REDUCTION OF THE TOTAL DEGREES OF FREEDOM IN FRAME ANALYSIS BY THE FIBERED PLASTIC HINGE MODEL

Abstract

 An accurate plastic hinge type beam elememt has been developed by the authors for three-dimensional (3-D) elastoplastic large deformation analysis of frames which contain all kinds of members: i.e. steel members, RC members, SRC members, CFT members, PC members, steel damper braces and tension braces. The element was originally proposed for pure steel frames by the first author (Shugyo 2003) and named Fibered Plastic Hinge Model (FPHM). The formulation procedure is a combination of the modified incremental stiffness method, the updated Lagrangian formulation, and numerical integration of fiber stiffnesses about the sections at the plastic hinges. The following assumptions are made to form the elastoplastic tangent stiffness matrix of the pure steel element: (1)members have thin walled closed or open sections, and cross sections remain plane and do not distort in the absence of cross-sectional warping, (2)deflection is large but elastic strain is small, (3)axial stress and the shear stress due to St. Venant torsion participate in yielding of fibers of members with closed sections, while only axial stress participates for members with open sections, (4)plastic deformation consists of only four components that correspond to axial force, biaxial bending moments, and torsional moment or bimoment, (5)there is no local buckling, (6)although an actual generalized plastic strain increments in a short element generally distribute nonlinearly, it is idealized as generalized plastic strain increments distribute linearly with the values at element nodes i and j, (7)incremental plastic deformations in the two half portions occur concentrically in the plastic hinge of zero length at element nodes i and j respectively. Because of the above mentioned assumption (6), the element requires at least four-element approximation for a frame member. This causes considerable increase of total degrees of freedom in the analysis of multi-bay multi-story frames.
 In this paper a method to reduce the total degrees of freedom in frame analysis by the FPHM is presented. Introducing the plastic deformation reduction coefficient, the assumption (6) is modified as one-element approximation for a frame member has sufficient accuracy for practical use. The optimum value of the plastic deformation reduction coefficient is examined by using quasi-static analysis of four kinds of one-bay one-story plane portal frames, 3-D quasi-static analysis of two-bay four-story steel frame which contains composite beams and semirigid column bases, and 3-D quasi-static analysis of twenty-story eccentric steel frame with H-shaped steel columns.