1.A subsystem is in equilibrium if the combined effect of all external forces produces zero translational and rotational acceleration.
If there is to be no translational acceleration, the forces must sum to zero: ΣF=0
If there is to be no rotational acceleration, the moments must sum to zero: ΣM|o =0
where O is any point on or off the body.
Force and moment summation should include all external forces acting directly on the subsystem,namely, the forces drawn in the FBD.
2.Equilibrium can be imposed along coordinate axes.
Vector equilibrium conditions are equivalent to individual force summations along each of three axes:
ΣFx=0 ΣFy=0 ΣFz=0
and moment summations about each of three axes:
ΣM|Ox=0 ΣM|Oy=0 ΣM|Oz=0
The axes for the moment summations can be through different points, not all through the same point O.
If loads can be represented by forces in a single plane, then there are only three independent equilibrium equations:
ΣFx=0 ΣFy=0 ΣM|O
where the moment is about the z-axis (perpendicular to the x-yaxes) through any point O.
3.Be sure to account for couples correctly when imposing equilibrium conditions.
Do not include couples in the force summations: each couple has zero net force!
In moment summations, include moments due to forces and due to couples.
The moment due to a couple which acts on the subsystem is independent of the couple’s location or the point about which the moment is taken.
4.Plan out the order in which you impose equations, and consider imposing equilibrium on multiple subsystems.
When the equilibrium equations for a given subsystem are sufficient to find the unknowns, it is often efficient first to sum moments about a carefully chosen point to find one force. Then, use the force summations to find the other forces.
If a desired unknown cannot be found using a single subsystem, draw FBDs of one or more additional subsystems and impose equilibrium on them to find intermediate unknowns.
If there is to be no translational acceleration, the forces must sum to zero: ΣF=0
If there is to be no rotational acceleration, the moments must sum to zero: ΣM|o =0
where O is any point on or off the body.
Force and moment summation should include all external forces acting directly on the subsystem,namely, the forces drawn in the FBD.
2.Equilibrium can be imposed along coordinate axes.
Vector equilibrium conditions are equivalent to individual force summations along each of three axes:
ΣFx=0 ΣFy=0 ΣFz=0
and moment summations about each of three axes:
ΣM|Ox=0 ΣM|Oy=0 ΣM|Oz=0
The axes for the moment summations can be through different points, not all through the same point O.
If loads can be represented by forces in a single plane, then there are only three independent equilibrium equations:
ΣFx=0 ΣFy=0 ΣM|O
where the moment is about the z-axis (perpendicular to the x-yaxes) through any point O.
3.Be sure to account for couples correctly when imposing equilibrium conditions.
Do not include couples in the force summations: each couple has zero net force!
In moment summations, include moments due to forces and due to couples.
The moment due to a couple which acts on the subsystem is independent of the couple’s location or the point about which the moment is taken.
4.Plan out the order in which you impose equations, and consider imposing equilibrium on multiple subsystems.
When the equilibrium equations for a given subsystem are sufficient to find the unknowns, it is often efficient first to sum moments about a carefully chosen point to find one force. Then, use the force summations to find the other forces.
If a desired unknown cannot be found using a single subsystem, draw FBDs of one or more additional subsystems and impose equilibrium on them to find intermediate unknowns.
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