The objective is to determine parameters of unstressed sections for the correct computation of the displacements of those structures and possible applications on structural failure theory. The experimental data from tests with 30 and 40 m long RC telecommunication towers, having circular cross-section with 50 cm diameter for the 30 m long structure and 60 cm diameter for the 40 m long structure, are used.

Inspired in Branson's equation (Branson [6], ACI [4], ABNT [3]), for cross-sections along the axis of the structure, the effective stiffness equation is derived in function of the bending moment level (the ratio between the characteristic bending moment and the ultimate moment of the cross-section). To accomplish the structural analysis, the structures are discretized and the differential equation of the elastic line integrated to obtain the rotations and displacements.

Optimization problems are defined so that the objective functions are the approximation errors, while the design variables are the coefficients of the effective bending stiffness equations of the cross-sections. Two different formulations are used to compute the effective stiffness. The first one gives one equation for each node section and the other formulation provides only one equation for the whole structure.

The effective stiffness is presented in graphs as function of the bending moment level. The sections where the largest stiffness losses are obtained were the sections that indeed collapsed in real similar structures.

We discuss the effect of the concrete elasticity modulus (ABNT [2,3]) on the obtained results, and possible applications to nonlinear dynamic analysis of RC structures subjected to wind loading (ABNT [1]) and to structure collapse. Directions for future research are also presented.

1

ABNT - Associação Brasileira de Normas Técnicas, NBR-6123: Forças Devidas ao Vento em Edificações, 1987.

2

ABNT - Associação Brasileira de Normas Técnicas, NBR-6118: Projeto e Execuçõo de Obras de Concreto Armado, 1978.

3

ABNT - Associação Brasileira de Normas Técnicas, Projeto de Obras de Concreto, 2003.

4

ACI - American Concrete Institute, ACI Committee 318 - Building Code Requirements for Reinforced Concrete, Detroit, EUA, 1971.

5

Arora, J.S., Introduction to Optimal Design, Second Edition, Elsevier Academic Press, 2004.

6

Branson, D.E., Instantaneous and Time-Dependent Deflections of Simple and Continuous Reinforced Concrete Beams, Report No. 7, Alabama Highway Research Report, Bureau of Public Roads, Aug. 1963, pp. 1-78, 1963.

7

Brasil, R.M.L.R.F. and Silva, M.A., Determination of Effective Bending Stiffness Using Optimization Techniques Applied To Experimental Results, XXV CILAMCE, Recife, Brazil, 2004.

8

Brasil, R.M.L.R.F. and Silva, M.A., "RC with Large Displacements: Optimization Applied to Experimental Results", in Proceedings of the Seventh International Conference on Computational Structures Technology, Topping, B.H.V. and Mota Soares, C.A., (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 76, 2004. doi:10.4203/ccp.79.76

9

Chahande, A.I. and Arora, J.S., Optimization of large structures subjected to dynamic loads with the multiplier method, International Journal For Numerical Methods in Engineering, 37, pp. 413-430, 1994. doi:10.1002/nme.1620370304

10

Silva, M.A. and Brasil, R.M.L.R.F., Técnicas de Otimização Aplicadas a Resultados Experimentais no Estudo da Redução da Rigidez Flexional em Estruturas de Concreto Armado, Boletim Técnico da EPUSP, BT-PEF-0401, São Paulo, 2004.

11

Silva, M.A. and Brasil, R.M.L.R.F., Nonlinear Dynamic Analysis Based on Experimental Results of RC Towers for Telecommunication Subjected to Wind Loading, DINCON2004 - 3o Congresso Temático de Dinâmica e Controle da SBMAC, Ilha Solteira, 2004.

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