Macaulay's method for a Timoshenko beam
Macaulay's method for a Timoshenko beam
The Macaulay bracket notation is familiar to many engineers for the deflection analsyis of a Euler-Bernoulli beam subject to multiple or discontinuous loads. An expression for the internal bending moment, and hence curbature, is valid at all locations along the beam, and the deflection curve can be calculated by integrating twice with respect to the axial coordinate. The notation obviates the need for matching of multiple constants of integration for the various sections of the beam. Here, the method is extended to a Timoshenko beam, which includes the additional deflection due to shear. This requires an additional expression for the shearing force, also valid at all locations along the beam.
macaulay, bracket notation, timoshenko beam
285-292
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
October 2007
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Stephen, N.G.
(2007)
Macaulay's method for a Timoshenko beam.
International Journal of Mechanical Engineering, 35 (4), .
Abstract
The Macaulay bracket notation is familiar to many engineers for the deflection analsyis of a Euler-Bernoulli beam subject to multiple or discontinuous loads. An expression for the internal bending moment, and hence curbature, is valid at all locations along the beam, and the deflection curve can be calculated by integrating twice with respect to the axial coordinate. The notation obviates the need for matching of multiple constants of integration for the various sections of the beam. Here, the method is extended to a Timoshenko beam, which includes the additional deflection due to shear. This requires an additional expression for the shearing force, also valid at all locations along the beam.
Text
Step_08b.pdf
- Accepted Manuscript
More information
Published date: October 2007
Keywords:
macaulay, bracket notation, timoshenko beam
Identifiers
Local EPrints ID: 43666
URI: http://eprints.soton.ac.uk/id/eprint/43666
ISSN: 0306-4190
PURE UUID: c69f2d34-dfab-4108-b90f-3a3c5d0eef4d
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Date deposited: 07 Jul 2008
Last modified: 15 Mar 2024 08:56
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