Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analytical solution of two-layer beam including interlayer slip and uplift

  • Kroflic, Ales (University of Ljubljana, Faculty of Civil and Geodetic Engineering) ;
  • Planinc, Igor (University of Ljubljana, Faculty of Civil and Geodetic Engineering) ;
  • Saje, Miran (University of Ljubljana, Faculty of Civil and Geodetic Engineering) ;
  • Cas, Bojan (University of Ljubljana, Faculty of Civil and Geodetic Engineering)
  • Received : 2008.07.14
  • Accepted : 2009.12.07
  • Published : 2010.04.20
⟨ Previous Next ⟩

Abstract

A mathematical model and its analytic solution for the analysis of stress-strain state of a linear elastic two-layer beam is presented. The model considers both slip and uplift at the interface. The solution is employed in assessing the effects of transverse and shear contact stiffnesses and the thickness of the interface layer on behaviour of nailed, two-layer timber beams. The analysis shows that the transverse contact stiffness and the thickness of the interface layer have only a minor influence on the stress-strain state in the beam and can safely be neglected in a serviceability limit state design.

Keywords

References

  1. Adekola, A.O. (1968), "Partial interaction between elastically connected elements of a composite beam", Int. J. Solids Struct., 4(11), 1125-1135. https://doi.org/10.1016/0020-7683(68)90027-9
  2. Ayoub, A. (2005), "A force-based model for composite steel-concrete beams with partial interaction", J. Constr. Steel Res., 61(3), 387-414. https://doi.org/10.1016/j.jcsr.2004.08.004
  3. Betti, R. and Gjelsvik, A. (1996), "Elastic composite beams", Comput. Struct., 59(3), 437-451. https://doi.org/10.1016/0045-7949(95)00275-8
  4. Cas, B., Saje, M. and Planinc, I. (2004a), "Non-linear finite element analysis of composite planar beams with an interlayer slip", Comput. Struct., 82, 1901-1912. https://doi.org/10.1016/j.compstruc.2004.03.070
  5. Cas, B., Saje, M., Bratina, S. and Planinc, I. (2004b), "Non-linear analysis of composite steel-concrete beams with incomplete interaction", Steel Compos. Struct., 4(6), 489-507. https://doi.org/10.12989/scs.2004.4.6.489
  6. Deo, S.G. and Ragmavendra, V. (1994), Ordinary Differential Equations and Stability Theory, 8th Edition, Tata McGraw-Hill Publishing Company Limited, New Delhi.
  7. Eurocode 5 (2004), "Design of composite steel and concrete structures - Part 1-1: General rules and rules for buildings", European Committee for Standardization.
  8. Fabbrocino, G., Manfredi, G. and Cosenza, E. (1999), "Non-linear analysis of composite beams under positive bending", Comput. Struct., 70, 77-89. https://doi.org/10.1016/S0045-7949(98)00173-4
  9. Fabbrocino, G., Manfredi, G. and Cosenza, E. (2000), "Analysis of continuous composite beams including partial interaction and bond", J. Struct. Eng-ASCE, 126(11), 1288-1294. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:11(1288)
  10. Gara, F., Ranzi, G. and Leoni, G. (2006), "Displacement-based formulations for composite beams with longitudinal slip and vertical uplift", Int. J. Numer. Meth. Eng., 65(8), 1197-1220. https://doi.org/10.1002/nme.1484
  11. Gattesco, N. (1999), "Analytical modeling of nonlinear behavior of composite beams with deformable connection", J. Constr. Steel Res., 52, 195-218. https://doi.org/10.1016/S0143-974X(99)00026-7
  12. Girhammar, U.A. and Gopu, V.K.A. (1993), "Composite beam-columns with interlayer slip-exact analysis", J. Struct. Eng-ASCE, 119(4), 1265-1282. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:4(1265)
  13. Girhammar, U.A. and Pan, D.H. (2007), "Exact static analysis of partially composite beams and beam-columns", Int. J. Mech. Sci., 49(2), 239-255. https://doi.org/10.1016/j.ijmecsci.2006.07.005
  14. Granholm, H. (1949), "On composite beams and columns with special regard to nailed timber structures", Trans. No. 88, Chalmers University of Technology, Goeteborg, Sweden (In Swedish).
  15. Hirst, M.J.S. and Yeo, M.Y. (1980), "The analysis of composite beams using standard finite element programs", Comput. Struct., 31(1-2), 155-168.
  16. Koc, P. and Sok, B. (2004), "Computer-aided identification of the yield curve of a sheet metal after onset of necking", Comput. Mater. Sci., 11(3), 233-237.
  17. Manfredi, G., Fabbrocino, G. and Cosenza, E. (1999), "Modeling of steel-concrete composite beams under negative bending", J. Eng. Mech-ASCE, 125(6), 654-662. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:6(654)
  18. Milner, H.R. and Tan, H.H. (2001), "Modelling deformation in nailed, thin-webbed timber box beams", Comput. Struct., 79, 2541-2546. https://doi.org/10.1016/S0045-7949(01)00138-9
  19. Newmark, N.M., Seiss, C.P. and Viest, I.M. (1951), "Tests and analysis of composite beams with incomplete interaction", Proc. Soc. Exp. Stress Anal., 9(1), 75-92.
  20. Nguyen, D.M., Chan, T.K. and Cheong, H.K. (2001), "Brittle failure and bond development length of CFRPconcrete beams", J. Compos. Constr., 5(1), 12-17. https://doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)
  21. Nie, J. and Cai, C.S. (2003), "Steel-concrete composite beams considering shear slip effects", J. Struct. Eng-ASCE, 129, 495-506. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:4(495)
  22. Oehlers, D.J., Nguyen, N.T., Ahmed, M. and Bradford, M.A. (1997), "Transverse and longitudinal interaction in composite bolted side-plated reinforced-concrete beams", Struct. Eng. Mech., 5(5), 553-563. https://doi.org/10.12989/sem.1997.5.5.553
  23. Pendhari, S.S., Kant, T. and Desai, Y.M. (2006), "Nonlinear analysis of reinforced concrete beams strengthened with polymer composites", Struct. Eng. Mech., 1(1), 1-18.
  24. Planinc, I., Schnabl, S., Saje, M., Lopati , J. and as, B. (2008), "Numerical and experimental analysis of timber composite beams with interlayer slip", Eng. Struct., 30 (11), 2959-2969. https://doi.org/10.1016/j.engstruct.2008.03.007
  25. Pleshkov, P.F. (1952), "Theoretical studies of composite wood structures", Soviet Union (In Russian).
  26. Rahimi, H. and Hutchinson, A. (2001), "Concrete beams strengthened with externally bonded FRP plates", J. Compos. Constr., 5(1), 44-56. https://doi.org/10.1061/(ASCE)1090-0268(2001)5:1(44)
  27. Ranzi, G., Bradford, M.A. and Uy, B. (2003), "A general method of analysis of composite beams with partial interaction", Steel Compos. Struct., 3(3), 169-184. https://doi.org/10.12989/scs.2003.3.3.169
  28. Ranzi, G. and Bradford, M.A. (2007), "Direct stiffness analysis of a composite beam-column element with partial interaction", Comput. Struct., 85(15-16), 1206-1214. https://doi.org/10.1016/j.compstruc.2006.11.031
  29. Rasheed, H.A. and Pervaiz, S. (2002), "Bond slip analysis of fiber-reinforced polymer-strengthened beams", J. Eng. Mech-ASCE, 128 (1), 78-86. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:1(78)
  30. Rassam, H.Y. and Goodman, J.R. (1970), "Buckling behavior of layered wood columns", Wood Sci., 2(4), 238-246.
  31. Robinson, H. and Naraine, K.S. (1988), "Slip and uplift effects in composite beams", Proceedings of an Engineering Foundation Conference ASCE, New England College, Henniker, New Hampshire.
  32. Salari, R., Spacone, E., Shing, P.B. and Frangopol, D.M. (1998), "Nonlinear analysis of composite beams with deformable shear connectors", J. Struct. Eng-ASCE, 124(10), 1148-1158. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:10(1148)
  33. Salari, M.R. and Spacone, E. (2001), "Analysis of steel-concrete composite frames with bond-slip", J. Struct. Eng-ASCE, 127 (11), 1243-1250. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:11(1243)
  34. Schnabl, S., Planinc, I., Saje, M., as, B. and Turk, G. (2006), "An analytical model of layered continuous beams with partial interaction", Struct. Eng. Mech., 22(3), 263-278. https://doi.org/10.12989/sem.2006.22.3.263
  35. Schnabl, S., Saje, M., Turk, G.. and Planinc, I. (2007a), "Locking-free two-layer Timoshenko beam element with interlayer slip", Finite Elem. Anal. Des., 43(9), 705-714. https://doi.org/10.1016/j.finel.2007.03.002
  36. Schnabl, S., Saje, M., Turk, G.. and Planinc, I. (2007b), "Analytical solution of two-layer beam taking into account interlayer slip and shear deformation", J. Struct. Eng-ASCE, 133(6), 886-894. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(886)
  37. Seracino, R., Oehlers, D.J. and Yeo, M.F. (2001), "Partial-ineraction flexural stresses in composite steel and concrete bridge beams", Eng. Struct., 23, 1186-1193. https://doi.org/10.1016/S0141-0296(00)00121-8
  38. Stussi, F. (1947), "Zusammengesetze Vollwandtrager", International Association for Bridge and Structural Engineering (IABSE), 8, 249-269.
  39. Sun, F.F. and Bursi, O.S. (2005), "Displacement-based and two-field mixed variational formulations for composite beams with shear lag", J. Eng. Mech-ASCE, 131(2), 199-210. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:2(199)
  40. Suzuki, H. and Chang, T.P. (1979), "Bending of laminated cantilever beams with interlayer slip", J. Struct. Div., ASCE, 105 (2), 269-281.
  41. Thompson, E.G., Googman, J.R. and Vanderbilt, M.D. (1975), "Finite element analysis of layered wood systems", J. Struct. Div., Proc. ASCE, 101(12), 2659-2672.
  42. Van Der Linden, M.L.R. (1999), "Timber-concrete composite beams", HERON, 44(3), 215-239.
  43. Viest, I.M. (1960), "Review of research on composite steel-concrete beams", J. Struct. Div. ASCE, 86(6), 1-21.
  44. Wang, Y.C. (1998), "Deflection of steel-concrete composite beams with partial shear interaction", J. Struct. Eng-ASCE, 124(10), 1159-1165. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:10(1159)
  45. Wheat, D.L. and Calixto, J.M. (1994), "Nonlinear analysis of two-layered wood members with interlayer slip", J. Struct. Eng-ASCE, 120(6), 1909-1929. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:6(1909)
  46. Wolfram Research Inc. (2005), Mathematica, Champaign, USA.
  47. Xu, R.Q. and Wu, Y.F. (2007), "Two-dimensional analytical solutions of simply supported composite beams with interlayer slips", Int. J. Solids Struct., 44(1), 165-175. https://doi.org/10.1016/j.ijsolstr.2006.04.027

Cited by

  1. Buckling Loads of Two-Layer Composite Columns with Interlayer Slip and Stochastic Material Properties vol.139, pp.8, 2013, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000478
  2. Exact finite elements for multilayered composite beam-columns with partial interaction vol.123, 2013, https://doi.org/10.1016/j.compstruc.2013.04.008
  3. Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects vol.33, pp.8, 2011, https://doi.org/10.1016/j.engstruct.2011.04.004
  4. Non-linear analysis of two-layer beams with interlayer slip and uplift 2011, https://doi.org/10.1016/j.compstruc.2011.06.007
  5. Analytical solution of linear elastic beams cracked in flexure and strengthened with side plates vol.47, pp.22, 2013, https://doi.org/10.1177/0021998312459780
  6. Analytical solutions of two-layer beams with interlayer slip and bi-linear interface law vol.50, pp.5, 2013, https://doi.org/10.1016/j.ijsolstr.2012.10.032
  7. Dynamic analysis and model test on steel-concrete composite beams under moving loads vol.18, pp.3, 2015, https://doi.org/10.12989/scs.2015.18.3.565
  8. Exact buckling loads of two-layer composite Reissner’s columns with interlayer slip and uplift vol.50, pp.1, 2013, https://doi.org/10.1016/j.ijsolstr.2012.08.027
  9. Non-linear analysis of side-plated RC beams considering longitudinal and transversal interlayer slips vol.16, pp.6, 2014, https://doi.org/10.12989/scs.2014.16.6.559
  10. Boundary-Layer Effect in Composite Beams with Interlayer Slip vol.24, pp.2, 2011, https://doi.org/10.1061/(ASCE)AS.1943-5525.0000027
  11. Analysis of a geometrically exact multi-layer beam with a rigid interlayer connection vol.225, pp.2, 2014, https://doi.org/10.1007/s00707-013-0972-5
  12. Three-dimensional bimetallic layered beams with interface compliance: Analytical solution pp.2041-3076, 2018, https://doi.org/10.1177/1464420718803704
  13. Analytical modelling of multilayer beams with compliant interfaces vol.44, pp.4, 2010, https://doi.org/10.12989/sem.2012.44.4.465
  14. Analytical solution of three-dimensional two-layer composite beam with interlayer slips vol.173, pp.None, 2018, https://doi.org/10.1016/j.engstruct.2018.06.108
  15. Description of behaviour of timber-concrete composite beams including interlayer slip, uplift, and long-term effects: Formulation of the model and coefficient inverse problem vol.194, pp.None, 2010, https://doi.org/10.1016/j.engstruct.2019.05.058