Pergamon 0045-7949(94)EO147-T Computers & Slrucrures Vol. 53. No. 3. pp. SW589. 1994 Copyright 3: 1994 Elxvier Science Ltd Printed in Great Britain. All rights reserved 0045-7949/w $7.00 + 0.00 A RELIABLE NUMERICAL METHOD FOR SIMULATING THE POST-FAILURE BEHAVIOUR OF CONCRETE FRAME STRUCTURES C. H. Sun, M. A. Bradford and R. I. Gilbert Department of Structural Engineering, School of Civil Engineering, The University of New South Wales, Kensington, NSW 2033, Australia (Received 30 March 1993) Abstract--A reliable layered finite element model combined with the arc-length method is developed for the nonlinear analysis of reinforced concrete framed structures. Accounting for both material and geometrical nonlinearities, the algorithms can analyse concrete frames up to and beyond the limit points. Comparison with experimental results demonstrates that reliable full-range behaviour can be traced. The package is shown to be an efficient tool for simulating the nonlinear hehaviour of reinforced concrete framed structures. I. INTRODUCTION It is always desirable for structural engineers to be able to estimate the ultimate strength of a structure accurately regardless of whether it is yet to be designed or whether it exists already. The real defi- nition of the strength of a structure should be based on its material or mechanism failure rather than on the so called ‘limit point’ of a cross-section, beyond which the numerical solution is more difficult. Struc- tural analysis by load control will inevitably fail to pass the limiting points. Even deformation control schemes can only successfully go beyond these limit- ing points under certain conditions, such as snap- through behaviour. Moreover, post-failure behaviour can be unstable and may result in a multi-equilibrium state. Therefore, a reliable numerical technique to overcome the difficulties near the limit points is essential. For a reinforced concrete structure, it is not always an easy task to analyse behaviour beyond the peak load. The difficulties are mainly a result of the highly nonlinear behaviour when concrete structures undergo very large deformation. Although many researchers over a long period have considered this problem, as yet a systematic and reliable package has not been developed. Bergan’s so-called current stiffness parameter method [l-3] can pass the limiting points, though it is not the best solution. Warner’s deformation approach [4, 51 is also able to tackle the same problem. However, the direct stiffness method hampers the efficiency and application as far as nonlinear analysis is concerned. Crisfield’s arc-length method [6-91 is probably the most success- ful numerical technique for analysing reinforced concrete structures up to and beyond their peak loads, and forms the basis of the method developed herein. This paper is the extension of the authors’ recent work [lo] on the nonlinear analysis of concrete frame structures. The main features of the numerical sol- ution procedure now include not only material and geometric nonlinearities, but also the arc-length method [6-91 to overcome the numerical difficulties encountered near the limiting points. The basic structural analysis still employs the finite element method using a layered element model [lo]. A com- prehensive description of the arc-length method com- bined with a line-search technique for the nonlinear analysis of concrete frame structures is presented here. A specific process to overcome the difficult numerical problems near limiting points is also described. After implementing the arc-length method, the present package becomes more accurate and less time consuming for the nonlinear analysis of concrete frames. Since the algorithms can overcome the numerical difficulties as the structure approaches and passes the limiting points, it is possible for the solution to continue as the structure undergoes very large defor- mations without breaking down the conventional nonlinear analysis procedures such as the modified Newton-Raphson method. A comparison with the laboratory work performed by Cranston [l l] shows good agreement between the experimental and analytical results. The package demonstrates good accuracy for predicting the behaviour of reinforced concrete frame structures up to and beyond failure. This technique will allow structural engineers not only to carry out limit design more accurately, but also to evaluate the safety factor and the ductility of existing structures more efficiently. 579