Self-Forming Hygrosensitive Tectonics

Self-Forming Hygrosensitive Tectonics Developing Doubly Curved Adaptive Morphologies from Uniplanar Bilaminate Construction Yin-Yu Fong (MArch) Kirk Gordon (MLA) Nicholas Grimes (MArch) Mengzhe Ye (MArch) Research Studio|Fall 2018 Wood Proto-Architecture

Integrating Design Computation and Materialization

Studio Instructors: Assistant Professor Thomas Jefferson Visiting Professor

Ehsan Baharlou Achim Menges

3

Contents Chapter 01: Hygroscopic Responsivity

Page 5

Chapter 02: Context and Relevance

Page 11

Chapter 03: Exploring Material Properties Page 19 Chapter 04: Aggregating Behavior

Page 29

Chapter 05: Computational Form-Finding

Page 33

Chapter 06: Final Design and Fabrication

Page 47

Chapter 07: Conclusion / Future Directions Page 75 Acknowledgements

Page 81

References

Page 83

5

Chapter 01 Hygroscopic Responsivity

FIGURE 1.1: Al Bahar Towers Responsive Facade.

(Source: Aedas Architects)

Responsive Architectures This research responds to the ever growing focus within architectural research on climatically responsive elements—facades, roofs, and other systems which adjust directly to changing temperature or humidity conditions to ensure comfort or energy efficiency. While many responsive elements rely on microelectronics such as sensors and actuators (Fig. 1.1), a parallel body of research has focused on the inherent chemical and physical properties of architectural materials as a catalyst for responsivity.

As a formerly living biomaterial, the complex material composition of wood is especially well-suited for these types of investigations. Wood is unique in comparison with other commonly-used responsive materials (like metals) because it is anisotropic—its performance differs quantitatively depending on

the directional relationship to the grain. While this is usually experienced negatively in the form of warping, buckling, or splitting in response to moisture or force, a growing body of research has attempted to leverage wood’s anisotropic composition to program highly curated responsive behaviors.

Introducing Hygroscopy Wood is a complex composition of differentiated cell structures, each with specialized roles and morphologies. While distinct differences occur within and between the categories of softwood and hardwood, wood is generally composed of a matrix of narrow, longitudinal cells offering nutrient transport and structural support, interdispersed with horizontal ray cells providing lateral nutrient transport (Fig.

7

FIGURE 1.2: Cellular Composition of Wood.

(Source: Alex Shigo)

1.2). Variations in precipitation or humidity alter the moisture content of the wood by occupying the interstitial space between these cells. This ability to take in moisture from the environment is referred to as hygroscopy, and in the case of wood, the radial, anisotropic arrangement of these various cells allow for variable expansion depending on the direction of the grain (Fig. 1.3).

Recent research in material responsivity has investigated leveraging these differences in hygroscopic expansion for architectural applications. Much of this research has focused on the production of bilaminates featuring two different species in opposing orientation. This composition creates an “active layer� which is allowed to shrink and expand with changes in moisture, and a passive layer which remains rela-

tively stable, creating a tension of forces that causes directional bending (Fig. 1.3). These biomemetic design principles recreate the biomechanical behavior of naturally-existing moisture-sensitive seedpods such as pinecones (Fig. 1.4). For architectural applications, hardwoods like maple and beech are often used as the active layer because they exhibit the most dramatic hygroscopic expansion, while softwoods like spruce are often used as the passive layer because they exhibit comparatively little expansion.

Passive layers of other materials, such as resin or glass fiber, have also been experimented with.

A majority of the research on hygroscopic architectural applications has been conducted at the Institute for Computational Design (ICD) at University of Stuttgart. Initial research focused on small scale

TIAL

LONGITUDINAL

%

0.01%

RADIAL

4%

TANGENTIAL

8%

RADIAL

4%

PASSIVE LAYER

0.01%

4% ACTIVE

4%

4%

PASSIVE 0.01%

PASSIVE

PASSIVE LAYER

0.01%

ACTIVE LAYER

FIGURE 1.3: Hygroscopic expansion in lumber and bilaminated elements.

(Source: Authors)

4%

0.01%

4% ACTIVE

4%

PASSIVE 0.01%

experimentation using wood veneer. These experiACTIVE LAYER ments resulted in a number of “metereosensitive” facade applications, typically consisting of individual responsive elements arranged across a non-responsive supporting structure (Fig. 1.5). More recently, experiments have begun investigating compositions of interconnected or joined elements of varying principle curvatures in order to achieve composite bending behavior and form (Fig. 1.6).

This research seeks to expand upon the existing research on architectural hygroscopy by focusing on mid-scale structural applications.

FIGURE 1.4: Hygroscopic behavior in pincones.

(Source: I. Kremsa, K. Nakakoji, & E. Santiago)

9

FIGURE 1.5: FAZ Pavilion Frankfurt.

(Source: Achim Menges)

FIGURE 1.6: Augmented Grain - An Aggregate Hygroscopic Structure.

(Source: Dylan Wood, ICD Stuttgart)

11

Chapter 02 Context and Relevance

A History of Informative Research Frei Otto’s Form Finding Grounding our inspiration is the work of Frei Otto, who celebrated the remarkable interplay between materiality and environment, matter and physics. In contrast with the top-down dictation of preconceived form inherent to most of architectural practice at the time, Otto’s work was a negotiation between designer and material desires. His work is often characterized by the creation of an initial apparatus or organizational framework (Fig. 2.1) through which his chosen materials could adjust to gravitational or physical pressures, settling in to a more “natural” configuration or morphology.

Otto understood these forms to more accurately embody the laws of physics which influence all construction. Of particular notoreity was his Multihalle Mannheim pavilion—a double gridded wooden matrix that, when pushed inward, rose into a materially inherent form that was then locked into place (Figs. 2.2 & 2.3)

FIGURE 2.2: Construction diagrams for Multihalle Manheim by Frei Otto (Source: Princeton University)

FIGURE 2.3: Multihalle Manheim by Frei Otto (Source: ArchDaily)

FIGURE 2.1: A form-finding experiment conducted by Frei Otto using bubbles.

(Source: ArchDaily)

Microelectronics & Digital Responsivity Thanks to the increased accessibility of digital sensors and microcontrollers, there has been an increase in research focused on adaptive architectures—elements and facades which respond to environmental conditions like sun, temperature, or wind to regulate the comfort and performance of architectural spaces. These active adaptive architectures usually feature an intricate array of sensors and actuators that allow for precise kinetic response. A lot of attention has been spent specifically on responsive facades, in which aperatures or blinds open and close to allow the flow of air or light (Figs. 2.4 & 2.5). More structural applications have also been investigated, including structures which can respond to changes in structural loads (Fig. 2.6), wind pressures, or earthquakes.

13

FIGURE 2.4: The precise mechanisms of the responsive solar apertures at the Institut du Monde Arabe.

(Source: IMA / Fabrice Cateloy)

FIGURE 2.5: The facade of the Al Bahar tower responds to sun exposure.

(Source: Aedas Architects)

FIGURE 2.6: The SmartShell uses responsive hydraulics to precisely respond to varying weightloads.

(Source: ILEK, Stuttgart)

Molecular Mechanics and Material Intelligence A parallel thread of research on adaptive architectures has focused on more passive actuation, leveraging principles of material science to exploit the the molecular kinetic potential inherent in various materials. Many of these investigations are biomemetic, inspired by mechanisms found in livings organisms. Recent projects have taken inspiration from the seed capsule dehiscence mechanisms of the ice plant (Fig. 2.7) and bird-of-paradise flower (Fig. 2.8). Developed at the MIT Media Lab, Active Auxetics (Fig. 2.7) is a flexible, wearable matrix which expands in response to an individual’s body heat. The FlectoFin (Fig. 2.8) leverages a minor actuation at the point of attachment to elicit a material deformation that resembles gills. These applications rely strictly on thermodynamic and chemical properties—no electricity or computer required.

FIGURE 2.7: Active Auxetics wearable matrix (Source: MIT Media Lab)

FIGURE 2.8: The FlectoFin technology is used in SOMA Architecture’s One Ocean Thematic Pavilion, opening based on moisture levels.

(Source: SOMA Architects)

FIGURE 2.9: “4D Printing” - polymer chainmail composed of semi-circular elements which bend in responsive to moisture exposure.

(Source: MIT Media Lab)

Hygroscopic Facades & Metereosensitive Pavilions Within this thread of new materialism, a specific thread of research has investigated the material intelligence of wood as a formerly living biomaterial evolutionarily designed for structural performance and organic responsivity. Much of this research is centered at the Institute for Computational Design at the University of Stuttgart, where researchers have been exploring the hygroscopic behavior of bilaminated elements, dictating precise variations in moisture content during fabrication to achieve a gradient of bending behaviors (Fig. 2.10). By leveraging differences in expansion rates between the two bilaminate layers, researchers have created facades and installations that can respond to changes in air moisture content, opening and closing depending on the humidity level (Figs. 2.11 & 2.12). While most of this research has involved an array of individual elements supported by a non-responsive structural backbone, more recent research has focused on directly connecting elements to achieve aggregate bending behavior and structural performativity.

FIGURE 2.11: Hygroscopic aperture performance under different humidity conditions (Source: Achim Menges)

FIGURE 2.12: Interior of the HygroSkin Metereosensitive Pavilion (Source: Achim Menges)

15

FIGURE 2.10: A gradient of hygroscopic behavior dictated during fabrication.

(Source: Achim Menges)

The Expanded Field: Architectural Installations Finally, our research embraces the sensibility of experimentation embodied by installations which blur the lines of art and architecture. In their book on the subject, Ila Berman and Douglas Burnham write that “through their fragmentation and theatricalization, [architectural installations] denaturalize architecture, freeing it from the normative scale of building and the permanence of its site to enable it to become a self-reflexive aesthetic object, whose experimental tectonics often move beyond standard modes of construction and whose experience and proramming is unhindered by the typical constraints of utility.”

Much of our design experimentation was inspired by the sculptural works of artists like Richard Serra and Alexander Calder (Figs.

2.15 & 2.16), whose artful manipulation of planar forms through bending and rotation offered key insights into the potential performative of simple hygroscopic maneuvers.

FIGURE 2.14: Bent wood installation by Jeremy Holmes at Drexel University (Source: DrexelNow)

FIGURE 2.15: “Band” by Richard Serra, at LACMA (Source: LACMA Collections)

FIGURE 2.13: Expanded Field by Ila Berman and Daniel Burnham.

17

FIGURE 2.16: Standing mobile by Alexander Calder (Source: Calder Foundation)

19

Chapter 03 Exploring Material Properties

Laser Cut

An Environment for Experimentation

e Glue ane Glue

Epoxy Resin Epoxy Resin

Multimeter Multimeter

CNC Router CNC Router

Creating Our Experimental Procedure

Polyurethane Glue

Epoxy Resin

Multimeter

CNC Router

We chose a lightweight experimental scale to run our initial material and design tests, opting for readily available wood veneer products that we could easily laser-cut, then glue and seal using a counter-top kitchen vacuum sealer.

EXPERIMENT TOOLS

bot

Laser Robot Cut

Chamber Chamber

Vacuum Seal Chamber

HUMIDITY CHAMBER

Spray Bottle

Vacuum Seal

Spray

Joint Study

Humidifier Humidifier

Polyurethane Glue

HYGROMETER Rhino

Fan Fan

PolyurethaneLaser Glue HumidifierCut

Spray Bottle Vacuum Seal Fan

HUMIDIFIER

Polyurethane Glue Equalize

FABRICATION TOOLS

Epoxy Resin

EXHAUST FAN

Polyurethane Glue Glue Polyurethane

Multimeter

Spray Bottle

CNC Router

Polyurethane Glue

Submerge

Grasshopper SPRAY BOTTLE Joint Study

Epoxy Resin

MOISTURE METER Kuka Rhino

Robot Grasshopper

Epoxy Resin Spray Bottle

EPOXY RESIN

Multimeter Laser Cut

LASER CUTTER Chamber Kuka

Multimeter Polyurethane Glue

POLYURETHANE GLUE

Poly

Vacuum Seal

CNC Router Epoxy Resin

VACUUM SEALER

Multimeter

CNC Router Vacuum Seal HumidifierRobot

Polyurethane Glue Fan Chamber

Spray Bottle Humidifier

Joint Study

Cherry

Rhino

Kuka

None

Beech

Grasshopper

Oak

Robot

Kuka

Basswood

Chamber

Robot

Maple

Humidifier

Designing the Humidity Chamber

Chamber

Spruce

Fan

Humidifier Joint Study

Fan Rhino

Grasshopper

Kuka

The ability to control humidity was a key factor in testing and manipulating hygroscopic behavior. For our initial experiements, we built a 24x16x16” sealed chamber out of plexiglass, and used a tabletop humidifier and hygrometer to control the humidity conditions inside. A grid pattern was placed on the bottom and back walls of the chamber to help us analyze dimensions from experiment footage and photography. A 4-inch diameter HVAC fan was installed on the top of the chamber to circulate the air, and two holes were cut in the top to allow use to arrange and glue pieces without having to remove the lid and expose the chamber to outside humidity levels. A hygrometer was used to check the moisture content of the pieces.

Epoxy Resin

Glass Fiber

Bilaminate

VENTILATION FAN

CONSTANT TEMPERATURE:

Horizontal

Vertical

75°F

Diagonal

CAPPED HOLES FOR NON-DISRUPTIVE CHAMBER ACCESS

PLEXIGLASS WALLS WITH SILICONE SEALANT 1:1

2:1 - Long.

2:1 - Lat.

2:2

HUMIDIFIER

riangle (H)

Triangle (V)

SURFACE GRID FOR DIMENSION ANALYSIS

Circle

FIGURE 3.1: Tabletop humidity chamber set for small-scale material experiments (Source: Authors) Loop

Zipper

Zig Zag

Loop - Ext.

Zipper - Ext.

Zig Zag - Ext.

Polyu

AVERAGE RATE OF HUMIDITY INCREASE IN CHAMBER RATE OF HUMIDITY INCREASE IN EXPERIMENT CHAMBER

100

Relative Humidity (%)

90

21

80 70 60 50 40 30

0

5

10

15

20

25

30

35

40

45

Minutes

AVERAGE INCREASE IN MOISTURE CONTENT OF VENEER PIECES

CONTROL

39 43 50 63 69 74 77 79 81 82 83 84 85 86 87 88 88 89 89 89 90 90 90 91 91 91 92 92 92 92 93 93 93 93 93 94 94 94 95 95 95 95 96 96 97 97 98

LAMINATE

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

FIGURE 3.2: Rates of change for internal chamber humidity (top) and subsequent material moisture content (middle & bottom) (Source: Authors)

Defining our Material System Species Existing research on hygroscopic bilaminates has tended to recommend the use of hardwoods for the active layer because of the high rates of expansion, and softwoods for the passive layer because of their relatively negligible expansion behavior. We tested the expansion and bending behavior of six different species: cherry, beech, oak, basswood, maple, and spruce. 2” x 2” veneer samples of each species where sprayed with water on one side and allowed to bend. Maple and beech exhibited the highest expansion rates, while spruce exhibited the least. We ultimately chose a bilaminate composition of a maple active layer and spruce passive layer.

CHERRY

BEECH

OAK

BASSWOOD

MAPLE

FIGURE 3.3: Comparative expansion curvature of wood veneer of various species when sprayed with water.

(Source: Authors)

Non-organic Passive Layers A number of alternative passive materials were investigated next to test which material encouraged the most dramatic bending behavior in maple. Epoxy resin as well as single and double layer glass fiber (adhered with resin) were tested. Of the non-bioresponsive materials, epoxy resin proved the easiest to apply and was used in subsequent experiments to for quick hygroscopic behavior tests.

EPOXY RESIN

GLASS FIBER

12 MINS

DOUBLED GLASS FIBER RH:

Maple Veneer .019in

Start EMC

Epoxy Resin .003in

Maple Veneer .019in

End

<5.0% 7.7%

33°

EMC

Glass Fiber .007in

Start

End

<5.0%

6.5%

57°

Maple Veneer .019in

EMC

Double Layer Glass Fiber

EMC: < 5.0%

.014in

Start

End

<5.0%

6.7%

42%

60°

FIGURE 3.4: Principle curvatures of maple veneer with epoxy and glass fiber passive layers exposed to high humidity.

(Source: Authors)

RH:

86%

EMC: ~ 7.1%

Wood Bilaminate Passive Layers We then conducted further testing on the use of spruce veneer as the passive layer, this time with multiple layers. Using a 1/8” thick beech as the active layer and setting a 4:1 single active-passive layer ratio as a control, we tested the effect of applying two and three passive layers of consistent and alternating orienta- 23 tions. Additional passive layer thickness reduced curvature by a proportion consistent with that predicted using the Tomishenko bending theoretical formula. We found that while alternating the grain direction of the two passive layers yielded increased bending in comparison with consistent grain orientation, alternating the grain orientation did not effect curvature when three layers were applied.

24 HRS RH:

42%

EMC: < 5.0%

Active [+]

[+-+-] [+---]

63° 63°

[ + - -]

76°

[+-+]

103°

[+-]

127°

12 HRS

RH:

99%

RH:

EMC:

20.0% EMC: < 5.0%

40%

CONTROL

Passive [-] Passive [+] Passive [-]

FIGURE 3.5: Principle curvatures of 1/8” beech active layer with aggregate spruce passive layers of varying orientation.

(Source: Authors)

Grain Orientation We next tested the curving direction in relation to various grain orientations within a 2” x 2” sample. The curving direction remained perpendicular to the active layer despite changes in grain orientation , and the principle curvature remained relatively consistent across experiments. We deemed that grain direction of effects curve direction but not the degree of curvature within individual pieces.

12 MINS RH:

42%

EMC: < 5.0%

HORIZONTAL

+ Maple Veneer - Epoxy Resin

VERTICAL

+ Maple Veneer - Epoxy Resin

FIGURE 3.6: Curvature direction after varying active layer grain orientation.

(Source: Authors)

DIAGONAL

+ Maple Veneer - Epoxy Resin

RH:

88%

EMC: ~ 7.3%

Dimension & Ratio We next tested whether dimensional ratio (L:W) effected curvature. We tested pieces with lateral active layer grain and 1:1, 2:1, and 2:2 dimensional ratios, as well as a 2:1 sample with longitudinal active layer grain. The degree of curvature proved to remain in a constant proportional relationship with the dimension of the piece (doubly wide pieces exhibited double the degree of curvature).

12 MIN

RH:

46%

RH:

EMC: < 5.0%

1:1

Maple Veneer

Epoxy Resin

.019in

EMC

2 : 1 - LONGITUDINAL

Maple Veneer

.003in

Start

End

<5.0%

8.7%

.019in

EMC

2 : 1 - LATERAL

Epoxy Resin

Maple Veneer

.003in

Start

End

<5.0%

6.9%

.019in

EMC

86 %

EMC: ~ 7.3%

2:2

Epoxy Resin

Maple Veneer

.003in

.019in

Start

End

<5.0%

7.6%

EMC

Epoxy Resin .003in

Start

End

<5.0%

5.9%

TOP VIEW

~115째

~115째

91째

35째

FIGURE 3.7: Principle curvatures of actuated hygroscopic elements of varying dimensional ratios.

(Source: Authors)

Geometry We next texted whether non-rectilinear geometry effected the curvature of pieces of not. We tested equilateral triangle pieces of lateral and longitudinal grain orientation as well as a circular piece with lateral grain orientation. The degree of curvature in all cases was dictated by the widest dimension of the shape and proved to match the proportionality found in previous experiments with rectilinear pieces.

TRIANGLE - VERTICAL

+ Maple Veneer - Epoxy Resin

TRIANGLE - HORIZONTAL

+ Maple Veneer - Epoxy Resin

CIRCLE

+ Maple Veneer - Epoxy Resin

FIGURE 3.8: Curvature direction of actuated hygroscopic elements of different geometries.

(Source: Authors)

12 MIN RH:

42%

RH:

EMC:

5.0%

EMC: ~ 7.4%

85%

Joinery We next tested finger joinery of various patterns and widths. Zig-zag, looped, and toothed patterns were tested at 1/8” and 1/4” width to join two 2” x 2” pieces. We found that the 1/8” toothed joinery rendered the smoothest and most dramatic curvature; thus, this joinery pattern was chosen and scaled up for future experiements and applications.

42 HRS

TOOTH

TOOTH - EXTENDED EMC - 19.7%

205°

EMC - 18.9%

RH:

42%

RH:

EMC:

5.0%

EMC: ~ 19%

99%

170°

LOOP

LOOP - EXTENDED EMC - 19.6%

176°

EMC - 18.5%

193°

FIGURE 3.9: Principle monoclastic curvatures of elements joined with joinery of various patterns and widths.

(Source: Authors)

Aggregation Pattern We next attempted various aggregation patterns using gridded and triangulated surface division, with connection points featuring a progression of two to six pieces. We found that connection points joining four or more pieces created multi-directional tension at the joints, leading to flat areas and inflexible curving. Linear, two-piece joints rendered smooth, mono-clastic curvature while triangulated joinery with connections points containing three pieces was able to render more complex, synclastic geometries.

24 HRS RH:

42%

EMC: < 5.0%

QUAD

HEX

FIGURE 3.10: Synclastic bending behavior of aggregated elements featuring three, four, and six radial pieces.

(Source: Authors)

6-9 HRS

RH:

99%

EMC:

18.0% EMC: < 5.0%

TRIAD

RH:

99%

25

Key Material Parameters Through these material experiments we found that the grain direction, dimension, and geometry of a piece could be altered to achieve various design goals with consistent effect. We found that a maple-spruce bilayer was consistently the best performer, and that triangulated aggregates with toothed finger joints yielded the most flexible composite bending.

ACTIVATION

SPECIES

PASSIVE LAYER

GRAIN ORIENTATION

SPRAY

CHERRY

NONE

HORIZONTAL

EQUALIZE

BEECH

EPOXY RESIN

VERTICAL

SUBMERGE

OAK

GLASS FIBER

DIAGONAL

BASSWOOD

BILAMINATION

MAPLE

SPRUCE

FIGURE 3.11: Key design decisions regarding our material system, informed by our initial experiments of hygroscopic behavior.

(Source: Authors)

27 DIMENSION

GEOMETRY

JOINT PATTERN

AGGREGATION

1 : 1

TRIANGLE ‐ HORIZONTAL

LOOP

PAIR

2 : 1 ‐ LONGITUDINAL

TRIANGLE ‐ VERTICAL

ZIPPER

TRIAD

2 : 1 ‐ LATERAL

CIRCLE

ZIG ZAG

QUAD

LOOP ‐ EXTENDED

HEX

2 : 2

ZIPPER ‐ EXTENDED

ZIG ZAG ‐ EXTENDED

29

Chapter 04 Aggregating Behavior

Investigating Design Applications Bidirectional Triad Aggregation Extending our material experiments toward design applications, we first developed a pattern to repeat and aggregate the triangulated joinery unit from our previous experiments. The end of each piece was extending outward, and the orientation of adjacent pieces was alternated to achieve bidirectional synclastic bending.

These larger aggregates could then be nestled within one another to produce thickened or â&#x20AC;&#x153;pocketedâ&#x20AC;? surfaces.

24 HRS RH:

42%

EMC: < 5.0%

6-9 HRS

RH:

99%

RH:

EMC:

18.0% EMC: < 5.0%

99%

FIGURE 4.1: The process of design adjustments allowing for nested triad aggregation.

(Source: Authors)

ACTIVE

4%

WET ACTIVE

Bidirectional Triad Incision

PASSIVE 0.01%

We then extended this bidirectional triad aggregation by creating incisions in the pieces to allow adjacent pieces to extend into one another. This effectively created a “finger” like appendage which rose up from within a piece, bending in the opposite direction, and thus potentially creating a multiplanar connection 31 point. Fingers were placed both in the middle of pieces (“middle fingers”) and on the edge (“pinky fingers”).

24 HRS RH:

42%

EMC: < 5.0%

6-9 HRS

RH:

99%

EMC:

18.0% EMC: < 5.0%

MIDDLE FINGER

RH:

99%

PINKY FINGER

MIDDLE FINGER

PINKY FINGER

FIGURE 4.2: The typology of incisions allowing for multiplanar “finger” connection points.

(Source: Authors)Glue Polyurethane Epoxy Resin Multimeter

Spray Bottle

CNC Router

33

Chapter 05 Computational Form Finding

(1)

Radius

Bilayer Angular Change

(2)

Parameter

FIGURE 5.1: The Timoshenko bilayer bending formula (top) modeled in Grasshopper (bottom) (Source: Authors)

Modeling the Timoshenko Bending Formula Through field experiments conducted as ETH Zurich, researchers have identified several computational parameters which, when modeled through mathematical formula, help to define the curvature of wooden bilayers (Rüggeberg & Burgert, 2015). Rüggeberg & Burgert successfully modeled the hygroscopic bending behaviors of bilaminated wood elements by adapting the Timoshenko bending formula. While the Timoshenko was originally defined to study the behavior of isotropic metal bilayers subjected to temperature flux, by substituting key variables it can be easily applied to hygroscopic behaviors of anisotropic materials such as wood.

In Ruggeberg and Burgert’s adaption, the temperature change (c-c0) is replaced by the change in moisture content. The swelling coefficients of the active and passive layers are defined by α2 and α1, respectively. Research on various wood species have defined the swelling coefficient of spruce (the passive layer) to be 0.7 ± 1.0*10-4 % while maple (the active layer) is defined at 3.53*10-3 % (Kretschmann, 1997). The longitudinal stiffness of spruce is represented as E1 while the tangential stiffness of maple is represented by E2 (Kretschmann, 1997). Through this formula, one can derive the radius of the bilaminate curvature when exposed to humidity flux (Fig. 5.1-1). This value an then be applied to the derive the change in the curvature angle (Fig. 5.1-2).

35

Spruce Thickness: 0.5 in

Spruce Thickness: 0.75 in

Spruce Thickness: 0.89 in

Spruce Thickness: 1.45 in

FIGURE 5.2: Curvature simulation of wooden bilayers with different spruce passive layer thicknesses.

(Source: Authors)

Triangulated Surface

Grain Direction Y-direction

FIGURE 5.3: A triangulated anticlastic geometry (top), with grain and curvature direction simulated for each piece (bottom) (Source: Authors)

Analyzing Top-Down, Predetermined Geometry By reconstructing the Timoshenko formula in Grasshopper, we were able to simulate a humidity driven bending behavior based on the fluctuation of the equilibrium moisture content (EMC) of our modeled wooden bilayers. The perpendicularly arranged grain direction of the two different wood species produced a synclastic surface which curved in the same direction on all sides (Fig. 5.2).

The second step of our computational research involved simulating the grain direction and individual bending behaviors for each piece within a triangulated anticlastic surface. A triangulated mesh of the modeled surface was derived using the Grasshopper plug-in Kangaroo. The surface was divided efficiently

using a circle packing method, in which all circles were mutally tangential and no two boundaries overlapped. From this loci of these circles we were able to develop a triangulated Delaunay mesh (Fig. 5.3).

The direction of max shrinking or swelling within each triangle was informed by the maximum principal curvature of the surface within each triangleâ&#x20AC;&#x2122;s boundary. By analyzing the shrinking/swelling direction of each piece, the correlating grain direction of the passive and active layers could then be derived (Fig. 5.3), as well as the curvature radii (Figs. 5.4 & 5.5).

Grain Direction Y-direction

37

FIGURE 5.4: The curvature radius of a single piece within the triangulated anticlastic geometry.

(Source: Authors)

While the triangulated simulation of the surface offered a high resolution in terms of curvature, when modeling the surface at the desired final installation size, the simulation required the fabrication of over 50 separate bilaminated elements, each with their own unique moisture content requirements.

In an attempt to reduce the number of unique pieces required for the final design, we modeled a second geometrical simulation, this time using a lower resolution quad division. The grain direction of each quadrilateral was determined using the same method as before.

For the both simulations, the principle curvature radius for each piece was then plugged into a reverse

to find the corresponding thickness ratio between the active (maple) and passive (spruce) layers.

With this information, we fabricated a small scale physical model of the triangulated anticlastic surface intially modeled in Grasshopper (Fig. 5.6). The aggregated pieces were joined using a joinery simulation that allowed for the fine-tuning of multiple variables (Fig. 5.10). Though we were able to achieve anticlastic behavior, we were unable to achieve it through a cohesive, single-surface construction due to the overlapping nature of the flattened anticlastic geometry. Only after significant bending behavior were we able to join the separate pieces into one cohesive anticlastic surface, and even so, the bent joinery was impossible to adhere together on all sides (Figs. 5.7 & 5.8).

Radius of each panel

FIGURE 5.5: Grasshopper script of individual pieceâ&#x20AC;&#x2122;s principle curvatures' radii (Source: Authors)

FIGURE 5.6: Multi-element anticlastic Maple-Spruce bilayer configuration (Source: Authors)

39

FIGURE 5.7: Multi-element Maple-Spruce bilayer final geometry (Source: Authors)

FIGURE 06:

FIGURE 5.8: The ill-fitting curved joinery of our anticlastic model, which could not be fabricated using flat, single-surface construction.

(Source: Authors)

SOLVING A QUADRATIC EQUATION BY FERRARIâ&#x20AC;&#x2122;S SOLUTION: Ax4 + Bx3 + Cx2 + Dx + E = 0 A=-5.45 B=55.63

41

C=112.39 D=55.63 E=0 x = m = h1 (Spruce Layer Thickness) / h2 ( Maple Layer Thickness) m = 0.89 If total thickness is 1 inch The maple layer thickness will be 0.53 inch The spruce layer thickness will be 0.47 inch

RADIUS INPUT

FIGURE 5.9: Grasshopper script of the reverse equation of the Timoshenko Formula, used to derive the active-passive layer thickness ratio (Source: Authors)

WIDTH

ANGLE

FREQUENCY

FILLET

FIGURE 5.10: Explanation of the reverse equation of the Timoshenko Formula, used to derive the active-passive layer thickness ratio (Source: Authors)

7 Inch wood bilayer panel 70 inch

A

Based on the 6.75" standardized width of each wood bilayer piece, a total 9 pieces are divided into three different radii. Sections 1 & 3 share the same curvature.

B

Connecting 4 separate parts together

FIGURE 5.11: Final design curvatures simulation process

Exploring Bottom-Up Form Finding The features of the final design were governed by both material and fabrication limitations. In terms of overall size, the project was limited to a flat footprint of 6' x 6' feet, as this was the maximum size that could be glued in its entirety in the humidity chamber. The 6.75" standardized width of each piece was a result of the minimum width of the maple lumber. By selecting a standard width, the spruce passive layer could all be cut to pieces of a uniform length.

The choice to pursue a monoclastic design arose due to i) the complexity otherwise introduced through the discretization of a large synclastic structure, requiring approximately ten times the number of pieces and producing more material waste due to the

different grain orientations of each piece and ii) for anticlastic curvature the necessity to design a flexible joint that would be able to respond to changes in moisture content and associated dimensional changes in the wood pieces, while at the same time being able to withstand the forces induced by hygroscopic bending behavior.

Furthermore, despite each piece's individual monoscopicity, the curvature of the piece as a whole was influenced by several factors: i) the difference in thickness of the active layers between different sections of the model (Figs. 5.11 & 5.12), which introduces unequal internal forces potentially resulting in a twisting behavior (Fig. 5.13), and ii) the incision

43

C

D

Geometrical simulation based on the curvature change when applying different thickness of spruce layer

Finding the smooth geometry by connect two panels with tangential direction of the end point of the first curvature.

in the design which allows for each half to bend in different directions, where the face of the surface at the transition point moves from positive to negative Gaussian curvature and iii) slight differences in the grain direction of each piece caused by natural variation or offset from the longitudinal centerline of the lumber stock in the manufacturing process.

These effects combine to generate synclastic and anticlastic curvature at different points in the model.

While the model's final curvature was intentionally manipulated, its final behavior could not be entirely anticipated prior to construction and is a result of the wood's inherent material properties.

6 .7

5 in

Spruce Thickness: 0.2 in

Radius: 21.8 Spruce Thickness: 0.13 in

Spruce Thickness: 0.225 in

Radius: 12.8

Radius: 13.4

Spruce Thickness: 0.13 in

Radius: 12.8

FIGURE 5.12: Grasshopper script of different principle curvatures' radius (Source: Authors)

ch

45

Maple Layer Thickness: 1/8"

Spruce Layer Thickness: 1/32" Spruce Layer Thickness: 3/32"

Spruce Layer Thickness: 3/32"

FIGURE 5.13: Small scale multi-element bilayer test (Source: Authors)

.5â&#x20AC;? Maple active layer

.25â&#x20AC;? Spruce passive layer

Exposed to water

Equalized at 35% RH

16.3o Principle curvature

47

Chapter 06 Final Design and Fabrication

CONTROL

+-

2 Passive Layers

+-+ +-Lamination prior to equalization

+-+

Lamination prior to equalization

+--

3 Passive Layers

+-++--Lamination prior to equalization

+-+-

Lamination prior to equalization

+---

FIGURE 6.1: Fabrication diagram and initial state to final state photos.

(Source: Authors)

Passive Layer Manipulation Based on our analysis of the Timoshenko equation and in an attempt to streamline the fabrication process of the final model we decided to investigate passive layer thickness as a design parameter. Our previous experiments have shown that the most difficult variable to control during fabrication was the internal moisture content of the wood. Achieving specific moisture contents required careful environmental regulation and was often subject to inaccuracies in measurement given the limitations of our pin-type moisture meter as well as the idiosyncratic nature of the wood pieces which were not uniform in their absorption and were affected by microclimatic conditions within the chamber itself. Manipulation of the passive layer thickness offered a more accurate way to manipulate the curvature of the piece as it was an immediately visible parameter that was more

easily measured and we could therefore ensure a more uniform result across the pieces as well as within a given piece.

The experiment we carried out in order to investigate the effect of the passive layer thickness on the curvature of the wood bilaminates utilized a .125â&#x20AC;? thick active layer of beech and up to three layers of .024â&#x20AC;? thick spruce veneer (Fig. 6.1). In addition to the cumulative thickness of the passive layers we were also interested in whether the grain direction of the successive spruce layers had any effect on the bending behavior, and whether laminating the spruce pieces prior to equalization resulted in a change in bending behavior compared to spruce pieces that were laminated at the time of bilamination. This experiment therefore tests three variables: the grain direction of successive spruce

[ + - + - ] 63° [ + - - - ] 63° [ + - - ] 76°

[ + - + ] 103° [ + - ] 127° CONTROL

FIGURE 6.2: Bending across experimental conditions.

(Source: Authors)

layers, the internal moisture content of the passive layer at the time of lamination, and total thickness of the passive spruce layers.

Eight maple-spruce bilaminate pieces were tested with one piece serving as a control. The experimental pieces had either two or three .024” spruce veneer pieces laminated onto them with matching or alternating grain directions in each successive spruce layer. For each experimental condition there was a version of the passive layer that had been equalized prior to lamination and then there was another that was laminated after the equalization of the individual pieces.

The internal moisture content of all pieces was measured at less than 5% prior to experimentation.

All pieces were equalized for 24hrs at 99% RH at a temperature of 73oF until reaching an internal moisture content of 20% as measured by a pin-type moisture meter. The pieces were then left in ambient indoor conditions (35% RH, 73oF) for 12 hours after which their curvature was measured.

The results of the experiment showed that the orientation of successive spruce layers had a significant effect on the curvature of a given piece (Fig. 6.2). Those pieces in which the grain direction of the passive layer was oriented perpendicular to that of the active layer produced the largest decrease in principle curvature. This is an effect of the strong axis orientation of the spruce piece; the greater the stiffness of the passive layer the more the bending is mitigated. These results are in line with what one would expect given the effect of material stiffness in

49

FIGURE 6.3: Maple-spruce bilamination, 1:10 scale model A. (Source: Authors)

the Timoshenko equation. What’s more, those pieces that were laminated prior to equalization showed an additional mitigation effect on wood bending. We believe this is due to the softening of the cell walls and therefore the reduction in stiffness caused by the interaction of water and cellulose. The spruce pieces that were laminated together prior to equalization were effectively sealed and remained drier than those laminated after equalization, making them more stiff and resistant to the deformation induced by the active maple pieces.

While the lamination of successive spruce layers proved fruitful for small-scale testing, it was more prone to delamination and our final installation would require much thicker passive layers, making the process of layering veneer impractical. We would opt instead to plane down thicker spruce pieces to the appropriate thickness.

Scale Model Tests After our investigation of passive layer thickness on bending behavior we made two mock-ups of our final model at 1:10 scale, each model measuring 7.5” x 7.5” when flat. The models were made using a .125” maple active layer and up to three layers of .024” spruce veneer passive layers. They also incorporated the incision concept we had been working with in previous small-scale material studies.

The spuce and maple pieces were equalized for 24hrs at 99% RH at a temperature of 73oF until reaching an internal moisture content of 20% as measured by a pin-type moisture meter after which point they were laminated and left to dry in a sealed vacuum bag. After four hours the pieces were removed and laser cut. The cut pieces were placed back into the humidity chamber, assembled using polyurethane

51

FIGURE 6.4: Maple-spruce bilamination, 1:10 scale model B. (Source: Authors)

glue, and left to dry for another four hours. After drying the pieces were removed from the humidity chamber and left in ambient indoor conditions (35% RH, 73oF) and allowed to bend.

These studies helped us to test the self-standing capabilities of the final design and also allowed us to investigate different curvature patterns. In model B (Fig. 6.4) the pieces at the top curve in opposite directions in every other piece resulting in a wavelike effect. We also angled some of the pieces so that the seams did not run exactly perpendicular to the ground to see if this would produce uneven bending behavior due to the change in the width of the wood at different points along its length. The effects of this were not immediately apparent or were otherwise too subtle to observe. We chose not to incorporate either feature into the design as we were concerned about the effect of the difference between the

internal forces of each section of the installation at the larger scale and the effects of the increased self-weight on the bending behavior. Our final design most closely resembles model A (Fig. 6.3) and the relative thickness of each section was influenced by the thickness ratios of this model.

Final Model Iterations After establishing the design concept and experimenting with the active-passive layer thickness ratios required to achieve different principle curvatures we used a series of physical and digital techniques (Figs. 6.5 & 6.6) to iterate designs that could be assembled from a planar sheet. This would simulate the way the final model was expected to be fabricated: assembled flat and then allowed to bend based on its inherent material properties.

FIGURE 6.5: Paper model iterations.

(Source: Authors)

53

6’ x 6’ DESIGN SPACE

FIGURE 6.6: Digital model iterations.

(Source: Authors)

Material Sourcing The maple used in the final installation was sourced from Northland Forest Products, a lumber mill 30 minutes east of Charlottesville in Troy, VA (Fig. 6.7). Ten pieces ranging in width from 7.25” to 9” and approximately 9’ long were handselected from their stock (Fig. 6.8) of .75” thick hard maple (Acer nigrum) and transported via rental truck to Campbell Hall (Fig. 6.9). The 100 board feet of spruce was less variable at .75” thick, 11.5” in width and 9’ in length and was special ordered from 84 Lumber in Charlottesville, 15 minutes north of UVA and delivered to the school.

FIGURE 6.7: Northland Forest Products, Troy, VA. (Source: Authors)

FIGURE 6.8: Lumber range at Northland, Hard Maple is just left of center.

(Source: Authors)

FIGURE 6.9: Material in transport.

(Source: Authors)

Header 03

Chamber Fabrication

Header 04

In order to fabricate our final design at the desired scale, we built a 7’ x 7’ x 7’ humidity chamber (Figs. 6.13, 6.14, 6.15) using 2x4s and sealed it with LDPE sheets. A chamber of this size was necessary not only to allow 55 for the equalization and storage of the final wood pieces which measured up to 6’ long, but would allow for multiple team members to enter the chamber at one time and manipulate the wood. This allowed for much more range of movement compared to the smallscale chamber which only allowed interaction with the wood samples via circular cut-outs in the lid. The internal footprint would also need to be large enough to accommodate the full size of the model when laid out flat on the floor. The final assembly of the model would need to take place in the chamber to avoid bending during the drying process.

FIGURE 6.10: Cutting chamber frame and shelving units to size.

(Source: Authors)

The chamber was assembled in approximately 9 hours using 24 2x4 studs (Figs. 6.10 & 6.11). The shelving inside the chamber was constructed from 20 2x3 pieces and the top shelf was covered in window screen mesh (Fig. 6.12) to allow for the arrangement of the smaller spruce pieces.

FIGURE 6.11: Chamber assembly, attaching sheeting to frames.

(Source: Authors)

FIGURE 6.12: Applying mesh screen to create shelving.

(Source: Authors)

FIGURE 6.13: Humidity chamber and shelving construction drawings, axonometric.

(Source: Authors)

57

FIGURE 6.14: Humidity chamber frame assembly.

(Source: Authors)

59

FIGURE 6.15: Humidity chamber shelving assembly.

(Source: Authors)

61

FIGURE 6.16: “Screen time” feat. surprisingly spicy pizza.

(Source: Authors)

FIGURE 6.17: Spruce pieces in the humidity chamber.

(Source: Authors)

63

FIGURE 6.18: Maple boards being sent through the planer, removing material in .125” increments.

(Source: Authors)

Material Preparation Our active layer maple lumber stock was planed down to .5” ±.03” (Fig. 6.18 & 6.19), and the spruce passive layer was planed to four different thickness ranging from .25” to .4” to allow for variable curvature in the final model design. It was then cut into to 7.5” x 11.5” pieces to allow for perpendicular arrangement along the length of the maple active layer.

The maple and spruce pieces were equalized in the chamber at 73oF and 99% relative humidity for 48hrs (Fig. 6.17) until reaching an internal moisture content between 18-19%. The pieces were glued with polyurethane glue (Fig. 6.20), wrapped in wax paper, and laminated using a large-scale vacuum bag (Fig. 6.21).

After initial installation-scale bending tests showed results that deviated from their expected principle curvature, the passive-layer side of the bilaminates was planed further (Fig. 6.22) to account for nonlinear Timoshenko curvature behavior, resulting in passive layer thickness ranging from .13” to .225”.

65

FIGURE 6.19: Digital calipers being used to measure a maple board.

(Source: Authors)

FIGURE 6.20: Gluing spruce sheets to maple boards.

(Source: Authors)

FIGURE 6.21: Placing bilaminated pieces in vacuum bag to dry.

(Source: Authors)

67

FIGURE 6.22: Preparing sheets for re-planing to adjust passive layer thickness.

(Source: Authors)

FIGURE 6.23: Joinery tests of different lengths and widths. 1mm offset.

(Source: Authors)

CNC Milling and Assembly After an initial joinery test (Fig. 6.23), joinery tolerances were reduced from 1mm to 1/64”. The thinnest and longest joint was chosen to reduce milling time. The final model is comprised of 13 pieces CNC milled from 10 maple-spruce bilaminated strips (Figs. 6.24 & 6.26). Each strip was screwed to a 1.51” thick jig during the milling process (Figs. 6.25 & 6.27) to reduce inaccuracies caused by hygroscopic bending behavior when exposed to the ambient humidity levels in the woodshop and to secure them during the milling process. The milled pieces, and especially the dovetail joints, were sanded smooth and the pieces were glued together with polyurethane glue and vacuum sealed in two groups resulting in two halves of the model.

Given the dimensions of the final installation of 5’ x 6’ the shop vacuum bag would prove unsuitable for the full model; the final two composite pieces were glued and clamped inside the humidity chamber in order to regulate moisture content and keep the pieces flat. Once the final piece was assembled, it was placed outside the chamber and allowed to equalize to the ambient humidity (26.8% RH, 72oF), reducing the internal moisture content percentage of the active later and resulting in the desired final curvature.

.25” Diameter

69

.22” Diameter

.75” .016” Offset

.9”

FIGURE 6.24: Joinery diagram and CNC cut file diagram showing grain direction.

(Source: Authors)

3.75

32.00

3.75

3.75

FIGURE 6.25: Final model nailing schedule.

(Source: Authors)

3.75

5.50

2.50

5.50

3.75

3.25

18.00

33.25 48.25

3.75

3.75

3.75 59.50

63.25

71

5.00

4.00

.125” Diameter bit

Securing screw

.3” Edge tolerance

FIGURE 6.26: CNC routing on the C.R. Onsrud.

(Source: Authors)

73

FIGURE 6.27: Marking and drilling nail holes, sanding completed pieces.

(Source: Authors)

Chapter 07 Conclusion and Future Directions

75

76

FIGURE 7.1: A scaffolding structure supported the installation for the first 24 hours, after which curving allowed the piece to stand on its own.

(Source: Authors)

Limitations and Possibilities The final installation shows the feasibility of passive layer manipulation in hygroscopically actuated spruce-maple bilaminate elements. Whatâ&#x20AC;&#x2122;s more, the scale of the model and the strong-axis orientation of the pieces speaks to the structural capabilities of the wood and offers new possibilities for hygroscopic behavior in larger wood members and over longer time scales. The results also offer many opportunities for further research.

The development of a computational model capable of predicting more nuanced wood behaviors would allow for the incorporation of hygroscopic elements in applications that require very specific bending behavior with low tolerance levels. This research could be coupled with feedback loops involving 3D scanning and object reconstruction to allow for

digital analysis and refinement of mathematical models of wood behavior.

Given the limitations in size of a given wood member, research into joinery methods that are feasible for on-site construction would be necessary for the commercial viability of bilaminated elements as a construction methodology. At current, there is limited on-site availability of CNC milling technology required for joinery work, which implies prefabrication or a novel method for incorporation into current construction practices.

In terms of passive layer manipulation, the longterm effects of thicker bilaminates requires further research, including active-layer splintering,

77

FIGURE 7.2: Removing the supporting scaffolding.

(Source: Authors)

bilamination, and creep. Given the effects of stiffness on bending behavior it is possible that hygroscopic behavior could increase over time as the passive layer become less resistant to deformation.

Passive layer thickness might also be used a compensatory measure for variable moisture content and provides an opportunity for on-site fabrication without the use of a humidity chamber.

Wood pieces would equalize according to exterior weather conditions and bending behavior would be manipulated based on variable equalized moisture content. This system would require careful manipulation of scale as the equalization time increases with volume of the members. This might generate opportunities for the aggregated lamination of smaller members with increased surface area to volume ratio as a way to decrease

equalization time while maintaining feasibility for load-bearing applications.

81

Acknowledgements Special thanks to Ehsan Baharlou and Achim Menges for your infinite wisdom, and to Michael Tucker and Melissa Goldman for your patience and guidance during the fabrication process.

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