Engineering Mechanics

(^326) „„„„„ A Textbook of Engineering Mechanics
Fig. 15.4.
Now draw the vector diagram as shown in Fig. 15.4 (b) and as discussed below :

1. Select some suitable joint p and draw a vertical line pq equal to the load 10 kN at C to
   some suitable scale.


2. Similarly, draw qr and rs qual to the loads 15 kN and 20 kN at D and E respectively to the
   scale.


3. Through p draw a line parallel to AC and through q draw a line parallel to CD meeting the
   first line at o.


4. Join or and os. By measurement, we find that tension in AC,
   Tension in AC = TAC (op) = 36.0 kN and Tension in CD = TCD (oq) = 31.6 kN,
   Tension in DE = TDE (or) = 30.4 kN and Tension in EB = TEB (os) = 39.1 kN

15.5.TENSION IN A STRING CARRYING UNIFORMLY DISTRIBUTED LOAD

Consider a string or cable suspended at two points A and B at the same level and carrying a

uniformly distributed load over the horizontal span of the cable as shown in Fig. 15.5.

Fig. 15.5. Tension in string AB,

Let w = Uniformly distributed load per unit length,

l = Span of the string, and

yc = Central dip of the string.

From the geometry of the figure, we know that vertical reaction at A,

AB 2

wl

VV==

Now consider the equilibrium of the cable AC. Taking moments about C and equating the same,

.–

224

cA

lwll

Hy V

⎛⎞⎛⎞

=×⎜⎟⎜⎟×

⎝⎠⎝⎠

2222

––

22 8 4 8 8

⎛⎞wl l wl wl wl wl

=×⎜⎟= =

⎝⎠