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National Advisory Committee for Aeronautics, Technical Notes - Bending with Large Deflection of a Clamped Rectangular Plate with Length Width Ratio of 1.5 Under Normal Pressure

The Von Karman equations for a thin flat plate with _ H
large deflections are solved for the special case of a plate
with clamped edges having a ratio of length to_width of_l.5'
and loaded by uniform normal pressure. Center deflections,
membrane stresses, and extreme-fiber bending stresses are
given as a function of pressure for center deflections up
to twice the thickness of the plate. For small deflections
the results coincide with those obtained by Hencky from the
linear theory.

The maximum stresses and center deflection at high
pressures differ less than 3 percent from those derived by
Boobnov for an infinitely long plate with clamped edges.
Thnsagreement suggests that clamped plates with a length—
to—width ratio greater than 1.5 may be regarded as infi—
nitely long plates for purposes of design.

An exact solution for the small deflection of a rec—
tangular plate with clamped edges having a ratio of _length_
to width of 1.5 was given by Hencky in reference 6 arnd an ‘
a-PPI‘o:r;irnate solution for large deflection was Presented by
Way in reference 7.

Exact solutions for plates with clamped edges under
normal pressure producing large deflections have been de— '
rived for the two extreme cases of the s uafe plate (ref—
erence 1) and the infinitely long plate fireference 2).
Comparison of these two solutions shows that the maximum
stresses and the center deflections differ more than 20
percent.

Experimental work (reference 5) indicates that a rec—
tangular plate having a length equal to twice its width.
behaves practically as an infinitely long plate.

It was decided to investigate theoretically the tran-
sition from the square plate to the infinitely long plate
by deriving the solution for a plate of finite length so
that b/a = 1.5.