Mechanics of materials CHAPTERIZ STAT CALLYADETERMINATE STRUCTURES
1 Mechanics of Materials
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CHAPTER 12 SATATICALLY INDETERMINATE PROBLEMS □]§12-1 SUMMARY OF STATICALLY INDETERMINATE STRUCTURES 8 12-2 SOLVE STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD DI812-3 SYMMETRY AND THE APPLICATION OF THE PROPERTIES OF SYMMETRY 812-4 CONTINUOUS BEAMS AND THREE-MOMENT EQUATIONS
3 CHAPTER 12 SATATICALLY INDETERMINATE PROBLEMS §12–1 SUMMARY OF STATICALLY INDETERMINATE STRUCTURES §12–2 SOLVE STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD §12–3 SYMMETRY AND THE APPLICATION OF THE PROPERTIES OF SYMMETRY §12-4 CONTINUOUS BEAMS AND THREE-MOMENT EQUATIONS
第十二章静不定结构 §12-1静不定结构概述 §122用力法解静不定结构 回§12-3对称及对称性质的应用 §12-4连续梁与三弯矩方程
4 第十二章 静不定结构 §12–1 静不定结构概述 §12–2 用力法解静不定结构 §12–3 对称及对称性质的应用 §12-4 连续梁与三弯矩方程
STATICALLYINDETERMINATE STRUCTURES 8 12-1 SUMMARY OF STATICALLY INDETERMINATE STRUCTURES Structures that the whole constraint reactions and the internal forces in such structures can not be determined only by the static equilibriumequations are all called statically indeterminate structures or systems In the statically indeterminate structure the constraints in excess of the number needed to support the structure in a statically determinate manner are called static redundant constraints. The reactions corresponding to the redundant constraints are called redundant reactions. The number of redundant reactions is the degree of static indeterminacy
5 Structures that the whole constraint reactions and the internal forces in such structures can not be determined only by the static equilibrium equations are all called statically indeterminate structures or systems. §12–1 SUMMARY OF STATICALLY INDETERMINATE STRUCTURES In the statically indeterminate structure the constraints in excess of the number needed to support the structure in a statically determinate manner are called static redundant constraints. The reactions corresponding to the redundant constraints are called redundant reactions. The number of redundant reactions is the degree of static indeterminacy
§12-1静不定结构概述 用静力学平衡方程无法确定全部约束力和内力的结构,统 称为静不定结构或系统,也称为超静定结构或系统。 在静不定结构中,超过维持静力学平衡所必须的约束称为多 余约束,多余约束相对应的反力称为多余约束反力,多余约束的 数目为结构的静不定次数
6 用静力学平衡方程无法确定全部约束力和内力的结构，统 称为静不定结构或系统，也称为超静定结构或系统。 §12–1 静不定结构概述 在静不定结构中，超过维持静力学平衡所必须的约束称为多 余约束，多余约束相对应的反力称为多余约束反力，多余约束的 数目为结构的静不定次数
STATICALLYINDETERMINATE STRUCTURES Classification of the statically indeterminate problems First class: There are redundant constraints only outside the structure that is the constraint reactions are statically indeterminate, such a structure is called the statically indeterminate system in constraint Second class: There are redundant constraints only inside the structure a stru ture Is called the statically indeterminate system in internal forces Third class: There are redundant constraints inside and outside the structure, that is the constraint reactions and internal forces are all statically indeterminate Analytical methods 1) Force method: In this method unknown forces are basic unknown quantities. 2) Displacement method: In this method unknown displacements are basic unknown quantities 7
7 Classification of the statically indeterminate problems Analytical methods First class：There are redundant constraints only outside the structure， that is the constraint reactions are statically indeterminate, such a structure is called the statically indeterminate system in constraint. Second class：There are redundant constraints only inside the structure， that is the internal forces are statically indeterminate, such a structure is called the statically indeterminate system in internal forces. Third class：There are redundant constraints inside and outside the structure，that is the constraint reactions and internal forces are all statically indeterminate. 1).Force method：In this method unknown forces are basic unknown quantities. 2).Displacement method：In this method unknown displacements are basic unknown quantities
静(第一类:仅在结构外部存在多余约束,即支反力是静 不 不定的,可称为外力静不定系统。 定 间第二类:仅在结构内部存在多余约束,即内力是静不 题 定的,可称为内力静不定系统。 类(第三类:在结构外部和内部均存在多余约束,即支反 力和内力是静不定的。 分析方法 1力法:以未知力为基本未知量的求解方法。 2.位移法:以未知位移为基本未知量的求解方法
8 静 不 定 问 题 分 类 第一类：仅在结构外部存在多余约束，即支反力是静 不定的，可称为外力静不定系统。 第二类：仅在结构内部存在多余约束，即内力是静不 定的，可称为内力静不定系统。 第三类：在结构外部和内部均存在多余约束，即支反 力和内力是静不定的。 分析方法 1.力法：以未知力为基本未知量的求解方法。 2.位移法：以未知位移为基本未知量的求解方法
STATICALLYINDETERMINATE STRUCTURES 山I First class Second class Third class
9 First class Second class Third class
山I 第一类 第二类 第三类
第一类 第二类 第三类 10