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Eric Apodaca & Christian Gomez
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Students: Eric A. / Christian G.
Biography FELIX CANDELA Felix Candela was born January 27, 1910 in Madrid, Spain and passed December 7, 1997. He was an architect, engineer, designer, and builder who was known for his “reinforced-concrete structures distinguished by thin, curved shells that are extremely strong and unusally economical.” (Brittanica)
Felix Candela c. 1956.
“The essential function of architecture is to limit a volume from the non-architectural extent of open space, so that within it man may develop his living activities undisturbed by weather in clemencies. The unique feature which distinguishes architecture from other plastic arts is precisely this dealing with internal hollow space.” - Candela
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Mathematical form The hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle.
Elliptic paraboloid equation
Equation behavior
Finding forms
Extreme Hyperbolic Paraboloid
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Structural Art
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Students: Eric A. / Christian G.
Los Manantiales Restaurant With the design for Los Manantiales, Felix Candela’s experimental form finding gave rise to an efficient, elegant, and enduring work of structural art.
Exterior view, via www.rkett.com
Interior view, via wikiaquitectura
Structural System Candela made his reputation with his designs for hyperbolic paraboloids (hypars), the thin concrete vaulted shells known for their unusual strength and flexibility.
Los Manantiales Restaurant, Study Model
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Chapel Lomas (Cuernavaca, Mexico)
Cnstruction Process / Scaffolding
Chapel Study Model
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
San Vicente de Paul Church
Study Model
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Phillips Pavillion (Le Corbusier)
Examples of Paraboloid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Sagrada Familia (Gaudi) Examples of Hyperboloid
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Students: Eric A. / Christian G.
Hyperboloid Rotation Studies
18°
36°
54°
72°
90°
108°
126°
144°
162°
180°
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Grid Analysis Triangular Grid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Grid Analysis Square Grid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Grid Analysis Pentagonal Grid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Grid Analysis Hexagonal Grid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Radial Array Analysis
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Hyperbolic Paraboloid Extraction
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Hyperboloid + Hyperboloid
Students: Eric A. / Christian G.
Hyperboloid + Hyperbolic Paraboloid + Hyperboloid
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Modeling Process #1
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid / Hyperboloid
Modeling Process CNC > Cut > Sand > Vacuum Form
1
2
3
4
5 324
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Modeling Process Vacuum Form Styrene
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
3. Modeling Process CNC > Cut > Sand
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Installation
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
Modeling Process #3
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Subject: Hyperbolic Paraboloid / Hyperboloid
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Students: Eric A. / Christian G.
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Medalla Milagrosa Hyperbolic Paraboloid Studies
Unit Leg
Plane
Medalla Milagrosa
Push Back
Move Up
More Pronounce Push
Perfect Unit
Moderate Unit
Extreme Unit
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Progressions of Medalla Milagrosa Hyperbolic Paraboloid Studies
Plane
Center X Axis Rotation
Middle Y Axis Center of Rotation
15 Degree Rotation
Cuvature Takes Place
45 Degree Rotation
Straight Lines Illusion
90 Degree Rotation
Chair Shape
Complex Lines
Almost 360 Degree Rotation
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Hyperbolic Paraboloid Form Finding Throught Circles and Division
Beggining Shape
Division
Polyline Conecting Rotating Star
Parabolic Shapes
Another Layer on Top
Hyperbolic Paraboloids
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Hyperbolic Paraboloid Studies throught Deform Ellipse
Plane
Rotation According to Width
Forming Paraboloids
Cuver Illusion
Moderate Rotations
Artistic Twist
334
Bigger Width Bigger Rotation
Formed Paraboloids
Hyperbolic Forms
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Hyperbolic Paraboloid Studies Stacking Method (Enclosure)
Diamonds
Dancing Diamonds
Falling Diamonds
Center X Axis Push
Space Ship
Bend Tips
Open Tips
Forming a Loft
Loft Space
335
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Separated Grid
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Layers
Paraboloids
Whole
Paraboloids
Whole
Connecting Hyperbolics
Whole
Elevation
Grid Cut Angle
Layers
Elevation
Join Grid
Layers
Elevation
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Hyperbolic Paraboloid Render Studies
Render
Render
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Hyperbolic Paraboloid Render Studies (Continuation..)
Render
338
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Construction of Scaffolding
Bottom Plate
Upper Plate
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Structure
Upper Structural Grid
Upper Plate
Bottom Structural Grid
Bottom Plate
Whole Piece
340
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Context
Aerial
In Context
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
First Cast concrete piece, of the Hyperbolic Paraboloid. By Eddie, William and DaJshey. Lower image demonstrated the separation between the grids, which was a key factor on the strength. Right image demostrates the grid on the piece of concrete
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Construction of Framework
Fishing Wire
Create Hyperbolic Paraboloids
343
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Finishing Wire and Textile
Finished Frame
Recover with Textile
344
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Concrete Application
Concrete Mix
Concrete Pouring
Covering All Surfaces
345
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Finished Piece
De-molding
Removing Textile
Curve Effect
346
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Sanding and Cleaning
347
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Final Piece
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ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Final Piece
349
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Final Piece
350
ARCH 491: Studio 5A Instructor: Yasushi Ishida
Students: Eric A. / Christian G.
Subject: Hyperbolic Paraboloid
Final Piece
351