Abstract
In this paper a boundary element method is developed for the second-order analysis of frames consisting of beams of arbitrary simply or multiply connected constant cross section, taking into account shear deformation effect. Each beam is subjected to an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Three boundary value problems are formulated with respect to the beam deflection, the axial displacement and to a stress function and solved employing a BEM approach. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress function using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The influence of both the shear deformation effect and the variableness of the axial loading are remarkable.
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References
Chen WF and Atsura T (1977). Theory of beam-column, vol I. McGraw-Hill Inc, New York, NY
Goto Y and Chen WF (1987). Second-order elastic analysis for frame design. ASCE J Struct Eng 113(7): 1501–1529
Rutenberg A (1981). A direct P-delta analysis using standard plane frame computer programs. Comp Struct 14(1–2): 97–102
Load and resistance factor design specifications for buildings (1994) American Institute of Steel Construction (AISC) Chicago, Ill
Chajes A and Churchill JE (1987). Íonlinear frame analysis by finite element methods. ASCE J Struct Eng 113(6): 1221–1235
Liew JYR and Chen WF (1994). Trends toward advanced analysis. In: Chenand, WF and Tom, S (eds) Advanced analysis of steel frames, pp 1–45. CRC Press Inc, Boca Raton
Goto Y (1994). Second-order elastic analysis of frames. In: Chenand, WF and Tom, S (eds) Advanced analysis of steel frames, pp 47–90. CRC Press Inc, Boca Raton
Vasek M (1993) The non-linear behaviour of large space bar and beam structures. In: Proceedings of Space Struct 4 Conf Thomas Telford Series, London, England vol 1, pp 665–673
Kim E-S, Park M and Choi S-H (2001). Direct design of three dimensional frames using practical advanced analysis. Eng Struct 23: 1491–1502
Rubin H (1997). Uniform formulae of first- and second-order theory for skeletal structures. Eng Struct 19(11): 903–909
Torkamani M, Sommez M and Cao J (1997). Second-order elastic plane-frame analysis using finite-element method. J Struct Eng ASCE 123(9): 1225–1235
Kim E-S, Lee J and Park J-S (2003). 3-D second-order plastic analysis accounting for local buckling. Eng Struct 25: 81–90
Kim E-S and Choi S-H (2005). Practical second-order inelastic analysis for three-dimensional steel frames subjected to distributed load. Thin-Walled Struct 43: 135–160
Kim E-S, Lee J and Kim E-S (2004). Practical second-order inelastic analysis for steel frames subjected to distributed load. Eng Struct 26: 51–61
Kim E-S, Ngo-Huu C and Lee D-H (2006). Second-order inelastic dynamic analysis of 3-D steel frames. Int J Solids Struct 43(6): 1693–1709
Machado PS and Cortinez VH (2005). Lateral buckling of thin-walled composite bisymmetric beams with prebuckling and shear deformation. Eng Struct 27: 1185–1196
Bach C and Baumann R (1924). Elastizität und Festigkeit, 9th edn. Springer, Berlin
Stojek D (1964). Zur Schubverformung im Biegebalken. Zeitschrift für Angewandte Mathematik und Mechanik 44: 393–396
Timoshenko SP and Goodier JN (1984). Theory of elasticity, 3rd edn. McGraw-Hill, New York
Cowper GR (1966). The shear coefficient in Timoshenko’s beam theory. J Appl Mech ASME 33(2): 335–340
Schramm U, Kitis L, Kang W and Pilkey WD (1994). On the shear deformation coefficient in beam theory. Finite Elem Anal Des 16: 141–162
Schramm U, Rubenchik V and Pilkey WD (1997). Beam stiffness matrix based on the elasticity equations. Int J Numer Methods Eng 40: 211–232
Stephen NG (1980). Timoshenko’s shear coefficient from a beam subjected to gravity loading. ASME J Appl Mech 47: 121–127
Hutchinson JR (2001). Shear coefficients for Timoshenko beam theory. ASME J Appl Mech 68: 87–92
Schramm U, Rubenchik V and Pilkey WD (1997). Beam stiffness matrix based on the elasticity equations. Int J Numer Methods Eng 40: 211–232
Sapountzakis EJ and Mokos VG (2005). A BEM solution to transverse shear loading of beams. Comput Mech 36: 384–397
Ramm E and Hofmann TJ (1995). Stabtragwerke, Der Ingenieurbau. In: Mehlhorn, G (eds) Band Baustatik/Baudynamik, pp. Ernst& Sohn, Berlin
Katsikadelis JT (2002). The analog equation method. A boundary-only integral equation method for nonlinear static and dynamic problems in general bodies. Theor Appl Mech 27: 13–38
Katsikadelis JT and Tsiatas GC (2003). Large deflection analysis of beams with variable stiffness. Acta Mech 164: 1–13
Gaul L and Fiedler C (1997). Methode der Randelemente in Statik und Dynamik. Vieweg, Braunschweig-Wiesbaden
Isaacson E and Keller HB (1966). Analysis of numerical methods. Wiley, New York
Sapountzakis EJ and Katsikadelis JT (1992). Unilaterally supported plates on elastic foundations by the boundary element method. J Appl Mech Trans ASME 59: 580–586
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Sapountzakis, E.J., Mokos, V.G. Shear deformation effect in second-order analysis of frames subjected to variable axial loading. Comput Mech 41, 429–439 (2008). https://doi.org/10.1007/s00466-007-0200-z
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DOI: https://doi.org/10.1007/s00466-007-0200-z