The moment of two equally opposing force would create a couple-moment. Since the couple-moment value is invariant to the point considered to calculate the couple-moment, I can replace the two equally opposing force by a couple moment. I can place the couple moment anywhere, but the position will change the bending moment diagram (BMD). Since the bending moment diagram is different for two equivalent force system I think I'm doing something wrong. Can anyone point out to me what is it?
Example: Say a 10m long cantilever beam has a couple-moment of 10 Nm at 8m distance from fixed position. Now it has a specific BMD. Now I can replace the couple-moment by two opposite forces of 2.5 N each 4m apart (one at 10m from fixed distance, and one at 6m from fixed distance). This new force system is equivalent to the first force system. But the second force system has different bending moment diagram. In fact I can move the couple-moment anywhere and still have an equivalent force system; but with different BMDs.
Summary: Since moment of a couple is always the same about any point I can move around the couple position having equivalent force systems. But these equivalent force systems will have different BMDs. Why this discrepancy?
Best Answer
I think I found my mistake.
I started with the fact that 'the moment of a couple is same about any point'(Fact -1). And stemming from this fact I assumed that I can move around this couple and still have equivalent force system. This assumption is wrong. When I move around a couple 'Fact -1' is still true but the force systems are not equivalent. The definition of equivalent force system is that 'Two or more systems of forces and moments are said to be equivalent iff they have the same resultant force and resultant moment about any (and all) points (i.e., BMD, shear force diagram, axial force diagram are all same). So the definition of equivalent force system is set in the way precisely so that we don't get the discrepancy I was seeing earlier!