Theoretical Mechanics Chapter 3 General Coplana Force System
1 Theoretical Mechanics
理论力学 三72
2
Statics Chapter 3: General Coplanar Force System General coplanar force system: Several forces act on a body, the lines of action of these forces are in a plane, but they dont intersect at one point and are not parallel. Example B YA P Reduction of a force system to a given point: Reduce an unknown force system(a general coplanar force system) to a known force system(a coplanar system of concurrent forces and a coplanar system of force couples) 3
3 Chapter 3: General Coplanar Force System General coplanar force system: Several forces act on a body, the lines of action of these forces are in a plane, but they don’t intersect at one point and are not parallel. [Example] Reduction of a force system to a given point: Reduce an unknown force system(a general coplanar force system) to a known force system(a coplanar system of concurrent forces and a coplanar system of force couples)
学 第三章平面任意力系 平面任意力系:各力的作用线在同一平面内,既不汇交为一点 又不相互平行的力系叫~ [例 B LA P N 力系向一点简化:把未知力系(平面任意力系)变成已知 力系(平面汇交力系和平面力偶系)
4 第三章 平面任意力系 平面任意力系：各力的作用线在同一平面内，既不汇交为一点 又不相互平行的力系叫∼。 [例] 力系向一点简化：把未知力系（平面任意力系）变成已知 力系（平面汇交力系和平面力偶系）
Chapter 3: General Coplanar force system s3-1 Theorem of translation of a force o83-2 Reduction of a general coplanar force system to a given point 83-3 Result of reduction of a general coplanar force system the law of the resultant moment 83-4 Conditions and equations for the equilibrium of a general coplanar force system b83-5 equilibrium equations of a coplanar system of parallel forces 83-6 The concepts of statically determinate and statically indeterminate problems the equilibrium of a body system 83-7 Analysis of internal force of simple plane truss Exercises
5 Chapter 3: General Coplanar Force System §3–1 Theorem of translation of a force §3–2 Reduction of a general coplanar force system to a given point §3–3 Result of reduction of a general coplanar force system • the law of the resultant moment §3–4 Conditions and equations for the equilibrium of a general coplanar force system §3–5 equilibrium equations of a coplanar system of parallel forces §3–6 The concepts of statically determinate and statically indeterminate problems • the equilibrium of a body system §3–7 Analysis of internal force of simple plane truss Exercises
第三章平面一般力系 §3-1力线平移定理 §3-2平面一般力系向一点简化 §3-3平面一般力系的简化结果·合力矩定理 §3-4平面一般力系的平衡条件和平衡方程 §3-5平面平行力系的平衡方程 一§36静定与静不定问题的概念·物体系统的平衡 口§3-7平面简单桁架的内力分析 平面一般力系习题课
6 第三章 平面一般力系 §3–1 力线平移定理 §3–2 平面一般力系向一点简化 §3–3 平面一般力系的简化结果 • 合力矩定理 §3–4 平面一般力系的平衡条件和平衡方程 §3–5 平面平行力系的平衡方程 §3–6 静定与静不定问题的概念•物体系统的平衡 §3–7 平面简单桁架的内力分析 平面一般力系习题课
Statics 83-1 Theorem of translation of a force Theorem of translation of a force: A force acting on a rigid body can be moved parallel to its lines of action to any point of the body, if we add a couple with a moment equal to the moment of the force about the point to which it is translated. Proof F→ orce system F, FF"→oreF+ force system(F,F) F FF F=P≌F m=Fd 7
7 §3-1 Theorem of translation of a force Theorem of translation of a force: A force acting on a rigid body can be moved parallel to its lines of action to any point of the body, if we add a couple with a moment equal to the moment of the force about the point to which it is translated. [proof] F force system force force system F,F ,F F+ （F，F）
学 §3-1力线平移定理 力的平移定理:可以把作用在刚体上点4的力严平行移到任一 点B,但必须同时附加一个力偶。这个力偶 的矩等于原来的力F对新作用点B的矩。 证]力F→力系F,FF→力F+力偶(F,P) F A F=F=F m=Fd
8 §3-1 力线平移定理 力的平移定理：可以把作用在刚体上点A的力 平行移到任一 点B，但必须同时附加一个力偶。这个力偶 的矩等于原来的力 F 对新作用点B的矩。 F [证] 力 F 力系 F,F ,F 力F+力偶（F，F）
Statics Explanation: (The theorem of translation of a force gives a relationship between the force and force couple: force force+force couple. @The condition of translation of a force is to add a force couple m, where m is given by m=. @ The theorem of translation of a force is the theoretical basis of the reduction of a force system. 9
9 ①The theorem of translation of a force gives a relationship between the force and force couple: force force+force couple. ②The condition of translation of a force is to add a force couple m, where m is given by m=F•d. ③The theorem of translation of a force is the theoretical basis of the reduction of a force system. Explanation:
学 说明: ①力线平移定理揭示了力与力偶的关系:力一力+力偶 (例断丝锥) ②力平移的条件是附加一个力偶m,且m与有关,m=Fd ③力线平移定理是力系简化的理论基础
10 ①力线平移定理揭示了力与力偶的关系：力 力+力偶 （例断丝锥） ②力平移的条件是附加一个力偶m，且m与d有关，m=F•d ③力线平移定理是力系简化的理论基础。 说明：