Combined Loadingmi@seer.cn
Combined Loading mi@seu.edu.cn
Contents·Unsymmetric Bending（不对称弯曲）·Tension&Bending（拉弯组合）·EccentricCompression（偏心压缩）·Core of Cross-sections（截面核心区域）·CoreofRectangularCross-sections（矩形截面核心区域）·CoreofCircularCross-sections（圆形截面核心区域）·Tension&Torsion（拉扭组合）·Bending＆Torsion（弯扭组合）·Tension,Bending&Torsion（拉弯扭组合）2
• Unsymmetric Bending（不对称弯曲） • Tension & Bending（拉弯组合） • Eccentric Compression（偏心压缩） • Core of Cross-sections（截面核心区域） • Core of Rectangular Cross-sections（矩形截面核心区域） • Core of Circular Cross-sections（圆形截面核心区域） • Tension & Torsion（拉扭组合） • Bending & Torsion（弯扭组合） • Tension, Bending & Torsion（拉弯扭组合） Contents 2
Introduction: A circular bar subjected to a single type of loadStressStresses Produced by Each Load IndividuallyStressesDistributionsBATorsionalTorsional shearLoadstressX(Torque )Txo = Tp/I,CTAxialB白ATensile averageFLoadAnormal stressOavg?(Force F)Cang=F/ADDBOMBending normalAPN.A--ACBstressBending门Loado, = My/lN.A(Transverse1ForceP)Transverseshear stressNATx = FsS*/1.b3
• A circular bar subjected to a single type of load 3 Introduction x z z M y I * xy z z F S I b S x p T I
Introduction: Prismatic bars are frequently subjected to several loadssimultaneously: The principle of superposition is used to determine theresultant stress & strain? Conditions for the principle of superposition- Linear elasticity & small deformation- No interaction between variously loads=100mm=100m=50mmRT-Pa1L4
• The principle of superposition is used to determine the resultant stress & strain • Prismatic bars are frequently subjected to several loads simultaneously • Conditions for the principle of superposition - Linear elasticity & small deformation 4 Introduction - No interaction between variously loads
Unsymmetric Bending:Analysis of pure bending has beenlimitedtomembers subjected to bending momentsVacting in a plane of symmetry.: Members remain symmetric and bend inthe plane of symmetryV.: The neutral axis of the cross sectioncoincides with the axis of the couple: Will now consider situations in which thebending couples do not act in a plane ofsymmetry..Cannot assumethat the memberwill bendin the plane of the couples.. In general, the neutral axis of the section willnot coincide with the axis of the couple5
Unsymmetric Bending • Analysis of pure bending has been limited to members subjected to bending moments acting in a plane of symmetry. • Will now consider situations in which the bending couples do not act in a plane of symmetry. • In general, the neutral axis of the section will not coincide with the axis of the couple. • Cannot assume that the member will bend in the plane of the couples. • The neutral axis of the cross section coincides with the axis of the couple • Members remain symmetric and bend in the plane of symmetry. 5