Bending and shear stresses developed by the instantaneous arrest of the root of a cantilever beam with a mass at its tip Page: 2 of 33
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3 1176 01357 2657
MR No. .K30
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Army Air Forces, Air Technical Service Command
BENDING AND SHEAR STRESSES DEVELOPED BY THE
INSTANTANEOUS ARREST OF THE ROOT OF A
CANTILEVER BEAM WITH A MASS AT ITS TIP
By Elbridge Z. Stowell, Edward B. Schwartz,
John C. Houbolt,and Albert K. Schmieder
A theoretical and experimental investigation has been
made of the behavior of a cantilever beam in transverse
motion with a mass at its tip when the root is suddenly
brought to rest. Equations are given for determining the
stresses, the deflections, and the accelerations that arise
in the beam as a result of the impact. The theoretical
equations, which have been confirmed experimentally, reveal
that for a beam with a given cross section and velocity at
impact and for a given ratio of tip mass to beam mass, the
bending stresses for a particular mode at a given percentage
of the distance from root to tip are independent of the
length of the beam; whereas, the shear stresses vary
inversely with the length.
The addition of a mass to the tip of a cantilever
beam increases appreciably the stresses produced by the
first mode of vibration but changes only slightly the
stresses contributed by the higher modes. The tip mass
increases the maximum bending stress much less than might
be expected on the basis of experience with the static
action of structures. For practical engineering analysis
tle maximum bending stress developed in a suddenly arrested
cantilever beam can be found by a simple addition of
stress amplitudes in the first few modes without regard
to phase relations between modes.
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Stowell, Elbridge Z.; Schwartz, Edward B.; Houbolt, John C. & 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 1944; (digital.library.unt.edu/ark:/67531/metadc62215/m1/2/: accessed February 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.