The principle of transmissibility and the concept of equivalent forces have limitations, however, which are explained below:
- Consider a short bar AB acted upon by equal and opposite axial forces P1 and P2 as shown in figure (a). According to the principle of transmissibility, the force P2 may be replaced by a force P2' having the same magnitude, same direction, and same line of action, but acting at A instead of B (figure (b)). The forces P1 and P2' acting on the same particle and being equal and opposite, their sum is found equal to zero. The original system of forces shown in figure (a) is thus equivalent to no force at all (figure (c)) from the point of view of the external behaviour of the bar.
- Consider now the two equal and opposite forces P1 and P2 acting on the bar AB as shown in figure (d). The force P2 may be replaced by a force P2' having the same magnitude, same direction, and same line of action, but acting at B instead of A (figure (b)). The forces P1 and P2' may then be added, and their sum is found again to be zero.
From the point of view of the mechanics of rigid bodies, the systems shown in figures (a) and (d) are thus equivalent. But the internal forces and deformations produces by the two systems are clearly different. The bar of figure (a) is in tension and, if not absolutely rigid, will increase in length slightly; the bar of figure (d) is in compression and, if not absolutely rigid, will decrease in length slightly.
Thus, while the principle of transmissibility may be used freely to determine the conditions of motion of equilibrium of rigid bodies and to compute the external forces acting on these bodies, it should be avoided, or at least used with care, in determining internal forces and deformations.