Building with Earth: Design and Technology of a Sustainable Architecture

122 Designs of building elements

A more exact method to derive ideal curve
is by graphic methods used in statics engi-
neering. At the BRL, these methods were
used to develop a computer programme.
Some results for eleven different dome
proportions from h = 1.5 r to h = 0.5 r
(where h is the height and r the half-span)
are plotted in 14.47. In each case, a skylight
opening of 0.2 r was taken into account.
Illustration 14.48shows the ideal curve in
comparison with a parabola, catenary and
semicircle.
In the section of the dome is inside the
ideal curve, as happens with the catenary,
compressive ring forces are created. If it is
outside, tensile ring forces will occur, as with
the lower part of a hemispherical dome.

Tensile ring forces usually lead to failure.

Compressive ring forces usually do not cre-

ate problems, except when interrupted by

large openings.

Table14. 51gives the coordinates of the ideal

line of support for seven different dome

proportions, from h = 0.8 r to h = 1.4 r

(where h is the height and r the half-span),

without taking into account any openings

at the apex.

To take into account asymmetric loads

which might occur in practice due to wind,

maintenance etc., and to conservatively

ensure that no tensile ring forces occur, it is

better to keep the section inside the ideal

curve, especially in the upper part.

14.47 Optimised cross-

sections with different h:r

ratios

14.48 Cross-sections

14.49 Nubian vault

Parabola

Optimised section

Semicircle

Catenary

14.47

14.48

14.49