Bending and shear stresses developed by the instantaneous arrest of the root of a cantilever beam with a mass at its tip Page: 3 of 33
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MR No. L4 30
When an airplane lands, the vertical component of
the velocity is rapidly reduced to zero. The shock of
the sudden change in motion gives rise to vibratory
stresses in the airplane. As a beginning in the study
of these stresses a previous report (reference 1) dis-
cussed in detail the behavior of a cantilever beam in
translational motion when its root is suddenly brought
to rest. In that paper equations are given for deter-
mining the stresses, the deflections, and the accelera-
tions that arise throughout the beam as a result of the
impact. The present report extends the basic problem of
reference 1 to include the effect of a concentrated mass
at the tip of the cantilever beam.
As in reference 1, the present paper is based on the
usual engineering beam theory. In this theory the
deflections are considered to be the result of bending
alone, shear deflections neglected. The theory as applied
to ordinary beams gives reasonably good results so long
as the distance between inflection points is greater than
a few times the depth of the beam. When this theory for
beam action is used in vibration problems, such as that
in the present paper, the results are satisfactory for
those modes of vibration for which the nodes are not too
This report summarizes the results of a theoretical
solution giien in appendix A and presents an experimental
verification of these results. A numerical example for
the calculation of the maximum stresses near the root of
the cantilever beam is given in appendix B.
E modulus of elasticity
Y weight density of material
X coefficient of equivalent viscous damping of
c velocity of sound in material
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Schmieder, Albert K. Bending and shear stresses developed by the instantaneous arrest of the root of a cantilever beam with a mass at its tip, report, November 1, 1944; (digital.library.unt.edu/ark:/67531/metadc62215/m1/3/: accessed October 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.