Building with earth - Gernot MINKE (1)

14.43 14.44
14.42
14.45
and divided into segments of equal length.
This gives segments of identical area and,
therefore, can be substituted by single loads
of equal magnitude acting at the centre of
each segment. However, in the case of a
dome, if we take a slice, as shown in the
figure on the right, and divide this into segments
of equal length, the widths and,
therefore, the areas are continuously
decreasing from the base to the apex. If
these segments are substituted by single
loads, then their loads are also thereby proportionally
decreased. If the ideal form is to
be derived from a model, then, corresponding
loads can be added to a chain which
then forms this ideal curve, as seen in 14.45.
Here, this ideal curve is shown in contrast
to a catenary. In 14.46, formulas are given
for calculating areas of the segments of a
sphere. However, since the ideal form is not
spherical, its segments have an area slightly
differing from the one that we started from.
Therefore, this procedure has to be considered
a first approximation, which is in practice
sufficiently accurate for smaller spans.
Greater accuracy can be achieved by successive
iterations, substituting the actual
changing radii of curvature of the segments
measured from the model and adjusting
the loads according to the surface areas of
the segments thus calculated.
The first assumption (that the dome is a
hemisphere) cannot be used if the height is
not equal to the half-span. In this case, one
should start from the shape of an ellipse
whose axis is below the base of the dome.
This stating assumption is already close to
the ideal form, which can then be refined
by the model.
Vault
14.46
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Designs of building elements