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Tensile structures innovative envelopes

ECOSTRUCTURES

Prof: Peter Land

Ricardo Urech

Spring 2015

Ricardo Urech Garcia de la Vega 1

Ecostructures Spring 2015

Outline

0. introduction

1. main concept

a. double curvature

b. tension

2. history

a. domes

b. cable suspended bridges

c. tents

3. mathematics

a. synclastic surfaces

b. anticlastic surfaces

4. physics

a. cables

b. joints

c. support elements

d. membranes

5. case studies

a. Frei Otto

b. Fazlur Khan

c. Bodo Rasch

6. innovation in tensile structures

7. conclusion



8. bibliography



0. introduction

The present paper summarizes the research Ive done on tensile structures, and

specifically membrane structures. The review will include a brief concept introduction, and

some historic references that need to be mentioned; also some mathematical concepts are

worth mentioning and the physical arrangement of these structures. Finally, we will see

some examples of these structures by masters of the technology and we will take a look into

the future of these fantastic architecture.

It is worth to say that this material has been developed and adopted by the same few

people in the most important examples. Ive become familiar with engineers and architects

like Fazlur R. Khan, Horst Berger, David Geiger, Paul Weidlinger or Frei Otto, a

generation that has become the masters and pioneers in the use of tensile structures.

1. main concepts: terminology

Tensile structures are possible because of two ideas, one physical and the other

mathematical: tension and double curvature. For the tensile structures to stand, a unique

equilibrium between shape and stress exists. This is the only way that membranes are able

to bear the weight of snow and wind forces.

Figure 1. Double curvature surface. Figure 2. Tension



Double curvature surfaces are surfaces that curve in two directions. They have two

main curves with which these surfaces can be generated.

Tension is an axial stress pulling to the ends of a rope or a cable. It is the opposite

stress to compression. Tensile members can be as thin as their tensile capacity allows

because they dont suffer from buckling, like compressed members do.

2. history

Some of the concepts that tensile structures use are not new. Humans have known

them for centuries and used them in previous developments. For example: first wooden

dwellings shaped like domes, cable bridges in China or tents used by many different

cultures in the world.

a.domes

Some of the first dwellings that humans erected were erected following the rules of

domes. For example, in Terra Amata, near Nize in France, there are remainders of these

type of dwellings. These people stuck tree saplings in the ground forming an oval floor

plan. Then they bent the saplings until they touched a ridge beam and laced to each other to

form arches. This structure was the thatched with palm or grass. The saplings were held to

the ground with rocks.

Figure 3. Sketch of dwelling in Terra Amata



Later on, Heinz Isler designed his super-thin concrete domes. These were designed

using the inverted catenary. This is important because the catenary is the form a cable

assumes under its own weight, it is the optimal form to carry tension loads. So Islers

domes are like inverted membranes that hang from four points. He was a pioneer using this

kind of form finding with wet cloths. Therefore the entire shell is under compression,

avoiding cracks. For example the indoor tennis sports center in Heimberg is a 3-inch thick

shell spanning 80 feet!

b. suspended bridges

Suspended bridges relay on the possiblity of cables to span long distances with little

material. We can trace the origin of cable suspended bridges in Asia. They use the principle

of load distribution.

The beautiful Kuanksien Anlan bridge is made of bamboo cables. It was constructed

more than 2000 years ago. The bridge is closed two months every year due to reparation

work as bamboo, even though it is a strong material, needs careful maintenance. The ropes

were made of bamboo and hemps, fibrous materials.

Figure 4. Heinz Islers concrete shell Figure 5. Interior of tennis courts.



Later on, wrought iron chains were used in bridges until the adoption of high

strength steel cables. This made possible larger spans with lesser material. Steel is an alloy

of iron and carbon with very interesting mechanical properties, it is because of the

existence of this material that we can build most of the structures of the world. Althoug

Brooklyn bridge is not the first example, it is indeed one of the first bridges and a great

example of cable bridges of the XX century.

c. tents

This is the most evident precedent of what we know today as tensile structures.

Humankind has had needs for portable housing due to many different reasons. Military

Figure 7. Brooklyn bridge.

Figure 6. Load distribution in cable. Figure 7. Kuanksien Anlan bridge.



armies since the Roman Empire used textile tents in their campaigns all over Europe. Even

today, tents are laid out on missions around the globe.

Also, nomadic cultures such as the Bedouins, Moors, Berbers of Mongols

developed tent structures which they could load onto their camels and horses and erect

anywhere in matter of minutes.

To erect tents, the fabric was put under stress to keep it from flapping in the wind.

Introducing internal stress is part of the assembly and erection process.

3. mathematics

In order to understand the forms that tensile structures adapt when subjected to

stress we must immerse ourselves into the world of mathematics (for a least a moment).

The inherent geometrical quality that enables the existence of tensile structures is the

double curvature. Without double curvature fabric and membranes would swing and flap

under wind forces and other stresses.

The double curvature can be represented in one number, the Gaussian curvature,

which is the product of the main curvatures. The sign of the Gaussian curvature can be used

to characterize the surface.

Figure 8. Catherine de Medici signs peace outside her tent. Figure 9. Tents provide shade in hot desert climates.



If both principal curvatures are the same sign: 12 > 0, then the Gaussian curvature

is positive and the surface is said to have an elliptic point. At such points the surface

will be dome like, locally lying on one side of its tangent plane. All sectional

curvatures will have the same sign.

If the principal curvatures have different signs: 12 < 0, then the Gaussian

curvature is negative and the surface is said to have a hyperbolic point. At such

points the surface will be saddle shaped. For two directions the sectional curvatures

will be zero giving the asymptotic directions.

If one of the principal curvature is zero: 12 = 0, the Gaussian curvature is zero and

the surface is said to have a parabolic point.

This abstract concept can be understood fairly easily with diagrams.

a. synclastic surfaces

Synclastic surfaces have positive Gaussian curvature. A typical example would be a

dome. But, regarding membrane structures, synclastics are usually pneumatic domes. Air

pressure inside puts stress into the membrane the stretches until it reaches its final form.

Figure 10. Example of three surfaces with different Gaussian curvature.



For example, David Geigers US pavilion for Expo 70 in Osaka was an air-

supported membrane roof. As we can see, the whole space is pressurized, this air-pressure

pushes the membrane outwards. To help shape the membrane, steel cables are attached to

the fabric forming a diagrid. Fabric was made of fiberglass coated with Teflon fluorocarbon

resin.

b. anticlastic surfaces

Anticlastic surfaces are mainly hyperboloids and paraboloids. In tensile structures

the most common geometries are related to the paraboloid, commonly known as saddle

surface.

The saddle surface is the easiest double curvature surface to build. The archetypical

method is called the drying clothesline problem, starting from the 4-point structure. Two

posts are stuck in the ground with a clothesline hanging in between. Another cable is

attached to the ground perpendicularly to the first rope passing over and tensioning it. This

process is repeated in both directions to increase the stiffness of the cable net.

Figure 11. Interior of the US pavilion with structure of the fabric Figure 12. Aerial view. Diagrid structure.



There are many examples of this 4 point surface in tensile structures. Most famous

where designed by Frei Otto, one of the pioneers in the developing of this technology. The

image in the left shows the music pavilion of the Bundesgarten in Kassel, Germany, erected

in 1955. Note that the masts are inclined to ease construction and their stress. The right one

shows an exhibition pavilion also designed by Otto in Leonberg, Germany, in 1988.

Frei Otto studied these surfaces with great attention. He figured out that saddle

surfaces can be combined in many ways which provide great flexibility and almost infinite

possibilities. Some of his sketches show this concern. Ridge and valley surfaces are

arranged this way.

Figure 13. Drying clothesline problem illustration.

Figure 14. Music pavilion in Kassel. Figure 15. Exhibition pavilion in Leonberg.



A very particular and interesting way to combine saddle surfaces is radially. It is

very typical to use fabric structures in stadiums and other constructions that usually have a

centralized shape. This common arrangement can be seen in the King Fahd International

Stadium designed by Ian Fraser, John Roberts & partners. However, structural engineer

Figure 16. Hand drawings from Frei Otto collection. Different combinations of saddle surfaces.

Figure 17. King Fahd International Stadium in Riyadh. Figure 18. Radial configuration o saddle surfaces.



was Horst Berger, very well known for other fabric structures such as the Denver

International Airport or the San Diego Convention Center.

Saddle surfaces are the most common anticlastic surfaces, however, there is another

family of surfaces related to polar geometry (surfaces of revolution). These are the tents,

also very common in fabric structures. A very popular example of tents is he Hajj Terminal

of h King Abdul Aziz International Airport in Jeddah. This will be studied in depth later.

4. physics

The other main concept discussed above of the tensile structures is the prestress

level it is submitted to. So now it is time to look into the materials and their properties.

a. cables

One of the main elements of the tensile structures are cables, they need to be

carefully calculated and placed because they are the main carriers of the load. Cables are

usually made of non-carbon steel alloys. They consist of strands twisted together. These

strands are also made of multiple wires twisted in the same direction or the opposite. The

twisting is made because when it is under high stress the strinds tend to bond together and

push each other to the center.

Figure 19. Radial tent Figure 20. Hajj Terminal in Jeddah by SOM.



These cables and their efficiency carrying axial loads made possible the existence of

tensile structures.

b. joints

A critical aspect of tensile structures is the joint between cables and supporting

elements. These are specially designed or the high stresses they suffer. There are many

different terminations, but must common are clams between cables, or clam with loop with

a thimble inside to help the cable not to break. Also here are swaged unions and eye splices

but they are rarer.

Figure 22. Different designs of clams for anchoring to a rigid structure.

Figure 22. Different designs of clams for anchoring to a rigid structure.



c. rigid elements

The main structure of a tensile structure carries the stresses down to the ground.

Different elements conform the rigid system, such as masts, poles, beams or buttresses.

And also, we have many different choices of materials to conform the rigid structure.

steel

The rigid elements in tensile structures must be strong, light, reliable, readily

available, but also easy to fabricate, transport and erect. Structural steel satisfies these

requirements excellently. Although, it needs protection against corrosion, either by

painting, or by galvanizing. With this material we can make steel masts or trussed arches,

and can satisfy infinite configurations.

The ASU Skysong campus shows the two configurations. It was designed by FTL

engineers in collaboration with Pei Cobb Freed & Partners.

Figure 23. ASU Skysong Campus. Figure 24. Curved triangulated beam.



precast concrete

Prefabricated concrete can also be used for

the rigid structure of a tensile structure. Pros are that

it is -reproof and also weather self-protecting. It is

available anywhere, and it is fairly inexpensive.

At the AELTC indoor practice facility the

fabric membrane hangs from precast concrete

arches connected to piers which are cast in place.

Designed by Ian C. King Associates and assisted by Horst Berger Associates.

glue laminated wood

Laminated wood is suitable for use in arches,

frames or columns. But, this material is vulnerable

to fire; nonetheless, fire protection measures can be

achieved easily enough and at a reasonable cost.

Glulam arches support the fabric membrane

at the Bullocks department store in San Jos,

California. Structural engineer was Horst Berger.

c. membrane

fabric

Membranes can be engineered to pass or reect light, heat, sound, or moisture, in

whatever combination of directions one chooses. Three are the main factors of a fabric

Figure 25. This glowing effect is thanks to the translucency of the fabric envelope. AELTC indoor practice.

Figure 26. Bullocks deparment store in San Jose, California.



membrane: structural strenght, behavior during construction and use; and surface

properties.

There are two main materials in this field: polyester fabric with PVC coating, which

is less expensive and can last 15 to 20 years; or Teflon-coated fiberglass, which has a

higher performance. It is the primary material in tensile architecture. It is chemically inert

and requires moisture protection. But, it is noncombustible, easy to keep clean, highly

reflective and highly translucent.

ETFE

ETFE is also a very innovative material. Totally inert, it can be formed in cushions

or in two-skin unique shapes. It is a great insulator, and also totally inert, and easy to clean.

It has been widely used in pneumatic domes, but also with a structural steel frame filled

Figure 27. Amphitheater in Grand Canyon designed by Structureflex. Fabric was made of polyester with a PVC coating.

Figure 28. The fabric in Riyadh King Fahd stadium was a Teflon-coated fiberglass.

Figure 29. ETFE pneumatic dome in BC place in Vancouver designed by David Geiger.

Figure 30. Interior of BC place. Sausage-like cushions.



with cushions as in the Beijing Watercube.

5. case studies

a. Frei Otto. German pavilion expo Montreal 67. Canada.

One of the earliest examples of tensile structures, the german pavilion was a cable

net tent structure supported by steel masts. A curvacelously swinging roofscape was spread

widely over a sculptured ground platform and differently raised exhibition terraces. The net

was made of steel ropes 1/2 thick with a mesh width of 20 and it covered an area of

86,000 sqft. A membrane of PVC-coated Polyester fabric was suspended under the net for

weather protection.

The pavilion was built according to Frei Ottos and Rolf Gutbrods competition

design in 1967.

Figure 34. Roof plan. Figure 33. Plan.

Figure 35. Section.

Figure 31. Exterior of the cable net tents. Figure 32. Interior of german pavilion in Expo 67 in Montreal.



The erection procedure followed a detailed sequence which before was elaborated

carefully in the trial run with the Vaihingen test structure of the later IL institute building.

First, all masts were put in position and stabilized with auxiliary guying cables. The cable

net sections (each delivered in 30ft wide rolls) were assembled on round around the masts

and hoisted up to the mast tops while further net sections for adjacent areas were added.

After the completion of the cable net it was attached to the exterior anchor points and to the

interior low points. The initial prestressing was achieved by jacking up the masts to their

definite height. The final prestressing was brought in by tensioning the edge cables in two

cycles around the perimeter outline. The roof membrane was assembled in parts on ground,

including the clear eye parts, drawn up piece by piece, attached pointwise under the cable

net and finally prestressed.

b. SOM. Hajj terminal of the King Abdul Aziz international airport. Jeddah.

Saudi Arabia.

The firm was approached to design a terminal for the pilgrims that travel to Makkah

every year via King Abdul-Aziz International Airport in Jeddah. They had some special

Figure 36. Steel fixture of the fabric to the cable net Figure 37. Steel fixture of the fabric to the cable net



requirements: tight schedule, grand open space for 500,000 pilgrims, only open one month

a year... And also the site had its complications: very high temperatures, ultraviolet rays and

a corrosive-marine environment.

The idea of creating a large enclosed artificial space was out of the question, and so

creating large concrete lattice structures. A new structural concept was needed to provide

shade and ventilation for 43 million square feet. To be able to erect the membrane, a second

ring was designed to fit with a previously lifted ring.

Figure 38. Model of the Hajj terminal. Figure 39. Environmental diagram.

Figure 40. Sketch of the rising of a tent. Figure 41. Sea of tents, note the person down to the left to get an idea of the scale of the project.



c. Bodo Rasch. Umbrellas of the Holy Mosque. Medina. Saudi Arabia.

The commission to design a convertible shade roof for two large courtyards of the

Holy Mosque of the Prophet in Medina presented an unusual architectural and technical

challenge. At this location, where tens of thousands of believers gather every day, the

climatic conditions had to be improved without destroying the character of the open

quadrangles and their familiar environment. The solution consisted of twelve convertible

parasols, 50x54 ft large and with a height of 45 ft at the eaves in their opened condition,

which fit in perfectly with the proportions of the courtyards. With a span of 75 ft, measured

diagonally across the corners, they are the largest ones built of this kind. The six parasols

with their funnel-shaped membranes create the effect of translucent vaults, spanning

between the columns and the arched arcades surrounding the courts, and produce a large

free space. Their timeless form with its carefully designed ornaments match harmoniously

with the traditional architecture.

The components of the parasol structure, mast column, arms and struts, are a welded

construction of a high-strength fine grain steel. For good precision of the movements the

bearing bores of the critical hinges were made by a (computer-controlled) NC-milling

Figure 42. Umbrellas shut down every evening when shading is not necessary anymore.

Figure 43. Umbrellas displayed to shade when hot temperatures.



machine. This manufacturing precision of the movable parts together with the placement of

the hydraulics pumping in a central plant makes an almost noiseless working of the parasols

possible.

The parasol has altogether 20 arms: four long diagonal arms with two short passive

arms each connected to them, eight middle arms, of which four are shorter and four longer.

The parasol is opened and closed by a hydraulic cylinder on the column axis, whose upper

end is pin-connected with all the active arms. In the closed condition the hydraulic cylinder

has driven out completely at the top; to open the parasol it drives down, whereby the struts,

Figure 44. Section showing the mechanism that allows the movement.

Figure 45. The masts allow the space to flow without distraction.

Figure 46. Diagram illustrating summer behavior of the place.

Figure 47. Diagram illustrating umbrellas reflecting sun light.



which are pinned above the capital, push the parasol arms, which are connected at the upper

end of the hydraulic cylinder, to the outside, prestressing the parasol membrane. The

electronic controls and hydraulic pump are housed in a central controls room in the

basement and connected with the 12 parasols via high pressure pipes under the marble floor

of the courtyards.

Opening and closing times of the parasols are computed electronically for every day

according to the position of the sun, dependent on the seasons, and allowing for weather

conditions, outside temperature, wind and cloud cover and the results fed into the parasol

controls. To make the climatic conditions in the courtyards more comfortable during the

summer months, when the air temperatures in the shade can exceed 45C, the parasols'

controls are coupled with the bulding's air-conditioning system. Air outlets in the base and

the capital of the parasol column distribute cool air noiselessly in a wide area, so that the

entire quadrangle is cooled evenly and effectively.

Wind stress is a huge problem for tensile structures. Wind tunnel tests for the

specific situation in the courtyards served as a basis for the design of the structural elements

of the parasols, which were designed for the opened and closed condition using a wind

speed of 100 mph. An anemometer connected with the central controls prevents the

opening and closing at wind speeds above 20 mph.



6. innovation in tensile structures

a. AWM carpark in Munich, 1999

This facility was designed by Kurt Ackermann and Partners, and is a very particular

mixture of concepts, its tents employ tensegrity ideas with tensile elements. Its very elegant

structure employs the least material possible.

The protected parking facilities for the city's 150 refuse vehicles form one section of

a three-part complex erected for the municipal Office for Waste Management. The roof

over the vehicle port is a point-supported membrane structure in translucent PTFE-coated

glass fiber fabric. The parking areas are laid out on two levels, consisting of an open

concrete upper deck erected within a solid tank structure sunk into the ground. The deck

also accommodates changing rooms and showers for 500 refuse workers. More than 85000

ft in area, the tent roof is supported by a grid of 88 steel columns laid out at 30 x 36 ft

centers. The membrane itself consists of 36 ft precut strips welded together on site.

Figure 48. Interior of the car park. Figure 49. Exterior view of the structure.



The inner columns are protected against ramming by concrete plinths and have

flexible seatings at the base. Horizontal loads are transmitted via raking peripheral columns

to the lower-floor structure. Each of the 70 bays of the membrane is tensioned by a central

Figure 50. Detail of the compression strud with the structure of the tent.

Figure 51. Detail view of an outside column.

Figure 53. Braces connect the main column with another that is leaning and anchored to the ground to help carry to the ground the high horizontal stresses.

Figure 52. Detail view of the anchor on top of the column.



steel suspended column on the underside. The roof is drained by a vacuum system within

the main steel columns. The lightweight membrane construction was facilitated by the fact

that it contains no members subject to bending. It was designed as a structurally continuous

area, with thin steel cables on top of the skin articulating the individual bays.

b. new roof for the AWM carpark in Munich, Taiyo engineering, 2012

An application that is gaining a lot of popularity is the integration of membranes

with photovoltaic systems. Large envelopes that are exposed to daylight many hours a day

are a perfect target to put PV panels and generate free electricity for an ever growing power

demand.

This is what Taiyo Europe achieved with their design for the AWM carpak in

Munich. It is a ETFE structure with integrated Flexible Photovoltaic (FPV) panels. The

80,000 square feet roof covers a vast commercial transport hub in Munich, Germany. In

total the long span roof houses 3080 FPV modules generating upwards of 141kW/hr. The

FPV panels are contained in a three layer ETFE cushion system, in total 220 ETFE

cushions form the blanket like roof.

Figure 54. Interior view of the new carport in Munich



The roof structure is made up of a three layer ETFE cushion system:

Inner layer: 250 micron film printed with negative dot pattern in silver color.

Middle layer: transparent 100 micron film fitted with integrated flexible

photovoltaic system.

Outer layer: transparent 250 micron film

Figure 55. Interior view. Trusses hang between steel columns. Between them the cushions span helped by a structure that also adapts some tensegrity concepts.

Figure 56. Accessibility was an important concern, as this structure was built after a failure of the previous one because of high snow loads.

Figure 57. The integration of ETFE with PV layers not only is efficient but also appealing in terms of aesthetics.



c. umbrellas in market square in Avenches

The original project, to develop a pergola for a restaurant in the marketplace of the

Swiss town of Avenches, was expanded at the suggestion of the architects into a flexible

covering for the entire square. This was ultimately commissioned by the local authority.

Each of the lightweight sunshades can be inserted in one of the 16 hinged

mountings, set upright and cranked taut. The cushion-like roof volumes consist of two

membranes sloping in opposite directions. The watertight junctions and the drainage of the

modules called for intensive development work. They are fitted with a zip on all four edges.

Rainwater flows from the upper membrane of one sunshade into the lower membrane of the

adjoining element and from there into the column and on to drainpipes beneath the square.

A medieval well discovered during foundation work now covered with glass and

illuminated forms a central feature of the market place design.

Figure 58. The umbrellas can be laid out in very different situations creating unique environments when the requirements of the weather or the program change.

Figure 59. When the maximum coverage is needed te umbrellas are squared and zipped altogether.



Figure 59. Detailed section of an umbrella

Figure 60. Zipped junction.

Figure 60. Drawings showing the anchorage of the structure to the ground. Figure 61. Axonometric.



d. new applications

heat responsive structures

Graduate students Felecia Davis and Delia Dumitrescu recently presented their

research on interactive, knitted tension structures that respond to heat or electrical current.

Using a tubular knitting machine, with electronic circuits running throughout the fabrics

tested, Davis and Dumitrescu, tested and created four tubular fabric structures that change

surface appearance when stimulated in response to current or heat. One prototype opens up

regular pores when heated to high temperature; another changes opacity depending on an

electrical current.

Figure 62. This prototypes make use of electric current to change their properties, like opacity or porosity.



7. conclusion

To conclude Id like to make some comments about what I believe is the strongest

in tensile structures and how do I see this structures in the future.

First, I believe that working mainly in tension, they are the most efficient structures

to enclose spaces. Where climate conditions are favorable, tensile structures are one of the,

if not the, best solution to cover large spaces such as stadiums, auditoriums or other spaces

where program is basically a gathering with no very specific functions. However, Denver

Airport proves that membranes can enclose also complex spaces. Anyway, I understand

that membranes are not the best solution in cooler climates where thin fabric wouldnt be

the best insulation. Lets see if flexible graphene proves itself to be the solution.

Second, it is aesthetically appealing. These structures are pure, are true, are

graceful. Combined with illumination a beautiful glow appears. They are light, and

portable, if different elastic membranes appear they can be transformable. Flexibility

matters, and in the XXI century more than ever before.

Finally, because they are easy. They are relatively easy to construct. Specialized

skill is not needed to erect them, and with computers helping out with the form finding, and

precise digitalized cutters cutting the pattern, we will be able to experiment with form in

ways we havent even imagined yet.



8. Bibliography

Berger, Horst. Light Structures, Structures of Light: The Art and Engineering of Tensile

Architecture. Basel: Birkhuser, 1996. Print.

"Ausgewhlte Arbeiten Von Frei Otto Und Seinen Teams." Ausgewhlte Arbeiten Von

Frei Otto Und Seinen Teams. N.p., n.d. Web.

Robbin, Tony. Engineering a New Architecture. New Haven: Yale UP, 1996. Print.

Khan, Yasmin S. Engineering Architecture: The Vision of Fazlur R. Khan. 1st ed. New

York: W. W. Norton, 2004. Print.

Otto, Frei, and Ludwig Glaeser. The Work of Frei Otto. New York: Museum of Modern

Art; Distributed by New York Graphic Society, Greenwich, Conn., 1972. Print.

"WEIDLINGER ASSOCIATES INC." WEIDLINGER ASSOCIATES INC. N.p.,

n.d. Web.

"SOM : Skidmore, Owings & Merrill LLP." SOM : Skidmore, Owings & Merrill LLP.

N.p., n.d. Web.

"Shade Sails and Outdoor Umbrellas." Shade Sails. N.p., n.d. Web.

BERGER ENGINEERING COMPANY. N.p., n.d. Web.

"SL RASCH - Special and Lightweight Structures - Institute for Scientific

Architecture." SL RASCH - Special and Lightweight Structures - Institute for

Scientific Architecture. N.p., n.d. Web.