Studying the shape of a helical ramp

The main purpose of this paper is to clarify the classification of helicoids and to introduce several types of hclicoids to engineers in terms of geometry, stress-strain behavior and exploitation parameters for the practical tasks. Mathematically helical ramps are usually designed in the shape of a right helicoid which is well-known among civil engineers and designers, while mechanical engineers also know evolvent and convolute helicoids and use them for screws. The paper mostly focuses on the civil engineering and architectural helical structures such as ramps. It is shown that designers generally do not pay proper attention to the way the surface for a ramp can be formed from mathematical point. However, different types of helicoids (and ramps as final structures) show different stress-strain and buckling behavior. The review of existing classifications, methods of calculation and differences in geometry of all five types of ruled helicoids are presented. The clear classification which can be used by both mathematicians and engineers is shown, along with the most appropriate methods for calculation. The geometry and stress-strain behavior comparison of several types of helicoids is done in order to find forms which are the most rational for application to ramps and screw elements of buildings.