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A New Approach to Analyzing Reactions and Deflections of Beams: Formulation and Examples

[+] Author Affiliations
I. C. Jong, J. J. Rencis

University of Arkansas

H. T. Grandin, Jr.

Worcester Polytechnic Institute

Paper No. IMECE2006-13902, pp. 91-96; 6 pages
doi:10.1115/IMECE2006-13902
From:
  • ASME 2006 International Mechanical Engineering Congress and Exposition
  • Innovations in Engineering Education: Mechanical Engineering Education, Mechanical Engineering Technology Department Heads
  • Chicago, Illinois, USA, November 5 – 10, 2006
  • Conference Sponsors: Mechanical Engineering Education, Mechanical Engineering Technology Department Heads
  • ISBN: 0-7918-4781-0 | eISBN: 0-7918-3790-4
  • Copyright © 2006 by ASME

abstract

This paper is aimed at developing a new approach to analyzing statically indeterminate reactions at supports, as well as the slopes and deflections, of beams. The approach uses a set of four general formulas, derived using singularity functions. These formulas are expressed in terms of shear forces, bending moments, distributed loads, slopes, and deflections of a beam having a constant flexural rigidity and carrying typical loads. These loads include (a) a bending moment and a shear force at the left, as well as at the right, end of the beam; (b) a concentrated force, as well as a concentrated moment, somewhere on the beam; and (c) a uniformly, as well as a linearly varying, distributed force over a portion of the beam. The approach allows one to treat reactions at supports (even supports not at the ends of a beam) as concentrated forces or moments, where corresponding boundary conditions at the points of supports are to be imposed. This feature allows one to readily determine reactions at supports as well as slopes and deflections of beams. A beam needs to be divided into segments for study if it contains discontinuities in slope at hinge connections or different flexural rigidities in different segments. Several examples are included to illustrate the new approach.

Copyright © 2006 by ASME
Topics: Deflection

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