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1、Chapter 4 Shear Forces and Bending Moments Mechanics of MaterialsIntroductionWelcome to mechancis of materials,in this video,we will start learn the chapter 4 in this course,shear forces and bending moment in beams.4.1 Introduction 4.2 Types of beams,loads,and reactions 4.3 Shear forces and bending
2、moments 4.4 Relationships among loads,shear forces,and bending moments4.5 Shear-force and bending-moment diagrams Outline 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 beams and loadings,and then we move to shear
3、forces and bending moments analysis.Particularly,the relationships between shear forces and bending moments with external loads.Beams-Important structural elementsOverview:Review 2D beam analysis,reactions-Statics Shear forces and bending momentsmethod of sectionsrelationship between them and applie
4、d loadsdiagrams to help beam analysisLater,use this to computer stresses,strains and deflectionsBeams are obviously important structural elements.They are subjected to loads and moments,we need to design them to resist loads on them.First of all,a brief review on two dimensional beam analysis,that i
5、s to find reaction forces for beams using the law of equilibrium,which is just statics.And then move on to calculation of shear forces and bending moments.Finding the shear forces and bending moments is an essential step in the design of any beam.Through analysis,we will find the relationship betwee
6、n shear forces/bending moments and applied loads,and then learn how to draw internal force diagrams to help analyze beams.Once the shear forces and bending moments are known,we will use these to calculate stress,strain and deformations in beams,as discussed later.Bending-Important mechanical deforma
7、tion type.-More complicated compared to axial and torsion deformation.-Involves two types of loading,i.e.shear forces and bending moments.Shear force-Shear deformation-Internal shear stressBending moment-Curvature deformation-Internal normal stressBending deformation is one of the four basic defroma
8、tion types.Bending is a somewhat more complicated affair compared to axial and torsion deformation.One major complication is that bending actually involves two types of loading.You have already encountered this in your previous course in statics.Generally,in bending,the applied loading will generate
9、 internal shear forces and bending moments.Each of these internal forces will produce a different type of deformation and a different type of internal stress.Shear forces produce shear deformation and inter shear stres,while bending moments produce curvature deformation and normal stress.Structural
10、members mainly in bending deformation are called beams.Beams-Important structural members.-Long,straight,slender members.-Carry lateral loadingBeams are important structural members resting on supports and subjected to transverse loading with their vectors perpendicular to the axis of the beam,such
11、as vertical loads and gravity loading.There are many structures having beam members,such as wooden roof truss,crane,bridges.Plane bending-Defelctions of the beam occur in the same plane with the external forces.-All external forces act in a planeLet us consider a model of bending,here is a simple be
12、am,all external forces act in one plane on this simple beam,when the plane of bending loads coincides with one of cross-sectional principal planes,and all deflections occur in the same plane,this type of bending called plane bending.Symmetrical bending-Beams have a plane of symmetry.-Special case in
13、 plane bending.-All external forces act in the plane of symmetry.The plane of symmetryMP1P2qUnsymmetric bending-Beams not have a plane of symmetry.-All external forces act in the plane of symmetry.Here is a special case in plane bending,as shown in the figure,when a beam possesses a plane of symmetr
14、y,and all external forces act in a plane of symmetry of the beam,this bending is called symmetrical bending.In the case of symmetrical bending,it is essential that the plane containing one of the principal axis of inertia,the plane of applied loads and the plane of deflection should coincide.The neu
15、tral axis will coincide with the other principal axis of inertia.While,if a beam does not possess any plane of symmetry,or the external forces do not act in a plane of symmetry of the beam with symmetric planes,this kind of bending is called unsymmetrical bending.In this course,we will mainly discuss beams under symmetrical bending.This is the end of this video.End