1.3.1 Modified Conventional Beam Theory Approach
Experimental data has shown that inflatable beams do not behave according to
traditional beam theory. With modification to the traditional beam theory, an accurate
model can be made. One study analyzed inflatable beam deflections and stresses for
loads between incipient buckling, where bending stress equals axial stress due to
pressure, and final collapse. It was shown that initially bending occurred with no
wrinkling. When wrinkling occurred, a slack region and a taught region were present. A
formulation for the stress was developed showing zero axial stress in the slack region and
a portion of the max stress carried in the taught region. By equating expressions for
maximum axial stress, a formulation for the relationship between internal pressure and
applied tip force was determined. The curvature was determined and integrated twice to
find the deflection due to bending. The deflection due to shear was also determined
noting that it is negligible when the length of the beam is much larger than the radius of
the cross section. The total deflection was then determined as the algebraic sum of the
deflections due to bending and shear. Similar results were obtained for a beam subject to
distributed load bending (Comer & Levy, 1963). This analysis shows when wrinkles
begin to form and where they form. The wrinkled membrane is shown to have some
rigidity. The effect of the wrinkling on the bending strength of the beam is determined.
Another study applies the modified traditional beam theory approach from Comer
and Levy for fabric materials. An experimentally determined modulus of membrane of
the fabric material was used in place of Young's modulus. This modulus of membrane is
defined as the slope of the experimental stress resultant vs. engineering strain plot, where
stress resultant is the force per width of a pull-test sample. Using an approach similar to
that of Comer and Levy, the curvature was integrated numerically to determine tip