第二章平面特殊力系 §2-1平面汇交力系合成和平衡的几何法 §2-2平面汇交力系合成和平衡的解析法 §2-3力矩、力偶的概念及其性质 §2-4平面力偶系的合成与平衡 §2.5平面平行力系的合成与平衡
6 §2–1 平面汇交力系合成和平衡的几何法 §2–2 平面汇交力系合成和平衡的解析法 §2–3 力矩 、力偶的概念及其性质 §2–4 平面力偶系的合成与平衡 §2–5 平面平行力系的合成与平衡 第二章 平面特殊力系
Statics 82-1 The graphical method of composition and the equilibrium of a coplanar system of concurrent forces I The graphical method of the composition of forces 1. The composition of two concurrent forces 2. The composition of any coplanar concurrent forces 180- Fi F R R Fi F2 A A∠ A A F2 cos(1809-a)=-cosa F3 F By the parallelogram rule or constructing a force triangle According to the law of cosines The fo F orce R VF+F+2F F coSa polygon Fi According to the law of cosines F R R the direction of the resultant force is sin sin( 180=0
7 §2–1 The graphical method of composition and the equilibrium of a coplanar system of concurrent forces Ⅰ The graphical method of the composition of forces 2 1 2 cos 2 2 2 R = F1 + F + F F 2. The composition of any coplanar concurrent forces The force polygon: 1.The composition of two concurrent forces According to the law of cosines, the direction of the resultant force is: According to the law of cosines: cos(180−)=−cos By the parallelogram rule or constructing a force triangle. sin sin(180 ) 1 − = F R
学 §2-1平面汇交力系合成与平衡的几何法 合成的几何法 1.两个共点力的合成 2任意个共点力的合成 F 180°a R R Fi Fi A∠q F2 F2 F2 A● F cos(80°a)=cos Fa 由力的平行四边形法则作, F 也可用力的三角形来作。 F2 F 由余弦定理: 为力多边形 R=√F2+F2+2 f, F coSa F 合力方向由正弦定理: sinsin( 180-c) R
8 §2-1 平面汇交力系合成与平衡的几何法 一、合成的几何法 2 1 2 cos 2 2 2 R = F1 + F + F F sin sin(180 ) 1 − = F R 2. 任意个共点力的合成 为力多边形 1.两个共点力的合成 合力方向由正弦定理： 由余弦定理： cos(180−)=−cos 由力的平行四边形法则作， 也可用力的三角形来作
Statics Conclusion: R=F+F+F,+E In general: R-EF The resultant of a coplanar system of concurrent forces is equal to the geometrical sum of these forces and it applies to the point of intersection of these forces. II The graphical condition of equilibrium The necessary and sufficient condition is R=∑F=0 If the resultant force is zero the force F2 F polygon draw with these forces is closed So the graphical condition of equilibrium of a coplanar system of concurrent forces is F5 R The force polygon is closed or The geometrical sum of all forces is zero
9 Conclusion: In general: The resultant of a coplanar system of concurrent forces is equal to the geometrical sum of these forces and it applies to the point of intersection of these forces. Ⅱ The graphical condition of equilibrium R=F R F1 F2 F3 F4 = + + + If the resultant force is zero, the force polygon draw with these forces is closed. So the graphical condition of equilibrium of a coplanar system of concurrent forces is: The necessary and sufficient condition is: R=F =0 The force polygon is closed or The geometrical sum of all forces is zero
学 结论:R=F+F+F+F 即:R=∑F 即:平面汇交力系的合力等于各分力的矢量和,合力的作用 线通过各力的汇交点。 二、平面汇交力系平衡的几何条件 平面汇交力系平衡的充要条件是:R=∑F=0 在上面几何法求力系的合力中,合力为 F2 F 零意味着力多边形自行封闭。所以平面 汇交力系平衡的必要与充分的几何条件 F5 R 是或 力多边形自行封闭 力系中各力的矢量和等于零 10
10 结论： 即： 即：平面汇交力系的合力等于各分力的矢量和，合力的作用 线通过各力的汇交点。 二、平面汇交力系平衡的几何条件 R=F R F1 F2 F3 F4 = + + + 在上面几何法求力系的合力中，合力为 零意味着力多边形自行封闭。所以平面 汇交力系平衡的必要与充分的几何条件 是： 平面汇交力系平衡的充要条件是： R=F =0 力多边形自行封闭 或 力系中各力的矢量和等于零