Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Three-point bending of beams with consideration of the shear effect

  • Magnucki, Krzysztof (Lukasiewicz Research Network - Institute of Rail Vehicles TABOR) ;
  • Paczos, Piotr (Poznan University of Technology) ;
  • Wichniarek, Radosław (Poznan University of Technology)
  • Received : 2020.05.05
  • Accepted : 2020.12.03
  • Published : 2020.12.25
⟨ Previous Next ⟩

Abstract

The subject of the paper pertains to simply supported beams with bisymmetrical cross sections under three-point bending with consideration of the shear effect. The deformation of a planar cross section of the beam is described taking into account the assumed nonlinear hypothesis-theory. Two differential equations of equilibrium are obtained based on the principle of stationary potential energy. This system is analytically solved and the shear coefficients and deflections of the beams are derived. Moreover, the Young's modules of the materials and deflections of the beams are experimentally determined on a test stand. The results of the studies are specified in tables and compared.

Keywords

Acknowledgement

The research was conducted within the framework of Scientific Activities of Łukasiewicz Research Network - Institute of Rail Vehicles and the framework of Statutory Activities of Poznan University of Technology. The raw data required to reproduce these findings are available to download from Mendeley Data - Data for: Three-point bending of beams with bisymmetrical cross sections with consideration of the shear effect - Analytical and experimental studies.

References

  1. Adamek, V. (2018), "The limits of Timoshenko beam theory applied to impact problems of layered beams", Int. J. Mech. Sci., 145, 128-137. https://doi.org/10.1016/j.ijmecsci.2018.07.001.
  2. Adil Dar, M., Subramanian, N., Dar, D.A., Anbarasu, M., Lim, J.B.P. and Mahjoubi, S. (2020a), "Flexural Strength of cold-formed steel built-up composite beams with rectangular compression flanges", Steel Compos. Struct., 34(2), 171-188. https://doi.org/10.12989/scs.2020.34.2.171.
  3. Adil Dar, M., Subramanian, N., Atif, M., Dar, A.R., Anbarasu, M. and Lim, J.B.P. (2020b), "Efficient cross-sectional profiling of built up CFS beams for improved flexural performance", Steel Compos. Struct., 34(3), 333-354. https://doi.org/10.12989/scs.2020.34.3.333.
  4. Amirpour, M., Das, R. and Saavedra Flores, E.I. (2016), "Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory", Compos. B Eng., 94, 109-121. https://doi.org/10.1016/j.compositesb.2016.03.040.
  5. Beck, A.T. and da Silva Jr., C.R.A. (2011), "Timoshenko versus Euler Beam theory: Pitfalls of a deterministic approach", Struct. Saf., 33(1), 19-25. https://doi.org/10.1016/j.strusafe.2010.04.006.
  6. DevilDesign (2019), https://devildesign.com/
  7. Endo, M. (2017), "One-half order shear deformation theory' as a new naming for the transverse, but not in-plane rotational, shear deformable structural models", Int. J. Mech. Sci., 122, 384-391. https://doi.org/10.1016/j.ijmecsci.2016.10.016.
  8. FormFutura (2019), https://www.formfutura.com
  9. Gorski, F., Wichniarek, R., Kuczko, W. and Andrzejewski, J. (2015), "Experimental determination of critical orientation of ABS parts manufactured using fused deposition modeling technology", J. Mach. Eng., 15, 121-132.
  10. Hutchinson, J.R. (2001), "Shear coefficients for Timoshenko beam theory", ASMEJ Appl. Mech., 68(1), 87-92. https://doi.org/10.1115/1.1349417.
  11. Kim, N.I. (2011), "Shear deformable doubly- and monosymmetric composite I-beams", Int. J. Mech. Sci., 53(1), 31-41. https://doi.org/10.1016/j.ijmecsci.2010.10.004.
  12. Lee, Y., Lee, S., Zhao, X.G., Lee, D., Kim, T., Jung, H. and Kim, N. (2018), "Impact of UV curing process on mechanical properties and dimensional accuracies of digital light processing 3D printed objects", Smart Struct. Syst., 22(2), 161-166. https://doi.org/10.12989/sss.2018.22.2.161.
  13. Magnucka-Blandzi, E., Magnucki, K. and Wittenbeck, L. (2015), "Mathematical modelling of shearing effect for sandwich beams with sinusoidal corrugated cores", Appl. Math. Model., 39(9), 2796-2808. https://doi.org/10.1016/j.apm.2014.10.069.
  14. Magnucki, K. (2019), "Bending of symmetrically sandwich beams and I-beams - Analytical study", Int. J. Mech. Sci., 150, 411-419. https://doi.org/10.1016/j.ijmecsci.2018.10.020.
  15. Magnucki, K. and Lewinski. J. (2018), "Analytical modeling of I-beam as a sandwich structures", Eng. Trans., 66(4), 357-373. https://doi.org/10.24423/EngTrans.898.20180809.
  16. Magnucki, K., Lewinski, J. and Cichy, R. (2019), "Bending of beams with bisymmetrical cross sections under non-uniformly distributed load - Analytical and numerical-FEM studies", Arch. Appl. Mech., 89(10), 2103-2114. https://doi.org/10.1007/s00419-019-01566-5.
  17. Magnucki, K., Malinowski, M., Magnucka-Blandzi, E. and Lewinski, J. (2017), "Three-point bending of a short beam with varying mechanical properties", Compos. Struct., 179, 552-557. https://doi.org/10.1016/j.compstruct.2017.07.040.
  18. Meradjah, M., Kaci, A., Houari, A.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809. http://dx.doi.org/10.12989/scs.2015.18.3.793.
  19. Nguyen, T.K., Nguyen, T.T.P., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory", Compos. B Eng, 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032.
  20. Paczos, P., Wichniarek, R. and Magnucki, K. (2018), "Three-point bending of the sandwich beam with special structures of the core", Compos. Struct., 201, 676-682. https://doi.org/10.1016/j.compstruct.2018.06.077.
  21. Reddy, J.N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48(11), 1507-1518. https://doi.org/10.1016/j.ijengsci.2010.09.020.
  22. Senjanovic, I., Vladimir, N., Hadzic, N. and Tomic, M. (2016). "New first order shear deformation beam theory with in-plane shear influence", Eng. Struct., 110, 169-183. https://doi.org/10.1016/j.engstruct.2015.11.032.
  23. Shi, G. and Voyiadjis, G.Z. (2011), "A sixth-order theory of shear deformable beams with variational consistent boundary conditions", ASMEJ Appl. Mech., 78(2), 021019. https://doi.org/10.1115/1.4002594.
  24. Somireddy, M., de Moraes, A.D. and Czekanski, A. (2012), "Flexural behavior of FDM parts: experimental, analytical and numerical study", Proceedings of the 28th Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference, Austin, August.
  25. Uddin, M.S., Sidek, M.F.R., Faizal, M.A., Ghomashchi, R. and Pramanik, A. (2017), "Evaluating Mechanical Properties and Failure Mechanisms of Fused Deposition Modeling Acrylonitrile Butadiene Styrene Parts", ASME J. Manuf. Sci. Eng., 139(8), 081018. https://doi.org/10.1115/1.4036713.
  26. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates, ELSEVIER SCIENCE Ltd., Oxford, England.