Equilibrium of a Rigid Body
Examples
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Draw the free-body diagram of the plate.
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Does this
free-body
diagram help?
Rx1
Rx2
Rx3
Ry1
Ry2
Ry3
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
You have to
consider one
reaction force
from the gusset
plate. The
components of this
force are Rx and
Ry .
Rx
Ry
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Draw the free-body diagram of the weight.
B
A
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Determine the force in each supporting wire.
TB
TA
TA and TB
are the
forces inside
the cables
and equal to
reaction
forces at A
and B.
W=50lb
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Spanner wrench
F
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Set up the following problem: Length A= 5 ft, and length
B =10 ft and angle α= 30o. Determine the angle β of
the smooth incline in order to maintain equilibrium.
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Use line-of-action to solve the problem
Statics (MET 2214)
Prof. Simin Nasseri
Example Problem
Statics (MET 2214)
Prof. Simin Nasseri
Class Problem
Set up the problem and how would you solve for the
resisting force at pin A to maintain equilibrium.
Statics (MET 2214)
Prof. Simin Nasseri
Class Problem
Set up the problem and how would you solve for the
resisting force at pin A to maintain equilibrium.
Statics (MET 2214)
Prof. Simin Nasseri
Class Problem
Statics (MET 2214)
Prof. Simin Nasseri
Example - Equilibrium
The tension force in AC is 28 kN,
determine the the required values
of tension in AB and AD so that
the resultant force of the three
forces applied at A is vertical.
Determine the resultant force.
Statics (MET 2214)
Prof. Simin Nasseri
FBD - Example
Free-body diagram:
(Anything missing?)
Add the
dimensions!
RA
TAC
TAD
Statics (MET 2214)
Prof. Simin Nasseri
TAB
Example-Equilibrium
The vector AB is
d x  16 m
d y  48 m
d z  12 m


AB  16 i  48 j  12 k m
AB 
16    48   12 
Statics (MET 2214)
Prof. Simin Nasseri
2
2
2
 52m
Example-Equilibrium
The unit vector in the AB direction is
uˆAB
AB  16
48
12



i
j
k m
AB  52
52
52 
The tension vector TAB is
TAB  TABuˆAB
16
48
12
 TAB i  TAB j  TAB k
52
52
52
Statics (MET 2214)
Prof. Simin Nasseri
Example-Equilibrium
The vector AD is
d x  14m
d y  48m
d z  0m


AD  14 i  48 j  0 k m
AD 
 14    48   0 
Statics (MET 2214)
Prof. Simin Nasseri
2
2
2
 50m
Example-Equilibrium
The unit vector in the AD direction is
uˆAD
AD  14
48
0 


i
j
k m
AD  50
50
50 
The tension vector TAD is
TAD  TADuˆAD
14
48
0
  TAD i  TAD j  TAD k
50
50
50
Statics (MET 2214)
Prof. Simin Nasseri
Example-Equilibrium
The vector AC is
d x  16m
d y  48m
d z  24m
AC  16 i  48 j  24 k
AC 
Statics (MET 2214)
Prof. Simin Nasseri
16    48   24 
2
2
2
 56 m
Example-Equilibrium
The unit vector in the AC direction is
uˆAC
AC  16
48
24 


i
j
k m
AC  56
56
56 
The tension vector TAC is
TAC  TACuˆAC
16
48
24
 TAC i  TAC j  TAC k
56
56
56
Statics (MET 2214)
Prof. Simin Nasseri
Example-Equilibrium
The tension vector TAC= 28 kN is
TAC
16
48
24
  28 kN  i   28 kN  j   28 kN  k
56
56
56
 8 kN i  24 kN j  12 kN k
The reaction at A
RA   RA j
Statics (MET 2214)
Prof. Simin Nasseri
Example-Equilibrium
Apply the equilibrium condition.
F  0 T
AB
 TAD TAC  RA  0
Combine the vectors
F  0
14
 16

  TAB  TAD  8 kN  i
50
 52

48
 48


TAB  TAD  24 kN  RA  j
50
 52

 12

  TAB  12 kN  k
 52

Statics (MET 2214)
Prof. Simin Nasseri
Example-Equilibrium
Break the components of the forces:
16
14
 F x  0  52 TAB  50 TAD  8 kN
48
48
 F y  0  52 TAB  50 TAD  24 kN  RA
12
 F z  0  52 TAB  12 kN
Use (3) to solve for TAB
 52 
TAB   12 kN  52 kN
 12 
Statics (MET 2214)
Prof. Simin Nasseri
1
 2
 3
Example-Equilibrium
Plug into (1), solve for magnitude of TAD
14
16
TAD  TAB  8 kN
50
52
14
16
TAD   52 kN   8 kN  24 kN
50
52
TAD  85.714 kN
Statics (MET 2214)
Prof. Simin Nasseri
Example-Equilibrium
Use the values to solve for RA
48
48
RA  TAB  TAD  24 kN
52
50
48
48
  52 kN    85.714 kN   24 kN
52
50
 154.286 kN
Statics (MET 2214)
Prof. Simin Nasseri