Building with earth - Gernot MINKE (1)

14.47
14.49
14.47 Optimised crosssections
with different h:r
ratios
14.48 Cross-sections
14.49 Nubian vault
Parabola
Optimised section
Semicircle
Catenary
14.48
A more exact method to derive ideal curve
is by graphic methods used in statics engineering.
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 14.48 shows 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 create
problems, except when interrupted by
large openings.
Table 14.51 gives 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.
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Designs of building elements