同济大学：《结构力学》课程教学资源（教案讲稿，打印版）02 Kinematic（运动学）analysis of structures

Chapter2 Kinematic(运动学) analysis of structures √Stability(稳定性)of structures √Degree of freedoms(自由度)of planar structures(平面结构) √Restraint(约束)of planar structures Kinematic rules of planar structures Kinematic analysis of planar structures √Static determinacy(静定)and stability √Space structures(空间结构) 同僑大学 土本2程学院 2.1 Stability(稳定性)of structures stable unstable √Rigid body(刚体)motion without any deformation(变形) Internal or external stability 同语大学 土亦1程学院 2

2.2 Degree of freedom(自由 of free body in a plane 0 Point A Rigid body(刚体)AB √DOF:no.of parameters(参数数目)possible to change independently. √There exist different sets of independent parameters(独立参数)， 同榜大学 土水2程学院 TONGII UNIVERSIT 2.3 Restraint(约束)of planar structures Restraint:device to reduce the DOFs of an object √Link(链杆) =1 restraint √Simple hinge(单铰) =2 restraint √Simple rigid joint(单刚)=3 restraint √Multiple hinge(复铰) =(n-1)simple hinge √Multiple rigid joint(复刚)=(n-1)simple rigid joint 同榜大学 土本工程学院 g TONGJI UNIVERSITY

Restraint l:link(链杆) y 0 DOF = before/after adding the link 0 细)同份大学 土本2程孕魔 6 TONGII UNIVERSITY COLLEGE OF CIVIL ENGINEEP a Restraint ll:hinge 0 y B DOF = ox before/after adding the hinge 0 土亦1程学院 6 TONGI UNIVER

Restraint Ill::rigid joint(刚结点) DOF = before/after adding the rigid joint 同陈大学 王水2程学院 DOF of planar structures W=3B-(L+2H+3R) B-no.of rigid bodies(刚体) L-no.of links H-no.of simple hinges R-no.of simple rigid joints W=3×9一(12X2+3)=0 同©大学 土亦1程学院 8 TONGJI UNIVERSIT

DOF of planar hinged structures (平面铰接结构) W=2J-L J-no.of joints L-no.of links W=2X6-12=0 同榜大学 土本2程学院 9 TONGJI UNIVERSIT DOF vs.stability W>0:insufficient restraints,unstable. W=0 or W<0,necessary but not sufficient for stability. 同濟大学 目土本红程学院 10 TONGJI UNIVERSIT

2.4 Kinematic(运动学)rules of planar structures Stability of a triangle(三角形) 三> Rule 1:1 rigid body joint Rule 2:2 rigid bodies Rule 3:3 rigid bodies 同榜大学 土水2程学院 Rule 1:1 rigid body joint Rule 1:rigid body I and joint C connected by two links form a stable system without (a) redundant restraint provided that the two 777777777 links do not lie on the (b) same straight line 同傍大学 土本1程学院 12

Rule 2:2 rigid bodies To form a stable system with no redundant restraint provided that A)the link do not cross the hinge B)the three links do not intersect at the same point 同榜大学 TONGII UNIVERS Rule 3:3 rigid bodies To form a stable system with no redundant restraint provided that the three hinges(A,B and C) do not lie on the same straight line 同榜大学 土本1程学院 14 TONGJI UNIVERSITY

Instantaneously unstable(瞬变) Become stable after small rigid body motion. 国月海大学 土水2程学院 15 TONGJI UNIVERSITY 2.5 Kinematic analysis of planar structures Hints: Example 1 √2 links crossing the same hinge 1 real hinge √ground=a whole rigid body 同海大学 土本工程学院 16 TONGI UNIVERSITY COLLEOE OF LTVIL ENGINEERING

Example 2 Hints: √Rigid body expansion 同倚大学 土本工程学院 17 Example 3 Hints: Rigid joints integrate B rigid bodies as a whole √A rigid body with only two external hinges a link crossing the hinges 同橋大学 土水2程学院 18

Example 4 86 Hints: √Rigid body expansion 同橋大学 土本2程学院 19 Example 5 Hints: √System reduction b 9 2 5 8 10 8 5 2 同僑大学 土亦2程学院 20