Advanced Methods of Structural Analysis

136 5Cables

Ta b l e 5. 2 Comparison
of parabolic and
catenary cables

Parabolic cable Catenary

f=l

ql

8H

.5:10/

H

ql



cosh

ql

2H

 1



.5:29/

tanmax

ql

2H

.5:9b/ sinh

ql

2H

.5:27/

Nmax

H

s

1 C



ql

2H

 2

.5:12/

r

1 Csinh^2

ql

2H

.5:28/

Some numerical results are presented in Fig.5.12and5.13. Comparison is made
for two types of cables having the sameql=Hratio.

Fig. 5.12 Dimensionless
sag–span ratio vs. total
load–thrust ratio for parabolic
and catenary cables

0.5 1.0 1.5 2.0 2.5 3.0 3.5 ql/H

0.0

f/l

0.1

0.2

0.3

0.4

0.5

0.6

Parabolic shape

Catenary

Fig. 5.13 Dimensionless
maximum cable
tension–thrust ratio vs. total
load–thrust ratio for parabolic
and catenary cables

0.5 1.0 1.5 2.0 2.5 3.0 3.5 ql/H

1.0

1.8

1.4

2.2

2.6

3.0

3.4

Nmax /H

Parabolic shape

Catenary

For thrust–shape problem the ratio ql=H is known. For relatively small
ql=H.<1:5/, dimensionless sagf=land maximum tensionNmax=Hfor parabolic
and catenary cables practically coincide. If loadqis fixed, then increasing ofql=H