Advanced Methods of Structural Analysis

5.1 Preliminary Remarks 111

for practice this type of problem does nothave a reasonable sense because shape

of the cable cannot be known in advance. Instead, an engineer knows allowable

horizontal force, which a tower can resist at the top. Based on this, we will consider

the following two fundamental practical problems for cables under fixed loads:

1.Find the shape of a cable and internal forces, if a thrust is given. This type of
problem is called the thrust–shape problem.
2.Compute thrust and internal forces, if a total length of a cable is given. This type
of problem is called the length–thrust problem.

5.1.2 Fundamental Relationships..................................

Let us consider a cable shown in Fig.5.2a. The cable is loaded by some vertical

concentrated loadsPi(the distance from left support arexi/and arbitrary loadq

distributed along horizontal. The self-weight of the cable may be neglected if this

weight comprises no more than 10% of an external load on the cable. Since the cable

is perfectly flexible, then axial forceNxat any section is directed along tangent at

this section. Axial forcesNAandNBat the supportsAandBare resolved into

two directions. They are the vertical direction and directionA–B. These forces are

b

H

N(x)

Q(x)

θ

NA

x

RA

y

H

N(x)

θ

x

q

P

α

K

A

a

q(x)

x dx

xi

Pi

rA

l

c

rB

hA A

φ

C B

NA

hB

NB

fC f 1 C

x

H

K

c

x

x dx

q

N

y N+dN

H

Q

H

Q+dQ

Fig. 5.2 (a) Cable subjected to arbitrary load; (b) free-body diagram of the part of the cable;

(c) free-body diagram of the elementary portion of the cable