Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 64
NonLinear Analysis of TimeDependent Response of Civil Engineering Structures J. Lopatic and F. Saje
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Slovenia J. Lopatic, F. Saje, "NonLinear Analysis of TimeDependent Response of Civil Engineering Structures", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 64, 2006. doi:10.4203/ccp.83.64
Keywords: concrete, rheology, ageing, shrinkage, creep, nonlinear analysis, timedependent response, numerical modelling, changeable structural system.
Summary
This paper deals with the mechanical and rheological properties of concrete and with
numerical modelling of the constitutive law of concrete considering ageing,
decomposition and nonlinear creep. The method developed for the general nonlinear
analysis of the timedependent response of concrete structures is also presented. It is
limited to reinforced, prestressed or composite plane frames. In addition to the
influences of rheology, including the nonlinear creep of concrete, the analyses also
take into account the timevariable structural system.
The numerical modelling of the influence of longterm changeable high stresses on the compressive strength of concrete (Lopatic [1]) is based on the generalisation of the CEBFIP model code 1990 [2] recommendations for concrete structures, which basically apply for constant stress level. Here, two opposite time effects are included at the same time. At low stress level the concrete strength increases due to the favourable influence of ageing, and on the other side concrete strength decreases due to its decomposition resulting from permanent action of high stresses. For the computational consideration of the influence of sustainable changeable high stress levels on the compressive strength of concrete, this paper gives a relatively simple model, where the whole history of previous loadings is included with the parameter of the already exploited limit time. With the help of this parameter it is possible to determine the compressive strength of concrete in an arbitrary time. As a basis for the development of the model and for the evaluation of the introduced model constant, the provisions of CEBFIP MC 1990 [2] were used, appertaining to the decreasing compressive strength of concrete at constant high stress. To include all types of nonlinearity, the constitutive equations of concrete are written in incremental form. The increment of constitutive strain is obtained with the sum of the increment of the mechanical part of strain , originating from nonlinear elastic behaviour of concrete under shortterm loading, the increment of concrete strain due to concrete creep and the increment of concrete strain due to concrete shrinkage . For modelling of the viscoelastic properties of ageing concrete the generalised Kelvin model consisting of nonlinear timedependent spring and a chain of Kelvin bodies has been used which can, in addition to experimentally acquired functions of concrete creep, also approximate the creep functions of concrete according to the CEBFIP 1990 model code [2]. The nonlinearity of creep was included by functions which, depending on the momentary stress level, increase the speed of creep (Bazant & Prasannan [3], Bazant & Kim [4]). The main advantage of the selected incremental constitutive law of concrete is that only the stress, the situation indicator (possible tensile or compressive failure) and the hidden variables of all Kelvin units [5] in the previous time period have to be saved for each integration point. This enables an analysis of large structures with an almost unlimited number of time steps to be performed by using a PC. The finite element method (FEM) has been applied in the presented analysis of timedependent response of structures. It is limited to plane frames that can be reinforced, prestressed or composite. The level of stress can be arbitrary. In addition to the geometrical nonlinearity of the structure, the nonlinearity of the constitutive laws of material at short term loading and basic rheological influences, as well as the influence of high stress levels to the increase of concrete creep and the influence of sustained high stress levels to the reduction of compressive strength of concrete are also considered. By taking into account the rheological influences according to the nonlinear theory, the constitutive law of concrete is carried out in the incremental form. Based on the given theoretical derivations, the NONREO computer program for the nonlinear analysis of timedependent response of reinforced concrete plane frames was prepared. Comparing the results of the computer simulations of structure behaviour with foreign experiments, the developed analysis method and the software have proven to be adequate and useful in practice. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
