FRAMES and MACHINES

1
Lecture 17

• FRAMES and MACHINES

2
Example 1

• Determine the forces acting on member ABCD.

600 N
F
E
50
D
A
B
C
50
50
50
50
Lecture 17
3
Example 1
600 N
SM(B) 0

F
-600(100) Cy(100) 0
FBD -1
E
Cy 600 N
50
Bx
B
C
Cx
SFy 0
Cy
By
By Cy - 600 0
By
Cy
Bx
Cx
By 0 N
D
A
B
C
FBD -2
50
50
50
50
4
Example 1

• member EC is a two force member

SM(at E on EC) 0

600 N
- Cy(50) Cx(50) 0
F
FBD -1
Bx
Cx 600 N
Ex
E
Ey
Ey
SFx 0
B
Ex
E
By
Ex - Cx 0
50
50
Cx
50
C
Ex 600 N
FBD -3
Cy
5
Example 1
By
Cy
Bx
Cx
SM(A) 0

D
A
B
C
-600(150) Dy (200) 0
50
50
50
50
Dy 450 N
SFx 0
Dx 0 N
600 N
600 N
600 N
A
D
SFy 0
Dx
B
C
-600 450 Ay 0
Dy
FBD -2
Ay 150 N
Ay
Lecture 17
6
Example 2 Tower Crane
10 m
8 m
4.4 m
E
- frictionless pulleys at A and E
6 m
C
D
B
A
1500 N
FBD -1
12 m
T

• Determine the forces acting
• on ABCD.

F
Fx
Fy
M
F
Lecture 17
7
Example 2 Tower Crane
Lecture 17
10 m
8 m
4.4 m
E

• frictionless pulleys at
• A and E

6 m
C
D
B
A
1500 N
FBD -1
T
equations of statics
12 m
SFx 0
Fx 0 (1)
F
Fx
?Fy 0
-T - 1500 Fy 0 (2)
Fy
M
SMz(F) 0
T(8) - 1500(10) MF 0 (3)
F
8
Example 2 Summary
?Fx 0
Fx 0 (1)
?Fy 0
-T - 1,500 Fy 0 (2)
?Mz(F) 0
T(8) - 1,500(10) MF 0 (3)
Fx 0 (1)
from (1)
Fy T 1,500 (2)
from (2)
MF 15,000 - 8T (3)
from (3)
Lecture 17
9
Example 2 Tower Crane
10 m
8 m
4.4 m
E
6 m
- frictionless pulleys at A and E
C
D
B
A
FBD - 1
1500 N
1) Draw FBD -2, 3 of the frictionless pulleys at
A and E.
T
12 m
2) Draw FBD -4 of EBF tower.
F
Fx
Fy
M
F
3) Draw FBD -5 of ABCD bar.
Lecture 17
10
Example 2 Tower Crane
10 m
8 m
4.4 m
E
6 m
- frictionless pulleys at A and E
C
D
B
A
1500 N
6
FBD - 1
T
14.4
T
8
6
Ex
E
T
12 m
T
Ax
8
A
6
Ey
F
Fx
Fy
M
Ay
FBD -3
F
T
FBD -2
Lecture 17
11
Example 2 FBD of the Pulleys
equations of statics
FBD -2
6
SFx 0
-Ax 8/10 T 0, Ax 0.8T
T
8
SFy 0
Ay - T 6/10 T 0, Ay 0.4T
Ax
Ay
equations of statics
T
14.4
-0.8T Ex 0.923T 0
SFx 0
6
Ex
E
Ex -0.123T
T
T
-0.6T Ey - 0.385T 0
SFy 0
6
Ey
8
Ey -0.985T
FBD -3
Lecture 17
12
Example 2 FBD - 4 of the Tower
0.985T
equations of statics
0.123T
SFx 0
0.123T Bx 0
Bx - 0.123T
6 m
FBD -4
Bx
SFy 0
T 1,500 - 0.985T By 0
B
By - 0.015T - 1500
By
SMz(B) 0
-0.123T(6) 15,000 - 8T 0

12 m
8.733T 15,000
T 1,717 N
15,000 - 8T
Bx 211 N
By 1,525 N
Lecture 17
T 1,500
13
Example 2 FBD - 5
687 N
660 N
211 N
A
C
1,585 N
1,373 N
B
D
1,525 N
1,500 N
FBD -5
Lecture 17
14
FRAMES and MACHINES

• Suggested Problems
• 6-67, 70, 83, 94