What is a catenary system?

Answer 1

The mathematical equation for creating a catenary curve is: y=acosh(x/a)

'a' is a variable, x and y are the axis of the graph. The steepness of the curve is inversely proportional to the size of the variable.

To answer the question less mathematically, the "catenary solution" is one where the engineer is able to reduce tensile stress within a structure and replace it with compressive stress. Put another way, a catenary arch is massively strong under compression, and requires almost no tensile strength to remain upright. It is therefore much stronger and more stable than conventional circular arches, in the absence of reinforcing steel, which provides the tensile strength in reinforced concrete structures.

Catenary arches are, and have been, widely used in the construction of kilns. Kilns are incredibly harsh environments, and the materials used to make them must withstand massive, rapid and frequent changes in temperature. Such changes tend to destroy the tensile strength of materials (things get brittle when you bake them), and so a structure possessing almost no need for tensile strength is a natural winner for building kilns.

A third way of answering this question is to say "Go hang a chain from two posts." The latin word catena means "chain", and it is from the curve of suspended chains and ropes that we derive the most natural and frequent catenary curves.

So the answer for the question "what is the catenary solution" is very much a question of the discipline to which it relates. It is a very poorly worded question, most likely put forward by a mathematician. Mathematics is a concise and specific language, where neat answers respond to neat questions, offering great enlightenment in the process. Regrettably, mathematicians often confuse the very complex and rich language of English for the language of mathematics, and thus ask very simple questions that they imagine will generate enlightening answers with merely a few words in response.

Sadly, the English language is full of complex curves and angles, and it is never quite apparent what sort of arrangement of words might stand up in argument, and which set may fail under load. Therefore is fair to submit that the final catenary solution is prison: for the accused to be chained to a wall and hung there, as due punishment for asking simple questions about complex things.

This last solution combines the three disciplines of mathematics, physics and philosophy, and so I offer it as the best all round solution for people who ask these sorts of questions.