THIN-SHELL CONCRETE
C.A.S.T. The Centre Centre for Architectural Structures Structures and Technology
FROM FABRIC MOLDS
University of of Manitoba Faculty of Architecture
Prepared by by Mark West, 2009
INTRODUCTION
This illustrated description shows several methods of forming prefabricated thin-shell concrete structures using molds made from hanging flat sheets of fabric. These fabric sheets are allowed to deflect into naturally occurring funicular geometries, producing molds for lightweight funicular compression vaults and stiff double curvature wall panels. These methods were developed at the Centre for Architectural Structures and Technology Technology (C.A.S.T.) (C.A.S.T.) at the University of Manitoba’s Faculty of Architecture. Some of the work illustrated here closely follows methods of funicular shell formation pioneered by Heinz Isler, who used small-scale funicular models to determine full-scale construction geometry and structural behavior of reinforced concrete thin-shells. Our work is aimed at making full-scale hanging fabric molds using powerful industrial fabrics - essentially scaling-up Isler’s model-making method into full-sized shell molds. The maximum size of these structures has yet to be determined. Our early small full-size constructions are illustrated here as indications of the potential for “self-forming” funicular fabric molds. Our work at CAST uses a simple set of construction tools, fasteners, and technologies. We do not “tailor” our fabric molds into pre-set curvatures - w e use only flat sheets of fabric taken right off the role. The shell geometries illustrated here are given to us by the natural deformations of these simple flat-sheets, and are, in this sense, “found”, “natural”, structures. The goal of this work is to invent simple, and beautiful structures that consume less material in construction, while opening new degrees of freedom to architects, engineers and builders in both high- and low-capital building cultures.
INTRODUCTION
This illustrated description shows several methods of forming prefabricated thin-shell concrete structures using molds made from hanging flat sheets of fabric. These fabric sheets are allowed to deflect into naturally occurring funicular geometries, producing molds for lightweight funicular compression vaults and stiff double curvature wall panels. These methods were developed at the Centre for Architectural Structures and Technology Technology (C.A.S.T.) (C.A.S.T.) at the University of Manitoba’s Faculty of Architecture. Some of the work illustrated here closely follows methods of funicular shell formation pioneered by Heinz Isler, who used small-scale funicular models to determine full-scale construction geometry and structural behavior of reinforced concrete thin-shells. Our work is aimed at making full-scale hanging fabric molds using powerful industrial fabrics - essentially scaling-up Isler’s model-making method into full-sized shell molds. The maximum size of these structures has yet to be determined. Our early small full-size constructions are illustrated here as indications of the potential for “self-forming” funicular fabric molds. Our work at CAST uses a simple set of construction tools, fasteners, and technologies. We do not “tailor” our fabric molds into pre-set curvatures - w e use only flat sheets of fabric taken right off the role. The shell geometries illustrated here are given to us by the natural deformations of these simple flat-sheets, and are, in this sense, “found”, “natural”, structures. The goal of this work is to invent simple, and beautiful structures that consume less material in construction, while opening new degrees of freedom to architects, engineers and builders in both high- and low-capital building cultures.
FIRST TEST OF FABRIC-FORMED MOLD FOR PRECAST THIN-SHELL FUNICULAR VAULTS Lafarge Precast Factory, Winnipeg, Canada -- April 2004
Our first test scaling-up a small funicular model was done in 2004 using an inexpensive woven polypropylene Geotextile (Propex 315ST). The span of this barrel vault was 2.5 meters (8 ft.). The procedure here was to make a funicular fabric-formed rigid mold that could be used to cast multiple funicular compression shells.
1. A flat rectangular sheet of geotextile fabric is hung from a steel frame
2. A uniform thickness of Glass Fiber Reinforced Concrete (GFRC) is applied to the hanging fabric - in this case as a spray application.
3. The resulting funicular shell is inverted to make a mold for precast production.
4. In this test, test, the fabric fabric was removed to expose the concrete surface, which was then sealed and oiled to provide a release surface for the mold. A single thin-shell GFRC vault was produced from this fabric-formed mold. No structural tests were performed.
DIRECT-CAST FABRIC-FORMED THIN-SHELL VAULTS / BEAMS C.A.S.T. Lab, Winnipeg, Canada -- May 2009 Example #1: Double-curvature funicular shell cast directly fr om a single hanging flat sheet of fabric
In this construction a single flat rectangle of fabric is hung from a simple perimeter frame and used as a mold to form a double curvature vault. A simple frame is provided to support the edges fabric ( Left Below). The fabric is stretched lengthwise to remove any wrinkles, and stapled to the sides of this frame ( Right Below).
Example #1 Continued: Instead of conventional steel reinforcing this vault was made with carbon grid reinforcing. Carbon reinforcing allows for a very thin section -- only 3 cm (1 in.) thick. Carbon, unlike steel, does not require an extra concrete covering to protect it from corrosion.
Example #2: Double-curvature lenticular shell cast directly from two flat sheets of fabric
This construction used the same curved edge supports as the previous example, but in this case a central “keel” was used to control the bottom curvature of the mold. This keel, made of two layers of 3/4” plywood, holds two flat sheets of fabric sandwiched between them ( Bottom Left, Bottom Centre). 1/8” plywood “feathers boards” were placed at the ends of the mold rig (seen Below) to ensure that the loaded fabric follows a smooth and fair transition to the flat support areas at either end of the vault.
When the concrete (a portland cement mortar) is troweled onto this mold, the fabric deflects downwards slightly under the weight. This shell was reinforced with carbon fibre, allowing a thickness of only 3 cm.
NEW FABRIC FOR MAKING FABRIC-FORMED RIGID MOLDS
Woven, high density, polyethylene or polypropylene fabrics can be manufactured with a smooth waterproof coating on one side, and a fuzzy non-woven fabric welded to the other side. When concrete is applied to the fuzzy non-woven side, the fabric will permanently adhere to it, providing a smooth, permanent, plastic-coated release surface for a mold. Concrete will not adhere to the smooth polyethylene or polypropylene coating of these fabrics. No oils or other release agents are needed, though the use of such release agents will prolong the life of these molds.
Prototype mold fabrics have been produced for CAST by Fabrene Inc., a manufacturer of industrial plastic fabrics. The (limited) test data for one such fabric (Fabrene “Development Product W756”) is shown below. This particular product adapts an existing fabric commonly used for inexpensive fabric covered agricultural and storage shelters. It is manufactured in 3 m. (10 ft.) wide r oles. It can be heat-welded into larger sheets, or reinforced in multiple layers. Stronger fabrics are also available for this application if required.
FABRIC FORMED MOLD FOR PRECAST THIN-SHELL VAULTS Lafarge Precast Factory, Winnipeg, Canada -- April 2007 This prototype rigid funicular fabric-formed mold is intended as formwork for thin-shell GFRC stay-inplace pan formwork for cast-in-place (CIP) floor slabs. The funicular compression shell shape given by these formwork pans allows a CIP concrete slab to span in pure compression between the integral support beams, thus reducing concrete and deadweight. Cast-in-place concrete Reinforcing steel in integral valley beams Prefabricated, fiberreinforced thin-shell formwork pans.
Floor structure viewed from below showing the pattern of individual precast compression vault formwork pans for a cast-in-place slab.
A uniform thickness of fiber-reinforced concrete is placed over the fabric. In this case a sprayed shotcrete was used, though hand-application of the concrete is also possible. The edges were reinforced with steel rebar.
A simple open frame is constructed to support and suspended a flat sheet of fuzz-backed formwork fabric (see previous page)
The fuzzy fabric backing adheres to the concrete, producing a plastic-coated mold for precast production of stay-in-place formwork pans or thinshell funicular compression vaults.
FABRIC-FORMED RIGID MOLD FOR PRECAST THIN-SHELL VAULTS A method for forming a prototype thin-shell vault cast from a rigid fabric-formed mold is shown below. This method, like much of our work at CAST, was developed using small plaster models. The model shown in the photographs below, was made by stretching a flat, fuzzy-backed, plastic sheet over a rigid framework rig (Bottom Left). The fuzzy side of the fabric is then sprayed with plaster (m odeling the thin uniform layer of glass fiber reinforced concrete (GFRC) used in full-scale construction). The resulting form is then lifted off the formwork rig and turned over (Top Left), providing a rigid, smooth, one-piece, fabric-lined female mold for casting thin shell vaults. The Vault model(s) produced from this mold are shown Top Right and Bottom Right. A wide range of vault shapes can be formed by altering the geometry of the support rig and by the strategies employed in restraining the flat fabric sheet and pulling it into place. The shape of this particular vault is designed to provide a compression vault form with its own integral tension restraint. The straight, flat, “keel” or ridge formed along the center-line of this vault contains the tension reinforcing required to restrain the horizontal thrust of the funicular compression vaults formed on either side. dge beams are formed at the support ends to transfer the horizontal thrust of the vaults to this central line of tension restraint. This structural shape combines the geometry of a bending-moment-shaped beam with tied funicular compression vaults.
FABRIC-FORMED RIGID MOLD FOR THIN-SHELL VAULTS: Full-Scale Prototype, C.A.S.T. Laboratory, Winnipeg, 2009 The 5-meter prototype vault mold constructed at CAST was produced in the rig shown in the photographs Below. This rig provides a straight central spine, formed by a 1.5 in.(4 cm) steel pipe and catenary-curved longitudinal edges formed in 3/4 in. plywood and 2x4 lumber following the shape of a simple hanging cord (Bottom Left and Bottom Center ). A single flat sheet of fuzzy-backed formwork fabric (Fabrene W756) is placed over this rig, and selectively pre-tensioned as shown ( Bottom Right). A thin, uniform layer of GFRC will be placed on this fuzzy-backed fabric to make a rigid mold for producing thin-shell vaults. Note that the pre-tensioning device is twisted ropes, with load cells attached to gauge the magnitude of the pretension forces. [A discussion of how selective pre-tensioning alters the shape of a flat fabric sheet follows the description of this mold.]
This photo shows the double curvature produced by pre-tensioning along the centre-line of the fabric sheet. The cut in the fabric controls where the induced curvature along the center-line begins.
End of the formwork rig prior to loading with points of pre-tensioning shown: A start-condition force of 40 kg (+ - ) is delivered to the centre of the sheet, and a mild 12 kg (+ - ) at the edges. Edge forces are increased to remove folds as the fabric is loaded with concrete. Load cells are used to keep track of the prestress force applied.
Glass fiber reinforced concrete (GFRC) is placed on top of the fabric, causing this formw ork membrane to deflect under the uniform applied load. Photos Below show the first layer of GRFC being applied.
The first thin layer of GFRC is placed over the entire fabric sheet. (Above). We did this by hand, though industrial methods include spray applications that are faster and more uniform. Then, a series of stiffening ribs, and a continuous glass fiber mesh, are added to strengthen the mold and give it sufficient rigidity to be lifted, flipped over, or transported.
These views from beneath the formwork rig show the preliminary shape of the fabric sheet before it is loaded (Left), and after it has taken the full weight of the wet GFRC ( Right). The weight of the concrete will gives the fabric sheet its final structural geometry. The resulting rigid fabric + GFRC construction will be lifted and turned over, providing a smooth polyethylene-coated mold.
These photos show the fabric-formed GFRC mold completed, prior to turning it over for use. This mold weighs less than 500 kg. (1,000 lb.)
Turning the mold over
These photographs show the finished fabric-formed GRFC mold turned over, with the coated polyethylene release surface ready for use. Here you can see how the flat fabric sheet has developed a “musculature” in response to the loads imposed on it. Although not strictly biomimetic, this natural development of resistant form is analogous to the development of structural form in living systems that produce material in response to stress concentrations (as in bones or tr ees for example). Here, the flat fabric sheet has developed structural depth in response to stress concentrations.
The finished mold is scanned with a laser pointcloud scanner (Left) to determine is precise curvature in three dimensions. This information is then used for the structural analysis/design of shells produced from the mold. After structural design is completed, a structural prototype thin-shell vault will be cast from this mold.
Test casts have been made from this mold using both GRFC and regular Portland cement mortar (Below). Wet mortar/concrete was placed by hand, as would be the case in low-capital construction cultures. Industrial spray application is also possible.
The first full-length test cast from this mold ( Above) was made using a regular Portland Cement mortar, with a combination of glass scrim and steel rebar reinforcing. This test cast is 2.5 cm (1 in.) thick.
FABRIC-COATED CONCRETE SHELLS The fuzzy-backed fabric can also be used to make a fabric-covered thin-shell cast: A sheet of this fabric is stretched over the mold, adopting the same flat-sheet geometry as the mold, and concrete is placed on the fuzzy side of this sheet (Thee images Left). This gives the resulting shell a permanently attached fabric coating on its underside, resulting in a perfectly smooth, textile finish (Below and Bottom).
PRE-TENSION CORRUGATIONS Deep corrugations can be “pre-loaded” into a flat sheet by selectively pre-tensioning the fabric across its span. This concentrated pre-tensioning causes the flat sheet to buckle normal to the principle line of tension stress. The resulting form will have a primary (funicular) curvature across its span, and a second curvature across the width of the vault that gives a deep, buckling-resistant, transverse section.
The double curvature of a pre-tensioned flat-sheet fabric model mold is shown Above Left, and a view of a plaster model vault cast from this mold is shown Above Right. The image Below shows the deep ridge(s) produced a pre-tensioned flat, r ectangular formwork sheet. Note the pattern of curved openings created by the naturally curved “free edges” of these vaults.
MULTIPLE CORRUGATIONS
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CONTROLLED EDGES
Multiple deep corrugations can be “loaded” into a flat sheet of formwork fabric by providing multiple lines of pre-tensioning, as illustrated by the fabric sheet shown Top Right.
The fabric shown Bottom Left is a flat, fuzzybacked, plastic sheet that has been selectively stretched along three lines of pre-tension. The edges of this mold-making rig provide flat, straight edges across the span, though the fabric is not supported from these edges. This fuzzy-backed fabric was then sprayed with a uniform layer of plaster to make the 2 meter-long model mold shown Bottom Right. This mold produced the thin-shell vault model shown Middle Right. The mold for this shell has a straight, horizontal, rectangular, perimeter around all four sides. This provides for a closed, horizontal, tension ring to be cast into the perimeter of this vault to restrain the lateral trusts of the funicular vault.
MODELS OF OTHER FABRIC-FORMED FUNICULAR SHELL MOLDS 1. Buckled Flat-Sheet Vault Forms Produce Buckling-Resistant Forms When a hanging flat sheet assumes a double curvature shape, it will tend to produce buckled folds. These corrugations tend to align with the principle lines of force in the fabric, producing deep “folded” sections in these areas. These folded corrugations can be formed in several ways. One way, illustrated previously, is by inducing deep folds by a concentrated pre-tensioning a fabric sheet (see “Pre-tension Corrugations” above). Another way, illustrated below, is through load-produced buckling. LOAD-PRODUCED CORRUGATIONS: The model fabric-formed mold shown here (Top Left) was made by supporting a flat sheet of fabric from its four corners. When loaded with a uniform layer of plaster (to model concrete), the flat sheet buckles along the principle lines of tension ‘flowing’ towards the four corner supports
The funicular compression shell cast from this mold (Bottom Left) acquires the deep corrugations given by the buckled fabric mold. This provides buckling-resistant sections aligned with the principle lines of compression force in the shell. Horizontal thrust forces can be contained by installing tension reinforcing, integrated into the shell along its perimeter, connecting the four support points in a tension ‘ring’, or by providing buttressed supports.
2. Flat-Sheet Vault Molds for Combinations of Concentrated and Uniformly Distributed Loads
A mold for a vault designed to support uniform plus concentrated loads can be made by placing proportional point loads on a flat fabric sheet ( Above Left) prior to placing a uniform load of concrete on the fabric. This method is illustrated by the model mold shown ( Above Center ) and the shell cast from this mold (Above Right). A shell such as this could be shaped to support, for example, its own dead-weight plus that of a raised-floor structure placed upon it.
The model mold shown Above Left, was formed by a rectangular sheet of fabric that was pre-tensioned by pushing upwards at two points (Above Right). The shells produced from this mold ( Bottom Left) are cantilevered shells -- their lower surface is in compression and their upper surface is reinforced for tension.
[Note: the branching columns shown here are also formed from flat sheets of fabric using another CAST formwork invention.]
3. “Flying” Vault Forms The “flying” vault shown below is formed by supporting a flat fabric sheet from three points while pulling outwards on the fourth point ( Below, Left). The mold formed by such a rig ( Below, Middle) produces the vault shown Below, Right. This vault is more or less balanced on the two supports to the left and right in the image Bottom. The support to the rear carries a very small part of the total load. It will be noted that the flat fabric sheet has spontaneously provided a deepened “arch” between its two principle supports. This buckling of the tension-laden fabric sheet has naturally formed a deep, buckling-resistant section along the principle line of compression force.
THIN-SHELL CURTAIN WALLS
THIN-SHELL PANELS FORMED FROM SHEETS OF HANGING FABRIC Lafarge Precast Factory, Winnipeg, Canada -- April 2007
A hanging sheet of fabric can be used as a mold to produce thin-shell wall panels. The panels show here (Above and Bottom Right)) are made from fiber-reinforced spray concrete applied to a hanging sheet of polyethylene fabric ( Bottom Left). These panels are less than 5 cm (2 in.) thick, with perimeter edges of 10 cm (4 in.) thick. A hanging flat sheet of fabric will naturally form itself into double curvature shapes that provide stiffness and strength to a thin concrete shell panel, while random fiber reinforcing gives the concrete significant flexural strength and ductility. Various fibers and concrete mix designs can be used for this kind of application, though Glass Fiber Reinforced Concrete (GFRC) is perhaps the best material choice.
Details of full-scale thin-shell, spray concrete, Curtain Wall constructions
Mock-ups and models of thin-shell Curtain Wall molds and constructions at C.A.S.T.
Plaster models of other possible thin-shell Curtain Wall constructions
