Ceramic Tectonics: Tile Grid Shell

Abstract

Funicular grid shells are typically constructed from steel or timber struts, but no examples are known using structural ceramics, a material known for its longevity and fire resistance. We report a method for the design and fabrication of a novel grid shell structure from unreinforced ceramic tile with minimal use of metal fasteners. Full-scale studies tested joinery and connection details, large-scale mockups helped to verify the assembly sequence, and physical component tests determined allowable strength values for structural design. A novel assembly sequence allows each rib to be installed vertically from above, eliminating the need for mechanical connections between ribs. A prototypical grid shell spans 6m with grid members fabricated from two layers of 6mm thick ceramic tile.

Full text

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
July 16-20, 2018, MIT, Boston, USA
Caitlin Mueller, Sigrid Adriaenssens (eds.)
Copyright © 2018 by Zach SEIBOLD, Milena STAVRIC, Olga MESA, Martin BECHTHOLD
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Ceramic Tectonics: Tile Grid Shell
Zach SEIBOLD*, Olga MESAa, Milena STAVRICb, Martin BECHTHOLD
*Material Processes and Systems Group, Harvard Graduate School of Design
48 Quincy St, Cambridge MA 02138
zseibold@gsd.harvard.edu
a Roger Williams University, Material Processes and Systems Group, Harvard Graduate School of Design
b Graz University of Technology
Abstract
Funicular grid shells are typically constructed from steel or timber struts, but no examples are known
using structural ceramics, a material known for its longevity and fire resistance. We report a method for
the design and fabrication of a novel grid shell structure from unreinforced ceramic tile with minimal
use of metal fasteners. Full-scale studies tested joinery and connection details, large-scale mockups
helped to verify the assembly sequence, and physical component tests determined allowable strength
values for structural design. A novel assembly sequence allows each rib to be installed vertically from
above, eliminating the need for mechanical connections between ribs. A prototypical grid shell spans
6m with grid members fabricated from two layers of 6mm thick ceramic tile.
Keywords: grid shell, kagome, structural ceramics, structural tile, digital workflow, prototyping
Figure 1: Ceramic tile grid shell installation
1. Introduction
Clay-based ceramics are one of humankind’s oldest material systems, notable for their hardness,
durability, fire resistance and wide array of finishes. New material processing and production
technologies have enabled the development of ceramic elements capable of performing thermally,
environmentally, and acoustically [1], [2]. A relatively recent development has been the manufacturing
of tiles in sizes up to 3.6m by 1.2m, with thicknesses between 3mm and 20mm. These elements are
currently used as non-structural surface finish, but earlier work by Harvard’s MaP+S group
demonstrated their ability to form self-supportive structures in the form of three 3.6m tall columns [3].

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Creativity in Structural Design
2
Conceiving these tiles as sheets opens up a host of applications, including primary structural uses like
those for plywood or metal. The brittleness of ceramics and its poor tensile strength, however, require
the development of structural design criteria and new construction strategies.
This paper presents design and construction methods for structural ceramic tile, developed through the
design of a full-scale ceramic grid shell. Following the brief review of precedents in structural ceramics
we present the design principles for a ceramic grid shell with a particular focus on connection design,
construction sequence and member redundancy. Material testing is reported as a method to confirm
structural design criteria that were then applied to the analysis of a small grid shell which was designed
and built in 2018 in Valencia, Spain.
1.1 Ceramics and Shell Structures
Several precedents exist for the use of ceramics in structural shells. The construction techniques
developed by Rafael Guastavino eliminated much of the formwork historically required for the erection
of masonry vaulting systems, adhering two or more layers of tiles laid at differing orientations with a
bonding agent [4]. Uruguayan engineer Eladio Dieste created reinforced brick shells using a material
system he referred to as “cerámica armada”, or reinforced ceramic [6]. His daring shells relied on post-
tensioning of brick-like ceramic tiles. This innovative material system “transformed our perception of
brick as a traditional material associated with heavy, vertical construction elements into one that allows
for extreme thinness and long spans” [6], [7]. Research by López López et al. has documented examples
of similar techniques deployed in the mid-20th century [8]. More recent work by the BLOCK Research
Group and others have adapted these techniques to more complex 3-dimensional forms [9], [10]. These
examples presented thin structural ceramic surfaces and related form-finding approaches, but they are
all characterized by the use of relatively small rectangular tiles bonded with mortar. Given the radically
enhanced production capacity of the industry designers are now investigating the tectonics of thin
ceramic tile.
1.2 Grid Shells
Grid shells include properties that pair well with the physical traits of large-format ceramic tile. These
types of rigid spatial structures take on the form of a doubly- or single curved surface that is discretized
into a grid pattern rather than a solid surface [11]. Grid shells are notable for their ability to achieve
large spans relative to their material usage. They are able to achieve these structural efficiencies with
discrete, often planar, elements rather than the continuous doubly-curved forms that are needed for
traditional shells. There are numerous examples of grid shells constructed mostly from steel or timber
struts, but no examples are known using structural ceramics [12].
2. Ceramic Shell Prototype
Figure 2: The form finding input and process, including steps for generating the initial shell form, generating and
mapping a 2d kagome grid, and creating and discretizing ribs based on constructional logic.
The prototype ceramic grid shell presented here has been constructed at CEVISAMA 2018 in Valencia,
Spain as a part of the Transhitos exhibition coordinated by Área de Hábitat del Instituto de Tecnología
Cerámica (ITC). The prototype grid shell is a structure with a span of 6m, a maximum interior height
of 2.48m, and an approximate occupiable interior area of 13.5sqm. It consists of 30 structural ribs
comprised of 462 unique elements ranging from 820mm - 1810mm in length. The elements were cut
from seventy-two 1.5m x 1.6m sheets of 6mm thick ceramic tile on a 2.5-axis CNC waterjet. The depth

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Creativity in Structural Design
3
of each element ranges from 180mm - 310mm, determined by a combination of structural and
construction needs. Vertical slots are devised as the main connection strategy without using metal
connectors. The slots lead to the effective structural depths being no less than 50% of the actual depth.
The ceramic elements measure 107.22sqm in total surface area. The key design constraints were the
mechanical properties of ceramics, the need for rapid assembly on-site, and the limited one-week
duration of the exhibition.
2.1 Material Tests and Structural Design Values
ASTM test standards for thin tiles do not include mechanical properties for primary structural use.
Structural safety factors are equally unknown. We are presenting three-point bending tests on laminated
tiles, as well as tests of a double lap joint using mechanical connectors. The mechanical data from both
tests was then used for the structural design of the prototypical grid shell.
2.1.1 Three-Point Bending Test
To verify the mechanical properties of the material, three-point bending tests were conducted with a
thinner, 3mm tile, made from the same material, produced by the same manufacturer. A total of 14
samples were tested. The span was 300mm, the depth 40mm for one set and 50mm for another set. Each
specimen consisted of four 3mm tiles, to a structural width of 12mm (Figure 3). Each specimen was
tested as a single beam section. The average bending stress at fracture was 40.4 MPa (5,856psi, standard
deviation 5.6 MPa), the average Young’s Modulus at fracture was 13,924 MPa (2,020ksi, standard
deviation 2,165 MPa). The stress values were consistent with data provided by the manufacturer. An
initial safety factor of 33% was applied and maximum allowable stresses in bending of 27MPa (3,916psi)
assumed for initial structural design studies.
2.1.2 Mechanical Joint Test
The team also conducted three-point bending tests to determine the capacity of a construction lap joint.
A total of five samples were tested, with a span of 300mm and a depth 50mm. Each sample consisted
of four 6mm tiles held such that areas of the four tiles overlapped in the middle. Here the tiles were
mechanically connected using two M5 steel bolts placed in 6mm holes spaced 100mm apart on center.
The test determined the peak load at fracture, which in turn allowed for the calculation of the equivalent
bending stress in the material had the 4 tiles been continuous, thus without mechanical connection. The
average bending stress based on peak load at fracture was 20.0 MPa (2903 psi, standard deviation 3.8
MPa), the average Young’s Modulus at Fracture was 3,231 MPa (469 ksi, standard deviation 2,107
MPa). Both values are significantly lower than the equivalent values for continuous tiles without
mechanical fasteners. Displacements at fracture were larger due to the slightly oversized bolt holes.
Assuming a safety factor of 33% the allowable stresses in bending for a construction joint is 13.3MPa
(1,929 psi).
Figure 3: Photograph of material test sample during three-point bending test.
2.2 Novel Design and Tectonic Strategies
2.2.1 Parametric Modeling Strategy
While material testing was ongoing a comprehensive parametric model was created that provided the
flexibility of changing grid configuration and rib depth in response to production and structural

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constraints, while allowing for a compressed fabrication and construction schedule. The model not only
generated and analyzed the global geometry of the pavilion, it also served to discretize the form into
components based on the size of available ceramic tile sheets, accommodate for assembly tolerances,
size individual members for local load conditions, and generate toolpaths for fabrication. This
functionality allowed for the adjustment of key design parameters to improve the global performance of
the structure until late in the design process. The design team endeavored to reduce the number of
independent parameters in the system, and designate as many geometric parameters as possible
dependent on those independent input parameters. The main parameters driving the outcome of the
parametric model included the span length and arch height of each opening, the thickness of the material
stock, and the planometric arrangement of the grid pattern. A selected range of geometric and
mechanical variables that were integrated into the model, and dependent on these base parameters is
shown in Figure 4.
Figure 4: Geometric parameters of the ceramic grid shell system, including: A) Notch Orientation; B) Element
Length; C) Spacing And Orientation Of Registration Holes; D) Base Structural Depth; E) Depth Increase Of
Primary Elements; F) Notch Orientation And Scaling; G) Kagome Grid Density; H) Connection Angle
2.2.2 Plan Geometry: Projective Kagome Grid Pattern
Figure 5: Parameters describing construction of the planometric geometry of the prototype, showing the first five
steps of the process, and the completed grid. The location of parameter T determines the pattern density the grid.
The designers employed a trihexagonal tiling pattern - also known as a kagome grid pattern - in the
planometric organization of the prototype grid shell (Figure 5). Kagome grid patterns can be found in
traditional Japanese basketry, and, at the architectural scale, were employed in Shigeru Ban’s Oita
Prefectural Art Museum, and Centre Pompidou in Metz [13]. When applied to the form of a funicular
shell, the kagome grid pattern allows for simple connections, as each node has the same valence as
quadrilateral grid shell, while the triangulated zones of the pattern provide in-plane stiffness. A
quadrangular grid pattern would have relied on the bending stiffness of connections at nodes, while a
stiffer triangulated grid pattern would have increased the complexity of connections at nodes due to the
higher valence of the base mesh. The structural performance of the kagome grid pattern in comparison
to a quadrilateral grid pattern has been explored previously and found to have a superior bearing capacity
[14][15].
In the case of the prototype, the kagome grid pattern was applied to a planar projective coordinate
system, enabling each of the three primary spanning directions of the system to align with one of the

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three support points. The coordinate system is defined by three points at the corners of one equilateral
triangle, and a fourth point T, which must not lay on one of the edges and defines with point T1 the
density of the grid pattern. This configuration can be interpreted as a planar projective coordinate system
with base points B0, B1, B2, T. B0 is the origin of the projective coordinate system, connection B1B2 is
the line at infinity and T1 is the unit point of the projective plane [16].
The geometric characteristics of the organizational strategy described above provided several
advantages. The closely spaced ribs near the supports provide structural redundancy in case one or
several ribs break. The low node valence and inherent stiffness of the pattern permitted the use of simple,
notched connections that are able to be assembled without mechanical fasteners.
2.2.3 Structural Rib Design
Figure 6: Drawing showing the assembly process of a typical rib, showing two staggered layers (A, B) forming a
primary and secondary segment (C), then a completed rib (D).
The prototype shell is constructed from 30 custom ribs, with each rib fabricated from two laminated
layers of 6mm tile 180 to 300mm in depth. Each rib is site-assembled from a staggered configuration
of approximately 15 components and acts as a continuous element within the structure (Figure 6). At
lap joints between staggered components, only one piece is continuous, while the other is connected
with a puzzle-jig type joint. Components were sized to be small enough to nest easily on the material
stock, and large enough to maintain a distance of at least one structural bay between adjacent lap joints.
Each rib is split into two segments, referred to as a primary and secondary segment. The individual
components that comprise each segment are laminated off site using a structural adhesive. 6mm holes
in components were used to align corresponding pieces, and were also used to secure pieces together
while adhesive cured. The two segments are connected on site via a mechanical bolted joint once both
are positioned in the structure. Primary segments overlap primary segments from opposing sides of the
structure by approximately 30 cm (Figure 2).
2.2.4 Assembly Process
An important innovation specific to the properties of ceramic tile involved the assembly sequence of the
prototype structure. The sequence was geared towards minimizing bending stresses both during
construction and upon completion of the structure, as the slender profiles could develop brittle fractures
as a result from bending in the weak axis of the rib. During construction, ribs must be installed vertically
from above, rather than tilted into place. Once installed, intersecting ribs may bear on one another along
the strong axis, but must be free to rotate relative to one another along the weak axis.
The assembly sequence of the rib segments reflects the construction logic of the underlying kagome grid
pattern. Rib segments are installed in a radial spiraling pattern from the center outwards (Figure 7). The
primary segments are installed following this pattern, which is then repeated for the 30 secondary
segments. During construction, the radial assembly sequence facilitates the transport and manipulation
of rib segments, and contributes to overall stability of the in-progress structure, as ribs and scaffolding
are loaded in a symmetrical fashion. The research team developed a custom CNC cut scaffolding system
fabricated from 19mm thick MDF panels that indicated position and assembly order of all ribs. The
design of the scaffolding allowed for the incremental decentering of the structure.

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Figure 7: A 1:4 scale prototype was set up to test the feasibility of the assembly sequence.
2.2.5 Connection Detailing
Each rib is slotted to accommodate intersecting rib members, with slot orientations determined by the
assembly sequence. Ribs that are installed first have slots on their upper edge to receive subsequent ribs
vertically from above. As primary segments are installed first, with only a single notched connection,
the majority of their slots are located on the upper edge. Accordingly, the slots of secondary elements
are usually located on the lower edge, which enables them to be supported by previously installed
elements. Once the primary and secondary segments of a single rib are mechanically fastened together,
the now-continuous rib acts as a reciprocal element - supporting any intersecting secondary segments,
while simultaneously being supported by any intersecting primary segments. This mutually supportive
arrangement satisfies conditions for structural stability, while also allowing each rib to be installed
vertically from above, without the need for mechanical connections between ribs.
2.3 Structural Analysis
An analysis model was set up in Multiframe Advanced v17.00.06.0, with each rib modeled as a sequence
of straight line segments at the centroid. Grid intersections were modeled with short connecting elements
using a rigid connection to one and a pin connection to the other rib. This configuration represents the
real nodal constraints while allowing the grid elements themselves to be structurally continuous. All grid
supports are pinned.
Figure 8: Structural analysis results, including A) Axial forces B) Bending moments C) Deflection D) Buckling
Analysis and E) Deformations under combined lateral and gravity loads. Values are shown for self-weight
unless otherwise noted.
2.3.1 Member Stresses
The structural analysis deployed a single section profile as the structural element. The grid sections for
the system are 2 tiles 6mm thick with varying depth no less than 90mm measured perpendicular to the
centroid. For the computational analysis, the section shape for the entire structure was a ceramic tile
element 6mm thick and 90mm deep. This is equivalent to the worst case situation at a sheet joint (only
one tile continuous) that also includes a notch. The vast majority of locations have much greater sectional
capacity.
The loads consist of the self-weight of the ceramic ribs, 2,334 kg/m3 (145 lbs/ft3) according to the
manufacturer’s data. To accommodate any additional fasteners an additional dead load of 0.036 KN/m
was applied onto each grid elements. As for lateral loads, no overall wind or seismic loads were modeled
since the structure was designed for a secure interior environment. To simulate a person pushing into
the structure a lateral load of 1000 N was applied at a height of 1.6m onto a node of the structure (Figure
8E). Member stresses are overall very small (Figure 8A, 8B). Maximum combined bending and axial
tensile stresses are 4 MPa – thus well below the allowable strength. Maximum deflections are 0.238 cm
with a vertical displacement at the top of the shell midpoint of 0.1 cm (Figure 8C).

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Low member stresses in combination with the kagome grid provided sufficient redundancy in case of a
local failure of a rib. Ceramic as an extremely brittle material could fracture through impact loads. In
that case neighboring ribs are able to take on additional load transfer, and forces can redistribute
throughout the grid. When removing 4 short rib segments maximum stresses remained well below 10
MPa.
2.3.2 Member Buckling
The longest member in compression is located near the support (Figure 8D). The effective length of that
member is 0.99m (continuous with pin ends). The maximum compression force is 0.277 KN. The cross-
section for the buckling analysis assumes the actual 12 x 200mm section, with E = 13,924 MPa as
reported in Section 2.1.1. Checking the weak direction shows that the critical buckling load is
magnitudes larger than the actual load. Pcrit =
p
2
E I / Le2 = 3.14
2
13,924 MPa (200mm (6mm)3/12) /
(990mm)2 = 504 KN.
2.3.3 Mechanical Joints
Since 10 ribs radiate from each corner there are a total of 5 different types of construction joints. The
analysis assumes 5mm diameter steel bolts are connecting across two tiles. Assume steel bolt M 5
according to ISO 898, property class 4.6 (lowest strength): the long term proof shear load is 3.2 KN,
ultimate loads are in the range of 5.6 KN. Assuming an area of 6mm x 5mm the bearing stress on the
tile for this load equals F/A = 106 MPa which is higher than the bearing strength. Assuming that bearing
and bending strength are equal at 27 MPa the maximum force that can be transferred with a single bolt
is 27 MPa = F / (5 x 6mm2) > F = 810 N = 0.81 KN. Assuming a spacing of 2 opposite bolts of 150mm
the maximum theoretical moment transfer is equal to 0.81 KN x 0.15m = 0.122 KN m. From the
computational analysis the maximum bending moment at the construction joint is equal to 0.036 KN m.
In the final detail the number of bolts were doubled to provide plenty of spare capacity to carry the
bending moments and increase rigidity.
3. Fabrication and Construction
Rib segments were CNC waterjet cut and pre-assembled in the shop. Several pieces broke at their
weakest areas – mostly near bolt holes, or near the connection slots. Fractures occurred prior to
lamination and whenever bending was unintentionally induced in the weak direction of the rib. Special
care had to be taken in transporting cut pieces to the lamination shop. No fractures were recorded in
laminated rib segments on site.
Ceramic is dimensionally extremely stable with respect to moisture or temperature fluctuations – and in
that respect differs from wood and metal. Given the precision of CNC waterjet cutting, construction
tolerances at each joint were only 2.5mm per side. The base support was carefully built to maximum
precision, and assembly was completed without any re-cutting or adapting of ribs. Upon completion of
construction, vertical deflection of the structure was measured at the three centermost rib intersections
and found to be within 9mm of the design values.
4. Conclusion
Although continuous shells have been built using ceramics, grid shells are most typically built using
steel or timber, and on occasion concrete. The paper investigates the feasibility of ceramics as a primary
structural material for grid shell systems, with a particular focus on large format ceramic tiles. Certain
attributes of ceramics, such as resistance to fire, mildew and pests make the material a promising choice
over other standard construction materials where durability and sanitary conditions might be desirable.
In addition, the capacity for being glazed and printed on may expand the aesthetic possibilities of grid
shells.
The paper presents a dedicated design and manufacturing workflow for ceramic grid shells. Material
and joint tests determined the design values used in the structural analysis. A limitation of ceramic
structural elements was found to be the risk of fractures during transport and fabrication. The
combination of large safety margins in the final structure along with system redundancy through the

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choice of the kagome grid pattern contributed to realizing an overall safe design. The geometric pattern,
joinery and sequence of assembly reflected principles of shell construction, as well as considerations
specific to the properties ceramic tile. As such, this work constitutes a promising development in the
implementation of ceramics as a material for the construction of grid shells.
Acknowledgements
The authors thank ASCER Tile of Spain for their continuing support. Cevisama 2018 provided
additional support for the exhibition. Javier Mira from the Instituto de Tecnología Cerámica as well as
Groupo on Market helped realize the design.
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