How do I interpret these kinds of moments?
The 20 kN.m moment is called a "couple" or “force couple”. A force couple is produced by equal and opposite parallel forces (net force = 0) about a point at the center between them. A couple causes pure rotation without translation.
A couple has the following properties:
It is equivalent to a single moment vector.
It induces the potential for rotation without translation (because for equal and opposite forces there is no net force)
In order to achieve equilibrium for the entire beam, a couple can only be counteracted by another equal and opposite couple.
The moment vector of the couple and be moved to any location without affecting static equilibrium requirements.
The following are answers to your specific questions. They assume you are only considering static equilibrium requirements for the beam, because the fourth property only applies to statics analysis (e.g.,. setting the sum of the forces and moments equal to zero to determine reactions at supports). For mechanics of materials problems, the location of the force couple is critical to determine bending moments and bending stresses.
Here the arrow goes around the point 2m from A. So does this mean there is an extra moment around this point?
Yes. But you don’t have to take the point where the couple is located into consideration because of the fourth property. You only need to take the location of the couple into consideration when you are determining bending moments and stresses in the beam, in other words, for mechanics of materials problems. For statics problems, where you are only trying to determine reactions at supports for static equilibrium, the location of the couple is unimportant.
But how does this moment affect the moment seen from other points, such as A? Or B? More specifically, if I wanted to form a moment equilibrium equation from A, would I simply add/subtract (depending on my definition of positive direction) 20kNm from/to the sum of moments about A?) And if I were to form moment equilibrium equations around another point like B, what would I do with 20kNm then?
If you want to sum moments about A, you can think of the couple being located at A and just add/subtract it to the other moments about A.
If you want to sum moments about B, you can think of the couple being located at B and just add/subtract it to the other moments about B.
You get the same results either way.
REMEMBER- This only applies to static equilibrium requirements. When you analyze bending moments and stresses in beams the couple location is critical;.
Also, how would this kind of moment occur in real world? It is a moment without a force or a distance, just a moment. How could I produce something like this? Thank you!
This is not a moment without a force. It is moment caused by two parallel equal and opposite forces. So it is a moment without a net force.
Think about the steering wheel of your car. To make a right hand turn, you exert a vertical upward force with your left hand and an equal and parallel downward vertical force with your right hand. Because your forces are equal, parallel, and opposite, you are creating a moment couple on the wheel. That is, you create a torque (moment) about the center of the steering wheel without any net force on the wheel.
The following link from an MIT site describes couples in more detail and gives examples (such as the steering wheel), including one involving a bridge.
Hope this helps.