Maya engineers were masters at combining high-strength materials and structural mechanics to satisfy the geometric requirements of their monumental buildings. Maya engineers invented a variety of structural systems to suit the unique style of their architecture. They capitalized on their homegrown feats of structural ingenuity, combined with high-strength building materials, to create column free interior spaces, erect multistory building, construct a skyscraping pyramid, and many other engineering feats.
The Maya Arch
The basic building block used in Maya structures was a closed structural element commonly known as the “Maya arch.” This element had multifaceted capabilities and could span between supports to create interior spaces in a building, span a gateway to develop an inspiring entrance, be elongated along its longitudinal axis to develop a large vault-like interior space, or be positioned vertically to form multistory vaulted buildings.
Scholars of Maya architecture often refer to the structural shape of the Maya arch as a “false arch” or a “corbelled arch.” However, as a structural mechanical element, the Maya arch is not a structural arch. This unique structural spanning system is a trapezoidal linear truss that resists gravity loads by axial force members flowing in a straight line load path within a closed circuit geometrical network from the roof to the foundation.
A corbelled arch is formed by stair-stepping successive blocks of masonry stone from the spring line upward in a manner that enables the shape of the interior structure to project up toward the center of the vault. Each supporting side will step upward and join at an intersection at the apex of the structure (Figure 7-2). The interior of the spanned space assumes a trapezoidal shape. The corbelled truss is not a true structural arch. All the interior stresses in the structure are transferred into linear compressive stresses. Corbelled arches require thick walls and an abutment to counteract the horizontal stresses generated from gravity loads, which would tend to collapse the archway without appropriate lateral stability.
Figure 7-2: Different types of arches. Note self-supporting nature of Maya arch. Author’s image.
The true arch is a circular structural shape assembled of cut stone in a uniform, upward, circular curve. The arch maintains its stability through the compressive pressure of the curved stone sections against the face of adjacent sections. The true arch must have lateral resistance at the spring line (Figure 7-2). Eurocentric archaeologists have used the circular Roman arch as the prototype for a non-linear structure spanning between two supports. That is why they use the term false arch for the interior space formed by structures in Maya architecture. Because it is not curved, ergo, it must be a “false” arch.
The Maya truss used in large structures, though capable of doing so, was seldom used to span large interior spaces. In the tropical environment of the Yucatán, the construction of large interior spaces for assembly was impractical, with average temperature hovering near 80 degrees Fahrenheit (26 degrees Celsius) year-round, with periods of higher temperatures in the 90s Fahrenheit. The assembly area for large gatherings in the sultry tropics took place outside in the open plazas to take advantage of the cooling trade winds. A large interior space crowded with people would be stifling and impractical. The Maya trapezium arch is the primary structural element or building block of large architectural constructions. (Figure C-5, Figure C-6, Figure 7-3, and Figure 7-4).
The Roman arch or true arch took the form of a semi-circle spanning between two supports. During the course of the Roman Empire, engineers combined cast-in-place concrete with facing bricks to increase the span of the arches. However, the construction of an arch required detailed workmanship. To erect the structure of a Roman arch, it was required to erect a wooden form with a scaffold system to support the stone or brick forming the arch. The formwork was erected prior to placing concrete. The forming device for the arch is called centering.
The stones or brick of the circular arch were required to be fabricated with the sides of the arch stones sloped radially. The formwork, scaffold system, and centering provided support for the wedge-shaped masonry elements of the arch. These trapezoidal elements are called “voussoirs” until they are in place. The wet cast-in-place concrete would then be placed in the space between the brick arches. A massive centering system was required to sustain the weight of the brick arch members and the wet concrete. When the concrete had gained sufficient strength, then the centering system could be removed. At this point, the arch would be self-supporting due to the composite action of the concrete and stone arch.
Figure 7-3: Construction of a typical Maya arch using composite stone and cast-in-place concrete. Author’s image.
Figure 7-4: Detail of typical arch construction at spring line and timber thrust beam. Author’s image.
As a structural unit, the Maya arch resists gravity loads as a trapezoidal truss consisting of linear structural members. The nature of the Maya trapezoidal structure resists large gravity loads in pure compression and tension members. Maya engineers used this trapezoidal structure to create long-span interior spaces. The use of the trapezoidal Maya arch permits an attractive, column-free structural system and is stronger than the curved arch. Computer analysis of the Maya structure has verified its superior strength, and time has proved the test of durability and its resistance to the environment (Figure 7-3 and Figure 7-4).
The construction of a Maya trapezoidal structure is less complex than the classic Roman arch. The Maya arch does not require formwork, special scaffolding, or the shaping of stones into trapezoidal voussoirs to form the basic shape and surface of the structure. The Maya arch is constructed using a system that employs the exterior and interior stonework at each face of the wall as the formwork for the cast-in-place concrete wall interiors. Interior timber thrust beams are used as an integral part of the structure and are used as interior scaffolding during construction. The construction of the basic, trapezoidal, single-story Maya structure utilized simplistic but brilliant methodologies. The process is repeated for multiple adjacent structures on the same plane or vertically for multistory structures.
The basic construction sequence is shown and described in Figure 7-5a through Figure 7-5d, and provides an overview of the construction of a single Maya arch module. A description of each stage follows. Multiple horizontal or vertical modules are constructed in a similar manner.
Figure 7-5a
The foundation for the basic structural module is constructed as continuous stonework is laid with leveling mortar upon the shallow limestone stratum. The walls are placed in lifts of approximately 1 meter, with cut stone masonry placed on each side of the wall. The walls are filled then with wet cast-in-place concrete and large stone aggregate. Once a concrete lift has set up, the next section of cut stone masonry interior and exterior walls are installed and the interior of the walls can be filled with concrete.
When the appropriate wall height has been constructed to the spring line, a high-strength circular timber member of 5 inches in diameter, called a “thrust beam,” is placed at strategic horizontal intervals along the spring line of the arch. The ends of the thrust beams are embedded approximately 1 meter into the concrete in opposing walls. The bonding of concrete to the rough surface of the timber thrust beam resists the lateral compression force generated by the structure during the construction phase. A 12.5-centimeter-diameter beam embedded 0.5 meter into the wall concrete can generate up to 30,000 pounds of lateral resistance at each end of the thrust beam.
Figure 7-5a: Stage 1 in the construction of the Maya arch. Author’s image.
Figure 7-5b
With the timber thrust beams in place, construction can proceed upward. The horizontal thrust beams can now be used as scaffold supports for workers to facilitate access for the construction of the inward structure element. The trapezium-shaped vault geometry is generated by installing cut limestone blocks on the outside and inside faces of the vault structure.
The interior stone is shaped with a flat face that is inclined
upward. The rear of the stone is a pinion shaped element contoured to optimize the bonding surface between the stone and the cast-in-place concrete wall interior. The exterior stone facing is placed vertically. The shape is similar to the interior block, with a pinion positioned to optimize the bond between the concrete infill and the cut stone. As the upper vault wall varies in width to form an isosceles triangle, the inward leaning geometry of the vault mass will alter the center of gravity of the structure. The alignment of the centroid of the mass with the center line of the vertical support wall moves inward to a position toward the center line of the shaped vault. The inward shift of the center of gravity will induce an inward bending moment in the upper wall. The inward bending moment would create instability in the partially constructed arch and would cause a collapse without the horizontal resistance of the thrust beam. Maya engineers were aware of the stability characteristics of this construction. The installation of the timber thrust beams resulted in a compressive member that will “push” back against the inward bending tendency of the inclined upper walls of the trapezium. Therefore, the high-strength timber thrust beam serves to stabilize the equilibrium of the construction.
Figure 7-5b: Stage 2 in the construction of the Maya arch. Author’s image.
Figure 7-5c
The construction of the angular upper section of the arch continues until the inward bending mass of composite structure again becomes unstable and an additional upper horizontal thrust beam is required. This high density timber member is a smaller diameter than the lower thrust beam, and embedding in the concrete is minimized due to the reduced levels of thrust. A 3-inch-diameter beam with an embedment of 24 inches into the concrete mass is adequate support for the upper thrust beam. The installation of the upper thrust beam enabled the Maya construction team to stabilize the structure and continue the upward development of the trapezoidal structural shape. The trapezoidal structure is completed with the installation of the horizontal capstone at the apex of the arch. The capstone and the opposite forces at the interface of the top elements of the arch structure stabilize the inward bending movement, reducing horizontal compressive forces in the system.
Figure 7-5c: Stage 3 in the construction of the Maya arch. Author’s image.
Figure 7-5d
When the capstone and top horizontal construction have been installed, the connection of the two vertical segments of the geometry completes the closed structural circuit of the trapezium structure. The structural vertical element may now be constructed. The structure is now a stable, load-carrying mechanism. The inward bending moments are stabilized and the closed circuit of the completed geometry alters the load paths of the structure. The gravity loads will follow the load paths through the angular roof structure and be supported by the vertical walls at the base of the system. This action of load resistance of the truss action, however, creates an outward horizontal force at the spring line. The lower thrust beam now reverses the nature of its stress from a compression member and becomes a tension member, resisting the outward movement on each side. The bonded embedment of the timber thrust beam into the concrete wall resists the tension “pull out” action caused by the horizontal vectors at the spring line. The lower walls react to transmit vertical loads, and the thrust beam is now a horizontal tension member. The two components combine to resist the vertical and horizontal vectors of the truss. The composite walls and the thrust beams now complete the closed circuit that develops a stable structure.
Figure 7-5d: Stage 4 in the construction of the Maya arch. Author’s image.
The Resolution of Horizontal Forces Over Time
The analysis of a typical Maya trapezium arch indicates that the tension resistance of the timber thrust beam is a permanent part of the stable structural system for the arch. Maya engineers anticipated the long-term resistance of the timber member as part of the monumental structure. For this reason, the engineers selected a dense, high-strength timber similar to chico zapote. This wood is highly resistant to termites and degradation. In addition, it has tensile strength of more than 20,000 psi, which is a strength similar to low-grade steel. In some cases, the tension beam has degraded over the centuries; however, in specific cases, the resistant timber thrust beam has survived into the 21st century. The timber thrust beams at Xtampak (Figure C-5) are survivors of the abandonment and are still functional tension members. When the trapezium structure fails, it is usually at the perimeter of the building. Interior arches in the same structure depend on the adjacency of the exterior line of trapezium structures. In these cases, the thrust beam at the perimeter has degraded and failed, and the horizontal tension forces have pushed the exterior wall outward. The interior arches remain intact due to the lateral support from the remains of failed exterior vaults.
The presence of the surviving timber thrust beams in Maya arches has long been a mystery in the annals of archaeology. The use of the beams has been opined by archaeologists to have multiple applications. They have been considered to be devices for the hanging of hammocks, curtains, or clothing, or used as storage platforms or as granaries. Legendary archaeologist Eric Thompson suggested that the timber beams were installed to hark back to the horizontal roof beams of the native huts. To the best of my knowledge, the use of the thrust beam as a structural member was first suggested by Lawrence Roys, an engineer who wrote The Engineering Knowledge of the Maya, published in 1934 by the Carnegie Institution of Washington. Mr. Roys was spot on: the timber beam was not an interior design accessory, but a vital structural member.
The stability and strength of concrete trapezium arch is superior to similar structural systems. Maya engineers developed this system for permanency. Its inherent strength is capable of resisting large levels of vertical and lateral gravity loading. Its strength and function enable its use as a basic module in a stand-alone configuration or in a series of horizontal and vertical structures arrayed in buildings and other applications.
Practical Applications of the Maya Arch
The basic geometric structural module of the Maya arch was used throughout the Maya world, further reinforcing the exchange of ideas and technology within the Maya sphere of influence. The structural component was used to generate interior clear spans in single-story and multistory structures, monumental portals, triumphant arches, underground water-storage reservoirs for water, bridges and support systems for stairs, tunnels, and aqueducts.
Examples of monumental stand-alone structures using the trapezium arch include the grand arch at Kabah and the entrance portal at Labná. The grand arch at Kabah (Figure C-6) is the largest known freestanding trapezium arch. This 6 meter × 7.5 meter structure is the grand entrance to the city of Kabah. The arch connects the city of Uxmal with Kabah via a 12-mile-long roadway or sacbe. The 3 meter × 3 meter vertical members of the structure resist the lateral forces of the arch. This arch has been remediated. However, in its failed state, the 3 meter × 3 meter members did not collapse but were converted to cantilevers due the concrete construction of the members.
The portal entrance at Labná is also one of Frederick Catherwood’s subjects. The portal arch is the entrance to the monumental structure to a major building group. A sacbe leads to the entrance. Catherwood’s illustration shows sculpted figures in the niches below the thatched roof sculptures at each side. They have now disappeared.
The Maya Vault Structure
The Maya trapezium arch is the basic building module for the construction of the classic Maya vault. Maya vault geometry is generated by extending the trapezium arch along its longitudinal axis (Figure 7-6). The Maya trapezium arch structure was applied to develop a closed interior space in Maya buildings. The vaults ranged in size based on their uses. Vaulted spaces at the exterior of buildings tended to be larger because of the advantage of air circulation. Larger buildings with multi-vault spans varied in size from a single-level vaulted space, to large palaces of 200 vaulted rooms. In multistory palaces, the structure rose to heights of five levels, with upper vault levels
connected to each other with exterior and interior stairs.
Figure 7-6: Typical vault construction formed by development of arch along longitudinal axis of vault. Author’s image.
The design of a specific type and size of building and its function dictated the size and number of vaulted rooms and their relative geometry. Once the size and position of the vaults in a building was established, and their egress and ingress openings as well as interior circulation was established, then the structural geometry of the vaults could be determined. Large buildings tended to position their vaulted interior spaces in parallel to the long facade of the building with wider and greater number of door openings at exterior vaults to enhance air circulation. The plan of large buildings maximized the number of exterior rooms while optimizing the structural capacity of the vaults. The adjacency of the vaults enhances the resistance to lateral forces.
The ability of the vault structure to solve the requirement for various living and working functions was very flexible. Vaults were constructed with linear shapes, crossing vaults (groin vaults), and circular vaults. The linear vault had a straight centerline with demising end walls constructed of masonry. This type of vault was used to develop the typical interior space for Maya structures. It was used in single and multistory buildings by Maya engineers (Figure C-5 and Figure 7-6). Additionally, Maya architecture used vaults that crossed at right angles. The crossing vaults form architectural groin geometry at their intersection. The groin is the intersection of two perpendicular vaults and creates structural stability at the intersection, as well as serving as an attractive aesthetic device.
The Lost Secrets of Maya Technology Page 16
