Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected] ENGI 1313 Mechanics I Lecture 33: Frames and Machines
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of [email protected]
ENGI 1313 Mechanics I
Lecture 33: Frames and Machines
2 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Chapter 33 Objectives
to illustrate the analysis of frames and machines by example
3 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-01
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.
4 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-01 (cont.)
What FBD to Analyze? Member DC
0MD
0m160sinkN7m4Cy
kN52.1kN515.1Cy
0Fx
060coskN7Dx
kN5.3Dx
16kN
Dx
Dy
Bx
ByAy
6kN
Dx
7kN
CyDy
5 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-01 (cont.)
Member DC
Dx
16kN 6kN
Dx
Dy
Bx
ByAy
7kN
Dy Cy
0Fy
060sinkN7kN515.1Dy
kN55.4kN547.4Dy
6 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-01 (cont.)
Member ABD What equilibrium
equation?
Dx
16kN 6kN
Dx
Dy
Bx
ByAy
7kN
Dy Cy
0MA
0m4kN16m10kN6
m14kN547.4m8By
kN5.23kN46.23By
7 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-01 (cont.)
Member ABD
Dx
16kN 6kN
Dx
Dy
Bx
ByAy
7kN
Dy Cy
0Fy
0kN6kN16kN547.4kN46.23Ay
kN09.3kN087.3Ay
0Fx
0kN5.3Bx
kN5.3Bx
8 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-02
Determine the horizontal and vertical components of force at each pin. The suspended cylinder has a weight of 80 lb.
9 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-02 (cont.)
Where to Start? Structural
characteristics• Pulley
• Two-force member DC
• Two-force member EB No. Why?
W
W
10 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-02 (cont.)
Draw FBD What FBD to
Analyze? Member ABC
W
W
WFCD
Bx
Ey
Ex
By
Bx
By
Ax
11 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-02 (cont.)
What Equilibrium Equation?
W
WFCDBy
BxAx
0MB
0ft4lb80ft364
ft4F
22CD
lb192lb3.192FCD
0Fy
0lb80ft52
ft4lb3.192By
lb7.26lb67.26By
12 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-02 (cont.)
Find Bx to Help Solve for Unknowns
W
Bx
Ey
Ex
By
0ME
0ft3lb80ft3lb67.26ft4Bx
lb80lb80Bx
0Fx
0lb80lb80Ex
lb0Ex
0Fy
0lb67.26Ey
lb7.26lb67.26Ey
13 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-02 (cont.)
Find Ax
W
WFCDBy
BxAx
0Fx
0ft52
ft6lb3.192lb80lb80Ax
lb160lb0.160Ax
14 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 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.
15 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 (cont.)
Any Structural Characteristic? Concurrent forces
16 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 (cont.)
FBD Assume 1 N
unit load at Ex
Ax
Ay
Ex
0MA
045sin05.045sinN
45cos05.0m08.0m1.045cosN
m100.0N1
B
B
N56.0N564.0NB
NB45
17 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 (cont.)
Equilibrium Analysis Ax
Ay
Ex
NB45
0Fy
045sin564.0Ay
N40.0N398.0Ay
18 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 (cont.)
Equilibrium Analysis Ax
Ay
Ex
NB45
045cos564.0N1Ax
N60.0N601.0Ay
0Fx
19 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 (cont.)
Equilibrium Analysis of Cylinder Ax
Ay
Ex
NB45
0Fy
045sin564.0NC
N40.0N398.0NC
20 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
Example 33-03 (cont.)
Equilibrium Analysis of Cylinder Ax
Ay
Ex
NB45
0Fx
045cos564.0ND
N40.0N398.0ND
21 ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng.
References
Hibbeler (2007) http://wps.prenhall.com/
esm_hibbeler_engmech_1
Related Documents
