A force system is replaced by its resultant: R = 80 N upward, with a resultant moment of 320 N·m clockwise about point A. You then compute the resultant moment about point B, located 2 m to the right of A. What changes?
ABoth the resultant force and the resultant moment change
BThe resultant force stays 80 N upward, but the resultant moment about B differs from 320 N·m
CNeither changes — the resultant is the same regardless of reference point
DThe resultant moment stays 320 N·m, but the resultant force direction changes
The resultant force vector R is invariant — it doesn't depend on where you compute it. But the resultant moment does change with reference point, predictably: M_B = M_A + r_AB × R. Moving 2 m to the right adds a moment contribution from R acting through that offset. This does not mean the two systems are no longer equivalent — it means the moment representation changes while the physical equivalence is preserved.
Question 2 Multiple Choice
An engineer wants to represent a distributed load on a beam as a single equivalent force with no accompanying couple. She can do this by finding the point where:
AThe distributed load has its maximum value
BThe shear force diagram crosses zero
CThe resultant moment about that point is zero
DThe bending moment is at its maximum
A single force (with no couple) can replace a force-moment system only when you find the point — the center of pressure or centroid — about which the resultant moment is zero. At that point, the original distributed load is fully represented by R alone. Options A and D describe structural analysis results (peak load location and max bending moment), not the condition for a single-force equivalent.
Question 3 True / False
If a force system has a resultant force of zero but a nonzero resultant moment, it cannot be reduced to a single force acting at any point.
TTrue
FFalse
Answer: True
True. A force-couple system with R = 0 is a pure couple. No matter where you choose to 'place' the force, a zero resultant force cannot produce any net moment from position alone. The couple moment is the complete description, and it cannot be eliminated by relocating a nonexistent force.
Question 4 True / False
Changing the reference point used to compute the resultant moment means the two original force systems are no longer equivalent — they now have different resultant moments.
TTrue
FFalse
Answer: False
False. Two systems that are equivalent (same R and same M about one point) remain equivalent about every point, because the transport formula M_B = M_A + r_AB × R applies identically to both systems. Both moments change by the same amount, so the difference between them — which is what equivalence tests — stays zero. Changing reference point changes the numerical value of the moment but cannot break equivalence.
Question 5 Short Answer
Why does the resultant moment of a force system change when you change the reference point, and why doesn't this affect whether two systems are equivalent?
Think about your answer, then reveal below.
Model answer: The resultant moment changes because shifting the reference point adds a moment contribution from the resultant force acting through the new offset: M_B = M_A + r_AB × R. Two systems are equivalent if they share the same R and M_A; when both are transported to a new point B using the same formula, their moments change by the same amount, so they remain equal. Equivalence is a property of the difference between two systems, not the absolute value of either moment.
The transport formula is the key: it tells you exactly how the moment changes with reference point, and it applies symmetrically to both systems being compared. Students who think changing the reference point 'breaks' equivalence are confusing the representation of a system with the physical fact of equivalence.