DOI QR코드

DOI QR Code

Deflections and rotations in rectangular beams with straight haunches under uniformly distributed load considering the shear deformations

  • Received : 2018.10.07
  • Accepted : 2018.11.24
  • Published : 2018.12.25

Abstract

This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear.

Keywords

Acknowledgement

Supported by : Autonomous University of Coahuila

References

  1. Akbas, S.D. (2015), "Large deflection analysis of edge cracked simple supported beams", Struct. Eng. Mech., 54(3), 433-451. https://doi.org/10.12989/SEM.2015.54.3.433
  2. Banerjee, A., Bhattacharya, B. and Mallik, A.K. (2008), "Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches", Int. J. Nonlinear. Mech., 43(5), 366-376. https://doi.org/10.1016/j.ijnonlinmec.2007.12.020
  3. Borboni, A. and De Santis, D. (2006), "Large deflection of a nonlinear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end", Meccanica, 49(6), 1327-1336. https://doi.org/10.1007/s11012-014-9895-z
  4. Bouchafa, A., Bouiadjra, M.B., Ahmed, H.M.S. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  5. Brojan, M., Cebron, M. and Kosel, F. (2012), "Large deflections of non-prismatic non-linearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end", Acta Mech. Sinica-PRC, 28(3), 863-869. https://doi.org/10.1007/s10409-012-0053-3
  6. Chen, L. (2010), "An integral approach for large deflection cantilever beams", Int. J. Nonlin. Mech., 45(3), 301-305. https://doi.org/10.1016/j.ijnonlinmec.2009.12.004
  7. Dado, M. and Al-Sadder, S. (2005), "A new technique for large deflection analysis of non-prismatic cantilever beams", Mech. Res. Commun., 32(6), 692-703. https://doi.org/10.1016/j.mechrescom.2005.01.004
  8. Debnath, V. and Debnath, B. (2014), "Deflection and stress analysis of a beam on different elements using ANSYS APDL", Int. J. Mech. Eng. Technol., 5(6), 70-79.
  9. Ju, M., Park, C. and Kim, Y. (2017), "Flexural behavior and a modified prediction of deflection of concrete beam reinforced with a ribbed GFRP bars", Comput. Concrete, 19(6), 631-639. https://doi.org/10.12989/CAC.2017.19.6.631
  10. Lee, K. (2002), "Large deflections of cantilever beams of nonlinear elastic material under a combined loading", Int. J. Nonlinear. Mech., 37(3), 439-443. https://doi.org/10.1016/S0020-7462(01)00019-1
  11. Li, J.l. and Chen, J.K. (2016), "Deflection of battened beams with shear and discrete effects", Struct. Eng. Mech., 59(5), 921-932. https://doi.org/10.12989/sem.2016.59.5.921
  12. Luevanos-Rojas, A. (2012), "Method of structural analysis for statically indeterminate beams", Int. J. Innov. Comput. I., 8(8), 5473-5486.
  13. Luevanos-Rojas, A. (2013a), "Method of structural analysis for statically indeterminate rigid frames", Int. J. Innov. Comput. I., 9(5), 1951-1970.
  14. Luevanos-Rojas, A. (2013b), "Method of structural analysis, taking into account deformations by flexure, shear and axial", Int. J. Innov. Comput. I., 9(9), 3817-3838.
  15. Luevanos-Rojas, A. (2013c), "A mathematical model for fixed-end moments of a beam subjected to a uniformly distributed load taking into account the shear deformations", ICIC Express Lett., 7(10), 2759-2764.
  16. Luevanos-Rojas, A. (2013d), "A mathematical model for fixed-end moments of a beam subjected to a triangularly distributed load taking into account the shear deformations", ICIC Express Lett., 7(11), 2941-2947.
  17. Luevanos-Rojas, A. (2014), "A mathematical model of elastic curve for simply supported beams subjected to a uniformly distributed load taking into account the shear deformations", ICIC Express Lett. Part B: Appl., 5(3), 885-890.
  18. Luevanos-Rojas, A. (2015), "Modelado para vigas de seccion transversal "I" sometidas a una carga uniformemente distribuida con cartelas rectas", Ingenieria Mecanica. Tecnologia y Desarrollo, 5(2), 281-292.
  19. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2016b), "Modelling for mechanical elements of rectangular members with straight haunches using software: part 1", Int. J. Innov. Comput. I., 12(3), 973-985.
  20. Luevanos-Rojas, A., Lopez-Chavarria, S. and Medina-Elizondo, M. (2016c), "Modelling for mechanical elements of rectangular members with straight haunches using software: part 2", Int. J. Innov. Comput. I., 12(4), 1027-1041.
  21. Luevanos-Rojas, A., Lopez-Chavarria, S., Medina-Elizondo, M. and Kalashnikov, V.V. (2016a), "A mathematical model of elastic curve for simply supported beams subjected to a concentrated load taking into account the shear deformations", Int. J. Innov. Comput. I., 12(1), 41-54.
  22. Luevanos-Soto, I. and Luevanos-Rojas, A., (2017), "Modeling for fixed-end moments of I-sections with straight haunches under concentrated load", Steel Compos. Struct., 23(5), 597-610. https://doi.org/10.12989/SCS.2017.23.5.597
  23. Majumder, G. and Kumar, K. (2013), "Deflection and stress analysis of a simply supported beam and its validation using ANSYS", Int. J. Mech. Eng. Comput. Appl., 1(5), 17-20.
  24. Ponnada, M.R. and Thonangi, R.S. (2015), "Deflections in non-prismatic simply supported prestressed concrete beams", Asian J. Civil Eng., 16(4), 557-565.
  25. Ponnada, M.R. and Vipparthy, R. (2013), "Improved method of estimating deflection in prestressed steel I-beams", Asian J. Civil Eng., 14(5), 765-772.
  26. Razavi, C.V., Jumaat, M.Z., EI-Shafie, A.H. and Ronagh, H.R. (2015), "Load-deflection analysis prediction of CFRP strengthened RC slab using RNN", Adv. Concrete Constr., 3(2), 91-102. https://doi.org/10.12989/acc.2015.3.2.091
  27. Sihua, D., Ze, Q. and Li, W. (2015), "Nonlinear analysis of reinforced concrete beam bending failure experimentation based on ABAQUS", International Conference on Information Sciences, Machinery, Materials and Energy, Published by Atlantis Press, 440-444.
  28. Solano-Carrillo, E. (2009), "Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behavior", Int. J. Nonlinear. Mech., 44(2), 253-256. https://doi.org/10.1016/j.ijnonlinmec.2008.11.007
  29. Timoshenko, S.P. (1947), Strength of Materials Part I Elementary Theory and Problems, 2nd Ed., Van Nostrand Company, Inc., New York.
  30. Timoshenko, S.P. and Gere, J.M. (1972), Mechanics of Materials, Van Nostrand Reinhold, New York.
  31. Unsal, I., Tokgoz, S., Cagatay, I.H. and Dundar, C. (2017), "A study on load-deflection behavior of two-span continuous concrete beams reinforced with GFRP and steel bars", Struct. Eng. Mech., 63(5), 629-637. https://doi.org/10.12989/SEM.2017.63.5.629
  32. Yau, J.D. (2010), "Closed-Form solution of large deflection for a guyed cantilever column pulled by an inclination cable", J. Mar. Sci. Tech.-Japan, 18(1), 130-136.
  33. Yuksel, S.B. (2009), "Behaviour of symmetrically haunched non-prismatic members subjected to temperature changes", Struct. Eng. Mech., 31(3), 297-314. https://doi.org/10.12989/sem.2009.31.3.297
  34. Yuksel, S.B. (2012), "Assessment of non-prismatic beams having symmetrical parabolic haunches with constant haunch length ratio of 0.5", Struct. Eng. Mech., 42(6), 849-866. https://doi.org/10.12989/sem.2012.42.6.849