一.超静定结构的静力特征和几何特征The static and geometrical features of statically independent structures (SIS)
几何特征:有多余约束的几何不变体系。Geometrical features: stable systems with redundant restraints.
静力特征:仅由静力平衡方程不能求出所有内力和反力. Static features: Internal forces and reactions can not be determined only by Static equilibrium conditions
超静定问题的求解要同时考虑结构的“变形、本构、平衡”.Deformation and equilibrium must be considered simultaneously
二.超静定结构的性质The properties of SIS
1.内力与材料的物理性质、截面的几何形状和尺寸有关。
The internal forces are related with the properties of materials, the
Geometrical form and sizes of the cross-section of the members
2.温度变化、支座移动一般会产生内力。Temperature change, movements of supports usually cause internal forces.
与静定结构相比, 超静定结构的优点为The advantages of SIS :
1.内力分布均匀the distribution of internal forces are distributed more uniformly;
2.抵抗破坏的能力强More resistance to fracture
三.超静定结构的计算方法Computation methods
1.力法force method----以多余约束力作为基本未知量
Take redundant forces as primary unknowns。
2.位移法displacement method-以结点位移作为基本未
知量. Take joint displacements as primary unknowns。
3.混合法combined method----以结点位移和多余约束力作为基本未知量.
4.力矩分配法moment distribution method----
近似计算方法approximation method.
5.矩阵位移法matrix displacement method----
结构矩阵分析法之一.
力法等方法的基本思想the idea of force method:
1.找出未知问题不能求解的原因find the reasons why
we can not solve the problem,
2.将其化成会求解的问题 transform it into solvable
problem,
3.找出改造后的问题与原问题的差别find the difference
between the transformed and original problems,
4.消除差别后,改造后的问题的解即为原问题的解
removing the difference, the transformed problem becomes
solvable.