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.
