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Forces could be either external or internal forces. Active external forces are those where the structure is constrained or fixed. The external work of the reaction forces will be zero when the external active forces applied are in equilibrium. We apply the Saint-Venant's Principle as the reference for the external forces applied in the nodes. We have to follow the following procedure:

1. Express the displacements as:

Nodal Displacement = (Sx * u) + (Sy * v) + (Sz * w)

2. Substitute inside the expression of the virtual work:

Virtual Work = ∫(Sx * Fx + Sy * Fy + Sz * Fz) dV

3. Consider the equivalent nodal forces:

Equivalent Nodal Forces = (Sx * Fx) + (Sy * Fy) + (Sz * Fz)

4. Calculate the virtual work:

Virtual Work = ∫(Sx * Fx + Sy * Fy + Sz * Fz) dV

By following these steps, we can determine the coordinate transformation from the global coordinate system to the local coordinate system.

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