Building with Earth: Design and Technology of a Sustainable Architecture

120 Designs of building elements

If two identical barrels converge in one strip
foundation, then the horizontal components
of the resultant thrust are neutralised (see
14.40 right). If, on the other hand, the bar-
rels have different shapes, then only a por-
tion of this horizontal thrust will be neu-
tralised (14.40 left).
Since adobe vaults can endure only very
small tensile forces, it is important to design
them so that, as nearly as possible, only
compressive forces occur. With a barrel vault
that bears only its own weight, this is the
case if its cross-section is an inverted cate-
nary curve, defined as the shape assumed
by a freely hanging chain, which is subject-
ed only to tractive force. When inverted, this
curve represents the ideal supporting line
(line of thrust) for a vault in which only
compressive forces occur under dead load
(14. 41). This line can be computed by the
catenary formula y = a cosh (x/a), and can
be defined by the position of the two points
of support and the apex (see 14.42). In a
semicircular vault, the line of support does
not run in the centre of the wall thickness.
It might even fall outside the structure, as
shown in 14.43 A. This causes bending
stresses and usually leads to failure. If the
thickness of the vault is large enough to

contain the line of thrust within its middle

third (14.43 B), then this danger is avoided.

The ideal cross-section of a dome under

dead load is that which only creates com-

pressive forces going downwards (merid-

ional). This means a form that creates nei-

ther tensile nor compressive ring forces.

If the cross-section has the shape of a

catenary, then compressive ring forces will

occur. This might be disadvantageous if

openings have to be cut into the dome, or

if it is a dome of large span.

To work out the ideal shape of a vault, a

slice as shown in 14.44, left, is taken out

14.39 Possibilities of

structural stabilisation

14.40 Horizontal forces

14.41 Reversed catenary

14.42 Catenaries of

same length

14.43 Lines of support

14.44 to 14.45 Simula-

tion of loads

14.46 Calculation of sur-

face areas

14.39

14.40 14.41