Civil Engineering Reference
In-Depth Information
and the treads sui ciently extended to af ord convenient working space, then a
pyramid of any height can be erected out of massive blocks without any installa-
tions other than the previously erected structure itself. On the other hand if the
faces of the pyramid are to be plane and inclined at an angle to the horizontal of
ca 50°, then:
Stepped
& true
pyramids
(a) blocks can not be levered up into position.
(b) h ey can not be lit ed into position vertically—unless the lit can be made to
transfer them horizontally over a distance of roughly the same order as the height
they have been lit ed (cf F. Abitz, “Shrägaufzug,”
ZAS
119, 1992, pp. 61-82).
h us they can be raised only by providing external ramps for hauling or steps for
levering, both of which involve massive constructions in themselves.
Here it is also to be noted that the antithesis goes not only to the construction
but also to the setting out and controlling of the exactitude of the structure erected
(cf P. Hodges,
How the Pyramids were Built
, Chap. 5, Setting out).
To set out the plan of a stepped pyramid all that is necessary is to mark out on
the ground the lines of a square somewhat larger than that of the designed plan
and to put down control points on these lines indicating the alignment of the
sides of the base of the pyramid. h ereat er the lines of the successive steps are
obtained by direct measurement inwards from the sides of the preceeding step.
Equally simply, the elevation is determined by i rst building the base as a level
platform and then directly measuring upwards from the previous level the rise of
each subsequent step.
h e setting out and control of a true pyramid, however, is a very dif erent
matter. h e base plan is obtained as described above but controlling the correct
construction in elevation is in no way simple.
Local checks on the plane surface of the sides can be ef ected by applying a
straight edge and checks on the correct angle of inclination by applying an appro-
priate triangle equipped with a plumb bob. However the overall exactitude of the
massive structure in elevation is revealed immediately to the eye only at the arrises,
the intersections of the four faces. h ese form four lines inclined upwards and
inwards from the base angles to the apex or summit of the pyramid, i.e. they lie
on the vertical planes of the diagonals. If these lines deviate in any way, this will
be apparent to view (whereas e.g. divergence from a plane surface in the sides of
a pyramid is not immediately visible to the naked eye. h us to control the exacti-
tude of construction of a pyramid some device must be available to check on the
rectilinearity of the arrises.
In modern times this would be ef ected by producing the diagonals of the pyra-
mid and setting up 4 theodolites, one at each extremity of the produced diagonals;
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