ARCHITECTURE DEPARTMENT CHINESE UNIVERSITY OF HONG KONG

MASTER OF ARCHITECTURE PROGRAMME 2008-2009 DESIGN REPORT

FROM COMPONENT TO FORM: EXPLORATION WITH PARAMETRIC MODELING TOOL

HAU Sum Ming Sam May 2009

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From Component to Form Exploration with Parametric Modeling Too Sam Hau Sum _ n g hausiimming@yahooxom.hk Technics Studio 2008-2009 Advisor; Prof tsoii Jiri Yeu

ABSTRACT This project will explore a design process based on geometrical and structural understanding of a component and explore the form variation with structural consideration and fabrication constraint.

STATEMENT In the current practice of architecture, parametric design tool is used for providing data of building components after the form finding phase. Since the form is defined independently with the components, architects have to deal with the specific configuration and more effort is needed. This project will explore the possibility of a design process in the reversed way. The design will start with a basic geometrical and structural understanding of a component and then explore the potential of form variation within the constraint of fabrication and structural geometry. The form will be further modified with the structural analysis and spatial concept, in order to transfer it to architecture. Therefore, an architectural design which is constructible with the components and within the structure and fabrication possibility can be realized.

Design process: The whole design process is composed by an open ended series of paths which accumulate different ideas and decisions around the same topics: What form can the components do and how does the form transfers to an architecture? Every ideas and decisions made are based on the previous stage of exploration. Therefore, the design developed is a Long chain of geometric dependency which connects different scale of design, from component to form.

PARTI ： GEOMETI^ICAL AND STRUCTURAL UNDERSTANDING OF A COIVIPONi

A component developed by combining the structural principle of a truss and bending surface will be used as an experimental module in this project. This part includes the fundamental understand-ing of geometry, like how the curves and surface defined. The loading performance of the assembled components will be analyzed. Based on the result of the analysis, the adjustment of the components will be proposed to enhance the structure. The geometrical and structural understanding helps to set up the fundamental constraints for the form variation in the next stage.

STRUCTURAL CONCEPT

The diagonal member of the truss is the critical structural element to resist the force of deformation

The additional strength is added to a bending sheet

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STRUCTURAL PERFORMANCE

Study model to experiment about the structural performance of the assembled components.

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.STRUCTURAL PERFORMANCE

Span: 24m Thickness:2m

Joint condition: Fixed Boundary condition: Pinned Loading: Distributed Loading kN/m

Member type: Pipe Diameter: 20mm Wall thickness: 2mm

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Loading

Stress diagram Deflected shape

lateral expansion

lateral expansion

Enhancement of the structure

The analysis shows that the deformation of the ring is the major deflection factor of the whole span. Therefore, more material is needed to maintain the shape of ring. Because the bucket shape of the module have more space to occupy more material on the ring layer. Therefore, the ring is the layer for compression and the edge is for tension.

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Compression

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FABRICATION PROCESS

Cutting and shearing

Oxygen-flame and plasma cutting Circle cutting machine

Bending and rolling

Line heating Line heating is flame bending performed on metal plate, rather than rolled shapes, pipe, tube. While line heating can be used in a variety of steel fabrication activites, shipbuilding is its principal use. Steel hull hull plates vary in size but are typically 6 by 21 feet (2.3 by 6.5 meters). Hull plate can run from about 1/2 inch to serveral inches in thickness.

Cold Rolling The metal sheet bending machine used for Richard Serra's sculpture is cold rolling. The roller is about 20 feet long. Picture two long steel rolls shaped like logs, about a foot in diameter each—with a larger one about two feet in diameter that comes between the two. You put the plate in between these three rollers and the middle one comes down, bending the plate, it's done very quickly. They turn on the machine and the plate rolls back and forth three times in three seconds, and you see metal fragments on the top surface crack and pop off like dust.

MATERIAL CONSIDERATION AND DETAILING

Aluminum is selected as the materal of the bending suface, because of its lightweight property. The density of aluminum is 2700 kg/m〕，compared to steel 7900 kg/irP. The structural aluminum al-loys (alloy 5083) achieve 345 N/mm^ comparable to the 410-560 N/mm^ for S275 steel. Therefore, aluminum alloy can offer better strength to weight basis.

There are nine series of aluminum alloy with different alloying elements. Each of them has differ-ent applications and are listed as followed.

Alloy series Alloying element properties Applications

1xxx None Excellent corrosion resistance, high thermal and electrical conductivities, low mechanical properties, excellent

workability

Chemical Equipment, reflectors, heat exchangers, electrical conductors

2xxx Copper Heat treatable, high strength to weight ratio, limited corrosion resis-

tance, limited weldabilty

Truck wheels, truck suspension components, aircraft fuselage

3xxx Manganese Moderate strength without heat treating

Beverage cans, cooking utensils, heat exchangers, storage tanks

4xxx Silicon Low thermal expansion, high wear resistance

Forged engine pistons, welding rod, brazing alloys, architectural

products,

5xxx Magnesium Good weldability, good corrosion resistance

Ornamental trim, cans, household appliances, boats and ships

6xxx Magnesium and Silicon Heat treatable, good formability, moderate-strength, good weldability, good machinability, good corrosion

resistance

Architectural applications, bridge railings, welded structures, racecar

compone 门 ts

7xxx Zinc Heat treatable, moderate to very high strength

Airframe structures, high-strength forgings

8xxx

9xxx

Other elements

Unused series

N/A

N/A

N/A

N/A

Because of the weldability and strength, the fifth and sixth series of aluminum alloy will be the first two material consideration.

PART2: EXPERIMENTS OF FORM VARIATION

This part will focus on exploring the geometrical variation of structure and module.

Different modeling procedures will be experimented and two main challenges of the experiments are listed as followed.

1) How can the circle packing pattern be done on a surface wtih double curvature 2) The modules can be adjusted automatically to fit different types of double curvature and the fabrication possibility of the bending surface is maintained

The following are the main constraints in all experiments 1) The circle of the modules has to be touching to that of the adjacent modules 2) The modules has to be positioned perpenicular to the adjacent modules. 3) The two ends of the edges has to be the projection of centre points of the adjacent circle 4) The surface is formed by the circle and the edge in each module

With the structural and fabrication consideration, 'prefect ring' and 'perpendicular relationship to the adjacent components' are the two main constraints in this stage of form exploration. Whether than a free from without appropriate reference for generating the form, this is a more formal way to describe the form. Setting the key parameters, appropriate formula and order to achieve the most form variation become the most critical task in this part.

A series of experiments have been tried out to pack the components with different forms (flat, arch, spherical surfaces，double curvature) with the constraints mentioned. Finally, the double curvature controlled by two parameters (profile radius and path radius with positive and negative directional variables) becomes the universal model for the next stage of exploration.

GEOMETRICAL RELATIONSHIP

Experiment 1 2 3 4 5 6

Profile Flat Arch Sphere Sphere Sphere Double curvature

Modeling method

Pre- drawn Profile

No No No Yes Yes Yes

Module Circle and Edge

Circle and Edge

Circle and Edge

Polyline and 5 points

Circle and 5 points

Sphere and 5 points

Depth of Profile

N/A N/A N/A Offset Pre- drawn lower profile

Determined by the

radius of each sphere

Grid of circle packing

XZ plane N/A N/A N/A Evenly radical division

Parallel to XZ plane

Division is determined

by the centre point of circle

Parallel to XZ plane

Division is determined by the cen-tre point of

sphere

YZ plane N/A N/A N/A Evenly radical divsion

Evenly radical divsion

Evenly radical divsion

Flipping (Concave

and convex) No No No No No Yes

Parameter Radius of circle

Radius of circle

Radius of circle

Radius of profile

Radius of profile

2 Radius of profile

Angle Angles of two types of modules

Angles of two types of modules

Depth of profile

Radius of the first circle Depth of profile

Radius of the first circle

Flipping

Ratio of depth to radius

Grid of circle packing

Evenly radical division

Flipping

radius of profile depth of profile

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Parallel to XZ plane Division is determined by the centre point of circle

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Concave Convex

Module inclined edge angle: 10 30 50 70

Experimenti: A basic testing of the parametric modeline. Aflat profile is composed by one type of module. The angle of the module is a parameter to determine the depth of the profile.

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angle"!: parameter

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Experiments: An arch profile is composed by two types of modules with different angles.

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nFOMETRICAL RELATIONSHIP

Experiments： This experiment is to test out whether a double curvature can be composed by two types of modules.

Experiment4: Reviewing the experiment 3，this experiment is trying to set up the profile first before consider the geometry of the modules. Modules will be generated by the grid and control points on the pre-drawn profile.

step 1 A spherical surface is drawn as a profile

Step 2 Evenly radical divisions in XZ and YZ planes divided the surface and gen-erated a grid on the spherical surface.

Step 3 Control points are generated by the grid.

Step 4 Modules are defined and generated based on the control ppoints.

The modules are defined by the control points The circle is drawn by spine line defined by the genera ted by the intersection of two divisions mid-points between the centre point and the

central points of the four adjacent centre points.

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Conclusion- Although the^model is succesfull filling in the spherical surface with the modules. ^ However circles at thefour corner are not a prefect cir lce^is not only because the circle is #：： drawn by spine line, but also the grid setting on the spherical surface.

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Experiments： This experiment has tried out a new grid setting on the spherical surface. The strategy is to draw the first row of circle. By rotation of the row of circles, the spherical surface can be packed by the circles.

The rotation of the first row of circles is along X axis. The grid of XZ plane will be parellal to YZ plane and positioned according to the centre points of circles. The grid of Y plane will be evenly radical division.

The depth of profile will be determined by a lower profile which has lower curvature, so the smaller modules at two ends of the structure will have less depth.

The main challenge in this experiment is how to set up the first row of circles with variable radius.

XZ plane YZ plane

step 5 Three points for defining fifth circle are generated based on the third and fourth circle. Point 1: Extreme point of fourth circle in Y axis Point 2: Extreme point of third circle in X axis Point 3: Extreme point of fourth circle in X axis

. M Step 6 The fifth circle is drawn by connecting the three points.

Step 2 Three points for defining third circle are generated based on the first two circle. Point 1: Extreme point of first circle in Y axis Point 2: Extreme point of first circle in X axis Point 3: Extreme point of secdon circle in X axis

Step 3 The third circle is drawn by connecting the three points.

Step 1 The first circle is drawn and projected on Step 4 The fourth circle is generated by mirroring the spherical surface. The second circle is drawn the third circle with the XZ plane by rotation of the first cirle with the angle mea-sured between the centre point of first circle，cen-tre point of the profile and the extreme point in Y axis

Setting up the first row of circles with variable radius

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Using the 6 steps method mentioned in the last page, the first row of circle can be g e n e r a t e d . Each circle is touching to the adjacent circle and fit to the spherical surface. The circles have different radius and be able to rotated and touching the adjacent row of circles.

The depth of the profile is define by a lower profile. The lower profile in this experiment have a small-er degree of curvature. Therefore, the larger modules in the middle part of the structure have more depth. This can maintain the proportion of each modules and prevent over bending of the surface.

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PART3: STRUCTURAL ANALYSIS AND MODIFICATION

STRUCTURAL PERFORMANCE

Joint condition: Fixed Boundary condition: Fixed Loading: Distributed Loading -5 kN/m

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Conclusion: The simulation has shown the stress concentrates at the area near the column sport. Modification of the structure has been explored and shown in the next page.

MODIFICATION OF STRUCTURE

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C Compression T Tension

Inverted roof

Based on the compression/ tension principle of a span, the roof with column support has to be inverted. Therefore, the ring which is the compression layer faces down.

Tree column

Based on the structural simulation, tree column is used to reduce the deformation of the inverted roof.

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TREE COLUMN

Three types of tree columns are designed for different sizes and proportions of roof. The geometry of columns are depended on the red and blue ring (path and radisu) which defined the curvature of the roof and assembled componets.

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PART4: DETAILING AND FABRICATION

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Exploration of parametric variables to understand the behavior of such system and then use this understanding to strategise the system's response to environmental condition and external forces. Predefined components, mass customization Digital fabrication to define project specific components New parametric design technologies and direct fabrication have served to break down the bound-ary of design and construction. One result is that material experiments in the design studio can be translated directly, with material consistency, to fabrication techniques in the workshop, so that ma-terial performances observed and studied at the design stage become integral to the final construc-tion.

Parameters of module

Standardised components for on-site construction

Radius: 333mm Length 1:697mm Lengih2: 697mm Angle 1; 88deg38min Angle2; 88deg38min Angle3; 86deg31min Angle4: 86deg49min Angles： 176deg50min

Module granerated with different parameters Components to be fabricated and welded in factory

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PARTS: SPATIAL CONCEPT

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The roof grid is adjusted for different programs. The dimension of the roof with column support is also corresponding to that of the span roof

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1) The design start with a orthorgonal grid with equal spacing.

2) The width of'inverted roof is reduced in order to provide larger void space

3) The span roof is developed with a va-riety of spacing for different functions of space.

^ ^ ^ Inverted roof, roof for column support (profile radius -ve, path radius -ve)

4) The width of 'inverted roof is further adjusted corresponding to the span of the adjacent roof.

wine making process

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Main access to vineyard

Access to rooftop vineyard and cellar

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Pressing grape Fermentation Wine storgae Cellar Bottling

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Level chanae is independent to the size of roof, in order to enhance the spatial variation

COMPOSITION

Profile radius Path radius

Profile radius Path radius

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