sir/madam,
would please help me by giving information on hyperboloid structures.

HYPERBOLOID STRUCTURES
Hyperboloid structures are architectural structures designed with hyperbolic geometry. Often these are tall structures such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, but hyperboloid geometry is also often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer Vladimir Shukhov (1853–1939).[1] The world's first hyperboloid tower is located in Polibino, Dankovsky District, Lipetsk Oblast, Russia.[/font]
Properties of hyperboloid structures

[color=#1E90FF]Hyperbolic structures have a negative Gaussian curvature, meaning they curve inward rather than outward or being straight. As doubly ruled surfaces, they can be made with a lattice of straight beams, hence are easier to build and, all else equal, stronger than curved surfaces that do not have a ruling and must instead be built with curved beams. Hyperboloid structures are superior in stability towards outside forces than "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency) and therefore are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features.
With cooling towers, a hyperbolic structure is preferred. At the bottom, the widening of the tower provides a large area for installation of fill to promote thin film evaporative cooling of the Circulated water. As the water first evaporates and rises, the narrowing effect helps accelerate the laminar flow, and then as it widens out, contact between the heated air and atmospheric air supports turbulent mixing.
These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built his first example as a water tower (hyperbolic shell) for the 1896 All-Russian Exposition. Subsequently, more have been designed by other architects, including Le Corbusier, Antoni Gaudí, Eduardo Torroja, Oscar Niemeyer and Ieoh Ming Pei.
The shapes are doubly ruled surfaces, which can be classed as:
Hyperbolic paraboloids, such as saddle roofs
Hyperboloid of one sheet, such as cooling towers

Hyperbola

Before you can understand what our project is you must first understand how it is formed from a hyperbola. A hyperbola is a curve, specifically a smooth curve that lies in a plane. A hyperbola has two pieces, called connected components or branches, which are mirror images of each other and resembling two infinite bows. The hyperbola is one of the four kinds of conic section, formed by the intersection of a plane and a cone. The other conic sections are the parabola, the ellipse, and the circle. The conic section that is formed depends on the angle the plane makes with the axis of the cone, compared with the angle a line on the surface of the cone makes with the axis of the cone. If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the conic is a hyperbola.
== Hyperboloid Structures ==

The equation for a hyperboloid is x2/a2 + y2/b2 - z2/c2=1 ,but it can also be defined by its physical properties. Hyperboloid structures have a negative Gaussian curvature, meaning they curve inward rather than outward or being straight. The structure is also a doubly ruled surfaces, which means it can be made with a crossing pattern of straight beams, hence are easier to build and are equal in length and area, also it makes the structure stronger than curved surfaces that must be built with curved beams. Another way to explain a doubly ruled surface is to describe it as a surface of revolution, which is symmetrical from above and whatever is true from on horizontal direction will also be true from any other direction. If you were to look down the x-axis, positive side and you found a place on the plane lets say the point is (a,0,0) you would plug those coordinates into the equation and you should come up with y^2/a^2=z^2/c^2 and then you cross multiple and you get + or - cy=az which in simple english means you have a straight line. Hyperboloid structures are superior in stability towards outside forces than "straight" buildings because of the distribution of weight from the negative Gaussian curvature, but they have shapes often creating large amounts of unusable volume and therefore are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers (for air flow and strength), and aesthetic features. [/font]