Effective Width of Thin Plates in Compression

The effective width is examined theoretically for ideally flat plates and for plates with small deviation from flatness. The edges parallel to the direction of forces are considered free to move or restrained to remain straight in the plane of the plate. The Von Karman's governing differential equations are satisfied with an approximate solution based on assuming that, the deflection form at the instant of buckling is preserved after the loading exceeds the buckling limit. This assumption limits the validity of the analysis to structural problems in which the load exceeds the buckling limit by relatively little magnitude. Formulas are obtained which show the effective width of the plate to be reduced when there is a small deviation from flatness and/or the edges parallel to loading are free to move in the plane of the plate. Comparison shows good agreement between a theoretically obtained formula and the equivalent Winter-formula which is based on experimental data and has been adopted by the American Iron and Steel Institute for their manual.