If a system is in equilibrium and the position of the system depends upon many independent variables, the principle of virtual work states that the partial derivatives of its total potential energy with respect to each of the independent variable must be

Explanation:

• Virtual work is the work done by a real force acting through a virtual displacement i.e. Virtual work done by real forces.
• A virtual displacement is any displacement consistent with the constraints of the structure, i.e., that satisfy the boundary conditions at the supports.
• A virtual force is any system of forces in equilibrium.
• The principle of virtual work states, for bodies in equilibrium, for a small arbitrary displacement, the total work done by the system is zero.
• In this method, the system is displaced through a small amount about a reference point and the work done by all the forces about the reference point is summed to zero to find the unknown reactions if any.
• The principle of virtual work states that, for a body to be in equilibrium, the virtual work should be zero.​

Principle of Virtual Work

It states that if a small imaginary displacement is given to the system under equilibrium. Then the algebraic sum of work done by the force and moment is always equal to zero or partial derivatives of its total potential energy with respect to each of the independent variable is zero.

If P1, P2,……………..Pn are force and

δ1, δ2…………………….δn are the corresponding displacement

If M1, M2,……………….Mn are moments and

δθ1, δθ2………………….. δθn  are corresponding angular displacement

Then according to the principle of virtual work total work is done is zero.

P1δ1 + P2δ2 …………… + M1 δθ1 + M­2 δθ2 + ……………….. = 0