What is a Equilibrium?
Various states of static equilibrium
are experinced throughout one's life. Think of the "teeter-totter"
at a playground or of a game of "tug-of-war." In the first case,
two or more individuals sit upon a board which has been fixed to a fulcrum
which allows rotation. If each of the individuals on the teeter totter weight
exaclty the same amount and sit at exactly the same distance from the fulcrum
the teeter-totter will not move. A state of equilibrium has been achieved.
The two will remain at rest until an action takes them out of equilibrium.
Such an action could be the addition of another person to the system
or it could be that one of the original two would change their position
slightly. In either case, the teeter-totter would most likely swing to one
side and rest upon the ground. A new state of equilibrium would have been
found. 
In this case, another child climbed on in front of the one already sitting
on the right. In order to put the system back into equilibrium the child
on the left had to move backwards along the board until she was far away.
The moment the two children created around the fulcrum almost doubled when
the second child climbed on. The girl knew that the only way that she could
increase the magnitude of the moment she created would be to increase the
moment arm (lever arm). Thus, she moved back until she was about twice as
far from the fulcrum. At that point the system would be put back into equilibrium.
Another example
of a state of equilibrium is the game of "tug-of-war." A rope
is pulled taut between two teams; each hopes to pull with at least a force
that equals the force imposed by the opposite team. Assume that each team
in the figure is pulling with a force of 220 pounds. The system is in equilibrium
long as each team maintains the tension force of 220 pounds. If a device
would be inserted between the two teams along the rope to measure the magnitude
of the tension force within the rope, it would read 220 pounds at each and
every point along the rope. This would be true at ANY point along the rope.
Equilibrium would be lost if either any of the competition would suddenly
release the rope.
A
structure is in equilibrium when all forces or moments acting upon
it are balanced. This means that each and every force acting upon a body,
or part of the body, is resisted by either another equal and opposite force
or set of forces whose net result is zero. Sir Issac Newton addressed this
issue when he noted that a body at rest will remain at rest until acted
upon by an external force. Every structure that can be seen to remain standing
on a daily basis is in equilibrium; it is at rest and each of its members,
combination of its members or any part of a member that is supporting a
load, are also at rest. There is a net result of zero in all directions
for all of the applied loads and reactions.
This is a node from the Olympic Stadium in Munich designed by Frei Otto.
The massive cast iron shape is held in place by the tensile forces imparted
by each of the cables which are attached to it.
In this illustration a piece of
split bamboo is held so that it is in equilibrium. The point of the fulcrum
is very close to the center of the length of the piece. This illustrates
a system in equilibrium under it's own weight. Two items are then added
to the bamboo; a coffee thermos and a pair of scissors.
The split bamboo beam remains in a state of equilibrium. The scissors rests
at a great distance from the fulcrum in order to balance the heavier weight
of the thermos on the opposite side. All of the forces and moments must
be balanced so that the system is in a stable equilibrium.
There are two types of equilibrium; External and Internal.
External equilibrium encompasses the loads upon, and reactions of, a structural
system as a whole. Internal equilibrium describes the various forces the
are acting within every member of the system. There are conditions of equilibrium
that must be satisfied for both types. These are:
Sum of All Vertical Forces (Fy) = 0
Sum of All Horizontal Forces (Fx) = 0
Sum of All Moments (Mz) = 0
(Sum of All Forces (Fz) = 0)
(Sum of All Moments (My) = 0)
(Sum of All Moments (Mx) = 0)
These six equations are all that can be used to determine every one of the forces that are acting with a structure. They are few, but very powerful. The first three are the most common equations and will be utilized in all of the problems asociated with this course. The other three are only necessary when considering three-dimensional force systems.
Questions for Thought
What other games developed your sense of equilibrium during play as a
child? How is equilibrium maintained by a large Oak tree when it must resist
the onslaught of a strong wind? How is equilibrium maintained by a tall
Douglas Fir tree when it must resist the onslaught of a strong wind? How
is equilibrium maintained by a building when it must resist the onslaught
of a hurricane? How is equilibrium maintained when a person rides a bicycle?
Problems
Associated Readings
Schodek. p. 40
