| Outriggers with large stiffness are often located between the core and the outside frame in engineering when the stiffness of frame-core is not enough for the resistance of lateral load. Sometimes belts beam or truss are set up when necessary. Presently, the so-called optimal location of outriggers is derived from the principle of minimum ultimate displacement, the sectional properties of the core, columns, and outriggers are constant throughout their height, the influence of horizontal members are ignored except outriggers. So, the actual rigidities of outriggers are used instead of the assumption of infinite rigidity in horizontal direction. The actual sectional properties of the core, columns, and outriggers and the influence of the floor beam are considered in the current study. The analytic model is more approach to the real case. The restraining moments of outriggers acting on the core wall, the horizontal top deflection and the influencing factors are analyzed with the improvement of the analytic model. At the present time the outrigger research is emphasized and the belt research is ignored. The mechanical performance of the outriggers and belts subjected to lateral load are analyzed and the belts influence in the strengthened story is emphasized in the paper.Firstly, the solution equations of the restraining moments of outriggers and the horizontal top deflection are created based on the assumption that the sectional properties of the core, columns, and outriggers are constant throughout their height. The deformation compatibility conditions between outriggers and core wall as well as the finite rigidities of outriggers are also considered. The normal expressions of restraining moments and the horizontal top deflection of the structure subjected to the lateral load with multi-outrigger are deduced. The expressions of restraining moments and the horizontal top deflection of the frame-core structure subjected to the del load with one or two outriggers are obtained. A study of one outrigger case is carried out to analyze the safety of the infinite rigidity assumption. Comparison analysis proceeded based on the calculation results of different analytic model.Secondly, the expressions of restraining moments and the horizontal top deflection of the frame-core structure subjected to the del load with one or two outriggers are deduced, based on the real case that the sectional properties of the core, columns, and outriggers are changed throughout their height. The influencing factors of the restraining moments of outriggers, horizontal top deflection such as the core-to-column rigiditiesα, core-to-outrigger rigiditiesβand variation of cross-section of frame-core are analyzed. The expression of reduction coefficient of the horizontal top deflection is deduced. Some conclusions are presented to the strengthened storey design of the high-rise building structures combined with case study.Thirdly, a plane analytical model is presented in the paper. The analytic model is optimized as well as the floor beam is considered. Structure with multi-outrigger is divided into substructure with outrigger located at the top. Strain energy expression of substructure subjected to the lateral load is obtained. Balance equation of substructure subjected to lateral load is established based on the minimum potential energy principle. Expression of deflection curve of substructure subjected to linear lateral load is obtained as well as the functional and variation calculus and natural boundary conditions are considered. Deflection curve of substructure subjected to top single load, uniform load, del load are obtained. Deflection curve of multi-outrigger frame-core structure subjected to the lateral load can be obtained based on the elastic superposition principle.Finally, analysis proceeded through a structure model established by the high-rise FEA software. The differences of mechanics performance influence of structure periods, core shearing force, horizontal top deflection subjected to wind load and horizontal seismic action are discussed. When the belt and outrigger are located at the same floor and belt and outrigger are located at different floor as well as the belts rigidity is changed. A method of belts institution is discussed. Belts advantages will be exerted and disadvantages will be avoided in the method.The strengthened story design will be more safe and reasonable and the application of strengthened story will be more abroad as the assumption revert to the real stress situation and the analytic theory will be more perfect.
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