Engineering Mechanics

Chapter 16 : Virtual Work „„„„„ 347

From the geometry of the figure, we find that when the virtual upward displacement of the

beam at the hinge (i.e. C) is y, then virtual displacement of B and E is^7
9

y and^6

10

y

=

3

5

y

respectively

as shown in Fig. 16.5.

∴ Total work done by the three reactions (RA, RB and RD)

7

[( 0) ( 0)]

9

AB D

y

RR R

⎛⎞

=+ × +⎜⎟× + ×

⎝⎠

7

B 9

y
=+R × ...(i)
...(Plus sign due to reactions acting upwards)
and virtual work done by the load
3
–700 –420
5

y
=×=y ...(ii)
...(Minus sign due to load acting downwards)
We know that from the principle of virtual work, that algebraic sum of the total virtual
works done is zero. Therefore
7
–420 0
B 9

y

Ry×=

or

9

420 540 N

B 7

Ry

y

=×= Ans.

Example 16.3. Two beams AE and BD are supported on rollers at B and C as shown in
Fig. 16.6.

Fig. 16.6.
Determine the reactions at the rollers B and C, using the method of virtual work.
Solution. Given : Length of beam AE = 6 m; Length of beam BD = 8 m; Distance AC = 5 m;
Load at E = 500 N; and load at F = 1000 N

Fig. 16.7.

Let RC = Reaction at the roller C, and

RB = Reaction at the roller B.

First of all, let us consider the beam AE with roller support at C as shown in Fig. 16.7 (a).