Hi all, im a little confused with a supposedly simple statics concept. The topic was on vector forces and the polygon of forces with respect to a static mechanics problem.

The text i was reading was a little confusing:

The text also shows a diagram both spacial and a 2D polygon of vectors diagram.

The text offers no explanation of why they must betaken in a specific order, or what that order is.

For example, the spacial diagram (which shows 4 tie-bars coincident at a point) has the forces numbered (1-4) in a clockwise direction about the common point. Then the polygon of forces 2D diagram shows the forces arranged (1-4) in a counter-clockwise direction showing how they form a polygon end-to-end.

Yet no justification or explanation of why the forces are drawn this way (other than it works, which isnt good enough for me :P).

Can anyone offer an explanation why the stated order works over any other possible combination of arrangements of forces?

I think "taken in order" means that the orientation of the arrows on each force must be retained...and these arrows are connected tail to head. (If they sum to zero, then the last head will meet the first tail.) However, the sum of the vectors A,B,C can be expressed in any order [using commutativity and associativity]: A+B+C or A+C+B or C+B+A, etc...