Ultimate
Strength of Plates
The collapse of columns
occurs either by elastic buckling if the column is slender (Euler or “ideal”
column buckling) or by the commencement of yielding which so seriously
decreases the column bending stiffness that collapse by inelastic buckling
follows almost immediately. In the case
of plating, the mechanism of collapse is more complex. Specifically, collapse of plating depends
upon type of loading, boundary conditions, aspect ratio, initial distortion,
and even residual stresses.
For “slender” plates
subject to an increasing compressive uni-axial stress (without lateral load),
the plate goes through a number of phases prior to ultimate failure or
collapse. At low levels of stress, the
plate remains flat, as the stress remains below the elastic buckling stress and
below the yield stress. The first noticeable
response when the stress reaches the elastic buckling stress is that the plate
buckles, and as a result the center portion of the plating partially “escapes”
from the
axial shortening being
applied by the compressive stress. As a
result the center buckled portion of the plate “sheds” some of the load, which
is transferred to the edges of the plate.
In this post-buckled state, the outer edges of the plate are carrying
higher stress (higher than the mean stress s) and the center portion carries a
lower stress. As the compressive stress continues to increase, eventually the
stress on the outer edges of the plate reaches the material yield stress, and
the edges yield (plastic deformation).
Eventually, as the center portion of the plate also yields, and the
plate collapses.
The extent to which a
plate will buckle and collapse depends upon several factors, including load
(magnitude, type, etc.), plate geometry (late aspect ratio a/b, thickness, initial
distortions), boundary conditions, and manufacturing variances (welds, voids,
etc.). Because of this highly variable
nature, evaluation of collapse of plate structures is usually investigated
using finite element analysis (FEA).
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