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

OCW Moment https://youtu.be/pSK1h1Aylsk?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Moment calculation scalar https://youtu.be/_xBHygW70tE?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Moment calculation vector https://youtu.be/Lg3P4uIlgeU?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Moment about a specified axis https://youtu.be/wfhYXm0l6BY?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh

OCW Principle of moments https://youtu.be/i7g2x8dn87Q?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Moment of a couple https://youtu.be/mNBQKPnri3E?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Simplification of a force and moment system https://youtu.be/FDCNEp3TQHg?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Reduction of a distributed load https://youtu.be/XrpGn2QVrT0?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh

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

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

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

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

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

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 ≡

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

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 ≡

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

Ex1. Door

Ex2. Weight

Ex3. Moment of Couple 200 N 0.8 m

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

Ex 5. Arm moment

Ex. 5 Body moment

Project. Container ship Industry 4.0: https://youtu.be/uBZmJOHIN8E Crain measure weight of container  SW select the position minimize Moment.