Principle of transmissibility and limitations

Principle of transmissibility

The external effect of a force on a rigid body (its tendency to move or rotate the body) remains unchanged if the force is moved to any other point on its line of action, provided its magnitude and direction are kept. So a force is a sliding vector: its line of action matters, not its point of application.

Example: a cart pulled by a rope with force F at the front, or pushed with the same force F at the back along the same line, moves in the same way. In terms of moments, the moment of F about any point O is F × d, and d (the perpendicular distance to the line of action) is the same wherever F is applied along its line.

   F ---->  o-----------o  <---- F      (same line of action,
   A        B           C               same effect on a rigid body)

Limitations

1. It holds only for rigid bodies. For a deformable body, shifting a force changes the internal stresses and deformation.
   • A bar pulled by two equal forces at its ends is in tension. If both forces are slid to the opposite ends, the bar is in compression, although the external effect (equilibrium) is the same.
2. It is valid only for the external effect. It cannot be used to find internal forces such as axial force, shear force or bending moment, as these change when the point of application changes.
3. It cannot be used to move a force off its line of action. Moving a force to a parallel line needs an added couple of moment F × d.
4. It applies only within one rigid body. A force cannot be slid off the body, or past a hinge or joint into another connected member, because that changes how the load is transferred.
5. It cannot be used in strength of materials or in finding internal forces in structural analysis, where the actual point of loading governs the stresses.