Advanced Methods of Structural Analysis

Problems 143

(a)Derive equation, which connects parametersq 0 ,l,H,andk
(b)Calculate the sag–span ratio for which the maximum tension in the cable is
equal to 0.75 of the total weight of the entire cable and corresponding value of
maximum tensionNmax.

Ans. (a).4k^2 1/sinh^2

q 0 l

2H

D 1 ; (b) 0.2121,NmaxD0:8337q 0 l

5.10.A uniform cable of weightq 0 per unit length, is suspended between two points
at the same elevation and a distancelapart. Determine the sag–span ratio, for which
the maximum tension is as small as possible.

Ans.fl D0:3377

5.11.A uniform cable of weightq 0 per unit length is suspended between two points
at the same elevation and a distancelapart. The sag of the cable, total length, and
thrust are denoted asf,L,andH, respectively. Calculate the maximum tensile
force. Present the result in three following forms (1) in terms ofH,q 0 ,l;(2)in
terms ofH,q 0 ,f; (3) in terms ofH,q 0 ,L

Ans. (1)NmaxDHcosh

q 0 l

2H

;(2)NmaxDq 0 fCH;(3)NmaxDH

s

1 C



q 0 L

2H

 2

5.12.Design diagram of flexible cable with support pointsAandBon different
levels, is presented in Fig.P5.12. The cable is subjected to linearly distributed load
q. At the middle pointCthe sag isfD4:5m. Find the shape of the cable, thrust,
and calculate distribution of internal forces. Parameters of the system are:lD 60 m,
cD 12 m,qD2:0kN=m. Use the concept of the reference beam.

l R

B

RA H

H

A

B

c

NA q

aA

NB

aB

Fig. P5.12

Ans.H D 100 kN,NAD107:76kN,NBD101:83kN,RAD 40 kN,RBD
20 kN