### CHAPTER VII - WARPED SURFACES

Warped surfaces have a great advantage for shell structures because they may be formed from straight form boards even though they are surfaces of double curvature. There are two types which are most useful: the conoid, which, as its name suggests, is a portion of a cone, and the hyperbolic paraboloid, a name for a particular mathematical surface. This type of shell structure can be built to what appears to be the ultimate in lightness of construction, minimum reinforcing and ease of moving forms.
Stresses in the hyperbolic paraboloid shell are almost entirely membrane (direct tension and compression), and all forces are delivered as shear parallel to the stiffening ribs. The shell thickness in structures built by Candela in Mexico, is on and one-half inches except for slight extra thickness at the intersection of the surfaces. This dimension is based on a cover of one centimeter on each side of two layers of bars and not an any structural requirement for strength. In this country, using No. 3 bars, (3/8 inch diameter), and a cover of ¾ inches, a minimum thickness of 2 ¼ inches is required.