This method is also known as unit load method. (4.12) will directly provide the displacement of point C due to applied external forces. Where f denotes the internal force in the members due to virtual unit load. Since δF is arbitrary and for convenience let δF=1 (i.e. (4.11) represents the internal work done by the virtual internal element forces d f moving through the displacement ΔL. On the other hand, the right hand side of Eq. (4.11) denotes the external work done by the virtual force δF moving through the real dispolacement Δ. The displacement of C in the required ditection be Δ and the internal elements deform by an amount ΔL.Using Eq. Next apply the external (real) loads acting on the structures as shown in Figure 4.12(a) with the virtual force remain in the position. First apply a virtual force at C in the required direction. This is the principle of complimentary virtual work and used for computing displacements.Ĭonsider a structure shown in Figure 4.12(a) and subjected to P force and it is required to find the displacement of point C in the direction specified. Let the structure acted upon by a virtual force is subjected to real displacements then the Eq. In order to use the above principle for practical applications, we have to interchange the role of the forces and displacement. If a system in equilibrium under a system of forces undergoes a deformation, the work done by the external forces ( P ) equals the work done by the internal stresses due to those forces,(σ P). These forces and virtual displacements must satisfy the principle of conservation of energy i.e. While the body is displaced, the real forces acting on the body move through these displacements. Let the body undergoes to a set of compatible virtual displacement δD.These displacements are imaginary and fictitious as shown by dotted line. Further, consider a small element within the structural system and stresses on the surfaces caused by the P forces are shown in Figure 4.11(b) and referred as σ p.
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