Structural Engineering and Mechanics

  • 제22권3호
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  • Pages.263-278
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  • 2006
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An analytical model of layered continuous beams with partial interaction

  • Schnabl, Simon (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) ;
  • Turk, Goran (University of Ljubljana, Faculty of Civil and Geodetic Engineering)
  • 투고 : 2004.12.10
  • 심사 : 2005.10.28
  • 발행 : 2006.02.20
⟨ 이전 논문 다음 논문 ⟩

초록

Starting with the geometrically non-linear formulation and the subsequent linearization, this paper presents a consistent formulation of the exact mechanical analysis of geometrically and materially linear three-layer continuous planar beams. Each layer of the beam is described by the geometrically linear beam theory. Constitutive laws of layer materials and relationships between interlayer slips and shear stresses at the interface are assumed to be linear elastic. The formulation is first applied in the analysis of a three-layer simply supported beam. The results are compared to those of Goodman and Popov (1968) and to those obtained from the formulation of the European code for timber structures, Eurocode 5 (1993). Comparisons show that the present and the Goodman and Popov (1968) results agree completely, while the Eurocode 5 (1993) results differ to a certain degree. Next, the analytical solution is used in formulating a general procedure for the analysis of layered continuous beams. The applications show the qualitative and quantitative effects of the layer and the interlayer slip stiffnesses on internal forces, stresses and deflections of composite continuous beams.

키워드

참고문헌

  1. Adekola, U.O. (1968), 'Partial interaction between elastically connected elements of a composite beam', Int. J. Solids Struct., 4, 1125-1135 https://doi.org/10.1016/0020-7683(68)90027-9
  2. Ayoub, A. and Filippou, F.C. (2000), 'Mixed formulation of nonlinear steel-concrete composite beam element', J. Struct. Eng, ASCE, 126(3), 371-381 https://doi.org/10.1061/(ASCE)0733-9445(2000)126:3(371)
  3. Ayoub, A. (2001), 'A two-field mixed variational principle for partially connected composite beams', Finite Elements in Analysis and Design, 37, 929-959 https://doi.org/10.1016/S0168-874X(01)00076-2
  4. Cas, B. (2004a), 'Non-linear analysis of composite beams with interlayer slip', PhD Thesis (in Siovenian), University of Ljubljana, Faculty of Civil and Geodetic Engineering
  5. Cas, B., Saje, M. and Planinc, I. (2004b), 'Non-linear finite element analysis of composite planar frames with an interlayer slip', Comput. Struct., 82, 1901-1912 https://doi.org/10.1016/j.compstruc.2004.03.070
  6. Cosenza, E. and Pecce, M. (2001), 'Shear and normal stresses interaction in coupled structural systems', J. Struct. Eng, ASCE, 127(1), 84-88 https://doi.org/10.1061/(ASCE)0733-9445(2001)127:1(84)
  7. Dall'Asta, A. and Zona, A. (2002), 'Nonlinear analysis of composite beams by displacement approach', Comput. Struct., 80, 2217-2228 https://doi.org/10.1016/S0045-7949(02)00268-7
  8. Eurocode 5 (1993), 'Design of timber structures, Part 1-1: General rules and rules for buildings', ENV 1995-1-1
  9. Fabbrocino, G, Manfredi, G and Cosenza, E. (2000), 'Analysis of continuous composite beams in eluding 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. Fabbrocino, G, Manfredi, G and Cosenza, E. (2002), 'Modelling of continuous steel-concrete composite beams: Computational aspects', Comput. Struct., 80, 2241-2251 https://doi.org/10.1016/S0045-7949(02)00257-2
  11. Faella, C., Martinelli, E. and Nigro, E. (2002), 'Steel and concrete composite beams with flexible shear connection: 'exact' analytical expression of the stiffuess matrix and applications', Comput. Struct., 80, 1001-1009 https://doi.org/10.1016/S0045-7949(02)00038-X
  12. Faella, C., Martinelli, E. and Nigro, E. (2003), 'Shear connection nonlinearity and deflections of steel-concrete composite beams with: A simplified method', J. Struct. Eng, ASCE, 129(1), 12-20 https://doi.org/10.1061/(ASCE)0733-9445(2003)129:1(12)
  13. Fragiacomo, M., Amadio, C. and Macorini, L. (2004), 'Finite-element model for collapse and long-term analysis of steel-concrete composite beams', J. Struct. Eng, ASCE, 130(3),489-497 https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(489)
  14. Gatessco, N. (1999), 'Analytical modeling of nonlinear behavior of composite beams with deformable connection', J. Const. Steel Res., 52, 195-218 https://doi.org/10.1016/S0143-974X(99)00026-7
  15. Girharnmar, U.A and Gopu, V.K.A (1993), 'Composite beam-columns with interlayer slip-exact analysis', J. Struct. Eng, ASCE, 199(4), 1265-1282
  16. Girhammar, U.A and Pan, D. (1993), 'Dynamic analysis of composite member with interlayer slip', Int. J. Solids Struct., 30(6), 797-823 https://doi.org/10.1016/0020-7683(93)90041-5
  17. Goodman, J.R. and Popov, E.P. (1968), 'Layered beam systems with interlayer slip', J. Struct. Div., ASCE, 94(11),2535-2547
  18. Goodman, J.R. and Popov, E.P. (1969), 'Layered wood systems with interlayer slip', Wood Science, 1(3), 148-158
  19. Heinisuo, M. (1988), 'An exact finite element technique for layered beams', Comput. Struct., 30(3), 615-622 https://doi.org/10.1016/0045-7949(88)90297-0
  20. Jasim, N.A (1997), 'Computation of deflections for continuous composite beams with partial interaction', Proc. of The Institution of Civil Engineers, Structures and Buildings, 122, 347-354
  21. Jasim, N.A and Mohamad, A.A (1997), 'Deflections of composite beams with partial shear connection', The Struct. Eng., 75(4), 58-61
  22. Jasim, N.A (1999), 'Deflections of partially composite beams with linear connector density', J. Const. Steel Res., 49, 241-254 https://doi.org/10.1016/S0143-974X(98)00206-5
  23. Kristek, V. and Studnicka, J. (1982), 'Analysis of composite girders with deformable connectors', Proc. of The Institution of Civil Engineers, Part 2,73,699-712
  24. Linden, M.V. (1999), 'Timber-concrete composite beams', HERON, 44(3), 215-239
  25. McCutheon, W.J. (1986), 'Stiffness of framing members with partial composite action', J. Struct. Eng, ASCE, 112(7), 1623-1637 https://doi.org/10.1061/(ASCE)0733-9445(1986)112:7(1623)
  26. Newmark, N.M., Siess, C.P. and Viest, I.M. (1951), 'Test and analysis of composite beams with incomplete interaction', Proc. ofthe Society for Experimental Stress Analysis, 1, 75-92
  27. Nie, J., Fan, J. and Cai, C.S. (2004), 'Stiffness and deflection of steel-concrete composite beams under negative bending', J Struct. Eng, ASCE, 130(11), 1842-1851 https://doi.org/10.1061/(ASCE)0733-9445(2004)130:11(1842)
  28. Oven, V.A, Burgess, l.W, Plank, R.J. and Abdul Wali, A.A (1997), 'An analytical model for the analysis of composite beams with partial interaction', Comput. Struct., 62(3), 493-504 https://doi.org/10.1016/S0045-7949(97)80001-2
  29. Plum, D.R. and Home, M.R. (1975), 'The analysis of continuous composite beams with partial interaction', Proc. of The Institution ofCivil Engineers, Structures and Buildings, Part 2,59,625-643
  30. Ranzi, G, Bradford, M.A and Uy, B. (2003), 'A general method of analysis of composite beams with partial interaction', Steel and Composite Structures, 3(3), 169-184 https://doi.org/10.12989/scs.2003.3.3.169
  31. Rassam, H.Y. and Goodman, J.R. (1971), 'Design of layered wood columns with interlayer slip', Wood Science, 3(3), 149-155
  32. Reissner, E. (1972), 'On one-dimensional nite-strain beam theory: The plane problem', J. of Appl. Mech. and Physics (ZAMP), 23, 795-804 https://doi.org/10.1007/BF01602645
  33. Silfwerbrand, J. (1997), 'Stresses and strains in composite concrete beams subjected to differential shrinkage', ACI Struct. J., 94(4), 347-353
  34. Smith, S.T. and Teng, J.G (2001), 'Interfacial stresses in plated beams', Eng Struct., 23, 857-871 https://doi.org/10.1016/S0141-0296(00)00090-0
  35. Thompson, E.G, Goodman, J.R. and Vanderbilt, M.D. (1975), 'Finite element analysis of layered wood systems', J. Struct. Div., ASCE, 101(ST12), 2659-2672
  36. 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)
  37. Wheat, D.L. and Calixto, J.M. (1994), 'Nonlinear analysis of two-layered wood members with inter-layer slip', J. Struct. Eng, ASCE, 120(6), 1909-1929 https://doi.org/10.1061/(ASCE)0733-9445(1994)120:6(1909)
  38. Wolfram, S. (2003), Mathematica, Addison-Wesley Publishing Company

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  8. 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
  9. Numerical and experimental analysis of timber composite beams with interlayer slip vol.30, pp.11, 2008, https://doi.org/10.1016/j.engstruct.2008.03.007
  10. Analytical and numerical analysis of multilayered beams with interlayer slip vol.32, pp.6, 2010, https://doi.org/10.1016/j.engstruct.2010.02.015
  11. Stability analysis of three-layer shear deformable partial composite columns vol.106-107, 2017, https://doi.org/10.1016/j.ijsolstr.2016.11.018
  12. 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
  13. Non-linear analysis of two-layer beams with interlayer slip and uplift 2011, https://doi.org/10.1016/j.compstruc.2011.06.007
  14. 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
  15. Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection vol.2014, 2014, https://doi.org/10.1155/2014/942763
  16. Full-scale long-term experiments of simply supported composite beams with solid slabs vol.67, pp.3, 2011, https://doi.org/10.1016/j.jcsr.2010.11.001
  17. The influence of boundary conditions and axial deformability on buckling behavior of two-layer composite columns with interlayer slip vol.32, pp.10, 2010, https://doi.org/10.1016/j.engstruct.2010.05.029
  18. Flexural vibrations of discontinuous layered elastically bonded beams vol.135, 2018, https://doi.org/10.1016/j.compositesb.2017.09.059
  19. Full-scale long-term and ultimate experiments of simply-supported composite beams with steel deck vol.67, pp.10, 2011, https://doi.org/10.1016/j.jcsr.2011.04.010
  20. Analysis of composite beams with longitudinal and transverse partial interactions using higher order beam theory vol.59, pp.1, 2012, https://doi.org/10.1016/j.ijmecsci.2012.03.012
  21. A force-based frame finite element formulation for analysis of two- and three-layered composite beams with material non-linearity vol.62, 2014, https://doi.org/10.1016/j.ijnonlinmec.2014.02.001
  22. 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
  23. A simplified analysis method for composite beams with interlayer slip vol.51, pp.7, 2009, https://doi.org/10.1016/j.ijmecsci.2009.05.003
  24. Short- and long-term analytical solutions for composite beams with partial interaction and shear-lag effects vol.10, pp.4, 2010, https://doi.org/10.1007/BF03215844
  25. Dynamic Response of Composite Beams with Partial Shear Interaction Using a Higher-Order Beam Theory vol.139, pp.1, 2013, https://doi.org/10.1061/(ASCE)ST.1943-541X.0000603
  26. A new model for composite beams with partial interaction vol.167, pp.1, 2014, https://doi.org/10.1680/eacm.12.00015
  27. Shrinkage effects on the flexural stiffness of composite beams with solid concrete slabs: An experimental study vol.33, pp.4, 2011, https://doi.org/10.1016/j.engstruct.2011.01.007
  28. Locking problems in the partial interaction analysis of multi-layered composite beams vol.30, pp.10, 2008, https://doi.org/10.1016/j.engstruct.2008.04.006
  29. Inelastic buckling of two-layer composite columns with non-linear interface compliance vol.53, pp.12, 2011, https://doi.org/10.1016/j.ijmecsci.2011.09.002
  30. A geometric nonlinear model for composite beams with partial interaction vol.32, pp.5, 2010, https://doi.org/10.1016/j.engstruct.2010.01.017
  31. Structural Response of Timber-Concrete Composite Beams Predicted by Finite Element Models and Manual Calculations vol.17, pp.11, 2014, https://doi.org/10.1260/1369-4332.17.11.1601
  32. Derivation of the exact stiffness matrix of shear-deformable multi-layered beam element in partial interaction vol.112, 2016, https://doi.org/10.1016/j.finel.2015.12.004
  33. Three-dimensional bimetallic layered beams with interface compliance: Analytical solution pp.2041-3076, 2018, https://doi.org/10.1177/1464420718803704
  34. Analytical solution of two-layer beam including interlayer slip and uplift vol.34, pp.6, 2006, https://doi.org/10.12989/sem.2010.34.6.667
  35. Analysis of composite frame structures with mixed elements - state of the art vol.41, pp.2, 2006, https://doi.org/10.12989/sem.2012.41.2.157
  36. Analytical modelling of multilayer beams with compliant interfaces vol.44, pp.4, 2006, https://doi.org/10.12989/sem.2012.44.4.465
  37. 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
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