1. Su-Jin Kim Gyeongsang National University Fall 2017
3. Moment
Su-Jin Kim
Gyeongsang National University
Fall 2017

2. OCW
Moment
Moment calculation scalar
Moment calculation vector
Moment about a specified axis

3. OCW
Principle of moments
Moment of a couple
Simplification of a force and moment system
Reduction of a distributed load

4. Index Moment Moment calculation Moment about a specified axis
Principle of moments
Moment of a couple
Simplification of a force and moment
Resultants

5. Moment Moment scalar : M = d F , M = r F sinα
Moment vector : M = r x F
Unit : Nm d F r M α

6. Moment calculation vector
Moment cross product : M = r x F
= (rx i + ry j + rz k) x (Fx i + Fy j + Fz k)
= (ry Fz - rz Fy) i + (rz Fx - rx Fz) j + (rx Fy - ry Fx) k F r M

7. Moment about a specified axis
Moment about axis a : Ma = M · n F r M n Ma a

8. Principle of moments Momnt of 2 forces = Sum of 2 moments
M = r x F = r x ( F1 + F2 ) = r x F1 + r x F2 = M1 + M2

9. Moment of Couple
Couple is the moment produced by two equal, opposite, non-collinear forces F,-F
Couple magnitude : M = d F M F -F d ≡

10. Moment of Couple Couple vector : M = r x F
is free vector (does not depend on the reference point) M F -F d r ≡

11. Resultants Force : R = F1 + F2 + F3 + … = Σ F
Rx = Σ Fx, Ry = Σ Fy, Rz = Σ Fz
Moment : M = M1 + M2 + … = Σ (r x F) F1 F3 F2
M1 M2 M3 M R ≡

12. Reduction of a distributed load
Distributed load  Centroid + resultant Force

13. Ex1. Door

14. Ex2. Weight

15. Ex3. Moment of Couple
200 N
0.8 m

16. Ex4. Angle moment graph a M
70 kg a
0.3 m

17. Ex 5. Arm moment

18. Ex. 5 Body moment

19. Project. Container ship
Industry 4.0:
Crain measure weight of container  SW select the position minimize Moment.