universaljoint_texas cantilever technical

7/31/2019 universaljoint_texas cantilever technical

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The Texas Cantilever (Grover Avenue Residence)

1. Introduction

The Grover Residence is a 267 square meter (2400 s.f.) cost-efficient, green and formally singular design-buildproject. The project incorporated 3D digital technologies in order to design, post-rationalize, document andconstruct the sculptural Iron Turtle you see in the images. Due to time constraints, the documentation for thisportion of the project was executed over the course of two evenings, while the main residence was underconstruction by the design-builder.The Iron Turtle demonstrates the immediacy possible in the conversion of a digital idea into an artifact. It is anearly example of the design-build Firms ongoing research into form generation and form rationalization forarchitectural scale constructions.

Fig 1. Grover Residence facing West.

2. Exposition

The Schematic Phase of the residence began with a Client Program calling for a beehive of artistic activity aswell as opportunities for star-gazing.The Design Development and Contract Document Phases of the project were taken up with architectural planning,Contract Documents, and permitting - as well as a lot subdivision of the Clients large lot via the Citys land

universal joint | the texas cantilever and the iron turtle - technical write-up

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development process. Additional complexity was added by the local jurisdictions McMansion Ordinance process- radically changing local zoning code while the project was under design and permitting in addition to a rapidlychanging lending environment while under bid.

From the outset the sculptural element was intended to act as a counterpoint to the otherwise rectilinear form of thelarger structure. A placeholder in the form of a simple series of filleted lines was inserted into the conventional2D CAD elevations while the residence proceeded to permitting, bid and eventual construction.The more conventional architectural aspects of the residence resulted in a compact, symmetrical design that wasable to add an additional 200 square meters (1800 s.f) in the form of north and south facing roofdecks, a streetfacing master porch, as well as 89 square meters (800 s.f.) of covered patio on the ground floor.

Fig 2. Structural cut list and take-off was executed in 3D CAD.

3. Digital Fabrication

The Iron Turtle is a direct descendent of the Firms digital design research presented as accepted juried work atSIGgraph in 2008. This work - a recreation of a classical mathematical model collection originally made by hand inplaster in the 1800s - resulted in 1:1 reproductions of the original models in a plaster based Rapid Prototyping (RP)process. This mathematically based RP work, in conjunction with academic research, has provided the Firm with aunique perspective into the constructional continuum that exists between geometry and architectural fabrications.

Figure 4. A recreation of a classical mathematical model collection: singularities possible on a cubic surface.

From the outset the intent was to work with mesh and effectuate as automated and minimalist a design process aspossible. Toward this end we began to focus on so-called box modeling as opposed to a better documentedmechanical approach for planar or nearly planar quads. Effectively, from a design perspective, we wished to takeour hands off the wheel to whatever extent it was practical; we wished to have as automated and parametric form-finding as possible while minimizing design moves. It was also decided from the outset to maintain aconventional 406.4mm (1-4) stud spacing. Thus we started with a very simple truncated frustum on a 406.4mm(1-4) module as the 3D equivalent to the 2D placeholder drawing.

Design Built Work in Austin, Texas



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Fig 3. Note ovoid form under south elevation at bottom.

With the technical assistance of an architectural geometry processing firm, early explorations yielded satisfactorytests for a fully automated, fully planarized version of the truncated frustum armature. This corporate assistance

provided immeasurable benefits for understanding the various geometric parameters involved in planar quad (PQ)mesh planarization, as well as for gaining a better intuitive-constructive feel for the movement and perturbation ofthe geometry in such a process.However, further computational work was necessary in order to balance full planarity of the quads against the fullvertical fairness of the proposed light gage stud frame. Ultimately time and scheduling constraints necessitated amore manual approach on our end. Thus at this point it was hoped that a more manual approach would yieldunanticipated benefits. However, at this point the result was also completely unknown.Straight off, we ran a Catmull-Clark subdivision with cubic continuity executed in T-Splines. One iteration of thisalgorithm yielded both results that fit roughly along the 406.4mm (1-4) spacing module and yielded quads that fit

roughly into 914 x 914 mm (3-0 x 3-0) templates.1

Figure 5. Catmull-Clark Subdivision procedure of the originalsimple truncated frustum armature (not shown).

4. The Frame

At this point an analysis of the non-planarity of the quads was undertaken and a manual edit minimizing the non-planarity of the most non-planar quads was executed in CAD. A rough determination was made that 12.7mm (0.5in.) maximum mean planar deviation (this is 50.8mm or 2.0 at any particular corner) was acceptable for 19.05mm(3/4) exterior plywood leftover from the construction of the house. A backup plan was to purchase thinner materialif this material was too stout.



1Interestingly, when dealing with planar quad templates in the field it is only necessary to have four portions of the four edges fitwithin the given template size. As long as one has the four edges shown on the template, one can complete the corners in thefield with a straightedge placed upon the template while on the actual material.


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Figure 6. Frame documentation and dimensioning in 3-dimensions. Note non-fairness of vertical seams ofthe quads as they relate to the light gage bents.

Figure 7. Metal stud bents with quad panels shown by amount of non-planarity.




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5. The Quad Shell

In addition to determining to move forward with the amount of non-planarity inherent in the quads in the 3D model,comparison of edge measurements on the most-curved 3D surfaces in relation to the edges of the stretched 2D

developments was determined to produce insignificant stretch when developing quadrilateral shapes at this scale.2

Figure 8. Master for full size templates.

6. Construction

As we noted, the documentation took place over the course of two evenings and in point of fact the actual

construction of the light gage stud frame overlapped with the CAD documentation of the quads.



2Some brief notes on the quadrilateral topology are appropriate at this point:

Note that we are using the term "quadrilateral" (or simply "quad") for any surface with four edges. And that in this case we canfurther describe these as convex quads, as opposed to concave quads (in the case of convex quads no point is interior to the otherthree). Also note that in some cases these four points are planar to each other (Planar Quads) or non-planar to each other (Non-Planar Quads). This geometric arrangment of points could be simply termed the geometries "topology".

However, as CAD practitioners will recognize, this geometric topology does not say anything with respect to whether thesegeometric entities are areNURBS(Non-Rational B-Spline Surfaces) geometry types orMesh geometry types. To furthercompound the issue, these two geometry types can often be maddeningly difficult to tell apart visually in many computer softwareprograms. That said, it is important to recognize that NURBS surfaces will be curvedand that mesh surfaces will be composed oftwo (obviously flat) pairs of triangles.

These latter meshed surfaces will be either "ridged tris" or "valley tris", dependent upon how the quad topology is "kited". Whilein the case of the NURBS surface you will have a curved, ruledsurface which is called a hyperbolic paraboloid (or "hypar" forshort).

The astute reader will go one step further and see that the images of this "Iron Turtle's surface looks intuitively like mesh - due tothe facetting - but that it is in fact composed ofcurvedsurfaces and not flat ones. For obvious reasons this can engender a lot ofconfusion. For reasons that we will describe elsewhere it is important to understand these distinctions when generating geometryfor large scale construction.


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Figure 9. Fabrication of light gage bents.

Figure 10. Sheathing Fabrication.

Figure 11. Cladding Fabrication.




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7. The Residence

The design-build method provided unique opportunities to collaborate with a sophisticated Client whileaccommodating, the exigencies of construction.The eventual vernacular manual approach to the design, in conjunction with the local indiginous constructionmethodology, yielded a repeatable, fully in-house design and construction methodology. In short, we believe this isan efficient and repeatable contemporary design and construction methodology for a range of shapes.

Figure 12. Looking North.

8 . Further Work

Our method for analyzing the planarity (or hyparability) of the quads in this construction was less automated thanideal. For production work we would like the ability to have this fully automated to segregate any set of quadsaccording to non-planarity, as well as to be able to conveniently run inclusive and exclusive sets. This was notavailable in this effort and involved some workarounds.We would also like to explore better tools for measuring non-planarity (or non-developability) vis--visconstructibility at scale. Currently the gaussian curvature metric as well as the best fit plane methodology (this isan averagednon-planarity) are extremely indirect tools when in-field tolerances are measured in linear units.Specifically it is the non-planarity of the frame (two pairs of non-planar lines) that is of consequence in the fieldand this will be measured in metric units not those of gaussian curvature. In the case of "best fit plane" we wouldprefer to see the absolute non-planarity of each of the "fourth" corner points in any non-planar quad, whichtranslates better in the field.This is a surprisingly complicated question to ask and we are currently in discussion with a well-known engineeringfirm to implement this metric into their in-house software. But it seems that it should be possible either measure thisdirectly or to even convert the gaussian curvature measurements into a linear measurement of non-planarity onquad topologies.

We would also like to explore additonal functionality in the script for developing these surfaces. Currently themethod throws the developed parts down onto the X-Y plane with no orientation with respect to the original Zdirection. Thus one is currently either relegated to manually re-orienting these 2D templates in CAD, while real-time referencing the 3D model, or one must pass this work off to workers in the field who may not have referenceto the 3D model.




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Additionally, it would be helpful to have an automated labeling routine that could incorporate a mirrored primelabeling system - and allow for a left hand-right hand labeling system - which would eliminate half the templates(and a good deal of work in the field) in symmetrical conditions.

From a pedagogical perspective we would say that a better understanding of developing, unfolding, ruling,curvature and the hyperbolic paraboloid topology in architectural education would be of benefit. As noted, someconfusion exists with regard to the nature of nurbs quads as opposed to mesh quads and this has not beenclarified for many students and practitioners, particularly with respect to large scale construction. In the same vein,when developing mesh or nurbs quads, more control over the type, direction and reporting of stretch would bewelcome.Gaudi called the hyperbolic paraboloid the Father of all geometry and - as large scale curved geometry continuesto influence architectural form-finding and construction - some focus on these small discrete elements that make upmuch larger shells would be of benefit to future practitioners.

References

GLYMPH, SHELDEN, CECCATO, MUSSEL and SCHOBER (2004) A Parametric Strategy for Free-Form GlassStructures Using Quadrilateral Planar Facets.Automation in Construction, 13.

POTTMANN, ASPER, HOFER and KILLIAN (2007)Architectural Geometry. Bentley Institute Press:Pennsylvania.

SCHMIEDHOFER, COKCAN, SCHIFTNER, and ZIEGLER (2008) Design and Panelization of ArchitecturalFreefrom Surfaces by Planar Quadrilateral Meshes. Advances in Architectural Geometry Symposium, 2008.

SCHOBER, H. (2003) Freeform Glass Structures. Proceedings of Glass Processing Days, 46 - 50.



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