Advanced Methods of Structural Analysis

116 5Cables

After that, the shape of the cable and internal forces in the cable may be defined

easily.

The special caseaD0:5lleads to the following results for thrust and sag

HD

P

2

q

l^20  1

;

fD

Pl

4H

D

l

2

q

l 02 1:

There are some interesting numerical results. Assume thatl 0 DLl D1:01.Inthis

casef D0:071 l, so if the total length of the cableLexceeds the spanlonly by

1%, then sag of the cable comprises 7% of the span.

5.2.2 Cable Subjected to Uniformly Distributed Load

Distributed load within the horizontal projection of the cable may be considered

for the case when the hangers (Fig.5.1) are located very often. Design diagram of

flexible cable under uniformly distributed load is presented in Fig.5.4.

Fig. 5.4 A cable under

uniformly distributed load

y

x

q

l

x

RB

H

RA

H

A

y(x)

B

5.2.2.1 Direct Problem

ThrustHof the cable is given. Determine the shape of the cable and calculate dis-

tribution of internal forces. For solving of this problem we will use two approaches.

1.Integration of fundamental equation of a flexible cable (5.8) leads to following
expressions for slope and shape of the cable

dy

dx

D

q

H

xCC 1 ;

yD

q

H

x^2

2

CC 1 xCC 2 :