Engineering Transactions, 0, 0, pp. , 0
10.24423/EngTrans.1174.20201120

A Shear Deformation Theory of Beams with Bisymmetrical Cross-Sections Based on the Zhuravsky Shear Stress Formula

Krzysztof MAGNUCKI
Lukasiewicz Research Network - Institute of Rail Vehicles TABOR
Poland

Jerzy LEWIŃSKI
Lukasiewicz Research Network - Institute of Rail Vehicles TABOR
Poland

Ewa MAGNUCKA-BLANDZI
Poznan University of Technology
Poland

This paper is devoted to simply supported beams with bisymmetrical cross-sections under a generalized load. Based on the Zhuravsky shear stress formula, the shear deformation theory of a planar beam cross-section is formulated. The deflections and the shear stresses of example beams are determined. Moreover, the numerical-FEM computations of these beams are carried out. The results of the research are shown in figures and tables.
Keywords: shear deformation theory; shear stress; beam deflection; shear effect
Full Text: PDF

References

Gere J.M., Timoshenko S.P., Mechanics of Materials, 2nd Ed., Books/Cole Engineering Division, Boston, 1984.

Rychter Z., A family of shear-deformation beam theories and a refined Bernoulli-Euler theory, International Journal of Engineering Science, 31(4): 559–567, 1993, doi: 10.1016/0020-7225(93)90049-Z.

Kathnelson A.N., Improved engineering theory for uniform beams, Acta Mechanica, 114(1–4): 225–229, 1996, doi: 10.1007/BF01170406.

Wang C.M., Reddy J.N., Lee K.H., Shear Deformable Beams and Plates: Relationships with classical Solutions, Elsevier, Amsterdam, Lausanne, New York, Oxford, Shannon, Singapore, Tokyo, 2000.

Hutchinson J.R., Shear coefficients for Timoshenko beam theory, ASME, Journal of Applied Mechanics, 68(1): 87–92, 2000, doi: 10.1115/1.1349417.

Kadoli R., Akhtar K., Ganesan N., Static analysis of functionally graded beams using higher order shear deformation theory, Applied Mathematical Modelling, 32(12): 2509–2525, 2008, doi: 10.1016/j.apm.2007.09.015.

Jun L., Hongxing H., Dynamic stiffness analysis of laminated composite beams using trigonometric shear deformation theory, Composite Structures, 89(3), 433–442, 2009, doi: 10.1016/j.compstruct.2008.09.002.

Reddy J.N., Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates, International Journal of Engineering Science, 48(11): 1507–1518, 2010, doi: 10.1016/j.ijengsci.2010.09.020.

Ghugal Y.M., Sharma R., A refined shear deformation theory for flexure of thick beams, Latin American Journal of Solids and Structures, 8(2): 183–195, 2011, doi: 10.1590/S1679-78252011000200005.

Thai H.-T., Vo T.P., A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, 54: 58–66, 2012.

Akgöz B., Civalek Ö., A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science, 70: 1–14, 2013, doi: 10.1016/j.ijengsci.2013.04.004.

Sawant M.K., Dahake A.G., A new hyperbolic shear deformation theory for analysis of thick beam, International Journal of Innovative Research in Science, Engineering and Technology, 3(2): 9636–9643, 2014.

Bourada M., Kaci A., Houari M.S.A., Tounsi A., A new simple shear and normal deformations theory for functionally graded beams, Steel and Composite Structures, 18(2): 409–423, 2015, doi: 10.12989/scs.2015.18.2.409.

Polizzotto C., From the Euler-Bernoulli beam to the Timoshenko one through a sequence of Reddy-type shear deformable beam models of increasing order, European Journal of Mechanics- A/Solids, 53: 62–74, 2015, doi: 10.1016/j.euromechsol.2015.03.005.

Endo M., Study on an alternative deformation concept for the Timoshenko beam and Mindlin plate models, International Journal of Engineering Science, 87: 32–46, 2015, doi: 10.1016/j.ijengsci.2014.11.001.

Endo M., ‘One-half order shear deformation theory’ as a new naming for the transverse, but not in-plane rotational, shear deformable structural models, International Journal of Mechanical Sciences, 122: 384–391, 2017, doi: 10.1016/j.ijmecsci.2016.10.016.

Endo M., Equivalent property between the one-half order and first-order shear deformation theories under the simply supported boundary conditions, International Journal of Mechanical Sciences, 131–132: 245–251, 2017, doi: 10.1016/j.ijmecsci.2017.07.005.

Kharlab V.D., On elementary theory of tangent stresses at simple bending of beams, Procedia Structural Integrity, 6: 286–291, 2017, doi: 10.1016/j.prostr.2017.11.044.

Genovese D., Elishakoff I., Shear deformable rod theories and fundamental principles of mechanics, Archive of Applied Mechanics, 89(10): 1995–2003, 2019, doi: 10.1007/s00419-019-01556-7.

Magnucki K., Lewinski J., Cichy R., Bending of beams with bisymmetrical cross sections under non-uniformly distributed load – Analytical and numerical-FEM studies, Archive of Applied Mechanics, 89(10): 2103–2114, 2019, doi: 10.1007/s00419-019-01566-5.

Magnucki K., Stawecki W., Magnucka-Blandzi E., Bending of beams with consideration of a seventh-order shear deformation theory, Engineering Transactions, 68(2): 119–135, 2020, doi: 10.24423/EngTrans.1129.20200214.




DOI: 10.24423/EngTrans.1174.20201120

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland