Engineering Mechanics

(^340) „„„„„ A Textbook of Engineering Mechanics
Maximum tension in the cable
We know that maximum tension in the cable is at A or B as both the supports are at the same
level as shown in Fig 15.16.
We also know that tension in the cable at A (or B)
T = wy = 25 (5 + c) = 25(5 + 7.5) = 312.5 N Ans.
EXERCISE 15.2

1. A suspension cable of span 30 m has a central dip of 3m. Find the length of the cable, if it
   carries a uniformly distributed load of 7.5 kN/m. (Ans. 30.8 m)


2. A wire is to be stretched between two pegs 50 m apart. Find the necessary length of the
   wire, if the central dip is 1/10th of the span. (Ans. 51.33 m)


3. A suspension cable of 120 m span hangs between two points which are 9 m and 4 m above
   the lowest point of the cable. Find the length of the cable. (Ans. 121 m)


4. A cable of span 50 m is suspended from two pegs 6 m and 1.25 m above the lowest point
   of the cable. Find (i) horizontal tension in the cable and (ii) length of the cable between
   two pegs. The cable is loaded with a uniformly distributed load of 5 kN/m.
   (Ans. 493.1 kN ; 50.8m)


5. A heavy string 40 metres long weighing 50 newtons per metre length is attached at its two
   ends in such a way that it is subjected to a horizontal force of 1 kN. Find the distance
   between the two supports. (Ans. 35.2 m)

[Hint. tan^50201

1000

ws

H

×

ψ== = or ψ = 45°

s=c tan ψ

20 = c × 1 or c = 20 m

∴ Distance between the supports

= 2 [2.3 c log (sec + tan ψ)]

= 2 [2.3 × 20 log (sec 45° + tan 45°)]

= 2 × 46 log (1.4142 + 1) = 92 log 2.4142

= 92 × 0.3827 = 35.2 m Ans.

QUESTIONS

1. Show that the shape of a string, when loaded with a uniformly distributed load, is a pa-
   rabola.


2. Derive expressions for the tension in a string when it is (i) carrying point loads only, and
   (ii) uniformly distributed load.


3. Obtain expression for the tensions at the two ends of a cable when it is supported at
   different levels.


4. What do you understand by the term ‘length of string’? Derive expressions for the length
   of a string when it is supported at the same level and at different levels.


5. What is catenary? Obtain an expression for the tension in a catenary.