ENGI 1313 Mechanics I Lecture 33: Frames and Machines Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected] Chapter 33

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Transcript ENGI 1313 Mechanics I Lecture 33: Frames and Machines Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected] Chapter 33 

ENGI 1313 Mechanics I
Lecture 33:
Frames and Machines
Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]
Chapter 33 Objectives

2
to illustrate the analysis of frames and
machines by example
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-01

3
The compound
beam is pin
supported at B and
supported by
rockers at A and C.
There is a hinge
(pin) at D.
Determine the
reactions at the
supports.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-01 (cont.)

What FBD to Analyze?

Member DC
M
D
0


Cy 4m  7 kN sin60 1m  0
7kN
Cy  1.515kN  1.52kN

F
x
Dx
0
Dy
16kN
Dx  7 kN cos60   0
Dx  3.5 kN
4
© 2007 S. Kenny, Ph.D., P.Eng.
6kN
Bx
Ay
Cy
By
ENGI 1313 Statics I – Lecture 33
Dy
Dx
Example 33-01 (cont.)
Member DC
 Fy  0

Dy 1.515kN  7 kN sin60  0
Dy  4.547 kN  4.55kN
7kN
Dx
Dy
16kN
6kN
Bx
Ay
5
© 2007 S. Kenny, Ph.D., P.Eng.
Cy
By
ENGI 1313 Statics I – Lecture 33
Dy
Dx
Example 33-01 (cont.)

Member ABD

What equilibrium
equation?
M
A
0
By 8m  4.547 kN14m  
7kN
Dx
6kN10m  16kN4m  0
Dy
By  23.46kN  23.5kN
16kN
6kN
Bx
Ay
6
© 2007 S. Kenny, Ph.D., P.Eng.
Cy
By
ENGI 1313 Statics I – Lecture 33
Dy
Dx
Example 33-01 (cont.)

Member ABD
 Fx  0
Bx  3.5 kN  0
Bx  3.5 kN

F
y
7kN
0
Dx
Ay  23.46kN  4.547kN 16kN  6kN  0
Dy
16kN
Ay  3.087 kN  3.09kN
6kN
Bx
Ay
7
© 2007 S. Kenny, Ph.D., P.Eng.
Cy
By
ENGI 1313 Statics I – Lecture 33
Dy
Dx
Example 33-02

8
Determine the
horizontal and
vertical components
of force at each pin.
The suspended
cylinder has a
weight of 80 lb.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-02 (cont.)

Where to Start?

Structural
characteristics
W
• Pulley
• Two-force member DC
• Two-force member EB

9
W
No. Why?
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-02 (cont.)
Draw FBD
 What FBD to
Analyze?


Member ABC
Ex
Ey
W
By
Bx
W
Ax
Bx
By
10
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
FCD
W
Example 33-02 (cont.)

What Equilibrium
Equation?
MB  0


 FCD  4 ft

2
2
 4 6


 3 ft   80 lb4 ft   0

FCD  192.3lb  192lb

F
0
 4ft 
By  192.3 lb
  80lb  0
 52ft 
By  26.67lb  26.7 lb 
11
y
© 2007 S. Kenny, Ph.D., P.Eng.
W
Ax
Bx
By
ENGI 1313 Statics I – Lecture 33
FCD
W
Example 33-02 (cont.)

Find Bx to Help Solve
for Unknowns
M
0
E
Ex
 Bx 4ft   26.67 lb3ft   80lb3ft   0
Ey
W
Bx  80lb  80lb


12
F
x
0


F
y
0
By
Ex  80lb  80lb  0
Ey  26.67lb  0
E x  0 lb
Ey  26.67 lb  26.7 lb
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Bx
Example 33-02 (cont.)

Find Ax

F
x
0
 6ft 
Ax  80lb  80lb  192.3 lb
0
 52ft 
Ax  160.0lb  160lb
W
Ax
Bx
By
13
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
FCD
W
Example 33-03

14
The link is used to hold
the rod in place.
Determine the required
axial force on the screw
at E if the largest force to
be exerted on the rod at
B, C, or D is to be 100 N.
Also, find the magnitude
of the force reaction at
pin A. Assume all
surfaces of contact are
smooth.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-03 (cont.)

Any Structural
Characteristic?

15
Concurrent forces
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-03 (cont.)

FBD

Ay
Assume 1 N
unit load at Ex
Ax
Ex
M
A
0
45
1N 0.100 m   
N
N
B

sin45 0.05 sin45   0

cos 45  0.1m  0.08 m  0.05 cos 45   

B
NB

NB  0.564N  0.56N
16
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33
Example 33-03 (cont.)

Equilibrium
Analysis

F
y
Ay
Ax
0
Ay  0.564 sin45  0

Ex
Ay  0.398N  0.40N
45
17
© 2007 S. Kenny, Ph.D., P.Eng.
NB
ENGI 1313 Statics I – Lecture 33
Example 33-03 (cont.)

Equilibrium
Analysis
 Fx  0
Ay
Ax
Ax  1N  0.564 cos 45  0

Ex
Ay  0.601N  0.60N 
45
18
© 2007 S. Kenny, Ph.D., P.Eng.
NB
ENGI 1313 Statics I – Lecture 33
Example 33-03 (cont.)

Equilibrium
Analysis of Cylinder A
Ay
x

F
y
0
NC  0.564 sin45  0

Ex
NC  0.398N  0.40N
45
19
© 2007 S. Kenny, Ph.D., P.Eng.
NB
ENGI 1313 Statics I – Lecture 33
Example 33-03 (cont.)

Equilibrium
Analysis of Cylinder A
 Fx  0
Ay
x
ND  0.564 cos 45  0

Ex
ND  0.398N  0.40N
45
20
© 2007 S. Kenny, Ph.D., P.Eng.
NB
ENGI 1313 Statics I – Lecture 33
References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1

21
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 33