Analysis of Transverse Loading on a Beam Utilizing the Beltrami-Michell Equations

Nathan A. Guido

Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico, USA.

Luo Li

Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico, USA.

Tariq Khraishi *

Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico, USA.

*Author to whom correspondence should be addressed.


Abstract

The stress field of a beam with a circular cross-section have been developed in the current work. One end of the beam is fixed while the other end is under traverse load at its center. The Beltrami-Michell compatibility equations were utilized to obtain coefficients in an assumed stress function which can be used to derive the stress field. To visualize the stress distribution in the beam, one can use MATLAB to generate surface plots and contour plots for the developed stress field. According to the plots, the maximum  can be found at the center area of the cross-section while the minimum  is captured at the same area. The maximum shear stress in the section occurs at points along the perimeter of the section. Moreover, the goal of this paper is to prove that any stress function with higher order terms always converge to the same stress solution for the beam utilizing lower order terms.

Keywords: Beam bending, circular cross-section, stress field


How to Cite

Guido, Nathan A., Luo Li, and Tariq Khraishi. 2022. “Analysis of Transverse Loading on a Beam Utilizing the Beltrami-Michell Equations”. Physical Science International Journal 26 (5):26-34. https://doi.org/10.9734/psij/2022/v26i5744.

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