EQUILIBRIUM
What is the meaning of Equilibrium?
Newton’s First Law: Any body at rest will remain at rest and any
body in motion will move uniformly in a straight line unless acted
upon by a force. (That means a body will be in EQUILIBRIUM)
The NET Force on the system is ZERO
When the net Force on the Bus is Zero, the
bus is in Equilibrium- it does not move
F=ma
Objective: To explain the concept of equilibrium
When Force is applied
through the engine, the bus
accelerates
While Forces are acting on the chair the NET FORCE on the
Chair is ZERO
Live Load due to
somebody sitting
Dead Load of chair
Reaction due to DL of
chair
Reaction due to LL
Objective: To explain the concept of equilibrium
EQUILIBRIUM EQUATIONS
Equilibrium means a state of rest or balance
That means in STATICS ,when a body is at rest ,the NET
RESULTANT FORCE acting on the system is ZERO.
COLLINEAR FORCE SYSTEM
Y
+
T
-
W
Ry =ΣFy =0 = +T −W =0
Objective: To explain the concept of equilibrium in one dimension (collinear system)
QUESTION?
If the Weight is W
what is the Tension in
the Rope?
Objective: An illustrative example
Collinear System
F1 F2
F3 F4
Rope
F5
F6
X
+
-
Rx = ΣFx = 0 = −F1 − F2 − F3 − F4 − F5 +F6= 0
Objective: To illustrate the concept of equilibrium in the x direction (collinear system)
Question 1?
If the big guy is pulling with a Force of 100 lb, and if
each of the small guys (5) is pulling with equal effort
what is their pulling Force?
Objective: An illustrative question for the equilibrium of a collinear system
New Question ?
T
T
w
W
Objective: To explain the concept of equilibrium of a concurrent force system
Concurrent Force System
Problem changed from a Collinear to a two
dimensional Concurrent Force Problem
Y
X
Rx = ΣFx = 0
R y = ΣFy = 0
Objective: To explain the equations that have to be satisfied for the equilibrium of a
concurrent force system
IfΣFx = 0
Do we achieve equilibrium?
& ΣFy = 0
F
No
Y
F
a
A
ΣM i = 0
B
C
x
a
C
Coplanar but not
F
Concurrent Force System
D
F
IfΣFx = 0
& ΣFy = 0
Do we achieve equilibrium?
Yes
Now let us move
the Forces.
No
Coplanar and
Concurrent Force System
Objective: To explain the concept of rotational equilibrium in Statics
IfΣFx = 0
Do we achieve equilibrium?
F
& ΣFy = 0
No
a
F
Now
ΣM i = 0
a
F
a
i
Taking Moment
about i:
a
And the body is in
Equilibrium
Fxa=Fxa
Coplanar but not a
Concurrent Force System
F
Objective: To establish the Third Equation of Equilibrium in Statics
ΣFx = 0
ΣFy = 0
ΣM
i
= 0
Objective: Statement of the Three Equations of Equilibrium for Coplanar Forces
Equilibrium Equations
General Coplanar Forces
Collinear Forces
ΣFx = 0
ΣFy = 0
ΣFx = 0
ΣFy = 0
ΣM i = 0
Concurrent Forces
y
x
ΣFx = 0
ΣFy = 0
The most Important
Equations of this
Course