Una cuerda pesada, flexible, inextensible y suspendida de dos puntos toma la forma de la catenaria. Esta catenaria es una curva plana cuya ecuación empleando coordenadas cartesianas (contenidas en el plano de la curva) y escogidas de manera que el eje Y coincida con el mínimo de la curva, resulta ser:.

La curva es simétrica con respecto al eje y, y cerca del punto más bajo se asemeja mucho a la parábola . Esta parábola pasa en todos los puntos por debajo de la catenaria. Esta curva tiene las siguientes propiedades:.

Generalizations

In general, the catenary equation refers to infinitely flexible and inextensible chains or ropes. The requirement of infinite flexibility refers to the fact that the flexural rigidity is zero and the requirement of inextensibility refers to the fact that the length of each section does not vary despite being subjected to forces. Obviously in real strings these requirements are only approximately met. For long ropes, the elasticity of the rope distances them from perfectly inextensible behavior. Although the catenary of an inextensible rope is always a flat curve, for thick cables of short length the finite flexural rigidity means that its deformation is not necessarily contained in a plane.

Given a linear element subjected only to vertical loads, the catenary shape is precisely the shape of the barycentric axis that minimizes stresses. This property can be used for the design of arches. In this way, an arch in the shape of an inverted catenary is precisely the way in which the appearance of stresses other than compression stresses, such as shearing or bending stresses, is avoided.

For this reason, an inverted catenary curve is a useful layout for an arch "Arch (construction)") in architecture, a form that was applied, among others, and fundamentally, by Antonio Gaudí, who used models to study these structures, and then put that information into the plans of his works.

Una cuerda pesada, flexible, inextensible y suspendida de dos puntos toma la forma de la catenaria. Esta catenaria es una curva plana cuya ecuación empleando coordenadas cartesianas (contenidas en el plano de la curva) y escogidas de manera que el eje Y coincida con el mínimo de la curva, resulta ser:.

La curva es simétrica con respecto al eje y, y cerca del punto más bajo se asemeja mucho a la parábola . Esta parábola pasa en todos los puntos por debajo de la catenaria. Esta curva tiene las siguientes propiedades:.

Generalizations

In general, the catenary equation refers to infinitely flexible and inextensible chains or ropes. The requirement of infinite flexibility refers to the fact that the flexural rigidity is zero and the requirement of inextensibility refers to the fact that the length of each section does not vary despite being subjected to forces. Obviously in real strings these requirements are only approximately met. For long ropes, the elasticity of the rope distances them from perfectly inextensible behavior. Although the catenary of an inextensible rope is always a flat curve, for thick cables of short length the finite flexural rigidity means that its deformation is not necessarily contained in a plane.

Given a linear element subjected only to vertical loads, the catenary shape is precisely the shape of the barycentric axis that minimizes stresses. This property can be used for the design of arches. In this way, an arch in the shape of an inverted catenary is precisely the way in which the appearance of stresses other than compression stresses, such as shearing or bending stresses, is avoided.

For this reason, an inverted catenary curve is a useful layout for an arch "Arch (construction)") in architecture, a form that was applied, among others, and fundamentally, by Antonio Gaudí, who used models to study these structures, and then put that information into the plans of his works.