Keywords: advanced analysis, semi-rigid connection, geometric non-linear, material non-linear, steel frames.

Conventional analysis of steel frame structures is usually carried out under the assumption that the beam-to-column connections are either fully rigid or ideally pinned. However, most connections used in current practice are semi-rigid type whose behavior lies between these two extreme cases. In the AISC-LRFD Specification (1993), two types of constructions are designated: Type FR (fully restrained) construction; and Type PR (partially restrained) construction. The LRFD Specification permits the evaluation of the flexibility of connections by rational means when the flexibility of connections is accounted for in the analysis and design of frames.

The semi-rigid connections influence the moment distribution in beams and columns as well as the drift (P-effect) of the frame. One way to account for all these effects in semi- rigid frame design is through the use of a direct second-order inelastic frame analysis known as "Advanced Analysis". Advanced analysis indicates a method that can sufficiently capture the limit state strength and stability of a structural system and its individual members so that separate member capacity checks are not required. Since the power of personal computers and engineering workstations is rapidly increasing, it is feasible to employ advanced analysis techniques directly in engineering design office.

During the past 20 years, research efforts have been devoted to the development and validation of several advanced analysis methods. The advanced analysis methods may be classified into two categories: (1) Plastic-zone method; and (2) Plastic hinge method. Whereas the plastic-zone solution is known as the "exact solution," but cannot be used for practical design purposes [1]. This is because the method is too intensive in computation and costly due to its complexity.

Advanced analysis using plastic-hinge concept for the space structures have been developed in references [2,3,4]. Orbison's method is an elastic-plastic hinge analysis without considering shear deformations. The material nonlinearity is considered by the tangent modulus and the geometric nonlinearity is by a geometric stiffness matrix. Orbison's method[2], however, underestimates the yielding strength up to 7% in stocky members subjected to axial force only. DRAIN-3DX developed by Prakash and Powell[3] is a modified version of plastic hinge methods. The material nonlinearity is considered by the stress-strain relationship of the fibers in a section. The geometric nonlinearity caused by axial force is considered by the use of the geometric stiffness matrix, but the nonlinearity caused by the interaction between the axial force and the bending moment is not considered. This method overestimates the strength and stiffness of the member subjected to significant axial force. Liew and Tang's method[4] is a refined plastic hinge analysis. The effect of residual stresses is taken into account in conventional beam-column finite element modelling. Nonlinear material behavior is taken into account by calibration of inelastic parameters describing the yield and bounding surfaces. Liew and Tang's method, however, underestimates the yielding strength up to 7% in stocky member subjected to axial force only. All of those three methods above, however, do not consider semi-rigid effect of connections.

In this paper, a practical advanced analysis of semi-rigid space frame is developed. The analysis is equivalent to the plastic-zone analysis in its accuracy but is much simpler than the plastic-zone analysis. Kishi-Chen power model is used to describe the nonlinear behavior of semi-rigid connections. Stability functions are used to capture second-order effects associated with P- and P- effects. The Column Research Council (CRC) tangent modulus and a softening plastic hinge model are used to represent material nonlinearity. The proposed analysis can predict accurately the combined nonlinear effects of connection, geometry, and material on the behavior and strength of semi-rigid frames. The load-displacements predicted by the proposed analysis compare well with those available experiments. A case study has been performed for a four story semi-rigid frame.

1

W.F. Chen, S. Toma, "Advanced analysis of steel frames", CRC Press, Boca Raton, Florida, 1994.

2

J.G. Orbison, "Nonlinear static analysis of three-dimensional steel frames", Report No. 82-6, Department of Structural Engineering, Cornell University, Ithaca, New York, 1982.

3

V. Prakash, G.H. Powell, "DRAIN-3DX: Base program user guide, version 1.10, A Computer Program Distributed by NISEE / Computer Applications", Department of Civil Engineering, University of California, Berkeley, 1993.

4

J.Y.R. Liew, L.K. Tang, "Nonlinear refined plastic hinge analysis of space frame structures", Research Report No. CE027/98, Department of Civil Engineering, National University of Singapore, Singapore, 1998.

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