Keywords: plastic zone analysis, semi-rigid space frameworks, large deflections, advanced analysis, pushover analysis.

With the rapid advancement of computer technology, research is currently in progress to develop advanced nonlinear inelastic analysis methods and integrate them into the new and more rational advanced analysis and design procedures [1,2,3,4,5]. This paper presents an integrated system for advanced structural analysis and seismic performance evaluation of three-dimensional steel frameworks with rigid or flexible connections. The nonlinear inelastic analysis employed in this paper uses the accuracy of the fibre element approach for inelastic frame analysis. Its efficiency and modelling shortcomings are addressed both at the element level, through the use of only one element to model each physical member of the frame, and at the cross-sectional level through the use of the path integral approach to numerical integration of the cross-sectional nonlinear characteristics. This is an essential requirement to approach real large spatial frame structures. Gradual yielding of cross-sections is modelled in two ways. In the first approach gradual plastification through the cross-section subjected to the combined action of axial force and bi-axial bending moments is described using basic equilibrium, compatibility and material nonlinear constitutive equations. In this way, the states of strain, stress and yield stress are monitored explicitly during each step of the analysis, the arbitrary cross-sectional shape and the effect of material imperfections such as residual stresses are accurately included in the analysis. Based on Green's integration formula the internal resultant efforts and tangent stiffness matrix coefficients of the section can be evaluated in terms of the boundary integral. This approach is extremely rapid because stress integrals need only be evaluated at a small number of points on the section boundary. In the second approach, gradual yielding is modelled using the nonlinear inelastic force strain relationships, numerically calibrated. In order to take into account more explicitly the effect of residual stresses of the cross-sections a new smooth force-strain curve is proposed to model the gradual-plastification. The method also ensures that the plastic bending moment is nowhere exceeded once a full plastified section develops. Using the flexibility approach the elasto-plastic tangent stiffness matrix of the three-dimensional beam-column element is developed. The geometrical nonlinear local effects are taken into account in the analysis by the use of stability stiffness functions. The behaviour of the connection element in each principal bending direction is represented by a rotational dimensionless spring attached to the member ends. Using an updated Lagrangian formulation, the global geometrical effects are considered updating the geometry of the structure at each load increment. The model has been implemented in an incremental-iterative matrix structural analysis program. The studies show that the proposed analysis compares very well to finite fibre element solution with much less computational effort.

1

C. Ngo-Huu, S.E. Kim, J.R. Oh, "Nonlinear analysis of steel frames using fiber plastic hinge concept", Engineering Structures, 29(4), 649-657, 2007. doi:10.1016/j.engstruct.2006.06.008

2

X.M. Jiang, H. Chen, J.Y.R. Liew, "Spread of plasticity analysis of three-dimensional steel frames", Journal of Constructional Steel Research, 58, 193-212, 2002. doi:10.1016/S0143-974X(01)00041-4

3

S. Antoniou, R. Pinho, "Development and verification of a displacement-based adaptive pushover procedures", Journal of Earthquake Engineering, 8(5), 643-661, 2004. doi:10.1080/13632460409350504

4

P. Fajfar, P. Gaspersic, "The N2 method for the seismic damage analysis of RC buildings", Earthquake Engineering and Structural Dynamics, 25, 31-46, 1996. doi:10.1002/(SICI)1096-9845(199601)25:1<31::AID-EQE534>3.0.CO;2-V

5

C.G. Chiorean, "A computer method for nonlinear inelastic analysis of 3D semirigid steel frameworks", Engineering Structures, 31(12), 3016-3033, 2009.

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