水平力を受ける弾性立体建築骨組のひずみ制御設計

抄録

The following two design problems have been formulated : [SCDR 1] Given the center-line dimensions of a three-dimensional multi-story multi-span frame, depths of all the members and the horizontal design loads with a specified common direction, find the set of all the member stiffnesses and the corresponding joint displacements such that all the governing equations and the maximum strain specifications are satisfied. [SCDR 2] Given the center-line dimensions of a three-dimensional multi-story multi-span frame, depths of all the members and the horizontal design loads without specification of directions, find the set of all the member stiffnesses and the corresponding joint displacements such that all the governing equations and all the specifications of maximum member end strains with respect to all the load directions are satisfied. The mathematical structure and essential characteristics of the problems [SCDR 1] and [SCDR2] are disclosed. A method of super-position and overlapping of the strain-controlled design solutions for constituent unit three-dimensional box frames has then been formulated for a subclass of problems of [SCDR 1] and [SCDR 2] such that practically meaningful design solutions exist. A set of closed-form solutions has been derived for a class of regular and setback building frames satisfying a set of constraint qualifications. The solution may be regarded as a set of design formulas for designing such building frames that would not exhibit any overall torsional deformation under the horizontal design loads acting in any direction. A method of assigning a desirable distribution of column shear forces in each story of a building frame has been devised. A strain-controlled design has been illustrated of a five-story setback building frame with three spans in one direction and two spans in the other direction orthogonal to the former. It has been demonstrated via this example that the proposed design formulas indeed provide a direct design procedure of finding an initial set of member stiffnesses and cross-sectional dimensions on the basis of which a variety of modifications for practical requirements can be started.