8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

1/10

To Cover A Swimming Pool with anExpandable StructureF. Escrig(*), J.P. Valcrcel(**)(*) School 01 Architecture 01 Seville (Spain)(**) School 01 Architecture 01 La Corua (Spain)ABSTRACTExpandable Space Structures based on X-frames will be of great use in solving special problems like movable Architecture.In this case we must provide a cover on a swirnming-pool for bioclimaticprofiting. This means that we need to e1iminate the cover for variable periods of time as well as extend it . The area covered is of 3.000 sqm. with asection of sphere that runs hanging below a spatial arch and folds at the topo1. INTRODUCTIONThe question to be solved is how to cover a swimmirng pool of great size (50X 21 sqm) with a structure able to be removed in the summer and erectedtemporarily during other seasons to capture solar energy to heat the air andthe water.To achieve this we provide an Expandable structure of bars based on mov-able X-frames in accordance with the model developed by authors [Ref. 1].Expandable X-frames are mechanisms capable of showing different geometrical configurations from minima when they are folded to great surfaces andwhen they are expanded. In both limit states they can be irnmobilized bymeans of the blockage of sorne elements to guarantee the global stiffness ofthe whole and we can achieve structures useful to building transformablearchitecture.Figure 1 shows how a set of 3-X-frames works while Figure 2 shows thefoldability of a multiple X-frame.

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

2/10

2. FORMAL PROPOSAL

Figure 2

Figure 1

To satisfy our need for a completely removable cover we propose a sphericalshell section 60 meters in diameter and 15 meters in height. This solutionhas sorne important advantages:

274 Rapidly Assembled Structures

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

3/10

RapidlyAssembled Structures 275a) The ratio between surfare enclosure and covered area is mnimum.b) Roof and walls are included into the same geometry.c) I t admits a well studied expandable X-frame.

There are a lot of spherical expandable X-frames to be used, out o whichwe select a triangular spherical grid according to the authors in [Ref. 2].This spacial frame will be supported along its boundaries when expandedand will be hung from a central point of a main arch when folded or duringthe folding process.3. DESIGN AND GEOMETRY OF GLOBAL X-FRAMEThe basic grid will be obtained from a triangular three way plane meshplared at ground level by projecting it on the sphere surfare from its farthest pole (Figure 3).

15 (n .

Figure 36Om.

Figure 4 shows the grid in this way.

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

4/10

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

5/10

Rapidly Assembled Structures 277Into thia spherical grid (D) we must now superimpose an expandable frame.To this we must solve the next system of equations (Figure 5) where (t i areknown for each line of triangular spherlcal three way grid.

Q;i-2=,8i-2+Q;i-lQ;i-l=,8i-l+,8iQ;i=,8i+,Bi-lQ;i+l=,8i+l+,Bi+2

In general this system is not compatible because it contains more equationsthan variables. Nevertheless we can optimize the solution to obtain accept-able tolerances to make the work of the structure possible.Grids projected from a pole are the best for our purpose.By fixing now the angle "{j" for maximum expandability we can determinethe frame (AB) that achieves the necessary conditions to guarantee thekinematic compatibility in the folded and completely expanded positions.Unfortunately the compatibility in intermediate positions is not assured andin most cases we must force the structure to pass through. Nevertheless withlittle imposed defiectioDS it can work in the complete range.Figure 6 shows the whole grid obtained with a = 0'15. Table II showslengths o the bars. Figures 7 and 8 give information on criteria used toidentify each bar position.

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

6/10

278 Rapidly Assembled Structures

Figure 6

Figure 7

6

Figure 8

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

7/10

Rapidly Assembled Structures 279TABLE 11: LENGTHS OF A THREE WAY SPHERICAL X-FRAME

ELE" 017 027 073 074 038 048 085 086 019 029 095 096E61 3.2121 3.1319 3.1895 3.1105 3.1895 3.1104 3.1895 3.1104 3.2120 3.1318 3.1895 3.1104E51 3.1892 3.1102 3.1236 3.0477 3.1238 3.0479 3.1479 3.0679 3.1894 3.1103 3.1451 3.0681E52 3.1895 3.1104 3.1452 3.0682 3.1449 3.0679 3.1238 3.0480 3.1892 3.1101 3.1235 3.0478E41 3.1230 3.0471 3.0195 2.9485 3.0201 2.9492 3.0597 2.9868 3.1235 3.0477 3.0601 2.9872E42 3.1447 3.0677 3.0604 2.9875 3.0603 2.9875 3.0603 2.9875 3.1447 3.0677 3.0603 2.9875E43 3.1236 3.0478 3.0601 2.9873 3.0597 2.9868 3.0201 2.9493 3.1229 3.0471 3.0195 2.9487E31 3.0186 2.9477 2.8849 2.8200 2.8860 2.8211 2.9404 2.8730 3.0197 2.9487 2.9408 2.8734E32 3.0593 2.9865 2.9414 2.8740 2.9423 2.8749 2.9594 2.8912 3.0603 2.9874 2.9597 2.8915E33 3.0603 2.9875 2.9598 2.9815 2.9594 2.8912 2.9423 2.8750 3.0593 2.9864 2.9413 2.8740E34 3.1097 2.9489 2.9409 2.8736 2.9404 2.8731 2.8860 2.8214 3.0186 2.9478 2.8849 2.8203E21 2.8839 2.8191 2.7285 2.6704 2.7299 2.6718 2.7952 2.7342 2.8854 2.8205 2.7956 2.7346E22 2.9399 2.8725 2.7962 2.7352 2.7976 2.7366 2.8299 2.7674 2.9413 2.8739 2.8302 2.7678E23 2.9592 2.9809 2.8313 2.7688 2.8312 2.7687 2.8312 2.7687 2.9591 2.8908 2.8312 2.7687E24 2.9414 2.8741 2.8303 2.7678 2.8299 2.7674 2.7976 2.7368 2.9399 2.8726 2.7962 2.7353E25 2.8855 2.8209 2.7957 2.7348 2.7952 2.7344 2.7299 2.6722 2.8839 2.8193 2.n88 2.6707El1 2.7277 2.6696 2.5588 2.5076 2.56D4 2.5092 2.6331 2.5789 2.7294 2.6713 2.6330 2.5788.E12 2.7948 2.7338 2.6335 2.5793 2.6351 2.5809 2.6796 2.6235 2.7965 2.7355 2.6795 2.6234E13 2.8296 2.7671 2.6806 2.6245 2.6822 2.6261 2.6952 2.6384 2.8312 2.7687 2.6951 2.6383E14 2.8312 2.7687 2.6952 2.6384 2.6952 2.6384 2.6822 2.6262 2.8295 2.7670 2.6806 2.6245E15 2.7976 2.7357 2.6796 2.6235 2.6796 2.6235 2.6352 2.5812 2.7948 2.7340 2.6335 2.5795E16 2.7295 2.6718 2.6331 2.5792 2.6331 2.5792 2.5604 2.5097 2.7277 2.6700 2.5587 2.5080

4. KINEMATICS OF THE X-FRAME GRIDTo fold and expand the grid, it will be supported by its highest node to aframed arch that moreover will contain the rod to facilitate the displacement o the other two nodes. These nodes guarantee the stability o thewhole.Figure 9 shows the arch with the mechanism of folding. The expanding isachieved by forces due to its own weight.

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

8/10

280 Rapidly Assembled Structures

8

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

9/10

Rapidly Assembled Structures 281Figure 10 shows details designed for joints and special pieces.

Figure 10

+ 1Ii--C-:::::>-II- '- '.1!'1

.1:.1;~ e : i \

Figure 11 shows the complete strueture folded while Figure 12 shows it ex-panded.

8/6/2019 1991-1 to Cover a Swimming Pool With an Expandable Structure

10/10

Figure 11

282 Rapidly Assembled Structures

Figure 125. ACKNOWLEDGEMENTSThis research has been achieved with financial support provided by DGICYT (Direccin General de Investigacin Cientifica y Tecnolgica).REFERENCES(1) ESCRIG, F. "Expandable Space Structu res", Space Structures Int.Journ. Vol. 1 numo 2., EIsevier pp 79-91.(2) ESCRIG, F. , P. VALCARCEL and J.R. GIL DELGADO "Design ofExpandable Spherical Grids", IASS Simp. 1989, Madrid, 16pp.