engineering statics lecture
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Engineering Statics Lecture PpsTRANSCRIPT
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