The conditions for plane sections remaining plane. (15th July 2022)

• Record Type: Journal Article
• Authors: Wu, Yu-Fei
• Is Part Of: Engineering structures. Volume 263(2022)
• Publication Date: 2022-07-15
• Subjects: Engineering mechanics -- Flexural members -- Beams -- Bernoulli hypothesis; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2022.114387
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: Bernoulli hypothesis is proved in the work. Thought experiment is used to prove the hypothesis. The plane section assumption is true under certain condition. The validity of the hypothesis is not related to magnitude of deformation. Abstract: The Euler–Bernoulli hypothesis that plane sections before bending remain plane after bending is a cornerstone of the sciences, especially in mechanics and engineering, and an enabler of the Second Industrial Revolution. Although it is widely applied in science and engineering, especially in structural engineering, its general validity has never been established theoretically, except in some special cases such as linear elastic and small deformation conditions. Its applicability to a particular problem requires extensive experimental evaluation or practical observation. Through a thought experiment commonly used in the derivation of physics theory, this paper rigorously deduces the theorem that gives the conditions for the Euler–Bernoulli hypothesis. The new theorem is general and applies to flexural members composed of any number of different materials, regardless of the properties of the materials, magnitude of deformation, and elastic or plastic strain conditions. This new theorem paves the way for future secure applications of this hypothesis without the need for experimental verification before use.