The role of geometrical features in the architectural- structural interaction: Some case studies of the Iranian ancient architecture

Abstract

This research aims to enhance the interaction between a structure and its architectural form. Having a qualitative approach, the present work discovers some successfully used geometrical features of the Iranian ancient architecture in terms of the architectural-structural interaction. We define four qualitative criteria for this assessment, i.e., construction-ability, cost effectiveness, participation of the structure in fulfillment of the visual, and functional-semantic needs of the architectural form. For this purpose, two case studies including the Jamé Mosque of Isfahan and the Soltaniyeh building are investigated. The outcomes of this research help designers to not only design efficient structures by adapting non-load bearing elements with the general form of the structure, but also meet concepts such as the unity or perfectionism in the structure.

Keywords

architectural-structural interaction / geometrical features / structure / architectural form / Iranian ancient architecture

Introduction

In Iranian ancient architecture, the geometrical features are considered in all design stages including the original concept, composition of the spaces and even in details of the buildings. In this architecture, the geometry creates harmony, transparency, order, balance, and beauty. However, it is more important because of its conceptual aspect. The geometry is a tool by which the human mind can understand the order and harmony in creatures, and consequently can realize the dimension of all elements of the universe [¹]. The geometrical features in the Iranian ancient architecture are observable in various aspects including harmony (balance and symmetry) of plans and elevations, the proportionality, geometrical motifs of two-dimensional and three-dimensional patterns, use of particular numbers and dimensions, and the modulation [²]. Application of the geometrical features leads to the emergence of some architectural forms which respond to aesthetics, functional, and conceptual demands which were already investigated by many researchers [³–¹³]. Lurzadeh [⁹] and Buzurgmihri and Mehrpooya [¹⁰] discussed about geometric patterns in Islamic architecture of Iran. Pirnia [¹²] and Abolqasemi [¹⁴] studied the proportionality while Al-Buzjani [¹¹] and Kashani [¹³] worked on geometric drawings.

The architectural-structural interaction (ASI) is not systematically investigated in literature. There are few works on some aspects of the ASI. Hejazi [¹⁵] shown that design of dome structures in Isfahan architecture is based on consideration of structural behavior. Zia-Abadi [¹⁶] described various types of “Karbandi” structures and analyzed their structural role in the buildings while Safaeipour et al. [¹⁷] studied the structural role of “Patkâné” in some buildings. These works analyzed the architectural and structural aspects of the buildings separately. however, the present research intends to consider the both aspects, concurrently, and investigates their interactions. We focus on the geometrical features which link and unify the architectural form and the structural stability to find how have they been used to achieve successful ASI?

The unity between the architectural form of the structure and its stability is observable in most often of ancient landmark Iranian buildings. We choose the Jamé Mosque of Isfahan and Soltaniyeh building as two important samples of Iranian historical and architectural heritages. There is a comprehensive data and information for the Jamé Mosque of Isfahan released by ICHHTO [¹⁸] and Galdari [¹⁹]. For the Soltaniyeh building there are also some pictures that show construction steps [²⁰] and could be used for analysis of the relationship between the geometry and the structure in this building.

The remainder of this paper is organized as follows: In Sections 2 and 3 the basic concepts and methodology are presented, respectively; Sections 4 and 5 contain the case studies and concluding remarks, respectively.

Basic concepts and definitions

The geometry is defined as the study of dimensions and the feature of shapes which are existed in an object [²¹]. In this research, the geometry is considered as the characteristics of shapes and relationships between values (proportions), the way that fits shapes together (geometric patterns) and spatial communication between the space and the architecture. The application of geometry in two chosen cases can be viewed and studied from both the architectural form and the structural attributes.

According to Pope [²²], the Jamé Mosque of Isfahan is one of the most beautiful structures in Iran, which is interesting in every aspect of aesthetics, geometry, and mechanics. Elegant and precise geometry in implementation of the dome structure, a variety of methods in construction of arches in the “Shabestans”, a variety of geometric patterns in bricklaying and the various methods of building muqarnas make it as a landmark heritage of the Iranian ancient architecture. The Soltaniyeh Monument has also a specific geometry in plans and sections. The existence of eight minarets with their special function on the roof, the huge and high arches in the interior, the use of multi-purposes elements such as porches, a variety of geometric patterns in bricklaying are among reasons for choosing Soltaniyeh building in this study.

Grütter [²³] defined the architectural form as an obvious manifestation and a physical totality of an architectural work consisting the combination of visual elements. In this research, the form is considered as a set of visual elements of an architecture that has spatial attributes while the structure refers to the sum of all load bearing parts of the building. In other words, the structure is defined as parts of a building that ensure its physical stability and strength.

The interaction is an action that occurs between two or more entities, objects, phenomena, or processes. The principle of interactivity states that the act of an entity is not carried out solely in terms of its plans and intentions, but also the probable plans and reactions of other things should be also taken into consideration. Thus, the architectural-structural interaction can be defined as the simultaneous formation of the form and the structure, considering the needs and functions of each other. In other words, the form of a building not only provides architectural needs but also facilitates its structural stability. On the other hand, the structure will also play an important role in elegancy of the architectural form in addition to providing sustainability of the building. Thus, in an ideal case it is not possible to distinguish between the structure and the form since the architectural form and the structure are designed for a unique purpose.

Methodology

In buildings where the architectural form and structure interact, the latter contributes to provide the former. From this view point we classify structures in the following categories:

1) The structure is “dominant” and has a clear presence in the visual form;

2) The structure is “hidden” and is indirectly linked to the form;

3) The structure is “compatible” and is in harmony with the spatial composition of the form and fulfills the architectural needs (i.e., social aspects, performance, beauty, and semantic needs).

The ASI is in fact a bilateral relationship. One side involves participation of the structure in realizing the needs of the architectural form which in this research are considered as the beauty, functional, and semantic requirements. The other side of the ASI is participation of the architectural form in fulfillment of the structural needs which in this research are ease of construction and cost parameters. In summary we define following four criteria to assess ASI:

1) How does the architectural form facilitate structural construction?

2) How does the architectural form serve structural cost issues?

3) How does the structure participate in fulfilling the visual requirements of the form?

4) How does the structure participate in fulfilling the functional and semantic requirements of the form?

Case study

In following sections, we analyze our two case studies in terms of the defined criteria.

How does the architectural form facilitate construction tasks?

This criterion will be satisfied if the non-structural elements of the architectural form are organized in such a manner that they support the structural framework in space. In this way, they display an obvious representation of the structure and inspire the sense of stability [²⁴]. Understanding the behavior of the structure within the architectural form is also a key factor in this criterion. So, even if the structural components are not visible within the form, their presence is sensible and provides a better understanding of the structural function in the building.

Ancient Iranian architects understood the forces which act on the building. They could precisely recognize the proportions and dimensions of all sections of the building [¹⁴]. In their work, parameters, such as choice of the ceiling’s type, detection of the force paths, and usage of native materials, had a decisive role on the architectural form [¹⁴]. We discuss about these parameters in following sections.

Shape of the ceilings and location of the load bearing elements within the form

The domes of Jamé Mosque of Isfahan are the most prominent elements of its architectural form, which in addition to providing architectural needs (including function, meaning and beauty) also have special structural solutions to cover large openings and transferring loads to the ground. The southern dome is the “Tarkin dome” with crossover “Karbandi”. According to Fig. 1, it consists of eight arch beams that cut off each other at a central point (i.e., the radial crossover). In the northern dome, the skeletons of the “Tarkins” cannot be seen. The interior shell of this dome is decorated with a five-star-shaped spatial form of “Karbandi” [²⁵]. According to Fig. 2, vertical integrity, supporting components, shape of corners and type of arch’s curve of the dome indicate a sense of sustainability in the form of dome houses. In addition to domes, the Jamé Mosque of Isfahan has a complete set of arched shaped structures, each of openings has different and specific features due to its dimensions, appearance, construction technique, and structural system [¹⁶]. In the mosque’s arch shaped ceilings, the existence of the structure can be seen directly in the interior. For example, in the vault of the northern portico of the mosque which is named “Ahang”, the presence of large piers on both sides of the porch which carry the thrust of pointed arch, gives a sense of confidence about the strength of the structure. In the “four sections vaults” on the winter “Shabestan” of the mosque, structural elements obviously display their stiffening performance. Columns in dome houses and “Shabestan” are other structural elements of the mosque form. The quadrilateral columns in the southern dome house and the cubic piers in the northern dome house, as well as the cylindrical columns with cubic crests, dominate the structural sense in these spaces.

In the Soltaniyeh dome, the brick girders, which have different shapes between two shells, create the main structure of the form. Modular system of brick arches that are in the form of a pointed arch between two shells is very similar to frames. The protective layer of the dome is connected to this system [²⁶]. The feeling of the stability of the structure is quite feasible because of the heavy piers and the eight high vaults in the dome house. Because of these vaults, pressure loads are applied on the fixed and separated points. According to Fig. 3, compressive forces which are created by the minarets and the porches around the dome house keep thrust forces within central one third of the wall thickness.

Proportions, modulation, simple geometric shapes, and symmetry in creation of the form and structure

1) Proportions

The application of some proportions can be seen predominantly in the Iranian ancient architecture, such as “the golden proportion”, \sqrt{\mathrm{2}}, \sqrt{\mathrm{3}}, and 1.118. The application of these proportions leads to better stability of the entire structure and determination of the architectural form [²⁷].

In the Jamé Mosque of Isfahan, the use of golden proportion in the geometry of Taj-al-Molk dome is related to the proper structural behavior of this dome [²⁸]. As Fig. 4 shows the geometric analysis of Taj-al-Molk dome demonstrates that the architect has chosen a pentagonal design considering the golden ratio. The golden proportions are detectable in sizing each component of the structure, such as the tip of the dome, the height of the entire transition region from the base to the dome, the octagonal arch’s tip, the lower main arch’s tip, the height of the lower arch and the height of the window [²⁸].

2) Modulation

In Iranian ancient architecture, the organization of the shape and space of buildings was possible by using traditional measurement units such as the “Gaz” and “Girih”, which were derived from human body dimensions. They led to the formation of the “Peymun” or module, matching all sizes [²⁷]. The emergence of the “Peymun” resulted in architect’s confidence about the stiffness of the building [²⁰]. In the Jamé Mosque of Isfahan, the “Peymun” is observable in the form of repeating square or rectangular modules consisting of four pillars in the “Shabestans”. As Fig. 5 shows, the roof of all modules is in the form of an arch. In the plan of Taj-al-Molk dome house one can recognize a 9-square checker network [²⁹].

3) Symmetry

In Iranian ancient architecture, the application of symmetry in the organization of structural elements plays an important role in understanding the behavior of the structure, ensuring its stability, and in the simultaneous formation of the form and the structure. The use of symmetry in the Soltaniyeh building can also be seen in the presence of minarets, porches, columns and heavy piers around the dome house. They are symmetrical towards dome house to withstand the thrust forces. The existence of eight minarets on the roof is one of the factors that play a significant role in static stability and transferring the thrust forces [²²].

4) Basic geometric shapes

In Iranian ancient architecture, the basic geometric shapes (such as triangle, circle, and square) are widely used, causing simplicity in the design and reliability of its strength. Three main spaces in the Soltaniyeh building are dome house, “Torbatkhaneh”, and “Sardabeh”. Acoording to Fig. 6, these spaces have simple octagonal and rectangular forms, they have dome and vault ceilings. The use of load bearing arches including the “Panj-o-Haft”, “Chamaneh”, trefoil, “Biz”, “Bastu” and “Sarvak” arcs are abundantly found in Iranian ancient architecture [³⁰]. These arches cover up to 16 “Gaz” and can withstand the loads. As Fig. 7 depicts, in the Soltaniyeh building, the main arch is “Chamaneh” which not only tolerates loads, but also creates a kind of so called “Sabuee” dome. The “Chamaneh” arch is beautiful and the simplest load bearing arch. In this arch, height to span ratio is 3/4, so it has a long height with substantial load bearing capacity. The porch arches are also “Panj-o-Haft”. The height of this arch is less than the half of its span.

Structural participation in fulfillment of visual needs of the form

The structure can be coherent with the architectural form by addressing its requirements. Applying decorations is one solution where the structural and decorative elements interact. The transformation of structural elements into ornament ones is a general rule in Islamic architecture [²,³¹,³²]. Squinch, muqarnas, “Karbandi”, and a variety of geometric patterns in brick decoration are very popular in Islamic architecture which are discussed in the following.

1) Squinch

Squinches were often used in the dome house transitional area. These elements convert the shape of the dome to the square or rectangle of the base, they also carry various loads and distribute forces. According to Fig. 8, in the dome of the Jamé Mosque, the squinch has structural performance, it also has the best and most attractive brickwork. Regular squinches in fact make the dome stable.

2) “Patkaneh” muqarnas

Muqarnases have had constructive and decorative functions over time [³³]. These elements are currently used mostly as decorations. In the Jamé Mosque of Isfahan, on the eastern and southern porches, the muqarnas coating is used to smooth sharp corners into the curve. These muqarnases have no load bearing function but a type of muqarnas called “Patkaneh” has decorative role and is self-stable. As shown in Fig. 9, this type of muqarnas is used in the western porch of the mosque. In the Soltaniyeh building, in the transition region of the dome, there are three rows of muqarnas. According to Fig. 10, this muqarnas has turned the octagonal plan into a circle and provided the base for the erection of the dome. Thus, the muqarnas in this building, in addition to the decorative role, has structural function as well transferring and distributing the dome loads.

3) “Rasmi-Karbandi”

When both sides of the “Karbandi” are in a same plane, it is called the “Rasmi-Karbandi” which can be assumed as a combination of an arch and a dome [³⁴]. Figure 11 [¹⁶] depicts this kind of “Karbandi” which can transfer loads as a full arc. According to Fig. 12 [²⁵], this type of “Karbandi” is used in many ceilings of the Jamé Mosque of Isfahan.

4) Bricklaying techniques

In addition to the above techniques, the combination of structural and decorative elements can be seen in bricklaying with variety of geometric patterns. A variety of bricklaying methods in Islamic architecture were adapted to the span, location and type of loads. There are three types of bricklaying: Roman, full, and blade types [³⁵]. In the composition of bricklayings, attention to the performance and durability of vaults is very important. In the Jamé Mosque of Isfahan, the “Khagi” dome is a masterpiece combining the functional and decorative aspects of the brickwork in its era. The use of brick to demonstrate the pressure patterns is more important than its decorative function. According to Fig. 13, in the Jamé Mosque vaults, structural use of brick is worth considering, the direction of rows is different in response to variable pressures [²²]. The dominant strength of the Mosque vaults originates from the brick patterns that demonstrate force paths, rather than the structural forms themselves.

The main body of the dome and the Soltaniyeh entire building is made with brick. It has a major role in the stability of the building as well as different decorative tasks.

Cost-effective structures

Cost-effective structures are characterized with the proper dimensions and shapes of the structural elements with attention to their location in height to balance the structure and avoid futility. In other words, in a cost-effective structure geometrical dimensions and used material are properly selected in accordance with the type and size of loads. The Taj-al-Molk dome of the Jamé Mosque of Isfahan is made of bricks, which have low tensile strength. In this dome, membrane stresses, tensile strength and bending forces are almost equal to zero under the weight load [²⁷]. The structural analysis of the dome by finite element method has shown that the stresses due to bending forces are negligible compared to the membrane forces not only for the weight load, but also for wind and temperature, and more importantly for the dynamic effects of the earthquake [¹⁵]. The analysis has also shown that the cross-section and shell thickness are properly sized [¹⁵].

Bricklaying at Soltaniyeh dome is such that the dome is elegant, beautiful and easy to erect. It has variable thickness [¹⁴], constructed without any buttress [³⁶] and the bricks are laid onto the bottom by mortar. During the lifetime of the dome, the bricks, are still retaining their lateral solidity, transferring their total force and weight to lower bricks [²²].

In Iranian ancient architecture wood has been used to withstand against tensile forces within arches. More specifically, when the arch has long height, a wooden tie beam between the two bases caries the thrust load. For the short height arches, such as the Soltaniyeh porches, the tie beam is located on top of the arches within the bricks. A sample of tensile wooden beams was found inside the structure on Soltaniyeh porches, which was skillfully buried within bricks.

Functional and semantic requirements of the form

In Iranian ancient architecture, the structure plays an effective role in realizing the spiritual values and functions of the architectural form. Islamic spirituality and technical principles of engineering in Iranian ancient architecture have reached a high degree of maturity that not only answers the necessities of the materialistic world but also fulfills spiritual needs of the supernatural world [³⁷].

The essence of Islam is summing up in monotheism and submission to the unity of God and the intuition derived from it. In Islam, unity, justice, and forgiveness are the main aspects of beauty [³⁸]. We call these qualities as unity, harmony, and perfection for further discussion as in the art, unity is the source of all perfections, justice leads to balance and forgiveness leads to perfection [³⁸]. From the point of view of the Muslim artist, abstract art represents a law that, in the most direct way, illustrates unity in plurality [³⁹]. In this regard, the arrangement of structural elements in Iranian architecture is such that manifests the principle of unity within plurality in the architectural form. An example of this manifestation can be found in the arrangement of structural elements in dome houses. For example, in the northern and southern domes of the Jamé Mosque of Isfahan, the ascent of the load bearing elements from the pillars and the arches to the squinches is such that their unity can be seen in creating an integrated dome form. Similarly, in the views of the central courtyard, the repetition of the arches towards the main central arch of the porches, shows another manifestation of the principle of plurality in unity. This fact can be also seen in the arrangement of architectural form elements such as squinch, “Karbandi”, “Patkaneh”, and muqarnas in the mosque. In the Soltaniyeh building, the arrangement of structural elements, including heavy piers and eight high vaults under the dome and its brick arches, lead to the creation of a monolithic dome house. The architectural form elements that contribute to the strength of the structure, such as the minarets and porches in the perimeter, are organized in such a way that contribute to the overall unity of the dome house.

Balance is another architectural requirement to achieve beauty. The proportions, modulation and symmetry are repeatedly used by Iranian architects. Application of these guidelines is one of the effective factors in balancing the form.

Perfectionism is defined as another requirement of the form to achieve beauty. Islamic architecture of Iran is also perfectionist and tries to pay attention to each component, perfectly [⁴⁰]. This feature can be seen in fully stressed structures, either in terms of the type of materials or dimensions and geometry.

Concluding remarks

The application of geometrical features in Iranian ancient architecture can be observed in all stages of the design, from the basic idea to the geometrical details of the buildings. This application leads to the emergence of such architectural forms that, not only satisfy the beauty, performance and semantic requirements but also reveal the principles of unity in all aspects of the architecture. One of these aspects is the interaction between the architectural form and the structure. Architects with Islamic thoughts have used geometric concepts and patterns to create buildings with a proper relationship between the form and the structure. We investigated two case studies including the Jamé Mosque of Isfahan and the Soltaniyeh building in Iran in terms of the architectural-structural interaction and outcomes are summarized in Table 1.

Taking the advantages of Iranian ancient architectural experiences for architectural-structural interaction in contemporary buildings, makes the scope of our present future research.

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