1. Chapter Summary
Moment of a Force
A force produces a turning effect about the point
O that does not lie on its line of action
In scalar form, moment magnitude, MO = Fd,
where d is the moment arm or perpendicular
distance from point O to its line of action of the
force
Direction of the moment is defined by right hand
rule
For easy solving,
- resolve the force components into x and y
components
2. Chapter Summary
Moment of a Force
- determine moment of each component about the
point
- sum the results
Vector cross product are used in 3D problems
MO = r X F
where r is a position vector that extends from point
O to any point on the line of action of F
3. Chapter Summary
Moment about a Specified Axis
Projection of the moment onto the axis is
obtained to determine the moment of a force
about an arbitrary axis provided that the distance
perpendicular to both its line of action and the
axis can be determined
If distance is unknown, use vector triple product
Ma = ua·r X F
where ua is a unit vector that specifies the
direction of the axis and r is the position vector
that is directed from any point on the axis to any
point on its line of action
4. Chapter Summary
Couple Moment
A couple consists of two equal but opposite
forces that act a perpendicular distance d apart
Couple tend to produce rotation without
translation
Moment of a couple is determined from M = Fd
and direction is established using the right-hand
rule
If vector cross product is used to determine the
couple moment, M = r X F, r extends from any
point on the line of action of one of the forces to
any point on the line of action of the force F
5. Chapter Summary
Reduction of a Force and Couple System
Any system of forces and couples can be reduced
to a single resultant force and a single resultant
couple moment acting at a point
Resultant force = sum of all the forces in the
system
Resultant couple moment = sum of all the forces
and the couple moments about the point
Only concurrent, coplanar or parallel force system
can be simplified into a single resultant force
6. Chapter Summary
Reduction of a Force and Couple System
For concurrent, coplanar or parallel force systems,
- find the location of the resultant force about a
point
- equate the moment of the resultant force about
the point to moment of the forces and couples in
the system about the same point
Repeating the above steps for other force system
will yield a wrench, which consists of resultant
force and a resultant collinear moment
7. Chapter Summary
Distributed Loading
A simple distributed loading can be replaced
by a resultant force, which is equivalent to
the area under the loading curve
Resultant has a line of action that passes
through the centroid or geometric center of
the are or volume under the loading diagram
