A three-dimensional elasticity solution for continuous beams

✍ Scribed by L.R. Herrmann

• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 586 KB
• Volume: 278
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90110-3

✦ Synopsis

A method for the development of solutions, within the framework of threedimensional elasticity, for continuous beam problems is illustrated. A three-dimensional continuous beam analysis will find utility in analyzing beam-like structures whose cross sectional dimensions, as compared to their span lengths, are such that neither the usual beam assumption (which yields a one-dimensional problem) or the plane stress aseumption (which yields a two-dimensional problem) can be invoked. Thus, since neither the beam nor plane stress assumptions have been applied, the structural element under consideration may be as deep or wide as desired. Additionally, a beam subjected to a Eoad which varies with the transverse direction may be Tigorously analyzed. The solution is restricted to a continuous beam in which the loading conditions are identical over each span.

The solution is in the form of two double series, the first of which is a double Fourier series, the second a combination Fourier and Fadle eigenfunction series.