Engineering Mechanics

(^346) „„„„„ A Textbook of Engineering Mechanics
From the geometry of the figure, we find that when the virtual upward displacement of the
beam at B is y, the virtual upward displacement of the beam at C is
2
5
y
= 0.4 y as shown in Fig. 16.3.
∴ Total virtual work done by the two reactions RA and RB
= +[(RA × 0) + (RB × y)] = + RB × y ...(i)
... (Plus sign due to the reactions acting upwards)
and virtual work done by the point load
==×=–Px – 2 0.4 – 0.8y ...(ii)
... (Minus sign due to the load acting downwards)
We know that from the principle of virtual work, that algebraic sum of the total virtual
works done is zero. Therefore
RB × y – 0.8 y=0
or RB= 0.8 y/y = 0.8 kN Ans.
and RA= 2 – 0.8 = 1.2 kN Ans.
Example 16.2. Two beams AC and CD of length 9 m and 10 m respectively are hinged at C.
These are supported on rollers at the left and right ends (A and D). A hinged support is provided at
B, 7m from A as shown in Fig. 16.4.
Fig. 16.4.
Using the principle of virtual work, determine the force transmitted by the hinge C and the
reaction at the support B, when a load of 700 N acts at a point 6 m from D.
Solution. Given : Length of beam AC = 9 m; Length of beam CD = 10 m and load at E = 700 N.
Fig. 16.5.
Let RA = Reaction at A,
RB= Reaction at B,
RD= Reaction at D, and
y = Virtual upward displacement of the beam at the hinge (i.e. C).