Reviewing statics and came across this problem

[Cyrus]

Im reviewing statics and came across this problem. There is a beam pin connected at one end and roller connected on the other. There is a moment at the pin and a force somewhere along the beam. Then they section it to find the internal normal shear and moment. One of the things i found slightly contraditory was that the moment can act anywhere along the beam. It causes the whole beam to rotate. But when the section the end where the roller is, they have to leave off the moment. This makes sense, I understand what there doing. The contradition seems to be that this end does not see the moment cuase where the pin is. Yet at the same time the moment at the pin causes the entire beam to rotate.

 

[Cyrus]

I think I figure it out. When you have the entire beam, all parts can "see" the couple moment because it is a free vector. When you section off a portion of the beam, it can no longer "see" the couple moment. This does not mean that this section does not want to roate in the direction of the moment anymore. It still does, when you reconnect it with the rest of the beam. But once you chop it off, it "sees" a different moment acting on it, or possibly no moment, and this due strictly to the internal moment of the section itself. The couple is a free vector, so if u do choose to place it where the section is, then in this case it will now act on the section, and you will get a different internal moment. So even though the couple is a free vector that can act anywhere on the beam, its placement on the beam DOES have an affect on the internal moments and stresses of that section.