the difference between a parabola and a catenary
In: Mathematics
In terms of engineering forms:
A parabola is the deflected shape that forms when the load is uniform along the *span* of a member (assuming uniform stiffness and pinned ends).
A catenary is when the load is uniform along the *length* or *slope* of the cable. The difference is that the cable has a slope to it, so if you take a 1 foot span (horizontal) length near the ends there will be maybe 1.2 feet of cable sloping down, while at the mid span a 1 foot length of span will be basically 1 foot as the cable is essentially flat. This means there’s somewhat more load towards the ends of the span than there is at the middle.
So things like chains and power cables hang as catenaries, while something like a suspension bridge will be hang as a catenary during construction (prior to hanging the deck from the cables) but will be *mostly* a parabola once complete as the deck is much heavier than the cables and applies a mostly uniform load to the span.
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