# In static equilibrium body, how can an applied moment about an axis contribute to reaction moment to another point away from the axis?

Determine the resultant internal loadings acting on the cross section at B of the pipe shown in Fig. 1–7a. End A is subjected to a vertical force of 50 N, a horizontal force of 30 N, and a couple moment of 70 N m. Neglect the pipe’s mass.

Well, I can't feel the solution. I would add upward reaction force (70/0.5=140 N) at B due to moment. But I wouldn't add 70 N m to moment equation at point B. can you explain the reason?

You cannot replace a couple moment with a single force. That would introduce an erroneous term to the vertical force balance.

There is a reason why it is called a couple moment. If you want to replace it with forces you can do the following. Add 2 forces that are equal in magnitude, opposite in direction and do not share the same line of action such that their net moment along the axis of interest gives you the same value.

Additionally, as long as you do not change the direction of axis, you can move the point of application of moments and even combine them all with one along each orthogonal direction. Therefore, you can imagine moving the moment at point A to point B and performing the moment balance to find your reaction forces.

Be careful, however, when you try to do the same with forces. In that case, you might have to add additional moments to your equations in order to include the effect of forces on moment balance.

• if I apply CW moment (about axis perpendicular to the face) on a point in one face of a cube shaped body, then the body can be balanced by another CCW same magnitude moment on any other point on that face/opposite face? (no gravity)