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A Cantilever Subjected to Axial Force, Bending Moment, and Shear Force

Published online by Cambridge University Press:  12 August 2014

W.-D. Tseng ,
J.-Q. Tarn  and
C.-C. Chang
W.-D. Tseng*
Affiliation:
Department of Construction Engineering, Nan Jeon University of Science and Technology, Tainan, Taiwan
J.-Q. Tarn
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan
C.-C. Chang
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan
*
*wdtseng@mail.nju.edu.tw
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Abstract

We present an exact analysis of the displacement and stress fields in an elastic 2-D cantilever subjected to axial force, shear force and moment, in which the end conditions are exactly satisfied. The problem is formulated on the basis of the state space formalism for 2-D deformation of an orthotropic body. Upon delineating the Hamiltonian characteristics of the formulation and by using eigenfunction expansion, a rigorous solution which satisfies the end conditions is determined. The results show that the end condition alters the stress significantly only near the end, and elementary solutions in the form of polynomials can give sufficiently accurate results except near the ends. Such a system would give rise to localized stresses and displacements in the immediate neighborhood of the ends, and the effect may be expected to diminish with distance on account of geometrical divergence.

Keywords

2-D cantileverEnd effectsHamiltonianState spaceSymplectic orthogonalityOrthotropic
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 5 , October 2014 , pp. 549 - 559
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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