Macaulay's method for a Timoshenko beam

Stephen, N.G. (2007) Macaulay's method for a Timoshenko beam. International Journal of Mechanical Engineering Education, 35, (4), 285-292.


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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.

Item Type: Article
ISSNs: 0306-4190 (print)
Keywords: macaulay, bracket notation, timoshenko beam
Subjects: Q Science > Q Science (General)
T Technology > TA Engineering (General). Civil engineering (General)
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences > Computational Engineering and Design
ePrint ID: 64151
Accepted Date and Publication Date:
October 2007Published
Date Deposited: 17 Dec 2008
Last Modified: 31 Mar 2016 12:48

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