Engineering Mechanics

Chapter 16 : Virtual Work „„„„„ 357

16.10.APPLICATION OF PRINCIPLE OF VIRTUAL WORK ON FRAMED
STRUCTURES

In a framed structure, first of all assume the member (in which force is required to be found
out) to be removed. Now find out the virtual works done by all the remaining members of the frame
and the force in the member, assumed to be removed. Now apply the principle of virtual work as
usual.
Example 16.11. A hexagonal frame is made up of six bars of equal length and cross-
section as shown in Fig. 16.21. The bar ED is fixed in a horizontal position.

Fig. 16.21.
A rod GH is fixed at the mid-points of the bars ED and AB. Using the principle of virtual
work, find the tension in the rod GH due to the weight of the bars.

Solution. Let W= Weight of each bar, and
T= Tension in the rod GH.
First of all, let us assume the rod GH to be removed.
Now let y = Virtual vertical upward displacement of the centre of gravity
of the bars CD and EF.
From the geometry of the figure, we find that when the virtual vertical downward displacement
of centre of gravity of the bars CD and EF is y (due to weight W), then the vertical downward virtual
displacement of the bars BC and AF is 3y; that of member AB is 4y and that of member ED is zero
(because it is fixed in horizontal position). The vertical virtual displacement of member GH is 4y.

∴Virtual work done by the tension in rod GH

= + T × 4y = + 4 Ty ...(i)

...(Plus sign due to tension)

and virtual work done by the bars = – [(2 × W × y) + (2 × W × 3y) + (W × 4y)]

= – 12 Wy ...(ii)
...(Minus sign due to downward movement of the bars)
We know that from the principle of virtual work, that algebraic sum of the virtual works
done is zero. Therefore

4 Ty – 12Wy= 0

or^123

4

Wy

TW

y

==^ Ans.