Advanced Methods of Structural Analysis

124 5Cables

The formulas above allows considering very important problem determining the
changeof the parameters of the cable if additional live loads are applied.

Example 5.2.The flexible, inextensible, and gentile cable is suspended between
two absolutely rigid supports of same elevation. The total length of the cable isL
and span equalsl. The cable is subjected to uniformly distributed dead loadqwithin
the horizontal line; corresponding thrust and sag areHqandfq. Calculate achange
of the thrust and sag of the cable, if the entire cable upon the loadqis loaded by
additional concentrated live loadPat the axis of symmetry of the cable (Fig.5.7).

Fig. 5.7 Cable carrying
uniformly distributed loadq
with additional forceP

RA RB

HH

l/ 2 l/ 2

AB

P

fq

f

q

a 1

yq

yq+P

L

Solution. If a cable is loaded by uniformly distributed loadqonly then load char-
acteristic isDqDq^2 l^3 =12.
Corresponding trust and sag areHqandfq. In this case (5.19) becomes

LDlC

1

2Hq^2

q^2 l^3

12

(a)

If additional loadPis applied at the middle of thecable then loadcharacteristic
accordingly (Table A.21, line 5) becomes (the subscript 1 is omitted)

DqCPD

q^2 l^3

12

.1C3C3^2 /; D

P

ql

:

Thus (5.19) becomes

LDlC

1

2Hq^2 CP

q^2 l^3

12

.1C3C3^2 /; (b)

whereHqCPis thrust due to the both loadsqandP.
Since the cable is inextensible then left parts of the (a) and (b) are same, therefore

lC

1

2Hq^2

q^2 l^3

12

DlC

1

2Hq^2 CP

q^2 l^3

12

.1C3C3^2 /;