Charts Giving Critical Compressive Stress of Continuous Flat Sheet Divided Into Parallelogram-Shaped Panels Page: 5 of 32
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NACA TN 2392
In order to establish a stability criterion for the configuration
analyzed, the energy method of analysis is used, and an approximation is
made for the deflection of the plate expressed in skew coordinates (see
appendix A). The deflection function used leads to the exact solution
of the differential equation of equilibrium of the plate loaded in com-
pression for the special case of rectangular panels and also for the
special case of equal-sided panels of arbitrary skewness subjected to
compressive loading perpendicular to one set of sides. The accuracy
of the rest of the data is indicated, where feasible, by comparison
with the results of more accurate energy solutions, which are given in
RESULTS AND DISCUSSION
The critical compressive stress for parallelogram-shaped plate's may
be given by the formula used for rectangular plates
ct =kb -
where the dimension b is the perpendicular distance between the sup-
ports alined in the x-direction, as in figure 1. The critical-stress
coefficient k depends on the panel aspect ratio P (defined as a/b),
the direction of the applied compressive stress, and the magnitude of
the skew angle 0.
For loading in the x-direction (stress acting parallel to a set of
sides), the chart for kx is given in figure 2. Note should be taken
that, for a given value of 0, the buckling coefficients indicated for
each curve are associated with panels of equal area. In order to facili-
tate association of the curves of figure 2 with the geometry of the
panels, figure 3 has been prepared. In this figure, sketches of the
panels of aspect ratios of 1, 2, and 3 are presented along with four of
the curves of figure 2. In each sketch the mode of buckling for the
panel is indicated. Figures 2 and 3 indicate that the stability of the
skewed panels is definitely increased relative to equivalent rectangular
panels of the same area over a wide range of panel aspect ratio. This
increase in stability is due partly to the change in panel shape but is
caused mainly by the restraint imposed on the mode of buckling due to
the presence of adjacent skewed panels. At aspect ratios of 4.5 and
greater, this restraint has largely disappeared and the coefficients
approach the value 4.
The curves presented in figures 2 and 3 were derived by the energy
method of analysis with the use of an assumed deflection function capable
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Anderson, Roger A. Charts Giving Critical Compressive Stress of Continuous Flat Sheet Divided Into Parallelogram-Shaped Panels, report, July 1951; (https://digital.library.unt.edu/ark:/67531/metadc59839/m1/5/: accessed May 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.