Key Concept:Values of forces (F), moments (M),
dimensions such as lengths (L) and
angles
(θ) as well as other parameters such as the value of the acceleration
of gravity (g) and
coefficient
of friction (μ) are typically provided as input information in
assigned problems.
You
are then asked to find some result such as an unknown force.
A
preferred approach is to use symbols rather than their values as you step through
your
solution.Symbolic solutions have
two distinct benefits as detailed in the table below.
Benefits
of using Symbolic Solutions
Benefit
1
As you proceed through your
solution you can check the
dimensions of each term to verify
that at each stage of the
solution your results check
dimensionally.If they do, then
your calculations are possibly correct. If not, then you have
an error somewhere and you should
review each intermediate
step leading up to your result.
Benefit
2
When
you arrive at your final result you can evaluate the influence
of
each variable or parameter on the unknown being calculated.
Also
for on-line, assigned problems, the values of input variables
may
change.So your symbolic solution
will be valid for any set of input data.You can simply enter the latest set of input data to arrive
at
your answer.
General Strategy to Solve
Equilibrium Problems in a Plane (2-D)
Solution
for equilibrium involves two key steps as detailed in the table below.
Draw a FBD of one or more parts to identify the forces
(and possibly moments)
that act on each part.This is the key step.If incorrect, then all remaining
calculations will be for naught.
Write equations of equilibrium
for each part.i.e.∑ Fx
= 0, ∑ Fy = 0, ∑ Mpoint = 0