Catenary reconsidered

Application of catenary structures must be carefully considered for use in different environments.  A few examples worth looking at include:

·        An environment without gravity.  If a structure is built in space, or acts as a satellite, or is built in conditions of very low gravity (like on an asteroid, or the moon, or even a buoyant ball) then the reasons for a catenary structure practically disappear.  Under these conditions a sphere or spherical dome is the optimal structure.

·         Very high external pressure.  If a structure is submerged to any depth, then an outside compressive force acts on the entire structure.  Under these conditions, again we find that a sphere is the strongest and most stable structure.  A catenary structure under great external pressure is weaker than a spherical structure.  (Do you ever crack an egg at the tip? No, you crack it on the weak side.)

·         Extreme loading from high velocity winds.  Such conditions are found in extreme storms, including hurricanes, typhoons, and tornadoes.  Under these conditions, the exposed surface area per unit volume is minimized by using a spherical form.  The profile is further minimized by using only a smaller segmental section of the spherical form, further reducing the profile of the structure.  A woven tensile geodesic web will help blocks resist suction forces in very high winds.

·         Earthquakes.  A catenary arch results from acceleration due to gravity.  In an earthquake, the ground can move in a sudden sideways fashion.  This results in acceleration in a sideways or lateral sense.   If a chain hangs from a rod, and the rod is tipped or inclined away from horizontal, then the catenary changes relative to the rod: the same way thrust force lines in a dome change relative to the horizontal ground movement during an earthquake. 

This situation is as if the arch was built on an inclined surface; the catenary still exists, but it is like a catenary on an inclined surface.  The direction of the inclined surface is relative to the motion of the ground.  The result of this sideways acceleration is that the catenary arch may eventually touch or exit the wall thickness; a hinge is created and the structure will buckle and collapse. 

Catastrophic failure of masonry arches during earthquakes can be prevented by using tensile elements woven into the arches as great circle arcs.  This geodesic tensile web will prevent the creation of hinges, catenary thrust force lines will not exit the wall thickness due to lateral acceleration.   Structural integrity is maintained if the hinges cannot open.   Tension is provided.

Tensile elements woven into a dome will help hold it together during an earthquake.