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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 91
Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
Paper 221

A Simplified Procedure for the Assessment of Second-Order Effects in Three-Dimensional Framed Structures

A.C. Sousa1, M. Pereira2 and R.C. Barros1

1Department of Civil Engineering, Faculty of Engineering, University of Porto, Portugal
2AFAConsult, V.N. de Gaia, Portugal

Full Bibliographic Reference for this paper
A.C. Sousa, M. Pereira, R.C. Barros, "A Simplified Procedure for the Assessment of Second-Order Effects in Three-Dimensional Framed Structures", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 221, 2009. doi:10.4203/ccp.91.221
Keywords: stiffness reduction factors, geometric and material nonlinearities, design codes, EC2, ACI.

The simplified assessment of second-order effects is usually done in most codes of practice (EC2, EC3, ACI and AISC) using the amplification of first-order moments in a relation between the structural element's axial load and its critical buckling load. Another method for the consideration of such effects is proposed in the CEB-FIP's Model Code 90 [1], using the increment due to the presence of vertical load on the deformed structure load is estimated by rotation of the structure due to first-order loads by a direct proportion. This allows the calculation of additional horizontal loads that simulate the second order effects and, as such, allows for a relatively simple linear elastic second-order calculation.

This paper presents an extension of the Model Code 90 method to three-dimensional framed structures. One of the problems in dealing with a three-dimensional extension is that the structure's global imperfections given according to its first buckling mode, do not necessarily have the same direction as the deformed structure imposed by the horizontal loads. A way of taking these two factors into consideration is presented, as well as a three-dimensional interpretation of the second-order increment as estimated using the Model Code. After the basic theory is presented, numerical examples of the proposed method are compared with a more accurate nonlinear geometric analysis, testing the validity of the proposed equations and outlining its principal limitations [2].

Comite Euro-International du Beton, "CEB-FIP model code 1990 design code", Thomas Telford, London, 1993.
A.C. Sousa, "Aspects on Nonlinear Geometric and Material Analysis of Three-Dimensional Framed Structures", in MSc Dept. of Civil Engineering, Faculty of Engineering, University of Porto, Portugal, 2009.

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