学 3、合力投影定理: 空间力系的合力在任一轴上的投影,等于各分力在同一轴 上投影的代数和。 合力FR+R2+R2=√∑X)2+(∑y)2+(∑Z)2 R R cosa=R,cOSB=R R 16
16 3、合力投影定理： 空间力系的合力在任一轴上的投影，等于各分力在同一轴 上投影的代数和。 = 2 + 2 + 2 = 2 + 2 + 2 :R R R R ( X) ( Y) ( Z) 合力 x y z R R R R R Rx y z cos= ,cos == ,cosg =
Statics 3. The equilibrium of a concurrent force system in space The necessary and sufficient condition of equilibrium is that the resultant force is zero R=∑F7=0 Hence the necessary and sufficient condition of equilibrium in the graphical metho i od is that the forces form a closed polygon Hence the necessary and sufficient condition of equilibrium in the analytical method is given by the equations 2X=0 They are called equilibrium equations =0 z=0 of a concurrent force system in space
17 3. The equilibrium of a concurrent force system in space: X =0 Y =0 Z =0 They are called equilibrium equations of a concurrent force system in space. Hence the necessary and sufficient condition of equilibrium in the analytical method is given by the equations Hence the necessary and sufficient condition of equilibrium in the graphical method is that the forces form a closed polygon. R =Fi =0 The necessary and sufficient condition of equilibrium is that the resultant force is zero:
学 空间汇交力系的平衡: 空间汇交力系平衡的充要条件是:力系的合力为零,即: R=∑F1=0 几何法平衡充要条件为该力系的力多边形封闭。 解析法平衡充要条件为: X=0 ∑Y=0 称为平衡方程 z=0 空间汇交力系的平衡方程 18
18 三、空间汇交力系的平衡： X =0 Y =0 Z =0 称为平衡方程 空间汇交力系的平衡方程 ∴解析法平衡充要条件为： ∴几何法平衡充要条件为该力系的力多边形封闭。 R =Fi =0 空间汇交力系平衡的充要条件是：力系的合力为零，即：
Statics 85-2 System of force couples in space 1. A force couple can be represented by a vector Beside the magnitude and the turning direction, the action plane of a force couple in space has to be determined therefore a force couple is represented by a vector The turning direction of the force couple is determined by the right- F hand rule. Looking from the bottom of the vector. the clock wise rotation is positive Force couple in space is a free vector 19
19 §5–2 System of force couples in space Beside the magnitude and the turning direction, the action plane of a force couple in space has to be determined, therefore a force couple is represented by a vector. 1. A force couple can be represented by a vector The turning direction of the force couple is determined by the righthand rule. Looking from the bottom of the vector, the clockwise rotation is positive. Force couple in space is a free vector
学 §5-2空间力偶系 、力偶矩用矢量表示 由于空间力偶除大小、转向外,还必须确定力偶的作用面, 所以空间力偶矩必须用矢量表示。 力偶的转向为右手螺旋定则。 FF 从力偶矢末端看去,顺时针转动 为正。 空间力偶是一个自由矢量 20
20 §5-2 空间力偶系 由于空间力偶除大小、转向外，还必须确定力偶的作用面， 所以空间力偶矩必须用矢量表示。 一、力偶矩用矢量表示： 力偶的转向为右手螺旋定则。 从力偶矢末端看去，顺时针转动 为正。 空间力偶是一个自由矢量