1,Chapter 2 Special cases of force systems in a plane,2,第二章 平面特殊力系,3,4,5,21 The graphical method of composition and the equilibrium of a coplanar system of concurrent forces21 平面汇交力系合成和平衡的几何法22 The analytical method of compositionand the equilibrium of a coplanar system ofconcurrent forces22 平面汇交力系合成和平衡的解析法,6,23 The concepts and the character of a moment and a force couple23 力矩 、力偶的概念及其性质24 The composition and the equilibrium of a coplanar system of force couples24 平面力偶系的合成与平衡25 The composition and the equilibrium of a coplanar system of parallel forces25 平面平行力系的合成与平衡,7,By the parallelogram rule or constructing a force triangle.由力的平行四边形法则作，也可用力的三角形来作。,8,9,10,11,12,13,F=11.5kN , NB=23.1kN.,14,15,X=Fx=Fcosa ：Y=Fy=Fsina=F cosb,16,17,即：,18,19,The magnitude of the resultant force: 合力的大小：Its direction: 方向：Its point of application: 作用点：,20,即：,21,Solution: 解： study the rod AB;研究AB杆draw its force diagram;画出受力图,22,write down the balanced equations;列平衡方程solve the equations.解平衡方程,；,23,24,25,26,27,28,When , the ball can leave the ground.,29,30,31,Solving a problem by the analytical method the direction of the forces can be assumed to bearbitrarily.5、解析法解题时，力的方向可以任意设，,32,If the result is negative, it denotes that the direction of the force is opposite to the assumed one. If a component subjected to the action of two forces, we commonly first assume that the forces is a tension. If the result is negative it denotes that the body is under compression. 如果求出负值，说明力方向与假设相反。对于二力构件，一般先设为拉力，如果求出负值，说明物体受压力。,33,34,35,36,od=ob+oc,37,Solution: Use the moment of aforce about a point: 解：用力对点的矩法,38, By the law of the moment of a resultant you get: 应用合力矩定理,39,Composition of two parallel forces of the same sense 两个同向平行力的合力 magnitude: R=Q+P大小：R=Q+Pdirection: parallel to Q、P,方向：平行于Q、P且指向一致,40,and is of same directionthe point of application: point C作用点：C处determine point C, by the law of the moment of a resultant: 确定C点，由合力距定理,Take into account,41,42,The point of application of the resultant is at infinity.,43,d,Proof that is a finite quantity,44,45,46,47,48,49,50,d,d,Therefore the total moment of the resultant force couples is,51,52,53,54,55,56,57,58,59,60,Hence:,61,62,63,64,例 已知：塔式起重机 P=700kN, W=200kN (最大起重量)，尺寸如图。求：保证满载和空载时不致翻倒，平衡块Q=？ 当Q=180kN时，求满载时轨道A、B给起重机轮子的反力？,Example The weight of a crane is P=700kN, the full load is W=200kN, dimensions are given in the fig. Determine:the range of the magnitude of Q to insure the crane never turns. let Q=180kN, W is the full load. Determine the reaction forces the railway apply on the wheels of the crane at the point A and B.,65,66,67,68,69,The end,Statics,70,静力学,本章结束,