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<p>Many engineering structures can be modeled as beam structures, where shear stress plays a critical role in stress intensity analysis. While the Euler-Bernoulli beam theory offers good comutational efficiency, it neglects the effects of shear deformation, limiting its accuracy in certain applications. This paper presents a method to accurately compute shear stress and its distribution in beam structures, based on the Euler-Bernoulli beam theory and partial differential equilibrium equations applied to the longitudinal section. The approach discretizes complex cross-sections using arc and rectangular elements. The Galerkin method is employed to solve boundary value problems and determine shear stress. This enhancement to the Euler-Bernoulli beam theory provides a more accurate shear correction and is applicable to a wide range of engineering problems.</p>

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Shear stress correction in Euler-Bernoulli beam theory

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Tianyu Wang,
  • Jinshuai Xu,
  • Zhaohui Qi,
  • Tianjiao Zhao

摘要

Many engineering structures can be modeled as beam structures, where shear stress plays a critical role in stress intensity analysis. While the Euler-Bernoulli beam theory offers good comutational efficiency, it neglects the effects of shear deformation, limiting its accuracy in certain applications. This paper presents a method to accurately compute shear stress and its distribution in beam structures, based on the Euler-Bernoulli beam theory and partial differential equilibrium equations applied to the longitudinal section. The approach discretizes complex cross-sections using arc and rectangular elements. The Galerkin method is employed to solve boundary value problems and determine shear stress. This enhancement to the Euler-Bernoulli beam theory provides a more accurate shear correction and is applicable to a wide range of engineering problems.