Advanced Methods of Structural Analysis

5.4 Cable with Self-Weight 125

which leads to the required relationship

HqCPDHq

p

1 C3C3^2 :

The sag of the cable

fqCPD

MCbeam

HqCP

D

ql^2

8

C

Pl

4

Hq

p

1 C3C3^2

Dfq

1 C2

p

1 C3C3^2

;fqD

ql^2

8Hq

:

LetDp=q lD0:2. In this case the thrust and sag of the cable are

HqCPDHq

p

1 C 3 0:2C 3 0:2^2 D1:31Hq;

fqCPDfq

1 C 2 0:2

p

1 C 3 0:2C 3 0:2^2

D1:068fq;

i.e., application of additional concentrated forceP D0:2qlleads to increasing
of the thrust and sag of the nonextensible cable on 31% and 6.8%, respectively.
Timoshenko was the first to solve this problem by other approach (1943).

5.4 Cable with Self-Weight

This section is devoted to analysis of cable carrying a load uniformly distributed
along the cable itself. Relationships between parameters of cable, its length, shape,
and internal forces are developed. The direct and inverse problems are considered.

5.4.1 Fundamental Relationships

A cable is supported at pointsAandBand loaded by uniformly distributed load
q 0 along the cableitself.This load presents not only dead load (self-weight of the
cable), but also a live load, such as a glazed ice. Cables of this type are called
thecatenary(Latin wordcatenameans a “chain”). It was named by Huygens in

1691. They-axis passes through the lowest pointC. Design diagram is presented
      in Fig.5.8. The following notations are used:sis curvilinear coordinate along the
      cable;W Dq 0 sis a total weight of portions;Nis a tension of the cable andH
      presents a thrust of the cable.
      For any point of the cable, relationship betweenN,H,andWobeys to law of
      force triangle:

ND

p

H^2 CW^2 : (5.21)