Fig. 1 Comparison of the conventional stress-strain behavior of a low-carbon steel,a strain-hardening material, and the idealized material assumed in limit analysis. all have the same yield strength. Buckling Collapse due to instability under compressive stress, or buckling, may or may not be permanent deformation, depending on whether or not the yield strength was exceeded. Long, slender, straight bars, tubes, or columns under axial compressive forces will buckle when the buckling load is exceeded. Buckling failure may also be encountered on the compressive sides of tubes, I-beams, channels, and angles under bending forces. Tubes may also buckle due to torsional forces, causing waves, or folds, generally perpendicular to the direction of the compressive-stress component. Parts under bending load are also subject to buckling failures on the compressive(concave)side(Fig. 2) c Fig 2 Buckled flange(lower arrow) of an extruded aluminum section deliberately loaded with a lateral force(upper arrow). Source: Ref 3. The buckling load depends only on the dimensions of the part and the modulus of elasticity of the material. Therefore, buckling cannot be prevented by changing the strength or hardness of the metal. The modulus of elasticity of a given metal is affected only by temperature, increasing at lower temperature and decreasing at higher temperature. buckling can be prevented only by changing the size or shape of the part with respect to the load imposed on it( Ref 3) The failure analyst should be sensitive to situations in which buckling has occurred but may not be immediately apparent a beam in bending will be more susceptible to buckling on the compression side if it is relatively deep and narrow. A thin, circular shaft in torsion may buckle into a helical configuration when a critical moment is exceeded. Creep or distortion from other causes may change the dimensions of a structure so that it becomes susceptible to buckling. Further details can be found in references such as ref 4 Safety Factors. In both classical design and limit analysis, yielding is assumed to be the criterion for calculating safe loads on statically loaded structures. For a given design and applied load, the two methods differ in that the safety factor( the ratio of the theoretical capacity of a structural member to the maximum allowable load)is generally higher when calculated by limit analysis. For example, classical design limits the capacity of a rectangular beam to the bending Thefileisdownloadedfromwww.bzfxw.comFig. 1 Comparison of the conventional stress-strain behavior of a low-carbon steel, a strain-hardening material, and the idealized material assumed in limit analysis. All have the same yield strength. Buckling. Collapse due to instability under compressive stress, or buckling, may or may not be permanent deformation, depending on whether or not the yield strength was exceeded. Long, slender, straight bars, tubes, or columns under axial compressive forces will buckle when the buckling load is exceeded. Buckling failure may also be encountered on the compressive sides of tubes, I-beams, channels, and angles under bending forces. Tubes may also buckle due to torsional forces, causing waves, or folds, generally perpendicular to the direction of the compressive-stress component. Parts under bending load are also subject to buckling failures on the compressive (concave) side (Fig. 2). Fig. 2 Buckled flange (lower arrow) of an extruded aluminum section deliberately loaded with a lateral force (upper arrow). Source: Ref 3. The buckling load depends only on the dimensions of the part and the modulus of elasticity of the material. Therefore, buckling cannot be prevented by changing the strength or hardness of the metal. The modulus of elasticity of a given metal is affected only by temperature, increasing at lower temperature and decreasing at higher temperature. Buckling can be prevented only by changing the size or shape of the part with respect to the load imposed on it (Ref 3). The failure analyst should be sensitive to situations in which buckling has occurred but may not be immediately apparent. A beam in bending will be more susceptible to buckling on the compression side if it is relatively deep and narrow. A thin, circular shaft in torsion may buckle into a helical configuration when a critical moment is exceeded. Creep or distortion from other causes may change the dimensions of a structure so that it becomes susceptible to buckling. Further details can be found in references such as Ref 4. Safety Factors. In both classical design and limit analysis, yielding is assumed to be the criterion for calculating safe loads on statically loaded structures. For a given design and applied load, the two methods differ in that the safety factor (the ratio of the theoretical capacity of a structural member to the maximum allowable load) is generally higher when calculated by limit analysis. For example, classical design limits the capacity of a rectangular beam to the bending The file is downloaded from www.bzfxw.com