《ch4拉压超静定w》PPT课件

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1、材料力学ProfessorShibinWANG（王世斌）关于超静定的基本概念静定问题与静定结构——未知力（内力或外力）个数等于独立的平衡方程数超静定问题与超静定结构——未知力个数多于独立的平衡方程数超静定次数——未知力个数与独立平衡方程数之差多余约束——保持结构静定多余的约束简单的超静定问题Ch.4IndeterminateStressSystem静定与超静定的辩证关系——多余约束的两种作用：增加了未知力个数，同时增加对变形限制与约束，前者使问题变为不可解，后者使问题变为可解。求解超静定问题的基本方法——平衡、变形协调、物性关系。现在的物性关系体现为力与变形关系。求解超静定问题

2、的基本方法简单的超静定问题Ch.4IndeterminateStressSystem拉压超静定问题E2A2l2E3A3l3=E2A2l2E1A1l1yxABCD例题5FPFPFN3FN2FN1ACh.4IndeterminateStressSystem平衡方程超静定次数：3-2=1yxFPFN3FN2FN1Ch.4IndeterminateStressSysteml1l3变形协调方程:各杆变形的几何关系E2A2l2E3A3l3=E2A2l2E1A1l1BCDAFPl2Ch.4IndeterminateStressSystem平衡方程:变形协调方程：物性关系:Ch.4Ind

3、eterminateStressSystem结果：由平衡方程、变形协调方程、物性关系联立解出例题5Ch.4IndeterminateStressSystemxyCh.4IndeterminateStressSystemsBigQuestion–WhatisanIndeterminateSystem?BigAnswer–Oneinwhichunknownforcescannotbedeterminedfromequilibriumalone.ThisisaDETERMINATEsystemForexample:P1P2RxSince:fromWehaveONEunknown,and

4、ONEavailableequilibriumrelationship.xyThisisanINDETERMINATEsystemPRAxSinceRAx&RBxCANNOTbefoundfromequilibrium:1equation,2unknownsRBxTherefore,weneedMOREINFORMATION!!!4.1Considerthefollowingproblem:ExamplesofStaticallyDeterminateSystems:Beams:Trusses:Other:10kNVAVBHAVAHAMAzVAVBHAVAHAMANomoreth

5、an2unknownsatajointExamplesofStaticallyIndeterminateSystems:Beams:Trusses:VBVAHAMAOther:Howmuchloadcarriedbyconcrete,howmuchbythesteel?10kNToomanyreactionsToomanyunknownsatajointVAHAMAMBHBVBxye.g.Weneedmoretools!4.2TheDirectMethodofAnalysisEquilibriumofForcesGeometricCompatibilityofDeformatio

6、nsHooke’sLawPRAxRBxABCuab12E,AEquilibrium:1Compatibility:2i.e.Contractionofpart=Extensionofpart12Hooke’sLaw:3xye.g.PRAxRBxABCuab12E,ARAxRBxabxyPPRAxRAxsx1sx1sx1sx2sx2Fu1Fu21(From)FromCompatibility:2abxyPsx1sx2E,A0u-ve+veCompressionTensionNOTE:Andfrom:2Considersomenumbers…P=20kNABCu200mm100mm1

7、2E=70GPa,A=100mm2AScottishengineer,Rankinemadeobservationsabouttheexpansionandcontractionofmaterialsduetochangesintemperature.4.3ThermalStrains(WilliamRankine,1870)xya=CoefficientofLinearExpansion(Amaterialproperty)Henotedthatthesedeflections