MECHANICS OF MATERIALS

1. MECHANICS OF
MATERIALS
RANA ATTA-UR-
REHMAN

2. GROUP MEMBER
ABDUL-
REHMAN
QAMAR
(19-ME-164)
ABDULLAH
AHSAN
(19-ME-162)
MUHAMMAD
RAHEEL
(19-ME-186)
MUHAMMAD
USMAN
(19-ME-169)
AZAM
YASEEN
(19-ME-185)

3. Principle of virtual
work
If a particle, rigid body, or system
of rigid bodies which is in
equilibrium under various forces is
given an arbitrary virtual
displacement, the net work done
by the external forces during that
displacement is zero.

4. INTRODUCTION:
• The principle of virtual work is particularly
useful when applied to the solution of
problems involving the equilibrium of
machines or mechanisms consisting of
several connected members.
• If a particle, rigid body, or system of rigid
bodies is in equilibrium, then the derivative
of its potential energy with respect to a
variable defining its position is zero.

5. The stability of an equilibrium position
can be determined from the second
derivative of the potential energy with
respect to the position variable.
Newton's laws state that at
equilibrium the applied forces are
equal and opposite to the reaction, or
constraint forces. This means
the virtual work of the constraint
forces must be zero as well.

6. Mathematical Form
Σi Fi Sჾi = 0
Then:
Σ Fi
ᵋ Sჾi = 0

7. STATIC
EQUILIBRIUM
Static equilibrium is a state in which the
net force and net torque acted upon the
system is zero. In other words,
both linear momentum and angular
momentum of the system are
conserved. The principle of virtual work
states that the virtual work of the
applied forces is zero for all virtual
movements of the system from static
equilibrium. This principle can be
generalized such that three-
dimensional rotations are included: the
virtual work of the applied forces and
applied moments is zero for all virtual
movements of the system from static
equilibrium.

8. PRINCIPLE OF
VIRTUAL
DISPLACEMENT
To derive the principle of virtual displacements in variational notations for supported bodies, we specify:
• Virtual displacements and strains as variations of the real displacements and strains using variational notation
such as & u≡u* and &Ɛ≡Ɛ* .
• Virtual displacements be zero on the part of the surface that has prescribed displacements, and thus the work
done by the reactions is zero. There remains only external surface forces on the part St that do work.

9. VIRTUAL
DISPLACEME
NT
Virtual displacement shows
how the mechanical system's
trajectory can hypothetically
deviate very slightly from the
actual trajectory gamma of
the system without violating
the system's constraints.

10. PRINCIPLE OF
VIRTUAL
FORCE
Here, we specify:
• Virtual forces and stresses as variations of the real
forces and stresses
• Virtual forces be zero on the part St of the
surface that has prescribed forces, and thus only
surface (reaction) forces on Su (where
displacements are prescribed) would do work.

11. WORK OF A FORCE

12. WORK OF A FORCE
DIFERRENT TYPES OF
FORCES
• Forces that do work are called active
force.
• Reactive and internal forces do not
do any work.
• Virtual displacements are to be
given carefully so that the active
forces are only the known forces
and the forces we are interested in
obtaining
• Similar to FBD we draw active force
diagram (AFD).

13. WORK OF A COUPLE

14. APPLICATION OF THE PRINCIPLE OF VIRTUAL WORK
Wish to determine the force of
the vice on the block for a
given force P.
If the virtual displacement is
consistent with the constraints
imposed by supports and
connections, only the work of
loads, applied forces, and
friction forces need be
considered.

15. PROBLEM
Determine the magnitude of the couple M
required to maintain the equilibrium of the
mechanism.

16. Apply the principle of virtual work

17. THANK YOU
FOR YOUR
ATTENTION