Statics—Representing Force Interactions

1.Represent forces of interaction as simply as possible.

• In general, two bodies contact at multiple points. Their interaction can be described by a combination of forces.

• For the purpose of Statics, any complex combination of forces can be represented by relatively simple loads,provided the simpler loads,when acting alone, would resist or cause the same motion as the actual, more complex forces.

• We seek to determine the unknown forces that two bodies exert on each other by representing the unknowns as simply as possible.

2.In simplifying forces,consider their tendencies to cause translational and rotational acceleration.

• A single force acting on a body tends to cause translational acceleration. The force also tends to cause rotational acceleration if it produces a non-zero moment about the center of mass, G. The moment due to the force,M|_G, is equal to the force,F, times the perpendicular distance, d.

• Two or more forces can still cause a rotational acceleration, even if they sum as vectors to zero net force. We sometimes represent such force combinations with a couple(often called a moment),
  which causes only rotational acceleration. The couple produces the same moment about any
  point.

• The translational and rotational acceleration produced by any combination of forces can be
  produced by one force and one couple, provided they are statically equivalent to the original
  combination. Two sets of forces and couples are statically equivalent if they correspond to the same
  net force and moment. We often represent a combination of forces by just a statically equivalent force and couple.

3.Represent the unknown interaction between two connected bodies by considering which motions
of one body the other can resist.
            Consider a pair of connected bodies. Hold one body and try to move the other body in various
ways. The first body may or may not be able to resist each motion, depending on the connection.
If a motion is resisted, the corresponding force or couple can act and must be included in the
representation of unknowns.
       More specifically,

•  Ask if a body can resist the connected body’s translation in some direction.
  If so, then the representation of the interaction must include a force that acts in that direction.
•  Ask if a body can resist the connected body’s rotation about some axis.
  If so, then the representation of the interaction must include a couple that acts about that axis.

4.Recall how interactions between bodies joined by common connections are represented.
Here are commonly encountered connections and how the interaction between the connected bodies is represented. We assume there is only loading in the plane (2-D).

• A cord that connects two bodies only resists each body’s translation parallel to the cord, away
  from each other. Only the magnitude F is unknown. There can be only a tensile  force (F>0)
  parallel to the cord.

• For a roller connection, translation perpendicular to the rolled-on surface is resisted, but not
  parallel translation or rotation. Only the magnitude F is unknown, and the force acts
  perpendicularly to the rolled-on surface.

• For a pin connection, translation in any direction is resisted, but not rotation. There can be a force
  in any direction in the plane but no couple. We can represent an arbitrary force in the plane with
  two independent unknown force components  Fx and Fy.

• .For a fixed or rigid connection, rotation and translation in any direction is resisted. There can
  be a force in any direction in the plane and a couple. The force magnitudes  , Fx , Fy and couple
  magnitude M are unknown

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