Advanced Methods of Structural Analysis

5.3 Effect of Arbitrary Load on the Thrust and Sag 123

Usually this formula is written in the following form

LDlC

D

2H^2

;DD

Zl

0

Q^2 .x/dx (5.19)

Table A.21, contains the load characteristicDfor most important cases of loading.

Equation (5.19) allows present the thrustHin terms of load characteristicDas

follows

HD

s

D

2l.l 0 1/

;l 0 D

L

l

(5.20)

It is possible to show that if support pointsAandBof the cable are located on the

different elevation then

LD

l

cos'

C

D

2H^2

cos^3 ';

where'is angle between chordABandx-axis.

Formulas (5.18)–(5.20) entirely solve the problem of determination of the thrust

of inextensible gentile cable with supportswithout their mutual displacements, sub-

jected toarbitraryvertical load. These formulas are approximate since for their

deriving have been used in approximate relationship (5.17).

Application of expression (5.20) for some classical loading cases is shown below.

1.A cable with total lengthLand spanlcarries a concentrated forcePthroughout
distanceastarting from the left end of the cable (Fig.5.3). Let’s dimensionless
parameters bel 0 D L=l D1:2and D a=l D0:4. Load characteristicD
(Table A.21) isDDP^2 l .1 /DP^2 l0:4.10:4/D0:24P^2 l.

The thrustHD

s

D

2l.l 0 1/

D

s

0:24P^2 l

2l.1:21/

D0:7746P. The exact solution is

HD0:7339P(Sect.5.2, Inverse problem). Error is 5.54%.

2.The cable of total lengthLand spanlcarries a uniformly distributed load
q(Fig.5.4). Load characteristic isD D q^2 l^3 =12(Table A.21). According to
formula (5.16)
l 0 D

L

l

Š 1 C

8

3

f^2

l^2

:

Therefore the thrust becomes

HD

s

D

2l.l 0 1/

D

v

u

u

u

t

q^2 l^3

12 2l



1 C

8

3

f^2

l^2

 1

D

ql^2

8f

:

This exact result has been obtained earlier by using formula (5.10).