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Keywords: second order theory, transfer matrix method, transfer functions, critical load, continuous variable Young's modulus, continuous variable shear modulus.

Summary

Based on [1] a calculation concept for structures with composite beams according to Second Order Theory can be presented. The cross-sections of the beams are constant, but the Young's Modulus E and the Shear-Modulus G can be variable along the length of the beam.

The bending stiffness EI, the extensional stiffness EA and shear-stiffness GA^~ have been described by polynomials of arbitrary degree. The special case of constant stiffness is included in the general case. The distribution of the Young's Modulus is continuous. In the special case of a discontinuity in the Young's modulus' distribution, the beams can be spilt in two or more sections with a continuous distribution.

The beam is calculated due to uniaxial bending. The axial force N^II according to Second Order is constant and for the special case of First Order Theory it is zero. Line loads can be described by polynomials of arbitrary degree. The special loads for Second Order Theory are also included in this concept. The thermal load Delta T can be considered by a constant curvature kappa^e = Delta T * alpha_T/h. alpha_T is the coefficient of thermal expansion and h is the depth of the beam.

First of all the differential equation for the lateral displacement w is derived. This differential equation of third degree can be solved using the Mathematica program. The solutions of the governing differential equations are used to present the moment M and the shear force Q.

The present calculation concept has been subjected to numerical testing on a single-beam-construction considering a variable bending stiffness EI, a variable extensional-stiffness EA and a variable shear stiffness GA^~.

The static program IQ 100 [2] can be used for calculations of beams with variable bending stiffness EI and variable extensional-stiffness EA, but without shear stiffness effect GA^~=infinity. In this case the results of the present calculation concept can be verified by the static program IQ100 and the critical load for that case can be gained too.

References

1: M. Aminbaghai, R. Binder "Analytische Berechnung von Voutenstäben nach Theorie II. Ordnung unter Berüchsichtigung der M- und Q-Verformungen", Bautechnik 83. Jahrgang, Heft 11, ISSN 0932-8352, Novermber 2006. doi:10.1002/bate.200610067
2: H. Rubin, M. Aminbaghai, H. Weier, "Schneider Bautabellen für Ingenieure", 17. Auflage, Werner Verlag.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 26 Analytical Calculation of Composite Beams According to Second Order Theory M. Aminbaghai and R. Binder Institute for Structural Analysis, Vienna University of Technology, Austria doi:10.4203/ccp.88.26 purchase the full-text of this paper Full Bibliographic Reference for this paper M. Aminbaghai, R. Binder, "Analytical Calculation of Composite Beams According to Second Order Theory", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 26, 2008. doi:10.4203/ccp.88.26 Keywords: second order theory, transfer matrix method, transfer functions, critical load, continuous variable Young's modulus, continuous variable shear modulus. Summary Based on [1] a calculation concept for structures with composite beams according to Second Order Theory can be presented. The cross-sections of the beams are constant, but the Young's Modulus E and the Shear-Modulus G can be variable along the length of the beam. The bending stiffness EI, the extensional stiffness EA and shear-stiffness GA^~ have been described by polynomials of arbitrary degree. The special case of constant stiffness is included in the general case. The distribution of the Young's Modulus is continuous. In the special case of a discontinuity in the Young's modulus' distribution, the beams can be spilt in two or more sections with a continuous distribution. The beam is calculated due to uniaxial bending. The axial force N^II according to Second Order is constant and for the special case of First Order Theory it is zero. Line loads can be described by polynomials of arbitrary degree. The special loads for Second Order Theory are also included in this concept. The thermal load Delta T can be considered by a constant curvature kappa^e = Delta T alpha_T/h. alpha_T* is the coefficient of thermal expansion and h is the depth of the beam. First of all the differential equation for the lateral displacement w is derived. This differential equation of third degree can be solved using the Mathematica program. The solutions of the governing differential equations are used to present the moment M and the shear force Q. The present calculation concept has been subjected to numerical testing on a single-beam-construction considering a variable bending stiffness EI, a variable extensional-stiffness EA and a variable shear stiffness GA^~. The static program IQ 100 [2] can be used for calculations of beams with variable bending stiffness EI and variable extensional-stiffness EA, but without shear stiffness effect GA^~=infinity. In this case the results of the present calculation concept can be verified by the static program IQ100 and the critical load for that case can be gained too. References 1 M. Aminbaghai, R. Binder "Analytische Berechnung von Voutenstäben nach Theorie II. Ordnung unter Berüchsichtigung der M- und Q-Verformungen", Bautechnik 83. Jahrgang, Heft 11, ISSN 0932-8352, Novermber 2006. doi:10.1002/bate.200610067 2 H. Rubin, M. Aminbaghai, H. Weier, "Schneider Bautabellen für Ingenieure", 17. Auflage, Werner Verlag. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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