Plane hollow reinforced concrete floors with two-dimensional structure

A plane, hollow, reinforced concrete floor slabs with two-dimensional structure and method for their production. Constructions developed by this technic will vary widely and with considerable profit replace conventional floor structures. The technique makes it possible to choose higher strength and stiffness, less volume of materials, greater flexibility, better economy or an arbitrary combination of these gains. The technique makes it possible to create a total balance between bending forces, shear forces and stiffness (deformations)--so that all design conditions can be fully optimized at the same time. The technique presents a distinct minimized construction--characterized by the ability that concrete can be placed exactly where it yields maximum capacity. The technique offers material and cost savings compared with the conventional compact two-way reinforced slab structure. The technique is suitable for both in situ works and for prefabrication.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates to plane, hollow, reinforced concrete floors with 
two-dimensional structure and span in arbitrary direction. The present 
floor structure is part of a complete construction system developed for 
obtaining increased flexibility and a large beamless span. 
2. Background Art 
The weakness of concrete floor structures is considered well-known. 
Concrete floor structures have one fault. The dead load is usually 2-4 
times heavier than the useful load capacity. This situation has resulted 
in numerous attempts being made to make the construction less heavy, 
mostly by forming various types of kind of internal cavities. Yet, no one 
has ever succeeded in finding a general solution to the problem. In order 
to obtain a practical solution, a large number of conflicting conditions 
necessarily have to be fulfilled. All previous attempts have been directed 
to the simple "one-dimensional" structure (span in one direction) rather 
than to the much more complex "two-dimensional" structure (span in 
arbitrary direction). The two constructions have quite different static 
functions and cannot be compared. 
Since the 1950's, floors with one-dimensional structure have been fully 
developed by means of the prefabricated and prestressed hollow concrete 
element, where the hollow profile is made by monolithic concreting around 
steel pipes, which are drawn out of the element after cementation leaving 
cylindrical cavities in the concrete. The floor achieves maximum bearing 
strength corresponding to the concrete volume. However, the floor 
construction can only be made as a prefabricated element, and the load 
capacity exists only in one direction. This shortcoming impedes the whole 
building structure, as the construction has to be adapted to the floor 
elements to a large extent. The building system suffers from the necessity 
of bearing walls or beams and offers no true flexibility. 
DE 2.116.479 (Hans Nyffeler April 1970) discloses the use of balls of 
lightweight materials instead of the mentioned pipes, whereby shortening 
of prefabricated pipes on the site may be avoided. In order to form a row 
of balls, the ball are provided with a through-going, central bore and 
threaded on a bar. The bars with the balls are supported by the 
reinforcement by means of chairs. 
This idea has several drawbacks, which make it quite unrealistic. For 
instance the hollow balls within the bore will be surrounded by concrete, 
whereby the method is extraordinarily difficult to carry out in practice. 
Consequently, it can be concluded that the idea is possible in theory, but 
is in no way realistic. In connection with two-dimensional structures, the 
idea cannot be implemented at all. It would be completely impossible to 
thread balls on crossed bars. 
Floors with a two-dimensional structure cannot be used rationally in 
conventional solid designs, especially in combination with supporting 
columns, because of the high weight/thickness ratio. 
Without the use of columns, the application of a solid floor is restricted 
to small elements with a side length of about 3 to 5 meters, whereby the 
whole building structure is restricted to a very small structural module, 
thus this system also has a very limited flexibility. 
No technique known from one-dimensional, hollow structures can be 
transferred to a two-dimensional, hollow structure. 
SUMMARY OF THE INVENTION 
The present invention solves the general problems of improving the shear 
conditions and providing internal cavities in a very simple manner. Hollow 
bodies (air pockets) and reinforcement are integrated in a locked 
geometric and static unit by arranging the hollow bodies in the 
reinforcement mesh, whereby the mutual position of the hollow bodies is 
essentially fixed in the horizontal direction. 
In vertical direction, the hollow bodies may be fixed by means of an upper 
mesh, which is connected to the reinforcement mesh by means of connection 
bars, whereby an internal lattice of steel and hollow bodies are formed 
for embedding in a monolithic concreting according to usual practice. 
The internal cavities formed by hollow bodies meet all seven technical 
conditions stated below 
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1. simple shape (feasibility) 
and arrangement 
2. closed body (water-tightness) 
3. strength (inflexibility at contact points) 
4. reliable fixing (during transportation and 
concreting) 
5. symmetrical body (2-axes of symmetry or 
rotation) 
6. symmetrical structure 
(2-axes of symmetry or 
rotation) 
7. no obstacles for (continuous) 
monolithic concreting. 
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From these criteria, hollow bodies have been developed with shapes 
essentially ellipsoidal and spherical. For practical reasons, the hollow 
bodies may be formed as separate members for assembly with possibilities 
for variation. 
By the present invention, 30-40% of the concrete may be replaced by air. 
The result is a two-dimensional plane, hollow floor structure weighing 
less, having higher strength and higher rigidity than all known floor 
structures and in fact having essentially an unlimited load capacity and 
versatility resulting in a better economy. The present invention has the 
following advantages in relation to traditional solid floors: 
A 40% to 50% saving in concrete materials is gained and 30% to 40% saving 
in steel materials is gained; or increased strength of 100% to 150% is 
gained or increased span of up to 200% is gained.

DESCRIPTION OF PREFERRED EMBODIMENTS 
There exists no substantial difference between carrying out prefabrication 
and in situ work, so the latter will be described below. A two-way 
reinforcement mesh 1 is arranged in the form 16 in ordinary manner (see 
FIGS. 6-13), and fixed to the bottom thereof. Then the hollow bodies 3 are 
placed directly on the reinforcement I in every second mesh 2. The bodies 
3 are retained in position by an upper net 12 as shown in FIG. 8. 
Alternatively, the bodies may be retained by a connecting bar or wire 
inserted into predetermined openings 15 in the bodies 3 as shown in FIG. 
6. The two steel nets 1,12 and the bodies 3 therebetween form a stable 
lattice, the two nets 1,12 being interconnected by means of conventional 
connecting bars or wires 13. 
The completed three-dimensional stable lattice of steel 1,12 and hollow 
bodies 3 are thus ready for concreting in the conventional manner. 
If desired, the vertical connection between the two nets may be made 
suitably loose to allow buoyancy to lift the bodies and thereby ensuring 
complete concreting of both mesh and bodies. 
The finished floor structure appears as a cross web construction with a 
plane upper and lower surface (a three-dimensional concrete lattice). It 
should be noted that the production thereof is no more time-consuming than 
a conventional floor construction with double reinforcement. 
The calculations below illustrate the advantages of the hollow body floor 
(o) according to the invention compared to a traditional solid floor (m) . 
A. Same Thickness of the Two Floors 
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A 32 CM SOLID FLOOR VS. A 32 CM HOLLOW 
BODY FLOOR 
solid floor hollow body 
Loads (m) floor (o) 
______________________________________ 
dead load g.sub.1 = 
7.7 .times. 10.sup.3 N/m.sup.2 
5.1 .times. 10.sup.3 
N/m.sup.2 
floor finish g.sub.2 = 
0.4 0.4 
light partitions g.sub.3 = 
0.5 0.5 
load capacity p = 
1.5 1.5 
##STR1## 
______________________________________ 
The calculations are based on the same static conditions in the two floors: 
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same effective thickness of the concrete h.sub.e 
same pressure zone = 20% of h.sub.e 
same moment arm = 90% of h.sub.e 
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h.sub.e being the total thickness of the floor and the concrete cover 
having a thickness of 3 cm. 
1. Gain in Load Capacity 
______________________________________ 
With the same support 
the load on the hollow 
body floor may be increased 
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by (10.6 - 8.0)/1.3 = 2.0 .times. 10.sup.3 N/m.sup.2 
to 1.5 + 2.0 = 3.5 .times. 10.sup.3 N/m.sup.2 
or 100 .times. 2.0/1.5 = 130% 
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2. Gain in Free Span 
If calculations are based on the bending force: 
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M (moment of force) = load (q) .times. width (k) .times. length (l) = 
load 
(q) .times. area (A) 
M.sub.m (solid).about.q.sub.m .times. A.sub.m = 10.6 A.sub.m 
M.sub.o (hollow body).about.q.sub.o .times. A.sub.o = 10.6 A.sub.o 
M.sub.m /M.sub.o = 10.6/8.0) .times. A.sub.m /A.sub.o = 1.33 A.sub.m 
/A.sub.o 
For M.sub.m = M.sub.o 
A.sub.o = 1,33 A.sub.m 
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Calculations based on shear force give a similar result. In both cases an 
increase of 33% is achieved, i.e. 16% in each direction. 
B. Same Load Capacity 
1. If a Solid Floor Should Have the Same Load Capacity as a Hollow Body 
Floor 
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With a load capacity .rho..sub.o = 3.5 .times. 10.sup.3 N/m.sup.2 
the thickness is as an 
estimate increased from 32 cm to 46 cm 
corresponding to an increase of 
the dead load of 45% 
or an extra dead load of 3.5 .times. 10.sup.3 N/m.sup.2 
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Control of Estimate 
The estimated thickness of 46 cm result in 
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a dead load of 7.7 .times. 46/32 = 11.0 .times. 10.sup.3 N/m.sup.2 
permanent load 0.9 .times. 10.sup.3 N/m.sup.2 
(load of floor finish (g.sub.2) and 
partition (g.sub.3) 
load capacity 3.5 .times. 10.sup.3 N/m.sup.2 
design load: q.sub.m 
16.4 .times. 10.sup.3 N/m.sup.2 
M.sub.m /M.sub.o = q.sub.m /q.sub.o = 16.4/8.0 = 2.1 
As M.sub.m/M O = (h.sub.m /h.sub.o).sup.2 = 2.1 
______________________________________ 
where h.sub.m and h.sub.o are the arm of moment for the solid floor and the 
hollow body floor, respectively 
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h.sub.m /h.sub.o = 1.45 
and h.sub.m = 32 .times. 1.45 = 46 cm, 
i.e. the estimate is correct. 
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2. Reduction in Thickness of a Hollow Body Floor (o) Having the Same Load 
Capacity as a Solid Floor (m) 
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load capacity .rho..sub.m = 1.5 .times. 10.sup.3 N/m.sup.2 
As an estimate the thickness 
20% 
could be reduced by 6 cm from 
32 cm to 26 cm corresponding to 
a reduction in the 
dead load of approx. 
or a total load reduction 7.7-7.7 (1.2).sup.2 = 3.5 .times. 10.sup.3 
N/m.sup.2 
corresponding to 45% 
Control of estimate 
5.1 .times. 26/32 = 4.2 .times. 10.sup.3 N/m.sup.2 
The estimated thickness of 26 cm 
results in a dead load of 
Permanent load (load of force 
0.9 .times. 10.sup.3 N/m.sup.2 
and floor finish (g.sub.2) and 
partitions (g.sub.3)) 
Load capacity 1.5 .times. 10.sup.3 N/m.sup.2 
Design load q.sub.o 
7.1 .times. 10.sup.3 N/m.sup.2 
M.sub.o /M.sub.m .about.q.sub.o /q.sub.m = 7.1/10.6 = 0.67 
As M.sub.o /M.sub.m .about.(h.sub.o /h.sub.m).sup.2 = 0.67 
Where h.sub.m and h.sub.o are the arm of 
moment for the solid floor and 
the hollow body floor, respectively 
h.sub.o /h.sub.m = 0.82 
and 
h.sub.o = 32 .times. 0.82 = 0.26 
The estimate is thus correct. 
______________________________________ 
C. Same Weight 
______________________________________ 
A 32 CM HOLLOW BODY FLOOR vs. A 21 CM 
SOLID FLOOR 
______________________________________ 
Same load 
dead load g.sub.1 = 5.1 .times. 10.sup.3 N/m.sup.2 
floor finish g.sub.2 = 0.4 
light partitions g.sub.3 = 0.5 
load capacity .rho. = 1.5 
##STR2## 
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1. Gain in Bending Strength 
______________________________________ 
M.sub.m = M.sub.o .about.qkl = qA 
As M.sub.o /M.sub.m = (h.sub.o /h.sub.m).sup.2 
M.sub.o /M.sub.m = (32-3/21-3).sup.2 = 2.6 
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Thus, the bending strength for hollow body floor is 160% larger than for a 
solid floor. 
2. Gain in Shear Strength 
The shear strength will also be increased by more than 100%, but depends 
on the width of the support besides the thickness. 
3. Gain in Free Span 
______________________________________ 
M.sub.o /M.sub.m = qA.sub.o /qA.sub.m = 2.6 
A.sub.o /A.sub.m = 2.6 
______________________________________ 
The free floor area (span) of a hollow body floor is 160% larger than the 
free area of a solid floor, or 60% in each direction.