Minoru Shugyo’s research while affiliated with Nagasaki University and other places

This paper presents a numerical method for three-dimensional (3D) seismic response analysis of a frame containing member failure. The base of proposed method is the Fibered Plastic Hinge Model (FPHM)9),10) in which elastic and plastic components of deformations of each element can be separated explicitly from a largely deformed frame. The analysis is performed with cancellation of a large unbalanced force vector caused by a sudden fracture of members in the dynamic elastoplastic incremental analysis of a frame. The FPHM program uses a gradient of existing elastic strain energy as an internal force vector, which is needed to evaluate unbalanced force vector, of a frame at each incremental step. A redistribution of member forces, which are axial force, biaxial bending moments, shear force and axial torsional moment, of early fractured low ductile member into the remaining members of the frame is done in each step, therefore, the dynamic response of a frame that contains both low ductile and ductile members can be obtained accurately. The validity of proposed method is verified through the numerical experiments on one-bay one-story braced steel frame having a low ductile tension brace. Then, a possibility to use proposed method as a collapse analysis method for a 3D frame is examined by utilizing available shaking table test results on full-scale two-bay four-story steel building¹³⁾ assuming a simple fracture criterion for an element: |ε|max = ηεy where |ε|max is the maximum value of axial strain of a fiber due to varying axial force and biaxial bending moments at the element ends, εy is the initial yield strain of a fiber, and η is a reference value. Since the FPHM divides the element-end sections to fine fibers, |ε|max can be easily obtained in the numerical procedure. Assuming η = 20, which was determined by trial and error, the obtained numerical results follow mostly the collapse behavior of the building, except that the deterioration behavior due to local buckling of the columns is different from the test result¹³⁾. In addition, the firstly and secondly fractured columns obtained by the present analysis are consistent with those observed in the test¹³⁾. Although a systematic way to estimate the value of η is unknown at the present time, η may be a parameter which relates a member which loses load carrying capacity by the local buckling to an element formulated according to the Bernoulli-Euler hypothesis.

As a frame deforms under increasing external loads, relatively brittle member in the frame may fracture at an early point on the loading process. This causes sudden and considerable unbalanced force vector in the frame and then the released forces, which are axial force, bending moment, shear force and axial torsional moment of early fractured member, are redistributed into the remaining members of the frame. The elastoplastic incremental analysis to estimate the restoring force characteristics of a frame must be carried out with cancellation of above mentioned unbalanced force vector. However, it seems the dealing of those unbalanced force vector in the present most analysis codes is not necessarily clear and this reduces the reliability of the obtained values of horizontal load-carrying capacity. In this paper a procedure to cancel a large unbalanced force vector in the elastoplastic incremental analysis of a frame is presented. The procedure is applicable only to the analysis method in which elastic and plastic components of deformations of each element can be separated explicitly from the largely deformed frame, e.g. the Fibered Plastic Hinge Method (FPHM)6), 7), 8). By using the procedure, redistribution of the released forces of early fractured relatively brittle member into the remaining members of the frame can be done, therefore, an accurate restoring force characteristics of the frame having both brittle and ductile members can be obtained. The validity and reliability of the procedure are demonstrated by the analysis of two-bay two-story steel frame. The obtained findings are as follows: 1. Using the present procedure, a discontinuous restoring force characteristics of the frame having both brittle and ductile members can be obtained. 2. A final behavior of the restoring force characteristics of the present example frame approaches to that of the frame excluded initially the fractured members. This agrees qualitatively with the schematic diagram presented in Commentary on Structural Regulations of the Building Standard Law of Japan 2015 Edition¹⁾. 3. The reliability of the horizontal load-carrying capacity of a frame obtained by the analysis without unbalanced force cancellation may not be sufficient.

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.

A plastic hinge type beam element for three-dimensional analysis of prestressed concrete beams and frames is presented. The element was originally proposed for pure steel frames and named "Fibered Plastic Hinge Model". 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. In this paper the element is extended for prestressed concrete members and its reliability is examined by using available experimental results on prestressed concrete beams and frames. Comparisons of numerical and experimental results show that the developed beam element has a sufficient accuracy concerning the laod-carrying capacity under cyclic loadings. The element may be used to examine a performance of prestressed concrete beams and frames.

An algorithm for elastoplastic seismic response analysis of a steel frame is presented and its reliability is examined by using the experimental results for full-scale 4-story steel building. The masses of members, slabs and attachments are lumped to the beam-column connection points in principle for dynamic analysis, while the restoring forces of the frame are estimated by the displacement increment analysis of whole frame using the Fibered Plastic Hinge Model (FPHM). The model can take the rotational stiffness of the column-base into account as the member-end compliance. The details of column-beam connection are ignored in the present analysis.

This paper presents some excellent numerical results of collapse analysis on an RC-steel hybrid frame used in a school gymnasium. The analyses are done by the fibered plastic hinge method. The limit bending moment and the limit shear force of the column base of the upper steel frame and the limit overturning moment of the RC base are checked in the analysis according to a currently recommended evaluation method. The bending strength of the footing is also checked. The influences of eccentricity between the chord members and the lattice members are taken into account. The numerical result is an upper bound solution, and at the same time, a lower bound solution for the idealized numerical model. The results are compared with those obtained by the conventional α-method.

The beam element for three-dimensional pure steel frames proposed by the first author is extended for steelconcrete composite members. The authors call this approach the "fibered plastic hinge method". The stress-strain relation of a concrete fiber is modeled as an elastic-perfectly plastic type in this study. Comparisons with the authors' experimental results on RC beams strengthened by carbon fiber sheet and available test results on steel-concrete composite columns and frames show that the developed beam element has a sufficient accuracy for bending problem although there are some limitations. The element may be used to examine a performance of moment-resistant steelconcrete composite frames.

Elastoplastic buckling behaviors of unequal-legged angle, which is a typical doubly asymmetric section member, under two different loading conditions are investigated by experiments and numerical analysis. The numerical model is of the plastic hinge type. The formulation procedure of the element stiffness matrix is a combination of the 'modified incremental stiffness method', the updated Lagrangian formulation, and a numerical integration of fiber stiffnesses about the element-end sections. The plastic deformation increments at the element-end sections are estimated through this numerical integrarion introducing some assumptions. The authors call this approach 'fibered plastic hinge method'. The specimens of the experiments are two fixed-pinned columns subjected to different eccentric axial loadings. Comparisons of the numerical results with the experimental ones about the load-displacement relations and load-strain relations for two cases show that the element has s sufficient accuracy for the elastoplastic large deformation analysis of unequal-legged angles.

The beam element for three-dimensional pure steel frames proposed by the first author is developed for steel-concrete composite members. The element is of the plastic hinge type. 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 authors call this approach "fibered plastic hinge method". The stress-strain relation of a concrete fiber is modeled as an elastic-perfectly plastic type in this study. Comparisons with existing test results on SC column and SRC columns show that the developed beam element has a good accuracy although there are some limitation in its use. The element may be used to examine a performance of steel-concrete composite frames.

Elastoplastic behaviors of unequal-legged angle, which is a typical doubly asymmetric section member, under some different boundary and loading conditions are investigated by experiments and numerical analyses. The numerical analyses are done by using a new straight beam element proposed by the first author. Comparisons of the numerical results with the experimental ones about the load-displacement relations and load-strain relations for four cases show that the beam element has a sufficient accuracy for the elastoplastic large deformation analysis of unequal-legged angles.