Advanced Methods of Structural Analysis

5.6 Effect of Axial Stiffness 137

caused by decreasing of the thrust leads to increasing of the sag. If thrustHis fixed,
then increasing ofql=Hcaused by increasing of the loadqleads to increasing of
the slope of the cable at support point, and as a result, increase in maximum internal
forceNmaxin cable.

5.6 Effect of Axial Stiffness

So far we have considered behavior of a cable without accounting for elastic prop-
erties of a cable itself. Elastic properties of a cable have considerable importance
in the distribution of tension of a cable and value of sag. Procedure of analysis of
elastic cables is presented below. Two casesare considered: cablewith concentrated
and uniformly distributed loads.

5.6.1 Elastic Cable with Concentrated Load

Design diagram of elastic cable is presented in Fig.5.14. The forcePis applied at
xDl=2. In the deformable state of thecable the sag and inclination arefand ̨,
respectively. Nondeformable length of the cable isL 0. It is necessary to calculate
the thrust and sag of the cable taking into account the stiffness of the cableEA.

Fig. 5.14 Elastic cable
subjected to concentrated
load

P

RA

a

x

HH

RB

y

l/ 2

l

A B

f

C

It is evident that the angle of inclination,y-coordinate, and sag of the cable at
pointCare

tan ̨D

RA

H

D

P

2H

yD

l

2

tan ̨D

Pl

4H

;fD

Pl

4H

:

Tension in the left and right portions of a cable may be presented in the form

ND

H

cos ̨

DH

p

1 Ctan^2 ̨DH

r

1 C

P^2

4H^2

: