Local Buckling

Buckling may sometimes occur in the form of wrinkles in thin elements such as webs, flanges, cover plates, and other parts that make up a section. This phenomenon is called local buckling.
The critical buckling stress in rectangular plates with various types of edge support and edge loading in the plane of the plates is given by

where k  constant that depends on the nature of loading, length-to-width ratio of plate, and edge conditions
E  modulus of elasticity
u Poisson’s ratio [Eq. (3.39)]
b  length of loaded edge of plate, or when the plate is subjected to shearing forces,
the smaller lateral dimension
t  plate thickness Table 3.5 lists values of k for various ztypes of loads and edge support conditions. (From formulas, tables, and curves in F.

NONLINEAR BEHAVIOR OF STRUCTURAL SYSTEMS
Contemporary methods of steel design require engineers to consider the behavior of a structure as it reaches its limit of resistance. Unless premature failure occurs due to local buckling, fatigue, or brittle fracture, the strength limit-state behavior will most likely include a nonlinear response. As a frame is being loaded, nonlinear behavior can be attributed primarily to second-order effects associated with changes in geometry and yielding of members and connections.