Bending and Shear Stresses Developed by the Instantaneous Arrest of the Root of a Cantilever Beam Rotating With Constant Angular Velocity About a Transverse Axis Through the Root Page: 2 of 26
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NACA ARR No. L5E25
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ADVANCE RESTRICTED REPORT
BE NDNG AND SHEAR STRESSES DEVELOPED BY THE INSTANTANEOUS
ARREST OF THE ROOT OF A CANTILEVER BEAM ROTATING
WITH CONSTANT ANGULAR VELOCITY ABOUT A
TRANSVERSE AXIS THROUGH THE ROOT
By Elbridge Z. Stowell, Edward B. Schwartz
and John C. Houbolt
SUMMARY
A theoretical investigation was made of the behavior
of a cantilever beam in rotational motion about a transverse
axis through the root when the rotation of the root is
suddenly stoDoed. Equations are given for determining
the stresses, the deflections, and the accelerations
that occur in the beam as a result of the arrest of motion.
The equations for bending and shear stress reveal
that, at a given percentage of the distance from root
to tip and at a given tip velocity, the bending stresses
for a particular mode are independent of the length of
the beam and the shear stresses vary inversely with the
length. When examined with respect to a given angular
velooity instead of a given tip velocity, the equations
reveal that the bending stress is proportional to the
length of the beam; whereas the shear stress is independent
of the length.
Sufficient experimental verification of the theory
has previously been given in connection with another
problem of the same type.
INTRODUCTION
Stresses occur in the structure of an airplane as a
result of the shooks experienced in landing. These- .
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Stowell, Elbridge Z.; Schwartz, Edward B. & Houbolt, John C. Bending and Shear Stresses Developed by the Instantaneous Arrest of the Root of a Cantilever Beam Rotating With Constant Angular Velocity About a Transverse Axis Through the Root, report, June 1945; (https://digital.library.unt.edu/ark:/67531/metadc63067/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.