Advanced Methods of Structural Analysis

110 5Cables

a

Anchor

span

Anchorage

Pillar

Hangers

Main span

Sag

Fig. 5.1 Suspension bridge

Another feature of cables is the high sensitivity of their shape, depending on the

total length of the cable, type of the load as well as a load location along the span.

The fundamental feature of a cable is its unknown shape in advance. Defining the

shape of a cable is one of the important problems.

The following types of external loads will be considered:

1.Cable with self-weight ignored (a cable subjected to concentrated loads, to uni-
formly distributed load as well as to arbitrary dead load and after that additional
any live load).
2.Cable with self-weight.

Under these loads the cable shape takes different forms. Shape of a cable in case of

concentrated loads is referred to slopes of straight portions of a cable. Shape of a

cable in case of distributed load along horizontal and along cable itself are parabola

and catenary, respectively.

Assumptions

1.The cable is inextensible one (elastic properties of the cable will be considered
in Sect.5.6).
2.The cable is perfectly flexible, i.e., the cable does not resist to shear and bending.
In this case the internal force in any point of a cable is tensile one, which is
directed along the tangent to this point of a cable.
Horizontal component of a tension force is called a thrust. Later it will be shown
that thrust remains constant along the length of the cable.

5.1.1 Direct and Inverse Problems.................................

The simplest problem is finding thrust, internal forces, and total length of a cable

if the shape of a cable is given. Solution of this problem is well known. However,