ON CANCELLATION OF UNBALANCED FORCE VECTOR IN THE ELASTOPLASTIC INCREMENTAL ANALYSIS OF A FRAME

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.