Building with Earth: Design and Technology of a Sustainable Architecture

soned adobes without structural beams,
and even without formworks. These tech-
niques are described in the following sec-
tions.

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 trans-
fer 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 14.32shows 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 geo-
metrical problem resides in the need to dis-
cover a transition from the circular geometry
of the dome to the square geometry
of the room. Illustration 14.33shows four
different systems for solving this problem.
Solution A is a truncated dome whose bot-
tom 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 sur-
faces, called squinches, are composed of
a series of arches of increasing radius. This
solution can also be described as a truncat-
ed 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 chang-

ing 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 perpendi-

cular direction) and continuing to the apex

with a synclastic (dome-shaped) curvature

(i.e., one that is similarly curved in both

directions).

Structural measures

Structurally speaking, vaults and domes are

curved surfaces that transfer almost exclu-

sively 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. 14.34bottom), 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 14.35and

14.36.

The main problem in constructing vaults is

how to transfer of the outward thrust force

at the bottom to the supports and founda-

tions. Illustration 14. 37shows how the

resultant forces at the support can be sepa-

rated into vertical and horizontal compo-

118 Designs of building elements

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 stranglehmtechnique

14. 31

14.32

14.33