If an elastic body in equilibrium under the action of external loads is given a virtual deformation from its equilibrium condition, the work done by the external loads during this deformation equals the change in the internal work or strain energy, that is, This example illustrates the principal of virtual work. Rotation) gives the corresponding force (or moment) at that location in the direction of the displacement (or rotation).Īfter the system comes to rest, a condition of equilibrium, the total internal work is 3.60a) made of an elastic material, such as steel, is gradually elongated an amount Zf by a force APf. The internal work U done on elastic members is called elastic potential energy, or strain energy.
However, the principle can be modified to apply to bodies that undergo linear and nonlinear elastic deformations. When the body is not rigid but can be distorted, the principle of virtual work as developed above cannot be applied directly. Hence W1a = W2b, which is the equilibrium condition that the sum of the moments of all forces about a support should be zero. If the lever is in equilibrium, SW = 0. Hence the virtual work during this rotation is If a virtual rotation of is applied, the virtual displacement for force W1 is a SQ , and for force W2, b SQ. 3.59 shows a horizontal lever, which can be idealized as a rigid body. This principle of virtual work can be applied to idealized systems consisting of rigid elements. In general, then, for a rigid body in equilibrium, SW = 0. Hence the virtual work done by the entire rigid body is zero. The virtual work done on each particle of the body when it is in equilibrium is zero. In a rigid body, distances between particles remain constant, since no elongation or compression takes place under the action of forces. That is, virtual work must be equal to zero for a single particle in equilibrium under a set 3.58b), then the total virtual work done by the forces is the sum of the virtual work generated by displacing each of the forces F1, F2, and F3. If the particle is displaced a virtual amount s along the x axis from A to A (Fig. Where 1, 2, 3 angle force makes with the x axis.
Hence equilibrium requires that the sum of the components of the forces along the x axis by zero: Consider a particle at location A that is in equilibrium under the concurrent forces F1, F2, and F3 (Fig. Virtual work also is done when a virtual force / acts over a displacement s. This displacement is called a virtual displacement, and the work W done by force F during the displacement s is called virtual work. Suppose a small displacement s is assumed but does not actually take place. Any displacement of the body from its original position will create work. Consider a body of negligible dimensions subjected to a force F.
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