out preliminary stressing of the whole structure, which enhances its strength and rigidity.
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Fig. 3. Tower-type support of high-voltage power line
a) front view; b) side view; c) top view; d) model
We have examined above tower structures outlined by the surface of the hyperboloid of
one sheet. Such surfaces may also be successfully used in other structures to be examined
herein-after.
Prefab water conduit chutes applied at present have external and internal cylindrical
(circular or parabolic) surfaces with pre-stressed reinforcement placed along the cylinder
generating lines, and they are fit with common reinforcing fabric in the transverse
direction. While the pre-stressed reinforcement ensures the strength, rigidity and crack
resistance of the chute as if it were a beam lying between two supports, - the transverse
reinforcement slightly hinders the formation of cracks oriented along the chute axis and
caused by bending forces acting within the chute edges resulting in a rapid increase in
water losses and reduction of the chute durability.
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One can prevent cracking either by increasing the chute wall thickness, in the percentage
of its reinforcement or in the concrete brand, or by pre-stressing the chute in the radial
direction, too, i.e. by the reduction of its edges. In the first case, the structure mass and the
consumption of funded materials (cement, steel) inevitably grow, while the second way is
unrealizable for the adopted shape of the chute wall external surface.
The external surface of the chute of proposed structure results in the dissection of a
hyperboloid of one sheet by a plane passing through its longitudinal axis, while the internal
(moistened) surface may represent a part of circular, elliptic, parabolic, etc, cylinder
(Fig.4).
Such a combination of two different surfaces creates the chute structure with variable
cross-section and increased thickness on the supports. I.e. foots without any kinks, which
favours the operation of large-span chutes under cutting forces.
Fig. 4. General appearance of water conduit chute
One can obtain optimum cross-section of a chute by varying different guiding curves of the
external (a circle, an ellipse) and internal (a circle, an ellipse, a parabola, etc,) surfaces.
The linearity of the generating lines of the hyperboloid of one sheet is used for the
orientation of pre-stressed reinforcement along them (Fig.5). In case of such a placement of
the reinforcement, one obtains a spatial frame consisting of mutually intersecting
reinforcing bars. Certain part of the reinforcement passes along the whole chute length and
is anchored in its end faces, while another part (which is especially important) reaches the
edge rims and is anchored there. Under the preliminary reduction of the structure,
concrete cells created by the stressed reinforcement intersection, take up a biaxial
reduction. Consequently, while the pre-stressed reinforcement located along the
longitudinal axis in the existing chutes imparts uniaxial reduction to the structure, - in our
case, due to the inclined arrangement of the reinforcement, the structure undergoes a
volumetric reduction, i.e. both longitudinal and radial reduction. This makes possible to
refuse a transverse grid used for the chute edges in the existing reinforcement method.
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Arch dams of original shape may be produced when using the hyperboloid of one sheet for
the design of its upstream and down-stream faces.
Fig. 5. Pre-stressed reinforcing cage of water conduit chute
Modern trends in the design of arch dams are characterized by the search for arch shapes
ensuring maximum utilization of concrete strength and elimination of tensile stresses
within the parts of the structure. It complicates more and more the arch outlines in the
horizontal plane (elliptic, parabolic, milti-centre) and leads to their bending in the vertical
plane, which is attributed to the striving to use the construction weight for the reduction of
tensile stresses in the upstream and downstream faces, as well as to the improvement of the
total spatial distribution of stresses within the shell in case of the principal and special
combination of loads.
Despite these measures, one cannot manage to avoid arise of tensile stresses. They basically
occur in the upstream face of the lower arch and in the downstream face, in the upper
third of the cantilever height. In certain cases, they reach the tensile strength of concrete
and even exceed the latter.
It is necessary to note that the technology of step-by-step erection of high arch dams
requires their subdivision into blocks. After the dam erection, vertical and horizontal joints
of these blocks are grouted under high pressure. However, regardless of all these structural
and technologic measures, the density of these joints proves to be low, and consequently,
they become the sites of origin for water seepage through the dam body, which exerts
negative influence upon the construction durability as a whole.
The most efficient means of the removal of tensile stresses in arch dams is their execution
in their pre-stressed modification. All operating dams are stressed either in horizontal
direction using jacks (Namb Falls dams in the USA) or in vertical direction using tension
bars or other devices (the dams "Kagi" in Costa Rica, Silvenstein in GFR, etc.). In such
cases, while we suppress tensile stresses and reduce construction joints in one direction,
other directions remain in the original state.
It seems impossible to eliminate these disadvantages by the arrangement of the stressing
reinforcement along two directions taking into account the trend to a stronger arch
bending and the traditional forms of arch dam surfaces. It could lead to significant
technological problems connected with the formation of curvilinear channels, with the
necessity to tighten curvilinear reinforcements, etc.
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Energyonline #1, 2009
The use of the surface of hyperboloid of one sheet for the design of downstream and
upstream dam faces in the cantilever direction will cause its inclination towards the waterhead (Fig.6), and the arches convex towards the same side will be characterized by circular
or elliptic outlines. The required dam thickness may be obtained by the choice of constant
coefficients in the equation of the surface of the hyperboloid of one sheet.
The pre-stressed reinforcement 1 arranged along mutually intersecting rectilinear
generating lines is anchored in the foundation and in the crest of a dam and forms a spatial
frame, its bars intersecting horizontal 3 and vertical 2 construction joints of the dam at
some angle. At the tensioning of reinforcement strands 1, the dam turns out to be
volumetrically reduced, which makes it possible to eliminate tensile stresses in the structure
in whole.
Thus, without customary technological difficulties, one may produce a pre-stressed arch
dam with concrete operating under the conditions of volumetric compression, which allows
to use its strength in the best possible way, to decrease the volume or to reduce the brand.
Such a structural approach makes it possible to design (7) a dam in its prefab modification
which is reasonable and efficient if the height does not exceed 70 m. Inclined pre-stressed
reinforcement 1 contributes to the execution of the joint 6 between prefab elements 4
without any additional measures, via their reduction from all sides. In those places where
prefab elements abut on the base, the latter is smoothed down by a layer of concrete 5
stretched below. It is not difficult to produce curvilinear prefab elements, since their shapes
are created using rectilinear elements which should be oriented along the surface
generating lines.
Retaining walls occupy a large volume in the complex of engineering structures, and their
production requires significant amount of materials and labour consumption.
Recently, one can have noticed a trend to the transition from flat gravitational reinforced
concrete structures of the retaining walls to spatial ones characterized by the minimum
material consumption and by the possibility to transform the existing bending moments
into longitudinal forces without any increase in the structure thickness.
In this respect, the application of the surface of a hyperboloid of one sheet in retaining
structures, side by side with the mentioned advantages, makes it possible to improve
service properties, as well.
As in case of the support of high-voltage power lines, here, the smaller diameter of the
surface should lie in the base, too.
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Fig. 6. Pre-stressed arch dam
a) reinforcement diagram; b) prefab modification;
c) top view of reinforcing cage; d) vertical section
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Fig. 7. Coast-protecting structure with the surface of one-sheet hyperboloid
a), b) diagram of formation; c) general view; d) diagram of reinforcement
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In order to render the form applicable for retaining structures to the surface, one should
draw two vertical planes (P1 and P2, Fig.7,a) passing through the generating lines of various
families (ab, dc and ab1, dc1) tangentially to the points a and d of the smaller lower
diameter of the hyperboloid of one sheet. These planes cut off the surface its parts 1 and 2.
Here the lobes abcd and ab1c1d (Fig.7,b) with double curvature are formed, and these lobes
may be employed for retaining constructions. Their horizontal convexity (ad,...bc) should
be orientated towards ground filling, and the lobe will be convexly (ab,...dc) (along the
vertical) turned to the external surface of the construction, i.e. will be inclined towards the
filling.
The linearity of generating lines of the hyperboloid of one sheet is applied for the
orientation of the pre-stressed reinforcement along them (Fig. 7,b). At such an
arrangement, a spatial frame-work consisting of mutually intersecting reinforcing bars is
formed. Certain part of the reinforcement passes by the whole construction height (1),
while another part reaches (2-4) side edges. Under the preliminary reduction of the
structure, concrete cells created by the intersection of the inclined stressed reinforcements
acquire a biaxial reduction, i.e. the structure undergoes a volumetric reduction, which
allows one to abandon transverse reinforcement (along horizontal arches).
In such a structure, due to the decrease in the surface curvature, the cross-section rigidity
grows upwards in accordance with the profile of the pressure of acting forces (filling), and
the structure inclination towards the filling decreases the ground pressure intensity upon
the former. The reinforcement orientation along rectilinear generating lines of the
hyperboloid of one sheet not only improves the technology of curvilinear surface prestressing (in such a case, rectilinear bars, and not the curvilinear reinforcements are
stressed), but also makes it possible to create a spatial pre-stressed grid with the spacing
decreasing downwards, and it becomes superfluous to install additional reinforcement in
the lower part where the external forces reach their maximum values.
A retaining wall with such a surface may be successfully applied as a coast-protecting
structure. Modern trends in the hydraulic engineering of coasts suggest the necessity to
substitute the passive principle of a protecting structure operation by the active one. Only
those structures which correspond most harmoniously to the natural coast and to the
parameters of the wave flow can "survive" and operate reliably. As numerous
investigations have shown, a coast protecting structure represents an analog of a twisting
coast, being in plan a curvilinear concrete faced slope with different curvatures of the
profile of its concave and convex parts. Such a shape is the most close to the suggested
shape of a retaining wall. It represents as if a synthesis of the decisions suggested by the
nature and the practice of coastal hydraulic engineering. As the experiments carried out in
the wave basin of Georgian Research Institute of Power Engineering and Power Structures
has shown a wall with the surface of the hyperboloid of one sheet plays, due to its shape, a
positive role in the preservation of local beach material in comparison with a vertical wall.
The constructions presented above, despite their different functional purposes, are united
by one attribute: a linear surface of the second order - a hyperboloid of one sheet - have
been used in their design.
Apart from aesthetic expressiveness, they are characterized by technical and economic
advantages. Thus, for instance, the cost of 30 m high chimney (Fig.1) has reduced by 32%
in comparison with a metallic one due to the use of the supporting structure of the
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suggested design, and the retaining wall with the surface of the hyperboloid of one sheet
constructed at the Black sea coast in Georgia has proved to be 23% more efficient than the
reinforced concrete wall with a flat surface.
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Sectional tower structure/ United Stads Patent/ N4196551.
Кубанеишвили А.С., Бондаренко В.Б. и др. Новая конструкция предварительного
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Кубанеишвили А.С., Меладзе Ф.Г. Новая конструкция берегозащитного
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АRCHIL KUBANEISHVILI. Doctor of Technical Sciences, Professor, Georgian Research
Institute of Power Engineering and Power Structures,
0171, Georgia, str. Kostava, 70.
Теl.: +995(32) 38-67-98; Моb.: +995 99 939496
E-mail: [email protected]
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