-
Virtual Work
Chen-Ching Ting()
Mechanical Engineering, National Taipei University of
Technology()
Homepage: http://cct.me.ntut.edu.tw/E-mail:
[email protected]
CCT Group
:
June 10, 2011
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 1 / 24
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1 (Virtual Work)
2 (Conservative Forces)
3 (Potential Energy)
4
5
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 2 / 24
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R.C Hibbeler, Statics, Pearson Education Inc.,
,ISBN=978-986-154-861-6, Chapter 11, 2009.
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 3 / 24
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Virtual Work
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 4 / 24
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(Virtual Work)
(FR = 0)(MR = 0)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 5 / 24
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Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 6 / 24
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(Jean Bernoulli)(~F )(d~r)(dU) dU = ~F d~r (1)
= Fcosdr (2)
= Fdrcos (3)
(r)(F)(U)
U = F rcos (4)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 7 / 24
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(W)(NormalForce, N)(y)U = 0
U = W y Ny (5)= 0 (6)
y 6= 0N=W
Fy = 0
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 8 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 9 / 24
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( ~M = ~r ~F )(dr = rd)(dU)
dU = Fdr (7)
= Frd (8)
= Md (9)
()(M)(U)
U = M (10)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 10 / 24
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B(U = 0)
U = Ay (l) P(l/2) (11)= (Ay l Pl/2) (12)= 0 (13)
6= 0Ay = P/2
MB = 0
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 11 / 24
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Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 12 / 24
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(Free-Body Diagram)(r)()(U = 0)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
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(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 13 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Conservative Forces
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 14 / 24
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(Conservative Forces)
(Initial)(Final)(Path)(ConservativeForces)(W )(Fs)
dU = ~W d~r = W (drcos) = Wdy
U = h0
Wdy = Wh
dU = ~Fs d~s = Fsds = ksds
U = s2s1
ksds = (12ks22
1
2ks21 )
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 15 / 24
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Potential Energy
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 16 / 24
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(Vg )(Ve)
Vg = Wy (14)
Ve =1
2ks2 (15)
ysys
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 17 / 24
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(Single Degree of Freedom)(V )
V = Vg + Ve (16)
= Wy + 12ky2 (17)
V12 = V (q1) V (q2) (18)
= W (y1 y2) +1
2k(y21 y22 )
q1q2V (q1)V (q2)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 18 / 24
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(Potential Energy Criterion for Equilibrium)
(dU)(q)(q+dq)
dU = V (q) V (q + dq) (19)dU = dV (20)
U = V = 0 (21)
V = (dV
dq)q = 0 (22)
q 6= 0dV
dq= 0 (23)
dV
dy= W + ky = 0 (24)
yeq =W
k(25)
yeq
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 19 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 20 / 24
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(One-Degree-of-FreedomSystem)Vq
1 (Stable Equilibrium)
dV
dq= 0,
d2V
dq2> 0 (26)
2 (Unstable Equilibrium)
dV
dq= 0,
d2V
dq2< 0 (27)
3 (Neutral Equilibrium)
dV
dq=
d2V
dq2=
d3V
dq3= . . . = 0 (28)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 21 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
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Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
-
Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
-
Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
-
Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
-
Engineering Mechanics: Statics, Twelfth EditionRussell C.
Hibbeler
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 22 / 24
flip_clock_black_12.swfMedia File
(application/x-shockwave-flash)
-
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 23 / 24
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(~F )(d~r)
Chen-Ching Ting () Mechanical Engineering, National Taipei
University of Technology () Homepage: http://cct.me.ntut.edu.tw/
E-mail: [email protected] CCT Group[2mm] : ()Virtual Work June
10, 2011 24 / 24
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(application/x-shockwave-flash)
(Virtual Work)
(Conservative Forces)(Potential Energy)
