Influence of Shear Strain on the Deflection of Girders

Antonia J. Lazarević, Tanja Mališ, Elizabeta Šamec, Elizabeta Jerečić

Abstract


Numerical calculations are a standard part of modern structural design. Engineers remain particularly interested in real problems where analytical and numerical solutions can be compared with experimental results. Such cases are typical examples of benchmarks because they are used to verify the assumptions introduced. This study shows in detail how shear stresses affect the deflection of a relatively short and high cantilever when the span-to-height ratio of the cross-section is less than five. Such models are frequently used in the design of cantilevers that support heavily loaded beams, for example in the cement industry (e.g., often as structural elements for a heat exchanger system) or for the assessment of short cantilever limit states that appear during excavation in rock sediments. The models are also suitable for designing the various details and joints in the industry of prefabricated elements. This work analyzes in depth the analytical solutions for the displacement field of the linear elastic plane stress theory with two displacement boundary conditions. Also, the solutions were compared with the beam, two-, and three-dimensional numerical models using SAP2000. The results highlight the fundamental principles and solutions behind plane stress and beam theories, with an insight into the advantages and limitations of such models.

 

Doi: 10.28991/CEJ-2024-010-05-04

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Keywords


Short Cantilever; Linear Elasticity Theory; Analytical Solution of the Displacement Field; Plane Stress State; SAP2000.

References


Byskov, E. (2013). Elementary Continuum Mechanics for Everyone. In Solid Mechanics and Its Applications. Springer, Dordrecht, Netherlands. doi:10.1007/978-94-007-5766-0.

Slaughter, W. S. (2002). The Linearized Theory of Elasticity. Birkhäuser Boston, Boston, United States. doi:10.1007/978-1-4612-0093-2.

Dvornik, J., & Lazarević, D. (2007). The Role of Creativity and Engineering Judgment in Construction Work. Građevinar, 59(03), 197-207.

Timoshenko, S., & Goodier, J. N. (1951). Theory of elasticity. McGraw-Hill Book, New York, United States.

Hjelmstad, K. D. (2007). Fundamentals of structural mechanics. Springer Science & Business Media, New York, United States.

Dvornik, J., Lazarević, D., & Bićanić, N. (2019). On the principles and procedures of budgeting of building structures. Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia. doi:10.5592/bo/2019.978-953-8168-31-4.

Ibrahimbegovic, A., & Mejia-Nava, R.-A. (2023). Structural Engineering. In Lecture Notes in Applied and Computational Mechanics. Springer International Publishing, Cham, Switzerland. doi:10.1007/978-3-031-23592-4.

R. Eugster, S. (2015). Geometric Continuum Mechanics and Induced Beam Theories. In Lecture Notes in Applied and Computational Mechanics. Springer International Publishing, Cham, Switzerland. doi:10.1007/978-3-319-16495-3.

Goldberg, D. (1991). What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys (CSUR), 23(1), 5–48. doi:10.1145/103162.103163.

Dvornik, J., & Lazarević, D. (2005). Shortcomings of Calculation Models of Engineering Structures. Građevinar, 57(04.), 227-236.

Bathe, K. J. (1996). Finite element procedures. Prentice Hall, New Jersey, United States.

Öchsner, A. (2021). Classical Beam Theories of Structural Mechanics. Springer International Publishing, Cham, Switzerland. doi:10.1007/978-3-030-76035-9.

Obert, L., & Duvall, W. I. (1967). Rock mechanics and the design of structures in rock. John Wiley and Sons, Hoboken, United States.

Ahmed, A. M., & M. Rifai, A. (2021). Euler-Bernoulli and Timoshenko Beam Theories Analytical and Numerical Comprehensive Revision. European Journal of Engineering and Technology Research, 6(7), 20–32. doi:10.24018/ejeng.2021.6.7.2626.

Rahmani, F., Kamgar, R., & Rahgozar, R. (2020). Finite element analysis of functionally graded beams using different beam theories. Civil Engineering Journal (Iran), 6(11), 2086–2102. doi:10.28991/cej-2020-03091604.

Gaur, A., & Dhurvey, P. (2020). Comparative Study of Beam Theories on the Effect of Span-Depth Ratio for Symmetric and Un-symmetric Loadings. IOP Conference Series: Materials Science and Engineering, 936(1), 012047. doi:10.1088/1757-899X/936/1/012047.

Zhang, G. Y., & Gao, X. L. (2020). A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory. Mathematics and Mechanics of Solids, 25(3), 630–643. doi:10.1177/1081286519886003.

Perez-Garcia, C., Aranda-Ruiz, J., Zaera, R., & Garcia-Gonzalez, D. (2022). Beam formulation and FE framework for architected structures under finite deformations. European Journal of Mechanics, A/Solids, 96. doi:10.1016/j.euromechsol.2022.104706.

Yawei, D., Yang, Z., & Jianwei, Y. (2020). Exact solutions of bending deflection for single-walled BNNTs based on the classical Euler-Bernoulli beam theory. Nanotechnology Reviews, 9(1), 961–970. doi:10.1515/ntrev-2020-0075.

Alavi, S. E., Sadighi, M., Pazhooh, M. D., & Ganghoffer, J. F. (2020). Development of size-dependent consistent couple stress theory of Timoshenko beams. Applied Mathematical Modelling, 79, 685–712. doi:10.1016/j.apm.2019.10.058.

Franza, A., Acikgoz, S., & DeJong, M. J. (2020). Timoshenko beam models for the coupled analysis of building response to tunnelling. Tunnelling and Underground Space Technology, 96. doi:10.1016/j.tust.2019.103160.

Davari, S. M., Malekinejad, M., & Rahgozar, R. (2019). Static analysis of tall buildings based on Timoshenko beam theory. International Journal of Advanced Structural Engineering, 11(4), 455–461. doi:10.1007/s40091-019-00245-7.


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DOI: 10.28991/CEJ-2024-010-05-04

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