Transcript Lecture 35 - Analysis of Frames and Machines (cont.)

ENGI 1313 Mechanics I
Lecture 35:
Analysis of Frames and Machines
Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]
Lecture 35 Objective

2
to illustrate the analysis of frames and
machines by example
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-01

3
The compound shears
are used to cut metal
parts. Determine the
vertical cutting force
exerted on the rod R if
a force of F = 20 lb is
applied at the grip G.
The lobe CDE is in
smooth contact with
the head of the shear
blade at E.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-01 (cont.)
 Draw
FBD
 GBA
 CDE
 FRE
F = 20 lb
FBC
Ax
Ay
FBC
Dy
Dx
Fy
Fx
NE
4
© 2007 S. Kenny, Ph.D., P.Eng.
NE
ENGI 1313 Statics I – Lecture 35
NR
Example 35-01 (cont.)
 What
FBD and
Equilibrium
Equations?
F = 20 lb
FBC
Ax
Ay
FBC
Dy
Dx
Fy
Fx
NE
5
© 2007 S. Kenny, Ph.D., P.Eng.
NE
ENGI 1313 Statics I – Lecture 35
NR
Example 35-01 (cont.)
 GBA
M
A
0
20lb1.6ft   FBC sin60 0.2ft   0
FBBC  184.8lb  185lb
F = 20 lb
FBC
Ax
Ay
6
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-01 (cont.)
 CDE
FBBC  184.8lb  185lb
M
D
0
184.8lb0.5ft   NE 0.5ft   0
FBC
Dy
NE  184.8lb  185 lb
Dx
NE
7
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-01 (cont.)
 FRE
NE  184.8lb  185 lb
M
F
0
184.8lb3.0ft   NR 2.5ft   0
NR  221.8lb  222lb
NE
Fy
Fx
NR
8
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-02

9
The kinetic sculpture
requires that each of the
three pinned beams be in
perfect balance at all times
during its slow motion. If
each member has a uniform
weight of 2 lb/ft and length
of 3 ft, determine the
necessary counterweights
W1, W2, and W3 which
must be added to the ends
of each member to keep the
system in balance for any
position. Neglect the size of
the counterweights.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-02 (cont.)
 FBD
A
B
L
W1
C
Ay
 Angles?

Ay
L
L

W2
10
By
By
© 2007 S. Kenny, Ph.D., P.Eng.

Cy
ENGI 1313 Statics I – Lecture 35
W3
Example 35-02 (cont.)
 Beam A
M
A
0
3

W1 1ft cos  2 lb / ft 3ft cos  ft  1ft   0
2

W1  3lb


F
y
0
Ay  3lb  2lb / ft 3ft   0
L
W1
Ay
Ay  9lb
11
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35

Example 35-02 (cont.)
 Beam
M
B
B
0
3

W2 1ft cos  2 lb / ft 3ft cos  ft  1ft  
2

 9lbcos 3ft  1ft   0
Ay
L
W2  21lb


F
y

0
W2
By
By  21lb  9lb  2lb / ft 3ft   0
By  36lb
12
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
Example 35-02 (cont.)
 Beam
C
M
0
C
3

 W3 1ft cos  2 lb / ft 3ft cos  ft  1ft  
2

L
 36 lbcos 3ft  1ft   0
W3  75 lb
By

Cy
13
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35
W3
References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1

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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 35