第三章 力系的平衡.pdf

ԛసჃॏຂԅ଼۹
ॏຂԅ଼۹ֺё 3-1­­­

඘ຂහԅ଼۹ԅ଼۹ذ඘ຂහذ 3-2­­­

ࡁՇူбࡁՇԅݮ·ؠ઱ 3-3­­­

ԛసჃॏຂԅ଼۹
ᴀゴᰃ䴭࡯ߚᵤⱘ䞡⚍ˈᅗⱘⷨおᮍ⊩᳝᱂䘡ᛣНDŽ
ᴀゴᇚᴀゴᇚⷨおぎ䯈ӏᛣ࡯㋏ǃぎ䯈⡍⅞࡯㋏˄ぎ䯈∛ⷨおぎ䯈ӏᛣ࡯㋏ǃぎ䯈⡍⅞࡯㋏˄ぎ䯈∛
ǃぎ䯈ᑇ㸠࡯㋏˅ǃᑇ䴶ӏᛣ㋏يѸ࡯㋏ǃぎ䯈࡯
ǃ㋏ي࡯㋏ǃᑇ䴶⡍⅞࡯㋏˄ᑇ䴶∛Ѹ࡯㋏ǃᑇ䴶࡯
ᑇ䴶ᑇ㸠࡯㋏˅ⱘᑇ㸵ᴵӊ੠䴭࡯ᑇ㸵ᮍ⿟DŽ
ॏຂԅ଼۹ֺё 3-1­­­
ࣂ޷ఉ࿉ॏຂԅ଼۹ֺё 3-1-1
ぎ䯈ӏᛣ࡯㋏ᑇ㸵ⱘܙߚᖙ㽕ᴵӊᰃ˖࡯㋏ⱘЏⶶ
੠࡯㋏ᇍӏϔ⚍ⱘЏⶽߚ߿ㄝѢ䳊DŽ
ܙߚᴵӊ˖
r r
′= =
FR 0 , M O 0 ė࡯㋏ᰃᑇ㸵࡯㋏DŽ
ᖙ㽕ᴵӊ˖
r r
′= =
࡯㋏ᰃᑇ㸵࡯㋏ėᖙৠᯊ⒵䎇 FR 0 , M O 0DŽDŽDŽ
༣༣༣ࣂ޷ఉ࿉ॏຂԅ଼۹ֺё 3-1-1
•ぎ䯈ӏᛣ࡯㋏ⱘᑇ㸵ᮍ⿟˖
∑ Fx = 0 , ∑ Fy = 0 , ∑ Fz = 0 
r r r 3-2
∑ M x (F) = 0 , ∑ M y (F) = 0 , ∑ M z (F) = 0
࡯㋏Ё৘࡯೼ϝϾℷѸ䕈Ϟᡩᕅⱘҷ᭄੠ߚ߿ㄝѢ䳊
੠৘࡯ᇍϝ䕈Пⶽⱘҷ᭄੠ߚ߿ㄝѢ䳊DŽ
ぎ䯈ӏᛣ࡯㋏ⱘᑇ㸵ᮍ⿟᳝ϝ࡯ⶽᓣǃಯ࡯ⶽᓣǃѨ
࡯ⶽᓣ៪݁࡯ⶽᓣDŽϡ䆎ાϔ⾡ᔶᓣˈぎ䯈ӏᛣ࡯㋏
া᳝6Ͼ⣀ゟⱘᑇ㸵ᮍ⿟ˈৃ∖㾷6Ͼ᳾ⶹ䞣DŽ
༣༣༣ࣂ޷උ೙ॏຂԅ଼۹ֺё 3-1-2
•ぎ䯈∛Ѹ࡯㋏ⱘᑇ㸵ᮍ⿟˖
⬅Ѣ৘࡯ᇍ∛Ѹ⚍ПⶽᘦㄝѢ䳊ˈ಴ℸ᳝
∑ Fx = 0

∑ Fy = 03-3

∑ Fz = 0
ぎ䯈∛Ѹ࡯㋏᳝3Ͼ⣀ゟⱘᑇ㸵ᮍ⿟DŽ
༣༣༣ࣂ޷උ೙ॏຂԅ଼۹ֺё 3-1-2
˖ⱘᑇ㸵ᮍ⿟㋏يぎ䯈࡯•
ⱘЏⶶᘦㄝѢ䳊ˈ಴ℸ᳝㋏يѢぎ䯈࡯⬅
r
∑ M x (F) = 0 
r 
∑ M y (F) = 0 3-4
r 
∑ M z (F) = 0 
᳝3Ͼ⣀ゟⱘᑇ㸵ᮍ⿟DŽ㋏يぎ䯈࡯
༣༣༣ࣂ޷උ೙ॏຂԅ଼۹ֺё 3-1-2
•ぎ䯈ᑇ㸠࡯㋏ⱘᑇ㸵ᮍ⿟˖
㢹পⳈ㾦തᷛ㋏ Oxyz ⱘⱘⱘ y 䕈Ϣぎ䯈ᑇ㸠࡯㋏ⱘ৘࡯
԰⫼㒓ᑇ㸠ˈ᳝
r
∑ Fx ≡,0 ∑ Fz ≡,0 ∑ M y (F) ≡ 0
಴ℸ᳝
∑ Fy = 0 
r 
∑ M x (F) = 0˄˄˄3-5˅˅˅
r 
∑ M z (F) = 0
ぎ䯈ᑇ㸠࡯㋏᳝3Ͼ⣀ゟⱘᑇ㸵ᮍ⿟DŽ

՟՟՟3-1 ೒⼎䔺ᑞЏ䕈ᅝ㺙೼䕈ᡓAϢϢϢBϞˈAЎℶ᥼䕈ᡓˈ
BЎ৥ᖗ䕈ᡓDŽᏆⶹa=50 mm  b=200 mm c=100mm ,
rC=100 mm  rD=50 mm ߛࠞ࡯৘ߚ䞣໻ᇣЎߛࠞ࡯৘ߚ䞣໻ᇣЎ
Fz=470N , Fx=350N, Fy=1400N DŽDŽDŽ䆩∖啓䕂DŽ䆩∖啓䕂 C ᠔ফⱘୂড়
࡯੠ϸ䕈ᡓⱘ㑺ᴳ࡯DŽ䚼ӊⱘ䞡䞣ϡ䅵DŽ
㾷˖প㋏㒳ᭈԧЎⷨおᇍ䈵DŽ
ᓎゟതᷛ㋏Axyz ˈˈˈ԰ফ࡯೒བ೒᠔⼎DŽˈ԰ফ࡯೒བ೒᠔⼎DŽ
Ўᮍ֓䍋㾕ˈᇚ৘࡯೼৘തᷛ䕈Ϟⱘᡩᕅ੠ᇍ৘䕈П
ⶽ߫㸼བϟ˖
Fx Fy Fz Mx My Mz
r
F FAx 0
rAx 0 0 0 0
F FAy 0
rAy 0 0 0 0
F 0 0F 0 0 0
rAz Az
F 0FBy 0 bF
rBy 0 0 By
−
FBz 0 0FBz 0 bFBz 0
r
α−α r F cos α
F 0 FP sin FP cos C P −aF cosα− aF sinα
rP P P
F − F −r F
rx x 0 0 0D x 0
−
Fy 0F 0rDFy 0 +
r y (b c)Fy
F −+
z 0 0Fz 0(b c)Fz 0