Building with earth - Gernot MINKE (1)

soned adobes without structural beams,
and even without formworks. These techniques
are described in the following sections.
On the geometry of vaults and domes
Vaults and domes are two-dimensional
curved structural elements that serve to
cover interior spaces. Shell structures with
the same geometry display very different
structural behaviours. They are able to transfer
bending moments to their supports.
However, masonry vaults and domes only
transfer loads under compression. If singly
curved, they are called vaults (14.31, left);
if doubly curved, they are called domes
(14.31, right). Vaults and domes can be built
from a variety of basic geometrical elements.
Illustration 14.32 shows two cross vaults
(A, B) and two domical vaults (C, D); all
forms are composed from the parts of a
barrel vault. With domes that form surfaces
of revolution, that is to say, whose forms
originate from the rotation of a curve around
a vertical axis (usually a circular arc), and
which are set above square rooms, the geometrical
problem resides in the need to discover
a transition from the circular geometry
of the dome to the square geometry
of the room. Illustration 14.33 shows four
different systems for solving this problem.
Solution A is a truncated dome whose bottom
circle is drawn around the square, and
vertical truncating planes meet the dome
surface to form arches. Solution B is called a
dome on pendentives. Here, a hemispherical
dome rests on the lower part of a truncated
dome. The doubly curved triangular surfaces
are called pendentives. Solution C shows a
squinch dome whose lower circle is inscribed
on the square and the interconnecting surfaces,
called squinches, are composed of
a series of arches of increasing radius. This
solution can also be described as a truncated
dome resting on the inscribed diagonal
square with the surfaces thus left (triangular
in plan) being the squinches.
Solution D is a partial squinch dome whose
bottom circle is drawn around the largest
regular octagon that fits the square, forming
truncated planes on four of the sides and
squinches on the other four. Solution E
shows a totally different way of solving this
problem and can be called a bell-shaped
dome. Here, we have a continuously changing
double curvature beginning at the
edges with an anticlastic (saddle-shaped)
curvature (i.e., a curvature that is convex in
one direction and concave in the perpendicular
direction) and continuing to the apex
with a synclastic (dome-shaped) curvature
(i.e., one that is similarly curved in both
directions).
Structural behaviour
Structurally speaking, vaults and domes are
curved surfaces that transfer almost exclusively
compressive forces to their supports.
They are usually constructed of baked bricks
or flat stones, with joints set perpendicular
to the surface of the dome, so that the
courses form a radial pattern as in 14.34
top. If the courses are set horizontally, so
that the masonry blocks create overhangs
within, (cf. 14.34 bottom), then we speak of
a ”false“ vault or dome. In such cases, since
each course is cantilevered over the one
before, the blocks are subjected to bending
forces. One example of a false dome is
shown in the model illustrated in 14.35 and
14.36.
The main problem in constructing vaults is
how to transfer of the outward thrust force
at the bottom to the supports and foundations.
Illustration 14.37 shows how the
resultant forces at the support can be separated
into vertical and horizontal compo-
14.31 Vault and dome
14.32 Shapes created by
intersecting vaults
14.33 Types of domes
over square plans
14.34 “True” and “false”
vaults
14.35 to 14.36 Model
of a building with “false”
vaults
14.37 Separation of
forces at the support
14.38 Deflection of the
resultant shear force into
the foundation
14.31
14.32
14.33
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Designs of building elements