Virtual Work
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
VIRTUAL WORK
F
F
1. Work on a particle:
U r F
r
The particle can move along a specified a path
2. Work on a rigid body:
F
i) Due to translation
F
U r F r W
r
M
ii) Due to rotation
M
U M
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
The equilibrium position of the particle under the action of different forces, needs to be determined
r is an imaginary and arbitrarily small
1
displacement away from its natural position.
r
2
4
3
It is called virtual displacement if it is consistent with the system constraints.
FBD of the particle at its natural position:
F1
F2
F4
F3
The virtual work ( U ) due to virtual displacement is,
U r F1 r F2 r F3 r F4 r F1 F2 F3 F4 r R
If the particle is in equilibrium i.e. R
0, the virtual work, U 0
So for any equilibrium system, the virtual work is always zero.
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
In case of rigid body under equilibrium condition:
As all particles inside the rigid body are in equilibrium, the virtual work on all of them will be zero
Thus the virtual work done on the entire rigid body is zero.
So the virtual work done by the external forces is zero since all internal forces occur in pairs of equal, opposite and collinear forces.
Y
C
P
Find out the reaction at B by method of virtual work
C,x
P
h
X
A
B
l
C, x h , B, y l
U P C , x RB, y B, y 0 RB, y
P C ,x
B, y
Ph l B, y
RB,y
Degrees of freedom (DoF)
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
Number of independent coordinates needed to completely specify the configuration of the system.
1 DoF system
1 DoF system
2 DoFs system
l1
A
h
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
Dept. of Applied Mechanics
IIT Madras, Chennai, India
VIRTUAL WORK
F
F
1. Work on a particle:
U r F
r
The particle can move along a specified a path
2. Work on a rigid body:
F
i) Due to translation
F
U r F r W
r
M
ii) Due to rotation
M
U M
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
The equilibrium position of the particle under the action of different forces, needs to be determined
r is an imaginary and arbitrarily small
1
displacement away from its natural position.
r
2
4
3
It is called virtual displacement if it is consistent with the system constraints.
FBD of the particle at its natural position:
F1
F2
F4
F3
The virtual work ( U ) due to virtual displacement is,
U r F1 r F2 r F3 r F4 r F1 F2 F3 F4 r R
If the particle is in equilibrium i.e. R
0, the virtual work, U 0
So for any equilibrium system, the virtual work is always zero.
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
In case of rigid body under equilibrium condition:
As all particles inside the rigid body are in equilibrium, the virtual work on all of them will be zero
Thus the virtual work done on the entire rigid body is zero.
So the virtual work done by the external forces is zero since all internal forces occur in pairs of equal, opposite and collinear forces.
Y
C
P
Find out the reaction at B by method of virtual work
C,x
P
h
X
A
B
l
C, x h , B, y l
U P C , x RB, y B, y 0 RB, y
P C ,x
B, y
Ph l B, y
RB,y
Degrees of freedom (DoF)
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics
IIT Madras, Chennai, India
Number of independent coordinates needed to completely specify the configuration of the system.
1 DoF system
1 DoF system
2 DoFs system
l1
A
h
by Dr. Abhijit Chaudhuri
Dept. of Applied Mechanics