Bearing walls in which circular steel tubes are closest-packed in column-beam frameworks have excellent characteristics as earthquake-resistant repair elements. The purpose of this paper is to present a simple model that can analyze the large deformation area with good convergence. One of the mechanisms that resists the seismic force of this wall is an out-of-plane bending deformation mechanism of the tube, and Yield Line Theory is often applied to evaluate its maximum strength.
In consideration of rotational symmetry, the upper half of a circular tube was modeled (Fig. 2). Yield lines 20, 40, 80, 100, 140 and 160 having a hinge moment
_{h}M are provided at positions separated from the rigid lines 0, 60, 120 and 180 by an angle η. Elements 10, 30, 50, 70, 90, 110, 130, 150 and 170 are rigid bodies and the element length is invariant. A horizontal displacement corresponding to the displacement w δ at the top of the wall is given to the nodes 60 and 120 and a condition for minimizing the sum of the absolute values of the hinge rotation angle increments of the nodes 20, 40, 80, 100, 140 and 160 is given, convergence calculation is performed , and obtains the rotation angle of the elements 10, 50, and 110. Because of the rotational symmetry, the rotation angle of the element 170 is equal to the rotation angle of the element 10.
The total of hinge rotation angle increment of all the circular steel tubes in the wall multiplied by
_{h}M is the increment of the inner work of the wall. The increment of internal work is set equal to the external work increment and divided by w δ increment is the wall shear force. Residual deformation occurs when unloading external force, but since the yield line has a rigid plastic rotation spring, the residual deformation is the same as before the unloading. This is called a vertical displacement free model (hereinafter referred to as a free model).
The axial displacement of the side column is restricted by the side columns, and the hinge rotation deformation of the rigid body and the yield line given by the yield line theory can not evaluate the restraint situation of the axial displacement of the side column. The side column axial displacement restraint model (hereafter called constraint model) constructed by this paper introduces a new circumferential direction linear slider in elements 30 and 150. This slider is one given a unidirectional property which permits elongation displacement with slider resistance
_{s}R but does not allow shrinkage displacement.
The value of the unknown η that defines the yield line position is almost constant as 0.305, and the rotation angle of the elements 50 and 110 hardly occurs. This is presumed to make the convergence favorable.
It is supposed that the increment of inner work multiplied by
_{s}R in the circumferential direction displacement obtained from the coordinates of the nodes 20, 30, 140 and 160 at the time of unloading of the external force of the free model is the difference between the free model and the constraint model. The scope of application of the presented model guaranteed by the experiment conducted to verify the validity is that the steel tube diameter thickness ratio is 55 or less, the yield ratio is 0.83 or less (limited to Round-House type), the welding length ratio is 0.53 or more, the wall thickness ratio is 0.13 or more, the aspect ratio is 0.48 or less, the member angle of 9/1000 or more, and 90/1000 or less. Experimental results revealed that calculated values using presented models correspond well to experimental values.
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