Cable Structures: Equilibrium

• It is possible to configure structural elements that have high strength and stiffness in tension, while have low or zero strength in compression, bending, and shear.
  • Ropes
  • Chains
  • Cables

• Since such elements cannot resist compression, bending or shear, they do not maintain their shape (e.g. they are unstable) under changing loads.

• The shape assumed by a cable is determined by requirements of statics.

• The shape is such that the cable's internal forces are tension only along it's axis.

• The following observations are true for the case of a horizontal span with vertical loads.

  • The shape of the cable is proportional to the moment diagram for the span and loading condition.

  • Specifically, the moment of the span at a point is equal to the sag of the cable at that point times the horizontal reaction of the cable.
    M(x) = H Y(x)

    where:

    M(x)	=	The value at point x along the span of the moment diagram for a beam with the same span and load condition.
    H	=	The horizontal support reaction for the cable.
    Y(x)	=	The sag of the cable at point x along the span.

  • This means that the proportionality factor between the moment diagram and the cable shape is equal to the horizontal reaction.

  • Therefore, increasing the sag of a cable decreases the horizontal reactions proportionally, and decreasing the sag increases the horizontal reactions proportionally.

  • The vertical component of the cable's internal tension is equal to the shear diagram value for the span and loading condition.