# Influence of couple-moment's position on bending moment diagram

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?

• How many forces are acting on the object under consideration? You cannot have an equilibrium situation with just one couple. Oct 9 '16 at 23:05
• Have added an example in the question to answer yours. Thanks Oct 10 '16 at 19:21