Statics 83-2 Reduction of a general coplanar force system to a given point E2 Fi 2F2 R an arbitrar point reduced to a a coplanar system of A general coplanar given center concurrent forces +a force system system of force couples (unknown force system) (known force system) A coplanar system Force R'(principal vector) of concurrent forces (acts on the given center a system of Force couple Mo(principal force couples moment)(acts in the plane
11 §3-2 Reduction of a general coplanar force system to a given point A general coplanar force system A coplanar system of concurrent forces + a system of force couples reduced to a given center (unknown force system) (known force system) A coplanar system of concurrent forces Force R' (principal vector) (acts on the given center) A system of force couples Force couple MO (principal moment) (acts in the plane) an arbitrary point
§3-2平面一般力系向一点简化 F2 R )≡ O 73 为任 选点 F3 一般力系(任意力系)向一点简化汇交力系+力偶系 (未知力系) (已知力系) 汇交力系—力,R(主矢),(作用在简化中心) 力偶系→力偶,MO(主矩),(作用在该平面上) 12
12 §3-2 平面一般力系向一点简化 一般力系（任意力系）向一点简化汇交力系+力偶系 （未知力系） （已知力系） 汇交力系 力 ， R'(主矢) ， (作用在简化中心) 力 偶 系 力偶 ，MO (主矩) ， (作用在该平面上)
Statics phi)or=+万++…=∑F principal moment Mo=m+m,+m,+ =m(F+m(2)+…=∑m(F magnitude:R=、R2+R2=√ΣX)2+(∑ Y)2 Principal vector Rdi R irection. a=tg tg moving effect ∑X for a given center of simplification (it is independent on the position of the given center) [because the principal vector equals to the resultant of the forces] 13
13 R = F1 + F2 + F3 + =Fi principal vector ' = + + = = + + + ( ) ( ) ( ) principal moment 1 2 1 2 3 O O O i O m F m F m F M m m m magnitude: Principal vector direction: for a given center of simplification (it is independent on the position of the given center). [because the principal vector equals to the resultant of the forces] R 2 2 2 2 R' = R' +R' = ( X ) + (Y) x y − − = = X Y R R x y 1 1 tg tg (moving effect)
学 主矢R=F+F2+F3+…∑F 主矩M=m1+m2+m3+ mb(F1)+m(F2)+…-=∑m0(F1) 大小:R=、R2+R,2=√(ΣX)2+( 主矢R方向: R a=tg tg (移动效应 ∑X 简化中心(与简化中心位置无关) [因主矢等于各力的矢量和]
14 大小： 主矢 方向： 简化中心 (与简化中心位置无关) [因主矢等于各力的矢量和] R R = F1 + F2 + F3 + = Fi 主矢 ' = + + = = + + + ( ) ( ) ( ) 1 2 1 2 3 O O O i O m F m F m F M m m m 主矩 2 2 2 2 R' = R' +R' = ( X ) + (Y) x y − − = = X Y R R x y 1 1 tg tg （移动效应）
Statics Principal magnitude:Mo=∑mo(F1) moment o direction: (rotating effect) The given center for simplification: (it is dependent on the position of the given center) [because the principal moment equals to the algebraic sum of moments of the forces about the given center] Fixed support (rigid embedding awning turning tool Often used in the engineering 15
15 magnitude: direction: + - The given center for simplification: (it is dependent on the position of the given center). [because the principal moment equals to the algebraic sum of moments of the forces about the given center] ( ) MO =mO Fi (rotating effect) Fixed support (rigid embedding) Often used in the engineering awning turning tool MO Principal moment