Research Article
Oct 1969
Base Moment for a Class of Linear Systems
Publication: Journal of the Engineering Mechanics Division
Volume 95, Issue 5
Abstract
Contributions of the second and higher modes to the overturning moment at the base of any classical linear system whose fundamental mode is given by a straight line are shown to vanish identically. A necessary and sufficient condition for a nonuniform shear beam to exhibit a linear first mode is obtained. In particular, it is shown that a shear beam with uniform cross section and mass density will have a linear fundamental mode shape if and only if the shearing stiffness is distributed parabolically. For such a beam, the higher mode shapes are given by odd degree Legendre polynomials.
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Published In
Journal of the Engineering Mechanics Division
Volume 95 • Issue 5 • October 1969
Pages: 1053 - 1062
Copyright
© 1969 American Society of Civil Engineers.
History
Published in print: Oct 1969
Published online: Feb 3, 2021
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Authors
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Jacobo Bielak, AM.ASCE
Grad. Student, Div. of Engrg. and Applied Science, California Inst. of Tech., Pasadena, Calif.
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Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.