Advanced Methods of Structural Analysis

130 5Cables

Equation of the curve and ordinateyfor support points are

y.x/D

H

q 0

cosh

q 0

H

xD4:42cosh0:22642x;

ymaxD4:42cosh

1:25

5:525

10 D21:46m:

Sag of the cable at lowest point C isfD21:464:42D17:04m.

5.4.3 Cable with Supports Located on the Different Elevations

In this case the shape of the cable is nonsymmetrical and position of the lowest
pointCis not known ahead. Availability of only two parameters, such as load per
unit length of the cableq 0 and spanl, are not enough for cable analysis. For deter-
mination of location of pointCwe need to formulate additional condition for curve
y.x/passing through pointsAandB. One of the additional parameter may be as
follows (1) Value of thrustH; (2) Total lengthL; (3) Coordinates of any additional
point of the cable. Two different cases are considered below. They are a saddle point
within or outside of the span.

5.4.3.1 Saddle Point Within the Span

The following example illustrates the thrust–length procedure of analysis of the
cable and corresponding peculiarities.

Example 5.4.A uniform cable with self-weightq 0 D1:25kN=m is suspended be-
tween two pointslD 20 m apart horizontally, with one point of support 18 m higher
than the other as shown in Fig.5.10. Thrust of the cable isHD5:6kN. Determine
shape of the cable, tension at supports, and total length of the cable. Assume that a
saddle point is placed between supports.

Fig. 5.10 Cable, carrying a
uniformly distributed load
along the cable itself

A

h

a

x

B

y

C

l=20m

18m

O

l 1 l 2