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BRANCHING STRUCTUREScast fromflat fabric sheet molds

NEW METHODS FOR ARCHITECTURAL AND STRUCTURAL CONCRETE FROM C.A.S.T.THE UNIVERSITY OF MANITOBA’S CENTRE FOR ARCHITECTURAL STRUCTURES AND TECHNOLOGY

by Mark West



BRANCHING STRATEGIESBranching structures are one of Nature’s favorite tricks

for efficiently distributing matter. Human constructions,

while fundamentally different in many ways from those

of Nature, can also partake of the elegance, efficiency,

and physical beauty offered by this essential spatial/structural strategy. For example, spreading columns

can reduce the span of the beams they support. Since

the bending work of a beam increases with the square

of its span, even a small reduction in span can offer

geometrically increased reductions in bending forces.

More efficient or optimal force paths can also be traced

through branching lines of support. The penchant for

constructing rectilinear structures is a product of our

tools, rigid materials, and (building) culture rather than

a rational response to purely structural imperatives.

This document describes ways of constructing branch-ing reinforced concrete structures in molds made from

flexible flat sheets of fabric



A flat membrane can be naturally buckled to form figures that enclose three dimensional volumes.

The photograph above, taken from the Institute for Lightweight Structures publication ILS 25, pg 2-80

(1990), shows a flat fabric sheet buckled into series of Y-shaped branching figures. The ILS looked

at this phenomenon as a problem to be understood and solved (they were hunting for non-buckled,

smooth shapes). These naturally occurring forms, however, can be used to construct simple fabric

molds for branching cast concrete structures using flat fabric sheet molds.Bottom Left: a flat fabric sheet buckled into parallel ridges by pushing the sheet together from the top

and bottom only - what we call a one-way ‘push-buckle’.

Bottom Middle: a fabric sheet buckled into Y-shaped branching volumes by pushing the sheet together

simultaneously from both top-bottom and left-right - what we call a two-way ‘push-buckle’.

Bottom Right: Construction of a fabric formwork mold using a two-way push-buckle induced in a flat

sheet of woven polyethylene geotextile material.

BRANCHING PATTERNS FROM BUCKLED FABRIC SHEETS



The small -scale (30cm tall) model shown Below illustrates the basic formwork method for a branchingcolumn utilizing the “Bulge-Wall” method developed at C.A.S.T. [for a full description of the bulge wallmethod, see the PDF document “Bulge Wall” available at: www.umanitoba.ca/cast_building/resources].These small models use light nylon fabric and plaster to develop construction methods and details forfull-scale construction using powerful industrial fabrics and concrete.

A view of the inside surface of the mold model, showing the

two facing flat fabric sheets let into the Y-shaped voids pro-

vided by the plywood cut-outs.

This is a view of the two outside faces of the mold model.

The branching figure cut out of the plywood panels will de-

termine the profile of the cast Y-shaped column.

This photo shows the mold model assembled and filled with

plaster, modeling a cast-in-place concrete column form.

As the lines of bulging fabric forming the ‘trunk’ and two ‘branches’ join at the crotch of the column form,the amount of fabric bulging outwards is increased at this point. The photos (Below) show two methodsof reducing the volume of concrete at this crucial point in the mold: Left Below and Centre Below showhow a rod (ex. a steel rebar) can be used to push the excess fabric inwards at the crotch. Right Below shows the fabric pulled together in a line of sewn ‘tucks’ that reduce bulging in this location.

FLAT SHEET MOLD METHOD

Two facing flat sheets of fabric are “buckled” into a branch-ing figure, allowing them to bulge outwards through open-ings cut in the plywood sheets on either side of a wall mold.



Left Above: The Y-shaped profile of the column has been cut out of a modified plywood wall form.

Centre Above: A flat sheet of geotextile fabric is smoothed and stretched into the Y-shaped void.

Right Above: The fabric is stapled to the plywood along the edges of the Y-shaped opening.

Left Below: The modified plywood wall formwork ready to receive concrete

Right Below: The formwork after it is filled with concrete.

CONSTRUCTION OF A THREE-METRE BRANCHING COLUMNOur 30 cm. high plaster models were directly translated to the full-scale construction of a three metre-

tall column - a ten-fold increase in the height, and a thousand-fold increase in volume. The ability to use

such small models to predict full-scale mold behavior is accounted for by the fact that tension structures

scale-up linearly. This makes it possible to intuit full-scale effects from small working models. Nearly

any structure that can be built with a miniature fabric mold can be built in a full-scale fabric mold.



Above Left: because the mold is flexible, the concrete can be externally vibrated by handAbove Center, Left & Right: In this cast, a self compacting concrete (SCC) was used. The highlyflowable and almost liquid character of SCC necessitated the use of a temporary “dam” or “collar”,

shown here placed at the base of the column to restrain the bottom free edge of the formwork fabric.This collar is held in place by a worker’s foot until the concrete has filled the first 15 or 20 cm. (6 or

8 in.) of the column, after which it can be removed for the rest of the pour (after applying this initialpressure, the fabric becomes stiff as it is tensioned). “Normal” concrete, which is not liquefied, can bepoured without need of such a collar.Above Right, Top: The formwork filled and bleeding excess mix water through the permeable geo-textile membrane -this loss of mix water significantly increases concrete strength and quality.Above Right, Bottom: Detail of formwork base, illustrating the free edge of the fabric against the

foundation. In this case the fabric was mistakenly cut 1.5 cm too short, yet the detail works perfectly.

Left: Formwork before placing concrete. Right: Formwork after placing concrete.

Note the “tuck” taken in the formwork by ropes threaded through the fabric. This is done to reduce the

bulging that would otherwise occur at this location due to the excess fabric gathered in the flat sheetat a branching point.



MULTIPLE BRANCHES FROM

A FLAT SHEET

Multiple branches may also be formed branch-

ing off a single trunk using a flat-sheet mold ina “Bulge Wall” type formwork. Though these

branches are limited to a single plane, there are

other ways (not shown here) to use flat-sheet

molds for casting columns with branches in more

than one plane. These more complex casts,

however, must be done as pre-cast pieces, not

as cast-in-place members as illustrated here in

these plaster models.

Left, Top: This image illustrates how multiple

branches can be formed using a flat-sheet form-liner that is allowed to deflect outwards from a

profiled opening cut out of a flat plywood sheet.

Bottom Left and Right: Small-scale plaster

models of multiple branching columns.



There is an inherent constructional and organizational simplicity to using ninety-degree joints in our

structures, and our tools and materials are, accordingly, made to facilitate these constructions. Branch-

ing structures, though theoretically more efficient in the use of materials, are difficult to build using con-

ventional tools and methods of construction. In order to build such a structure with the straight, milled,

sticks and sheets of conventional steel or wood construction, a multiplicity of individually angled andfitted members and joints are required.

Cast concrete, on the other hand, can eliminate this proliferation and complexity of parts because it

can be monolithically formed into any shape, as long as a suitable mold can be provided -- and therein

lies the trick. Conventional formwork construction is inherently ill-suited to the production of branching

shapes. Flexible fabric formwork, however, can easily form branching molds, even when using simple

flat sheets of fabric without patterns or tailoring.

With fabric formwork, the difficulties faced in constructing a branching structure are not in the molds,

but in the structural design and analysis methods they may require, and in their reinforcing design and

assembly. Research points to simple solutions on both counts, though more work is required to refine

and test their efficacy in commercial applications. One way to simplify both structural analysis and

reinforcing design, while forming beautiful structures that use a minimum of materials, is to use these

branching concrete forms to build structures that follow naturally efficient compression force paths. In

terms of material use, this is a very good way to use concrete (which loves compression). Architectur-

ally it suggests the discovery and invention of a new kind of compression-based architecture.

The single most efficient way to carry a load is through linear tension (ex. the tension “arch” of a hanging

chain). The second most efficient structure is the compression arch (in the form of an inverted tension

arch). The price for this efficiency is “paid for” in the lateral thrust an arch produces. Significantly, the force

of this thrust increases dramatically as the depth of the arch is reduced. These forces must be resisted

either by providing a “tie” to close the arch at its springing points, or by providing well buttressed supports.

Either solution adds complexity to the overall construction. Beams, on the other hand, span through bend-

ing, a mechanism that combines and joins tension and compression within a single member, eliminatinglateral thrust to the supports. This lack of thrust makes beams very easy to use in construction, though

this structural convenience is “paid for” by reduced material efficiency; bending structures such as beams

and flat slabs require more material to carry the same load as a compression arch or tension span. All of

these factors must be dealt with any proposed alternative to rectangular frame and slab structures.

BRANCHING vs. RECTANGULAR CONSTRUCTIONS

- a new compression architecture -

An inverted photograph showing a “gravity drawing” at CAST studying forms for branching columns

and arches. We use these hanging chain models, much as Antoni Gaudi did, as our form calculators.



The drawing (Above) illustrates branching columns sup-porting branching funicular fabric-cast trusses that utilize

a combination of tension and compression arches. Cast

plaster models of these reinforced concrete trusses are

shown Left Top, and the mold for these models is shown

Bottom Left. The formwork method uses flat sheets of

fabric stretched across a simple rigid “frame”. A full-scale,

4-meter reinforced concrete truss is shown with its form-

work Bottom Right. [C.A.S.T. technology for manufac-

turing fabric-cast trusses is described in the article “Fab-

ric-formed Truss” available at: http://www.umanitoba.ca/

cast_building/resources.html.]

IN BRANCHING STRUCTURESCAST TRUSSES

A branching structure is used here (Top and Left, Top -Bottom) to make a light-weight structure that is also stiff.

Efficiently shaped trusses are more flexible than equiva-

lent depth uniform-section beams. The branching arms

of the columns stiffen this structure by reducing the effec-

tive span while at the same time completing an integral

compression arch, leading to a stiffer structure than simply

supported trusses on vertical columns.



BRANCHING SUPPORTS FOR

VAULTS

Branching supports can also be used to gather and

resolve the natural thrust lines produced in com-

pression shell structures as illustrated by the hang-

ing “gravity drawing” shown (Left Top). Compres-

sion shells can be easily produced from flat fabricmolds as described in the articles “Thin Shell Walls

and Vaults for the Open City” and “Thin Shell Con-

crete from Fabric Forms”, both available from http://

www.umanitoba.ca/cast_building/resources.html

* See, for example, P. Block & J. Ochsendorf.

(2007) “Thrust network analysis: a new methodol-

ogy for three-dimensional equilibrium” Journal of

the International Association for Shell and Spatial

Structures, Vol. 48, No 3, pp. 167-173.

Interactive engineering design software for shap-

ing and calculating compression shell structures is

currently being developed by engineers at MIT in

the U.S. and the ETH in Switzerland*.

Dr. John Ochsendoft: Massachusetts Institute of

Technology in Cambridge, MA (USA). Dr. Phillippe

Block: The Swiss Federal Institute of Technology

(ETH) in Zurich Switzerland.



A flat fabric sheet held at its four corners (Top Left) can form a mold to produce a precast compression shell (TopRight). The buckles that naturally form along the principle lines of tension stress, radiating from the corner supportsof the fabric mold sheet, translate to deep buckling-resistant corrugations or ”ribs” in the shell cast from this mold.Likewise, a flat fabric mold can be shaped by selective pretensioning as shown in the plaster shell models MiddleLeft and Bottom Left, and the full-scale mold-making rig Middle Right. In this mold, the flat sheet is pretensionedalong its centre-line. A full-scale thin-shell vault being cast from this kind of prestressed fabric sheet mold is shownBottom Right. Note the naturally formed deep corrugations branching from the end supports of this vault. [see

“Thin Shell Concrete from Fabric Forms”: http://www.umanitoba.ca/cast_building/resources.html]

BRANCHING STRUCTURAL FOLDS AND “RIBS”



BRANCHING RIBS IN A SLAB

Ribs can be formed to stiffen a slab by using pull-buckles that are

guided into specific openings in a flat deck formwork. The Photo

Left Middle shows a plywood formwork deck with cut outs at the

rib locations. Left Bottom shows how flat sheets of fabric on either

side of the mold can be pre-tensioned into these cutouts to makebranching rib forms. Bottom Left is a view of a prefabricated ribbed

T-beam cast from this mold. Below is a photo of plaster models

showing the underside of a roof or floor structure utilizing these

ribbed T-Beams. The Photo Top Left shows a single rib formed in

this manner from a fabric formwork model filled with plaster.



BRANCHING BEAMS AND RIBS



The same formwork techniques described above for casting branching structures in cast-in-place wall

forms can also be deployed in horizontal formwork to cast branching beam structures. Below Left is

a photograph of a model formwork for a branching beam-drop in a flat slab structure. Below Right is

the small-scale plaster model cast from this mold. The photograph Above shows one possible spatial

arrangement of these beam + slab structures.

Following Page Top shows a close-up view of a model beam-drop at its branching point.

Following Page Bottom is a view of the underside of a modeled slab + beam structure. Branched sup-

port columns are shown in Pink/Red.



CREDITS

Thanks to CAST Research Assistants Aynslee Hurdal, Leif Friggstad, Mike Johnson, Kyle Mar-

tens and CAST Research Associate Ronnie Araya who helped make and develop these things.

Thanks also to the Lafarge Building Materials Group precast factory in Winnipeg Manitoba.

branching structures small

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