Equilibrium of forces
Consider supporting the member in the vertical plane using two smooth rods.
Is it possible to support it this way?
Yes
No
Pi
Gr
Yes
No
Pi
Gr
Yes
No
Pi
Gr
Yes
No
Pi
Gr
Equilibrium of forces
Consider supporting the member in the vertical plane using two smooth rods.
W
A
a
B
b
2h
ΣFy = 0: A + B = W
ΣM|L = 0: Aa - Wh + Bb = 0
For b > a
B = W- A
A= W (b-h)/(b-a)
b > h ; A > 0 B < W (support from below)
b < h ; A < 0 B > W (support from top)
Equilibrium of forces
Consider supporting the member in the vertical plane using two smooth rods.
Is it possible to support it this way?
No
Gr
Yes
Pi
Yes
Pi
No
Gr
Equilibrium of forces
Consider supporting the member in the vertical plane using one smooth rod.
Can the body be supported by one rod located
somewhere under the right half of the horizontal part?
Yes
No
Pi
Gr
Equilibrium of forces
Consider supporting the member in the vertical plane using one smooth rod.
Can the body be supported by one rod located
somewhere under the horizontal part?
Yes
No
Pi
Gr
Equilibrium of forces
Consider supporting the member in the vertical plane using a rubber band.
2h
h
x
Given the ratio of lengths of the two parts is 2:1
where exactly should the band be placed under the
horizontal part to balance the member?
x=h
Gr
x=2/3 h
Pi
x=1/2 h
Bl
x=5/3 h
Ye
x=3/2 h
Wh
Equilibrium of forces
Consider supporting the member in the vertical plane with a rubber band.
T
2h
h
W
2W
x
ΣM|z = 0: xT – h2W
ΣFy = 0: T=3W
x=2/3 h
Pi
The band should be placed in line with the centroid of the L-shaped
member in order to balance it.
Equilibrium of forces
Consider supporting the member in the vertical plane using two smooth rods.
2h
B
C
A
Can the body be supported by:
one rod placed in region A and one rod placed in region B?
Yes
No
Gr
Can the body be supported by:
one rod placed in region A and one rod placed in region C?
Yes
No
Gr
Pi
Pi
Equilibrium of forces
The body can not be supported by one rod placed in region A and one rod placed in
region C.
C
A
Which equations of equilibrium can never be satisfied:
Yes
No
ΣFx = 0
Pi
Gr
ΣFy = 0
Pi
Gr
ΣM|z = 0
Pi
Gr
Equilibrium of forces
The body can not be supported by one rod placed in region A and one rod placed in
region C.
C
A
W
Which equations of equilibrium can never be satisfied :
Yes
No
ΣFx = 0
Pi
Gr
ΣFy = 0
Pi
Gr
ΣM|z = 0
Pi
Gr
Equilibrium of forces
Consider supporting the member in the vertical plane using three smooth rods.
Which combination of rods will keep the body in equilibrium?
Gr
Bl
Pi
Equilibrium of forces
L1
L3
L2
3W
A
B
C
ΣFy = -3W + A = 0
A = 3W
ΣFx = - C + B = 0
C= B
ΣM|c = 3W (L1) + B (L2 ) - B (L3 ) = 0
L2 < L3
Equilibrium of forces
Consider supporting the member in the vertical plane using three smooth rods.
This will keep the body be in equilibrium:
Pi