HYPERBOLIC PARABOLOIDAL SURFACE
The hyperbolic paraboloid surface is so useful for shell structures that it is important to describe the method of constructing the surface. It is formed in the following manner: 1) Lines OA and OB are level and at right angles to each other, 2) Lines AC and C are also level and are shown above and dotted, 3) Point C* is directly below point C, 4) Mark off equal intervals on line OB and divide line AC* into the same number of increments (but of slightly greater length). Connect intervals on line OB with those on line AC* with straight lines, 5) Repeat for OA and BC*, 6) The surface formed by this network is a hyperbolic paraboloidal surface.
In practice, lines OA and OB may not be level and at right angles to each other and point C* may be above C. Also, only part of the surface may be used, so that the boundaries are not along OA, OB, BX* and AC*.
Note that a diagonal from A to B has a sag which is in the shape of a tension catenary. The diagonal OC* (not drawn above) has a corresponding arch shape.