caa a22 4500 467913773 CHVBK 20180406152856.0 cr unu---uuuuu 170328e20060901xx s 000 0 eng 10.1007/s10999-007-9028-0 doi (NATIONALLICENCE)springer-10.1007/s10999-007-9028-0 Estimating the stresses in cantilever beam loaded by a parabolically distributed load with Airy stress functions [Elektronische Daten] [Abbas Rastgoo, Armen Amirian] This study presents three mathematical methods namely the polynomial stress function approach, the Fourier series form approach and the approximated equations form approach for finding the stress distribution in a cantilever beam with rectangular cross section loaded by a parabolically distributed load. By taking the stress function as a polynomial of the seventh degree, it is attempted to find the coefficients either in complete or in full shape of the polynomial. In the Fourier series approach, the load is discreted to unlimited series of harmonic loads and superposing resultant stresses is the affect of parabolically distributed load on the beam. The resultant stresses are compared with some approximated stress formulas which have been provided before. Finite element analysis are done for square, short, medium and long cantilever beams and the mathematical results of stress distribution in five different height of the beam was compared with FEM results. It was found good results for τ yy and τ xy in all cross section of the beams and acceptable results for τ xx only in y=0. It is found that discreting loads to even a limit number of harmonic loads and superposing the resultant stresses can give the distribution of τ yy and τ xy with the acceptable precision in medium and long cantilever beams with rectangular cross section. Springer Science+Business Media, Inc., 2007 Cantilever beam nationallicence Parabolically loading nationallicence Airy stress function nationallicence Polynomial nationallicence Fourier series nationallicence Rastgoo Abbas Mechanical Engineering department, University of Tehran, Tehran, Iran aut Amirian Armen Mechanical Engineering department, University of Tehran, Tehran, Iran aut International Journal of Mechanics and Materials in Design Springer Netherlands 3/3(2006-09-01), 253-264 1569-1713 3:3<253 2006 3 10999 https://doi.org/10.1007/s10999-007-9028-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10999-007-9028-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rastgoo Abbas Mechanical Engineering department, University of Tehran, Tehran, Iran aut NATIONALLICENCE 700 1- Amirian Armen Mechanical Engineering department, University of Tehran, Tehran, Iran aut NATIONALLICENCE 773 0- International Journal of Mechanics and Materials in Design Springer Netherlands 3/3(2006-09-01), 253-264 1569-1713 3:3<253 2006 3 10999 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer