////////surface active structures///////////// (TEAM) Gabriela Gonzรกles Juan Diego Ardila Mauricio Valenzuela

(Tutor) Manja van de Worp

(main subjects) Minimal surface analysis Folded structure analysis Folded plate structure development

Minimal surface

(Structure utilization)

TOPOLOGY FAMILY

As in previous analysis (Displacement), the support location, quantity and conditions are the same for the following analysis, where the cross section is the variation:

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option 1

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utilization

utilization

utilization

1.7 %

2.3 %

1.7 %

34.1 %

49.6 %

34.1 %

66.5 %

11.8 %

66.5 %

MATERIAL-Steel Supports-Moment Fixed no. supports-4 cross section height-25

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option 2

TOPOLOGY FAMILY

option 3

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option 1

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utilization

utilization

0.1 %

0.5 %

0.1 %

5.6 %

6.3 %

4.9 %

9.6 %

12 %

9.6 %

+ MATERIAL-Steel Supports-Moment Fixed no. supports-4 cross section height-75

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option 2

utilization

option 3

/// The results are similar to the displacement analysis, since the utilisation is optimal for the second option of cross section (75). /// Geometry 2 has dramatical differences between one cross section and the other one, also compared to the other geometries. /// Geometries 1 and 3 are the optimal surface + optimal cross section + good results for how hard the material is working (utilisation). /// Geometry 3 performs slightly better than geometry 1.

[Minimal surface - revolved surface analysis]

(Structure stress lines)

Three related geometries, generated in order to be analyzed and to conclude which one is the optimal effective structure:

(Geometry variations)

option 3

option 2

option 1

(GEOMETRY DISPLACEMENT)

/// Option 2, is the one that has less density, and good distribution of stress lines, in all of its surface.

The condition of the cross section is the parameter that is being tested: -2.24 e -08

-2.56 e -09

TOPOLOGY FAMILY

2.24 e +00

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Material - Steel Supports - Moment Fixed No. supports - 4 Cross section height-25

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+ -2.00 e -08 2.00 e +00

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2.56e +01

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Material - Steel Supports - Moment Fixed No. supports - 4 Cross section height-75

+ -2.17 e -09 2.17 e +01

+ -1.25 e -08

-1.50 e -09

1.25 e +00

1.50 e +01

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/// The second option for cross section (75), is the one that has the less displacement for the geometries, specially as observed in the upper part of geometry - option 2. /// For geometries 1 and 3, the displacement is not as dramatic from one cross section to the other. /// The displacement is similar in both, slightly less for geometry 3.

(Support & JOINT variation)

tension - compression

TENSION Compression

TENSION Compression

TENSION Compression

/// For variation 1, 6 supports meaning 3 per main beam, where moment fixed, and the joint conditions were moment-fixed in the y axis.

/// For variation 2, the supports remained in the same location as the previous analysis, but 2 were moment fixed, and 4 were pinned. The joint conditions had no variation.

/// For variation 3, the supports remained as in the previous analysis,(2 moment fixed, 4 pinned). The joint conditions were modified, in order to explore radically different behavior of the forces, were for the main beam the joints are at the beggining and end of node: moment-fixed in y axis; the same as the secondary beams, the joint has at the end of node: moment fixed in y axis.

(grid variation)

(FORCES BEHAVIORS)

TENSION Compression

(grid optimization) /// Grid 1 supports tension and compression, distributed almost evenly, but for one support. /// Grid 2 supports compression as Grid 1, but for tension, it seems as the beams are not working Symmetrically. /// Grid 3, performs tension and compression as Grid 1.

[Joint variations] As a conclusion of the previous exercise, Grid 3 was selected to proceed to beams analysis. Three supports +joints variaton of conditions were studied, to decide once again, the optimal structure.

MY

/// For variation 1 and 2, the results are very similar, but for Torsion in X axis, reflecting the effect of having 60% of the supports pinned except than momentfixed.

/// If a decision has to be made among these three options, the conditions setled in the first anaylis are the most convenient ones, since the bending and torsion moments are less, than the other variations.

/// For variation 3, the results are dramatically different from the previous ones, reflecting the removal of the moment-fixed in the x and z axis, at the starting node of the main beams.

MZ

MX

[Forces Behaviors]

As a conclusion of the previous exercise, Geometry 3 was selected to proceed to beams analysis. Three grid structures are proposed, and the behavior of the forces will provide the data needed to decide once again, the optimal structure.

/// Grid 2 has most of the forces behavior at the base, almost no behavior from the middle to the top.

/// Grid 1 performs as a shell, therefore, the loads are distributed almost evenly in all of the beams (shell components) from the middle to the bottom, where most of it is concentrated.

/// Grid 3, shows a natural scale of the forces actuating from the top to the bottom, where the forces and loads converge the most.

GEOMETRY â&#x20AC;&#x153;gridsâ&#x20AC;?

option 1

option 2

option 3

STRONG AXIS SHEAR (vz)

AXIAL FORCE (nx)

BENDING in strong axis (my)

BENDING in weak axis (mz)

BENDING (vy)

STRESS nx+my+mz+vy+vz

FOLDED PLATE: (1) Shell configurations

(folded structure)

(Structure stress lines) Approximate flows of a network of perpendicular lines of pure tensile and pure compressive stresses

Folded plates are thin structural surfaces that can achieve remarkable sapns without the complexity of constructing a single or double curved surface. The primary fold lines represent lines of stiffness in the system. They have to run approximately along the spanning direction of the system. Adjacent plates give support to each other across the fold lines. Equivalent continuous beam, with typical deflections for uniform load shown dashed. In this direction the plates work in pure bending.

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option 2

= Across the main span the system acts as a slab in bending, with each fold acting like a support.

The deformation of the structure itâ&#x20AC;&#x2122;s determinated in our analisys basicly by the CROSS SECTION HIGHT and the changes in the geometry.

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option 1

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Original_More curvature definition.

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-2.08 e -08

-8.07 e -09

2.08 e +00

8.07 e +00

TOPOLOGY FAMILY

option 2

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MATERIAL-Concrete supports-Fixed no. supports-5 each side cross section height-40

-5.20 e -08 5.20 e +00

MATERIAL-Concrete supports-Fixed no. supports-5 each side cross section height-75

-1.86 e -08 1.86 e +00

option 1

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Original_More curvature definition.

-2.91 e -08

-7.08 e -08

2.91 e +00

7.08 e +00

In order get the original geometry itâ&#x20AC;&#x2122;s necessary to encrease the cross section and avoid the displacement

(Structure utilization) With both different cross section section hight, the joints between the plates are where the material itâ&#x20AC;&#x2122;s working more and is major utilization of .In the cases of the Original shape, just because represent a defined curvature, these kind of utilization decrease over these joints.

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TOPOLOGY FAMILY

option 2

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MATERIAL-Concrete supports-Fixed no. supports-5 each side cross section height-40

option 1

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Original_More curvature definition.

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TOPOLOGY FAMILY

option 2

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option 1

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Original_More curvature definition.

MATERIAL-Concrete supports-Fixed no. supports-5 each side cross section height-75

FOLDED PLATE: (2) grid configurations

(grid variation)

(material utilization)

hEIGHT-100 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 (MAIN STRUCTURE) hEIGHT-100 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 (2ND STRUCTURE) hEIGHT-60 UPPER WIDTH-30 LOWER WIDTH-30 THICK-4 hEIGHT-50 UPPER WIDTH-30 LOWER WIDTH-30 THICK-4

(grid optimization) The hexagonal patterns occur when structures have to absorb two dimensional stress in all directions. Matter apparently shapes itself into to sort of structure that is best fit to absorb stress becauses the forces need to move along the shortest distances.

(structure displacement)

(FORCES BEHAIVORS) AXIAL FORCE (nx)

STRONG AXIS SHEAR (vz)

TORSION (mx)

BENDING in strong axis (my)

BENDING in weak axis (mz)

FOLDED PLATE: (3) beams hierarchy and type of joins

(structure a) (main structure) hEIGHT-80 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 Joins-FIXED (Structure no. 1) hEIGHT-20 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 Joins-MZ (Both nodes) (Structure no. 2) hEIGHT-20 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 Joins-FIXED (Structure no. 3) hEIGHT-20 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 Joins-MZ (Both nodes)

y z

(utilization)

(bending moment)

(tension range)

(compression range)

(utilization)

(bending moment)

(tension range)

(compression range)

Bending Moment

(structure b) (main structure) hEIGHT-20 UPPER WIDTH-20 LOWER WIDTH-20 THICK-4 Joins-FIXED

Bending Moment

///conclusions///////// (1 ) Shell configurations 1.The use of a higher cross section helps the structure to avoid major displacements . 2. A geometry with higher definition (less angles between plates and major density of plates) decrease the amount material utilization in the encounter between plates. 3. A geometry with higher definition its easer to deform by the loads. The geometry with more angles between plates works better. 4. A geometry with higher defintiion contains more stress lines.

(2 ) grid configurations 1.A rhombus grid works better than any of the different grids tried within the exercise. 2. By increasing the density of the grid to the higher level, the structure stop working as a grid and works as a shell.

(3 ) beams hierarchy and type of joins 1.The different analisys over the two structures demostrate that the various results were almost the same (In the cases of utilization, bending moment, compression range and tension range). 2. The structure with a hierarchy grid its more affected by bending that the one that possess the same with the same beams all over the structure. 3. In the hierarchy system, by changing the kind of joint does not affect the structure behaivor and make a flexible structure.

folded forest

(1st experiments- 3 strategies ) (strategie one)

(strategie two)

(strategie three)

large gaps random triangles size random organization

no gaps random triangles sizes random organization

no gaps similar triangles sizes regular organization

(2nd experiments- 3 strategies ) (strategie one)

(strategie two)

(strategie three)

Regulation of gaps increasing size of triangles exploration of linear axis

doble side triangles achieving movement to both sides

double paper movement to both sides

(comparative models- material utilization- structure deformation )

1. Use of trinagular plates over the flexible membrane 2. Vertical Growth. 3. Diagonal Growth. 4. Cantiliver structure.

(comparative models- material utilization- structure deformation )

(models selection from analisys )

(Pilot structure)

(Structure variation No.1) (pilot model- structure characteristics) -cross section: 75 -Material: Steel -Number of support: 6 -Type of supports: fixed -Type of structure: folded plate shell.

(Structure variation No.2)

(structure variation no.2 )

(Structure variation No.3)