Advanced Methods of Structural Analysis

5.5 Comparison of Parabolic and Catenary Cables 135

Expressions (5.36) allows calculating the tension at supportsAandB

NAD1:7834

r

1 Csinh^2

18:34

127:41

D1:802kNI

NBD1:7834

r

1 Csinh^2

18:34C 100

127:41

D2:609kN:

Control. Ordinates of support points are

yADacosh

xA

a

D127:41cosh

18:34

127:41

D128:73mI

yBD127:41cosh

18:34C 100

127:41

D186:43m:

Vertical distance between pointsAandBequalsh 0 DyByAD186:43m
128:73mD57:7m.
Equilibrium equation

P

YD 0 for cable in whole leads to the following result

NAsinACNBsinBL 0 qD1:8020:1431C2:609

0:7304117:70:014

D1:9057C1:9056Š0:

Pay attention that vertical reaction of the supportAis directeddownwardas shown
in Fig.5.11.
Trust can be calculated by formulas

HDNAcosAD1:8020:9897D1:783;

HDNBcosBD2:6090:6830D1:782:

5.5 Comparison of Parabolic and Catenary Cables

Let us compare the main results for parabolic and catenary cables. Assume, that
both cables are inextensible, supported on same elevation, and support points does
not allow to mutual displacements of the ends of the cable. Both cables have the
same spanl, subjected to uniformly distributed loadq.Iftheloadqis distributed
within the horizontal foot then a curve of the cable is parabola (parabolic shape),
if the load is distributed within the cable itself, then curve of the cable is cate-
nary. Table5.2contains some fundamental parameters for both cables. They are
dimensionless sag–span ratiof=l, slope tanat the supports and dimensionless
maximum cable tension–thrust ratioNmax=H. Correspondence formulae are pre-
sented in brackets. The formulas for parabolic cable may be derived if hyperbolic
functions to present as series sinhzDzC.z^3 =3Š/C:::I coshzD^1 C.z^2 =2Š/C:::.