材料力学课堂教学软件（英文版）-范钦珊-Strength of Materials－9.pptVIP

Chapter 9 Stability analysis and design of rods in compression ? Slenderness and non-elastic buckling O ? ?cr Euler’s curve Long rod ?p ?P Euler’s curve To calculate critical loads in this intermediate range ,we need a theory of inelastic buckling. C D B C There are some theories for inelastic buckling, now we only introduce the simplified linear theory. ? Diagram of critical stress Chapter 9 Stability analysis and design of rods in compression ? Slenderness and non-elastic buckling There are some theories for inelastic buckling, now we only introduce the simplified linear theory. O ? ?cr Euler’s curve Long rod ?p ?P Euler’s curve D B According to this theory, the expression of critical loads of the compressive rods with intermediate length is(see curve CA in the figure). A C E A ?s or ?b ?s Intermediate rod ? Diagram of critical stress Chapter 9 Stability analysis and design of rods in compression ? Slenderness and non-elastic buckling When a compressive member is very short it will fail by yielding or crushing of the material , and no buckling and stability considerations are involved . ?s or ?b ?s ?p ?P O ? ?cr Long rod C Euler’s curve D Intermediate rod Short rod Euler’s curve B C A C E A In such a case , we can define an ultimate compressive stress ?s or ?b for the material. This stress establishes a strength limit for the compressive rod, represented by the horizontal line EA. ? Diagram of critical stress Chapter 9 Stability analysis and design of rods in compression ? Slenderness and non-elastic buckling The strength limit is much higher than the proportional limit since it represents the ultimate stress in compression. In such a case , we can define an ultimate compressive stress ?s or ?b for the material. This stress establishes a strength limit for the compressive rod,represented by the horizontal line EA. So that the expression of critical loads of the compressive