When the interior must be kept free, then the framing may be composed of a succession of ribs standing upon a continuous circular curb of timber, as seen at Figs. 95 and 96 - the latter being a plan and the former a section. This curb must be well secured, as it serves in the place of a tie-beam to resist the lateral thrust of the ribs. In small domes these ribs may be easily cut from wide plank; but where an extensive structure is required, they must be built in two thicknesses so as to break joints, in the same manner as is described for a roof at Art. 231. They should be placed at about two feet apart at the base, and strutted as at a in Fig. 95.

236 Ribbed Dome 127

Fig. 96.

The scantling of each thickness of the rib may be as follows:

For domes of 24 feet diameter, 1 x 8 inches.

"

"

"

36

"

"

1 1/2

x

10

"

"

"

"

60

"

"

2

x

13

"

"

"

"

90

"

"

2 1/2

x

13

"

"

"

"

108

"

"

3

x

13

"

237. - Dome: Curve of Equilibrium. - The surfaces of a dome may be finished to any curve that may be desired, but the framing should be constructed of such form that the curve of equilibrium shall be sure to pass through the middle of the depth of the framing. The nature of this curve is such that, if an arch or dome be constructed in accordance with it, no one part of the structure will be less capable than another of resisting the strains and pressures to which the whole fabric may be exposed. The curve of equilibrium for an arched vault or a roof, where the load is equally diffused over the whole surface, is that of a parabola (Art. 460); for a dome having no lantern, tower, or cupola above it, a cubic parabola (Fig. 97); and for one having a tower, etc., above it, a curve approaching that of an hyperbola must be adopted, as the greatest strength is required at its upper parts. If the curve of a dome be circular (as in the vertical section, Fig.95), the pressure will have a tendency to burst the dome outwards at about one third of its height. Therefore, when this form is used in the construction of an extensive dome, an iron band should be placed around the framework at that height; and whatever may be the form of the curve, a band or tie of some kind is necessary around or across the base.

Curve Of Equilibrium
Curve Of Equilibrium 128

Fig. 97.

If the framing be of a form less convex than the curve of equilibrium, the weight will have a tendency to crush the ribs inwards, but this pressure may be effectually overcome by strutting between the ribs; and hence it is important that the struts be so placed as to form continuous horizontal circles.