Arch Structures: Form and Equilibrium

• By arranging material along the opposite profile of a sagging cable, it is possible to make a spanning structure that works in pure compression.

• It is common to use arches with pin supports and an internal hinge connection. This configuration is called a three-hinged arch. They were particularly popular in the 19th and early 20th centuries because they are statically determinate.

Unbalanced Loading

• Unlike cables, which can reconfigure to a different stable profile when the load pattern changes, arches cannot.

• A loading that does not correspond to the arch's funicular profile will be called a non-funicular loading or unbalanced loading.

• The bending moment due to an unbalanced loading pattern on a three-hinged arch can be calculated as the horizontal reaction times the deviation of the arch from the load pattern's funicular profile which passes through the hinge.

  M_b(x) = Hd(x)

  Mb(x)	=	Bending moment in the arch rib at location x.
  H	=	The horizontal reaction.
  d(x)	=	The deviation at point x of the structure from the funicular profile of the load

  

  

• Typically, an arch's profile is based on the funicular profile corresponding to dead load acting alone, and the arch rib is designed to resist shear and bending moments resulting from unbalanced live loads. The arch must be designed to resist both extremes.

• It is common to vary the depth of the rib member according to the pattern of the moment for unbalanced loading.

  

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