Bock Hyeng 1 , S. Krivoshapko 2 1 Ph. Market St. Parametrical equations of the surfaces are presented and the influence of constant parameters containing in the equations of these surfaces on their form is studied in detail. All surfaces are pictured by means of computer graphics.
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Bock Hyeng 1 , S. Krivoshapko 2 1 Ph. Market St. Parametrical equations of the surfaces are presented and the influence of constant parameters containing in the equations of these surfaces on their form is studied in detail.
All surfaces are pictured by means of computer graphics. Architecture of spatial structures can be a main sphere of their application. Keywords: architectural engineering, differential geometry, geometric design, spatial structures, translational surface, umbrella-type surface, umbrella surface I. The domes with ribs known in architecture as umbrella shells attract special attention.
Besides strength, rigidity, and stability, they possess aesthetic and economic advantages and modern thin-walled structures give an opportunity to add lightness and airiness to them. The Roman emperor Hadrian first applied an umbrella shell as a covering of the villa in Tivoli built in — years.
Until the middle of the 20 th century, any principles of design of middle surfaces of umbrella domes were absent, and it delayed the development of methods of strength analysis. The erection of a reinforced concrete structure of an umbrella type without intermediate supports in Royan France is a new progressive phenomenon in the history of the application of umbrella shells. Horizontal sections of this covering are sinusoidal curves but diagonals have parabolic form.
Nervi and F. Candela also worked with umbrella shells and designed interesting buildings, for example, Church of the Priority, St.
But this definition narrows the class of umbrella surfaces. It is better to name these surfaces as hyperbolic paraboloid umbrella surfaces  or inverted, doubly-curved umbrella, hyperbolic paraboloid surfaces . According to another definition, an umbrella dome is a cyclical symmetrical spatial structure formed by several identical elements, but curves derived as a result of intersection of the middle surfaces of identical elements are generatrixes of any surface of revolution.
In some papers, umbrella domes are called multiple, pumpkin, melon, scalloped, or parachute domes. Contour surface is called dome-formed surface of revolution on which contour curves of dome elements are laid. Contour curves of the element are the curves limiting the contour of a middle surface of the dome element. Surfaces of umbrella type or umbrella-type surfaces are called cyclical symmetrical surfaces consisting of several identical elements. But a complete surface of umbrella type and all surfaces of its identical elements are described by the same Cartesian equation or by the same parametrical equations.
A monograph of G. Brankov  may be one of the first books on geometry of surfaces of umbrella type. Later, the descriptions of umbrella surfaces and surfaces of umbrella type as applied to realizable factory- made goods or buildings began to be published . In this paper, a class of surfaces of umbrella type is supplemented and broadened, and it can result in expansion of the sphere of their application.
Some of the umbrella forms were already applied, others are in the initial stage of their application, and the third will be used in the future, while the remaining ones will have only purely theoretical meaning. In this paper, the 16 new umbrella-type surfaces are proposed for the introduction in the architecture. Two new umbrella surfaces were applied in the real computer-aided design of the entertainment center. All equations of the examined surfaces were derived by the author with carrying out of the condition that a plane meridian passes through any point of www.
The analogous approach will be used in all parts of the paper. Availability of parametrical equations of umbrella-type surfaces clears wide possibilities for computer design.
Engineering Drawing Syllabus
Draw the curve traced out by a point P on the circumference, foe one complete revolution of the circle. Name the curve. Draw a tangent to the curve at a point on it 27 mm from the line. Procedure :- Draw a circle of diameter 40 mm and mark its centre as C.
Mikalar Online Help Let a second circle of radius 6 roll around the outside of the first circle without slipping. The rolling circle with a 60 mm diameter rolls along the arc of the circle with a mm radius Sirja How to construct an epicycloid with steps and procedures? Constructipn epicycloid is the curve epicycloif by a point on the circumference of the rolling circle. Coordinate system Si is rigidly connected to gear 1. Contact the MathWorld Team.