142 5Cables
(a)ThrustHis (1) remains the same; (2) twice as much; (3) half as much
(b)Maximum axial force is (1) remains the same; (2) twice as much; (3) half as
much
(c)Slope at the support is (1) remains the same; (2) twice as much; (3) half as much
5.6.The cable with support points on the same elevation is subjected to uniformly
distributed loadqalong horizontal projection of the cable. The span of the cable is
lm. If loadqincreases by two times, but the thrustHremains the same, then
(a)Sag of the cable is (1) remains the same; (2) greater; (3) twice as much; (4) half
as much.
(b)Maximum axial force is (1) remains the same; (2) greater; (3) twice as much;
(4)halfasmuch.
(c)Slope at the support is (1) remains the same; (2) greater; (3) twice as much; (4)
half as much.
5.7.The flexible inextensible cable with support points on the same levels is sub-
jected to uniformly distributed loadq 1 andq 2 within the horizontal line, as shown
in Fig.P5.7; the span of the cable islm and maximum sag isf. Calculate the thrust
of the cable. Consider limiting casesq 1 Dq 2 andq 2 Dq 1.
H HlAB
f
aq (^1) q
2
b
Fig. P5.7
Ans.HD
q 1 a^2 C2q 2 blq 2 b^2
2
8q 2 fl^2
5.8.The flexible inextensible cable with support points on the same elevation is
subjected to uniformly distributed loadqwithin the horizontal line; the span of the
cable islm. Derive expression for maximum tensionNmaxin terms of sag-to-span
ratio ̨Df=l.
Ans.NmaxD
ql
8
1
̨
p
1 C16 ̨^2
5.9.A uniform cable of weightq 0 per unit length is suspended between two points
at the same elevation and a distancelapart. Let the maximum axial forceNmaxand
total weight of the cableW be related asNmaxDkW,wherekis any positive
number.