Since 1963
ARTICLE
Three-point bending of an expanded-tapered beam with consideration of the shear effect
1
Łukasiewicz Research Network – Institute of Rail Vehicles “TABOR”, Poznan, Poland
2
Poznan University of Technology, Institute Mathematics, Poznan, Poland
Submission date: 2019-09-23
Final revision date: 2019-11-05
Acceptance date: 2019-11-07
Online publication date: 2020-07-15
Publication date: 2020-07-15
Journal of Theoretical and Applied Mechanics 2020;58(3):661-672
KEYWORDS
TOPICS
ABSTRACT
The paper is devoted to an expanded-tapered beam of rectangular cross section subjected
to three-point bending. The analytical model of the beam is formulated with consideration
of a non-linear hypothesis of the cross section deformation. The problem of shear stress
distribution in the beam is analysed based on the above mentioned hypothesis. Moreover,
a numerical FEM model (SolidWorks) is developed. Examplary computations have been
carried out based on the analytical and numerical models.
REFERENCES (25)
1.
Attarnejad R., Shahba A., Semnani S.J., 2011, Analysis of non-prismatic Timoshenko beams using basic displacement functions, Advanced Structural Engineering, 14, 2, 319-332.
2.
Auciello N.M., Ercolano A., 2004, A general solution for dynamic response of axially loaded non-uniform Timoshenko beams, International Journal of Solids and Structures, 41, 18-19, 4861-4874.
3.
Auricchio F., Balduzzi G., Lovadina C., 2015, The dimensional reduction approach for 2D non-prismatic beam modelling: A solution based on Hellinger-Reissner principle, International Journal of Solids and Structures, 63, 264-276.
4.
Balduzzi G., Aminbaghai M., Sacco E., Fűssl J., Eberhardsteiner J., Auricchio F., 2016, Non-prismatic beams: A simple and effective Timoshenko-like model, International Journal of Solids and Structures, 90, 236-250
5.
Balduzzi G., Hochreiner G., Fűssl J., 2017, Stress recovery from one dimensional models for tapered bi-symmetric thin-walled I beams: deficiencies in modern engineering tools and procedures, Thin-Walled Structures, 119, 934-944.
6.
Bertolini P., Eder M.A., Taglialegne L., Valvo P.S., 2019, Stresses in constant tapered beams with thin-walled rectangular and circular cross sections, Thin-Walled Structures, 137, 527-540.
7.
Carrera E., Giunta G., 2010, Refined beam theories based on a unified formulation, International Journal of Applied Mechanics, 2, 1, 117-143.
8.
Dado M., Al-Sadder S., 2005, A new technique for large deflection analysis of non-prismatic cantilever beams, Mechanics Research Communications, 32, 6, 692-703.
9.
De Rosa M.A., Lippiello M., 2009, Natural vibration frequencies of tapered beams, Engineering Transactions, 57, 1, 45-66.
10.
Ghayesh M.H., 2018, Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams, Applied Mathematical Modelling, 59, 583-596.
11.
Huang Y., Wu J.X., Li X.F., Yang L.E., 2013, Higher-order theory for bending and vibration of beams with circular cross section, Journal of Engineering Mathematics, 80, 1, 91-104.
12.
Maalek S., 2004, Shear deflections of tapered Timoshenko beams, International Journal of Mechanical Sciences, 46, 5, 783-805.
13.
Magnucki K., 2019, Bending of symmetrically sandwich beams and I-beams – Analytical study, International Journal of Mechanical Sciences, 150, 411-419.
14.
Magnucki K., Lewinski J., Stawecka H., 2019, Stress state in the tapered beam bending – Analytical and numerical FEM studies, Rail Vehicles, 2, 1-8.
15.
Rajasekaran S., 2008, Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods, Structural Engineering Mechanics, 28, 2, 221-238.
16.
Rajasekaran S., 2013, Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods, Applied Mathematical Modelling, 37, 6, 4440-4463.
17.
Reddy J.N., 2010, Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates, International Journal of Engineering Sciences, 48, 1507-1518.
18.
Shahba A., Attarnejad R., Tavanaie Marvi M., Hajilar S., 2011, Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions, Composites Part B: Engineering, 42, 4, 801-808.
19.
Slivker V., 2007, Mechanics of Structural Elements: Theory and Applications, Springer, Berlin, Heidelberg, New York.
20.
Taha M.H., Nassar M., 2014, Analysis of axially loaded tapered beams with general end restraints on two-parameter foundation, Journal of Theoretical and Applied Mechanics, 55, 1, 215-225.
21.
Timoshenko S.P., 1921, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41, 245, 744-746.
22.
Trahair N., Ansourian P., 2016, In-plane behaviour of web-tapered beams, Engineering Structures, 108, 47-52.
23.
Wang C.Y., 2012, Large post-buckling of heavy tapered elastica cantilevers and its asymptotic analysis. Brief Note, Archives of Mechanics, 64, 2, 207-220.
24.
Wang C.M., Reddy J.N., Lee K.H., 2000, Shear Deformable Beams and Plates, Elsevier, Amsterdam, Lausanne, New York, Shannon, Singapore, Tokyo.
25.
Zhou D., Cheung K., 2001, Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam functions, ASME: Journal of Applied Mechanics, 68, 4, 596-602.
| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
