Building with earth - Gernot MINKE (1)

14.39
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 barrels
have different shapes, then only a portion
of this horizontal thrust will be neutralised
(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 catenary
curve, defined as the shape assumed
by a freely hanging chain, which is subjected
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
14.40 14.41
contain the line of thrust within its middle 14.39 Possibilities of
third (14.43 B), then this danger is avoided. structural stabilisation
14.40 Horizontal forces
The ideal cross-section of a dome under
14.41 Reversed catenary
dead load is that which only creates compressive
forces going downwards (merid-
same length
14.42 Catenaries of
14.43 Lines of support
ional). This means a form that creates neither
tensile nor compressive ring forces. tion of loads
14.44 to 14.45 Simula-
If the cross-section has the shape of a
14.46 Calculation of surface
areas
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
120
Designs of building elements