Buckling defined

When Zotefoam HDPE materials of density 98 kg m" were subjected to a single major compressive impact (419), after recovery at 50 °C for 1 hour, the performance, defined as the energy density absorbed before the compressive stress reached 2.5 MPa was back to 75% of the initial value. Further severe impacts caused a further deterioration of the performance of the recovered foam. Peak compressive strains of 80 to 90% caused some permanent buckling of the cell walls of HDPE foams. The recovery is much slower than the 0.1 second impact time, so is not a conventional linear viscoelastic response. It must be driven by the compressed air in internal cells in the gas, with some contribution from viscoelasticity of the polymer. Recovery of dimensions had slowed to a very low rate after 10 seconds at 20 °C or after 10 seconds at 50 °C. 

Fig. 17 Schematic representation of the interfacial failure process which is induced by the transverse contraction of the substrate in the y direction. The system is submitted to uniaxial tension in the x direction, (a) the decohesion and buckling of a strip of the cracked film, defined by two consecutive transverse cracks, is decomposed in, (b) a decohesion stage, and (c) a buckling stage of the decohered part of the strip.

Figure 13. Top and side views of the Cu 100 -c(4x4)-Pb surface alloy. The top view (above) indicates the two in-equivalent Cu atoms in the outermost layer (1 and 2) and two inequivalent Pb sites (1 and 2 ). The side view (below) defines the major geometric parameters. Re-drawn from [113]. A represents the Pb-Cu top layer buckling quoted with respect to the centre of mass of the Pb and Cu rows.

Fig. 7 Representative cryo-TEM micrographs obtained after exposing a perpendicular and b parallel aligned PS-fc-PI-b-PS-fi-PI-fi-PS-fi-PI-fi-PS to tetradecane, a solvent for Pl and a nonsolvent for PS. Pl domains were stained by OSO4 and appear dark. The structure is viewed along shear direction. Perpendicular lamellae were unaffected by solvent, whereas parallel lamellae displayed extensive buckling and delamination, indicating loop formation. The coordinate system is defined in Fig. 6. From [44]. Copyright 2004 American Chemical Society...

For AS ME Code vessels the allowable compressive stress is Factor B. The ASME Code, factor B. considers radius and length but does not consider length unless external pressure is involved. This procedure illustrates other methods of defining critical stress and the allowable buckling stress for vessels during transport and erection as well as equipment not designed to the ASME Code. For example, shell compressive stresses are developed in tall silos and bins due to the side wall friction of the contents on the bin wall. 

The terms buckling and collapse are often used interchangeably. Buckling is defined as localized failure caused by overstress or instability of the wall under compressive loading. Collapse is a general failure of the entire cross section by flattening due to external pressure. 

There are three lands of buckling elastic, inelastic, and plastic. This procedure is concerned with elastic buckling only. AISC assumes that the upper limit of elastic buckling is defined by an average stress equal to one-half the yield point. 

The out-of-plane equilibrium of a plate subject to in-plane forces Nx, Ny and Nxy which give rise to buckling instability is defined by... 

Figure 4.12 Comparison of (a) buckling strains and (b) threshold strains for first four interfaces of [45/0/-45/90]4s and [(45/—45/45/—45)2/(90/0/90/0)2ls laminates. A 30 mm diameter delamination is assumed at each interface in turn and material properties are defined in Table 4.4.

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