Analysis on Deformation and Stress of Bending Stratum Based on the Elastic Theory for Curved Beams

BU Wankui; XU Hui; ZHAO Yucheng

doi:10.21656/1000-0887.400081

Volume 41 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(3): 302-318

BU Wankui, XU Hui, ZHAO Yucheng. Analysis on Deformation and Stress of Bending Stratum Based on the Elastic Theory for Curved Beams[J]. Applied Mathematics and Mechanics, 2020, 41(3): 302-318. doi: 10.21656/1000-0887.400081

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Analysis on Deformation and Stress of Bending Stratum Based on the Elastic Theory for Curved Beams

doi: 10.21656/1000-0887.400081

¹College of Urban Construction, Heze University, Heze, Shandong 274015, P.R.China;²School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P.R.China

Funds: The National Natural Science Foundation of China(General Program)（51574228）

Received Date: 2019-03-01
Rev Recd Date: 2019-04-02
Publish Date: 2020-03-01

Abstract

Abstract

A displacement function suitable for plane curved beams in polar coordinates was introduced, and the partial differential governing equation for plane curved beams was obtained through theoretical analysis. Then, the displacement components and stress components were formulated with the displacement function. On this basis, the finite difference schemes of the partial differential governing equation, the displacement components and the stress components for the curved beam in polar coordinates were presented. Finally, these theoretical formulas were applied to analyze the displacement and stress distributions of the bending stratum. The results indicate that: 1) The bending stratum sinks down after excavation of the coal seam, and there are both tension and compression in the circumferential direction. 2) The radial stress reaches a peak value not far from the openoff cut and increases gradually from the inner surface to the outer surface along the radial direction; the circumferential stress reaches the peak value not far behind the working face and may cause circumferential compressive fracture in the bending stratum; the shear stress reaches the peak value not far from the openoff cut and increases from the inner surface to the outer surface along the radial direction for smallangle sections. The work provides a scientific basis and reference for coal mining engineering.
- curved beam,
- theory of elasticity,
- finite difference,
- deformation of overburden rock,
- stress analysis

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References

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