Teatro Auditorio Gota de Plata [Structural Analysis]

Teatro Auditorio Gota de Plata Jaime Varon | Abraham Metta | Alex Metta | Migdal Arquitectos

America Castillo + Daniel Preston

ARCH 2613/5613 Fall 2013

Teatro Auditorio Gota de Plata Structural Investigation ARCH 2613/5613: Structural Systems America Castillo | amc479 Daniel Preston | dap264 Fall 2013

Teatro Auditorio Gota de Plata

FIGURE 1: Northeast elevation at dusk

Architect: Jamie Varon, Abraham Metta, Alex Metta | Migdal Arquitectos Structural Engineer: Impulsora Tlaxcalteca de Industrias Site Management: Impulsora Tlaxcalteca de Industrias Location: Pachuca, Hildago Date: 2005 Public Space | Theater

Teatro Auditorio Gota de Plata

‘The Silver Drop’

STRUCTURAL AND ARCHITECTURAL INVESTIGATION

Formally known as Teatro Auditorio Gota de Plata, the “Silver Drop” of Pachuca, Hidalgo Mexico was completed in 2005 by Jaime Varon, Abraham Metta, and Alex Metta, of Midgal Arquitectos with structural engineering completed by Impulsora Tlaxcalteca de Industrias. The theater forms part of the twenty-five hectare David Ben Gurinón Cultural Complex, known locally as Parque Cultural y Recreativo David Ben Gurinón. This cultural complex, offset around an exceptionally long and artfully tiled promenade, is home to many of the city’s greatest public landmarks, including a contemporary art museum, Audiorama, Sculpture Park, convention center, and encompassing it all, Gota de Plata is situated at the far end of the promenade bookmarking the cultural heritage of Pachuca.

FIGURE 2.2: Axial Promenade culminating at Gota de Plata

FIGURE 2.1: Site Plan

Teatro Auditorio Gota de Plata

Cantilever + Structure

Perhaps the most striking aspect of Gota

de Plata and the primary focus of our investigation is its magnificent cantilevering roof. Perched on top a central axis, like a perfectly balanced seesaw, the cantilever begins to embrace the expansive plaza in front. Not only does it quite literally reflect the stunning mosaic of this esplanade through tilted mirrors on its underside but also, it reaches out forty meters into the landscape and seemingly grasps the central promenade and Pachuca’s entire cultural heritage.

Defining Space

Although the architects responsible for

the design of the theater made the intentional decision to clad the structural formwork with a metallic concrete mixture, embracing Pachuca’s metalworking history,1 it is necessary to recognize that the internal structural systems are completely dependent on one another. As previously mentioned, the series of five steel trusses cantilever from one central point where they are

system, which is supported by two reinforced concrete shear walls. The downward forces acting upon the trusses as well as its self-weight of nearly 1500 tons2 are transported through the 1 2

“Gota de Plata”, En Pachuca, 2006 “Gota de Plata”, En Pachuca, 2006

FIGURE 3.1: Longitudinal Section

rigidly fixed to a transversal braced steel frame

Teatro Auditorio Gota de Plata

diagonal members of the truss, down the shear wall, and eventually disseminate into the theaters foundation. However, as can be seen in the longitudinal section, and construction photographs, the public space beneath the cantilever (the theater and central reception area) is virtually separated from the private space (stage and backstage) both structurally and aesthetically. While the public space is served by the cantilever the backstage has an entirely different aesthetic feel and constructed in a completely different manor. This is perhaps in part due to the notion of the “flying” cantilever embracing Pachuca’s cultural heritage while at the same time, directing ones attention to the performers who are responsible for this sense of communal pride.

Unlike a seesaw, each side of the cantilever is dependent from its partner. The vertical

member supporting the cantilever is rigidly attached to the concrete shear wall in such a way that the half cantilevering over the promenade does not rely on the half which spans the auditorium, thus they become two independent systems that share one common support.3 In fact, as can be seen in the construction photograph, the two halves were built independently of each other off site 3

“Teatro Auditorio Gota de Plata / Migdal Arquitectos”, Plata Forma Arquitectura, September 28th 2011

FIGURE 3.2: Construction Photograph of trusses spaning between central support and stage

Teatro Auditorio Gota de Plata

and then hoisted into place where they were joined.

Both cantilevers cover an approxi-

mate area of 18,000 square meters4 containing the theater space in the rear and an expansive reception mezzanine in the front.

FIGURE 3.3: Cantilevering roof plane emphasizing the apparent thinness of the overhang

It has become evident throughout

an analysis of this project that the architects truly used structure as a space-defining boundary. This has already seen in use of the ‘flying’ roof as a grasp of the theaters cultural surround but it can also be seen while examining the plan of Gota de Plata.

The cantilever informs the use of the space below and as can be seen, the cantilever tapers to form a trapezoid with the small face culminating at the stage. Not only does this

FIGURE 3.4: Disconnect between cantilever and truses spanning over the auditorium

put less strain on he transversal supports but it also begins to direct your eye to the stage.

This trapezoidal plan is entirely dependent on the cantilevering system above.

Moreover, the structural span over the auditorium allows for a completely unobstructed space. The enormous trusses span across the entire extent of the theater and thus allowing the space to be free of any 4 “Gota de Plata Auditorium Theatre / Migdal Arquitectos”, Style of Design, June, 11th 2013

Teatro Auditorio Gota de Plata

FIGURE 3.5: Configuration of trusses, rigid supports, and concrete members

Teatro Auditorio Gota de Plata

clutter that might be needed to support the roof above.

Additionally, the cantilever seems to have a remarkable thinness to it. This can be attributed to the aes-

thetic desire to have a roof that simply seems to dissipate, or perhaps a roof that pierces the air and the surrounding landscape. However, it can also be attributed to the structural need for a tapered truss. By shaping the trusses to a point as they move farther and farther out from the central support, it begins to lighten the trusses self weight.5 By reducing this weight, less stress is placed on the transversal member responsible for carrying the load of the cantilever.

Wind Load

It is necessary to recognize the intensive lateral loading, due to wind that the trusses and cantilever need

to restrain. As wind approaches the theater from the northeast it gets trapped on the underside of the cantilever.

As shown in the diagram, the wind forces under the cantilever have a tendency to lift the overhang upwards, acting like a sail and creating tension forces within the concrete members supporting it. These concrete members have been reinforced with steel rebar which allow a material that can only perform well under compressive forces to be able to resist the tension forces.

Additionally as wind moves over the structure it begins to create suction forces on the leeward side of 5

“Gota de Plata Auditorium�, Nicholas Socrates: Architecture and Urban Design, 2013

FIGURE 3.6: Affect of lateral wind loads on cantilever and structural system

Teatro Auditorio Gota de Plata

the building while it creates a large pressure force on the wayward face. All of these fluctuations in pressure need to be accounted for by the steel structure.6 While the theater is very orthogonal in form and therefore is affected by the lateral wind loads in a more dramatic way, its exterior shell is very smooth which assists the airflow around and over the infrastructure. Moreover, parts of the theater, particularly the doubly pinned columns beneath the cantilever, are flexible structures that dissipate some of the lateral forces.

Furthermore, the presence of shear walls is essential for the stability of the building and its ability to deal with fluctuating lateral forces. In order to prevent lateral load restricting systems from failing under torsion, the building needs to provide load-resisting systems in more then one direction.

While at first glance, the building only seems to have shear walls in the longitudinal direction, a deeper look reveals transversal structure that resists dynamic wind forces. Spanning between the concrete members in both the auditorium and between the stage is a network of braced frames. These braced frames provide the third directional resistive force necessary for the buildings strength.

Seismic Loads

Considering the geographical location of the theater, in an area that has high seismic ac-

tivity, the lateral forces that are characteristic of the occasional earthquake needs to be accounted for. Given slight indications in the sectional drawing, the foundation of the theater and the column footings seem to be somewhat detached from the ground. Understandably, this connection has to do with adding certain flexibilities to the structure that is easily subjected to dynamic lateral loads.

Additionally, the architect deliberately incorporated the six concrete shear walls in multiple directions in order to counter act these varying seismic loads. The architects must ensure that an adequate load path is provided to distribute seismic loads into the vertical shear walls. Since the shear walls are in differing directions, they provide strength from multiple facets and optimally strengthen the structure.

6

“Loads�, The Structural Basis of Architecture: Second Edition, 2011. Print.

Teatro Auditorio Gota de Plata

FIGURE 3.6.1: Seperation between foundation and earth to strengthen structure when seismic loading is applied

FIGURE 3.6: Gravitational loads acting upon the cantilever and their movement throught the structure

Gravitational Loading and Self-Weight

Perhaps the greatest load that Gota de Plata faces is the downward gravitational force acting upon

the forty-meter cantilever. These forces, determined by the self-weight of the overhang, are static and constant in magnitude; therefore, they are easier to contend with than the dynamicity of the wind loads.

FIGURE 3.7: Tension and compression forces acting within the trusses responsible for cantilever

Teatro Auditorio Gota de Plata

In order to counteract the gravitational loads that want to push down the edge of the cantilever, the connection at the base becomes one of the most important forces in the structure.

In order to contend with this force, the five trusses of the overhang are firmly secured to a system of braced framing which spans between the two prominent concrete supports. This transverse bracing system serves as the structural backbone for the cantilevering trusses. This brace is interlaced with a multitude of x-braces that not only distribute the tremendous loads of the cantilever through tension and compression forces but also keep the top and bottom spanning beams perpendicular The five cantilevering steel trusses are strengthened from lateral forces through a series of transverse diagonal bracing. These small scale trusses counteract the forces applied to the structure from both the dynamic wind forces and potential seismic forces. In places where the cantilever is likely to greater loads, like the underside of the covered plaza, there are more transverse trusses with a greater quantity of diagonal braces.

Additionally, there will always be the trusses self-weight which needs to be accounted for

in the resistance of downward forces. In this case almost 1500 tons of steel and concrete cladding need to be resisted by the fixed connection with the transversal braced frame system. The upward force from the concrete pillars needs to be strong enough to resist this massive downward load.

Teatro Auditorio Gota de Plata

Columns + Structure Column Form and Material

Although the cantilever has the appearance of being solely supported by one transversal

member, in fact, the entrance faรงade and at various other points throughout the structure, the projecting roof is supported by thin and slender columns which taper to a point at their head and their base. In order for these columns to be so slim, they could only be created from reinforced concrete, which has a dramatically increased capacity in comparison to masonry or concrete without reinforcement.

These columns provide valuable insight to the structural network hidden behind the cladding. The pillars are slender in profile, thus allowing the cantilever to be supported in a minimal manor, whereas other forms of support such as a solid shear wall, would need to be tall, solid, and thick, consequently obstructing the view out to the promenade and endless mosaic. But by removing an unpleasant system such as these shear walls and replacing them with columns that

FIGURE 4.2: Pinned-ended column connections showing deflection under lateral loads

Teatro Auditorio Gota de Plata

distribute the gravitational and lateral loads of the cantilever evenly through the ground, the architects were able to create an expansive network of glass across the front façade, allowing one to gaze endlessly down the promenade and over Pachuca’s other cultural buildings.

There are two layers of columns, constructed of the same material and with the same

aesthetic feel and structural need. Both layers of columns serve to support the tremendous cantilever above.7 There is an interior set of columns on the first floor mezzanine level and an exterior set of columns that are both constructed of reinforced concrete, reminiscent of the buildings exterior cladding. Both layers of columns are fastened to the overhang above via a pinned connection and are then connected to the foundation through the same method.

Pinned-Ended Column Connections

The shapes of the columns are of utmost importance. Having a larger diameter in the

middle, and smaller diameters at the base and crown, the entasis of these columns allude to the great theaters of Greece and of Rome. However, more importantly it emphasizes and embraces the minimalist structure. By tapering to a point at both the tip and the base it seems as if the cantilever is balancing on the supports and possibly seem as if the two structural entities are not even touching. It truly minimalizes the columns appearance.

In order for these columns to have this tapered appearance, they had to be connected via

pinned joints to the foundation and at the cantilevered trusses. Pinned supports allow the rotation and deflection of the column. Additionally, the doubly pinned connection allows the column ends to rotate freely when the column deflects. Doubly pinned connections are often objected to because it allows the column to be deflected without restraint; however, these conditions must be equalized through the other structural systems.8

The columns appear to only be present on the northeast side of the cantilever. The

asymmetrical shape of the cantilever causes this asymmetry. While both the cantilever and the spanning joists over the auditorium project the same distance away from their central supports, 7

“Gota de Plata Auditorium Theatre / Migdal Arquitectos”, Style of Design, June, 11th 2013

8

“The Column and the Wall”, The Structural Basis of Architecture: Second Edition, 2011. Print.

Teatro Auditorio Gota de Plata

the trapezoidal plan creates a greater load for the transverse members to support on one side.

Evidentially this load is far to great for those transverse members to support on their own; therefore, the assistance of some other structural system is needed.

Concrete + Structure

Concrete formwork serves as the foundation for the entire theater and begins to creep

its way up to inform the structural systems and to denote space within the complex. The auditorium is formed by six concrete elements placed as a sort of backbone for the cantilever and exterior cladding.9 Concrete walls and frames serve to enclose certain service areas and precast beams support the theaters 530 seats. Without the interplay between the steel of the columns and trusses and the compressed concrete, the structural magnificence of the buildings cantilever would never be able to be achieved.

Defining Space

The six concrete members that comprise the backbone of the theater are arranged sym-

metrically along the southeast and northwest facades. Two concrete members flank either side of the entry stairs and support the infrastructure needed for the underground parking garage as well as the floor of the reception lobby and auditorium. Additionally, there are two vertical members with braced steel frames spanning between them that separate the mezzanine from the auditorium. This concrete system of shear walls supports the forty-meter cantilever of the front façade.

Lastly, there are again two vertical concrete members that support the steel trusses spanning over the central auditorium space and define the stage. Each one of these is arranged orthogonally as seen in plan and provides lateral resistance from only one face. However, interlaced between these heavy concrete walls are a series of perpendicular shear walls that protect against lateral loads in the perpendicular direction. These six members are highly reinforced and are capable of withstanding both gravitational and lateral forces acting on them and the various structural 9

“Gota de Plata�, En Pachuca, 2006

Teatro Auditorio Gota de Plata

FIGURE 5.1: Plan emphasizeing the concrete members which define space and provide structure

Teatro Auditorio Gota de Plata

members they are supporting.

The vertical concrete members serve as bookends that not only provide support for the

rigidly framed cantilevering trusses but also begin to frame space. Each concrete couple denotes a new space with a new purpose. The first, the long, lateral, and low profile members that support the subterranean parking garage begin to create a space that becomes inhabited by cars and vehicles as well as transient people. The second, the tall and vertical concrete members that maintain the structural integrity of the cantilever and auditorium roof, creates a space that becomes inhabited by theatergoers and opera patrons. Lastly, the vertical members at the far end of the structure that support the truss span over the central auditorium space creates the stage and frames the actors, singers and musicians. Thus not only do the concrete members serve the structural needs of the construction but also inform visitors to the theater of designated areas that each serves their own unique purposes.

FIGURE 6.2: Longitudinal Section emphasizing the concrete members which define space and provide structure

Teatro Auditorio Gota de Plata

Additionally, while the six concrete members designate space, they also begin to create a

distinction between public space and utilitarian space. For instance, the set of concrete members that frame the stage also disguises its mechanical workings. From lighting equipment to stage props to the actors themselves, this structural system disguises the inner workings necessary for an on stage production. Furthermore, the concrete members situated in the center of the structure, which support the forty-meter cantilever, distinguish an axis in which the private functions of the auditorium are disguised, including restrooms, box offices, and janitorial closets. And lastly, the low profile concrete walls in the front of the theater cover what would be an unsightly parking lot while at the same time providing a public plaza on top, which serves as a viewing platform for the expansive mosaic promenade.

Concrete Cladding

Lastly, the entire exterior envelope is clad with high-quality precast concrete panels, which

give the building its silver glow. Although the exterior cladding is not the focus of this investigation, it is important to recognize the significant presence they have on the other structural systems. These precast faรงade pieces were fabricated using a reinforced concrete and fiberglass mixture. In fact, over four thousand square meters of the faรงade is coated with these precast panels, which provided a sharp contrast of materials on the exterior. Additionally this choice of materials was an attempt

FIGURE 6.3: Concrete and fiber glass cladding on exterior of theater

Teatro Auditorio Gota de Plata

FIGURE 6.4: Concrete and fiber glass cladding on exterior of theater

to be practical both economically and efficiently. However, with such an extensive amount of concrete cladding, the load bearing properties had to have been considered in the construction of the trusses and interior framing. The main theater is sheathed in 186 of these concrete segments while the rear of the auditorium is clad with another 138 pieces and even more coat the projecting cantilever. Although the introduction of fiberglass in the concrete mix dramatically reduced the materials self weight by 60%, the massive amount of material still created an enormous load that all the other structural components would have to contend with.1 The loading produced by the self-weight of the concrete panels needs to be distributed along the steel beams and trusses and carried through the vertical concrete components and into the foundation.

1

“Gota de Plata�, En Pachuca, 2006

Teatro Auditorio Gota de Plata

Construction Proposal Considering the dimensions of Gota de Plata, 260 feet wide and 360 feet long, the model will likely be a 1’16 scale representation. Therefore, the final model at this scale will fit into approximately a 30”x16”x12” volume. Additionally the model will be constructed in a manor similar to the construction phases of the actual theater, starting from the concrete members to the columns and finally ending with the trusses and cantilevers.

Base For the model, we plan on constructing a wood base that serves as the foundation for all the structural systems we will be focusing on. It will serve as the foundation to which we will attach all systems. The solid piece of wood will be milled so that the stage and seating areas are represented as cuts, grooves or carving on the surface, and all form part of a same mass. Over it the trusses, the concrete walls and the columns will be modeled. This would follow the previously discussed logic of recognizing the auditorium and promenade as structurally independent from the other important structural systems. However, at the same time it will still demonstrate an understanding of the relationship that the less significant aspects of the building hold with the rest of the structural elements both in terms of design concepts and strategies.

For this reason, the base has been considered to be interpretation of the existing surrounding complex, particularly, paying attention to the mosaic mural plaza that extends 100 meters perpendicular from the northeast façade of the theater. In order to emphasize the length of the promenade and the relationship it has with the theater, the base for the model will be relatively long, with the actual building model only occupying about half of the available length. The mosaic will be illustrated as a simple rectangular box leading up to the structure, without focusing on the decorative details and literal design of the existing work of art. We believe this will be enough to

Teatro Auditorio Gota de Plata

highlight the relationship between the changing heights of the cantilever and the importance of opening up the entrance space to allow a minimal distinction between interior and exterior in this area.

Concrete The various concrete walls that provide the main supports for the backbone structure will be similarly modeled. First, adequate molds of finely grained wood will be fashioned for each type of wall, taking into account that some span longer distances than others. For example the concrete elements that create enclosure for the garage space are of different dimensions of those that support the x-braced trusses. The connections between the base and the pieces will be achieved by casting rockite directly into pre-milled foundations in the base.

Columns

Considering the existing columns are pinned-end, the model’s column system will also be

represented with the given floor- to-column connections at a small scale. The pinned connection will be accurately represented with a folded metal plane held in place by a metal pin. The type of connection at the base, in reality, allows for the columns to be slightly inclined, rather than perfectly perpendicular to the ground.

At full scale the columns are prefabricated concrete pieces. Likewise, we will also produce them by creating the necessary tapered molds and cast the identical forms as many times as necessary.

Cantilever Following the original buildings construction methods, we will model the existing cantilever and trusses as steel members of adequate proportions. Joints within the truss system that comprises the cantilevered structure will be soldered together. The cantilever will be comprised with all the diagonal members as represented by the actual structure. The transverse x-braced trusses

Teatro Auditorio Gota de Plata

will be modeled in a similar way by soldering the joints.. Connections between the truss ends to the concrete backbone structure will be carefully modeled so as to make it clear that, in fact, the cantilever only extends to that point and does not actually connect directly to the juxtaposed steel trusses running in the same direction. Modeled steel frames will also include the simple transverse trusses that provide support across the front of the cantilever and between the two rigid framed trusses located between the concrete walls.

Steel beams supporting the floor will also be modeled for the form an important part in bringing down gravitational and some lateral loads.

In order to ensure the accuracy of all identical members, a form will be either milled or laser cut in which all appropriate members will be placed and soldered.

Teatro Auditorio Gota de Plata

Works Cited “Teatro Auditorio Gota de Plata / Migdal Arquitectos”, Plata Forma Arquitectura, September 28th 2011 2

“Gota de Plata”, En Pachuca, 2006

3

“Gota de Plata”, En Pachuca, 2006

4

“Teatro Auditorio Gota de Plata / Migdal Arquitectos”, Plata Forma Arquitectura, September 28th 2011

5

“Gota de Plata Auditorium Theatre / Migdal Arquitectos”, Style of Design, June, 11th 2013

6

“Gota de Plata Auditorium”, Nicholas Socrates: Architecture and Urban Design, 2013

7

“Loads”, The Structural Basis of Architecture: Second Edition, 2011. Print.

8

“Gota de Plata Auditorium Theatre / Migdal Arquitectos”, Style of Design, June, 11th 2013

9

“The Column and the Wall”, The Structural Basis of Architecture: Second Edition, 2011. Print.

10

“Gota de Plata”, En Pachuca, 2006

11

“Gota de Plata”, En Pachuca, 2006

Teatro Auditorio Gota de Plata

Documentation | Process

FIGURE 7.1: Construction | Base

Teatro Auditorio Gota de Plata

FIGURE 7.2: Construction | Base FIGURE 7.3: Construction | Base

Teatro Auditorio Gota de Plata

FIGURE 7.4: Construction | Base | CBC Mill

Teatro Auditorio Gota de Plata

FIGURE 7.5: Construction | Trusses | Welded Steel FIGURE 7.6: Construction | Trusses | Welded Steel

Teatro Auditorio Gota de Plata

Documentation | Result

FIGURE 8.1: Elevation [1]

Teatro Auditorio Gota de Plata

FIGURE 8.2: Perspective [1]

Teatro Auditorio Gota de Plata

FIGURE 8.3: Plan

Teatro Auditorio Gota de Plata

FIGURE 8.4: Elevation [2] | Close-up

Teatro Auditorio Gota de Plata

FIGURE 8.5: Perspective [2] | Close-up

Teatro Auditorio Gota de Plata

FIGURE 8.6: Detail [1] | Shadows

Teatro Auditorio Gota de Plata

FIGURE 8.6: Perspective [3]

Teatro Auditorio Gota de Plata

FIGURE 8.7: Perspective [4]

Teatro Auditorio Gota de Plata

FIGURE 8.8: Detail [2] | Beams

Teatro Auditorio Gota de Plata

FIGURE 8.9: Detail [3] | Back