Building with Earth: Design and Technology of a Sustainable Architecture

121 Designs of building elements

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 seg-

ments 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 pro-

portionally decreased. If the ideal form is to

be derived from a model, then, correspon-

ding 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 consid-

ered a first approximation, which is in prac-

tice sufficiently accurate for smaller spans.

Greater accuracy can be achieved by suc-

cessive 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

14.43 14.44

14.45 14.46

14.42