Skip to main content

Simplified Formulation of Solution for Beams on Winkler Foundation allowing Discontinuities due to Loads and Constraints

Buy Article:

$28.00 plus tax (Refund Policy)

Abstract:

The paper discusses material for a course in Structural Mechanics addressed to second-year Civil Engineering students. The response of beams on a Winkler foundation characterized by discontinuities in both the displacements (deflections and/or slopes) and forces (internal forces and/or loads) is studied. In particular, a simplified formulation for the solution of the discontinuous differential equation governing this problem is given. In some cases, the formulation is able to give the exact solution in a closed form. This is made possible through the use of the generalized functions, such as the well-known Unit Step Function and the Dirac delta function. The cases of discontinuities due to both loads and constraints are treated. The method of presentation of this material is by lecture. The time required to cover the arguments is 2 to 3 hours with 1 to 2 hours of revision. The lecture must be given after the classical beam theory has been covered. The new formulation presented in this paper will demonstrate that some particular aspects of mathematician analysis may be used to advantage to simplify an important problem in structural mechanics.

Keywords: DISCONTINUOUS BEAM SOLUTION; GENERALIZED FUNCTIONS; WINKLER FOUNDATION

Document Type: Research Article

Publication date: 2009-01-01

More about this publication?
  • This journal serves as an international interdisciplinary forum of reference for engineering education.
    A balance between papers on developments in educational methods technology, case studies, laboratory applications, new theoretical approaches, educational policy and survey papers is aimed for.
    Comprehensive coverage of new education schemes and techniques makes the journal a unique source of ideas for engineering educators who are keen to keep abreast of latest developments in educational applications in all fields of engineering.
    Some of the areas covered more extensively in recent issues are: CAD, CAE, computer applications in teaching thermodynamics, material science, electrical engineering, new courses and curricula, engineering management, control engineering, mechanical engineering, engineering design, student evaluation and institutional accreditation.
  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more