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1、Chapter 10 Statically indeterminate beams Mechanics of MaterialsIntroductionWelcome to mechancis of materials,in this video,we will start learn the chapter 10 in this course,Statically indeterminate beams.10.1 Introduction 10.2 Types of statically indeterminate beams10.3 Analysis by the differential
2、 equations of the deflection curve 10.4 Method of superpositionOutline These are the topics we will look at here.We are now doing the introduction for this chapter,then we will look at different types of statically indeterminate beams,and then we move to methods for analyzing a statically indetermin
3、ate beam,especially the second method-superposition.Statically indeterminate beamsStatically determinate beams:-the number of reactions the number of independent equations of equilibrium.-the number of reactions =the number of independent equations of equilibrium.Statically indeterminate beamsIn the
4、 previous study of*beams in this course,all reactions,shear forces,and bending moments of beams can be obtained from free-body diagrams and equations of equilibrium,because*the number of reactions euqals to the number of independent equations of equilibrium,such beams are said to be*statically deter
5、minate beams.Then,knowing the shear forces and bending moments,the stresses and deflections are computed.But for*beams with*redundancies,the reactions of such beams cannot be determined by statics alone,becuase in those beams*the number of reactions exceeds the number of independent equations of equ
6、ilibrium,such beams are said to be*statically indeterminate beams.Degree of static indeterminancy-Draw FBD and count number of redundancies.-4 reactions -3 equilibrium equations 4 3=11st degree statically indeterminate-6 reactions -3 equilibrium equations 6 3=33rd degree statically indeterminate-The
7、 number of reactions in excess of the number of equilibrium equations.Degree of static indeterminacy is*the number of reactions in excess of the number of equilibrium equations.To report the degree of static indeterminacy,*drawing FDB for the entire stucture is helpful.Now lets look at two examples
8、to see how to get the degree of static indeterminacy.example 1*,here is its*FBD,now we can see,there are*4 reactions and*3 equilibrium equations,and so the number of reactions exceeds the number of equilibrium equation is*1.Therefore,this beam is statically indeterminate to the first degree.For the
9、second*example,*the number of reactions exceeds the number of equilibrium equations by 3,so this beam is statically indeterminate to the third degree.Methods-method of superposition-differential equations of the deflection curve for only the simplest types of statically indeterminate beamsapplicable
10、 to a wide variety of structuresAdditional equations are needed!When a beam is statically indeterminate,the equilibrium equations are not sufficient,and*additional equations are needed for analyzing a statically indeterminate beam.*Two methods will be introduced.The most fundamental method is to sol
11、ve the differential equations of the deflection curve,as described in Section 10.3.*It is practical for only the simplest types of statically indeterminate beams.Therefore,the focus here is on the method of superposition described in Section 10.4,that is*applicable to a wide variety of structures.Classify each of the beams shown as statically determinate or statically indeterminate.Exercise 1This is the end of this video.End