Page 24 - mechanics

Chapter – 4 Non-Concurrent forces and Moments

Another way to obtain the moment about an axis AB is by
first computing the moment of the force about any point O on
the axis as

i jk
MO = r  F = rx ry rz

Fx Fy Fz

Then determine M AB by using
M AB = MO  uAB

and
MAB = M AB uAB

The shortest (perpendicular) distance from the axis AB to the
force F is

d = M AB (4.14)
F

Finally, if the resultant moment of a system of forces is to

be computed about a line, then the moment components of

each force are added together algebraically, since each

component lies along the same axis. Thus the magnitude of

MRAB is determined as (4.15)

 ( )MRAB = ((r  F)  uAB ) = (r  F)  uAB

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